diff --git a/changelog b/changelog index 9cce51b..f20e014 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100609 tpd src/axiom-website/patches.html 20100609.03.tpd.patch +20100609 tpd src/input/Makefile rule-based trig integration +20100609 tpd src/input/richtrig300-399.input rule-based trig integration 20100609 tpd src/axiom-website/patches.html 20100609.02.tpd.patch 20100609 tpd src/input/Makefile rule-based trig integration 20100609 tpd src/input/richtrig200-299.input rule-based trig integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index b378718..26213d9 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2870,6 +2870,8 @@ books/bookvol5 add David Parnas to credits
src/input/richtrig100-199.input rule-based trig integration
20100609.02.tpd.patch src/input/richtrig200-299.input rule-based trig integration
+20100609.03.tpd.patch +src/input/richtrig300-399.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index fd85faa..0c340e8 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -379,6 +379,7 @@ REGRES= ackermann.regress \ richtrig000-099.regress \ richtrig100-199.regress \ richtrig200-299.regress \ + richtrig300-399.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -701,6 +702,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ ${OUT}/richtrig200-299.input \ + ${OUT}/richtrig300-399.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1052,6 +1054,7 @@ DOCFILES= \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ ${DOC}/richtrig200-299.input.dvi \ + ${DOC}/richtrig300-399.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ ${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \ diff --git a/src/input/richtrig300-399.input.pamphlet b/src/input/richtrig300-399.input.pamphlet new file mode 100644 index 0000000..304096f --- /dev/null +++ b/src/input/richtrig300-399.input.pamphlet @@ -0,0 +1,76437 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig300-399.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig300-399.output +)spool richtrig300-399.output +)set message auto off +)clear all + +--S 1 of 528 +t0300:= 1/(a*sec(x)^3)^(1/2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 3 +--R \|a sec(x) +--R Type: Expression Integer +--E 1 + +--S 2 of 528 +r0300:= 2/3*sec(x)*(EllipticF(1/2*x,2)/cos(x)^(1/2)+sin(x))/(a*sec(x)^3)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 528 +a0300:= integrate(t0300,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------- d%R +--R ++ +----------+ +--R | 3 +--R \|a sec(%R) +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 528 +m0300:= a0300-r0300 +--R +--R +--R x +--R ++ 1 +--R (3) | ------------- d%R - r0300 +--R ++ +----------+ +--R | 3 +--R \|a sec(%R) +--R Type: Expression Integer +--E 4 + +--S 5 of 528 +d0300:= D(m0300,x) +--R +--R +--R 1 +--R (4) ------------ +--R +---------+ +--R | 3 +--R \|a sec(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 528 +t0301:= 1/(a-a*sec(c+d*x)) +--R +--R +--R 1 +--R (5) - ------------------ +--R a sec(d x + c) - a +--R Type: Expression Integer +--E 6 + +--S 7 of 528 +r0301:= x/a+sin(c+d*x)/a/d/(1-cos(c+d*x)) +--R +--R +--R - sin(d x + c) + d x cos(d x + c) - d x +--R (6) --------------------------------------- +--R a d cos(d x + c) - a d +--R Type: Expression Integer +--E 7 + +--S 8 of 528 +a0301:= integrate(t0301,x) +--R +--R +--R d x sin(d x + c) + cos(d x + c) + 1 +--R (7) ----------------------------------- +--R a d sin(d x + c) +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 528 +m0301:= a0301-r0301 +--R +--R +--R 2 2 +--R sin(d x + c) + cos(d x + c) - 1 +--R (8) ------------------------------------ +--R (a d cos(d x + c) - a d)sin(d x + c) +--R Type: Expression Integer +--E 9 + +--S 10 of 528 +d0301:= D(m0301,x) +--R +--R +--R (9) +--R 4 2 4 +--R sin(d x + c) + (cos(d x + c) - 1)sin(d x + c) - cos(d x + c) +--R + +--R 3 2 +--R cos(d x + c) + cos(d x + c) - cos(d x + c) +--R / +--R 2 2 +--R (a cos(d x + c) - 2a cos(d x + c) + a)sin(d x + c) +--R Type: Expression Integer +--E 10 + +--S 11 of 528 +t0302:= (3+3*sec(x))^(1/2) +--R +--R +--R +-----------+ +--R (10) \|3sec(x) + 3 +--R Type: Expression Integer +--E 11 + +--S 12 of 528 +r0302:= 2*3^(1/2)*atan((-1+sec(x))^(1/2))*tan(x)/(-1+sec(x))^(1/2)/(1+sec(x))^(1/2) +--R +--R +--R +-+ +----------+ +--R 2\|3 tan(x)atan(\|sec(x) - 1 ) +--R (11) ------------------------------ +--R +----------+ +----------+ +--R \|sec(x) - 1 \|sec(x) + 1 +--R Type: Expression Integer +--E 12 + +--S 13 of 528 +a0302:= integrate(t0302,x) +--R +--R +--R (12) 0 +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 528 +m0302:= a0302-r0302 +--R +--R +--R +-+ +----------+ +--R 2\|3 tan(x)atan(\|sec(x) - 1 ) +--R (13) - ------------------------------ +--R +----------+ +----------+ +--R \|sec(x) - 1 \|sec(x) + 1 +--R Type: Expression Integer +--E 14 + +--S 15 of 528 +d0302:= D(m0302,x) +--R +--R +--R (14) +--R +-+ 2 +-+ 2 +-+ +----------+ +--R (2\|3 tan(x) - 2\|3 sec(x) + 2\|3 )atan(\|sec(x) - 1 ) +--R + +--R +-+ +-+ 2 +----------+ +--R (- \|3 sec(x) - \|3 )tan(x) \|sec(x) - 1 +--R / +--R 2 +----------+ +----------+ +--R (sec(x) - 1)\|sec(x) - 1 \|sec(x) + 1 +--R Type: Expression Integer +--E 15 + +--S 16 of 528 +t0303:= (3-3*sec(x))^(1/2) +--R +--R +--R +-------------+ +--R (15) \|- 3sec(x) + 3 +--R Type: Expression Integer +--E 16 + +--S 17 of 528 +r0303:= 2*3^(1/2)*atan((-1-sec(x))^(1/2))*tan(x)/(-1-sec(x))^(1/2)/(1-sec(x))^(1/2) +--R +--R +--R +-+ +------------+ +--R 2\|3 tan(x)atan(\|- sec(x) - 1 ) +--R (16) -------------------------------- +--R +------------+ +------------+ +--R \|- sec(x) - 1 \|- sec(x) + 1 +--R Type: Expression Integer +--E 17 + +--S 18 of 528 +a0303:= integrate(t0303,x) +--R +--R +--R +-+ +-+ +--R +-+ 2\|3 cos(x) + \|3 +--R (17) \|3 atan(-----------------------) +--R +-------------+ +--R |- 3cos(x) - 3 +--R 2cos(x) |------------- +--R \| cos(x) +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 528 +m0303:= a0303-r0303 +--R +--R +--R (18) +--R +-+ +------------+ +--R - 2\|3 tan(x)atan(\|- sec(x) - 1 ) +--R + +--R +-+ +-+ +--R +-+ +------------+ +------------+ 2\|3 cos(x) + \|3 +--R \|3 \|- sec(x) - 1 \|- sec(x) + 1 atan(-----------------------) +--R +-------------+ +--R |- 3cos(x) - 3 +--R 2cos(x) |------------- +--R \| cos(x) +--R / +--R +------------+ +------------+ +--R \|- sec(x) - 1 \|- sec(x) + 1 +--R Type: Expression Integer +--E 19 + +--S 20 of 528 +d0303:= D(m0303,x) +--R +--R +--R (19) +--R +-------------+ +--R +-+ 2 +-+ 2 +-+ |- 3cos(x) - 3 +--R (2\|3 cos(x)tan(x) - 2\|3 cos(x)sec(x) + 2\|3 cos(x)) |------------- +--R \| cos(x) +--R * +--R +------------+ +--R atan(\|- sec(x) - 1 ) +--R + +--R +-------------+ +--R +-+ +-+ 2 +------------+ |- 3cos(x) - 3 +--R (\|3 cos(x)sec(x) - \|3 cos(x))tan(x) \|- sec(x) - 1 |------------- +--R \| cos(x) +--R + +--R 2 +------------+ +------------+ +--R (- 3sec(x) + 3)sin(x)\|- sec(x) - 1 \|- sec(x) + 1 +--R / +--R +-------------+ +--R 2 +------------+ +------------+ |- 3cos(x) - 3 +--R (cos(x)sec(x) - cos(x))\|- sec(x) - 1 \|- sec(x) + 1 |------------- +--R \| cos(x) +--R Type: Expression Integer +--E 20 + +--S 21 of 528 +t0304:= (a+a*sec(x))^(1/2) +--R +--R +--R +------------+ +--R (20) \|a sec(x) + a +--R Type: Expression Integer +--E 21 + +--S 22 of 528 +r0304:= 2*a*atan((-1+sec(x))^(1/2))*tan(x)/(-1+sec(x))^(1/2)/(a+a*sec(x))^(1/2) +--R +--R +--R +----------+ +--R 2a tan(x)atan(\|sec(x) - 1 ) +--R (21) ---------------------------- +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R Type: Expression Integer +--E 22 + +--S 23 of 528 +a0304:= integrate(t0304,x) +--R +--R +--R (22) +--R [ +--R +---+ +--R \|- a +--R * +--R log +--R +------------+ +--R 2 +---+ |a cos(x) + a 3 +--R (- 8cos(x) + 4cos(x))sin(x)\|- a |------------ + 8a cos(x) +--R \| cos(x) +--R + +--R - 7a cos(x) + a +--R / +--R cos(x) + 1 +--R / +--R 2 +--R , +--R +------------+ +--R +-+ |a cos(x) + a +--R 2cos(x)sin(x)\|a |------------ +--R +-+ \| cos(x) +--R \|a atan(--------------------------------)] +--R 2 +--R 2a cos(x) + a cos(x) - a +--R Type: Union(List Expression Integer,...) +--E 23 + +--S 24 of 528 +m0304a:= a0304.1-r0304 +--R +--R +--R (23) +--R +---+ +----------+ +------------+ +--R \|- a \|sec(x) - 1 \|a sec(x) + a +--R * +--R log +--R +------------+ +--R 2 +---+ |a cos(x) + a 3 +--R (- 8cos(x) + 4cos(x))sin(x)\|- a |------------ + 8a cos(x) +--R \| cos(x) +--R + +--R - 7a cos(x) + a +--R / +--R cos(x) + 1 +--R + +--R +----------+ +--R - 4a tan(x)atan(\|sec(x) - 1 ) +--R / +--R +----------+ +------------+ +--R 2\|sec(x) - 1 \|a sec(x) + a +--R Type: Expression Integer +--E 24 + +--S 25 of 528 +d0304a:= D(m0304a,x) +--R +--R +--R (24) +--R 4 2 2 +--R (16a cos(x) - 14a cos(x) + 2a cos(x))tan(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 14a cos(x) - 2a cos(x))sec(x) + 16a cos(x) +--R + +--R 2 +--R - 14a cos(x) + 2a cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +--R |------------ +--R \| cos(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) - 8a cos(x) + 8a cos(x))sin(x)tan(x) +--R + +--R 3 2 2 3 +--R (16a cos(x) + 8a cos(x) - 8a cos(x))sec(x) - 16a cos(x) +--R + +--R 2 +--R - 8a cos(x) + 8a cos(x) +--R * +--R sin(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R atan(\|sec(x) - 1 ) +--R + +--R 3 2 2 3 2 +--R (- 8cos(x) - 4cos(x) + 4cos(x))sec(x) + 8cos(x) + 4cos(x) +--R + +--R - 4cos(x) +--R * +--R +------------+ +--R +---+ |a cos(x) + a +--R sin(x)\|- a |------------ +--R \| cos(x) +--R + +--R 2 2 2 +--R (- 4a cos(x) - 6a cos(x) + a)sec(x) + 4a cos(x) + 6a cos(x) +--R + +--R - a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (4a cos(x) + 2a cos(x) - 2a cos(x) )sec(x) - 4a cos(x) +--R + +--R 3 2 +--R - 2a cos(x) + 2a cos(x) +--R * +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R + +--R 4 2 4 +--R (- 8a cos(x) + 7a cos(x) - a cos(x))sec(x) - 8a cos(x) +--R + +--R 2 +--R 7a cos(x) - a cos(x) +--R * +--R +------------+ +--R 2 |a cos(x) + a +--R tan(x) |------------ +--R \| cos(x) +--R + +--R 3 2 3 +--R (8a cos(x) + 4a cos(x) - 4a cos(x))sec(x) + 8a cos(x) +--R + +--R 2 +--R 4a cos(x) - 4a cos(x) +--R * +--R 2 +---+ +--R sin(x)tan(x) \|- a +--R * +--R +----------+ +--R \|sec(x) - 1 +--R / +--R 4 2 2 4 2 +--R (8cos(x) - 7cos(x) + cos(x))sec(x) - 8cos(x) + 7cos(x) +--R + +--R - cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +--R |------------ +--R \| cos(x) +--R + +--R 3 2 2 3 2 +--R (- 8cos(x) - 4cos(x) + 4cos(x))sec(x) + 8cos(x) + 4cos(x) +--R + +--R - 4cos(x) +--R * +--R +---+ +--R sin(x)\|- a +--R * +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R Type: Expression Integer +--E 25 + +--S 26 of 528 +m0304b:= a0304.2-r0304 +--R +--R +--R (25) +--R +----------+ +--R - 2a tan(x)atan(\|sec(x) - 1 ) +--R + +--R +------------+ +--R +-+ |a cos(x) + a +--R 2cos(x)sin(x)\|a |------------ +--R +-+ +----------+ +------------+ \| cos(x) +--R \|a \|sec(x) - 1 \|a sec(x) + a atan(--------------------------------) +--R 2 +--R 2a cos(x) + a cos(x) - a +--R / +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R Type: Expression Integer +--E 26 + +--S 27 of 528 +d0304b:= D(m0304b,x) +--R +--R +--R (26) +--R 2 2 4 2 2 +--R (8a cos(x) sin(x) + 8a cos(x) - 6a cos(x) + 2a cos(x))tan(x) +--R + +--R 2 2 2 2 +--R (- 8a cos(x) sec(x) + 8a cos(x) )sin(x) +--R + +--R 4 2 2 4 +--R (- 8a cos(x) + 6a cos(x) - 2a cos(x))sec(x) + 8a cos(x) +--R + +--R 2 +--R - 6a cos(x) + 2a cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +----------+ +--R |------------ atan(\|sec(x) - 1 ) +--R \| cos(x) +--R + +--R 2 2 2 +--R ((4a cos(x) + 2a cos(x) + a)sec(x) - 4a cos(x) - 2a cos(x) - a) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (4a cos(x) + 2a cos(x) - 2a cos(x) )sec(x) - 4a cos(x) +--R + +--R 3 2 +--R - 2a cos(x) + 2a cos(x) +--R * +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R + +--R 2 2 2 +--R (- 4a cos(x) sec(x) - 4a cos(x) )sin(x) +--R + +--R 4 2 4 +--R (- 4a cos(x) + 3a cos(x) - a cos(x))sec(x) - 4a cos(x) +--R + +--R 2 +--R 3a cos(x) - a cos(x) +--R * +--R +------------+ +--R 2 |a cos(x) + a +----------+ +--R tan(x) |------------ \|sec(x) - 1 +--R \| cos(x) +--R / +--R 2 2 2 2 +--R (4cos(x) sec(x) - 4cos(x) )sin(x) +--R + +--R 4 2 2 4 2 +--R (4cos(x) - 3cos(x) + cos(x))sec(x) - 4cos(x) + 3cos(x) - cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +----------+ +------------+ +--R |------------ \|sec(x) - 1 \|a sec(x) + a +--R \| cos(x) +--R Type: Expression Integer +--E 27 + +--S 28 of 528 +t0305:= (a-a*sec(x))^(1/2) +--R +--R +--R +--------------+ +--R (27) \|- a sec(x) + a +--R Type: Expression Integer +--E 28 + +--S 29 of 528 +r0305:= 2*a*atan((-1-sec(x))^(1/2))*tan(x)/(-1-sec(x))^(1/2)/(a-a*sec(x))^(1/2) +--R +--R +--R +------------+ +--R 2a tan(x)atan(\|- sec(x) - 1 ) +--R (28) -------------------------------- +--R +--------------+ +------------+ +--R \|- a sec(x) + a \|- sec(x) - 1 +--R Type: Expression Integer +--E 29 + +--S 30 of 528 +a0305:= integrate(t0305,x) +--R +--R +--R (29) +--R - +--R +----+ +--R \|- 4a +--R * +--R log +--R +--------------+ +--R 2 +----+ |- a cos(x) - a 2 +--R (4cos(x) + 2cos(x))\|- 4a |-------------- - 8a cos(x) +--R \| cos(x) +--R + +--R - 8a cos(x) - a +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 30 + +--S 31 of 528 +m0305:= a0305-r0305 +--R +--R +--R (30) +--R - +--R +----+ +--------------+ +------------+ +--R \|- 4a \|- a sec(x) + a \|- sec(x) - 1 +--R * +--R log +--R +--------------+ +--R 2 +----+ |- a cos(x) - a 2 +--R (4cos(x) + 2cos(x))\|- 4a |-------------- - 8a cos(x) +--R \| cos(x) +--R + +--R - 8a cos(x) - a +--R + +--R +------------+ +--R - 8a tan(x)atan(\|- sec(x) - 1 ) +--R / +--R +--------------+ +------------+ +--R 4\|- a sec(x) + a \|- sec(x) - 1 +--R Type: Expression Integer +--E 31 + +--S 32 of 528 +d0305:= D(m0305,x) +--R +--R +--R (31) +--R 3 2 2 +--R (16a cos(x) + 16a cos(x) + 2a cos(x))tan(x) +--R + +--R 3 2 2 3 +--R (- 16a cos(x) - 16a cos(x) - 2a cos(x))sec(x) + 16a cos(x) +--R + +--R 2 +--R 16a cos(x) + 2a cos(x) +--R * +--R +--------------+ +--R |- a cos(x) - a +--R |-------------- +--R \| cos(x) +--R + +--R 3 2 2 +--R (8a cos(x) + 12a cos(x) + 4a cos(x))tan(x) +--R + +--R 3 2 2 3 +--R (- 8a cos(x) - 12a cos(x) - 4a cos(x))sec(x) + 8a cos(x) +--R + +--R 2 +--R 12a cos(x) + 4a cos(x) +--R * +--R +----+ +--R \|- 4a +--R * +--R +------------+ +--R atan(\|- sec(x) - 1 ) +--R + +--R 2 2 2 +----+ +--R ((4cos(x) + 2cos(x))sec(x) - 4cos(x) - 2cos(x))sin(x)\|- 4a +--R * +--R +--------------+ +--R \|- a sec(x) + a +--R + +--R 3 2 3 +--R (8a cos(x) + 8a cos(x) + a cos(x))sec(x) - 8a cos(x) +--R + +--R 2 +--R - 8a cos(x) - a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R +--------------+ +--R +------------+ |- a cos(x) - a +--R \|- sec(x) - 1 |-------------- +--R \| cos(x) +--R + +--R 2 2 2 +--R (- 8a cos(x) - 8a cos(x) - a)sec(x) + 8a cos(x) + 8a cos(x) +--R + +--R a +--R * +--R +--------------+ +--R sin(x)\|- a sec(x) + a +--R + +--R 3 2 3 +--R (4a cos(x) + 6a cos(x) + 2a cos(x))sec(x) - 4a cos(x) +--R + +--R 2 +--R - 6a cos(x) - 2a cos(x) +--R * +--R 2 +----+ +--R tan(x) \|- 4a +--R * +--R +------------+ +--R \|- sec(x) - 1 +--R / +--R 3 2 2 3 2 +--R ((8cos(x) + 8cos(x) + cos(x))sec(x) - 8cos(x) - 8cos(x) - cos(x)) +--R * +--R +--------------+ +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a sec(x) + a \|- sec(x) - 1 |-------------- +--R \| cos(x) +--R + +--R 3 2 2 3 2 +--R (4cos(x) + 6cos(x) + 2cos(x))sec(x) - 4cos(x) - 6cos(x) +--R + +--R - 2cos(x) +--R * +--R +----+ +--------------+ +------------+ +--R \|- 4a \|- a sec(x) + a \|- sec(x) - 1 +--R Type: Expression Integer +--E 32 + +--S 33 of 528 +t0306:= (a+b*sec(c+d*x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (32) b sec(d x + c) + 3a b sec(d x + c) + 3a b sec(d x + c) + a +--R Type: Expression Integer +--E 33 + +--S 34 of 528 +r0306:= a^3*x+3*a^2*b*atanh(sin(c+d*x))/d+1/2*b^3*atanh(sin(c+d*x))/d+3*a*b^2*tan(c+d*x)/d+1/2*b^3*sec(c+d*x)*tan(c+d*x)/d +--R +--R +--R (33) +--R 3 2 3 2 +--R (b + 6a b)atanh(sin(d x + c)) + (b sec(d x + c) + 6a b )tan(d x + c) +--R + +--R 3 +--R 2a d x +--R / +--R 2d +--R Type: Expression Integer +--E 34 + +--S 35 of 528 +a0306:= integrate(t0306,x) +--R +--R +--R (34) +--R 3 2 2 sin(d x + c) + cos(d x + c) + 1 +--R (b + 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 sin(d x + c) - cos(d x + c) - 1 +--R (- b - 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 2 3 3 2 +--R (6a b cos(d x + c) + b )sin(d x + c) + 2a d x cos(d x + c) +--R / +--R 2 +--R 2d cos(d x + c) +--R Type: Union(Expression Integer,...) +--E 35 + +--S 36 of 528 +m0306:= a0306-r0306 +--R +--R +--R (35) +--R 3 2 2 sin(d x + c) + cos(d x + c) + 1 +--R (b + 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 sin(d x + c) - cos(d x + c) - 1 +--R (- b - 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 +--R (- b - 6a b)cos(d x + c) atanh(sin(d x + c)) +--R + +--R 3 2 2 2 +--R (- b cos(d x + c) sec(d x + c) - 6a b cos(d x + c) )tan(d x + c) +--R + +--R 2 3 +--R (6a b cos(d x + c) + b )sin(d x + c) +--R / +--R 2 +--R 2d cos(d x + c) +--R Type: Expression Integer +--E 36 + +--S 37 of 528 +d0306:= D(m0306,x) +--R +--R +--R (36) +--R 3 3 2 3 4 +--R (- 2b cos(d x + c) sec(d x + c) - 6a b cos(d x + c) )sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (2b cos(d x + c) + 4b cos(d x + c) + 4b cos(d x + c) ) +--R * +--R sec(d x + c) +--R + +--R 2 5 2 4 2 3 +--R 6a b cos(d x + c) + 12a b cos(d x + c) + 12a b cos(d x + c) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (- 2b cos(d x + c) - 4b cos(d x + c) - 2b cos(d x + c) ) +--R * +--R sec(d x + c) +--R + +--R 2 5 2 4 2 3 +--R - 6a b cos(d x + c) - 12a b cos(d x + c) - 6a b cos(d x + c) +--R * +--R 2 +--R tan(d x + c) +--R + +--R 2 3 6 +--R (6a b cos(d x + c) + 2b )sin(d x + c) +--R + +--R 3 3 3 2 2 3 +--R - b cos(d x + c) sec(d x + c) + (- 2b - 6a b - 12a b)cos(d x + c) +--R + +--R 3 2 2 3 2 3 +--R (- b - 12a b )cos(d x + c) + (- 4b - 12a b )cos(d x + c) - 4b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (b cos(d x + c) + 2b cos(d x + c) + 2b cos(d x + c) )sec(d x + c) +--R + +--R 3 2 5 3 2 4 +--R (- 2b - 12a b)cos(d x + c) + (- 2b - 6a b)cos(d x + c) +--R + +--R 2 2 3 2 2 +--R (6a b + 12a b)cos(d x + c) + 12a b cos(d x + c) +--R + +--R 3 2 3 +--R (4b + 6a b )cos(d x + c) + 2b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (- b cos(d x + c) - 2b cos(d x + c) - b cos(d x + c) )sec(d x + c) +--R + +--R 3 2 6 3 2 4 3 3 +--R (- b - 6a b)cos(d x + c) + (2b + 6a b)cos(d x + c) + 2b cos(d x + c) +--R + +--R 3 2 +--R b cos(d x + c) +--R / +--R 3 4 +--R 2cos(d x + c) sin(d x + c) +--R + +--R 5 4 3 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 4cos(d x + c) )sin(d x + c) +--R + +--R 5 4 3 +--R 2cos(d x + c) + 4cos(d x + c) + 2cos(d x + c) +--R Type: Expression Integer +--E 37 + +--S 38 of 528 +t0307:= (a+b*sec(c+d*x))^2 +--R +--R +--R 2 2 2 +--R (37) b sec(d x + c) + 2a b sec(d x + c) + a +--R Type: Expression Integer +--E 38 + +--S 39 of 528 +r0307:= a^2*x+2*a*b*atanh(sin(c+d*x))/d+b^2*tan(c+d*x)/d +--R +--R +--R 2 2 +--R 2a b atanh(sin(d x + c)) + b tan(d x + c) + a d x +--R (38) ------------------------------------------------- +--R d +--R Type: Expression Integer +--E 39 + +--S 40 of 528 +a0307:= integrate(t0307,x) +--R +--R +--R (39) +--R sin(d x + c) + cos(d x + c) + 1 +--R 2a b cos(d x + c)log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) - cos(d x + c) - 1 2 +--R - 2a b cos(d x + c)log(-------------------------------) + b sin(d x + c) +--R cos(d x + c) + 1 +--R + +--R 2 +--R a d x cos(d x + c) +--R / +--R d cos(d x + c) +--R Type: Union(Expression Integer,...) +--E 40 + +--S 41 of 528 +m0307:= a0307-r0307 +--R +--R +--R (40) +--R sin(d x + c) + cos(d x + c) + 1 +--R 2a b cos(d x + c)log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) - cos(d x + c) - 1 +--R - 2a b cos(d x + c)log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 2 +--R - 2a b cos(d x + c)atanh(sin(d x + c)) - b cos(d x + c)tan(d x + c) +--R + +--R 2 +--R b sin(d x + c) +--R / +--R d cos(d x + c) +--R Type: Expression Integer +--E 41 + +--S 42 of 528 +d0307:= D(m0307,x) +--R +--R +--R (41) +--R 2 2 4 +--R - b cos(d x + c) sin(d x + c) +--R + +--R 2 4 2 3 2 2 2 +--R (b cos(d x + c) + 2b cos(d x + c) + 2b cos(d x + c) )sin(d x + c) +--R + +--R 2 4 2 3 2 2 +--R - b cos(d x + c) - 2b cos(d x + c) - b cos(d x + c) +--R * +--R 2 +--R tan(d x + c) +--R + +--R 2 6 +--R b sin(d x + c) +--R + +--R 2 2 2 2 4 +--R ((- b - 4a b)cos(d x + c) - 2b cos(d x + c) - 2b )sin(d x + c) +--R + +--R 4 3 2 2 +--R - 4a b cos(d x + c) - 2a b cos(d x + c) + (b + 4a b)cos(d x + c) +--R + +--R 2 2 +--R 2b cos(d x + c) + b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 5 3 +--R - 2a b cos(d x + c) + 2a b cos(d x + c) +--R / +--R 2 4 +--R cos(d x + c) sin(d x + c) +--R + +--R 4 3 2 2 +--R (- cos(d x + c) - 2cos(d x + c) - 2cos(d x + c) )sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) + 2cos(d x + c) + cos(d x + c) +--R Type: Expression Integer +--E 42 + +--S 43 of 528 +t0308:= 1/(3+5*sec(c+d*x)) +--R +--R +--R 1 +--R (42) ----------------- +--R 5sec(d x + c) + 3 +--R Type: Expression Integer +--E 43 + +--S 44 of 528 +r0308:= 1/3*x-5/6*atan(1/2*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R tan(-------) +--R 2 +--R - 5atan(------------) + 2d x +--R 2 +--R (43) ---------------------------- +--R 6d +--R Type: Expression Integer +--E 44 + +--S 45 of 528 +a0308:= integrate(t0308,x) +--R +--R +--R sin(d x + c) +--R - 5atan(-----------------) + 2d x +--R 2cos(d x + c) + 2 +--R (44) --------------------------------- +--R 6d +--R Type: Union(Expression Integer,...) +--E 45 + +--S 46 of 528 +m0308:= a0308-r0308 +--R +--R +--R d x + c +--R tan(-------) +--R 2 sin(d x + c) +--R 5atan(------------) - 5atan(-----------------) +--R 2 2cos(d x + c) + 2 +--R (45) ---------------------------------------------- +--R 6d +--R Type: Expression Integer +--E 46 + +--S 47 of 528 +d0308:= D(m0308,x) +--R +--R +--R (46) +--R 2 2 d x + c 2 +--R (- 5sin(d x + c) + 10cos(d x + c) + 30cos(d x + c) + 20)tan(-------) +--R 2 +--R + +--R 2 2 +--R - 35sin(d x + c) - 20cos(d x + c) + 20 +--R / +--R 2 2 d x + c 2 +--R (6sin(d x + c) + 24cos(d x + c) + 48cos(d x + c) + 24)tan(-------) +--R 2 +--R + +--R 2 2 +--R 24sin(d x + c) + 96cos(d x + c) + 192cos(d x + c) + 96 +--R Type: Expression Integer +--E 47 + +--S 48 of 528 +t0309:= 1/(5+3*sec(c+d*x)) +--R +--R +--R 1 +--R (47) ----------------- +--R 3sec(d x + c) + 5 +--R Type: Expression Integer +--E 48 + +--S 49 of 528 +r0309:= 1/5*x-3/10*atanh(1/2*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R tan(-------) +--R 2 +--R - 3atanh(------------) + 2d x +--R 2 +--R (48) ----------------------------- +--R 10d +--R Type: Expression Integer +--E 49 + +--S 50 of 528 +a0309:= integrate(t0309,x) +--R +--R +--R (49) +--R sin(d x + c) + 2cos(d x + c) + 2 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) - 2cos(d x + c) - 2 +--R 3log(--------------------------------) + 4d x +--R cos(d x + c) + 1 +--R / +--R 20d +--R Type: Union(Expression Integer,...) +--E 50 + +--S 51 of 528 +m0309:= a0309-r0309 +--R +--R +--R (50) +--R sin(d x + c) + 2cos(d x + c) + 2 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R d x + c +--R tan(-------) +--R sin(d x + c) - 2cos(d x + c) - 2 2 +--R 3log(--------------------------------) + 6atanh(------------) +--R cos(d x + c) + 1 2 +--R / +--R 20d +--R Type: Expression Integer +--E 51 + +--S 52 of 528 +d0309:= D(m0309,x) +--R +--R +--R (51) +--R 2 2 d x + c 2 +--R (3sin(d x + c) + 18cos(d x + c) + 30cos(d x + c) + 12)tan(-------) +--R 2 +--R + +--R 2 2 +--R - 27sin(d x + c) - 12cos(d x + c) + 12 +--R / +--R 2 2 d x + c 2 +--R (10sin(d x + c) - 40cos(d x + c) - 80cos(d x + c) - 40)tan(-------) +--R 2 +--R + +--R 2 2 +--R - 40sin(d x + c) + 160cos(d x + c) + 320cos(d x + c) + 160 +--R Type: Expression Integer +--E 52 + +--S 53 of 528 +t0310:= 1/(a+b*sec(c+d*x))^2 +--R +--R +--R 1 +--R (52) ---------------------------------------- +--R 2 2 2 +--R b sec(d x + c) + 2a b sec(d x + c) + a +--R Type: Expression Integer +--E 53 + +--S 54 of 528 +r0310:= x/a^2-2*b^3*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(3/2)/d-4*b*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)/d+b^2*sin(c+d*x)/a/(a^2-b^2)/d/(b+a*cos(c+d*x)) +--R +--R +--R (53) +--R d x + c +--R (b - a)tan(-------) +--R 3 3 4 2 2 2 +--R ((2a b - 4a b)cos(d x + c) + 2b - 4a b )atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 3 2 +--R (- a b sin(d x + c) + (a b - a )d x cos(d x + c) + (b - a b)d x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d cos(d x + c) + (a b - a b)d)\|- b + a +--R Type: Expression Integer +--E 54 + +--S 55 of 528 +a0310:= integrate(t0310,x) +--R +--R +--R (54) +--R [ +--R 3 3 4 2 2 +--R ((a b - 2a b)cos(d x + c) + b - 2a b ) +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R 2 2 3 3 2 +--R (- a b sin(d x + c) + (a b - a )d x cos(d x + c) + (b - a b)d x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d cos(d x + c) + (a b - a b)d)\|- b + a +--R , +--R +--R 3 3 4 2 2 +--R ((- 2a b + 4a b)cos(d x + c) - 2b + 4a b ) +--R * +--R +-------+ +--R | 2 2 +--R sin(d x + c)\|b - a +--R atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R 2 2 3 3 2 +--R (- a b sin(d x + c) + (a b - a )d x cos(d x + c) + (b - a b)d x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d cos(d x + c) + (a b - a b)d)\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 55 + +--S 56 of 528 +m0310a:= a0310.1-r0310 +--R +--R +--R (55) +--R 3 2 +--R (b - 2a b) +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R d x + c +--R (b - a)tan(-------) +--R 3 2 2 +--R (- 2b + 4a b)atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 4 | 2 2 +--R (a b - a )d\|- b + a +--R Type: Expression Integer +--E 56 + +--S 57 of 528 +d0310a:= D(m0310a,x) +--R +--R +--R (56) +--R 4 3 2 2 3 2 +--R (- b + a b + 2a b - 2a b)sin(d x + c) +--R + +--R 3 3 2 +--R (a b - 2a b)cos(d x + c) +--R + +--R 4 3 2 2 3 4 2 2 +--R (b + a b - 2a b - 2a b)cos(d x + c) + b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b - a b + 2a b + 2a b)sin(d x + c) +--R + +--R 3 3 2 +--R (- a b + 2a b)cos(d x + c) +--R + +--R 4 3 2 2 3 4 2 2 +--R (- b + a b + 2a b - 2a b)cos(d x + c) + b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 4 5 2 3 4 +--R ((b - 3a b + 2a b)cos(d x + c) + b - 3a b + 2a b)sin(d x + c) +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 2 3 4 5 2 3 4 +--R ((b - 3a b + 2a b)cos(d x + c) - b + 3a b - 2a b)sin(d x + c) +--R / +--R 2 4 3 3 4 2 5 2 +--R (a b - a b - a b + a b)cos(d x + c) +--R + +--R 5 2 4 5 6 2 4 3 3 4 2 5 +--R (a b - a b - a b + a )cos(d x + c) + a b - a b - a b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 4 3 3 4 2 5 2 +--R (a b + a b - a b - a b)cos(d x + c) +--R + +--R 5 2 4 5 6 2 4 3 3 4 2 5 +--R (a b + a b - a b - a )cos(d x + c) + a b + a b - a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (a b - a b - 2a b + 2a b + a b - a )cos(d x + c) + a b - a b +--R + +--R 3 4 4 3 5 2 6 +--R - 2a b + 2a b + a b - a b +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (a b + a b - 2a b - 2a b + a b + a )cos(d x + c) + a b + a b +--R + +--R 3 4 4 3 5 2 6 +--R - 2a b - 2a b + a b + a b +--R * +--R sin(d x + c) +--R Type: Expression Integer +--E 57 + +--S 58 of 528 +m0310b:= a0310.2-r0310 +--R +--R +--R (57) +--R d x + c +--R +-------+ (b - a)tan(-------) +--R 3 2 | 2 2 2 +--R (- 2b + 4a b)\|b - a atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 sin(d x + c)\|b - a +--R (- 2b + 4a b)\|- b + a atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R / +--R +---------+ +-------+ +--R 2 2 4 | 2 2 | 2 2 +--R (a b - a )d\|- b + a \|b - a +--R Type: Expression Integer +--E 58 + +--S 59 of 528 +d0310b:= D(m0310b,x) +--R +--R +--R (58) +--R 4 3 2 2 3 2 +--R (- b + a b + 2a b - 2a b)sin(d x + c) +--R + +--R 4 3 2 2 3 2 +--R (- b + 3a b + 2a b - 6a b)cos(d x + c) +--R + +--R 3 3 4 3 2 2 3 +--R (4a b - 8a b)cos(d x + c) + b + a b - 2a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b - 3a b + 2a b + 6a b)sin(d x + c) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - a b + 2a b + 2a b)cos(d x + c) + b + a b - 2a b - 2a b +--R / +--R 2 4 3 3 5 6 2 +--R (a b - 2a b + 2a b - a )sin(d x + c) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (a b - 2a b + a )cos(d x + c) + (2a b - 4a b + 2a )cos(d x + c) +--R + +--R 2 4 4 2 6 +--R a b - 2a b + a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 4 4 2 6 2 +--R (a b - 2a b + a )sin(d x + c) +--R + +--R 2 4 3 3 5 6 2 +--R (a b + 2a b - 2a b - a )cos(d x + c) +--R + +--R 2 4 3 3 5 6 2 4 3 3 5 6 +--R (2a b + 4a b - 4a b - 2a )cos(d x + c) + a b + 2a b - 2a b - a +--R Type: Expression Integer +--E 59 + +--S 60 of 528 +t0311:= 1/(a+b*sec(c+d*x))^3 +--R +--R +--R 1 +--R (59) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b sec(d x + c) + 3a b sec(d x + c) + 3a b sec(d x + c) + a +--R Type: Expression Integer +--E 60 + +--S 61 of 528 +r0311:= x/a^3-6*b^3*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(3/2)/d-6*b*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)/d-b^3*(a^2+2*b^2)*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(5/2)/d-1/2*b^3*sin(c+d*x)/a^2/(a^2-b^2)/d/(b+a*cos(c+d*x))^2+3/2*b^4*sin(c+d*x)/a^2/(a^2-b^2)^2/d/(b+a*cos(c+d*x))+3*b^2*sin(c+d*x)/a^2/(a^2-b^2)/d/(b+a*cos(c+d*x)) +--R +--R +--R (60) +--R 2 5 4 3 6 2 +--R (4a b - 10a b + 12a b)cos(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (8a b - 20a b + 24a b )cos(d x + c) + 4b - 10a b + 12a b +--R * +--R d x + c +--R (b - a)tan(-------) +--R 2 +--R atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cos(d x + c) - 2a b + 5a b )sin(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x cos(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 8a b + 4a b)d x cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d cos(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d cos(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 61 + +--S 62 of 528 +a0311:= integrate(t0311,x) +--R +--R +--R (61) +--R [ +--R 2 5 4 3 6 2 +--R (2a b - 5a b + 6a b)cos(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (4a b - 10a b + 12a b )cos(d x + c) + 2b - 5a b + 6a b +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cos(d x + c) - 2a b + 5a b )sin(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x cos(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 8a b + 4a b)d x cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d cos(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d cos(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 2 5 4 3 6 2 +--R (- 4a b + 10a b - 12a b)cos(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (- 8a b + 20a b - 24a b )cos(d x + c) - 4b + 10a b - 12a b +--R * +--R +-------+ +--R | 2 2 +--R sin(d x + c)\|b - a +--R atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cos(d x + c) - 2a b + 5a b )sin(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x cos(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 8a b + 4a b)d x cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d cos(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d cos(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 62 + +--S 63 of 528 +m0311a:= a0311.1-r0311 +--R +--R +--R (62) +--R 5 2 3 4 +--R (2b - 5a b + 6a b) +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R d x + c +--R (b - a)tan(-------) +--R 5 2 3 4 2 +--R (- 4b + 10a b - 12a b)atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 4 5 2 7 | 2 2 +--R (2a b - 4a b + 2a )d\|- b + a +--R Type: Expression Integer +--E 63 + +--S 64 of 528 +d0311a:= D(m0311a,x) +--R +--R +--R (63) +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b + 2a b + 5a b - 5a b - 6a b + 6a b)sin(d x + c) +--R + +--R 5 3 3 5 2 +--R (2a b - 5a b + 6a b)cos(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (2b + 2a b - 5a b - 5a b + 6a b + 6a b)cos(d x + c) + 2b +--R + +--R 2 4 4 2 +--R - 5a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b - 2a b + 5a b + 5a b - 6a b - 6a b)sin(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 2a b + 5a b - 6a b)cos(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2b + 2a b + 5a b - 5a b - 6a b + 6a b)cos(d x + c) + 2b +--R + +--R 2 4 4 2 +--R - 5a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (2b - 7a b + 11a b - 6a b)cos(d x + c) + 2b - 7a b + 11a b +--R + +--R 6 +--R - 6a b +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (2b - 7a b + 11a b - 6a b)cos(d x + c) - 2b + 7a b - 11a b +--R + +--R 6 +--R 6a b +--R * +--R sin(d x + c) +--R / +--R 3 6 4 5 5 4 6 3 7 2 8 2 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a b)cos(d x + c) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (2a b - 2a b - 2a b + 2a b - 2a b + 2a b + 2a b - 2a ) +--R * +--R cos(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 2a b - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 2 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a b)cos(d x + c) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (2a b + 2a b - 2a b - 2a b - 2a b - 2a b + 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 2a b + 2a b - 4a b - 4a b + 2a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a b +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (2a b + 2a b - 6a b - 6a b + 6a b + 6a b - 2a b - 2a ) +--R * +--R cos(d x + c) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 2a b + 2a b - 6a b - 6a b + 6a b + 6a b - 2a b - 2a b +--R * +--R sin(d x + c) +--R Type: Expression Integer +--E 64 + +--S 65 of 528 +m0311b:= a0311.2-r0311 +--R +--R +--R (64) +--R d x + c +--R +-------+ (b - a)tan(-------) +--R 5 2 3 4 | 2 2 2 +--R (- 2b + 5a b - 6a b)\|b - a atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 5 2 3 4 | 2 2 sin(d x + c)\|b - a +--R (- 2b + 5a b - 6a b)\|- b + a atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R / +--R +---------+ +-------+ +--R 3 4 5 2 7 | 2 2 | 2 2 +--R (a b - 2a b + a )d\|- b + a \|b - a +--R Type: Expression Integer +--E 65 + +--S 66 of 528 +d0311b:= D(m0311b,x) +--R +--R +--R (65) +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b + 2a b + 5a b - 5a b - 6a b + 6a b)sin(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b + 6a b + 5a b - 15a b - 6a b + 18a b)cos(d x + c) +--R + +--R 5 3 3 5 6 5 2 4 3 3 +--R (8a b - 20a b + 24a b)cos(d x + c) + 2b + 2a b - 5a b - 5a b +--R + +--R 4 2 5 +--R 6a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b - 6a b + 5a b + 15a b - 6a b - 18a b)sin(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 5 +--R (- 2b - 2a b + 5a b + 5a b - 6a b - 6a b)cos(d x + c) + 2b + 2a b +--R + +--R 2 4 3 3 4 2 5 +--R - 5a b - 5a b + 6a b + 6a b +--R / +--R 3 6 4 5 5 4 6 3 7 2 8 9 2 +--R (2a b - 4a b - 2a b + 8a b - 2a b - 4a b + 2a )sin(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (2a b - 6a b + 6a b - 2a )cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 3 6 5 4 7 2 +--R (4a b - 12a b + 12a b - 4a )cos(d x + c) + 2a b - 6a b + 6a b +--R + +--R 9 +--R - 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 6 5 4 7 2 9 2 +--R (2a b - 6a b + 6a b - 2a )sin(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 2 +--R (2a b + 4a b - 2a b - 8a b - 2a b + 4a b + 2a )cos(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 3 6 +--R (4a b + 8a b - 4a b - 16a b - 4a b + 8a b + 4a )cos(d x + c) + 2a b +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R 4a b - 2a b - 8a b - 2a b + 4a b + 2a +--R Type: Expression Integer +--E 66 + +--S 67 of 528 +t0312:= (1+sec(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (66) \|sec(x) + 1 +--R Type: Expression Integer +--E 67 + +--S 68 of 528 +r0312:= asinh(1/2*2^(1/2)*tan(x))+atan(tan(x)/(2+tan(x)^2)^(1/2)) +--R +--R +--R +-+ +--R tan(x) \|2 tan(x) +--R (67) atan(--------------) + asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression Integer +--E 68 + +--S 69 of 528 +a0312:= integrate(t0312,x) +--R +--R +--R (68) +--R - +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R sin(x) +--R - atan(------) +--R cos(x) +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 69 + +--S 70 of 528 +m0312:= a0312-r0312 +--R +--R +--R (69) +--R - +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R +-+ +--R tan(x) sin(x) \|2 tan(x) +--R - 2atan(--------------) - atan(------) - 2asinh(----------) +--R +-----------+ cos(x) 2 +--R | 2 +--R \|tan(x) + 2 +--R / +--R 2 +--R Type: Expression Integer +--E 70 + +--S 71 of 528 +d0312:= D(m0312,x) +--R +--R +--R (70) +--R 17 16 15 14 +--R - 1024cos(x) - 1024cos(x) - 768cos(x) - 768cos(x) +--R + +--R 13 12 11 10 +--R 1280cos(x) + 1280cos(x) + 816cos(x) + 816cos(x) +--R + +--R 9 8 7 6 +--R - 540cos(x) - 540cos(x) - 275cos(x) - 275cos(x) +--R + +--R 5 4 3 2 +--R 72cos(x) + 72cos(x) + 30cos(x) + 30cos(x) + cos(x) + 1 +--R * +--R 4 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 2048cos(x) - 2048cos(x) - 2048cos(x) - 2048cos(x) +--R + +--R 15 14 13 12 +--R 896cos(x) + 896cos(x) + 384cos(x) + 384cos(x) +--R + +--R 11 10 9 8 +--R - 264cos(x) - 264cos(x) + 632cos(x) + 632cos(x) +--R + +--R 7 6 5 4 3 +--R 238cos(x) + 238cos(x) - 176cos(x) - 176cos(x) - 60cos(x) +--R + +--R 2 +--R - 60cos(x) - 2cos(x) - 2 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 1024cos(x) - 1024cos(x) - 1280cos(x) - 1280cos(x) +--R + +--R 17 16 15 14 +--R 1152cos(x) + 1152cos(x) + 1488cos(x) + 1488cos(x) +--R + +--R 13 12 11 10 +--R - 524cos(x) - 524cos(x) - 533cos(x) - 533cos(x) +--R + +--R 9 8 7 6 5 +--R 132cos(x) + 132cos(x) + 39cos(x) + 39cos(x) - 17cos(x) +--R + +--R 4 3 2 +--R - 17cos(x) + 6cos(x) + 6cos(x) + cos(x) + 1 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 17 15 13 11 +--R 2048cos(x) + 2560cos(x) - 2048cos(x) - 2976cos(x) +--R + +--R 9 7 5 3 +--R 600cos(x) + 1130cos(x) - 6cos(x) - 138cos(x) - 16cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 19 17 15 13 +--R 4096cos(x) + 6144cos(x) - 256cos(x) - 1920cos(x) +--R + +--R 11 9 7 5 3 +--R 464cos(x) - 1064cos(x) - 1124cos(x) + 268cos(x) + 284cos(x) +--R + +--R 32cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 +--R 2048cos(x) + 3584cos(x) - 1280cos(x) - 4320cos(x) +--R + +--R 13 11 9 7 5 +--R - 72cos(x) + 1774cos(x) + 70cos(x) - 244cos(x) + 34cos(x) +--R + +--R 3 +--R - 2cos(x) - 8cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 17 16 15 14 +--R - 1024cos(x) - 1024cos(x) - 1536cos(x) - 1536cos(x) +--R + +--R 13 12 11 10 +--R 320cos(x) + 320cos(x) + 1184cos(x) + 1184cos(x) +--R + +--R 9 8 7 6 5 +--R 188cos(x) + 188cos(x) - 222cos(x) - 222cos(x) - 62cos(x) +--R + +--R 4 3 2 +--R - 62cos(x) - 2cos(x) - 2cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 16 15 14 +--R 2048cos(x) + 2048cos(x) + 3072cos(x) + 3072cos(x) +--R + +--R 13 12 11 10 +--R - 896cos(x) - 896cos(x) - 2624cos(x) - 2624cos(x) +--R + +--R 9 8 7 6 +--R - 184cos(x) - 184cos(x) + 636cos(x) + 636cos(x) +--R + +--R 5 4 3 2 +--R 90cos(x) + 90cos(x) - 30cos(x) - 30cos(x) - 2cos(x) - 2 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R 1024cos(x) + 1024cos(x) + 1536cos(x) + 1536cos(x) +--R + +--R 17 16 15 14 +--R - 1344cos(x) - 1344cos(x) - 2464cos(x) - 2464cos(x) +--R + +--R 13 12 11 10 +--R 644cos(x) + 644cos(x) + 1470cos(x) + 1470cos(x) +--R + +--R 9 8 7 6 5 +--R - 134cos(x) - 134cos(x) - 378cos(x) - 378cos(x) + 6cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 34cos(x) + 34cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R tan(x) +--R + +--R 17 16 15 14 +--R - 2048cos(x) - 2048cos(x) - 3072cos(x) - 3072cos(x) +--R + +--R 13 12 11 10 +--R 640cos(x) + 640cos(x) + 2368cos(x) + 2368cos(x) +--R + +--R 9 8 7 6 5 +--R 376cos(x) + 376cos(x) - 444cos(x) - 444cos(x) - 124cos(x) +--R + +--R 4 3 2 +--R - 124cos(x) - 4cos(x) - 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 16 15 14 +--R 4096cos(x) + 4096cos(x) + 6144cos(x) + 6144cos(x) +--R + +--R 13 12 11 10 +--R - 1792cos(x) - 1792cos(x) - 5248cos(x) - 5248cos(x) +--R + +--R 9 8 7 6 +--R - 368cos(x) - 368cos(x) + 1272cos(x) + 1272cos(x) +--R + +--R 5 4 3 2 +--R 180cos(x) + 180cos(x) - 60cos(x) - 60cos(x) - 4cos(x) - 4 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R 2048cos(x) + 2048cos(x) + 3072cos(x) + 3072cos(x) +--R + +--R 17 16 15 14 +--R - 2688cos(x) - 2688cos(x) - 4928cos(x) - 4928cos(x) +--R + +--R 13 12 11 10 +--R 1288cos(x) + 1288cos(x) + 2940cos(x) + 2940cos(x) +--R + +--R 9 8 7 6 5 +--R - 268cos(x) - 268cos(x) - 756cos(x) - 756cos(x) + 12cos(x) +--R + +--R 4 3 2 +--R 12cos(x) + 68cos(x) + 68cos(x) + 4cos(x) + 4 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 17 15 13 11 +--R 2048cos(x) + 4096cos(x) + 640cos(x) - 2944cos(x) +--R + +--R 9 7 5 3 +--R - 1368cos(x) + 448cos(x) + 312cos(x) + 32cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 15 13 11 +--R - 4096cos(x) - 8192cos(x) - 768cos(x) + 6656cos(x) +--R + +--R 9 7 5 3 +--R 2544cos(x) - 1504cos(x) - 688cos(x) + 56cos(x) + 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 +--R - 2048cos(x) - 4096cos(x) + 1408cos(x) + 6528cos(x) +--R + +--R 13 11 9 7 5 +--R 728cos(x) - 3968cos(x) - 880cos(x) + 1088cos(x) + 256cos(x) +--R + +--R 3 +--R - 112cos(x) - 24cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 17 15 13 11 +--R 4096cos(x) + 8192cos(x) + 1280cos(x) - 5888cos(x) +--R + +--R 9 7 5 3 +--R - 2736cos(x) + 896cos(x) + 624cos(x) + 64cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 15 13 11 +--R - 8192cos(x) - 16384cos(x) - 1536cos(x) + 13312cos(x) +--R + +--R 9 7 5 3 +--R 5088cos(x) - 3008cos(x) - 1376cos(x) + 112cos(x) + 48cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 +--R - 4096cos(x) - 8192cos(x) + 2816cos(x) + 13056cos(x) +--R + +--R 13 11 9 7 5 +--R 1456cos(x) - 7936cos(x) - 1760cos(x) + 2176cos(x) + 512cos(x) +--R + +--R 3 +--R - 224cos(x) - 48cos(x) +--R / +--R 17 16 15 14 +--R 1024cos(x) + 1024cos(x) + 1536cos(x) + 1536cos(x) +--R + +--R 13 12 11 10 +--R - 320cos(x) - 320cos(x) - 1184cos(x) - 1184cos(x) +--R + +--R 9 8 7 6 5 +--R - 188cos(x) - 188cos(x) + 222cos(x) + 222cos(x) + 62cos(x) +--R + +--R 4 3 2 +--R 62cos(x) + 2cos(x) + 2cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 16 15 14 +--R - 2048cos(x) - 2048cos(x) - 3072cos(x) - 3072cos(x) +--R + +--R 13 12 11 10 +--R 896cos(x) + 896cos(x) + 2624cos(x) + 2624cos(x) +--R + +--R 9 8 7 6 5 +--R 184cos(x) + 184cos(x) - 636cos(x) - 636cos(x) - 90cos(x) +--R + +--R 4 3 2 +--R - 90cos(x) + 30cos(x) + 30cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 1024cos(x) - 1024cos(x) - 1536cos(x) - 1536cos(x) +--R + +--R 17 16 15 14 +--R 1344cos(x) + 1344cos(x) + 2464cos(x) + 2464cos(x) +--R + +--R 13 12 11 10 +--R - 644cos(x) - 644cos(x) - 1470cos(x) - 1470cos(x) +--R + +--R 9 8 7 6 5 +--R 134cos(x) + 134cos(x) + 378cos(x) + 378cos(x) - 6cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) - 34cos(x) - 34cos(x) - 2cos(x) - 2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 17 15 13 11 +--R - 2048cos(x) - 4096cos(x) - 640cos(x) + 2944cos(x) +--R + +--R 9 7 5 3 +--R 1368cos(x) - 448cos(x) - 312cos(x) - 32cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 15 13 11 +--R 4096cos(x) + 8192cos(x) + 768cos(x) - 6656cos(x) +--R + +--R 9 7 5 3 +--R - 2544cos(x) + 1504cos(x) + 688cos(x) - 56cos(x) - 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 13 +--R 2048cos(x) + 4096cos(x) - 1408cos(x) - 6528cos(x) - 728cos(x) +--R + +--R 11 9 7 5 3 +--R 3968cos(x) + 880cos(x) - 1088cos(x) - 256cos(x) + 112cos(x) +--R + +--R 24cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression Integer +--E 71 + +--S 72 of 528 +t0313:= (1-sec(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (71) \|- sec(x) + 1 +--R Type: Expression Integer +--E 72 + +--S 73 of 528 +r0313:= -cot(x)*log(cos(x))*(-tan(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (72) - cot(x)log(cos(x))\|- tan(x) +--R Type: Expression Integer +--E 73 + +--S 74 of 528 +a0313:= integrate(t0313,x) +--R +--R +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R (73) atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Union(Expression Integer,...) +--E 74 + +--S 75 of 528 +m0313:= a0313-r0313 +--R +--R +--R (74) +--R +---------+ +--R | 2 +--R cot(x)log(cos(x))\|- tan(x) +--R + +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Expression Integer +--E 75 + +--S 76 of 528 +d0313:= D(m0313,x) +--R +--R +--R (75) +--R x 6 x 2 x 4 +--R - cos(x)sin(-) + (- 3cos(-) + 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 6 x 4 x 2 +--R (- 3cos(-) - 1)cos(x)sin(-) + (- cos(-) - 2cos(-) + 3cos(-) )cos(x) +--R 2 2 2 2 2 +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R + +--R x 6 x 2 x 4 +--R - cos(x)cot(x)sin(-) + (- 3cos(-) + 2)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R * +--R 3 +--R tan(x) +--R + +--R 2 x 6 +--R (cos(x)cot(x) + cos(x))sin(-) +--R 2 +--R + +--R x 2 2 x 2 x 4 +--R ((3cos(-) - 2)cos(x)cot(x) + (3cos(-) - 2)cos(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 +--R (3cos(-) - 12cos(-) + 1)cos(x)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (3cos(-) - 12cos(-) + 1)cos(x) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R 2 +--R tan(x) +--R + +--R x 6 x 2 x 4 +--R - cos(x)cot(x)sin(-) + (- 3cos(-) + 2)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R * +--R tan(x) +--R * +--R log(cos(x)) +--R + +--R x 6 x 2 x 4 +--R cot(x)sin(-) + (3cos(-) - 2)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cot(x) +--R 2 2 2 +--R * +--R 2 +--R sin(x)tan(x) +--R / +--R x 6 x 2 x 4 +--R cos(x)sin(-) + (3cos(-) - 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression Integer +--E 76 + +--S 77 of 528 +t0314:= (-1+sec(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (76) \|sec(x) - 1 +--R Type: Expression Integer +--E 77 + +--S 78 of 528 +r0314:= -cot(x)*log(cos(x))*(tan(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (77) - cot(x)log(cos(x))\|tan(x) +--R Type: Expression Integer +--E 78 + +--S 79 of 528 +a0314:= integrate(t0314,x) +--R +--R +--R 2 2cos(x) +--R (78) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 79 + +--S 80 of 528 +m0314:= a0314-r0314 +--R +--R +--R +-------+ +--R | 2 2 2cos(x) +--R (79) cot(x)log(cos(x))\|tan(x) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Integer +--E 80 + +--S 81 of 528 +d0314:= D(m0314,x) +--R +--R +--R (80) +--R +-------+ +--R | 2 +--R - sin(x)\|tan(x) +--R + +--R 3 2 2 +--R cos(x)cot(x)tan(x) + (- cos(x)cot(x) - cos(x))tan(x) +--R + +--R cos(x)cot(x)tan(x) +--R * +--R log(cos(x)) +--R + +--R 2 +--R - cot(x)sin(x)tan(x) +--R / +--R +-------+ +--R | 2 +--R cos(x)\|tan(x) +--R Type: Expression Integer +--E 81 + +--S 82 of 528 +t0315:= (-1-sec(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (81) \|- sec(x) - 1 +--R Type: Expression Integer +--E 82 + +--S 83 of 528 +r0315:= atan(cot(x)*(-2-tan(x)^2)^(1/2))-atanh(tan(x)/(-2-tan(x)^2)^(1/2)) +--R +--R +--R +-------------+ +--R tan(x) | 2 +--R (82) - atanh(----------------) + atan(cot(x)\|- tan(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression Integer +--E 83 + +--S 84 of 528 +a0315:= integrate(t0315,x) +--R +--R +--R (83) +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R - +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R - +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 84 + +--S 85 of 528 +m0315:= a0315-r0315 +--R +--R +--R (84) +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R - +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R - +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R +-------------+ +--R tan(x) | 2 +--R 2atanh(----------------) - 2atan(cot(x)\|- tan(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R / +--R 2 +--R Type: Expression Integer +--E 85 + +--S 86 of 528 +d0315:= D(m0315,x) +--R +--R +--R (85) +--R +---+ 6 +---+ 4 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - \|- 1 cot(x) (%e ) - 9\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 +--R - 21\|- 1 cot(x) (%e ) - 9\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (- 2\|- 1 cot(x) + \|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (- 18\|- 1 cot(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (- 42\|- 1 cot(x) + 21\|- 1 )(%e ) - 18\|- 1 cot(x) +--R + +--R +---+ +--R 9\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - cot(x)(%e ) - 7cot(x)(%e ) - 13cot(x)(%e ) +--R + +--R - 7cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) + 1)(%e ) + (14cot(x) + 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (26cot(x) + 13)(%e ) + 14cot(x) + 7 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - cot(x)(%e ) - 7cot(x)(%e ) - 13cot(x)(%e ) +--R + +--R - 7cot(x) +--R * +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (4cot(x) + 1)(%e ) + (28cot(x) + 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (52cot(x) + 13)(%e ) + 28cot(x) + 7 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R \|- 1 cot(x) (%e ) + 12\|- 1 cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R 44\|- 1 cot(x) (%e ) + 48\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R 7\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (2\|- 1 cot(x) - \|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (24\|- 1 cot(x) - 12\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (88\|- 1 cot(x) - 44\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +---+ +--R (96\|- 1 cot(x) - 48\|- 1 )(%e ) + 14\|- 1 cot(x) - 7\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 x\|- 1 +--R cot(x)(%e ) + 10cot(x)(%e ) + 30cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 30cot(x)(%e ) + 9cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) - 1)(%e ) + (- 20cot(x) - 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 60cot(x) - 30)(%e ) + (- 60cot(x) - 30)(%e ) +--R + +--R 2 +--R - 18cot(x) - 9 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 x\|- 1 +--R cot(x)(%e ) + 10cot(x)(%e ) + 30cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 30cot(x)(%e ) + 9cot(x) +--R * +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 4cot(x) - 1)(%e ) + (- 40cot(x) - 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 120cot(x) - 30)(%e ) + (- 120cot(x) - 30)(%e ) +--R + +--R 2 +--R - 36cot(x) - 9 +--R / +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R cot(x) (%e ) + 7cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R 13cot(x) (%e ) + 7cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) - 1)(%e ) + (14cot(x) - 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (26cot(x) - 13)(%e ) + 14cot(x) - 7 +--R * +--R +--------------------------------+ +--R +-------------+ | +---+ 4 +---+ 2 +--R | 2 | x\|- 1 x\|- 1 +--R \|- tan(x) - 2 \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R - cot(x) (%e ) - 10cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R - 30cot(x) (%e ) - 30cot(x) (%e ) - 9cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) + 1)(%e ) + (- 20cot(x) + 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 60cot(x) + 30)(%e ) + (- 60cot(x) + 30)(%e ) +--R + +--R 2 +--R - 18cot(x) + 9 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression Integer +--E 86 + +--S 87 of 528 +t0316:= (a+b*sec(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (86) \|b sec(x) + a +--R Type: Expression Integer +--E 87 + +--S 88 of 528 +r0316:= a^(1/2)*atan(a^(1/2)*tan(x)/(a+b*sec(x)^2)^(1/2))+b^(1/2)*atanh(cot(x)*(a+b*sec(x)^2)^(1/2)/b^(1/2)) +--R +--R +--R +-------------+ +--R | 2 +-+ +--R +-+ cot(x)\|b sec(x) + a +-+ tan(x)\|a +--R (87) \|b atanh(----------------------) + \|a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b sec(x) + a +--R Type: Expression Integer +--E 88 + +--S 89 of 528 +a0316:= integrate(t0316,x) +--R +--R +--R (88) +--R [ +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 +--R (- 96a b + 224a b)cos(x) +--R + +--R 2 2 3 7 +--R (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R sin(x) +--R - a atan(------) +--R cos(x) +--R / +--R +-+ +--R 2\|a +--R , +--R +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R - +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - 2b +--R + +--R sin(x) +--R - a atan(------) +--R cos(x) +--R / +--R +-+ +--R 2\|a +--R ] +--R Type: Union(List Expression Integer,...) +--E 89 + +--S 90 of 528 +m0316a:= a0316.1-r0316 +--R +--R +--R (89) +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 2 2 3 7 +--R (- 96a b + 224a b)cos(x) + (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R +-------------+ +--R | 2 +--R +-+ +-+ cot(x)\|b sec(x) + a +--R - 2\|a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R +-+ +--R tan(x)\|a sin(x) +--R - 2a atan(----------------) - a atan(------) +--R +-------------+ cos(x) +--R | 2 +--R \|b sec(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 90 + +--S 91 of 528 +--d0316a:= D(m0316a,x) +--E 91 + +--S 92 of 528 +m0316b:= a0316.2-r0316 +--R +--R +--R (90) +--R +-------------+ +--R | 2 +--R +-+ +-+ cot(x)\|b sec(x) + a +--R - 2\|a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R - +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - 2b +--R + +--R +-+ +--R tan(x)\|a sin(x) +--R - 2a atan(----------------) - a atan(------) +--R +-------------+ cos(x) +--R | 2 +--R \|b sec(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 92 + +--S 93 of 528 +d0316b:= D(m0316b,x) +--R +--R +--R (91) +--R 7 2 16 7 2 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 3 7 2 14 +--R (- 6144a b + 4608a b )cos(x) +--R + +--R 6 3 7 2 13 +--R (- 6144a b + 4608a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (- 6912a b + 13056a b - 3456a b )cos(x) +--R + +--R 5 4 6 3 7 2 11 +--R (- 6912a b + 13056a b - 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (- 3584a b + 13536a b - 9216a b + 864a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 9 +--R (- 3584a b + 13536a b - 9216a b + 864a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 5 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (- 12a b + 60a b )cos(x) + (- 12a b + 60a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 16 8 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 7 2 8 14 +--R (- 6144a b + 4608a b)cos(x) +--R + +--R 7 2 8 13 +--R (- 6144a b + 4608a b)cos(x) +--R + +--R 6 3 7 2 8 12 +--R (- 6912a b + 13056a b - 3456a b)cos(x) +--R + +--R 6 3 7 2 8 11 +--R (- 6912a b + 13056a b - 3456a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 10 +--R (- 3584a b + 13536a b - 9216a b + 864a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 3584a b + 13536a b - 9216a b + 864a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 7 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 6 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 5 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 4 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 3 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 3 6 4 5 2 3 6 4 5 +--R (- 12a b + 60a b )cos(x) + (- 12a b + 60a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 16 7 2 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 3 7 2 14 6 3 7 2 13 +--R (6144a b - 4608a b )cos(x) + (6144a b - 4608a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (6912a b - 13056a b + 3456a b )cos(x) +--R + +--R 5 4 6 3 7 2 11 +--R (6912a b - 13056a b + 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (3584a b - 13536a b + 9216a b - 864a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 9 +--R (3584a b - 13536a b + 9216a b - 864a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (840a b - 6192a b + 8736a b - 2160a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 +--R (840a b - 6192a b + 8736a b - 2160a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (72a b - 1170a b + 3456a b - 1854a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 5 +--R (72a b - 1170a b + 3456a b - 1854a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (a b - 63a b + 495a b - 617a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (a b - 63a b + 495a b - 617a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (12a b - 60a b )cos(x) + (12a b - 60a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 18 7 2 17 +--R - 4096a b cos(x) - 4096a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 14336a b + 10752a b - 512a b)cos(x) +--R + +--R 6 3 7 2 8 15 +--R (- 14336a b + 10752a b - 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 19968a b + 34560a b - 13184a b + 640a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 13 +--R (- 19968a b + 34560a b - 13184a b + 640a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 14080a b + 42976a b - 36064a b + 8032a b +--R + +--R 8 +--R - 96a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 14080a b + 42976a b - 36064a b + 8032a b +--R + +--R 8 +--R - 96a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 7 2 8 +--R - 1592a b - 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 7 2 8 +--R - 1592a b - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 6 3 7 2 +--R - 3710a b - 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 6 3 7 2 +--R - 3710a b - 192a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 6 3 +--R - 173a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 6 3 +--R - 173a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 5 4 +--R - 57a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 5 4 +--R - 57a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 18 8 17 +--R - 4096a b cos(x) - 4096a b cos(x) +--R + +--R 7 2 8 9 16 +--R (- 14336a b + 10752a b - 512a )cos(x) +--R + +--R 7 2 8 9 15 +--R (- 14336a b + 10752a b - 512a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (- 19968a b + 34560a b - 13184a b + 640a )cos(x) +--R + +--R 6 3 7 2 8 9 13 +--R (- 19968a b + 34560a b - 13184a b + 640a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 14080a b + 42976a b - 36064a b + 8032a b - 96a ) +--R * +--R 12 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 14080a b + 42976a b - 36064a b + 8032a b - 96a ) +--R * +--R 11 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 8 9 +--R - 1592a b - 72a +--R * +--R 10 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 8 9 +--R - 1592a b - 72a +--R * +--R 9 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 7 2 8 +--R - 3710a b - 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 7 2 8 +--R - 3710a b - 192a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 7 2 +--R - 173a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 7 2 +--R - 173a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 6 3 +--R - 57a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 6 3 +--R - 57a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 18 7 2 17 +--R 4096a b cos(x) + 4096a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (14336a b - 10752a b + 512a b)cos(x) +--R + +--R 6 3 7 2 8 15 +--R (14336a b - 10752a b + 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (19968a b - 34560a b + 13184a b - 640a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 13 +--R (19968a b - 34560a b + 13184a b - 640a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (14080a b - 42976a b + 36064a b - 8032a b + 96a b) +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (14080a b - 42976a b + 36064a b - 8032a b + 96a b) +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 5264a b - 25968a b + 38608a b - 18896a b + 1592a b +--R + +--R 8 +--R 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 5264a b - 25968a b + 38608a b - 18896a b + 1592a b +--R + +--R 8 +--R 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 984a b - 7818a b + 19106a b - 17534a b + 3710a b +--R + +--R 7 2 +--R 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 984a b - 7818a b + 19106a b - 17534a b + 3710a b +--R + +--R 7 2 +--R 192a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 74a b - 1059a b + 4224a b - 7058a b + 3214a b +--R + +--R 6 3 +--R 173a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 74a b - 1059a b + 4224a b - 7058a b + 3214a b +--R + +--R 6 3 +--R 173a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (b - 45a b + 332a b - 1060a b + 1115a b + 57a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (b - 45a b + 332a b - 1060a b + 1115a b + 57a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (4a b - 28a b + 116a b + 4a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R (4a b - 28a b + 116a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 20 7 2 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 3 7 2 8 18 +--R (- 8192a b + 6144a b - 512a b)cos(x) +--R + +--R 6 3 7 2 8 17 +--R (- 8192a b + 6144a b - 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (- 13056a b + 23552a b - 9216a b + 1152a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (- 13056a b + 23552a b - 9216a b + 1152a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a b) +--R * +--R 13 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 8 +--R 216a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 8 +--R 216a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 7 2 +--R 864a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 7 2 +--R 864a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 6 3 +--R 1341a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 6 3 +--R 1341a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- b + 84a b - 1066a b + 3434a b - 3393a b + 998a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- b + 84a b - 1066a b + 3434a b - 3393a b + 998a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (- 28a b + 44a b )cos(x) + (- 28a b + 44a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 20 8 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 7 2 8 9 18 +--R (- 8192a b + 6144a b - 512a )cos(x) +--R + +--R 7 2 8 9 17 +--R (- 8192a b + 6144a b - 512a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (- 13056a b + 23552a b - 9216a b + 1152a )cos(x) +--R + +--R 6 3 7 2 8 9 15 +--R (- 13056a b + 23552a b - 9216a b + 1152a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a ) +--R * +--R 14 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a ) +--R * +--R 13 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 9 +--R 216a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 9 +--R 216a +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 8 +--R 864a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 8 +--R 864a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 7 2 +--R 1341a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 7 2 +--R 1341a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 84a b - 1066a b + 3434a b - 3393a b +--R + +--R 6 3 +--R 998a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 84a b - 1066a b + 3434a b - 3393a b +--R + +--R 6 3 +--R 998a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 4 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 3 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 3 6 4 5 2 3 6 4 5 +--R (- 28a b + 44a b )cos(x) + (- 28a b + 44a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 20 7 2 19 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 3 7 2 8 18 +--R (8192a b - 6144a b + 512a b)cos(x) +--R + +--R 6 3 7 2 8 17 +--R (8192a b - 6144a b + 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (13056a b - 23552a b + 9216a b - 1152a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (13056a b - 23552a b + 9216a b - 1152a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 14 +--R (10496a b - 35456a b + 29536a b - 8448a b + 864a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 13 +--R (10496a b - 35456a b + 29536a b - 8448a b + 864a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4424a b - 26304a b + 39824a b - 20736a b + 4248a b +--R + +--R 8 +--R - 216a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4424a b - 26304a b + 39824a b - 20736a b + 4248a b +--R + +--R 8 +--R - 216a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 912a b - 9816a b + 26354a b - 23592a b + 8070a b +--R + +--R 7 2 +--R - 864a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 912a b - 9816a b + 26354a b - 23592a b + 8070a b +--R + +--R 7 2 +--R - 864a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 73a b - 1644a b + 8403a b - 13295a b + 7452a b +--R + +--R 6 3 +--R - 1341a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 73a b - 1644a b + 8403a b - 13295a b + 7452a b +--R + +--R 6 3 +--R - 1341a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R (b - 84a b + 1066a b - 3434a b + 3393a b - 998a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 5 +--R (b - 84a b + 1066a b - 3434a b + 3393a b - 998a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (25a b - 291a b + 655a b - 349a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (25a b - 291a b + 655a b - 349a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (28a b - 44a b )cos(x) + (28a b - 44a b )cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 7 2 16 6 3 7 2 14 +--R 4096a b cos(x) + (14336a b - 9216a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (19456a b - 30720a b + 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (12800a b - 38976a b + 21888a b - 1728a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (4144a b - 23232a b + 25824a b - 5184a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (584a b - 6420a b + 13776a b - 5652a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (24a b - 672a b + 3144a b - 2656a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (- 12a b + 216a b - 476a b )cos(x) - 16a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 16 7 2 8 14 +--R 4096a b cos(x) + (14336a b - 9216a b)cos(x) +--R + +--R 6 3 7 2 8 12 +--R (19456a b - 30720a b + 6912a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 10 +--R (12800a b - 38976a b + 21888a b - 1728a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (4144a b - 23232a b + 25824a b - 5184a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 6 +--R (584a b - 6420a b + 13776a b - 5652a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 4 +--R (24a b - 672a b + 3144a b - 2656a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 3 6 +--R (- 12a b + 216a b - 476a b )cos(x) - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 16 6 3 7 2 14 +--R - 4096a b cos(x) + (- 14336a b + 9216a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (- 19456a b + 30720a b - 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (- 12800a b + 38976a b - 21888a b + 1728a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (- 4144a b + 23232a b - 25824a b + 5184a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (- 584a b + 6420a b - 13776a b + 5652a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (- 24a b + 672a b - 3144a b + 2656a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (12a b - 216a b + 476a b )cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 18 +--R 8192a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (32768a b - 21504a b + 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (53248a b - 79872a b + 26880a b - 1280a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R 45056a b - 117824a b + 85184a b - 16704a b +--R + +--R 8 +--R 192a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 21088a b - 87616a b + 110048a b - 45664a b +--R + +--R 7 2 8 +--R 3280a b + 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R 5312a b - 34340a b + 69412a b - 52036a b +--R + +--R 6 3 7 2 +--R 8988a b + 456a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 632a b - 6704a b + 21408a b - 27880a b + 9752a b +--R + +--R 6 3 +--R 520a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 24b - 532a b + 2820a b - 6564a b + 4708a b +--R + +--R 5 4 +--R 248a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 8b + 104a b - 480a b + 888a b + 40a b )cos(x) +--R + +--R 2 7 +--R 32a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 18 +--R 8192a b cos(x) +--R + +--R 7 2 8 9 16 +--R (32768a b - 21504a b + 1024a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (53248a b - 79872a b + 26880a b - 1280a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (45056a b - 117824a b + 85184a b - 16704a b + 192a ) +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R 21088a b - 87616a b + 110048a b - 45664a b +--R + +--R 8 9 +--R 3280a b + 144a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 5312a b - 34340a b + 69412a b - 52036a b +--R + +--R 7 2 8 +--R 8988a b + 456a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 632a b - 6704a b + 21408a b - 27880a b + 9752a b +--R + +--R 7 2 +--R 520a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 24a b - 532a b + 2820a b - 6564a b + 4708a b +--R + +--R 6 3 +--R 248a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (- 8a b + 104a b - 480a b + 888a b + 40a b )cos(x) +--R + +--R 3 6 +--R 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 18 +--R - 8192a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 32768a b + 21504a b - 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 53248a b + 79872a b - 26880a b + 1280a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 45056a b + 117824a b - 85184a b + 16704a b - 192a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 21088a b + 87616a b - 110048a b + 45664a b +--R + +--R 7 2 8 +--R - 3280a b - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 5312a b + 34340a b - 69412a b + 52036a b - 8988a b +--R + +--R 7 2 +--R - 456a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 632a b + 6704a b - 21408a b + 27880a b - 9752a b +--R + +--R 6 3 +--R - 520a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 24b + 532a b - 2820a b + 6564a b - 4708a b +--R + +--R 5 4 +--R - 248a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 2 7 +--R (8b - 104a b + 480a b - 888a b - 40a b )cos(x) - 32a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 20 6 3 7 2 8 18 +--R 4096a b cos(x) + (18432a b - 12288a b + 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (33792a b - 53248a b + 18944a b - 2304a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (32256a b - 92928a b + 68160a b - 18048a b + 1728a b) +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 16944a b - 82944a b + 106944a b - 49632a b + 9360a b +--R + +--R 8 +--R - 432a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 4728a b - 39536a b + 86260a b - 65952a b + 20172a b +--R + +--R 7 2 +--R - 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 608a b - 9456a b + 36204a b - 45964a b + 22020a b +--R + +--R 6 3 +--R - 3492a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 24b - 912a b + 7100a b - 16260a b + 12684a b +--R + +--R 5 4 +--R - 3148a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 16b + 452a b - 2436a b + 3564a b - 1452a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (- 76a b + 360a b - 300a b )cos(x) - 16a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 20 7 2 8 9 18 +--R 4096a b cos(x) + (18432a b - 12288a b + 1024a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (33792a b - 53248a b + 18944a b - 2304a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (32256a b - 92928a b + 68160a b - 18048a b + 1728a ) +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 16944a b - 82944a b + 106944a b - 49632a b + 9360a b +--R + +--R 9 +--R - 432a +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4728a b - 39536a b + 86260a b - 65952a b + 20172a b +--R + +--R 8 +--R - 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 608a b - 9456a b + 36204a b - 45964a b + 22020a b +--R + +--R 7 2 +--R - 3492a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 24a b - 912a b + 7100a b - 16260a b + 12684a b +--R + +--R 6 3 +--R - 3148a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (- 16a b + 452a b - 2436a b + 3564a b - 1452a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 3 6 +--R (- 76a b + 360a b - 300a b )cos(x) - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 20 6 3 7 2 8 18 +--R - 4096a b cos(x) + (- 18432a b + 12288a b - 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (- 33792a b + 53248a b - 18944a b + 2304a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 32256a b + 92928a b - 68160a b + 18048a b - 1728a b) +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 16944a b + 82944a b - 106944a b + 49632a b - 9360a b +--R + +--R 8 +--R 432a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 4728a b + 39536a b - 86260a b + 65952a b - 20172a b +--R + +--R 7 2 +--R 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 608a b + 9456a b - 36204a b + 45964a b - 22020a b +--R + +--R 6 3 +--R 3492a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 24b + 912a b - 7100a b + 16260a b - 12684a b +--R + +--R 5 4 +--R 3148a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (16b - 452a b + 2436a b - 3564a b + 1452a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (76a b - 360a b + 300a b )cos(x) + 16a b +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 3 16 6 3 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 5 4 6 3 14 5 4 6 3 13 +--R (7168a b - 4096a b )cos(x) + (7168a b - 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 12 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 11 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 10 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 9 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 5 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R * +--R 2 4 +--R cot(x)sec(x) sin(x) +--R + +--R 6 3 7 2 18 6 3 7 2 17 +--R (2048a b - 2048a b )cos(x) + (2048a b - 2048a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (7168a b - 15360a b + 4096a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (7168a b - 15360a b + 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (9728a b - 37376a b + 24320a b - 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (9728a b - 37376a b + 24320a b - 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 3 +--R - 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 3 +--R - 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 4 +--R - 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 4 +--R - 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R * +--R 2 2 +--R cot(x)sec(x) sin(x) +--R + +--R 7 2 20 7 2 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 3 7 2 18 +--R (- 9216a b + 6144a b )cos(x) +--R + +--R 6 3 7 2 17 +--R (- 9216a b + 6144a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (- 16896a b + 26624a b - 6912a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (- 16896a b + 26624a b - 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (- 16128a b + 46464a b - 28800a b + 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (- 16128a b + 46464a b - 28800a b + 3456a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 6 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 9 8 2 7 3 6 3 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 8 2 7 2 8 2 7 +--R (32a b - 96a b )cos(x) + (32a b - 96a b )cos(x) +--R * +--R 2 +--R cot(x)sec(x) +--R * +--R tan(x) +--R + +--R 6 3 7 2 16 +--R (- 2048a b - 2048a b )cos(x) +--R + +--R 6 3 7 2 15 +--R (- 2048a b - 2048a b )cos(x) +--R + +--R 5 4 6 3 7 2 14 +--R (- 7168a b - 3072a b + 4096a b )cos(x) +--R + +--R 5 4 6 3 7 2 13 +--R (- 7168a b - 3072a b + 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 12 +--R (- 9728a b + 3584a b + 10496a b - 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 11 +--R (- 9728a b + 3584a b + 10496a b - 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 6 3 +--R - 156a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 6 3 +--R - 156a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 232a b - 584a b - 224a b + 500a b +--R + +--R 5 4 +--R - 104a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 232a b - 584a b - 224a b + 500a b +--R + +--R 5 4 +--R - 104a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (4b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R (4b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 16 6 3 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 5 4 6 3 14 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 5 4 6 3 13 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 12 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 11 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 10 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 9 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 5 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R * +--R 2 +--R sec(x) +--R + +--R 7 2 8 16 +--R (- 2048a b - 2048a b)cos(x) +--R + +--R 7 2 8 15 +--R (- 2048a b - 2048a b)cos(x) +--R + +--R 6 3 7 2 8 14 +--R (- 7168a b - 3072a b + 4096a b)cos(x) +--R + +--R 6 3 7 2 8 13 +--R (- 7168a b - 3072a b + 4096a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 12 +--R (- 9728a b + 3584a b + 10496a b - 2816a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 11 +--R (- 9728a b + 3584a b + 10496a b - 2816a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b) +--R * +--R 10 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 8 +--R - 72a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 8 +--R - 72a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 7 2 +--R - 156a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 7 2 +--R - 156a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 232a b - 584a b - 224a b + 500a b +--R + +--R 6 3 +--R - 104a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 232a b - 584a b - 224a b + 500a b +--R + +--R 6 3 +--R - 104a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (4a b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (4a b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 8 18 +--R (- 2048a b + 2048a b)cos(x) +--R + +--R 6 3 8 17 +--R (- 2048a b + 2048a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (- 7168a b + 8192a b + 11264a b - 4096a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (- 7168a b + 8192a b + 11264a b - 4096a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 9728a b + 27648a b + 13056a b - 21504a b +--R + +--R 8 +--R 2816a b +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 9728a b + 27648a b + 13056a b - 21504a b +--R + +--R 8 +--R 2816a b +--R * +--R 13 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 6400a b + 35712a b - 9472a b - 36992a b +--R + +--R 7 2 8 +--R 13824a b - 768a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 6400a b + 35712a b - 9472a b - 36992a b +--R + +--R 7 2 8 +--R 13824a b - 768a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 6 3 7 2 8 +--R 24280a b - 3328a b + 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 6 3 7 2 8 +--R 24280a b - 3328a b + 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 292a b + 6352a b - 19020a b - 1096a b +--R + +--R 5 4 6 3 7 2 +--R 18988a b - 5352a b + 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 292a b + 6352a b - 19020a b - 1096a b +--R + +--R 5 4 6 3 7 2 +--R 18988a b - 5352a b + 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 5 4 6 3 +--R - 3940a b + 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 5 4 6 3 +--R - 3940a b + 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 20b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 5 4 +--R 124a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 20b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 5 4 +--R 124a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 4b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R (- 4b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 7 2 18 +--R (- 2048a b + 2048a b )cos(x) +--R + +--R 6 3 7 2 17 +--R (- 2048a b + 2048a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (- 7168a b + 15360a b - 4096a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (- 7168a b + 15360a b - 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (- 9728a b + 37376a b - 24320a b + 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (- 9728a b + 37376a b - 24320a b + 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 2 +--R 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 2 +--R 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 3 +--R 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 3 +--R 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 4 +--R 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 4 +--R 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R * +--R 2 +--R sec(x) +--R + +--R 7 2 9 18 7 2 9 17 +--R (- 2048a b + 2048a )cos(x) + (- 2048a b + 2048a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (- 7168a b + 8192a b + 11264a b - 4096a )cos(x) +--R + +--R 6 3 7 2 8 9 15 +--R (- 7168a b + 8192a b + 11264a b - 4096a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 9728a b + 27648a b + 13056a b - 21504a b + 2816a ) +--R * +--R 14 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 9728a b + 27648a b + 13056a b - 21504a b + 2816a ) +--R * +--R 13 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 6400a b + 35712a b - 9472a b - 36992a b + 13824a b +--R + +--R 9 +--R - 768a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 6400a b + 35712a b - 9472a b - 36992a b + 13824a b +--R + +--R 9 +--R - 768a +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 7 2 8 9 +--R 24280a b - 3328a b + 72a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 7 2 8 9 +--R 24280a b - 3328a b + 72a +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 6352a b - 19020a b - 1096a b + 18988a b +--R + +--R 7 2 8 +--R - 5352a b + 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 6352a b - 19020a b - 1096a b + 18988a b +--R + +--R 7 2 8 +--R - 5352a b + 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 6 3 7 2 +--R - 3940a b + 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 6 3 7 2 +--R - 3940a b + 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 20a b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 6 3 +--R 124a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 20a b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 6 3 +--R 124a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (- 4a b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 4a b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 8 20 7 2 8 19 +--R (2048a b + 2048a b)cos(x) + (2048a b + 2048a b)cos(x) +--R + +--R 6 3 7 2 8 18 +--R (9216a b + 3072a b - 6144a b)cos(x) +--R + +--R 6 3 7 2 8 17 +--R (9216a b + 3072a b - 6144a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (16896a b - 9728a b - 19712a b + 6912a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (16896a b - 9728a b - 19712a b + 6912a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a b) +--R * +--R 13 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 8 +--R 648a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 8 +--R 648a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 7 2 +--R 2484a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 7 2 +--R 2484a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 6 3 +--R 3672a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 6 3 +--R 3672a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 444a b + 2904a b - 2904a b - 3684a b +--R + +--R 5 4 +--R 2580a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 444a b + 2904a b - 2904a b - 3684a b +--R + +--R 5 4 +--R 2580a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 8b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 8b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 8 2 7 3 6 2 +--R (- 32a b + 64a b + 96a b )cos(x) +--R + +--R 8 2 7 3 6 +--R (- 32a b + 64a b + 96a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 20 7 2 19 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 3 7 2 18 6 3 7 2 17 +--R (9216a b - 6144a b )cos(x) + (9216a b - 6144a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (16896a b - 26624a b + 6912a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (16896a b - 26624a b + 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (16128a b - 46464a b + 28800a b - 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (16128a b - 46464a b + 28800a b - 3456a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 12 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 11 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 10 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 9 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 8 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 7 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 6 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 9 8 2 7 3 6 3 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 8 2 7 2 8 2 7 +--R (- 32a b + 96a b )cos(x) + (- 32a b + 96a b )cos(x) +--R * +--R 2 +--R sec(x) +--R + +--R 8 9 20 8 9 19 +--R (2048a b + 2048a )cos(x) + (2048a b + 2048a )cos(x) +--R + +--R 7 2 8 9 18 +--R (9216a b + 3072a b - 6144a )cos(x) +--R + +--R 7 2 8 9 17 +--R (9216a b + 3072a b - 6144a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (16896a b - 9728a b - 19712a b + 6912a )cos(x) +--R + +--R 6 3 7 2 8 9 15 +--R (16896a b - 9728a b - 19712a b + 6912a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 14 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 13 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 9 +--R 648a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 9 +--R 648a +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 8 +--R 2484a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 8 +--R 2484a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 7 2 +--R 3672a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 7 2 +--R 3672a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (12a b - 444a b + 2904a b - 2904a b - 3684a b + 2580a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (12a b - 444a b + 2904a b - 2904a b - 3684a b + 2580a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (- 8a b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 3 +--R (- 8a b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 +--R (- 32a b + 64a b + 96a b )cos(x) +--R + +--R 2 7 3 6 4 5 +--R (- 32a b + 64a b + 96a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 7 3 16 6 4 7 3 14 +--R - 4096a b cos(x) + (- 16384a b + 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 12 +--R (- 26112a b + 30720a b - 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 10 +--R (- 20992a b + 45056a b - 19456a b + 1536a b )cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 +--R (- 8848a b + 32384a b - 25600a b + 4736a b - 144a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 6 +--R (- 1824a b + 11616a b - 15808a b + 5312a b - 384a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 4 +--R (- 146a b + 1848a b - 4500a b + 2568a b - 346a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (- 2b + 88a b - 476a b + 472a b - 114a b )cos(x) - 8a b +--R + +--R 2 8 3 7 +--R 16a b - 8a b +--R * +--R 2 4 +--R cot(x)sec(x) sin(x) +--R + +--R 7 3 8 2 18 +--R (- 4096a b + 4096a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (- 16384a b + 32768a b - 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (- 26112a b + 89600a b - 52736a b + 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (- 20992a b + 118016a b - 126464a b + 32000a b - 1536a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 8848a b + 82448a b - 149248a b + 69248a b - 7568a b +--R + +--R 8 2 +--R 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1824a b + 30304a b - 92768a b + 73520a b - 14368a b +--R + +--R 7 3 +--R 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 146a b + 5258a b - 29268a b + 40076a b - 13226a b +--R + +--R 6 4 +--R 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 2b + 316a b - 3964a b + 10392a b - 5986a b + 460a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (2b - 136a b + 964a b - 1144a b + 122a b )cos(x) + 8a b +--R + +--R 2 8 3 7 +--R - 48a b + 8a b +--R * +--R 2 2 +--R cot(x)sec(x) sin(x) +--R + +--R 8 2 20 7 3 8 2 18 +--R 4096a b cos(x) + (20480a b - 12288a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (42496a b - 59392a b + 13824a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (47104a b - 118016a b + 64512a b - 6912a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (29840a b - 123520a b + 122496a b - 31104a b + 1296a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R (10672a b - 72240a b + 120576a b - 56304a b + 5616a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 8 +--R (1970a b - 22920a b + 64572a b - 51880a b + 9666a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 +--R (148a b - 3456a b + 17832a b - 25184a b + 8292a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 4 +--R (2b - 168a b + 2076a b - 5896a b + 3602a b )cos(x) +--R + +--R 9 2 8 3 7 2 2 8 +--R (48a b - 480a b + 688a b )cos(x) + 32a b +--R * +--R 2 +--R cot(x)sec(x) +--R * +--R tan(x) +--R + +--R 7 3 8 2 16 +--R (4096a b + 4096a b )cos(x) +--R + +--R 6 4 7 3 8 2 14 +--R (16384a b + 8192a b - 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 12 +--R (26112a b - 4608a b - 25088a b + 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (20992a b - 24064a b - 25600a b + 17920a b - 1536a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 8848a b - 23536a b - 6784a b + 20864a b - 4592a b +--R + +--R 8 2 +--R 144a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 1824a b - 9792a b + 4192a b + 10496a b - 4928a b +--R + +--R 7 3 +--R 384a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 146a b - 1702a b + 2652a b + 1932a b - 2222a b +--R + +--R 6 4 +--R 346a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 2 +--R (2b - 86a b + 388a b + 4a b - 358a b + 114a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R 8a b - 8a b - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 16 6 4 7 3 14 +--R 4096a b cos(x) + (16384a b - 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 12 +--R (26112a b - 30720a b + 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 10 +--R (20992a b - 45056a b + 19456a b - 1536a b )cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 +--R (8848a b - 32384a b + 25600a b - 4736a b + 144a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 6 +--R (1824a b - 11616a b + 15808a b - 5312a b + 384a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 4 +--R (146a b - 1848a b + 4500a b - 2568a b + 346a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (2b - 88a b + 476a b - 472a b + 114a b )cos(x) + 8a b +--R + +--R 2 8 3 7 +--R - 16a b + 8a b +--R * +--R 2 +--R sec(x) +--R + +--R 8 2 9 16 +--R (4096a b + 4096a b)cos(x) +--R + +--R 7 3 8 2 9 14 +--R (16384a b + 8192a b - 8192a b)cos(x) +--R + +--R 6 4 7 3 8 2 9 12 +--R (26112a b - 4608a b - 25088a b + 5632a b)cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 10 +--R (20992a b - 24064a b - 25600a b + 17920a b - 1536a b)cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 8848a b - 23536a b - 6784a b + 20864a b - 4592a b +--R + +--R 9 +--R 144a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 1824a b - 9792a b + 4192a b + 10496a b - 4928a b +--R + +--R 8 2 +--R 384a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (146a b - 1702a b + 2652a b + 1932a b - 2222a b + 346a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 2 +--R (2a b - 86a b + 388a b + 4a b - 358a b + 114a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 +--R 8a b - 8a b - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 9 18 +--R (4096a b - 4096a b)cos(x) +--R + +--R 6 4 7 3 8 2 9 16 +--R (16384a b - 16384a b - 24576a b + 8192a b)cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (26112a b - 63488a b - 36864a b + 47104a b - 5632a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 20992a b - 97024a b + 8448a b + 94464a b - 30464a b +--R + +--R 9 +--R 1536a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 8848a b - 73600a b + 66800a b + 80000a b - 61680a b +--R + +--R 8 2 9 +--R 7424a b - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 1824a b - 28480a b + 62464a b + 19248a b - 59152a b +--R + +--R 7 3 8 2 +--R 13840a b - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 146a b - 5112a b + 24010a b - 10808a b - 26850a b +--R + +--R 6 4 7 3 +--R 12496a b - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2b - 314a b + 3648a b - 6428a b - 4406a b +--R + +--R 5 5 6 4 +--R 5526a b - 460a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 2b + 134a b - 828a b + 180a b + 1022a b - 122a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 8a b + 40a b + 40a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 8 2 18 +--R (4096a b - 4096a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (16384a b - 32768a b + 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (26112a b - 89600a b + 52736a b - 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (20992a b - 118016a b + 126464a b - 32000a b + 1536a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 8848a b - 82448a b + 149248a b - 69248a b + 7568a b +--R + +--R 8 2 +--R - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 1824a b - 30304a b + 92768a b - 73520a b + 14368a b +--R + +--R 7 3 +--R - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 146a b - 5258a b + 29268a b - 40076a b + 13226a b +--R + +--R 6 4 +--R - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (2b - 316a b + 3964a b - 10392a b + 5986a b - 460a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (- 2b + 136a b - 964a b + 1144a b - 122a b )cos(x) - 8a b +--R + +--R 2 8 3 7 +--R 48a b - 8a b +--R * +--R 2 +--R sec(x) +--R + +--R 8 2 10 18 +--R (4096a b - 4096a )cos(x) +--R + +--R 7 3 8 2 9 10 16 +--R (16384a b - 16384a b - 24576a b + 8192a )cos(x) +--R + +--R 6 4 7 3 8 2 9 10 14 +--R (26112a b - 63488a b - 36864a b + 47104a b - 5632a )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 20992a b - 97024a b + 8448a b + 94464a b - 30464a b +--R + +--R 10 +--R 1536a +--R * +--R 12 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 8848a b - 73600a b + 66800a b + 80000a b - 61680a b +--R + +--R 9 10 +--R 7424a b - 144a +--R * +--R 10 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 1824a b - 28480a b + 62464a b + 19248a b - 59152a b +--R + +--R 8 2 9 +--R 13840a b - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 146a b - 5112a b + 24010a b - 10808a b - 26850a b +--R + +--R 7 3 8 2 +--R 12496a b - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 2a b - 314a b + 3648a b - 6428a b - 4406a b + 5526a b +--R + +--R 7 3 +--R - 460a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R (- 2a b + 134a b - 828a b + 180a b + 1022a b - 122a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 +--R - 8a b + 40a b + 40a b - 8a b +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 9 20 +--R (- 4096a b - 4096a b)cos(x) +--R + +--R 7 3 8 2 9 18 +--R (- 20480a b - 8192a b + 12288a b)cos(x) +--R + +--R 6 4 7 3 8 2 9 16 +--R (- 42496a b + 16896a b + 45568a b - 13824a b)cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (- 47104a b + 70912a b + 53504a b - 57600a b + 6912a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 29840a b + 93680a b + 1024a b - 91392a b + 29808a b +--R + +--R 9 +--R - 1296a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 10672a b + 61568a b - 48336a b - 64272a b + 50688a b +--R + +--R 8 2 +--R - 5616a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1970a b + 20950a b - 41652a b - 12692a b + 42214a b +--R + +--R 7 3 +--R - 9666a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 148a b + 3308a b - 14376a b + 7352a b + 16892a b +--R + +--R 6 4 +--R - 8292a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 2b + 166a b - 1908a b + 3820a b + 2294a b - 3602a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 2 2 8 3 7 +--R (- 48a b + 432a b - 208a b - 688a b )cos(x) - 32a b - 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 2 20 7 3 8 2 18 +--R - 4096a b cos(x) + (- 20480a b + 12288a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (- 42496a b + 59392a b - 13824a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (- 47104a b + 118016a b - 64512a b + 6912a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (- 29840a b + 123520a b - 122496a b + 31104a b - 1296a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 10 +--R (- 10672a b + 72240a b - 120576a b + 56304a b - 5616a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 8 +--R (- 1970a b + 22920a b - 64572a b + 51880a b - 9666a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 +--R (- 148a b + 3456a b - 17832a b + 25184a b - 8292a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 4 +--R (- 2b + 168a b - 2076a b + 5896a b - 3602a b )cos(x) +--R + +--R 9 2 8 3 7 2 2 8 +--R (- 48a b + 480a b - 688a b )cos(x) - 32a b +--R * +--R 2 +--R sec(x) +--R + +--R 9 10 20 +--R (- 4096a b - 4096a )cos(x) +--R + +--R 8 2 9 10 18 +--R (- 20480a b - 8192a b + 12288a )cos(x) +--R + +--R 7 3 8 2 9 10 16 +--R (- 42496a b + 16896a b + 45568a b - 13824a )cos(x) +--R + +--R 6 4 7 3 8 2 9 10 14 +--R (- 47104a b + 70912a b + 53504a b - 57600a b + 6912a )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 29840a b + 93680a b + 1024a b - 91392a b + 29808a b +--R + +--R 10 +--R - 1296a +--R * +--R 12 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 10672a b + 61568a b - 48336a b - 64272a b + 50688a b +--R + +--R 9 +--R - 5616a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 1970a b + 20950a b - 41652a b - 12692a b + 42214a b +--R + +--R 8 2 +--R - 9666a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 148a b + 3308a b - 14376a b + 7352a b + 16892a b +--R + +--R 7 3 +--R - 8292a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R (- 2a b + 166a b - 1908a b + 3820a b + 2294a b - 3602a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 2 3 7 4 6 +--R (- 48a b + 432a b - 208a b - 688a b )cos(x) - 32a b - 32a b +--R * +--R 2 +--R cot(x) +--R / +--R 6 2 16 6 2 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 5 3 6 2 14 +--R (7168a b - 4096a b )cos(x) +--R + +--R 5 3 6 2 13 +--R (7168a b - 4096a b )cos(x) +--R + +--R 4 4 5 3 6 2 12 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 4 4 5 3 6 2 11 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 5 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 7 16 7 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 2 7 14 6 2 7 13 +--R (7168a b - 4096a b)cos(x) + (7168a b - 4096a b)cos(x) +--R + +--R 5 3 6 2 7 12 +--R (9728a b - 13312a b + 2816a b)cos(x) +--R + +--R 5 3 6 2 7 11 +--R (9728a b - 13312a b + 2816a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 10 +--R (6400a b - 16384a b + 8320a b - 768a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 9 +--R (6400a b - 16384a b + 8320a b - 768a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 7 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 5 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 4 +--R (12a b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 3 +--R (12a b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 2 +--R (- 4a b + 44a b - 60a b + 20a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R (- 4a b + 44a b - 60a b + 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 16 6 2 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 5 3 6 2 14 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 5 3 6 2 13 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 4 4 5 3 6 2 12 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 4 4 5 3 6 2 11 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 5 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 7 18 6 2 7 17 +--R (2048a b - 2048a b)cos(x) + (2048a b - 2048a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (7168a b - 15360a b + 4096a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (7168a b - 15360a b + 4096a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (9728a b - 37376a b + 24320a b - 2816a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (9728a b - 37376a b + 24320a b - 2816a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 +--R - 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 +--R - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 2 +--R - 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 2 +--R - 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 3 +--R - 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 3 +--R - 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 7 8 18 7 8 17 +--R (2048a b - 2048a )cos(x) + (2048a b - 2048a )cos(x) +--R + +--R 6 2 7 8 16 +--R (7168a b - 15360a b + 4096a )cos(x) +--R + +--R 6 2 7 8 15 +--R (7168a b - 15360a b + 4096a )cos(x) +--R + +--R 5 3 6 2 7 8 14 +--R (9728a b - 37376a b + 24320a b - 2816a )cos(x) +--R + +--R 5 3 6 2 7 8 13 +--R (9728a b - 37376a b + 24320a b - 2816a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a ) +--R * +--R 12 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a ) +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 8 +--R - 72a +--R * +--R 10 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 8 +--R - 72a +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 7 +--R - 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 7 +--R - 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 12a b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 6 2 +--R - 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 12a b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 6 2 +--R - 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 4 +--R (- 20a b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 3 +--R (- 20a b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 2 +--R (4a b - 76a b + 156a b - 20a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R (4a b - 76a b + 156a b - 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 7 18 6 2 7 17 +--R (- 2048a b + 2048a b)cos(x) + (- 2048a b + 2048a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (- 7168a b + 15360a b - 4096a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (- 7168a b + 15360a b - 4096a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (- 9728a b + 37376a b - 24320a b + 2816a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (- 9728a b + 37376a b - 24320a b + 2816a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 +--R 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 +--R 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 2 +--R 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 2 +--R 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 3 +--R 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 3 +--R 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 20 7 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 2 7 18 6 2 7 17 +--R (- 9216a b + 6144a b)cos(x) + (- 9216a b + 6144a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (- 16896a b + 26624a b - 6912a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (- 16896a b + 26624a b - 6912a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (- 16128a b + 46464a b - 28800a b + 3456a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (- 16128a b + 46464a b - 28800a b + 3456a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 6 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 8 7 2 6 3 5 3 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 7 2 6 2 7 2 6 +--R (32a b - 96a b )cos(x) + (32a b - 96a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 20 8 19 +--R - 2048a cos(x) - 2048a cos(x) +--R + +--R 7 8 18 7 8 17 +--R (- 9216a b + 6144a )cos(x) + (- 9216a b + 6144a )cos(x) +--R + +--R 6 2 7 8 16 +--R (- 16896a b + 26624a b - 6912a )cos(x) +--R + +--R 6 2 7 8 15 +--R (- 16896a b + 26624a b - 6912a )cos(x) +--R + +--R 5 3 6 2 7 8 14 +--R (- 16128a b + 46464a b - 28800a b + 3456a )cos(x) +--R + +--R 5 3 6 2 7 8 13 +--R (- 16128a b + 46464a b - 28800a b + 3456a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 11 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b) +--R * +--R 10 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b) +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R (- 12a b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 5 +--R (- 12a b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 4 +--R (8a b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 3 +--R (8a b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 2 6 3 5 2 2 6 3 5 +--R (32a b - 96a b )cos(x) + (32a b - 96a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 20 7 19 6 2 7 18 +--R 2048a b cos(x) + 2048a b cos(x) + (9216a b - 6144a b)cos(x) +--R + +--R 6 2 7 17 +--R (9216a b - 6144a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (16896a b - 26624a b + 6912a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (16896a b - 26624a b + 6912a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (16128a b - 46464a b + 28800a b - 3456a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (16128a b - 46464a b + 28800a b - 3456a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 12 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 11 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 10 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 9 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 8 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 7 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 6 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 8 7 2 6 3 5 3 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 7 2 6 2 7 2 6 +--R (- 32a b + 96a b )cos(x) + (- 32a b + 96a b )cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 7 2 16 6 3 7 2 14 +--R - 4096a b cos(x) + (- 16384a b + 8192a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (- 26112a b + 30720a b - 5632a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (- 20992a b + 45056a b - 19456a b + 1536a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 8848a b + 32384a b - 25600a b + 4736a b - 144a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 1824a b + 11616a b - 15808a b + 5312a b - 384a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (- 146a b + 1848a b - 4500a b + 2568a b - 346a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (- 2b + 88a b - 476a b + 472a b - 114a b )cos(x) - 8a b +--R + +--R 2 7 3 6 +--R 16a b - 8a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 16 7 2 8 14 +--R - 4096a b cos(x) + (- 16384a b + 8192a b)cos(x) +--R + +--R 6 3 7 2 8 12 +--R (- 26112a b + 30720a b - 5632a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 10 +--R (- 20992a b + 45056a b - 19456a b + 1536a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 8 +--R (- 8848a b + 32384a b - 25600a b + 4736a b - 144a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 1824a b + 11616a b - 15808a b + 5312a b - 384a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 4 +--R (- 146a b + 1848a b - 4500a b + 2568a b - 346a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 2 7 +--R (- 2a b + 88a b - 476a b + 472a b - 114a b )cos(x) - 8a b +--R + +--R 3 6 4 5 +--R 16a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 16 6 3 7 2 14 +--R 4096a b cos(x) + (16384a b - 8192a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (26112a b - 30720a b + 5632a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (20992a b - 45056a b + 19456a b - 1536a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (8848a b - 32384a b + 25600a b - 4736a b + 144a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 6 +--R (1824a b - 11616a b + 15808a b - 5312a b + 384a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (146a b - 1848a b + 4500a b - 2568a b + 346a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (2b - 88a b + 476a b - 472a b + 114a b )cos(x) + 8a b +--R + +--R 2 7 3 6 +--R - 16a b + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 8 18 +--R (- 4096a b + 4096a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 16384a b + 32768a b - 8192a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 26112a b + 89600a b - 52736a b + 5632a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 20992a b + 118016a b - 126464a b + 32000a b - 1536a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 8848a b + 82448a b - 149248a b + 69248a b - 7568a b +--R + +--R 8 +--R 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 1824a b + 30304a b - 92768a b + 73520a b - 14368a b +--R + +--R 7 2 +--R 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 146a b + 5258a b - 29268a b + 40076a b - 13226a b +--R + +--R 6 3 +--R 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- 2b + 316a b - 3964a b + 10392a b - 5986a b + 460a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (2b - 136a b + 964a b - 1144a b + 122a b )cos(x) + 8a b +--R + +--R 2 7 3 6 +--R - 48a b + 8a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 9 18 +--R (- 4096a b + 4096a )cos(x) +--R + +--R 7 2 8 9 16 +--R (- 16384a b + 32768a b - 8192a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (- 26112a b + 89600a b - 52736a b + 5632a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 20992a b + 118016a b - 126464a b + 32000a b - 1536a ) +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 8848a b + 82448a b - 149248a b + 69248a b - 7568a b +--R + +--R 9 +--R 144a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 1824a b + 30304a b - 92768a b + 73520a b - 14368a b +--R + +--R 8 +--R 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 146a b + 5258a b - 29268a b + 40076a b - 13226a b +--R + +--R 7 2 +--R 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 2a b + 316a b - 3964a b + 10392a b - 5986a b +--R + +--R 6 3 +--R 460a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 2 7 +--R (2a b - 136a b + 964a b - 1144a b + 122a b )cos(x) + 8a b +--R + +--R 3 6 4 5 +--R - 48a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 8 18 +--R (4096a b - 4096a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (16384a b - 32768a b + 8192a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (26112a b - 89600a b + 52736a b - 5632a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 12 +--R (20992a b - 118016a b + 126464a b - 32000a b + 1536a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 8848a b - 82448a b + 149248a b - 69248a b + 7568a b +--R + +--R 8 +--R - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 1824a b - 30304a b + 92768a b - 73520a b + 14368a b +--R + +--R 7 2 +--R - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 146a b - 5258a b + 29268a b - 40076a b + 13226a b +--R + +--R 6 3 +--R - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (2b - 316a b + 3964a b - 10392a b + 5986a b - 460a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (- 2b + 136a b - 964a b + 1144a b - 122a b )cos(x) - 8a b +--R + +--R 2 7 3 6 +--R 48a b - 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 20 7 2 8 18 +--R 4096a b cos(x) + (20480a b - 12288a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (42496a b - 59392a b + 13824a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (47104a b - 118016a b + 64512a b - 6912a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 12 +--R (29840a b - 123520a b + 122496a b - 31104a b + 1296a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 10 +--R (10672a b - 72240a b + 120576a b - 56304a b + 5616a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (1970a b - 22920a b + 64572a b - 51880a b + 9666a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (148a b - 3456a b + 17832a b - 25184a b + 8292a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (2b - 168a b + 2076a b - 5896a b + 3602a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (48a b - 480a b + 688a b )cos(x) + 32a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 9 20 8 9 18 +--R 4096a cos(x) + (20480a b - 12288a )cos(x) +--R + +--R 7 2 8 9 16 +--R (42496a b - 59392a b + 13824a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (47104a b - 118016a b + 64512a b - 6912a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 12 +--R (29840a b - 123520a b + 122496a b - 31104a b + 1296a )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 10 +--R (10672a b - 72240a b + 120576a b - 56304a b + 5616a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (1970a b - 22920a b + 64572a b - 51880a b + 9666a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 6 +--R (148a b - 3456a b + 17832a b - 25184a b + 8292a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (2a b - 168a b + 2076a b - 5896a b + 3602a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 3 6 +--R (48a b - 480a b + 688a b )cos(x) + 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 20 7 2 8 18 +--R - 4096a b cos(x) + (- 20480a b + 12288a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 42496a b + 59392a b - 13824a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 47104a b + 118016a b - 64512a b + 6912a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 12 +--R (- 29840a b + 123520a b - 122496a b + 31104a b - 1296a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 10 +--R (- 10672a b + 72240a b - 120576a b + 56304a b - 5616a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (- 1970a b + 22920a b - 64572a b + 51880a b - 9666a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (- 148a b + 3456a b - 17832a b + 25184a b - 8292a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 2b + 168a b - 2076a b + 5896a b - 3602a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (- 48a b + 480a b - 688a b )cos(x) - 32a b +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R Type: Expression Integer +--E 93 + +--S 94 of 528 +t0317:= 1/(1+sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (92) -------------- +--R +-----------+ +--R | 2 +--R \|sec(x) + 1 +--R Type: Expression Integer +--E 94 + +--S 95 of 528 +r0317:= atan(tan(x)/(2+tan(x)^2)^(1/2)) +--R +--R +--R tan(x) +--R (93) atan(--------------) +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression Integer +--E 95 + +--S 96 of 528 +a0317:= integrate(t0317,x) +--R +--R +--R (94) +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R sin(x) +--R - atan(------) +--R cos(x) +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 96 + +--S 97 of 528 +m0317:= a0317-r0317 +--R +--R +--R (95) +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R tan(x) sin(x) +--R - 2atan(--------------) - atan(------) +--R +-----------+ cos(x) +--R | 2 +--R \|tan(x) + 2 +--R / +--R 2 +--R Type: Expression Integer +--E 97 + +--S 98 of 528 +d0317:= D(m0317,x) +--R +--R +--R (96) +--R 13 12 11 10 +--R 64cos(x) + 64cos(x) + 112cos(x) + 112cos(x) +--R + +--R 9 8 7 6 5 +--R - 40cos(x) - 40cos(x) - 89cos(x) - 89cos(x) + 6cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 16cos(x) + 16cos(x) + cos(x) + 1 +--R * +--R 2 +--R sin(x) +--R + +--R 15 14 13 12 11 +--R 64cos(x) + 64cos(x) + 48cos(x) + 48cos(x) - 88cos(x) +--R + +--R 10 9 8 7 6 +--R - 88cos(x) - 49cos(x) - 49cos(x) + 43cos(x) + 43cos(x) +--R + +--R 5 4 3 2 +--R 14cos(x) + 14cos(x) - 7cos(x) - 7cos(x) - cos(x) - 1 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 13 11 9 7 5 +--R - 128cos(x) - 288cos(x) - 16cos(x) + 238cos(x) + 58cos(x) +--R + +--R 3 +--R - 50cos(x) - 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 15 13 11 9 7 +--R - 128cos(x) - 160cos(x) + 144cos(x) + 190cos(x) - 60cos(x) +--R + +--R 5 3 +--R - 72cos(x) + 10cos(x) + 8cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 15 14 13 12 +--R - 256cos(x) - 256cos(x) - 256cos(x) - 256cos(x) +--R + +--R 11 10 9 8 7 +--R 192cos(x) + 192cos(x) + 192cos(x) + 192cos(x) - 34cos(x) +--R + +--R 6 5 4 3 2 +--R - 34cos(x) - 34cos(x) - 34cos(x) - 2cos(x) - 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 16 13 12 11 +--R - 256cos(x) - 256cos(x) + 448cos(x) + 448cos(x) - 64cos(x) +--R + +--R 10 9 8 7 6 +--R - 64cos(x) - 258cos(x) - 258cos(x) + 60cos(x) + 60cos(x) +--R + +--R 5 4 3 2 +--R 50cos(x) + 50cos(x) - 12cos(x) - 12cos(x) - 2cos(x) - 2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 15 13 11 9 7 +--R 512cos(x) + 768cos(x) - 192cos(x) - 608cos(x) - 64cos(x) +--R + +--R 5 3 +--R 120cos(x) + 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R 512cos(x) + 256cos(x) - 960cos(x) - 288cos(x) + 672cos(x) +--R + +--R 7 5 +--R 80cos(x) - 192cos(x) + 16cos(x) +--R / +--R 15 14 13 12 +--R 256cos(x) + 256cos(x) + 256cos(x) + 256cos(x) +--R + +--R 11 10 9 8 +--R - 192cos(x) - 192cos(x) - 192cos(x) - 192cos(x) +--R + +--R 7 6 5 4 3 +--R 34cos(x) + 34cos(x) + 34cos(x) + 34cos(x) + 2cos(x) +--R + +--R 2 +--R 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 16 13 12 11 +--R 256cos(x) + 256cos(x) - 448cos(x) - 448cos(x) + 64cos(x) +--R + +--R 10 9 8 7 6 +--R 64cos(x) + 258cos(x) + 258cos(x) - 60cos(x) - 60cos(x) +--R + +--R 5 4 3 2 +--R - 50cos(x) - 50cos(x) + 12cos(x) + 12cos(x) + 2cos(x) + 2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 15 13 11 9 7 +--R - 512cos(x) - 768cos(x) + 192cos(x) + 608cos(x) + 64cos(x) +--R + +--R 5 3 +--R - 120cos(x) - 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R - 512cos(x) - 256cos(x) + 960cos(x) + 288cos(x) - 672cos(x) +--R + +--R 7 5 +--R - 80cos(x) + 192cos(x) - 16cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression Integer +--E 98 + +--S 99 of 528 +t0318:= 1/(1-sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (97) ---------------- +--R +-------------+ +--R | 2 +--R \|- sec(x) + 1 +--R Type: Expression Integer +--E 99 + +--S 100 of 528 +r0318:= log(sin(x))*tan(x)/(-tan(x)^2)^(1/2) +--R +--R +--R tan(x)log(sin(x)) +--R (98) ----------------- +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression Integer +--E 100 + +--S 101 of 528 +a0318:= integrate(t0318,x) +--R +--R +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R (99) atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Union(Expression Integer,...) +--E 101 + +--S 102 of 528 +m0318:= a0318-r0318 +--R +--R +--R (100) +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +---------+ +--R 2 2 2 2 2 | 2 +--R atan(-------------------------------------------)\|- tan(x) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R - tan(x)log(sin(x)) +--R / +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression Integer +--E 102 + +--S 103 of 528 +d0318:= D(m0318,x) +--R +--R +--R (101) +--R x 6 x 2 x 4 x 4 x 2 +--R - sin(-) + (- 3cos(-) + 2)sin(-) + (- 3cos(-) - 1)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - cos(-) - 2cos(-) + 3cos(-) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- tan(x) +--R + +--R x 6 x 2 x 4 +--R - cos(x)sin(-) + (- 3cos(-) + 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R tan(x) +--R / +--R x 6 x 2 x 4 x 4 x 2 x 2 +--R sin(-) + (3cos(-) - 2)sin(-) + (3cos(-) - 12cos(-) + 1)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- tan(x) +--R Type: Expression Integer +--E 103 + +--S 104 of 528 +t0319:= 1/(-1+sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (102) -------------- +--R +-----------+ +--R | 2 +--R \|sec(x) - 1 +--R Type: Expression Integer +--E 104 + +--S 105 of 528 +r0319:= log(sin(x))*tan(x)/(tan(x)^2)^(1/2) +--R +--R +--R tan(x)log(sin(x)) +--R (103) ----------------- +--R +-------+ +--R | 2 +--R \|tan(x) +--R Type: Expression Integer +--E 105 + +--S 106 of 528 +a0319:= integrate(t0319,x) +--R +--R +--R sin(x) 2 +--R (104) - log(----------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 106 + +--S 107 of 528 +m0319:= a0319-r0319 +--R +--R +--R +-------+ +--R sin(x) 2 | 2 +--R (- log(----------) + log(----------))\|tan(x) - tan(x)log(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (105) ------------------------------------------------------------------- +--R +-------+ +--R | 2 +--R \|tan(x) +--R Type: Expression Integer +--E 107 + +--S 108 of 528 +d0319:= D(m0319,x) +--R +--R +--R +-------+ +--R | 2 +--R - cos(x)\|tan(x) - cos(x)tan(x) +--R (106) --------------------------------- +--R +-------+ +--R | 2 +--R sin(x)\|tan(x) +--R Type: Expression Integer +--E 108 + +--S 109 of 528 +t0320:= 1/(-1-sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (107) ---------------- +--R +-------------+ +--R | 2 +--R \|- sec(x) - 1 +--R Type: Expression Integer +--E 109 + +--S 110 of 528 +r0320:= atanh(tan(x)/(-2-tan(x)^2)^(1/2)) +--R +--R +--R tan(x) +--R (108) atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression Integer +--E 110 + +--S 111 of 528 +a0320:= integrate(t0320,x) +--R +--R +--R (109) +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R - log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 111 + +--S 112 of 528 +m0320:= a0320-r0320 +--R +--R +--R (110) +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R - log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R tan(x) +--R - 2atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R / +--R 2 +--R Type: Expression Integer +--E 112 + +--S 113 of 528 +d0320:= D(m0320,x) +--R +--R +--R (111) +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R \|- 1 (%e ) + 7\|- 1 (%e ) + 11\|- 1 (%e ) +--R + +--R +---+ +--R 5\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) - 9(%e ) - 19(%e ) - 3 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - \|- 1 (%e ) - 10\|- 1 (%e ) - 28\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 22\|- 1 (%e ) - 3\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 12(%e ) + 42(%e ) + 36(%e ) + 5 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +-------------+ +--R x\|- 1 x\|- 1 x\|- 1 | 2 +--R ((%e ) + 9(%e ) + 19(%e ) + 3)\|- tan(x) - 2 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 12(%e ) - 42(%e ) - 36(%e ) - 5) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression Integer +--E 113 + +--S 114 of 528 +t0321:= 1/(a+b*sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (112) ---------------- +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R Type: Expression Integer +--E 114 + +--S 115 of 528 +r0321:= atan(a^(1/2)*tan(x)/(a+b*sec(x)^2)^(1/2))/a^(1/2) +--R +--R +--R +-+ +--R tan(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R (113) ---------------------- +--R +-+ +--R \|a +--R Type: Expression Integer +--E 115 + +--S 116 of 528 +a0321:= integrate(t0321,x) +--R +--R +--R (114) +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x))\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R sin(x) +--R - atan(------) +--R cos(x) +--R / +--R +-+ +--R 2\|a +--R Type: Union(Expression Integer,...) +--E 116 + +--S 117 of 528 +m0321:= a0321-r0321 +--R +--R +--R (115) +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x))\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R +-+ +--R tan(x)\|a sin(x) +--R - 2atan(----------------) - atan(------) +--R +-------------+ cos(x) +--R | 2 +--R \|b sec(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression Integer +--E 117 + +--S 118 of 528 +d0321:= D(m0321,x) +--R +--R +--R (116) +--R 5 13 5 12 4 5 11 +--R 512a cos(x) + 512a cos(x) + (1536a b - 640a )cos(x) +--R + +--R 4 5 10 +--R (1536a b - 640a )cos(x) +--R + +--R 3 2 4 5 9 +--R (1568a b - 1984a b + 96a )cos(x) +--R + +--R 3 2 4 5 8 +--R (1568a b - 1984a b + 96a )cos(x) +--R + +--R 2 3 3 2 4 5 7 +--R (640a b - 1936a b + 512a b + 72a )cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (640a b - 1936a b + 512a b + 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (90a b - 680a b + 554a b + 84a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (90a b - 680a b + 554a b + 84a b)cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (2b - 64a b + 170a b + 20a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 4 4 +--R (2b - 64a b + 170a b + 20a b )cos(x) + 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 15 5 14 4 5 13 +--R 512a cos(x) + 512a cos(x) + (1536a b - 1152a )cos(x) +--R + +--R 4 5 12 3 2 4 5 11 +--R (1536a b - 1152a )cos(x) + (1696a b - 3264a b + 864a )cos(x) +--R + +--R 3 2 4 5 10 +--R (1696a b - 3264a b + 864a )cos(x) +--R + +--R 2 3 3 2 4 5 9 +--R (832a b - 3312a b + 2304a b - 216a )cos(x) +--R + +--R 2 3 3 2 4 5 8 +--R (832a b - 3312a b + 2304a b - 216a )cos(x) +--R + +--R 4 2 3 3 2 4 7 +--R (170a b - 1416a b + 2130a b - 540a b)cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (170a b - 1416a b + 2130a b - 540a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (10b - 222a b + 774a b - 450a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (10b - 222a b + 774a b - 450a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 6b + 84a b - 134a b )cos(x) +--R + +--R 5 4 2 3 2 4 4 +--R (- 6b + 84a b - 134a b )cos(x) - 8a b cos(x) - 8a b +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 13 5 6 11 +--R - 1024a cos(x) + (- 3584a b + 1280a )cos(x) +--R + +--R 4 2 5 6 9 +--R (- 4544a b + 4608a b - 192a )cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 2528a b + 5696a b - 1120a b - 144a )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 580a b + 2880a b - 1596a b - 240a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 38a b + 522a b - 778a b - 106a b )cos(x) +--R + +--R 5 2 4 3 3 +--R (16a b - 104a b - 8a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 15 5 6 13 +--R - 1024a cos(x) + (- 3584a b + 2304a )cos(x) +--R + +--R 4 2 5 6 11 +--R (- 4800a b + 7680a b - 1728a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 3040a b + 9600a b - 5472a b + 432a )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 900a b + 5472a b - 6348a b + 1296a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 102a b + 1350a b - 3210a b + 1386a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 2b + 102a b - 630a b + 610a b )cos(x) +--R + +--R 5 2 4 +--R (- 24a b + 88a b )cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 15 6 14 5 6 13 +--R - 2048a cos(x) - 2048a cos(x) + (- 6144a b + 4096a )cos(x) +--R + +--R 5 6 12 +--R (- 6144a b + 4096a )cos(x) +--R + +--R 4 2 5 6 11 +--R (- 6912a b + 11264a b - 2816a )cos(x) +--R + +--R 4 2 5 6 10 +--R (- 6912a b + 11264a b - 2816a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 3584a b + 11264a b - 6912a b + 768a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (- 3584a b + 11264a b - 6912a b + 768a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 840a b + 4928a b - 5888a b + 1600a b - 72a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 840a b + 4928a b - 5888a b + 1600a b - 72a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 72a b + 880a b - 2016a b + 1056a b - 120a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 72a b + 880a b - 2016a b + 1056a b - 120a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- b + 44a b - 234a b + 228a b - 53a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- b + 44a b - 234a b + 228a b - 53a b )cos(x) +--R + +--R 5 2 4 3 3 5 2 4 3 3 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 8a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 6 16 5 6 15 +--R - 2048a cos(x) - 2048a cos(x) + (- 6144a b + 6144a )cos(x) +--R + +--R 5 6 14 +--R (- 6144a b + 6144a )cos(x) +--R + +--R 4 2 5 6 13 +--R (- 6912a b + 17408a b - 6912a )cos(x) +--R + +--R 4 2 5 6 12 +--R (- 6912a b + 17408a b - 6912a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (- 3584a b + 18048a b - 18432a b + 3456a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (- 3584a b + 18048a b - 18432a b + 3456a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 840a b + 8256a b - 17472a b + 8640a b - 648a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 840a b + 8256a b - 17472a b + 8640a b - 648a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (- 72a b + 1560a b - 6912a b + 7416a b - 1512a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 1560a b - 6912a b + 7416a b - 1512a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b + 84a b - 990a b + 2468a b - 1161a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- b + 84a b - 990a b + 2468a b - 1161a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 24a b + 240a b - 312a b )cos(x) +--R + +--R 5 2 4 3 3 2 2 4 2 4 +--R (- 24a b + 240a b - 312a b )cos(x) - 16a b cos(x) - 16a b +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 15 5 6 13 +--R 4096a cos(x) + (14336a b - 8192a )cos(x) +--R + +--R 4 2 5 6 11 +--R (19456a b - 26624a b + 5632a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (12800a b - 32768a b + 16640a b - 1536a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (4144a b - 18816a b + 17984a b - 3968a b + 144a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (584a b - 4960a b + 8544a b - 3520a b + 312a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (24b - 488a b + 1656a b - 1208a b + 208a b )cos(x) +--R + +--R 6 5 2 4 3 3 +--R (- 8b + 88a b - 120a b + 40a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 5 6 15 +--R 4096a cos(x) + (14336a b - 12288a )cos(x) +--R + +--R 4 2 5 6 13 +--R (19456a b - 40960a b + 13824a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (12800a b - 51968a b + 43776a b - 6912a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (4144a b - 30976a b + 51648a b - 20736a b + 1296a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (584a b - 8560a b + 27552a b - 22608a b + 3672a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (24b - 896a b + 6288a b - 10624a b + 3672a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 16b + 432a b - 1904a b + 1488a b )cos(x) +--R + +--R 5 2 4 +--R (- 64a b + 192a b )cos(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 15 6 14 5 6 13 +--R 2048a cos(x) + 2048a cos(x) + (6144a b - 4096a )cos(x) +--R + +--R 5 6 12 +--R (6144a b - 4096a )cos(x) +--R + +--R 4 2 5 6 11 +--R (6912a b - 11264a b + 2816a )cos(x) +--R + +--R 4 2 5 6 10 +--R (6912a b - 11264a b + 2816a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (3584a b - 11264a b + 6912a b - 768a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (3584a b - 11264a b + 6912a b - 768a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (840a b - 4928a b + 5888a b - 1600a b + 72a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (840a b - 4928a b + 5888a b - 1600a b + 72a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (72a b - 880a b + 2016a b - 1056a b + 120a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (72a b - 880a b + 2016a b - 1056a b + 120a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (b - 44a b + 234a b - 228a b + 53a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (b - 44a b + 234a b - 228a b + 53a b )cos(x) +--R + +--R 5 2 4 3 3 5 2 4 3 3 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 6 16 5 6 15 +--R 2048a cos(x) + 2048a cos(x) + (6144a b - 6144a )cos(x) +--R + +--R 5 6 14 4 2 5 6 13 +--R (6144a b - 6144a )cos(x) + (6912a b - 17408a b + 6912a )cos(x) +--R + +--R 4 2 5 6 12 +--R (6912a b - 17408a b + 6912a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (3584a b - 18048a b + 18432a b - 3456a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (3584a b - 18048a b + 18432a b - 3456a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (840a b - 8256a b + 17472a b - 8640a b + 648a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (840a b - 8256a b + 17472a b - 8640a b + 648a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (72a b - 1560a b + 6912a b - 7416a b + 1512a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (72a b - 1560a b + 6912a b - 7416a b + 1512a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - 84a b + 990a b - 2468a b + 1161a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (b - 84a b + 990a b - 2468a b + 1161a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (24a b - 240a b + 312a b )cos(x) +--R + +--R 5 2 4 3 3 2 2 4 2 4 +--R (24a b - 240a b + 312a b )cos(x) + 16a b cos(x) + 16a b +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 15 5 6 13 +--R - 4096a cos(x) + (- 14336a b + 8192a )cos(x) +--R + +--R 4 2 5 6 11 +--R (- 19456a b + 26624a b - 5632a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 12800a b + 32768a b - 16640a b + 1536a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 4144a b + 18816a b - 17984a b + 3968a b - 144a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 584a b + 4960a b - 8544a b + 3520a b - 312a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 24b + 488a b - 1656a b + 1208a b - 208a b )cos(x) +--R + +--R 6 5 2 4 3 3 +--R (8b - 88a b + 120a b - 40a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 5 6 15 +--R - 4096a cos(x) + (- 14336a b + 12288a )cos(x) +--R + +--R 4 2 5 6 13 +--R (- 19456a b + 40960a b - 13824a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (- 12800a b + 51968a b - 43776a b + 6912a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 4144a b + 30976a b - 51648a b + 20736a b - 1296a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (- 584a b + 8560a b - 27552a b + 22608a b - 3672a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 24b + 896a b - 6288a b + 10624a b - 3672a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (16b - 432a b + 1904a b - 1488a b )cos(x) +--R + +--R 5 2 4 +--R (64a b - 192a b )cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R Type: Expression Integer +--E 118 + +--S 119 of 528 +t0322:= (1+sec(x)^2)^(3/2) +--R +--R +--R +-----------+ +--R 2 | 2 +--R (117) (sec(x) + 1)\|sec(x) + 1 +--R Type: Expression Integer +--E 119 + +--S 120 of 528 +r0322:= 2*asinh(1/2*2^(1/2)*tan(x))+atan(tan(x)/(2+tan(x)^2)^(1/2))+1/2*tan(x)*(2+tan(x)^2)^(1/2) +--R +--R +--R +-----------+ +-+ +--R tan(x) | 2 \|2 tan(x) +--R 2atan(--------------) + tan(x)\|tan(x) + 2 + 4asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|tan(x) + 2 +--R (118) ----------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 120 + +--S 121 of 528 +a0322:= integrate(t0322,x) +--R +--R +--R (119) +--R 6 5 4 3 +--R (- 16cos(x) - 16cos(x) - 8cos(x) - 8cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) + 32cos(x) + 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (8cos(x) + 8cos(x) + 4cos(x) + 4cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 16cos(x) - 16cos(x) - 2cos(x) +--R * +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R 6 5 4 3 sin(x) +--R (- 8cos(x) - 8cos(x) - 4cos(x) - 4cos(x) )atan(------) +--R cos(x) +--R + +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) + 8cos(x) + 8cos(x) + cos(x) + 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 sin(x) +--R (16cos(x) + 16cos(x) + 2cos(x) )atan(------) +--R cos(x) +--R + +--R 5 3 +--R (- 16cos(x) - 24cos(x) - 8cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R Type: Union(Expression Integer,...) +--E 121 + +--S 122 of 528 +m0322:= a0322-r0322 +--R +--R +--R (120) +--R 6 5 4 3 +--R (- 16cos(x) - 16cos(x) - 8cos(x) - 8cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) + 32cos(x) + 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (8cos(x) + 8cos(x) + 4cos(x) + 4cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 16cos(x) - 16cos(x) - 2cos(x) +--R * +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R 6 5 4 3 +--R (- 16cos(x) - 16cos(x) - 8cos(x) - 8cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) + 32cos(x) + 4cos(x) +--R * +--R tan(x) +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 6 5 4 3 +--R (- 8cos(x) - 8cos(x) - 4cos(x) - 4cos(x) )tan(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R (16cos(x) + 16cos(x) + 2cos(x) )tan(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 6 5 4 3 sin(x) +--R (- 8cos(x) - 8cos(x) - 4cos(x) - 4cos(x) )atan(------) +--R cos(x) +--R + +--R +-+ +--R 6 5 4 3 \|2 tan(x) +--R (- 32cos(x) - 32cos(x) - 16cos(x) - 16cos(x) )asinh(----------) +--R 2 +--R + +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) + 8cos(x) + 8cos(x) + cos(x) + 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 sin(x) +--R (16cos(x) + 16cos(x) + 2cos(x) )atan(------) +--R cos(x) +--R + +--R +-+ +--R 6 4 2 \|2 tan(x) +--R (64cos(x) + 64cos(x) + 8cos(x) )asinh(----------) +--R 2 +--R + +--R 5 3 +--R (- 16cos(x) - 24cos(x) - 8cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R Type: Expression Integer +--E 122 + +--S 123 of 528 +d0322:= D(m0322,x) +--R +--R +--R (121) +--R 26 25 24 +--R 131072cos(x) + 131072cos(x) + 655360cos(x) +--R + +--R 23 22 21 +--R 655360cos(x) + 1122304cos(x) + 1122304cos(x) +--R + +--R 20 19 18 +--R 589824cos(x) + 589824cos(x) - 428544cos(x) +--R + +--R 17 16 15 +--R - 428544cos(x) - 634368cos(x) - 634368cos(x) +--R + +--R 14 13 12 +--R - 183872cos(x) - 183872cos(x) + 80512cos(x) +--R + +--R 11 10 9 8 +--R 80512cos(x) + 63954cos(x) + 63954cos(x) + 14898cos(x) +--R + +--R 7 6 5 4 +--R 14898cos(x) + 1324cos(x) + 1324cos(x) + 32cos(x) +--R + +--R 3 +--R 32cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 28 27 26 +--R - 393216cos(x) - 393216cos(x) - 1245184cos(x) +--R + +--R 25 24 23 +--R - 1245184cos(x) - 1646592cos(x) - 1646592cos(x) +--R + +--R 22 21 20 +--R - 1241088cos(x) - 1241088cos(x) - 211456cos(x) +--R + +--R 19 18 17 +--R - 211456cos(x) + 900864cos(x) + 900864cos(x) +--R + +--R 16 15 14 +--R 948544cos(x) + 948544cos(x) + 165344cos(x) +--R + +--R 13 12 11 +--R 165344cos(x) - 217414cos(x) - 217414cos(x) +--R + +--R 10 9 8 7 +--R - 111339cos(x) - 111339cos(x) - 7462cos(x) - 7462cos(x) +--R + +--R 6 5 4 3 +--R 4678cos(x) + 4678cos(x) + 815cos(x) + 815cos(x) +--R + +--R 2 +--R 28cos(x) + 28cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 30 29 28 +--R - 1179648cos(x) - 1179648cos(x) - 4063232cos(x) +--R + +--R 27 26 25 +--R - 4063232cos(x) - 4857856cos(x) - 4857856cos(x) +--R + +--R 24 23 22 +--R - 1359872cos(x) - 1359872cos(x) + 2152960cos(x) +--R + +--R 21 20 19 +--R 2152960cos(x) + 2220544cos(x) + 2220544cos(x) +--R + +--R 18 17 16 +--R 540736cos(x) + 540736cos(x) - 328448cos(x) +--R + +--R 15 14 13 +--R - 328448cos(x) - 193122cos(x) - 193122cos(x) +--R + +--R 12 11 10 9 +--R 8602cos(x) + 8602cos(x) + 5348cos(x) + 5348cos(x) +--R + +--R 8 7 6 5 +--R - 14858cos(x) - 14858cos(x) - 6604cos(x) - 6604cos(x) +--R + +--R 4 3 2 +--R - 862cos(x) - 862cos(x) - 28cos(x) - 28cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 +--R - 655360cos(x) - 655360cos(x) - 2162688cos(x) +--R + +--R 29 28 27 +--R - 2162688cos(x) - 1695744cos(x) - 1695744cos(x) +--R + +--R 26 25 24 +--R 1617920cos(x) + 1617920cos(x) + 2812416cos(x) +--R + +--R 23 22 21 +--R 2812416cos(x) + 316672cos(x) + 316672cos(x) +--R + +--R 20 19 18 +--R - 1303872cos(x) - 1303872cos(x) - 566368cos(x) +--R + +--R 17 16 15 +--R - 566368cos(x) + 186358cos(x) + 186358cos(x) +--R + +--R 14 13 12 11 +--R 160887cos(x) + 160887cos(x) + 13740cos(x) + 13740cos(x) +--R + +--R 10 9 8 7 +--R - 12277cos(x) - 12277cos(x) - 3781cos(x) - 3781cos(x) +--R + +--R 6 5 4 3 +--R - 402cos(x) - 402cos(x) - 13cos(x) - 13cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 26 24 22 +--R - 262144cos(x) - 1441792cos(x) - 2867200cos(x) +--R + +--R 20 18 16 +--R - 2154496cos(x) + 476160cos(x) + 1748480cos(x) +--R + +--R 14 12 10 8 +--R 878464cos(x) - 74816cos(x) - 212484cos(x) - 74438cos(x) +--R + +--R 6 4 2 +--R - 10362cos(x) - 510cos(x) - 4cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 28 26 24 +--R 786432cos(x) + 2883584cos(x) + 4440064cos(x) +--R + +--R 22 20 18 +--R 3866624cos(x) + 1377280cos(x) - 1770496cos(x) +--R + +--R 16 14 12 +--R - 2772352cos(x) - 1072896cos(x) + 407660cos(x) +--R + +--R 10 8 6 4 +--R 422940cos(x) + 84166cos(x) - 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524288cos(x) - 524288cos(x) - 1835008cos(x) +--R + +--R 25 24 23 +--R - 1835008cos(x) - 1998848cos(x) - 1998848cos(x) +--R + +--R 22 21 20 +--R 16384cos(x) + 16384cos(x) + 1476608cos(x) +--R + +--R 19 18 17 +--R 1476608cos(x) + 822272cos(x) + 822272cos(x) +--R + +--R 16 15 14 +--R - 120064cos(x) - 120064cos(x) - 224896cos(x) +--R + +--R 13 12 11 10 +--R - 224896cos(x) - 53256cos(x) - 53256cos(x) + 3588cos(x) +--R + +--R 9 8 7 6 +--R 3588cos(x) + 2374cos(x) + 2374cos(x) + 190cos(x) +--R + +--R 5 4 3 +--R 190cos(x) + 2cos(x) + 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 +--R - 262144cos(x) - 262144cos(x) - 917504cos(x) - 917504cos(x) +--R + +--R 28 27 26 25 +--R - 770048cos(x) - 770048cos(x) + 761856cos(x) + 761856cos(x) +--R + +--R 24 23 22 21 +--R 1426432cos(x) + 1426432cos(x) + 165376cos(x) + 165376cos(x) +--R + +--R 20 19 18 17 +--R - 764032cos(x) - 764032cos(x) - 341312cos(x) - 341312cos(x) +--R + +--R 16 15 14 13 +--R 139516cos(x) + 139516cos(x) + 114818cos(x) + 114818cos(x) +--R + +--R 12 11 10 9 +--R 4614cos(x) + 4614cos(x) - 11526cos(x) - 11526cos(x) +--R + +--R 8 7 6 5 4 +--R - 2822cos(x) - 2822cos(x) - 194cos(x) - 194cos(x) - 2cos(x) +--R + +--R 3 +--R - 2cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 28 26 24 +--R - 524288cos(x) - 2097152cos(x) - 2916352cos(x) +--R + +--R 22 20 18 +--R - 1015808cos(x) + 1386496cos(x) + 1478656cos(x) +--R + +--R 16 14 12 10 +--R 315648cos(x) - 217856cos(x) - 142152cos(x) - 31104cos(x) +--R + +--R 8 6 +--R - 2680cos(x) - 64cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 +--R 1048576cos(x) + 4194304cos(x) + 5701632cos(x) +--R + +--R 22 20 18 +--R 1572864cos(x) - 3280896cos(x) - 2981888cos(x) +--R + +--R 16 14 12 10 +--R - 292352cos(x) + 643072cos(x) + 276496cos(x) + 16832cos(x) +--R + +--R 8 6 4 +--R - 9872cos(x) - 1656cos(x) - 56cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 30 28 26 +--R 524288cos(x) + 2097152cos(x) + 2392064cos(x) - 950272cos(x) +--R + +--R 24 22 20 18 +--R - 3713024cos(x) - 1527808cos(x) + 1603328cos(x) + 1382144cos(x) +--R + +--R 16 14 12 10 +--R - 88504cos(x) - 386304cos(x) - 86288cos(x) + 29568cos(x) +--R + +--R 8 6 4 +--R 14336cos(x) + 1776cos(x) + 56cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression Integer +--E 123 + +--S 124 of 528 +t0323:= (1-sec(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (122) (- sec(x) + 1)\|- sec(x) + 1 +--R Type: Expression Integer +--E 124 + +--S 125 of 528 +r0323:= -1/2*cot(x)*(-tan(x)^2)^(1/2)*(2*log(cos(x))+tan(x)^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 2cot(x)log(cos(x)) - cot(x)tan(x) )\|- tan(x) +--R (123) -------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 125 + +--S 126 of 528 +a0323:= integrate(t0323,x) +--R +--R +--R (124) +--R x 16 x 2 x 14 x 4 x 12 +--R sin(-) + 8cos(-) sin(-) + (28cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (56cos(-) - 8cos(-) )sin(-) + (70cos(-) - 68cos(-) + 6)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) - 112cos(-) - 40cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) - 68cos(-) + 164cos(-) + 4)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (8cos(-) - 8cos(-) - 40cos(-) - 24cos(-) )sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R * +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R x x 11 x 3 x 9 x 5 x 7 +--R - 8cos(-)sin(-) - 24cos(-) sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 7 x 5 x 9 x x 3 +--R 16cos(-) sin(-) + (24cos(-) + 8cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 11 x 3 x +--R (8cos(-) - 8cos(-) )sin(-) +--R 2 2 2 +--R / +--R x 16 x 2 x 14 x 4 x 12 +--R sin(-) + 8cos(-) sin(-) + (28cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (56cos(-) - 8cos(-) )sin(-) + (70cos(-) - 68cos(-) + 6)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) - 112cos(-) - 40cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) - 68cos(-) + 164cos(-) + 4)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (8cos(-) - 8cos(-) - 40cos(-) - 24cos(-) )sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R Type: Union(Expression Integer,...) +--E 126 + +--S 127 of 528 +m0323:= a0323-r0323 +--R +--R +--R (125) +--R x 16 x 2 x 14 +--R 2cot(x)sin(-) + 16cos(-) cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 12 +--R (56cos(-) + 8)cot(x)sin(-) +--R 2 2 +--R + +--R x 6 x 2 x 10 +--R (112cos(-) - 16cos(-) )cot(x)sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (140cos(-) - 136cos(-) + 12)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) - 224cos(-) - 80cos(-) )cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) - 136cos(-) + 328cos(-) + 8)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 +--R (16cos(-) - 16cos(-) - 80cos(-) - 48cos(-) )cot(x)sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 +--R (2cos(-) + 8cos(-) + 12cos(-) + 8cos(-) + 2)cot(x) +--R 2 2 2 2 +--R * +--R log(cos(x)) +--R + +--R x 16 x 2 x 14 +--R cot(x)sin(-) + 8cos(-) cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 12 +--R (28cos(-) + 4)cot(x)sin(-) +--R 2 2 +--R + +--R x 6 x 2 x 10 +--R (56cos(-) - 8cos(-) )cot(x)sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (70cos(-) - 68cos(-) + 6)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) - 112cos(-) - 40cos(-) )cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) - 68cos(-) + 164cos(-) + 4)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 +--R (8cos(-) - 8cos(-) - 40cos(-) - 24cos(-) )cot(x)sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 +--R (cos(-) + 4cos(-) + 6cos(-) + 4cos(-) + 1)cot(x) +--R 2 2 2 2 +--R * +--R 2 +--R tan(x) +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R + +--R x 16 x 2 x 14 x 4 x 12 +--R 2sin(-) + 16cos(-) sin(-) + (56cos(-) + 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 +--R (112cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (140cos(-) - 136cos(-) + 12)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) - 224cos(-) - 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) - 136cos(-) + 328cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (16cos(-) - 16cos(-) - 80cos(-) - 48cos(-) )sin(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 8cos(-) + 12cos(-) + 8cos(-) + 2 +--R 2 2 2 +--R * +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R x x 11 x 3 x 9 x 5 x 7 +--R - 16cos(-)sin(-) - 48cos(-) sin(-) - 32cos(-) sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 7 x 5 x 9 x x 3 +--R 32cos(-) sin(-) + (48cos(-) + 16cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 11 x 3 x +--R (16cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R / +--R x 16 x 2 x 14 x 4 x 12 +--R 2sin(-) + 16cos(-) sin(-) + (56cos(-) + 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (112cos(-) - 16cos(-) )sin(-) + (140cos(-) - 136cos(-) + 12)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) - 224cos(-) - 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) - 136cos(-) + 328cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (16cos(-) - 16cos(-) - 80cos(-) - 48cos(-) )sin(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 8cos(-) + 12cos(-) + 8cos(-) + 2 +--R 2 2 2 +--R Type: Expression Integer +--E 127 + +--S 128 of 528 +d0323:= D(m0323,x) +--R +--R +--R (126) +--R x 30 x 2 x 28 +--R - 2cos(x)sin(-) + (- 30cos(-) + 4)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 210cos(-) + 48cos(-) - 6)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 910cos(-) + 260cos(-) - 38cos(-) + 8)cos(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 2730cos(-) + 832cos(-) - 20cos(-) - 80cos(-) - 18)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 1716cos(-) + 572cos(-) - 320cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 586cos(-) + 28 +--R 2 +--R * +--R x 20 +--R cos(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 10010cos(-) + 2288cos(-) + 2750cos(-) + 1040cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 2722cos(-) - 1248cos(-) - 54 +--R 2 2 +--R * +--R x 18 +--R cos(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 12870cos(-) + 1716cos(-) + 6798cos(-) + 7624cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1174cos(-) - 6348cos(-) + 978cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)sin(-) +--R 2 +--R + +--R x 16 x 12 x 10 x 8 +--R - 12870cos(-) + 10824cos(-) + 17888cos(-) - 14900cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 6080cos(-) + 3432cos(-) - 672cos(-) - 86 +--R 2 2 2 +--R * +--R x 14 +--R cos(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 10010cos(-) - 1716cos(-) + 11880cos(-) + 21952cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 39900cos(-) + 5016cos(-) + 9000cos(-) + 2656cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 262cos(-) + 92 +--R 2 +--R * +--R x 12 +--R cos(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 6006cos(-) - 2288cos(-) + 9174cos(-) + 14624cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 47740cos(-) + 1408cos(-) + 17388cos(-) - 8736cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 3214cos(-) + 304cos(-) - 66 +--R 2 2 +--R * +--R x 10 +--R cos(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 2730cos(-) - 1716cos(-) + 4950cos(-) + 4120cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 6 +--R - 29908cos(-) - 16152cos(-) + 19324cos(-) + 6942cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 4748cos(-) - 50cos(-) + 40 +--R 2 2 +--R * +--R x 8 +--R cos(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 910cos(-) - 832cos(-) + 1804cos(-) - 656cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 8346cos(-) - 12864cos(-) + 14408cos(-) + 8736cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 17346cos(-) - 6272cos(-) - 3924cos(-) - 144cos(-) - 22 +--R 2 2 2 2 +--R * +--R x 6 +--R cos(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 260cos(-) + 412cos(-) - 640cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 370cos(-) + 1036cos(-) + 8904cos(-) - 2656cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 3602cos(-) + 4532cos(-) + 6812cos(-) - 608cos(-) + 78cos(-) +--R 2 2 2 2 2 +--R + +--R 4 +--R * +--R x 4 +--R cos(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 22 x 20 +--R - 30cos(-) - 48cos(-) + 50cos(-) - 48cos(-) + 698cos(-) +--R 2 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 2400cos(-) + 3226cos(-) + 672cos(-) - 1242cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1200cos(-) - 3658cos(-) + 528cos(-) + 190cos(-) - 2 +--R 2 2 2 2 +--R * +--R x 2 +--R cos(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R - 2cos(-) - 4cos(-) + 2cos(-) + 24cos(-) + 94cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 36cos(-) + 194cos(-) - 80cos(-) + 74cos(-) - 156cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R - 74cos(-) - 72cos(-) - 38cos(-) - 4cos(-) + 6cos(-) +--R 2 2 2 2 2 +--R * +--R cos(x) +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R + +--R x 30 x 2 x 28 +--R - 2cos(x)cot(x)sin(-) + (- 30cos(-) + 4)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 210cos(-) + 72cos(-) - 14)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 910cos(-) + 540cos(-) - 102cos(-) + 24)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 2730cos(-) + 2320cos(-) - 228cos(-) + 192cos(-) - 42) +--R 2 2 2 2 +--R * +--R x 22 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 6468cos(-) + 220cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 78cos(-) + 60 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 10010cos(-) + 12408cos(-) + 2310cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 282cos(-) + 72cos(-) - 70 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 12870cos(-) + 16764cos(-) + 5742cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1422cos(-) - 1764cos(-) + 90cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R - 12870cos(-) + 15840cos(-) + 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 34176cos(-) + 4188cos(-) + 5856cos(-) + 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 192cos(-) - 70 +--R 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 10010cos(-) + 9900cos(-) + 5544cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 10164cos(-) + 31608cos(-) - 1144cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 150cos(-) + 60 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 6006cos(-) + 3256cos(-) + 990cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 16884cos(-) + 35376cos(-) - 13236cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1410cos(-) - 168cos(-) - 42 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 2730cos(-) - 396cos(-) - 2090cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 17052cos(-) + 3096cos(-) - 25812cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9426cos(-) - 1452cos(-) + 30cos(-) + 24 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 910cos(-) - 1008cos(-) - 2244cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 9582cos(-) - 11808cos(-) - 17080cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 39150cos(-) + 12432cos(-) + 1596cos(-) - 14 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 500cos(-) - 1092cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 2298cos(-) - 2100cos(-) - 984cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 12222cos(-) - 8796cos(-) - 8100cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 42cos(-) + 4 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 30cos(-) - 120cos(-) - 278cos(-) - 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1224cos(-) + 1482cos(-) + 2496cos(-) + 3158cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1944cos(-) + 2382cos(-) + 576cos(-) + 630cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 24cos(-) - 2 +--R 2 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R - 2cos(-) - 12cos(-) - 30cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 138cos(-) - 180cos(-) - 310cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 390cos(-) - 180cos(-) - 282cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 110cos(-) - 12cos(-) - 18cos(-) +--R 2 2 2 +--R * +--R cos(x)cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 2 x 30 +--R (2cos(x)cot(x) + 2cos(x))sin(-) +--R 2 +--R + +--R x 2 2 x 2 x 28 +--R ((30cos(-) - 4)cos(x)cot(x) + (30cos(-) - 4)cos(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 +--R (210cos(-) - 72cos(-) + 14)cos(x)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (210cos(-) - 72cos(-) + 14)cos(x) +--R 2 2 +--R * +--R x 26 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 2 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cos(x)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cos(x) +--R 2 2 2 +--R * +--R x 24 +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42) +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42) +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 78cos(-) - 60 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 78cos(-) - 60 +--R 2 +--R * +--R cos(x) +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 19320cos(-) - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 14 x 12 x 10 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 19320cos(-) - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 34176cos(-) - 4188cos(-) - 5856cos(-) - 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 192cos(-) + 70 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 16 x 14 x 12 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 34176cos(-) - 4188cos(-) - 5856cos(-) - 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 192cos(-) + 70 +--R 2 +--R * +--R cos(x) +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 32928cos(-) - 10164cos(-) - 31608cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1144cos(-) + 1536cos(-) - 150cos(-) - 60 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 18 x 16 x 14 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 32928cos(-) - 10164cos(-) - 31608cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1144cos(-) + 1536cos(-) - 150cos(-) - 60 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9024cos(-) - 1410cos(-) + 168cos(-) + 42 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9024cos(-) - 1410cos(-) + 168cos(-) + 42 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 61920cos(-) + 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 61920cos(-) + 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 43968cos(-) - 39150cos(-) - 12432cos(-) +--R 2 2 2 +--R + +--R x 4 +--R - 1596cos(-) + 14 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 43968cos(-) - 39150cos(-) - 12432cos(-) +--R 2 2 2 +--R + +--R x 4 +--R - 1596cos(-) + 14 +--R 2 +--R * +--R cos(x) +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 12160cos(-) + 12222cos(-) + 8796cos(-) + 8100cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 912cos(-) + 42cos(-) - 4 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 12160cos(-) + 12222cos(-) + 8796cos(-) + 8100cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 912cos(-) + 42cos(-) - 4 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 1224cos(-) - 1482cos(-) - 2496cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 3158cos(-) - 1944cos(-) - 2382cos(-) - 576cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 630cos(-) - 24cos(-) + 2 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 1224cos(-) - 1482cos(-) - 2496cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 3158cos(-) - 1944cos(-) - 2382cos(-) - 576cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 630cos(-) - 24cos(-) + 2 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 138cos(-) + 180cos(-) + 310cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 390cos(-) + 180cos(-) + 282cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 110cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 30 x 28 x 26 x 24 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 138cos(-) + 180cos(-) + 310cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 390cos(-) + 180cos(-) + 282cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 110cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 +--R * +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R x 30 x 2 x 28 +--R - 2cos(x)cot(x)sin(-) + (- 30cos(-) + 4)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 210cos(-) + 72cos(-) - 14)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 910cos(-) + 540cos(-) - 102cos(-) + 24)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 2730cos(-) + 2320cos(-) - 228cos(-) + 192cos(-) - 42) +--R 2 2 2 2 +--R * +--R x 22 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 6468cos(-) + 220cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 78cos(-) + 60 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 10010cos(-) + 12408cos(-) + 2310cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 282cos(-) + 72cos(-) - 70 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 12870cos(-) + 16764cos(-) + 5742cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1422cos(-) - 1764cos(-) + 90cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R - 12870cos(-) + 15840cos(-) + 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 34176cos(-) + 4188cos(-) + 5856cos(-) + 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 192cos(-) - 70 +--R 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 10010cos(-) + 9900cos(-) + 5544cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 10164cos(-) + 31608cos(-) - 1144cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 150cos(-) + 60 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 6006cos(-) + 3256cos(-) + 990cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 16884cos(-) + 35376cos(-) - 13236cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1410cos(-) - 168cos(-) - 42 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 2730cos(-) - 396cos(-) - 2090cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 17052cos(-) + 3096cos(-) - 25812cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9426cos(-) - 1452cos(-) + 30cos(-) + 24 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 910cos(-) - 1008cos(-) - 2244cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 9582cos(-) - 11808cos(-) - 17080cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 39150cos(-) + 12432cos(-) + 1596cos(-) - 14 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 500cos(-) - 1092cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 2298cos(-) - 2100cos(-) - 984cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 12222cos(-) - 8796cos(-) - 8100cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 42cos(-) + 4 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 30cos(-) - 120cos(-) - 278cos(-) - 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1224cos(-) + 1482cos(-) + 2496cos(-) + 3158cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1944cos(-) + 2382cos(-) + 576cos(-) + 630cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 24cos(-) - 2 +--R 2 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R - 2cos(-) - 12cos(-) - 30cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 138cos(-) - 180cos(-) - 310cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 390cos(-) - 180cos(-) - 282cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 110cos(-) - 12cos(-) - 18cos(-) +--R 2 2 2 +--R * +--R cos(x)cot(x) +--R * +--R tan(x) +--R * +--R log(cos(x)) +--R + +--R x 30 x 2 x 28 +--R - 3cos(x)cot(x)sin(-) + (- 45cos(-) + 6)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 315cos(-) + 108cos(-) - 21)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 1365cos(-) + 810cos(-) - 153cos(-) + 36)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 4095cos(-) + 3480cos(-) - 342cos(-) + 288cos(-) - 63)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 9009cos(-) + 9702cos(-) + 330cos(-) - 360cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 117cos(-) + 90 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 15015cos(-) + 18612cos(-) + 3465cos(-) - 8064cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 423cos(-) + 108cos(-) - 105 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 19305cos(-) + 25146cos(-) + 8613cos(-) - 28980cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 2133cos(-) - 2646cos(-) + 135cos(-) + 120 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 19305cos(-) + 23760cos(-) + 11484cos(-) - 51264cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 6282cos(-) + 8784cos(-) + 1116cos(-) - 288cos(-) - 105 +--R 2 2 2 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 15015cos(-) + 14850cos(-) + 8316cos(-) - 49392cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 15246cos(-) + 47412cos(-) - 1716cos(-) - 2304cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 225cos(-) + 90 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 9009cos(-) + 4884cos(-) + 1485cos(-) - 21888cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 25326cos(-) + 53064cos(-) - 19854cos(-) + 13536cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 2115cos(-) - 252cos(-) - 63 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 4095cos(-) - 594cos(-) - 3135cos(-) + 2556cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 25578cos(-) + 4644cos(-) - 38718cos(-) - 92880cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 14139cos(-) - 2178cos(-) + 45cos(-) + 36 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 1365cos(-) - 1512cos(-) - 3366cos(-) + 7200cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 14373cos(-) - 17712cos(-) - 25620cos(-) + 65952cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 58725cos(-) + 18648cos(-) + 2394cos(-) - 21 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 315cos(-) - 750cos(-) - 1638cos(-) + 2520cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 3447cos(-) - 3150cos(-) - 1476cos(-) - 18240cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 18333cos(-) - 13194cos(-) - 12150cos(-) - 1368cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 63cos(-) + 6 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 45cos(-) - 180cos(-) - 417cos(-) - 261cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1836cos(-) + 2223cos(-) + 3744cos(-) + 4737cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 2916cos(-) + 3573cos(-) + 864cos(-) + 945cos(-) + 36cos(-) +--R 2 2 2 2 2 +--R + +--R - 3 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R - 3cos(-) - 18cos(-) - 45cos(-) - 108cos(-) - 207cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 270cos(-) - 465cos(-) - 360cos(-) - 585cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R - 270cos(-) - 423cos(-) - 108cos(-) - 165cos(-) - 18cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R - 27cos(-) +--R 2 +--R * +--R cos(x)cot(x) +--R * +--R 5 +--R tan(x) +--R + +--R 2 x 30 +--R (cos(x)cot(x) + cos(x))sin(-) +--R 2 +--R + +--R x 2 2 x 2 x 28 +--R ((15cos(-) - 2)cos(x)cot(x) + (15cos(-) - 2)cos(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 +--R (105cos(-) - 36cos(-) + 7)cos(x)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (105cos(-) - 36cos(-) + 7)cos(x) +--R 2 2 +--R * +--R x 26 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 2 +--R (455cos(-) - 270cos(-) + 51cos(-) - 12)cos(x)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (455cos(-) - 270cos(-) + 51cos(-) - 12)cos(x) +--R 2 2 2 +--R * +--R x 24 +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (1365cos(-) - 1160cos(-) + 114cos(-) - 96cos(-) + 21)cos(x) +--R 2 2 2 2 +--R * +--R 2 +--R cot(x) +--R + +--R x 8 x 6 x 4 x 2 +--R (1365cos(-) - 1160cos(-) + 114cos(-) - 96cos(-) + 21)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 3003cos(-) - 3234cos(-) - 110cos(-) + 120cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 39cos(-) - 30 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 10 x 8 x 6 x 4 +--R 3003cos(-) - 3234cos(-) - 110cos(-) + 120cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 39cos(-) - 30 +--R 2 +--R * +--R cos(x) +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 5005cos(-) - 6204cos(-) - 1155cos(-) + 2688cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 141cos(-) - 36cos(-) + 35 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 12 x 10 x 8 x 6 +--R 5005cos(-) - 6204cos(-) - 1155cos(-) + 2688cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 141cos(-) - 36cos(-) + 35 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 6435cos(-) - 8382cos(-) - 2871cos(-) + 9660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 711cos(-) + 882cos(-) - 45cos(-) - 40 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 14 x 12 x 10 x 8 +--R 6435cos(-) - 8382cos(-) - 2871cos(-) + 9660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 711cos(-) + 882cos(-) - 45cos(-) - 40 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 6435cos(-) - 7920cos(-) - 3828cos(-) + 17088cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2094cos(-) - 2928cos(-) - 372cos(-) + 96cos(-) + 35 +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 16 x 14 x 12 x 10 +--R 6435cos(-) - 7920cos(-) - 3828cos(-) + 17088cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2094cos(-) - 2928cos(-) - 372cos(-) + 96cos(-) + 35 +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 5005cos(-) - 4950cos(-) - 2772cos(-) + 16464cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 5082cos(-) - 15804cos(-) + 572cos(-) + 768cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 75cos(-) - 30 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 18 x 16 x 14 x 12 +--R 5005cos(-) - 4950cos(-) - 2772cos(-) + 16464cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 5082cos(-) - 15804cos(-) + 572cos(-) + 768cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 75cos(-) - 30 +--R 2 +--R * +--R cos(x) +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 3003cos(-) - 1628cos(-) - 495cos(-) + 7296cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 8442cos(-) - 17688cos(-) + 6618cos(-) - 4512cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 705cos(-) + 84cos(-) + 21 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 20 x 18 x 16 x 14 +--R 3003cos(-) - 1628cos(-) - 495cos(-) + 7296cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 8442cos(-) - 17688cos(-) + 6618cos(-) - 4512cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 705cos(-) + 84cos(-) + 21 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 1365cos(-) + 198cos(-) + 1045cos(-) - 852cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 8526cos(-) - 1548cos(-) + 12906cos(-) + 30960cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4713cos(-) + 726cos(-) - 15cos(-) - 12 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 22 x 20 x 18 x 16 +--R 1365cos(-) + 198cos(-) + 1045cos(-) - 852cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 8526cos(-) - 1548cos(-) + 12906cos(-) + 30960cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4713cos(-) + 726cos(-) - 15cos(-) - 12 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 455cos(-) + 504cos(-) + 1122cos(-) - 2400cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 4791cos(-) + 5904cos(-) + 8540cos(-) - 21984cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 19575cos(-) - 6216cos(-) - 798cos(-) + 7 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 24 x 22 x 20 x 18 +--R 455cos(-) + 504cos(-) + 1122cos(-) - 2400cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 4791cos(-) + 5904cos(-) + 8540cos(-) - 21984cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 19575cos(-) - 6216cos(-) - 798cos(-) + 7 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 105cos(-) + 250cos(-) + 546cos(-) - 840cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1149cos(-) + 1050cos(-) + 492cos(-) + 6080cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6111cos(-) + 4398cos(-) + 4050cos(-) + 456cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 21cos(-) - 2 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 26 x 24 x 22 x 20 +--R 105cos(-) + 250cos(-) + 546cos(-) - 840cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1149cos(-) + 1050cos(-) + 492cos(-) + 6080cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6111cos(-) + 4398cos(-) + 4050cos(-) + 456cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 21cos(-) - 2 +--R 2 +--R * +--R cos(x) +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 15cos(-) + 60cos(-) + 139cos(-) + 87cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 612cos(-) - 741cos(-) - 1248cos(-) - 1579cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 972cos(-) - 1191cos(-) - 288cos(-) - 315cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 12cos(-) + 1 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 28 x 26 x 24 x 20 +--R 15cos(-) + 60cos(-) + 139cos(-) + 87cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 612cos(-) - 741cos(-) - 1248cos(-) - 1579cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 972cos(-) - 1191cos(-) - 288cos(-) - 315cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 12cos(-) + 1 +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R cos(-) + 6cos(-) + 15cos(-) + 36cos(-) + 69cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 90cos(-) + 155cos(-) + 120cos(-) + 195cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 141cos(-) + 36cos(-) + 55cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R cos(-) + 6cos(-) + 15cos(-) + 36cos(-) + 69cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 90cos(-) + 155cos(-) + 120cos(-) + 195cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 141cos(-) + 36cos(-) + 55cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 2 2 +--R * +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R x 30 x 2 x 28 +--R - 3cos(x)cot(x)sin(-) + (- 45cos(-) + 6)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 315cos(-) + 108cos(-) - 21)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 1365cos(-) + 810cos(-) - 153cos(-) + 36)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 4095cos(-) + 3480cos(-) - 342cos(-) + 288cos(-) - 63)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 9009cos(-) + 9702cos(-) + 330cos(-) - 360cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 117cos(-) + 90 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 15015cos(-) + 18612cos(-) + 3465cos(-) - 8064cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 423cos(-) + 108cos(-) - 105 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 19305cos(-) + 25146cos(-) + 8613cos(-) - 28980cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 2133cos(-) - 2646cos(-) + 135cos(-) + 120 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 19305cos(-) + 23760cos(-) + 11484cos(-) - 51264cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 6282cos(-) + 8784cos(-) + 1116cos(-) - 288cos(-) - 105 +--R 2 2 2 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 15015cos(-) + 14850cos(-) + 8316cos(-) - 49392cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 15246cos(-) + 47412cos(-) - 1716cos(-) - 2304cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 225cos(-) + 90 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 9009cos(-) + 4884cos(-) + 1485cos(-) - 21888cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 25326cos(-) + 53064cos(-) - 19854cos(-) + 13536cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 2115cos(-) - 252cos(-) - 63 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 4095cos(-) - 594cos(-) - 3135cos(-) + 2556cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 25578cos(-) + 4644cos(-) - 38718cos(-) - 92880cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 14139cos(-) - 2178cos(-) + 45cos(-) + 36 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 1365cos(-) - 1512cos(-) - 3366cos(-) + 7200cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 14373cos(-) - 17712cos(-) - 25620cos(-) + 65952cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 58725cos(-) + 18648cos(-) + 2394cos(-) - 21 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 315cos(-) - 750cos(-) - 1638cos(-) + 2520cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 3447cos(-) - 3150cos(-) - 1476cos(-) - 18240cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 18333cos(-) - 13194cos(-) - 12150cos(-) - 1368cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 63cos(-) + 6 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 45cos(-) - 180cos(-) - 417cos(-) - 261cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1836cos(-) + 2223cos(-) + 3744cos(-) + 4737cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 2916cos(-) + 3573cos(-) + 864cos(-) + 945cos(-) + 36cos(-) +--R 2 2 2 2 2 +--R + +--R - 3 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R - 3cos(-) - 18cos(-) - 45cos(-) - 108cos(-) - 207cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 270cos(-) - 465cos(-) - 360cos(-) - 585cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R - 270cos(-) - 423cos(-) - 108cos(-) - 165cos(-) - 18cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R - 27cos(-) +--R 2 +--R * +--R cos(x)cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R x 30 x 2 x 28 +--R 2cot(x)sin(-) + (30cos(-) - 4)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (210cos(-) - 72cos(-) + 14)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42)cot(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) + 78cos(-) +--R 2 2 2 2 2 +--R + +--R - 60 +--R * +--R x 20 +--R cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R x 18 +--R cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) + 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 +--R * +--R x 16 +--R cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) + 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 4188cos(-) - 5856cos(-) - 744cos(-) + 192cos(-) + 70 +--R 2 2 2 2 +--R * +--R x 14 +--R cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) + 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 10164cos(-) - 31608cos(-) + 1144cos(-) + 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 150cos(-) - 60 +--R 2 +--R * +--R x 12 +--R cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) - 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 1410cos(-) + 168cos(-) + 42 +--R 2 2 +--R * +--R x 10 +--R cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) + 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 +--R * +--R x 8 +--R cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) - 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 39150cos(-) - 12432cos(-) - 1596cos(-) + 14 +--R 2 2 2 +--R * +--R x 6 +--R cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) + 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 12222cos(-) + 8796cos(-) + 8100cos(-) + 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 42cos(-) - 4 +--R 2 +--R * +--R x 4 +--R cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1224cos(-) - 1482cos(-) - 2496cos(-) - 3158cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1944cos(-) - 2382cos(-) - 576cos(-) - 630cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 24cos(-) + 2 +--R 2 +--R * +--R x 2 +--R cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) + 138cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 180cos(-) + 310cos(-) + 240cos(-) + 390cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R 180cos(-) + 282cos(-) + 72cos(-) + 110cos(-) + 12cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R 18cos(-) +--R 2 +--R * +--R cot(x) +--R * +--R 2 +--R sin(x)tan(x) +--R / +--R x 30 x 2 x 28 +--R 2cos(x)sin(-) + (30cos(-) - 4)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (210cos(-) - 72cos(-) + 14)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cos(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) + 78cos(-) +--R 2 2 2 2 2 +--R + +--R - 60 +--R * +--R x 20 +--R cos(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R x 18 +--R cos(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) + 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) + 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 4188cos(-) - 5856cos(-) - 744cos(-) + 192cos(-) + 70 +--R 2 2 2 2 +--R * +--R x 14 +--R cos(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) + 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 10164cos(-) - 31608cos(-) + 1144cos(-) + 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 150cos(-) - 60 +--R 2 +--R * +--R x 12 +--R cos(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) - 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 1410cos(-) + 168cos(-) + 42 +--R 2 2 +--R * +--R x 10 +--R cos(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) + 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) - 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 39150cos(-) - 12432cos(-) - 1596cos(-) + 14 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) + 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 12222cos(-) + 8796cos(-) + 8100cos(-) + 912cos(-) + 42cos(-) +--R 2 2 2 2 2 +--R + +--R - 4 +--R * +--R x 4 +--R cos(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 x 18 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) - 1224cos(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 1482cos(-) - 2496cos(-) - 3158cos(-) - 1944cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2382cos(-) - 576cos(-) - 630cos(-) - 24cos(-) + 2 +--R 2 2 2 2 +--R * +--R x 2 +--R cos(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) + 138cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 180cos(-) + 310cos(-) + 240cos(-) + 390cos(-) + 180cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 282cos(-) + 72cos(-) + 110cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 2 2 +--R * +--R cos(x) +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression Integer +--E 128 + +--S 129 of 528 +t0324:= (-1+sec(x)^2)^(3/2) +--R +--R +--R +-----------+ +--R 2 | 2 +--R (127) (sec(x) - 1)\|sec(x) - 1 +--R Type: Expression Integer +--E 129 + +--S 130 of 528 +r0324:= 1/2*cot(x)*(tan(x)^2)^(1/2)*(2*log(cos(x))+tan(x)^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (2cot(x)log(cos(x)) + cot(x)tan(x) )\|tan(x) +--R (128) ---------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 130 + +--S 131 of 528 +a0324:= integrate(t0324,x) +--R +--R +--R 2 2 2 2cos(x) 2 +--R 2cos(x) log(----------) - 2cos(x) log(- ----------) + cos(x) - 1 +--R cos(x) + 1 cos(x) + 1 +--R (129) ----------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression Integer,...) +--E 131 + +--S 132 of 528 +m0324:= a0324-r0324 +--R +--R +--R (130) +--R +-------+ +--R 2 2 2 | 2 +--R (- 2cos(x) cot(x)log(cos(x)) - cos(x) cot(x)tan(x) )\|tan(x) +--R + +--R 2 2 2 2cos(x) 2 +--R 2cos(x) log(----------) - 2cos(x) log(- ----------) + cos(x) - 1 +--R cos(x) + 1 cos(x) + 1 +--R / +--R 2 +--R 2cos(x) +--R Type: Expression Integer +--E 132 + +--S 133 of 528 +d0324:= D(m0324,x) +--R +--R +--R (131) +--R +-------+ +--R 2 | 2 +--R (2cos(x) - 2)sin(x)\|tan(x) +--R + +--R 3 3 3 2 3 2 +--R - 2cos(x) cot(x)tan(x) + (2cos(x) cot(x) + 2cos(x) )tan(x) +--R + +--R 3 +--R - 2cos(x) cot(x)tan(x) +--R * +--R log(cos(x)) +--R + +--R 3 5 3 2 3 4 +--R - 3cos(x) cot(x)tan(x) + (cos(x) cot(x) + cos(x) )tan(x) +--R + +--R 3 3 2 2 +--R - 3cos(x) cot(x)tan(x) + 2cos(x) cot(x)sin(x)tan(x) +--R / +--R +-------+ +--R 3 | 2 +--R 2cos(x) \|tan(x) +--R Type: Expression Integer +--E 133 + +--S 134 of 528 +t0325:= (-1-sec(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (132) (- sec(x) - 1)\|- sec(x) - 1 +--R Type: Expression Integer +--E 134 + +--S 135 of 528 +r0325:= -2*atan(cot(x)*(-2-tan(x)^2)^(1/2))+atanh(tan(x)/(-2-tan(x)^2)^(1/2))-1/2*tan(x)*(-2-tan(x)^2)^(1/2) +--R +--R +--R (133) +--R +-------------+ +--R tan(x) | 2 +--R 2atanh(----------------) - 4atan(cot(x)\|- tan(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +-------------+ +--R | 2 +--R - tan(x)\|- tan(x) - 2 +--R / +--R 2 +--R Type: Expression Integer +--E 135 + +--S 136 of 528 +a0325:= integrate(t0325,x) +--R +--R +--R (134) +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 20\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 28\|- 1 (%e ) - 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 32\|- 1 (%e ) + 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 64\|- 1 (%e ) + 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 5(%e ) - 7(%e ) - 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 8(%e ) + 18(%e ) + 16(%e ) + 5 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 20\|- 1 (%e ) + 28\|- 1 (%e ) +--R + +--R +---+ +--R 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 32\|- 1 (%e ) - 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 64\|- 1 (%e ) - 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) + 5(%e ) + 7(%e ) + 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) - 8(%e ) - 18(%e ) - 16(%e ) - 5 +--R * +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +---+ 4 +--R x\|- 1 | x\|- 1 x\|- 1 x\|- 1 +--R (- 8(%e ) - 8)\|(%e ) + 6(%e ) + 1 + 8(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 32(%e ) + 8 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) + 10(%e ) + 14(%e ) + 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) - 16(%e ) - 36(%e ) - 32(%e ) - 10 +--R Type: Union(Expression Integer,...) +--E 136 + +--S 137 of 528 +m0325:= a0325-r0325 +--R +--R +--R (135) +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 20\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 28\|- 1 (%e ) - 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 32\|- 1 (%e ) + 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 64\|- 1 (%e ) + 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 5(%e ) - 7(%e ) - 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 8(%e ) + 18(%e ) + 16(%e ) + 5 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 20\|- 1 (%e ) + 28\|- 1 (%e ) +--R + +--R +---+ +--R 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 32\|- 1 (%e ) - 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 64\|- 1 (%e ) - 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) + 5(%e ) + 7(%e ) + 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) - 8(%e ) - 18(%e ) - 16(%e ) - 5 +--R * +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- 2(%e ) - 10(%e ) - 14(%e ) - 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R 2(%e ) + 16(%e ) + 36(%e ) + 32(%e ) + 10 +--R * +--R tan(x) +--R atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (4(%e ) + 20(%e ) + 28(%e ) + 12) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 4(%e ) - 32(%e ) - 72(%e ) - 64(%e ) - 20 +--R * +--R +-------------+ +--R | 2 +--R atan(cot(x)\|- tan(x) - 2 ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) + 5(%e ) + 7(%e ) + 3)tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 2 +--R x\|- 1 +--R - 8(%e ) - 8 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 8(%e ) - 18(%e ) - 16(%e ) - 5) +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|- tan(x) - 2 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 8(%e ) + 32(%e ) + 8 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) + 10(%e ) + 14(%e ) + 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) - 16(%e ) - 36(%e ) - 32(%e ) - 10 +--R Type: Expression Integer +--E 137 + +--S 138 of 528 +d0325:= D(m0325,x) +--R +--R +--R (136) +--R +---+ 18 +---+ 16 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R \|- 1 cot(x) (%e ) + 27\|- 1 cot(x) (%e ) +--R + +--R +---+ 14 +--R +---+ 2 x\|- 1 +--R 302\|- 1 cot(x) (%e ) +--R + +--R +---+ 12 +--R +---+ 2 x\|- 1 +--R 1806\|- 1 cot(x) (%e ) +--R + +--R +---+ 10 +--R +---+ 2 x\|- 1 +--R 6216\|- 1 cot(x) (%e ) +--R + +--R +---+ 8 +--R +---+ 2 x\|- 1 +--R 12348\|- 1 cot(x) (%e ) +--R + +--R +---+ 6 +--R +---+ 2 x\|- 1 +--R 13482\|- 1 cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R 7290\|- 1 cot(x) (%e ) + 1663\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R 129\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +--R +---+ 2 +---+ x\|- 1 +--R (2\|- 1 cot(x) - \|- 1 )(%e ) +--R + +--R +---+ 16 +--R +---+ 2 +---+ x\|- 1 +--R (54\|- 1 cot(x) - 27\|- 1 )(%e ) +--R + +--R +---+ 14 +--R +---+ 2 +---+ x\|- 1 +--R (604\|- 1 cot(x) - 302\|- 1 )(%e ) +--R + +--R +---+ 12 +--R +---+ 2 +---+ x\|- 1 +--R (3612\|- 1 cot(x) - 1806\|- 1 )(%e ) +--R + +--R +---+ 10 +--R +---+ 2 +---+ x\|- 1 +--R (12432\|- 1 cot(x) - 6216\|- 1 )(%e ) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (24696\|- 1 cot(x) - 12348\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (26964\|- 1 cot(x) - 13482\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (14580\|- 1 cot(x) - 7290\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (3326\|- 1 cot(x) - 1663\|- 1 )(%e ) + 258\|- 1 cot(x) +--R + +--R +---+ +--R - 129\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R - cot(x) (%e ) - 21cot(x) (%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R - 182cot(x) (%e ) - 850cot(x) (%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R - 2352cot(x) (%e ) - 4004cot(x) (%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R - 4210cot(x) (%e ) - 2646cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R - 903cot(x) (%e ) - 127cot(x) +--R * +--R 6 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (- 4cot(x) + 1)(%e ) + (- 84cot(x) + 21)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (- 728cot(x) + 182)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 3400cot(x) + 850)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (- 9408cot(x) + 2352)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 16016cot(x) + 4004)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (- 16840cot(x) + 4210)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 10584cot(x) + 2646)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (- 3612cot(x) + 903)(%e ) - 508cot(x) + 127 +--R * +--R 4 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R x\|- 1 x\|- 1 +--R 2cot(x)(%e ) + 42cot(x)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R x\|- 1 x\|- 1 +--R 364cot(x)(%e ) + 1700cot(x)(%e ) +--R + +--R +---+ 10 +---+ 8 +--R x\|- 1 x\|- 1 +--R 4704cot(x)(%e ) + 8008cot(x)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 +--R 8420cot(x)(%e ) + 5292cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 1806cot(x)(%e ) + 254cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R - 8cot(x) (%e ) - 168cot(x) (%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R - 1456cot(x) (%e ) - 6800cot(x) (%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R - 18816cot(x) (%e ) - 32032cot(x) (%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R - 33680cot(x) (%e ) - 21168cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R - 7224cot(x) (%e ) - 1016cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R x\|- 1 x\|- 1 +--R 2cot(x)(%e ) + 42cot(x)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R x\|- 1 x\|- 1 +--R 364cot(x)(%e ) + 1700cot(x)(%e ) +--R + +--R +---+ 10 +---+ 8 +--R x\|- 1 x\|- 1 +--R 4704cot(x)(%e ) + 8008cot(x)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 +--R 8420cot(x)(%e ) + 5292cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 1806cot(x)(%e ) + 254cot(x) +--R * +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (- 8cot(x) - 2)(%e ) + (- 168cot(x) - 42)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (- 1456cot(x) - 364)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 6800cot(x) - 1700)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (- 18816cot(x) - 4704)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 32032cot(x) - 8008)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (- 33680cot(x) - 8420)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 21168cot(x) - 5292)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (- 7224cot(x) - 1806)(%e ) - 1016cot(x) - 254 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 20 +---+ 18 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - \|- 1 cot(x) (%e ) - 30\|- 1 cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - 379\|- 1 cot(x) (%e ) - 2616\|- 1 cot(x) (%e ) +--R + +--R +---+ 12 +--R +---+ 2 x\|- 1 +--R - 10706\|- 1 cot(x) (%e ) +--R + +--R +---+ 10 +--R +---+ 2 x\|- 1 +--R - 26388\|- 1 cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - 38118\|- 1 cot(x) (%e ) - 30168\|- 1 cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - 11789\|- 1 cot(x) (%e ) - 2046\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R - 127\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +--R +---+ 2 +---+ x\|- 1 +--R (- 2\|- 1 cot(x) + \|- 1 )(%e ) +--R + +--R +---+ 18 +--R +---+ 2 +---+ x\|- 1 +--R (- 60\|- 1 cot(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 16 +--R +---+ 2 +---+ x\|- 1 +--R (- 758\|- 1 cot(x) + 379\|- 1 )(%e ) +--R + +--R +---+ 14 +--R +---+ 2 +---+ x\|- 1 +--R (- 5232\|- 1 cot(x) + 2616\|- 1 )(%e ) +--R + +--R +---+ 12 +--R +---+ 2 +---+ x\|- 1 +--R (- 21412\|- 1 cot(x) + 10706\|- 1 )(%e ) +--R + +--R +---+ 10 +--R +---+ 2 +---+ x\|- 1 +--R (- 52776\|- 1 cot(x) + 26388\|- 1 )(%e ) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (- 76236\|- 1 cot(x) + 38118\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (- 60336\|- 1 cot(x) + 30168\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (- 23578\|- 1 cot(x) + 11789\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (- 4092\|- 1 cot(x) + 2046\|- 1 )(%e ) - 254\|- 1 cot(x) +--R + +--R +---+ +--R 127\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R cot(x) (%e ) + 24cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R 241cot(x) (%e ) + 1324cot(x) (%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R 4382cot(x) (%e ) + 9100cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R 11998cot(x) (%e ) + 9908cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R 4881cot(x) (%e ) + 1276cot(x) (%e ) + 129cot(x) +--R * +--R 6 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (4cot(x) - 1)(%e ) + (96cot(x) - 24)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R (964cot(x) - 241)(%e ) + (5296cot(x) - 1324)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (17528cot(x) - 4382)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (36400cot(x) - 9100)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (47992cot(x) - 11998)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (39632cot(x) - 9908)(%e ) + (19524cot(x) - 4881)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (5104cot(x) - 1276)(%e ) + 516cot(x) - 129 +--R * +--R 4 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R x\|- 1 x\|- 1 +--R - 2cot(x)(%e ) - 48cot(x)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R x\|- 1 x\|- 1 +--R - 482cot(x)(%e ) - 2648cot(x)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R x\|- 1 x\|- 1 +--R - 8764cot(x)(%e ) - 18200cot(x)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R x\|- 1 x\|- 1 +--R - 23996cot(x)(%e ) - 19816cot(x)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R - 9762cot(x)(%e ) - 2552cot(x)(%e ) - 258cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R 8cot(x) (%e ) + 192cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R 1928cot(x) (%e ) + 10592cot(x) (%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R 35056cot(x) (%e ) + 72800cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R 95984cot(x) (%e ) + 79264cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R 39048cot(x) (%e ) + 10208cot(x) (%e ) + 1032cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R x\|- 1 x\|- 1 +--R - 2cot(x)(%e ) - 48cot(x)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R x\|- 1 x\|- 1 +--R - 482cot(x)(%e ) - 2648cot(x)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R x\|- 1 x\|- 1 +--R - 8764cot(x)(%e ) - 18200cot(x)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R x\|- 1 x\|- 1 +--R - 23996cot(x)(%e ) - 19816cot(x)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R - 9762cot(x)(%e ) - 2552cot(x)(%e ) - 258cot(x) +--R * +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (8cot(x) + 2)(%e ) + (192cot(x) + 48)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R (1928cot(x) + 482)(%e ) + (10592cot(x) + 2648)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R (35056cot(x) + 8764)(%e ) + (72800cot(x) + 18200)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (95984cot(x) + 23996)(%e ) + (79264cot(x) + 19816)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (39048cot(x) + 9762)(%e ) + (10208cot(x) + 2552)(%e ) +--R + +--R 2 +--R 1032cot(x) + 258 +--R / +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R cot(x) (%e ) + 21cot(x) (%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R 182cot(x) (%e ) + 850cot(x) (%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R 2352cot(x) (%e ) + 4004cot(x) (%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R 4210cot(x) (%e ) + 2646cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R 903cot(x) (%e ) + 127cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) - 1)(%e ) + (42cot(x) - 21)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R (364cot(x) - 182)(%e ) + (1700cot(x) - 850)(%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R (4704cot(x) - 2352)(%e ) + (8008cot(x) - 4004)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (8420cot(x) - 4210)(%e ) + (5292cot(x) - 2646)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (1806cot(x) - 903)(%e ) + 254cot(x) - 127 +--R * +--R +--------------------------------+ +--R +-------------+ | +---+ 4 +---+ 2 +--R | 2 | x\|- 1 x\|- 1 +--R \|- tan(x) - 2 \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R - cot(x) (%e ) - 24cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R - 241cot(x) (%e ) - 1324cot(x) (%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R - 4382cot(x) (%e ) - 9100cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R - 11998cot(x) (%e ) - 9908cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R - 4881cot(x) (%e ) - 1276cot(x) (%e ) - 129cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) + 1)(%e ) + (- 48cot(x) + 24)(%e ) +--R + +--R +---+ 16 +--R 2 x\|- 1 +--R (- 482cot(x) + 241)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (- 2648cot(x) + 1324)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 8764cot(x) + 4382)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (- 18200cot(x) + 9100)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 23996cot(x) + 11998)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (- 19816cot(x) + 9908)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 9762cot(x) + 4881)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (- 2552cot(x) + 1276)(%e ) - 258cot(x) + 129 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression Integer +--E 138 + +--S 139 of 528 +t0326:= (a+b*sec(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (137) (b sec(x) + a)\|b sec(x) + a +--R Type: Expression Integer +--E 139 + +--S 140 of 528 +r0326:= a^(3/2)*atan(a^(1/2)*tan(x)/(a+b*sec(x)^2)^(1/2))+3/2*a*b^(1/2)*atanh(cot(x)*(a+b*sec(x)^2)^(1/2)/b^(1/2))+1/2*b^(3/2)*atanh(cot(x)*(a+b*sec(x)^2)^(1/2)/b^(1/2))+1/2*b*(a+b*sec(x)^2)^(1/2)*tan(x) +--R +--R +--R (138) +--R +-------------+ +--R | 2 +-+ +--R +-+ cot(x)\|b sec(x) + a +-+ tan(x)\|a +--R (b + 3a)\|b atanh(----------------------) + 2a\|a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b sec(x) + a +--R + +--R +-------------+ +--R | 2 +--R b tan(x)\|b sec(x) + a +--R / +--R 2 +--R Type: Expression Integer +--E 140 + +--S 141 of 528 +a0326:= integrate(t0326,x) +--R +--R +--R (139) +--R [ +--R 2 6 2 5 +--R (4a b + 12a )cos(x) + (4a b + 12a )cos(x) +--R + +--R 2 4 2 3 +--R (2b + 6a b)cos(x) + (2b + 6a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a b)cos(x) +--R + +--R 3 2 2 +--R (- b - 3a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 +--R (- 96a b + 224a b)cos(x) +--R + +--R 2 2 3 7 +--R (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) ) +--R * +--R sin(x) +--R atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R , +--R +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +---+ +-+ | 4a cos(x) + 4b +--R \|- b \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) - 2b +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) ) +--R * +--R sin(x) +--R atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 141 + +--S 142 of 528 +m0326a:= a0326.1-r0326 +--R +--R +--R (140) +--R 2 6 2 5 2 4 +--R (4a b + 12a )cos(x) + (4a b + 12a )cos(x) + (2b + 6a b)cos(x) +--R + +--R 2 3 +--R (2b + 6a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a b)cos(x) +--R + +--R 3 2 2 +--R (- b - 3a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 2 2 3 7 +--R (- 96a b + 224a b)cos(x) + (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R cot(x)\|b sec(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 16a cos(x) - 16a cos(x) - 8a b cos(x) - 8a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (32a cos(x) + 32a b cos(x) + 4a b cos(x) )\|a +--R * +--R +-+ +--R tan(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 5 2 4 2 3 +-+ +--R (- 8a b cos(x) - 8a b cos(x) - 4b cos(x) - 4b cos(x) )tan(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 3 2 +--R (16a b cos(x) + 16a b cos(x) + 2b cos(x) )tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 3 6 3 5 2 4 2 3 sin(x) +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) )atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R Type: Expression Integer +--E 142 + +--S 143 of 528 +--d0326a:= D(m0326a,x) +--E 143 + +--S 144 of 528 +m0326b:= a0326.2-r0326 +--R +--R +--R (141) +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R cot(x)\|b sec(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +---+ +-+ | 4a cos(x) + 4b +--R \|- b \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) - 2b +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 16a cos(x) - 16a cos(x) - 8a b cos(x) - 8a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (32a cos(x) + 32a b cos(x) + 4a b cos(x) )\|a +--R * +--R +-+ +--R tan(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 5 2 4 2 3 +-+ +--R (- 8a b cos(x) - 8a b cos(x) - 4b cos(x) - 4b cos(x) )tan(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 3 2 +--R (16a b cos(x) + 16a b cos(x) + 2b cos(x) )tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 3 6 3 5 2 4 2 3 sin(x) +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) )atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R Type: Expression Integer +--E 144 + +--S 145 of 528 +--d0326b:= D(m0326b,x) +--E 145 + +--S 146 of 528 +t0327:= x/sec(x)^(3/2)-1/3*x*sec(x)^(1/2) +--R +--R +--R 2 +--R - x sec(x) + 3x +--R (142) ---------------- +--R +------+ +--R 3sec(x)\|sec(x) +--R Type: Expression Integer +--E 146 + +--S 147 of 528 +r0327:= 2/9*(2*cos(x)+3*x*sin(x))/(1/cos(x))^(1/2) +--R +--R +--R 6x sin(x) + 4cos(x) +--R (143) ------------------- +--R +------+ +--R | 1 +--R 9 |------ +--R \|cos(x) +--R Type: Expression Integer +--E 147 + +--S 148 of 528 +a0327:= integrate(t0327,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 148 + +--S 149 of 528 +m0327:= a0327-r0327 +--R +--R +--R +------+ +--R | 1 +--R 9a0327 |------ - 6x sin(x) - 4cos(x) +--R \|cos(x) +--R (144) ------------------------------------- +--R +------+ +--R | 1 +--R 9 |------ +--R \|cos(x) +--R Type: Expression Integer +--E 149 + +--S 150 of 528 +d0327:= D(m0327,x) +--R +--R +--R 2 2 +--R x sin(x) - 2x cos(x) +--R (145) ---------------------- +--R +------+ +--R | 1 +--R 3cos(x) |------ +--R \|cos(x) +--R Type: Expression Integer +--E 150 + +--S 151 of 528 +t0328:= x/sec(x)^(5/2)-3/5*x/sec(x)^(1/2) +--R +--R +--R 2 +--R - 3x sec(x) + 5x +--R (146) ----------------- +--R 2 +------+ +--R 5sec(x) \|sec(x) +--R Type: Expression Integer +--E 151 + +--S 152 of 528 +r0328:= 4/25/sec(x)^(5/2)+2/5*x*sin(x)/sec(x)^(3/2) +--R +--R +--R 10x sec(x)sin(x) + 4 +--R (147) -------------------- +--R 2 +------+ +--R 25sec(x) \|sec(x) +--R Type: Expression Integer +--E 152 + +--S 153 of 528 +a0328:= integrate(t0328,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 153 + +--S 154 of 528 +m0328:= a0328-r0328 +--R +--R +--R 2 +------+ +--R 25a0328 sec(x) \|sec(x) - 10x sec(x)sin(x) - 4 +--R (148) ----------------------------------------------- +--R 2 +------+ +--R 25sec(x) \|sec(x) +--R Type: Expression Integer +--E 154 + +--S 155 of 528 +d0328:= D(m0328,x) +--R +--R +--R (3x sec(x)sin(x) + 2)tan(x) - 2sec(x)sin(x) - 2x cos(x)sec(x) +--R (149) ------------------------------------------------------------- +--R 2 +------+ +--R 5sec(x) \|sec(x) +--R Type: Expression Integer +--E 155 + +--S 156 of 528 +t0329:= x/sec(x)^(7/2)-5/21*x*sec(x)^(1/2) +--R +--R +--R 4 +--R - 5x sec(x) + 21x +--R (150) ------------------ +--R 3 +------+ +--R 21sec(x) \|sec(x) +--R Type: Expression Integer +--E 156 + +--S 157 of 528 +r0329:= 2/441*(18*cos(x)^3+70*cos(x)+63*x*sin(x)*cos(x)^2+105*x*sin(x))/(1/cos(x))^(1/2) +--R +--R +--R 2 3 +--R (126x cos(x) + 210x)sin(x) + 36cos(x) + 140cos(x) +--R (151) --------------------------------------------------- +--R +------+ +--R | 1 +--R 441 |------ +--R \|cos(x) +--R Type: Expression Integer +--E 157 + +--S 158 of 528 +a0329:= integrate(t0329,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 158 + +--S 159 of 528 +m0329:= a0329-r0329 +--R +--R +--R (152) +--R +------+ +--R | 1 2 3 +--R 441a0329 |------ + (- 126x cos(x) - 210x)sin(x) - 36cos(x) - 140cos(x) +--R \|cos(x) +--R ------------------------------------------------------------------------- +--R +------+ +--R | 1 +--R 441 |------ +--R \|cos(x) +--R Type: Expression Integer +--E 159 + +--S 160 of 528 +d0329:= D(m0329,x) +--R +--R +--R 2 2 4 2 +--R (15x cos(x) + 5x)sin(x) - 6x cos(x) - 10x cos(x) +--R (153) ---------------------------------------------------- +--R +------+ +--R | 1 +--R 21cos(x) |------ +--R \|cos(x) +--R Type: Expression Integer +--E 160 + +--S 161 of 528 +t0330:= x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x sec(x) + 3x +--R (154) ----------------- +--R +------+ +--R 3sec(x)\|sec(x) +--R Type: Expression Integer +--E 161 + +--S 162 of 528 +r0330:= 2/27*(12*x*cos(x)^(3/2)-8*EllipticF(1/2*x,2)-8*cos(x)^(1/2)*sin(x)+9*x^2*sin(x)*cos(x)^(1/2))/cos(x)^(1/2)/(1/cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial Fraction Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 528 +a0330:= integrate(t0330,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 163 + +--S 164 of 528 +m0330:= a0330-r0330 +--R +--R +--R (155) - r0330 + a0330 +--R Type: Polynomial Integer +--E 164 + +--S 165 of 528 +d0330:= D(m0330,x) +--R +--R +--R (156) 0 +--R Type: Polynomial Integer +--E 165 + +--S 166 of 528 +t0331:= sec(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +--R sec(\|x ) +--R (157) --------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 166 + +--S 167 of 528 +r0331:= 2*atanh(sin(x^(1/2))) +--R +--R +--R +-+ +--R (158) 2atanh(sin(\|x )) +--R Type: Expression Integer +--E 167 + +--S 168 of 528 +a0331:= integrate(t0331,x) +--R +--R +--R +-+ +-+ +--R (159) log(sin(\|x ) + 1) - log(sin(\|x ) - 1) +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 528 +m0331:= a0331-r0331 +--R +--R +--R +-+ +-+ +-+ +--R (160) log(sin(\|x ) + 1) - log(sin(\|x ) - 1) - 2atanh(sin(\|x )) +--R Type: Expression Integer +--E 169 + +--S 170 of 528 +d0331:= D(m0331,x) +--R +--R +--R (161) 0 +--R Type: Expression Integer +--E 170 + +--S 171 of 528 +t0332:= csc(a+b*x) +--R +--R +--R (162) csc(b x + a) +--R Type: Expression Integer +--E 171 + +--S 172 of 528 +r0332:= -atanh(cos(a+b*x))/b +--R +--R +--R atanh(cos(b x + a)) +--R (163) - ------------------- +--R b +--R Type: Expression Integer +--E 172 + +--S 173 of 528 +a0332:= integrate(t0332,x) +--R +--R +--R sin(b x + a) +--R log(----------------) +--R cos(b x + a) + 1 +--R (164) --------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 173 + +--S 174 of 528 +m0332:= a0332-r0332 +--R +--R +--R sin(b x + a) +--R log(----------------) + atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R (165) ------------------------------------------- +--R b +--R Type: Expression Integer +--E 174 + +--S 175 of 528 +d0332:= D(m0332,x) +--R +--R +--R 2 3 +--R cos(b x + a)sin(b x + a) + cos(b x + a) - cos(b x + a) +--R (166) -------------------------------------------------------- +--R 2 +--R (cos(b x + a) - 1)sin(b x + a) +--R Type: Expression Integer +--E 175 + +--S 176 of 528 +t0333:= csc(a+b*x)^3 +--R +--R +--R 3 +--R (167) csc(b x + a) +--R Type: Expression Integer +--E 176 + +--S 177 of 528 +r0333:= -1/2*atanh(cos(a+b*x))/b-1/2*cot(a+b*x)*csc(a+b*x)/b +--R +--R +--R - atanh(cos(b x + a)) - cot(b x + a)csc(b x + a) +--R (168) ------------------------------------------------ +--R 2b +--R Type: Expression Integer +--E 177 + +--S 178 of 528 +a0333:= integrate(t0333,x) +--R +--R +--R 2 sin(b x + a) +--R (cos(b x + a) - 1)log(----------------) + cos(b x + a) +--R cos(b x + a) + 1 +--R (169) ------------------------------------------------------- +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Union(Expression Integer,...) +--E 178 + +--S 179 of 528 +m0333:= a0333-r0333 +--R +--R +--R (170) +--R 2 sin(b x + a) +--R (cos(b x + a) - 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (cos(b x + a) - 1)atanh(cos(b x + a)) +--R + +--R 2 +--R (cos(b x + a) - 1)cot(b x + a)csc(b x + a) + cos(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Expression Integer +--E 179 + +--S 180 of 528 +d0333:= D(m0333,x) +--R +--R +--R (171) +--R 3 2 2 +--R (cos(b x + a) + cos(b x + a) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 4 2 2 4 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2)cot(b x + a) - cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) - 1 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 5 3 +--R cos(b x + a) - 2cos(b x + a) + cos(b x + a) +--R / +--R 4 2 +--R (2cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R Type: Expression Integer +--E 180 + +--S 181 of 528 +t0334:= csc(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (172) \|csc(b x + a) +--R Type: Expression Integer +--E 181 + +--S 182 of 528 +r0334:= 2*csc(a+b*x)^(1/2)*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 528 +a0334:= integrate(t0334,x) +--R +--R +--R x +--R ++ +-------------+ +--R (173) | \|csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 183 + +--S 184 of 528 +m0334:= a0334-r0334 +--R +--R +--R x +--R ++ +-------------+ +--R (174) | \|csc(%R b + a) d%R - r0334 +--R ++ +--R Type: Expression Integer +--E 184 + +--S 185 of 528 +d0334:= D(m0334,x) +--R +--R +--R +------------+ +--R (175) \|csc(b x + a) +--R Type: Expression Integer +--E 185 + +--S 186 of 528 +t0335:= csc(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (176) csc(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 186 + +--S 187 of 528 +r0335:= -2*(1/sin(a+b*x))^(1/2)*(cos(a+b*x)+EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 528 +a0335:= integrate(t0335,x) +--R +--R +--R x +--R ++ +-------------+ +--R (177) | csc(%R b + a)\|csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 188 + +--S 189 of 528 +m0335:= a0335-r0335 +--R +--R +--R x +--R ++ +-------------+ +--R (178) | csc(%R b + a)\|csc(%R b + a) d%R - r0335 +--R ++ +--R Type: Expression Integer +--E 189 + +--S 190 of 528 +d0335:= D(m0335,x) +--R +--R +--R +------------+ +--R (179) csc(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 190 + +--S 191 of 528 +t0336:= csc(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (180) csc(b x + a) \|csc(b x + a) +--R Type: Expression Integer +--E 191 + +--S 192 of 528 +r0336:= 2/3*(1/sin(a+b*x))^(1/2)*(-cos(a+b*x)+EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2))/b/sin(a+b*x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 528 +a0336:= integrate(t0336,x) +--R +--R +--R x +--R ++ 2 +-------------+ +--R (181) | csc(%R b + a) \|csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 193 + +--S 194 of 528 +m0336:= a0336-r0336 +--R +--R +--R x +--R ++ 2 +-------------+ +--R (182) | csc(%R b + a) \|csc(%R b + a) d%R - r0336 +--R ++ +--R Type: Expression Integer +--E 194 + +--S 195 of 528 +d0336:= D(m0336,x) +--R +--R +--R 2 +------------+ +--R (183) csc(b x + a) \|csc(b x + a) +--R Type: Expression Integer +--E 195 + +--S 196 of 528 +t0337:= 1/csc(a+b*x)^(1/2) +--R +--R +--R 1 +--R (184) --------------- +--R +------------+ +--R \|csc(b x + a) +--R Type: Expression Integer +--E 196 + +--S 197 of 528 +r0337:= 2*csc(a+b*x)^(1/2)*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 528 +a0337:= integrate(t0337,x) +--R +--R +--R x +--R ++ 1 +--R (185) | ---------------- d%R +--R ++ +-------------+ +--R \|csc(%R b + a) +--R Type: Union(Expression Integer,...) +--E 198 + +--S 199 of 528 +m0337:= a0337-r0337 +--R +--R +--R x +--R ++ 1 +--R (186) | ---------------- d%R - r0337 +--R ++ +-------------+ +--R \|csc(%R b + a) +--R Type: Expression Integer +--E 199 + +--S 200 of 528 +d0337:= D(m0337,x) +--R +--R +--R 1 +--R (187) --------------- +--R +------------+ +--R \|csc(b x + a) +--R Type: Expression Integer +--E 200 + +--S 201 of 528 +t0338:= 1/csc(a+b*x)^(3/2) +--R +--R +--R 1 +--R (188) --------------------------- +--R +------------+ +--R csc(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 201 + +--S 202 of 528 +r0338:= 2/3*(-cos(a+b*x)*sin(a+b*x)^(1/2)+EllipticF(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/(1/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 202 + +--S 203 of 528 +a0338:= integrate(t0338,x) +--R +--R +--R x +--R ++ 1 +--R (189) | ----------------------------- d%R +--R ++ +-------------+ +--R csc(%R b + a)\|csc(%R b + a) +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 528 +m0338:= a0338-r0338 +--R +--R +--R x +--R ++ 1 +--R (190) | ----------------------------- d%R - r0338 +--R ++ +-------------+ +--R csc(%R b + a)\|csc(%R b + a) +--R Type: Expression Integer +--E 204 + +--S 205 of 528 +d0338:= D(m0338,x) +--R +--R +--R 1 +--R (191) --------------------------- +--R +------------+ +--R csc(b x + a)\|csc(b x + a) +--R Type: Expression Integer +--E 205 + +--S 206 of 528 +t0339:= 1/csc(a+b*x)^(5/2) +--R +--R +--R 1 +--R (192) ---------------------------- +--R 2 +------------+ +--R csc(b x + a) \|csc(b x + a) +--R Type: Expression Integer +--E 206 + +--S 207 of 528 +r0339:= 2/5*(-cos(a+b*x)*sin(a+b*x)^(3/2)+3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/(1/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 528 +a0339:= integrate(t0339,x) +--R +--R +--R x +--R ++ 1 +--R (193) | ------------------------------ d%R +--R ++ 2 +-------------+ +--R csc(%R b + a) \|csc(%R b + a) +--R Type: Union(Expression Integer,...) +--E 208 + +--S 209 of 528 +m0339:= a0339-r0339 +--R +--R +--R x +--R ++ 1 +--R (194) | ------------------------------ d%R - r0339 +--R ++ 2 +-------------+ +--R csc(%R b + a) \|csc(%R b + a) +--R Type: Expression Integer +--E 209 + +--S 210 of 528 +d0339:= D(m0339,x) +--R +--R +--R 1 +--R (195) ---------------------------- +--R 2 +------------+ +--R csc(b x + a) \|csc(b x + a) +--R Type: Expression Integer +--E 210 + +--S 211 of 528 +t0340:= (c*csc(a+b*x))^(1/2) +--R +--R +--R +--------------+ +--R (196) \|c csc(b x + a) +--R Type: Expression Integer +--E 211 + +--S 212 of 528 +r0340:= 2*(c*csc(a+b*x))^(1/2)*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 528 +a0340:= integrate(t0340,x) +--R +--R +--R x +--R ++ +---------------+ +--R (197) | \|c csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 213 + +--S 214 of 528 +m0340:= a0340-r0340 +--R +--R +--R x +--R ++ +---------------+ +--R (198) | \|c csc(%R b + a) d%R - r0340 +--R ++ +--R Type: Expression Integer +--E 214 + +--S 215 of 528 +d0340:= D(m0340,x) +--R +--R +--R +--------------+ +--R (199) \|c csc(b x + a) +--R Type: Expression Integer +--E 215 + +--S 216 of 528 +t0341:= (c*csc(a+b*x))^(3/2) +--R +--R +--R +--------------+ +--R (200) c csc(b x + a)\|c csc(b x + a) +--R Type: Expression Integer +--E 216 + +--S 217 of 528 +r0341:= -2*c^2*(cos(a+b*x)+EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2))/sin(a+b*x)/(c/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 217 + +--S 218 of 528 +a0341:= integrate(t0341,x) +--R +--R +--R x +--R ++ +---------------+ +--R (201) | c csc(%R b + a)\|c csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 218 + +--S 219 of 528 +m0341:= a0341-r0341 +--R +--R +--R x +--R ++ +---------------+ +--R (202) | c csc(%R b + a)\|c csc(%R b + a) d%R - r0341 +--R ++ +--R Type: Expression Integer +--E 219 + +--S 220 of 528 +d0341:= D(m0341,x) +--R +--R +--R +--------------+ +--R (203) c csc(b x + a)\|c csc(b x + a) +--R Type: Expression Integer +--E 220 + +--S 221 of 528 +t0342:= (c*csc(a+b*x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (204) c csc(b x + a) \|c csc(b x + a) +--R Type: Expression Integer +--E 221 + +--S 222 of 528 +r0342:= 2/3*c^2*(c/sin(a+b*x))^(1/2)*(-cos(a+b*x)+EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2))/b/sin(a+b*x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 528 +a0342:= integrate(t0342,x) +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (205) | c csc(%R b + a) \|c csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 528 +m0342:= a0342-r0342 +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (206) | c csc(%R b + a) \|c csc(%R b + a) d%R - r0342 +--R ++ +--R Type: Expression Integer +--E 224 + +--S 225 of 528 +d0342:= D(m0342,x) +--R +--R +--R 2 2 +--------------+ +--R (207) c csc(b x + a) \|c csc(b x + a) +--R Type: Expression Integer +--E 225 + +--S 226 of 528 +t0343:= 1/(c*csc(a+b*x))^(1/2) +--R +--R +--R 1 +--R (208) ----------------- +--R +--------------+ +--R \|c csc(b x + a) +--R Type: Expression Integer +--E 226 + +--S 227 of 528 +r0343:= 2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b/(c*csc(a+b*x))^(1/2)/sin(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 528 +a0343:= integrate(t0343,x) +--R +--R +--R x +--R ++ 1 +--R (209) | ------------------ d%R +--R ++ +---------------+ +--R \|c csc(%R b + a) +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 528 +m0343:= a0343-r0343 +--R +--R +--R x +--R ++ 1 +--R (210) | ------------------ d%R - r0343 +--R ++ +---------------+ +--R \|c csc(%R b + a) +--R Type: Expression Integer +--E 229 + +--S 230 of 528 +d0343:= D(m0343,x) +--R +--R +--R 1 +--R (211) ----------------- +--R +--------------+ +--R \|c csc(b x + a) +--R Type: Expression Integer +--E 230 + +--S 231 of 528 +t0344:= 1/(c*csc(a+b*x))^(3/2) +--R +--R +--R 1 +--R (212) ------------------------------- +--R +--------------+ +--R c csc(b x + a)\|c csc(b x + a) +--R Type: Expression Integer +--E 231 + +--S 232 of 528 +r0344:= 2/3/c*(-cos(a+b*x)*sin(a+b*x)^(1/2)+EllipticF(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/(c/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 528 +a0344:= integrate(t0344,x) +--R +--R +--R x +--R ++ 1 +--R (213) | --------------------------------- d%R +--R ++ +---------------+ +--R c csc(%R b + a)\|c csc(%R b + a) +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 528 +m0344:= a0344-r0344 +--R +--R +--R x +--R ++ 1 +--R (214) | --------------------------------- d%R - r0344 +--R ++ +---------------+ +--R c csc(%R b + a)\|c csc(%R b + a) +--R Type: Expression Integer +--E 234 + +--S 235 of 528 +d0344:= D(m0344,x) +--R +--R +--R 1 +--R (215) ------------------------------- +--R +--------------+ +--R c csc(b x + a)\|c csc(b x + a) +--R Type: Expression Integer +--E 235 + +--S 236 of 528 +t0345:= 1/(c*csc(a+b*x))^(5/2) +--R +--R +--R 1 +--R (216) -------------------------------- +--R 2 2 +--------------+ +--R c csc(b x + a) \|c csc(b x + a) +--R Type: Expression Integer +--E 236 + +--S 237 of 528 +r0345:= 2/5*(-cos(a+b*x)*sin(a+b*x)^(3/2)+3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/(c/sin(a+b*x))^(1/2)/b/c^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 528 +a0345:= integrate(t0345,x) +--R +--R +--R x +--R ++ 1 +--R (217) | ---------------------------------- d%R +--R ++ 2 2 +---------------+ +--R c csc(%R b + a) \|c csc(%R b + a) +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 528 +m0345:= a0345-r0345 +--R +--R +--R x +--R ++ 1 +--R (218) | ---------------------------------- d%R - r0345 +--R ++ 2 2 +---------------+ +--R c csc(%R b + a) \|c csc(%R b + a) +--R Type: Expression Integer +--E 239 + +--S 240 of 528 +d0345:= D(m0345,x) +--R +--R +--R 1 +--R (219) -------------------------------- +--R 2 2 +--------------+ +--R c csc(b x + a) \|c csc(b x + a) +--R Type: Expression Integer +--E 240 + +--S 241 of 528 +t0346:= x*csc(a+b*x) +--R +--R +--R (220) x csc(b x + a) +--R Type: Expression Integer +--E 241 + +--S 242 of 528 +r0346:= -(2*x*atanh(exp(%i*(a+b*x)))*b-%i*polylog(2,-exp(%i*(a+b*x)))+%i*polylog(2,exp(%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 528 +a0346:= integrate(t0346,x) +--R +--R +--R x +--R ++ +--R (221) | %R csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 528 +m0346:= a0346-r0346 +--R +--R +--R x +--R ++ +--R (222) | %R csc(%R b + a)d%R - r0346 +--R ++ +--R Type: Expression Integer +--E 244 + +--S 245 of 528 +d0346:= D(m0346,x) +--R +--R +--R (223) x csc(b x + a) +--R Type: Expression Integer +--E 245 + +--S 246 of 528 +t0347:= x^2*csc(a+b*x) +--R +--R +--R 2 +--R (224) x csc(b x + a) +--R Type: Expression Integer +--E 246 + +--S 247 of 528 +r0347:= -2*(x^2*atanh(exp(%i*(a+b*x)))*b^2-%i*polylog(2,-exp(%i*(a+b*x)))*x*b+%i*polylog(2,exp(%i*(a+b*x)))*x*b+polylog(3,-exp(%i*(a+b*x)))-polylog(3,exp(%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 528 +a0347:= integrate(t0347,x) +--R +--R +--R x +--R ++ 2 +--R (225) | %R csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 248 + +--S 249 of 528 +m0347:= a0347-r0347 +--R +--R +--R x +--R ++ 2 +--R (226) | %R csc(%R b + a)d%R - r0347 +--R ++ +--R Type: Expression Integer +--E 249 + +--S 250 of 528 +d0347:= D(m0347,x) +--R +--R +--R 2 +--R (227) x csc(b x + a) +--R Type: Expression Integer +--E 250 + +--S 251 of 528 +t0348:= x^3*csc(a+b*x) +--R +--R +--R 3 +--R (228) x csc(b x + a) +--R Type: Expression Integer +--E 251 + +--S 252 of 528 +r0348:= -(2*x^3*atanh(exp(%i*(a+b*x)))*b^3-3*%i*polylog(2,-exp(%i*(a+b*x)))*x^2*b^2+3*%i*polylog(2,exp(%i*(a+b*x)))*x^2*b^2+6*polylog(3,-exp(%i*(a+b*x)))*x*b-6*polylog(3,exp(%i*(a+b*x)))*x*b+6*%i*polylog(4,-exp(%i*(a+b*x)))-6*%i*polylog(4,exp(%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 528 +a0348:= integrate(t0348,x) +--R +--R +--R x +--R ++ 3 +--R (229) | %R csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 253 + +--S 254 of 528 +m0348:= a0348-r0348 +--R +--R +--R x +--R ++ 3 +--R (230) | %R csc(%R b + a)d%R - r0348 +--R ++ +--R Type: Expression Integer +--E 254 + +--S 255 of 528 +d0348:= D(m0348,x) +--R +--R +--R 3 +--R (231) x csc(b x + a) +--R Type: Expression Integer +--E 255 + +--S 256 of 528 +t0349:= x^2*csc(a+b*x)^2 +--R +--R +--R 2 2 +--R (232) x csc(b x + a) +--R Type: Expression Integer +--E 256 + +--S 257 of 528 +r0349:= -(%i*x^2*b^2+x^2*cot(a+b*x)*b^2-2*x*log(1-exp(2*%i*(a+b*x)))*b+%i*polylog(2,exp(2*%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 257 + +--S 258 of 528 +a0349:= integrate(t0349,x) +--R +--R +--R x +--R ++ 2 2 +--R (233) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 258 + +--S 259 of 528 +m0349:= a0349-r0349 +--R +--R +--R x +--R ++ 2 2 +--R (234) | %R csc(%R b + a) d%R - r0349 +--R ++ +--R Type: Expression Integer +--E 259 + +--S 260 of 528 +d0349:= D(m0349,x) +--R +--R +--R 2 2 +--R (235) x csc(b x + a) +--R Type: Expression Integer +--E 260 + +--S 261 of 528 +t0350:= x^3*csc(a+b*x)^2 +--R +--R +--R 3 2 +--R (236) x csc(b x + a) +--R Type: Expression Integer +--E 261 + +--S 262 of 528 +r0350:= -1/2*(2*%i*x^3*b^3+2*x^3*cot(a+b*x)*b^3-6*x^2*log(1-exp(2*%i*(a+b*x)))*b^2+6*%i*x*polylog(2,exp(2*%i*(a+b*x)))*b-3*polylog(3,exp(2*%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 528 +a0350:= integrate(t0350,x) +--R +--R +--R x +--R ++ 3 2 +--R (237) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 263 + +--S 264 of 528 +m0350:= a0350-r0350 +--R +--R +--R x +--R ++ 3 2 +--R (238) | %R csc(%R b + a) d%R - r0350 +--R ++ +--R Type: Expression Integer +--E 264 + +--S 265 of 528 +d0350:= D(m0350,x) +--R +--R +--R 3 2 +--R (239) x csc(b x + a) +--R Type: Expression Integer +--E 265 + +--S 266 of 528 +t0351:= x*csc(a+b*x)^3 +--R +--R +--R 3 +--R (240) x csc(b x + a) +--R Type: Expression Integer +--E 266 + +--S 267 of 528 +r0351:= -x*atanh(exp(1)^(%i*b*x+%i*a))/b-1/2*csc(a+b*x)/b^2-1/2*x*cot(a+b*x)*csc(a+b*x)/b+1/2*%i*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-1/2*%i*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 528 +a0351:= integrate(t0351,x) +--R +--R +--R x +--R ++ 3 +--R (241) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 268 + +--S 269 of 528 +m0351:= a0351-r0351 +--R +--R +--R x +--R ++ 3 +--R (242) | %R csc(%R b + a) d%R - r0351 +--R ++ +--R Type: Expression Integer +--E 269 + +--S 270 of 528 +d0351:= D(m0351,x) +--R +--R +--R 3 +--R (243) x csc(b x + a) +--R Type: Expression Integer +--E 270 + +--S 271 of 528 +t0352:= x^2*csc(a+b*x)^3 +--R +--R +--R 2 3 +--R (244) x csc(b x + a) +--R Type: Expression Integer +--E 271 + +--S 272 of 528 +r0352:= -x^2*atanh(exp(1)^(%i*b*x+%i*a))/b-atanh(cos(a+b*x))/b^3-x*csc(a+b*x)/b^2-1/2*x^2*cot(a+b*x)*csc(a+b*x)/b+%i*x*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-%i*x*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+polylog(3,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 528 +a0352:= integrate(t0352,x) +--R +--R +--R x +--R ++ 2 3 +--R (245) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 273 + +--S 274 of 528 +m0352:= a0352-r0352 +--R +--R +--R x +--R ++ 2 3 +--R (246) | %R csc(%R b + a) d%R - r0352 +--R ++ +--R Type: Expression Integer +--E 274 + +--S 275 of 528 +d0352:= D(m0352,x) +--R +--R +--R 2 3 +--R (247) x csc(b x + a) +--R Type: Expression Integer +--E 275 + +--S 276 of 528 +t0353:= (c+d*x)*csc(a+b*x) +--R +--R +--R (248) (d x + c)csc(b x + a) +--R Type: Expression Integer +--E 276 + +--S 277 of 528 +r0353:= (-2*atanh(exp(%i*(a+b*x)))*c*b-2*atanh(exp(%i*(a+b*x)))*d*x*b+%i*d*polylog(2,-exp(%i*(a+b*x)))-%i*d*polylog(2,exp(%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 528 +a0353:= integrate(t0353,x) +--R +--R +--R x +--R ++ +--R (249) | (%R d + c)csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 278 + +--S 279 of 528 +m0353:= a0353-r0353 +--R +--R +--R x +--R ++ +--R (250) | (%R d + c)csc(%R b + a)d%R - r0353 +--R ++ +--R Type: Expression Integer +--E 279 + +--S 280 of 528 +d0353:= D(m0353,x) +--R +--R +--R (251) (d x + c)csc(b x + a) +--R Type: Expression Integer +--E 280 + +--S 281 of 528 +t0354:= (c+d*x)^2*csc(a+b*x) +--R +--R +--R 2 2 2 +--R (252) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 281 + +--S 282 of 528 +r0354:= -2*(c+d*x)^2*atanh(exp(1)^(%i*b*x+%i*a))/b+2*%i*d*(c+d*x)*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-2*%i*d*(c+d*x)*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-2*d^2*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+2*d^2*polylog(3,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 528 +a0354:= integrate(t0354,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (253) | (%R d + 2%R c d + c )csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 283 + +--S 284 of 528 +m0354:= a0354-r0354 +--R +--R +--R x +--R ++ 2 2 2 +--R (254) | (%R d + 2%R c d + c )csc(%R b + a)d%R - r0354 +--R ++ +--R Type: Expression Integer +--E 284 + +--S 285 of 528 +d0354:= D(m0354,x) +--R +--R +--R 2 2 2 +--R (255) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 285 + +--S 286 of 528 +t0355:= (c+d*x)^3*csc(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R (256) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 286 + +--S 287 of 528 +r0355:= -2*(c+d*x)^3*atanh(exp(1)^(%i*b*x+%i*a))/b+3*%i*d*(c+d*x)^2*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-3*%i*d*(c+d*x)^2*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-6*d^2*(c+d*x)*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+6*d^2*(c+d*x)*polylog(3,exp(1)^(%i*b*x+%i*a))/b^3-6*%i*d^3*polylog(4,-exp(1)^(%i*b*x+%i*a))/b^4+6*%i*d^3*polylog(4,exp(1)^(%i*b*x+%i*a))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 528 +a0355:= integrate(t0355,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (257) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 288 + +--S 289 of 528 +m0355:= a0355-r0355 +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (258) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a)d%R - r0355 +--R ++ +--R Type: Expression Integer +--E 289 + +--S 290 of 528 +d0355:= D(m0355,x) +--R +--R +--R 3 3 2 2 2 3 +--R (259) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 290 + +--S 291 of 528 +t0356:= (c+d*x)^2*csc(a+b*x)^2 +--R +--R +--R 2 2 2 2 +--R (260) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 291 + +--S 292 of 528 +r0356:= -%i*(c+d*x)^2/b-(c+d*x)^2*cot(a+b*x)/b+2*d*(c+d*x)*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^2-%i*d^2*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 292 + +--S 293 of 528 +a0356:= integrate(t0356,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (261) | (%R d + 2%R c d + c )csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 293 + +--S 294 of 528 +m0356:= a0356-r0356 +--R +--R +--R x +--R ++ 2 2 2 2 +--R (262) | (%R d + 2%R c d + c )csc(%R b + a) d%R - r0356 +--R ++ +--R Type: Expression Integer +--E 294 + +--S 295 of 528 +d0356:= D(m0356,x) +--R +--R +--R 2 2 2 2 +--R (263) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 295 + +--S 296 of 528 +t0357:= (c+d*x)^3*csc(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 2 +--R (264) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 296 + +--S 297 of 528 +r0357:= -%i*(c+d*x)^3/b-(c+d*x)^3*cot(a+b*x)/b+3*d*(c+d*x)^2*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^2-3*%i*d^2*(c+d*x)*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^3+3/2*d^3*polylog(3,exp(1)^(2*%i*a+2*%i*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 528 +a0357:= integrate(t0357,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (265) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 298 + +--S 299 of 528 +m0357:= a0357-r0357 +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (266) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a) d%R - r0357 +--R ++ +--R Type: Expression Integer +--E 299 + +--S 300 of 528 +d0357:= D(m0357,x) +--R +--R +--R 3 3 2 2 2 3 2 +--R (267) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 300 + +--S 301 of 528 +t0358:= (c+d*x)*csc(a+b*x)^3 +--R +--R +--R 3 +--R (268) (d x + c)csc(b x + a) +--R Type: Expression Integer +--E 301 + +--S 302 of 528 +r0358:= -(c+d*x)*atanh(exp(1)^(%i*b*x+%i*a))/b-1/2*d*csc(a+b*x)/b^2-1/2*(c+d*x)*cot(a+b*x)*csc(a+b*x)/b+1/2*%i*d*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-1/2*%i*d*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 528 +a0358:= integrate(t0358,x) +--R +--R +--R x +--R ++ 3 +--R (269) | (%R d + c)csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 303 + +--S 304 of 528 +m0358:= a0358-r0358 +--R +--R +--R x +--R ++ 3 +--R (270) | (%R d + c)csc(%R b + a) d%R - r0358 +--R ++ +--R Type: Expression Integer +--E 304 + +--S 305 of 528 +d0358:= D(m0358,x) +--R +--R +--R 3 +--R (271) (d x + c)csc(b x + a) +--R Type: Expression Integer +--E 305 + +--S 306 of 528 +t0359:= (c+d*x)^2*csc(a+b*x)^3 +--R +--R +--R 2 2 2 3 +--R (272) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 306 + +--S 307 of 528 +r0359:= -(c+d*x)^2*atanh(exp(1)^(%i*b*x+%i*a))/b-d^2*atanh(cos(a+b*x))/b^3-d*(c+d*x)*csc(a+b*x)/b^2-1/2*(c+d*x)^2*cot(a+b*x)*csc(a+b*x)/b+%i*d*(c+d*x)*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-%i*d*(c+d*x)*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-d^2*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+d^2*polylog(3,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Complex Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 528 +a0359:= integrate(t0359,x) +--R +--R +--R x +--R ++ 2 2 2 3 +--R (273) | (%R d + 2%R c d + c )csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 308 + +--S 309 of 528 +m0359:= a0359-r0359 +--R +--R +--R x +--R ++ 2 2 2 3 +--R (274) | (%R d + 2%R c d + c )csc(%R b + a) d%R - r0359 +--R ++ +--R Type: Expression Integer +--E 309 + +--S 310 of 528 +d0359:= D(m0359,x) +--R +--R +--R 2 2 2 3 +--R (275) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression Integer +--E 310 + +--S 311 of 528 +t0360:= (csc(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (276) \|csc(x) +--R Type: Expression Integer +--E 311 + +--S 312 of 528 +r0360:= -acsch(tan(x)) +--R +--R +--R (277) - acsch(tan(x)) +--R Type: Expression Integer +--E 312 + +--S 313 of 528 +a0360:= integrate(t0360,x) +--R +--R +--R sin(x) +--R (278) log(----------) +--R cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 313 + +--S 314 of 528 +m0360:= a0360-r0360 +--R +--R +--R sin(x) +--R (279) log(----------) + acsch(tan(x)) +--R cos(x) + 1 +--R Type: Expression Integer +--E 314 + +--S 315 of 528 +d0360:= D(m0360,x) +--R +--R +--R (280) +--R +-----------+ +--R 2 2 | 2 +--R (sin(x) + cos(x) + cos(x))tan(x)\|tan(x) + 1 +--R + +--R 2 +--R (- cos(x) - 1)sin(x)tan(x) + (- cos(x) - 1)sin(x) +--R / +--R +-----------+ +--R | 2 +--R (cos(x) + 1)sin(x)tan(x)\|tan(x) + 1 +--R Type: Expression Integer +--E 315 + +--S 316 of 528 +t0361:= (a*csc(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (281) \|a csc(x) +--R Type: Expression Integer +--E 316 + +--S 317 of 528 +r0361:= -atanh(cos(x))*(a*csc(x)^2)^(1/2)*sin(x) +--R +--R +--R +---------+ +--R | 2 +--R (282) - sin(x)atanh(cos(x))\|a csc(x) +--R Type: Expression Integer +--E 317 + +--S 318 of 528 +a0361:= integrate(t0361,x) +--R +--R +--R +-+ sin(x) +--R (283) \|a log(----------) +--R cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 318 + +--S 319 of 528 +m0361:= a0361-r0361 +--R +--R +--R +---------+ +--R | 2 +-+ sin(x) +--R (284) sin(x)atanh(cos(x))\|a csc(x) + \|a log(----------) +--R cos(x) + 1 +--R Type: Expression Integer +--E 319 + +--S 320 of 528 +d0361:= D(m0361,x) +--R +--R +--R (285) +--R +---------+ +--R 2 3 +-+ | 2 +--R ((cos(x) - 1)sin(x) + cos(x) - cos(x))\|a \|a csc(x) +--R + +--R 2 2 2 +--R (- a cos(x) + a)cot(x)csc(x) sin(x) +--R + +--R 3 2 +--R (a cos(x) - a cos(x))csc(x) sin(x) +--R * +--R atanh(cos(x)) +--R + +--R 2 3 +--R a csc(x) sin(x) +--R / +--R +---------+ +--R 2 | 2 +--R (cos(x) - 1)sin(x)\|a csc(x) +--R Type: Expression Integer +--E 320 + +--S 321 of 528 +t0362:= (a*csc(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (286) \|a csc(x) +--R Type: Expression Integer +--E 321 + +--S 322 of 528 +r0362:= -2*(a*csc(x)^3)^(1/2)*(cos(x)+EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*sin(x) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 528 +a0362:= integrate(t0362,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--R (287) | \|a csc(%R) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 323 + +--S 324 of 528 +m0362:= a0362-r0362 +--R +--R +--R x +----------+ +--R ++ | 3 +--R (288) | \|a csc(%R) d%R - r0362 +--R ++ +--R Type: Expression Integer +--E 324 + +--S 325 of 528 +d0362:= D(m0362,x) +--R +--R +--R +---------+ +--R | 3 +--R (289) \|a csc(x) +--R Type: Expression Integer +--E 325 + +--S 326 of 528 +t0363:= (csc(x)^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (290) csc(x) \|csc(x) +--R Type: Expression Integer +--E 326 + +--S 327 of 528 +r0363:= -1/2*acsch(tan(x))-1/2*cot(x)*(csc(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R - cot(x)\|csc(x) - acsch(tan(x)) +--R (291) ---------------------------------- +--R 2 +--R Type: Expression Integer +--E 327 + +--S 328 of 528 +a0363:= integrate(t0363,x) +--R +--R +--R 2 sin(x) +--R (cos(x) - 1)log(----------) + cos(x) +--R cos(x) + 1 +--R (292) ------------------------------------- +--R 2 +--R 2cos(x) - 2 +--R Type: Union(Expression Integer,...) +--E 328 + +--S 329 of 528 +m0363:= a0363-r0363 +--R +--R +--R (293) +--R +-------+ +--R 2 | 2 2 sin(x) +--R (cos(x) - 1)cot(x)\|csc(x) + (cos(x) - 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (cos(x) - 1)acsch(tan(x)) + cos(x) +--R / +--R 2 +--R 2cos(x) - 2 +--R Type: Expression Integer +--E 329 + +--S 330 of 528 +d0363:= D(m0363,x) +--R +--R +--R (294) +--R 3 2 5 3 +--R ((cos(x) - cos(x) + 2)sin(x) + cos(x) - 2cos(x) + cos(x))tan(x) +--R * +--R +-------+ +--R | 2 +--R \|csc(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1) +--R * +--R 2 +--R csc(x) sin(x)tan(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 1 +--R + +--R 4 2 2 +--R (- cos(x) + 2cos(x) - 1)sin(x)tan(x) +--R + +--R 4 2 +--R (- cos(x) + 2cos(x) - 1)sin(x) +--R * +--R +-------+ +--R | 2 +--R \|csc(x) +--R / +--R +-------+ +-----------+ +--R 4 2 | 2 | 2 +--R (2cos(x) - 4cos(x) + 2)sin(x)tan(x)\|csc(x) \|tan(x) + 1 +--R Type: Expression Integer +--E 330 + +--S 331 of 528 +t0364:= (a*csc(x)^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (295) a csc(x) \|a csc(x) +--R Type: Expression Integer +--E 331 + +--S 332 of 528 +r0364:= -1/2*a*(a*csc(x)^2)^(1/2)*(atanh(cos(x))+cot(x)*csc(x))*sin(x) +--R +--R +--R +---------+ +--R | 2 +--R (- a sin(x)atanh(cos(x)) - a cot(x)csc(x)sin(x))\|a csc(x) +--R (296) ------------------------------------------------------------ +--R 2 +--R Type: Expression Integer +--E 332 + +--S 333 of 528 +a0364:= integrate(t0364,x) +--R +--R +--R 2 +-+ sin(x) +-+ +--R (a cos(x) - a)\|a log(----------) + a cos(x)\|a +--R cos(x) + 1 +--R (297) ------------------------------------------------- +--R 2 +--R 2cos(x) - 2 +--R Type: Union(Expression Integer,...) +--E 333 + +--S 334 of 528 +m0364:= a0364-r0364 +--R +--R +--R (298) +--R 2 +--R (a cos(x) - a)sin(x)atanh(cos(x)) +--R + +--R 2 +--R (a cos(x) - a)cot(x)csc(x)sin(x) +--R * +--R +---------+ +--R | 2 +--R \|a csc(x) +--R + +--R 2 +-+ sin(x) +-+ +--R (a cos(x) - a)\|a log(----------) + a cos(x)\|a +--R cos(x) + 1 +--R / +--R 2 +--R 2cos(x) - 2 +--R Type: Expression Integer +--E 334 + +--S 335 of 528 +d0364:= D(m0364,x) +--R +--R +--R (299) +--R 3 2 5 3 +--R (a cos(x) - a cos(x) + 2a)sin(x) + a cos(x) - 2a cos(x) +--R + +--R a cos(x) +--R * +--R +---------+ +--R +-+ | 2 +--R \|a \|a csc(x) +--R + +--R 2 4 2 2 2 2 2 +--R (- a cos(x) + 2a cos(x) - a )cot(x)csc(x) sin(x) +--R + +--R 2 5 2 3 2 2 +--R (a cos(x) - 2a cos(x) + a cos(x))csc(x) sin(x) +--R * +--R atanh(cos(x)) +--R + +--R 2 2 2 2 3 +--R (a cos(x) - a )csc(x) sin(x) +--R + +--R 2 4 2 2 2 2 2 4 2 2 +--R (- 3a cos(x) + 6a cos(x) - 3a )cot(x) - a cos(x) + 2a cos(x) +--R + +--R 2 +--R - a +--R * +--R 3 2 +--R csc(x) sin(x) +--R + +--R 2 5 2 3 2 3 +--R (a cos(x) - 2a cos(x) + a cos(x))cot(x)csc(x) sin(x) +--R / +--R +---------+ +--R 4 2 | 2 +--R (2cos(x) - 4cos(x) + 2)sin(x)\|a csc(x) +--R Type: Expression Integer +--E 335 + +--S 336 of 528 +t0365:= (a*csc(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (300) a csc(x) \|a csc(x) +--R Type: Expression Integer +--E 336 + +--S 337 of 528 +r0365:= -2/21*a*(a*csc(x)^3)^(1/2)*(5*cot(x)+3*cot(x)*csc(x)^2-5*EllipticF(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*sin(x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 528 +a0365:= integrate(t0365,x) +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (301) | a csc(%R) \|a csc(%R) d%R +--R ++ +--R Type: Union(Expression Integer,...) +--E 338 + +--S 339 of 528 +m0365:= a0365-r0365 +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (302) | a csc(%R) \|a csc(%R) d%R - r0365 +--R ++ +--R Type: Expression Integer +--E 339 + +--S 340 of 528 +d0365:= D(m0365,x) +--R +--R +--R +---------+ +--R 3 | 3 +--R (303) a csc(x) \|a csc(x) +--R Type: Expression Integer +--E 340 + +--S 341 of 528 +t0366:= 1/(a*csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (304) ------------ +--R +---------+ +--R | 2 +--R \|a csc(x) +--R Type: Expression Integer +--E 341 + +--S 342 of 528 +r0366:= -cot(x)/(a*csc(x)^2)^(1/2) +--R +--R +--R cot(x) +--R (305) - ------------ +--R +---------+ +--R | 2 +--R \|a csc(x) +--R Type: Expression Integer +--E 342 + +--S 343 of 528 +a0366:= integrate(t0366,x) +--R +--R +--R cos(x) +--R (306) - ------ +--R +-+ +--R \|a +--R Type: Union(Expression Integer,...) +--E 343 + +--S 344 of 528 +m0366:= a0366-r0366 +--R +--R +--R +---------+ +--R | 2 +-+ +--R - cos(x)\|a csc(x) + cot(x)\|a +--R (307) --------------------------------- +--R +---------+ +--R +-+ | 2 +--R \|a \|a csc(x) +--R Type: Expression Integer +--E 344 + +--S 345 of 528 +d0366:= D(m0366,x) +--R +--R +--R +---------+ +--R +-+ | 2 +--R sin(x)\|a \|a csc(x) - a +--R (308) -------------------------- +--R +---------+ +--R | 2 +--R a\|a csc(x) +--R Type: Expression Integer +--E 345 + +--S 346 of 528 +t0367:= 1/(a*csc(x)^3)^(1/2) +--R +--R +--R 1 +--R (309) ------------ +--R +---------+ +--R | 3 +--R \|a csc(x) +--R Type: Expression Integer +--E 346 + +--S 347 of 528 +r0367:= -2/3*csc(x)*(cos(x)-EllipticF(-1/4*%pi+1/2*x,2)/sin(x)^(1/2))/(a*csc(x)^3)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression Integer +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 528 +a0367:= integrate(t0367,x) +--R +--R +--R x +--R ++ 1 +--R (310) | ------------- d%R +--R ++ +----------+ +--R | 3 +--R \|a csc(%R) +--R Type: Union(Expression Integer,...) +--E 348 + +--S 349 of 528 +m0367:= a0367-r0367 +--R +--R +--R x +--R ++ 1 +--R (311) | ------------- d%R - r0367 +--R ++ +----------+ +--R | 3 +--R \|a csc(%R) +--R Type: Expression Integer +--E 349 + +--S 350 of 528 +d0367:= D(m0367,x) +--R +--R +--R 1 +--R (312) ------------ +--R +---------+ +--R | 3 +--R \|a csc(x) +--R Type: Expression Integer +--E 350 + +--S 351 of 528 +t0368:= 1/(a+a*csc(c+d*x)) +--R +--R +--R 1 +--R (313) ------------------ +--R a csc(d x + c) + a +--R Type: Expression Integer +--E 351 + +--S 352 of 528 +r0368:= x/a+cos(c+d*x)/a/d/(1+sin(c+d*x)) +--R +--R +--R d x sin(d x + c) + cos(d x + c) + d x +--R (314) ------------------------------------- +--R a d sin(d x + c) + a d +--R Type: Expression Integer +--E 352 + +--S 353 of 528 +a0368:= integrate(t0368,x) +--R +--R +--R d x sin(d x + c) + (d x + 2)cos(d x + c) + d x + 2 +--R (315) -------------------------------------------------- +--R a d sin(d x + c) + a d cos(d x + c) + a d +--R Type: Union(Expression Integer,...) +--E 353 + +--S 354 of 528 +m0368:= a0368-r0368 +--R +--R +--R (316) +--R 2 +--R (cos(d x + c) + 2)sin(d x + c) - cos(d x + c) + cos(d x + c) + 2 +--R / +--R 2 +--R a d sin(d x + c) + (a d cos(d x + c) + 2a d)sin(d x + c) +--R + +--R a d cos(d x + c) + a d +--R Type: Expression Integer +--E 354 + +--S 355 of 528 +d0368:= D(m0368,x) +--R +--R +--R (317) +--R 4 3 +--R - sin(d x + c) + (2cos(d x + c) - 1)sin(d x + c) +--R + +--R 2 +--R (2cos(d x + c) + 1)sin(d x + c) +--R + +--R 3 2 +--R (2cos(d x + c) - cos(d x + c) - 2cos(d x + c) + 1)sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) + 2cos(d x + c) - cos(d x + c) - 2cos(d x + c) +--R / +--R 4 3 +--R a sin(d x + c) + (2a cos(d x + c) + 4a)sin(d x + c) +--R + +--R 2 2 +--R (a cos(d x + c) + 6a cos(d x + c) + 6a)sin(d x + c) +--R + +--R 2 2 +--R (2a cos(d x + c) + 6a cos(d x + c) + 4a)sin(d x + c) + a cos(d x + c) +--R + +--R 2a cos(d x + c) + a +--R Type: Expression Integer +--E 355 + +--S 356 of 528 +t0369:= 1/(a-a*csc(c+d*x)) +--R +--R +--R 1 +--R (318) - ------------------ +--R a csc(d x + c) - a +--R Type: Expression Integer +--E 356 + +--S 357 of 528 +r0369:= x/a-cos(c+d*x)/a/d/(1-sin(c+d*x)) +--R +--R +--R d x sin(d x + c) + cos(d x + c) - d x +--R (319) ------------------------------------- +--R a d sin(d x + c) - a d +--R Type: Expression Integer +--E 357 + +--S 358 of 528 +a0369:= integrate(t0369,x) +--R +--R +--R d x sin(d x + c) + (- d x + 2)cos(d x + c) - d x + 2 +--R (320) ---------------------------------------------------- +--R a d sin(d x + c) - a d cos(d x + c) - a d +--R Type: Union(Expression Integer,...) +--E 358 + +--S 359 of 528 +m0369:= a0369-r0369 +--R +--R +--R (321) +--R 2 +--R (cos(d x + c) + 2)sin(d x + c) + cos(d x + c) - cos(d x + c) - 2 +--R / +--R 2 +--R a d sin(d x + c) + (- a d cos(d x + c) - 2a d)sin(d x + c) +--R + +--R a d cos(d x + c) + a d +--R Type: Expression Integer +--E 359 + +--S 360 of 528 +d0369:= D(m0369,x) +--R +--R +--R (322) +--R 4 3 +--R - sin(d x + c) + (- 2cos(d x + c) + 1)sin(d x + c) +--R + +--R 2 +--R (2cos(d x + c) + 1)sin(d x + c) +--R + +--R 3 2 +--R (- 2cos(d x + c) + cos(d x + c) + 2cos(d x + c) - 1)sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) + 2cos(d x + c) - cos(d x + c) - 2cos(d x + c) +--R / +--R 4 3 +--R a sin(d x + c) + (- 2a cos(d x + c) - 4a)sin(d x + c) +--R + +--R 2 2 +--R (a cos(d x + c) + 6a cos(d x + c) + 6a)sin(d x + c) +--R + +--R 2 2 +--R (- 2a cos(d x + c) - 6a cos(d x + c) - 4a)sin(d x + c) + a cos(d x + c) +--R + +--R 2a cos(d x + c) + a +--R Type: Expression Integer +--E 360 + +--S 361 of 528 +t0370:= (3+3*csc(x))^(1/2) +--R +--R +--R +-----------+ +--R (323) \|3csc(x) + 3 +--R Type: Expression Integer +--E 361 + +--S 362 of 528 +r0370:= -2*3^(1/2)*atan((-1+csc(x))^(1/2))*cot(x)/(-1+csc(x))^(1/2)/(1+csc(x))^(1/2) +--R +--R +--R +-+ +----------+ +--R 2\|3 cot(x)atan(\|csc(x) - 1 ) +--R (324) - ------------------------------ +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R Type: Expression Integer +--E 362 + +--S 363 of 528 +a0370:= integrate(t0370,x) +--R +--R +--R +-------------+ +--R +-+ +-+ +-+ |- 9cos(x) - 9 +--R (2\|3 sin(x) + 2\|3 cos(x) - 2\|3 ) 4|------------- +--R +-+ \| 4cos(x) - 4 +--R (325) \|3 atan(---------------------------------------------------) +--R +-------------+2 +--R |- 9cos(x) - 9 +--R (2cos(x) - 2) 4|------------- - 3sin(x) + 3 +--R \| 4cos(x) - 4 +--R Type: Union(Expression Integer,...) +--E 363 + +--S 364 of 528 +m0370:= a0370-r0370 +--R +--R +--R (326) +--R +-+ +----------+ +--R 2\|3 cot(x)atan(\|csc(x) - 1 ) +--R + +--R +-+ +----------+ +----------+ +--R \|3 \|csc(x) - 1 \|csc(x) + 1 +--R * +--R +-------------+ +--R +-+ +-+ +-+ |- 9cos(x) - 9 +--R (2\|3 sin(x) + 2\|3 cos(x) - 2\|3 ) 4|------------- +--R \| 4cos(x) - 4 +--R atan(---------------------------------------------------) +--R +-------------+2 +--R |- 9cos(x) - 9 +--R (2cos(x) - 2) 4|------------- - 3sin(x) + 3 +--R \| 4cos(x) - 4 +--R / +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R Type: Expression Integer +--E 364 + +--S 365 of 528 +d0370:= D(m0370,x) +--R +--R +--R (327) +--R +-+ 2 +-+ +-+ 2 +--R (- 8\|3 cos(x) + 16\|3 cos(x) - 8\|3 )csc(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ 2 +--R (8\|3 cos(x) - 16\|3 cos(x) + 8\|3 )cot(x) + 8\|3 cos(x) +--R + +--R +-+ +-+ +--R - 16\|3 cos(x) + 8\|3 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (- 32\|3 cos(x) + 64\|3 cos(x) - 32\|3 cos(x))csc(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x))cot(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16\|3 cos(x) + 64\|3 cos(x) - 80\|3 cos(x) +--R + +--R +-+ +--R 32\|3 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 16\|3 cos(x) - 64\|3 cos(x) + 80\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16\|3 cos(x) - 64\|3 cos(x) + 80\|3 cos(x) - 32\|3 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R - 32\|3 cos(x) + 64\|3 cos(x) - 32\|3 cos(x) +--R + +--R +-+ +-+ +--R - 32\|3 cos(x) + 32\|3 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R 32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x) +--R + +--R +-+ +-+ +--R 32\|3 cos(x) - 32\|3 +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +-+ +--R 32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x) + 32\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8\|3 cos(x) + 48\|3 cos(x) - 40\|3 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|3 cos(x) + 64\|3 cos(x) + 32\|3 cos(x) - 32\|3 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 8\|3 cos(x) - 48\|3 cos(x) + 40\|3 cos(x) + 64\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 64\|3 cos(x) - 32\|3 cos(x) + 32\|3 +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 8\|3 cos(x) - 48\|3 cos(x) + 40\|3 cos(x) + 64\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 64\|3 cos(x) - 32\|3 cos(x) + 32\|3 +--R * +--R +-------------+3 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 2 +-+ 2 +--R (24\|3 cos(x) - 24\|3 )csc(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 24\|3 cos(x) + 24\|3 )cot(x) - 24\|3 cos(x) + 24\|3 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 48\|3 cos(x) + 48\|3 )csc(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (48\|3 cos(x) - 48\|3 )cot(x) + 48\|3 cos(x) - 48\|3 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|3 cos(x) - 24\|3 )csc(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 24\|3 cos(x) + 24\|3 )cot(x) - 24\|3 cos(x) + 24\|3 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 48\|3 cos(x) + 96\|3 cos(x) - 48\|3 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (48\|3 cos(x) - 96\|3 cos(x) + 48\|3 )cot(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 48\|3 cos(x) - 96\|3 cos(x) + 48\|3 +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 24\|3 cos(x) + 96\|3 cos(x) - 120\|3 cos(x) + 48\|3 ) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (24\|3 cos(x) - 96\|3 cos(x) + 120\|3 cos(x) - 48\|3 )cot(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 24\|3 cos(x) - 96\|3 cos(x) + 120\|3 cos(x) - 48\|3 +--R * +--R +-------------+ +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R atan(\|csc(x) - 1 ) +--R + +--R 2 2 2 +--R (- 12cos(x) - 6cos(x) + 18)csc(x) + 12cos(x) + 6cos(x) +--R + +--R - 18 +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (24cos(x) - 6cos(x) - 18)csc(x) - 24cos(x) + 6cos(x) +--R + +--R 18 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 +--R (- 42cos(x) + 42cos(x) + 12cos(x) - 12)csc(x) + 42cos(x) +--R + +--R 2 +--R - 42cos(x) - 12cos(x) + 12 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (24cos(x) - 6cos(x) - 12cos(x) - 30cos(x) + 24)csc(x) +--R + +--R 5 4 3 2 +--R - 24cos(x) + 6cos(x) + 12cos(x) + 30cos(x) - 24 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (12cos(x) - 36cos(x) - 12cos(x) + 60cos(x) - 24cos(x))csc(x) +--R + +--R 6 5 4 3 +--R - 12cos(x) + 36cos(x) + 12cos(x) - 60cos(x) + 24cos(x) +--R * +--R +-------------+2 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R 2 5 +--R (9csc(x) - 9)sin(x) +--R + +--R 2 2 2 +--R ((- 18cos(x) + 9cos(x) - 18)csc(x) + 18cos(x) - 9cos(x) + 18) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 +--R (- 36cos(x) + 27cos(x) + 9cos(x) + 27)csc(x) + 36cos(x) +--R + +--R 2 +--R - 27cos(x) - 9cos(x) - 27 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 +--R (45cos(x) - 54cos(x) - 18cos(x) + 18)csc(x) - 45cos(x) +--R + +--R 2 +--R 54cos(x) + 18cos(x) - 18 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 36cos(x) + 18cos(x) + 63cos(x) + 27cos(x) - 36cos(x) +--R + +--R - 36 +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 36cos(x) - 18cos(x) - 63cos(x) - 27cos(x) + 36cos(x) + 36 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 18cos(x) + 36cos(x) - 54cos(x) - 72cos(x) + 36cos(x) +--R + +--R 36cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 18cos(x) - 36cos(x) + 54cos(x) + 72cos(x) - 36cos(x) - 36cos(x) +--R * +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 4\|3 cos(x) + 8\|3 cos(x) - 4\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 4\|3 cos(x) + 8\|3 cos(x) - 4\|3 )cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (- 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x))cot(x) csc(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (- 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x))cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8\|3 cos(x) + 32\|3 cos(x) - 40\|3 cos(x) +--R + +--R +-+ +--R 16\|3 cos(x) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8\|3 cos(x) + 32\|3 cos(x) - 40\|3 cos(x) +--R + +--R +-+ +--R 16\|3 cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R - 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) +--R + +--R +-+ +-+ +--R - 16\|3 cos(x) + 16\|3 +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R - 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) +--R + +--R +-+ +-+ +--R - 16\|3 cos(x) + 16\|3 +--R * +--R 2 +--R cot(x) +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 4\|3 cos(x) + 24\|3 cos(x) - 20\|3 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|3 cos(x) + 32\|3 cos(x) + 16\|3 cos(x) - 16\|3 +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 4\|3 cos(x) + 24\|3 cos(x) - 20\|3 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|3 cos(x) + 32\|3 cos(x) + 16\|3 cos(x) - 16\|3 +--R * +--R 2 +--R cot(x) +--R * +--R +-------------+3 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 24\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 24\|3 )cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 )cot(x) csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 )cot(x) +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 12\|3 cos(x) + 48\|3 cos(x) - 60\|3 cos(x) + 24\|3 ) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 12\|3 cos(x) + 48\|3 cos(x) - 60\|3 cos(x) + 24\|3 )cot(x) +--R * +--R +-------------+ +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R \|csc(x) - 1 +--R / +--R 2 2 2 4 +--R ((4cos(x) - 8cos(x) + 4)csc(x) - 4cos(x) + 8cos(x) - 4)sin(x) +--R + +--R 3 2 2 3 +--R (16cos(x) - 32cos(x) + 16cos(x))csc(x) - 16cos(x) +--R + +--R 2 +--R 32cos(x) - 16cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))csc(x) - 8cos(x) +--R + +--R 3 2 +--R 32cos(x) - 40cos(x) + 16cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 2 +--R (16cos(x) - 32cos(x) + 16cos(x) + 16cos(x) - 16)csc(x) +--R + +--R 5 4 2 +--R - 16cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + 16 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) - 24cos(x) + 20cos(x) + 32cos(x) - 32cos(x) +--R + +--R - 16cos(x) + 16 +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) + 24cos(x) - 20cos(x) - 32cos(x) + 32cos(x) +--R + +--R 16cos(x) - 16 +--R * +--R +-------------+3 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 4 +--R ((- 12cos(x) + 12)csc(x) + 12cos(x) - 12)sin(x) +--R + +--R 2 2 2 3 +--R ((24cos(x) - 24)csc(x) - 24cos(x) + 24)sin(x) +--R + +--R 2 2 2 2 +--R ((- 12cos(x) + 12)csc(x) + 12cos(x) - 12)sin(x) +--R + +--R 4 2 2 4 2 +--R (24cos(x) - 48cos(x) + 24)csc(x) - 24cos(x) + 48cos(x) +--R + +--R - 24 +--R * +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (12cos(x) - 48cos(x) + 60cos(x) - 24)csc(x) - 12cos(x) +--R + +--R 4 2 +--R 48cos(x) - 60cos(x) + 24 +--R * +--R +-------------+ +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R Type: Expression Integer +--E 365 + +--S 366 of 528 +t0371:= (3-3*csc(x))^(1/2) +--R +--R +--R +-------------+ +--R (328) \|- 3csc(x) + 3 +--R Type: Expression Integer +--E 366 + +--S 367 of 528 +r0371:= -2*3^(1/2)*atan((-1-csc(x))^(1/2))*cot(x)/(-1-csc(x))^(1/2)/(1-csc(x))^(1/2) +--R +--R +--R +-+ +------------+ +--R 2\|3 cot(x)atan(\|- csc(x) - 1 ) +--R (329) - -------------------------------- +--R +------------+ +------------+ +--R \|- csc(x) - 1 \|- csc(x) + 1 +--R Type: Expression Integer +--E 367 + +--S 368 of 528 +a0371:= integrate(t0371,x) +--R +--R +--R (330) 0 +--R Type: Union(Expression Integer,...) +--E 368 + +--S 369 of 528 +m0371:= a0371-r0371 +--R +--R +--R +-+ +------------+ +--R 2\|3 cot(x)atan(\|- csc(x) - 1 ) +--R (331) -------------------------------- +--R +------------+ +------------+ +--R \|- csc(x) - 1 \|- csc(x) + 1 +--R Type: Expression Integer +--E 369 + +--S 370 of 528 +d0371:= D(m0371,x) +--R +--R +--R (332) +--R +-+ 2 +-+ 2 +-+ +------------+ +--R (- 2\|3 csc(x) + 2\|3 cot(x) + 2\|3 )atan(\|- csc(x) - 1 ) +--R + +--R +-+ 2 +-+ 2 +------------+ +--R (\|3 cot(x) csc(x) - \|3 cot(x) )\|- csc(x) - 1 +--R / +--R 2 +------------+ +------------+ +--R (csc(x) - 1)\|- csc(x) - 1 \|- csc(x) + 1 +--R Type: Expression Integer +--E 370 + +--S 371 of 528 +t0372:= (a+a*csc(x))^(1/2) +--R +--R +--R +------------+ +--R (333) \|a csc(x) + a +--R Type: Expression Integer +--E 371 + +--S 372 of 528 +r0372:= -2*a*atan((-1+csc(x))^(1/2))*cot(x)/(-1+csc(x))^(1/2)/(a+a*csc(x))^(1/2) +--R +--R +--R +----------+ +--R 2a cot(x)atan(\|csc(x) - 1 ) +--R (334) - ---------------------------- +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression Integer +--E 372 + +--S 373 of 528 +a0372:= integrate(t0372,x) +--R +--R +--R (335) +--R [ +--R +---+ +--R \|- a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R / +--R 2 +--R , +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R +-+ \| 4cos(x) - 4 +--R \|a atan(-----------------------------------------------)] +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R Type: Union(List Expression Integer,...) +--E 373 + +--S 374 of 528 +m0372a:= a0372.1-r0372 +--R +--R +--R (336) +--R +---+ +----------+ +------------+ +--R \|- a \|csc(x) - 1 \|a csc(x) + a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R + +--R +----------+ +--R 4a cot(x)atan(\|csc(x) - 1 ) +--R / +--R +----------+ +------------+ +--R 2\|csc(x) - 1 \|a csc(x) + a +--R Type: Expression Integer +--E 374 + +--S 375 of 528 +d0372a:= D(m0372a,x) +--R +--R +--R (337) +--R 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a)csc(x) +--R + +--R 2 2 2 +--R (32a cos(x) - 64a cos(x) + 32a)cot(x) + 32a cos(x) +--R + +--R - 64a cos(x) + 32a +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 32a cos(x) + 64a cos(x) + 8a cos(x) - 80a cos(x) + 40a) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R (32a cos(x) - 64a cos(x) - 8a cos(x) + 80a cos(x) - 40a) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 +--R 32a cos(x) - 64a cos(x) - 8a cos(x) + 80a cos(x) - 40a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R - 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 16a cos(x) - 16a cos(x) - 16a cos(x) + 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 24a cos(x) + 16a cos(x) - 24a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 24a cos(x) - 16a cos(x) + 24a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 16a cos(x) - 24a cos(x) - 16a cos(x) + 24a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (16a cos(x) + 8a cos(x) - 40a cos(x) - 8a cos(x) + 24a ) +--R * +--R 2 +--R csc(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 16a cos(x) - 8a cos(x) + 40a cos(x) + 8a cos(x) - 24a ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 16a cos(x) - 8a cos(x) + 40a cos(x) + 8a cos(x) - 24a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R atan(\|csc(x) - 1 ) +--R + +--R 3 2 2 3 +--R (- 16cos(x) + 32cos(x) - 16cos(x))csc(x) + 16cos(x) +--R + +--R 2 +--R - 32cos(x) + 16cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (8cos(x) - 16cos(x) + 8cos(x))csc(x) - 8cos(x) + 16cos(x) +--R + +--R - 8cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 2 2 2 +--R ((- 4a cos(x) + 4a cos(x))csc(x) + 4a cos(x) - 4a cos(x)) +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 4a cos(x) + 4a cos(x) + 4a cos(x) - 4a cos(x))csc(x) +--R + +--R 4 3 2 +--R 4a cos(x) - 4a cos(x) - 4a cos(x) + 4a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (4a cos(x) - 2a cos(x) - a )csc(x) - 4a cos(x) + 2a cos(x) +--R + +--R 2 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 3 2 +--R (- 8a cos(x) + 9a cos(x) - a )csc(x) + 8a cos(x) - 9a cos(x) +--R + +--R 2 +--R a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 4a cos(x) + 6a cos(x) + 4a cos(x) - 6a cos(x))csc(x) +--R + +--R 2 4 2 3 2 2 2 +--R 4a cos(x) - 6a cos(x) - 4a cos(x) + 6a cos(x) +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R + +--R 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a)cot(x) +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 32a cos(x) + 4a cos(x) - 40a cos(x) + 20a) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 32a cos(x) + 4a cos(x) - 40a cos(x) + 20a) +--R * +--R 2 +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a )cot(x) +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a ) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a )cot(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R \|csc(x) - 1 +--R / +--R 2 2 2 +--R ((16cos(x) - 32cos(x) + 16)csc(x) - 16cos(x) + 32cos(x) - 16) +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (16cos(x) - 32cos(x) - 4cos(x) + 40cos(x) - 20)csc(x) +--R + +--R 4 3 2 +--R - 16cos(x) + 32cos(x) + 4cos(x) - 40cos(x) + 20 +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a)csc(x) +--R + +--R 3 2 +--R 8a cos(x) - 8a cos(x) - 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 3 2 2 3 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 8a cos(x) + 8a cos(x) - 8a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 +--R (8a cos(x) - 12a cos(x) - 8a cos(x) + 12a)csc(x) +--R + +--R 3 2 +--R - 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 8a cos(x) - 4a cos(x) + 20a cos(x) + 4a cos(x) - 12a)csc(x) +--R + +--R 4 3 2 +--R 8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression Integer +--E 375 + +--S 376 of 528 +m0372b:= a0372.2-r0372 +--R +--R +--R (338) +--R +----------+ +--R 2a cot(x)atan(\|csc(x) - 1 ) +--R + +--R +-+ +----------+ +------------+ +--R \|a \|csc(x) - 1 \|a csc(x) + a +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R / +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression Integer +--E 376 + +--S 377 of 528 +d0372b:= D(m0372b,x) +--R +--R +--R (339) +--R 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a)csc(x) +--R + +--R 2 2 2 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x) + 8a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a cos(x))csc(x) +--R + +--R 3 2 2 3 +--R (32a cos(x) - 64a cos(x) + 32a cos(x))cot(x) + 32a cos(x) +--R + +--R 2 +--R - 64a cos(x) + 32a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 64a cos(x) - 80a cos(x) + 32a cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 2 +--R (16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x))cot(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) - 32a cos(x) +--R + +--R 32a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 2 +--R 32a cos(x) - 64a cos(x) + 32a cos(x) + 32a cos(x) +--R + +--R - 32a +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 +--R 32a cos(x) - 64a cos(x) + 32a cos(x) + 32a cos(x) - 32a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 48a cos(x) - 40a cos(x) - 64a cos(x) +--R + +--R 2 +--R 64a cos(x) + 32a cos(x) - 32a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 16a cos(x) + 16a )csc(x) + (16a cos(x) - 16a )cot(x) +--R + +--R 2 2 2 +--R 16a cos(x) - 16a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a )csc(x) +--R + +--R 2 4 2 2 2 2 2 4 +--R (16a cos(x) - 32a cos(x) + 16a )cot(x) + 16a cos(x) +--R + +--R 2 2 2 +--R - 32a cos(x) + 16a +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a )csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (8a cos(x) - 32a cos(x) + 40a cos(x) - 16a )cot(x) +--R + +--R 2 6 2 4 2 2 2 +--R 8a cos(x) - 32a cos(x) + 40a cos(x) - 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R atan(\|csc(x) - 1 ) +--R + +--R 2 2 2 +--R (- 4a cos(x) - 2a cos(x) + 6a)csc(x) + 4a cos(x) +--R + +--R 2a cos(x) - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 +--R (8a cos(x) - 2a cos(x) - 6a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 2a cos(x) + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 +--R (- 14a cos(x) + 14a cos(x) + 4a cos(x) - 4a)csc(x) +--R + +--R 3 2 +--R 14a cos(x) - 14a cos(x) - 4a cos(x) + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (8a cos(x) - 2a cos(x) - 4a cos(x) - 10a cos(x) + 8a) +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 2a cos(x) + 4a cos(x) + 10a cos(x) - 8a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 12a cos(x) - 4a cos(x) + 20a cos(x) +--R + +--R - 8a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 12a cos(x) + 4a cos(x) - 20a cos(x) + 8a cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 5 +--R (a csc(x) - a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 2a cos(x) + a cos(x) - 2a )csc(x) + 2a cos(x) - a cos(x) +--R + +--R 2 +--R 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 4a cos(x) + 3a cos(x) + a cos(x) + 3a )csc(x) + 4a cos(x) +--R + +--R 2 2 2 2 +--R - 3a cos(x) - a cos(x) - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (5a cos(x) - 6a cos(x) - 2a cos(x) + 2a )csc(x) - 5a cos(x) +--R + +--R 2 2 2 2 +--R 6a cos(x) + 2a cos(x) - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 4a cos(x) + 2a cos(x) + 7a cos(x) + 3a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 4a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R 4a cos(x) - 2a cos(x) - 7a cos(x) - 3a cos(x) + 4a cos(x) + 4a +--R * +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 2a cos(x) + 4a cos(x) - 6a cos(x) - 8a cos(x) + 4a cos(x) +--R + +--R 2 +--R 4a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R - 2a cos(x) - 4a cos(x) + 6a cos(x) + 8a cos(x) - 4a cos(x) +--R + +--R 2 +--R - 4a cos(x) +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R + +--R 2 2 +--R (- 4a cos(x) + 8a cos(x) - 4a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 4a cos(x) + 8a cos(x) - 4a)cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x))cot(x) csc(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x))cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a cos(x)) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 4 3 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a cos(x))cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R - 16a cos(x) + 32a cos(x) - 16a cos(x) - 16a cos(x) +--R + +--R 16a +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 5 4 2 +--R - 16a cos(x) + 32a cos(x) - 16a cos(x) - 16a cos(x) +--R + +--R 16a +--R * +--R 2 +--R cot(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 24a cos(x) - 20a cos(x) - 32a cos(x) +--R + +--R 2 +--R 32a cos(x) + 16a cos(x) - 16a +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 24a cos(x) - 20a cos(x) - 32a cos(x) +--R + +--R 2 +--R 32a cos(x) + 16a cos(x) - 16a +--R * +--R 2 +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4a cos(x) - 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 +--R (- 8a cos(x) + 8a )cot(x) csc(x) +--R + +--R 2 2 2 2 +--R (- 8a cos(x) + 8a )cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4a cos(x) - 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 4 2 2 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 4a cos(x) + 16a cos(x) - 20a cos(x) + 8a )cot(x) csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 4a cos(x) + 16a cos(x) - 20a cos(x) + 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R \|csc(x) - 1 +--R / +--R 2 2 2 4 +--R ((4cos(x) - 8cos(x) + 4)csc(x) - 4cos(x) + 8cos(x) - 4)sin(x) +--R + +--R 3 2 2 3 +--R (16cos(x) - 32cos(x) + 16cos(x))csc(x) - 16cos(x) +--R + +--R 2 +--R 32cos(x) - 16cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))csc(x) - 8cos(x) +--R + +--R 3 2 +--R 32cos(x) - 40cos(x) + 16cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 2 +--R (16cos(x) - 32cos(x) + 16cos(x) + 16cos(x) - 16)csc(x) +--R + +--R 5 4 2 +--R - 16cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + 16 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) - 24cos(x) + 20cos(x) + 32cos(x) - 32cos(x) +--R + +--R - 16cos(x) + 16 +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) + 24cos(x) - 20cos(x) - 32cos(x) + 32cos(x) +--R + +--R 16cos(x) - 16 +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 4 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 2 2 2 3 +--R ((8a cos(x) - 8a)csc(x) - 8a cos(x) + 8a)sin(x) +--R + +--R 2 2 2 2 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 4 2 2 4 +--R (8a cos(x) - 16a cos(x) + 8a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 16a cos(x) - 8a +--R * +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (4a cos(x) - 16a cos(x) + 20a cos(x) - 8a)csc(x) - 4a cos(x) +--R + +--R 4 2 +--R 16a cos(x) - 20a cos(x) + 8a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression Integer +--E 377 + +--S 378 of 528 +t0373:= (a-a*csc(x))^(1/2) +--R +--R +--R +--------------+ +--R (340) \|- a csc(x) + a +--R Type: Expression Integer +--E 378 + +--S 379 of 528 +r0373:= -2*a*atan((-1-csc(x))^(1/2))*cot(x)/(-1-csc(x))^(1/2)/(a-a*csc(x))^(1/2) +--R +--R +--R +------------+ +--R 2a cot(x)atan(\|- csc(x) - 1 ) +--R (341) - -------------------------------- +--R +--------------+ +------------+ +--R \|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression Integer +--E 379 + +--S 380 of 528 +a0373:= integrate(t0373,x) +--R +--R +--R (342) +--R [ +--R +---+ +--R \|- a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R / +--R 2 +--R , +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R +-+ \| 4cos(x) - 4 +--R - \|a atan(-----------------------------------------------)] +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R Type: Union(List Expression Integer,...) +--E 380 + +--S 381 of 528 +m0373a:= a0373.1-r0373 +--R +--R +--R (343) +--R +---+ +--------------+ +------------+ +--R \|- a \|- a csc(x) + a \|- csc(x) - 1 +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R + +--R +------------+ +--R 4a cot(x)atan(\|- csc(x) - 1 ) +--R / +--R +--------------+ +------------+ +--R 2\|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression Integer +--E 381 + +--S 382 of 528 +d0373a:= D(m0373a,x) +--R +--R +--R (344) +--R 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a)csc(x) +--R + +--R 2 2 2 +--R (32a cos(x) - 64a cos(x) + 32a)cot(x) + 32a cos(x) +--R + +--R - 64a cos(x) + 32a +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (32a cos(x) - 64a cos(x) - 8a cos(x) + 80a cos(x) - 40a) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R (- 32a cos(x) + 64a cos(x) + 8a cos(x) - 80a cos(x) + 40a) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 +--R - 32a cos(x) + 64a cos(x) + 8a cos(x) - 80a cos(x) + 40a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R - 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R - 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 24a cos(x) + 16a cos(x) - 24a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 24a cos(x) - 16a cos(x) + 24a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 16a cos(x) - 24a cos(x) - 16a cos(x) + 24a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 16a cos(x) - 8a cos(x) + 40a cos(x) + 8a cos(x) - 24a ) +--R * +--R 2 +--R csc(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (16a cos(x) + 8a cos(x) - 40a cos(x) - 8a cos(x) + 24a ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 16a cos(x) + 8a cos(x) - 40a cos(x) - 8a cos(x) + 24a +--R * +--R +---+ +--R \|- a +--R * +--R +------------+ +--R atan(\|- csc(x) - 1 ) +--R + +--R 3 2 2 3 +--R (16cos(x) - 32cos(x) + 16cos(x))csc(x) - 16cos(x) +--R + +--R 2 +--R 32cos(x) - 16cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (8cos(x) - 16cos(x) + 8cos(x))csc(x) - 8cos(x) + 16cos(x) +--R + +--R - 8cos(x) +--R * +--R +---+ +--------------+ +--R \|- a \|- a csc(x) + a +--R + +--R 2 2 +--R (16a cos(x) - 32a cos(x) + 16a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a)cot(x) +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 32a cos(x) + 4a cos(x) - 40a cos(x) + 20a) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 4 3 2 2 +--R (16a cos(x) - 32a cos(x) - 4a cos(x) + 40a cos(x) - 20a)cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 2 2 2 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 4 3 2 2 +--R (- 4a cos(x) + 4a cos(x) + 4a cos(x) - 4a cos(x))csc(x) +--R + +--R 4 3 2 +--R 4a cos(x) - 4a cos(x) - 4a cos(x) + 4a cos(x) +--R * +--R +---+ +--------------+ +--R \|- a \|- a csc(x) + a +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (4a cos(x) - 2a cos(x) - a )csc(x) - 4a cos(x) + 2a cos(x) +--R + +--R 2 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 3 2 +--R (8a cos(x) - 9a cos(x) + a )csc(x) - 8a cos(x) + 9a cos(x) +--R + +--R 2 +--R - a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 4a cos(x) + 6a cos(x) + 4a cos(x) - 6a cos(x))csc(x) +--R + +--R 2 4 2 3 2 2 2 +--R 4a cos(x) - 6a cos(x) - 4a cos(x) + 6a cos(x) +--R * +--R +--------------+ +--R \|- a csc(x) + a +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 12a cos(x) - 8a cos(x) + 12a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a )cot(x) +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a ) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 4a cos(x) + 20a cos(x) + 4a cos(x) - 12a )cot(x) +--R * +--R +---+ +--R \|- a +--R * +--R +------------+ +--R \|- csc(x) - 1 +--R / +--R 2 2 2 +--R ((16cos(x) - 32cos(x) + 16)csc(x) - 16cos(x) + 32cos(x) - 16) +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 16cos(x) + 32cos(x) + 4cos(x) - 40cos(x) + 20)csc(x) +--R + +--R 4 3 2 +--R 16cos(x) - 32cos(x) - 4cos(x) + 40cos(x) - 20 +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 3 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a)csc(x) + 8a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 3 2 2 3 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a)csc(x) + 8a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) + 8a +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 3 +--R (8a cos(x) - 12a cos(x) - 8a cos(x) + 12a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 12a cos(x) + 8a cos(x) - 12a +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a)csc(x) +--R + +--R 4 3 2 +--R - 8a cos(x) - 4a cos(x) + 20a cos(x) + 4a cos(x) - 12a +--R * +--R +---+ +--------------+ +------------+ +--R \|- a \|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression Integer +--E 382 + +--S 383 of 528 +m0373b:= a0373.2-r0373 +--R +--R +--R (345) +--R +------------+ +--R 2a cot(x)atan(\|- csc(x) - 1 ) +--R + +--R - +--R +-+ +--------------+ +------------+ +--R \|a \|- a csc(x) + a \|- csc(x) - 1 +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R / +--R +--------------+ +------------+ +--R \|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression Integer +--E 383 + +--S 384 of 528 +d0373b:= D(m0373b,x) +--R +--R +--R (346) +--R 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a)csc(x) +--R + +--R 2 2 2 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x) + 8a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (32a cos(x) - 64a cos(x) + 32a cos(x))csc(x) +--R + +--R 3 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a cos(x))cot(x) +--R + +--R 3 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 64a cos(x) - 80a cos(x) + 32a cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 2 +--R (16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x))cot(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R 32a cos(x) - 64a cos(x) + 32a cos(x) + 32a cos(x) +--R + +--R - 32a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) - 32a cos(x) +--R + +--R 32a +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) - 32a cos(x) + 32a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 48a cos(x) - 40a cos(x) - 64a cos(x) +--R + +--R 2 +--R 64a cos(x) + 32a cos(x) - 32a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (16a cos(x) - 16a )csc(x) + (- 16a cos(x) + 16a )cot(x) +--R + +--R 2 2 2 +--R - 16a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (16a cos(x) - 32a cos(x) + 16a )csc(x) +--R + +--R 2 4 2 2 2 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a )cot(x) - 16a cos(x) +--R + +--R 2 2 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a )csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (8a cos(x) - 32a cos(x) + 40a cos(x) - 16a )cot(x) +--R + +--R 2 6 2 4 2 2 2 +--R 8a cos(x) - 32a cos(x) + 40a cos(x) - 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +--R atan(\|- csc(x) - 1 ) +--R + +--R 2 2 +--R (4a cos(x) - 8a cos(x) + 4a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 4a cos(x) + 8a cos(x) - 4a)cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x))cot(x) csc(x) +--R + +--R 3 2 2 +--R (16a cos(x) - 32a cos(x) + 16a cos(x))cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 +--R (8a cos(x) - 32a cos(x) + 40a cos(x) - 16a cos(x))cot(x) +--R * +--R csc(x) +--R + +--R 4 3 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a cos(x))cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x) - 16a cos(x) + 16a) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 5 4 2 2 +--R (16a cos(x) - 32a cos(x) + 16a cos(x) + 16a cos(x) - 16a)cot(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 24a cos(x) + 20a cos(x) + 32a cos(x) +--R + +--R 2 +--R - 32a cos(x) - 16a cos(x) + 16a +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 24a cos(x) - 20a cos(x) - 32a cos(x) +--R + +--R 2 +--R 32a cos(x) + 16a cos(x) - 16a +--R * +--R 2 +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 +--R (4a cos(x) + 2a cos(x) - 6a)csc(x) - 4a cos(x) - 2a cos(x) +--R + +--R 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (8a cos(x) - 2a cos(x) - 6a)csc(x) - 8a cos(x) + 2a cos(x) +--R + +--R 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 +--R (14a cos(x) - 14a cos(x) - 4a cos(x) + 4a)csc(x) - 14a cos(x) +--R + +--R 2 +--R 14a cos(x) + 4a cos(x) - 4a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (8a cos(x) - 2a cos(x) - 4a cos(x) - 10a cos(x) + 8a)csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 2a cos(x) + 4a cos(x) + 10a cos(x) - 8a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R (- 4a cos(x) + 12a cos(x) + 4a cos(x) - 20a cos(x) + 8a cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 12a cos(x) - 4a cos(x) + 20a cos(x) - 8a cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 4a cos(x) + 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 8a cos(x) + 8a )cot(x) csc(x) + (8a cos(x) - 8a )cot(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 4a cos(x) + 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 4 2 2 2 2 +--R (8a cos(x) - 16a cos(x) + 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (4a cos(x) - 16a cos(x) + 20a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 4a cos(x) + 16a cos(x) - 20a cos(x) + 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 5 +--R (a csc(x) - a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (2a cos(x) - a cos(x) + 2a )csc(x) - 2a cos(x) + a cos(x) +--R + +--R 2 +--R - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 4a cos(x) + 3a cos(x) + a cos(x) + 3a )csc(x) + 4a cos(x) +--R + +--R 2 2 2 2 +--R - 3a cos(x) - a cos(x) - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 5a cos(x) + 6a cos(x) + 2a cos(x) - 2a )csc(x) + 5a cos(x) +--R + +--R 2 2 2 2 +--R - 6a cos(x) - 2a cos(x) + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 4a cos(x) + 2a cos(x) + 7a cos(x) + 3a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 4a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R 4a cos(x) - 2a cos(x) - 7a cos(x) - 3a cos(x) + 4a cos(x) + 4a +--R * +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R - 2a cos(x) - 4a cos(x) + 6a cos(x) + 8a cos(x) - 4a cos(x) +--R + +--R 2 +--R - 4a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 2a cos(x) + 4a cos(x) - 6a cos(x) - 8a cos(x) + 4a cos(x) +--R + +--R 2 +--R 4a cos(x) +--R * +--R +--------------+ +------------+ +--R \|- a csc(x) + a \|- csc(x) - 1 +--R / +--R 2 2 2 4 +--R ((4cos(x) - 8cos(x) + 4)csc(x) - 4cos(x) + 8cos(x) - 4)sin(x) +--R + +--R 3 2 2 3 +--R (- 16cos(x) + 32cos(x) - 16cos(x))csc(x) + 16cos(x) +--R + +--R 2 +--R - 32cos(x) + 16cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))csc(x) - 8cos(x) +--R + +--R 3 2 +--R 32cos(x) - 40cos(x) + 16cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 2 +--R (- 16cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + 16)csc(x) +--R + +--R 5 4 2 +--R 16cos(x) - 32cos(x) + 16cos(x) + 16cos(x) - 16 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) - 24cos(x) + 20cos(x) + 32cos(x) - 32cos(x) +--R + +--R - 16cos(x) + 16 +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) + 24cos(x) - 20cos(x) - 32cos(x) + 32cos(x) + 16cos(x) +--R + +--R - 16 +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 4 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 2 2 2 3 +--R ((- 8a cos(x) + 8a)csc(x) + 8a cos(x) - 8a)sin(x) +--R + +--R 2 2 2 2 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 4 2 2 4 +--R (- 8a cos(x) + 16a cos(x) - 8a)csc(x) + 8a cos(x) +--R + +--R 2 +--R - 16a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (4a cos(x) - 16a cos(x) + 20a cos(x) - 8a)csc(x) - 4a cos(x) +--R + +--R 4 2 +--R 16a cos(x) - 20a cos(x) + 8a +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R Type: Expression Integer +--E 384 + +--S 385 of 528 +t0374:= 1/(a+a*csc(x))^(1/2) +--R +--R +--R 1 +--R (347) --------------- +--R +------------+ +--R \|a csc(x) + a +--R Type: Expression Integer +--E 385 + +--S 386 of 528 +r0374:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a+a*csc(x))^(1/2))+2*atan((-a+a*csc(x))^(1/2)/a^(1/2)))*(-a+a*csc(x))^(1/2)*(a+a*csc(x))^(1/2)*tan(x)/a^(3/2) +--R +--R +--R (348) +--R +------------+ +--R +------------+ +------------+ \|a csc(x) - a +--R - 2tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +------------+ +------------+ \|2 \|a +--R - \|2 tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 386 + +--S 387 of 528 +a0374:= integrate(t0374,x) +--R +--R +--R (349) +--R [ +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) - cos(x) + 1) |- 4|--------------- +--R +---+ |2 \|a \| 4cos(x) - 4 +--R - 2\|- a |- atan(-------------------------------------------) +--R \|a cos(x) +--R / +--R +---+ +--R 2\|- a +--R , +--R +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List Expression Integer,...) +--E 387 + +--S 388 of 528 +m0374a:= a0374.1-r0374 +--R +--R +--R (350) +--R +-+ +--R a\|a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R + +--R +------------+ +--R +---+ +------------+ +------------+ \|a csc(x) - a +--R 4tan(x)\|- a \|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +-+ +--R \|a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) - cos(x) + 1) |- 4|--------------- +--R +---+ |2 +-+ \|a \| 4cos(x) - 4 +--R - 2a\|- a |- \|a atan(-------------------------------------------) +--R \|a cos(x) +--R + +--R +-+ +-+ +--R +-+ +---+ +------------+ +------------+ \|2 \|a +--R 2\|2 tan(x)\|- a \|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression Integer +--E 388 + +--S 389 of 528 +d0374a:= D(m0374a,x) +--R +--R +--R (351) +--R 6 5 4 3 +--R 32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) +--R + +--R 3 2 +--R - 64cos(x) + 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 4 3 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 6 5 4 3 2 +--R (32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) - 48cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) - 64cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 3 +--R (16a cos(x) - 32a cos(x) + 16a)cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) +--R + +--R 3 2 +--R - 48a cos(x) - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 +--R (16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) - 48a cos(x) +--R + +--R 2 +--R - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) + 8a cos(x) - 8a cos(x) - 8a )cot(x)csc(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R +-+ +--R \|a +--R * +--R +------------+ +--R \|a csc(x) - a +--R atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) + 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 32\|2 cos(x) + 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) + 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 3 +--R (8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 40a\|2 cos(x) + 28a\|2 cos(x) + 16a\|2 cos(x) - 12a\|2 +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) +--R + +--R 2 +-+ +--R - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R (4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 ) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) + 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R +-+ +--R \|a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R + +--R 3 2 3 +--R (- 16cos(x) + 8cos(x) + 24cos(x) - 16)sin(x) +--R + +--R 5 4 3 2 +--R (- 24cos(x) + 20cos(x) + 34cos(x) - 28cos(x) - 6cos(x) + 4) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 16cos(x) - 40cos(x) - 2cos(x) + 70cos(x) - 34cos(x) +--R + +--R - 30cos(x) + 20 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 8cos(x) - 4cos(x) + 40cos(x) - 16cos(x) - 32cos(x) +--R + +--R 2 +--R 20cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 4cos(x) + 4cos(x))sin(x) +--R + +--R 4 3 2 3 +--R (8cos(x) - 4cos(x) - 8cos(x) + 4cos(x))sin(x) +--R + +--R 5 3 7 6 +--R (4cos(x) - 8cos(x) + 4cos(x))sin(x) + 4cos(x) - 12cos(x) +--R + +--R 4 3 2 +--R 20cos(x) - 8cos(x) - 8cos(x) + 4cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 4 +--R (4a cos(x) + 2a cos(x) - 3a cos(x) - a)sin(x) +--R + +--R 4 2 3 +--R (- 8a cos(x) + 3a cos(x) + 5a)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 27a cos(x) + 11a cos(x) +--R + +--R 11a cos(x) - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 4a cos(x) - 19a cos(x) + 2a cos(x) +--R + +--R 2 +--R 20a cos(x) + 2a cos(x) - 9a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 4a cos(x) + 2a cos(x) + 2a cos(x) - 4a cos(x) + 8a cos(x) +--R + +--R 2 +--R 2a cos(x) - 6a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (4a cos(x) - 4a cos(x) - 18a cos(x) + 2a cos(x) + 12a)sin(x) +--R + +--R 5 4 2 2 +--R (- 2a cos(x) - 10a cos(x) + 10a cos(x) + 2a cos(x))sin(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 6a cos(x) - 22a cos(x) + 8a cos(x) +--R + +--R 2 +--R 30a cos(x) - 2a cos(x) - 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 6a cos(x) - 10a cos(x) + 10a cos(x) + 20a cos(x) +--R + +--R 3 2 +--R - 2a cos(x) - 10a cos(x) - 2a cos(x) +--R * +--R +---+ +--R \|- a +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R + +--R 6 5 4 3 2 +--R (- 16cos(x) + 40cos(x) - 8cos(x) - 40cos(x) + 24cos(x) ) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 3 +--R 16cos(x) - 8cos(x) - 48cos(x) + 32cos(x) + 32cos(x) +--R + +--R 2 +--R - 24cos(x) +--R * +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R tan(x)\|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 3 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x)sin(x) +--R + +--R 5 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 8a cos(x) - 16a cos(x) + 8a cos(x) +--R + +--R 2 +--R 16a cos(x) - 8a +--R * +--R cot(x)sin(x) +--R + +--R 7 5 4 3 +--R - 8a cos(x) + 34a cos(x) - 10a cos(x) - 42a cos(x) +--R + +--R 2 +--R 18a cos(x) + 16a cos(x) - 8a +--R * +--R cot(x) +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R tan(x) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 +--R (8a cos(x) - 4a cos(x) - 20a cos(x) + 4a cos(x) + 12a)cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 24a cos(x) + 12a cos(x) + 48a cos(x) - 24a cos(x) +--R + +--R - 24a cos(x) + 12a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 24a cos(x) - 12a cos(x) - 60a cos(x) + 24a cos(x) +--R + +--R 2 +--R 48a cos(x) - 12a cos(x) - 12a +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R - 8a cos(x) + 4a cos(x) + 32a cos(x) - 20a cos(x) +--R + +--R 3 2 +--R - 40a cos(x) + 28a cos(x) + 16a cos(x) - 12a +--R * +--R cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +---+ |- a cos(x) - a +--R tan(x)\|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 3 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a )cot(x)sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R 4a cos(x) - 4a cos(x) - 9a cos(x) + 7a cos(x) + 5a cos(x) +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 4a cos(x) + 4a cos(x) + 14a cos(x) - 8a cos(x) +--R + +--R 2 2 2 2 +--R - 16a cos(x) + 4a cos(x) + 6a +--R * +--R cot(x)sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 4a cos(x) - 8a cos(x) - 13a cos(x) + 21a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 14a cos(x) - 18a cos(x) - 5a cos(x) + 5a +--R * +--R cot(x) +--R * +--R tan(x) +--R * +--R +------------+ +--R \|a csc(x) - a +--R / +--R 6 5 4 3 2 +--R (16cos(x) - 40cos(x) + 8cos(x) + 40cos(x) - 24cos(x) )sin(x) +--R + +--R 7 6 5 4 3 +--R - 16cos(x) + 8cos(x) + 48cos(x) - 32cos(x) - 32cos(x) +--R + +--R 2 +--R 24cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 3 +--R (- 8a cos(x) + 16a cos(x) - 8a)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) - 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 8a cos(x) + 16a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 16a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 5 4 3 2 +--R 8a cos(x) - 34a cos(x) + 10a cos(x) + 42a cos(x) - 18a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (- 8a cos(x) + 4a cos(x) + 20a cos(x) - 4a cos(x) - 12a)sin(x) +--R + +--R 5 4 3 2 +--R 24a cos(x) - 12a cos(x) - 48a cos(x) + 24a cos(x) +--R + +--R 24a cos(x) - 12a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 24a cos(x) + 12a cos(x) + 60a cos(x) - 24a cos(x) +--R + +--R 2 +--R - 48a cos(x) + 12a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 8a cos(x) - 4a cos(x) - 32a cos(x) + 20a cos(x) + 40a cos(x) +--R + +--R 2 +--R - 28a cos(x) - 16a cos(x) + 12a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 3 +--R (- 4a cos(x) - 4a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R - 4a cos(x) + 4a cos(x) + 9a cos(x) - 7a cos(x) - 5a cos(x) +--R + +--R 2 +--R 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 4a cos(x) - 4a cos(x) - 14a cos(x) + 8a cos(x) + 16a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 6a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R - 4a cos(x) + 8a cos(x) + 13a cos(x) - 21a cos(x) - 14a cos(x) +--R + +--R 2 2 2 2 +--R 18a cos(x) + 5a cos(x) - 5a +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R Type: Expression Integer +--E 389 + +--S 390 of 528 +m0374b:= a0374.2-r0374 +--R +--R +--R (352) +--R +------------+ +--R +------------+ +------------+ \|a csc(x) - a +--R 2tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +-+ +--R \|a +--R + +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R a atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - a |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R + +--R +-+ +-+ +--R +-+ +------------+ +------------+ \|2 \|a +--R \|2 tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 390 + +--S 391 of 528 +d0374b:= D(m0374b,x) +--R +--R +--R (353) +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 +--R ((- 32cos(x) + 32cos(x))csc(x) + 32cos(x) - 32cos(x)) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (- 32cos(x) + 64cos(x) - 32cos(x))csc(x) + 32cos(x) +--R + +--R 3 +--R - 64cos(x) + 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 3 +--R (32cos(x) - 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 2 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 5 3 2 +--R (32cos(x) - 64cos(x) + 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 7 5 3 2 +--R (16cos(x) - 64cos(x) + 80cos(x) - 32cos(x))cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 3 +--R ((- 32cos(x) + 32cos(x))csc(x) + 32cos(x) - 32cos(x))sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (- 32cos(x) + 64cos(x) - 32cos(x))csc(x) + 32cos(x) +--R + +--R 3 +--R - 64cos(x) + 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 3 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x)) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 4 +--R (16a cos(x) - 16a cos(x) )csc(x) - 16a cos(x) +--R + +--R 2 +--R 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 4a cos(x) + 4a cos(x))cot(x)csc(x) sin(x) +--R + +--R 4 2 2 3 +--R (- 16a cos(x) + 16a cos(x) )cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R (- 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) ) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 4 2 2 4 +--R (16a cos(x) - 16a cos(x) )csc(x) - 16a cos(x) +--R + +--R 2 +--R 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) )csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +--R \|a csc(x) - a +--R atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (- 16\|2 cos(x) + 16\|2 cos(x))csc(x) + 16\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 3 +--R (16\|2 cos(x) - 16\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 2 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x))cot(x)csc(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (- 16\|2 cos(x) + 16\|2 cos(x))csc(x) + 16\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) + 16\|2 cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (8a\|2 cos(x) - 8a\|2 cos(x) )csc(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ +--R - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 2a\|2 cos(x) + 2a\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 4 +-+ 2 2 3 +--R (- 8a\|2 cos(x) + 8a\|2 cos(x) )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (8a\|2 cos(x) - 8a\|2 cos(x) )csc(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R + +--R 5 +--R (4cos(x) + 2)sin(x) +--R + +--R 3 2 4 +--R (4cos(x) + 6cos(x) - 12cos(x) - 8)sin(x) +--R + +--R 4 3 2 3 +--R (8cos(x) - 2cos(x) - 14cos(x) + 6cos(x) + 4)sin(x) +--R + +--R 4 3 2 2 +--R (- 2cos(x) - 4cos(x) - 12cos(x) + 4cos(x) + 16)sin(x) +--R + +--R 6 5 4 3 2 +--R (8cos(x) - 6cos(x) - 28cos(x) + 6cos(x) + 36cos(x) - 16) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 4cos(x) - 8cos(x) + 12cos(x) + 16cos(x) - 8cos(x) - 8cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 5 +--R (- a cos(x) - a)sin(x) +--R + +--R 3 2 4 +--R (- 2a cos(x) - a cos(x) + 5a cos(x) + 4a)sin(x) +--R + +--R 4 3 2 3 +--R (4a cos(x) + 9a cos(x) + 4a cos(x) - 3a cos(x) - 2a)sin(x) +--R + +--R 4 3 2 2 +--R (- 3a cos(x) + a cos(x) + 2a cos(x) - 10a cos(x) - 8a)sin(x) +--R + +--R 6 5 4 3 2 +--R 4a cos(x) + 10a cos(x) + 3a cos(x) - 17a cos(x) - 14a cos(x) +--R + +--R 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 2a cos(x) - 2a cos(x) - 10a cos(x) - 2a cos(x) + 8a cos(x) +--R + +--R 2 +--R 4a cos(x) +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R + +--R 3 4 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 3 3 +--R (16cos(x) - 16cos(x))cot(x)sin(x) +--R + +--R 3 2 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 5 3 +--R (16cos(x) - 32cos(x) + 16cos(x))cot(x)sin(x) +--R + +--R 7 5 3 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R tan(x) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 2a cos(x) + 2a cos(x))cot(x)sin(x) +--R + +--R 4 2 3 +--R (- 8a cos(x) + 8a cos(x) )cot(x)sin(x) +--R + +--R 5 4 3 2 +--R (- 4a cos(x) + 8a cos(x) + 4a cos(x) - 8a cos(x) )cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 8a cos(x) +--R + +--R - 8a cos(x) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R - 2a cos(x) + 8a cos(x) + 10a cos(x) - 16a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) + 8a cos(x) + 8a cos(x) +--R * +--R cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R tan(x) 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +--R \|a csc(x) - a +--R / +--R 3 4 3 3 +--R (8cos(x) - 8cos(x))sin(x) + (- 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 +--R (8cos(x) - 8cos(x))sin(x) +--R + +--R 5 3 7 5 +--R (- 16cos(x) + 32cos(x) - 16cos(x))sin(x) - 8cos(x) + 32cos(x) +--R + +--R 3 +--R - 40cos(x) + 16cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 4 2 3 +--R (2a cos(x) - 2a cos(x))sin(x) + (8a cos(x) - 8a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (4a cos(x) - 8a cos(x) - 4a cos(x) + 8a cos(x) )sin(x) +--R + +--R 6 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 8a cos(x) + 8a cos(x)) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 2a cos(x) - 8a cos(x) - 10a cos(x) + 16a cos(x) + 16a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R Type: Expression Integer +--E 391 + +--S 392 of 528 +t0375:= 1/(a-a*csc(x))^(1/2) +--R +--R +--R 1 +--R (354) ----------------- +--R +--------------+ +--R \|- a csc(x) + a +--R Type: Expression Integer +--E 392 + +--S 393 of 528 +r0375:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a-a*csc(x))^(1/2))+2*atan((-a-a*csc(x))^(1/2)/a^(1/2)))*(-a-a*csc(x))^(1/2)*(a-a*csc(x))^(1/2)*tan(x)/a^(3/2) +--R +--R +--R (355) +--R +--------------+ +--R +--------------+ +--------------+ \|- a csc(x) - a +--R - 2tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +--------------+ +--------------+ \|2 \|a +--R - \|2 tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 393 + +--S 394 of 528 +a0375:= integrate(t0375,x) +--R +--R +--R (356) +--R [ +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) + cos(x) - 1) |- 4|--------------- +--R +---+ |2 \|a \| 4cos(x) - 4 +--R 2\|- a |- atan(-------------------------------------------) +--R \|a cos(x) +--R / +--R +---+ +--R 2\|- a +--R , +--R +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R - atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List Expression Integer,...) +--E 394 + +--S 395 of 528 +m0375a:= a0375.1-r0375 +--R +--R +--R (357) +--R +-+ +--R a\|a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) + cos(x) - 1) |- 4|--------------- +--R +---+ |2 +-+ \|a \| 4cos(x) - 4 +--R 2a\|- a |- \|a atan(-------------------------------------------) +--R \|a cos(x) +--R + +--R +--------------+ +--R +---+ +--------------+ +--------------+ \|- a csc(x) - a +--R 4tan(x)\|- a \|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +---+ +--------------+ +--------------+ \|2 \|a +--R 2\|2 tan(x)\|- a \|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression Integer +--E 395 + +--S 396 of 528 +d0375a:= D(m0375a,x) +--R +--R +--R (358) +--R 6 5 4 3 +--R 32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) - 64cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 4 3 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) +--R + +--R 3 2 +--R - 64cos(x) + 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 6 5 4 3 2 +--R (32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) - 48cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) - 64cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 32a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 3 +--R (16a cos(x) - 32a cos(x) + 16a)cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) +--R + +--R 2 +--R - 48a cos(x) - 48a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) +--R + +--R 3 2 +--R - 48a cos(x) - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 +--R (16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) - 48a cos(x) +--R + +--R 2 +--R - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) + 8a cos(x) - 8a cos(x) - 8a )cot(x)csc(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R \|- a csc(x) - a +--R atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 32\|2 cos(x) + 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) + 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 3 +--R (8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) + 42a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 40a\|2 cos(x) - 28a\|2 cos(x) - 16a\|2 cos(x) + 12a\|2 +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) +--R + +--R 2 +-+ +--R - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R (4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 ) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) + 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R +-+ +--R \|a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R + +--R 3 2 3 +--R (16cos(x) - 8cos(x) - 24cos(x) + 16)sin(x) +--R + +--R 5 4 3 2 +--R (- 24cos(x) + 20cos(x) + 34cos(x) - 28cos(x) - 6cos(x) + 4) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) + 40cos(x) + 2cos(x) - 70cos(x) + 34cos(x) +--R + +--R 30cos(x) - 20 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 8cos(x) - 4cos(x) + 40cos(x) - 16cos(x) - 32cos(x) +--R + +--R 2 +--R 20cos(x) +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 6 5 4 3 2 +--R (- 16cos(x) + 40cos(x) - 8cos(x) - 40cos(x) + 24cos(x) ) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 3 +--R - 16cos(x) + 8cos(x) + 48cos(x) - 32cos(x) - 32cos(x) +--R + +--R 2 +--R 24cos(x) +--R * +--R cot(x) +--R * +--R +---+ +--------------+ +--R tan(x)\|- a \|- a csc(x) - a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 4cos(x) + 4cos(x))sin(x) +--R + +--R 4 3 2 3 +--R (- 8cos(x) + 4cos(x) + 8cos(x) - 4cos(x))sin(x) +--R + +--R 5 3 7 6 +--R (- 4cos(x) + 8cos(x) - 4cos(x))sin(x) + 4cos(x) - 12cos(x) +--R + +--R 4 3 2 +--R 20cos(x) - 8cos(x) - 8cos(x) + 4cos(x) +--R * +--R +---+ +--------------+ +--------------+ +--R \|- a \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 4 2 3 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) - 8a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 8a cos(x) - 16a cos(x) + 8a cos(x) +--R + +--R 2 +--R 16a cos(x) - 8a +--R * +--R cot(x)sin(x) +--R + +--R 7 5 4 3 +--R 8a cos(x) - 34a cos(x) + 10a cos(x) + 42a cos(x) +--R + +--R 2 +--R - 18a cos(x) - 16a cos(x) + 8a +--R * +--R cot(x) +--R * +--R +--------------+ +--R tan(x)\|- a csc(x) - a +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 4 +--R (4a cos(x) + 2a cos(x) - 3a cos(x) - a)sin(x) +--R + +--R 4 2 3 +--R (8a cos(x) - 3a cos(x) - 5a)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 27a cos(x) + 11a cos(x) +--R + +--R 11a cos(x) - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 4a cos(x) + 19a cos(x) - 2a cos(x) +--R + +--R 2 +--R - 20a cos(x) - 2a cos(x) + 9a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 4a cos(x) + 2a cos(x) + 2a cos(x) - 4a cos(x) + 8a cos(x) +--R + +--R 2 +--R 2a cos(x) - 6a cos(x) +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 4 3 2 +--R (8a cos(x) - 4a cos(x) - 20a cos(x) + 4a cos(x) + 12a)cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 24a cos(x) - 12a cos(x) - 48a cos(x) + 24a cos(x) +--R + +--R 24a cos(x) - 12a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 24a cos(x) - 12a cos(x) - 60a cos(x) + 24a cos(x) +--R + +--R 2 +--R 48a cos(x) - 12a cos(x) - 12a +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R 8a cos(x) - 4a cos(x) - 32a cos(x) + 20a cos(x) +--R + +--R 3 2 +--R 40a cos(x) - 28a cos(x) - 16a cos(x) + 12a +--R * +--R cot(x) +--R * +--R +---+ +--------------+ +--R tan(x)\|- a \|- a csc(x) - a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (- 4a cos(x) + 4a cos(x) + 18a cos(x) - 2a cos(x) - 12a)sin(x) +--R + +--R 5 4 2 2 +--R (- 2a cos(x) - 10a cos(x) + 10a cos(x) + 2a cos(x))sin(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 6a cos(x) + 22a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 30a cos(x) + 2a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 6a cos(x) - 10a cos(x) + 10a cos(x) + 20a cos(x) - 2a cos(x) +--R + +--R 2 +--R - 10a cos(x) - 2a cos(x) +--R * +--R +---+ +--------------+ +--------------+ +--R \|- a \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 2 3 2 2 2 2 3 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a )cot(x)sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R - 4a cos(x) + 4a cos(x) + 9a cos(x) - 7a cos(x) - 5a cos(x) +--R + +--R 2 +--R 3a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 4a cos(x) + 4a cos(x) + 14a cos(x) - 8a cos(x) +--R + +--R 2 2 2 2 +--R - 16a cos(x) + 4a cos(x) + 6a +--R * +--R cot(x)sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 4a cos(x) + 8a cos(x) + 13a cos(x) - 21a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 14a cos(x) + 18a cos(x) + 5a cos(x) - 5a +--R * +--R cot(x) +--R * +--R +--------------+ +--R tan(x)\|- a csc(x) - a +--R / +--R 6 5 4 3 2 +--R (16cos(x) - 40cos(x) + 8cos(x) + 40cos(x) - 24cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R 16cos(x) - 8cos(x) - 48cos(x) + 32cos(x) + 32cos(x) - 24cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +--------------+ +--------------+ |- a cos(x) - a +--R \|- a \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 3 +--R (- 8a cos(x) + 16a cos(x) - 8a)sin(x) +--R + +--R 5 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 8a cos(x) + 16a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 16a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 5 4 3 2 +--R - 8a cos(x) + 34a cos(x) - 10a cos(x) - 42a cos(x) + 18a cos(x) +--R + +--R 16a cos(x) - 8a +--R * +--R +---------------+2 +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (- 8a cos(x) + 4a cos(x) + 20a cos(x) - 4a cos(x) - 12a)sin(x) +--R + +--R 5 4 3 2 +--R - 24a cos(x) + 12a cos(x) + 48a cos(x) - 24a cos(x) +--R + +--R - 24a cos(x) + 12a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 24a cos(x) + 12a cos(x) + 60a cos(x) - 24a cos(x) +--R + +--R 2 +--R - 48a cos(x) + 12a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 8a cos(x) + 4a cos(x) + 32a cos(x) - 20a cos(x) - 40a cos(x) +--R + +--R 2 +--R 28a cos(x) + 16a cos(x) - 12a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +--------------+ +--------------+ |- a cos(x) - a +--R \|- a \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 3 +--R (- 4a cos(x) - 4a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R 4a cos(x) - 4a cos(x) - 9a cos(x) + 7a cos(x) + 5a cos(x) +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 4a cos(x) - 4a cos(x) - 14a cos(x) + 8a cos(x) + 16a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 6a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R 4a cos(x) - 8a cos(x) - 13a cos(x) + 21a cos(x) + 14a cos(x) +--R + +--R 2 2 2 2 +--R - 18a cos(x) - 5a cos(x) + 5a +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R Type: Expression Integer +--E 396 + +--S 397 of 528 +m0375b:= a0375.2-r0375 +--R +--R +--R (359) +--R +--------------+ +--R +--------------+ +--------------+ \|- a csc(x) - a +--R 2tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +--------------+ +--------------+ \|2 \|a +--R \|2 tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R + +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R - a atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - a |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R / +--R +-+ +--R a\|a +--R Type: Expression Integer +--E 397 + +--S 398 of 528 +d0375b:= D(m0375b,x) +--R +--R +--R (360) +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 3 +--R ((32cos(x) - 32cos(x))csc(x) - 32cos(x) + 32cos(x))sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (32cos(x) - 64cos(x) + 32cos(x))csc(x) - 32cos(x) +--R + +--R 3 +--R 64cos(x) - 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 3 +--R (- 32cos(x) + 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 2 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 5 3 2 +--R (- 32cos(x) + 64cos(x) - 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 7 5 3 2 +--R (16cos(x) - 64cos(x) + 80cos(x) - 32cos(x))cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 3 +--R ((32cos(x) - 32cos(x))csc(x) - 32cos(x) + 32cos(x))sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (32cos(x) - 64cos(x) + 32cos(x))csc(x) - 32cos(x) +--R + +--R 3 +--R 64cos(x) - 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 3 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x)) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 16a cos(x) )csc(x) + 16a cos(x) +--R + +--R 2 +--R - 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 4a cos(x) + 4a cos(x))cot(x)csc(x) sin(x) +--R + +--R 4 2 2 3 +--R (16a cos(x) - 16a cos(x) )cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R (- 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) ) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 16a cos(x) )csc(x) + 16a cos(x) +--R + +--R 2 +--R - 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) )csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +--------------+ +--R \|- a csc(x) - a +--R atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (16\|2 cos(x) - 16\|2 cos(x))csc(x) - 16\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 3 +--R (- 16\|2 cos(x) + 16\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 2 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x))cot(x) +--R * +--R 2 +--R csc(x) sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (16\|2 cos(x) - 16\|2 cos(x))csc(x) - 16\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) + 16\|2 cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (- 8a\|2 cos(x) + 8a\|2 cos(x) )csc(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ +--R - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 2a\|2 cos(x) + 2a\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 4 +-+ 2 2 3 +--R (8a\|2 cos(x) - 8a\|2 cos(x) )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (- 8a\|2 cos(x) + 8a\|2 cos(x) )csc(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R + +--R 3 4 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 3 3 +--R (- 16cos(x) + 16cos(x))cot(x)sin(x) +--R + +--R 3 2 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 5 3 +--R (- 16cos(x) + 32cos(x) - 16cos(x))cot(x)sin(x) +--R + +--R 7 5 3 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ |- a cos(x) - a +--R tan(x)\|- a csc(x) - a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 5 3 2 4 +--R (4cos(x) + 2)sin(x) + (- 4cos(x) - 6cos(x) + 12cos(x) + 8)sin(x) +--R + +--R 4 3 2 3 +--R (8cos(x) - 2cos(x) - 14cos(x) + 6cos(x) + 4)sin(x) +--R + +--R 4 3 2 2 +--R (2cos(x) + 4cos(x) + 12cos(x) - 4cos(x) - 16)sin(x) +--R + +--R 6 5 4 3 2 +--R (8cos(x) - 6cos(x) - 28cos(x) + 6cos(x) + 36cos(x) - 16)sin(x) +--R + +--R 7 6 5 4 3 2 +--R 4cos(x) + 8cos(x) - 12cos(x) - 16cos(x) + 8cos(x) + 8cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 2a cos(x) + 2a cos(x))cot(x)sin(x) +--R + +--R 4 2 3 +--R (8a cos(x) - 8a cos(x) )cot(x)sin(x) +--R + +--R 5 4 3 2 2 +--R (- 4a cos(x) + 8a cos(x) + 4a cos(x) - 8a cos(x) )cot(x)sin(x) +--R + +--R 6 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 8a cos(x) + 8a cos(x)) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R - 2a cos(x) + 8a cos(x) + 10a cos(x) - 16a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) + 8a cos(x) + 8a cos(x) +--R * +--R cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ |- a cos(x) - a +--R tan(x)\|- a csc(x) - a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 5 +--R (- a cos(x) - a)sin(x) +--R + +--R 3 2 4 +--R (2a cos(x) + a cos(x) - 5a cos(x) - 4a)sin(x) +--R + +--R 4 3 2 3 +--R (4a cos(x) + 9a cos(x) + 4a cos(x) - 3a cos(x) - 2a)sin(x) +--R + +--R 4 3 2 2 +--R (3a cos(x) - a cos(x) - 2a cos(x) + 10a cos(x) + 8a)sin(x) +--R + +--R 6 5 4 3 2 +--R 4a cos(x) + 10a cos(x) + 3a cos(x) - 17a cos(x) - 14a cos(x) +--R + +--R 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 2a cos(x) + 2a cos(x) + 10a cos(x) + 2a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 4a cos(x) +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R / +--R 3 4 3 3 +--R (8cos(x) - 8cos(x))sin(x) + (16cos(x) - 16cos(x))sin(x) +--R + +--R 3 2 +--R (8cos(x) - 8cos(x))sin(x) +--R + +--R 5 3 7 5 +--R (16cos(x) - 32cos(x) + 16cos(x))sin(x) - 8cos(x) + 32cos(x) +--R + +--R 3 +--R - 40cos(x) + 16cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 4 2 3 +--R (2a cos(x) - 2a cos(x))sin(x) + (- 8a cos(x) + 8a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (4a cos(x) - 8a cos(x) - 4a cos(x) + 8a cos(x) )sin(x) +--R + +--R 6 4 3 2 +--R (- 8a cos(x) + 16a cos(x) + 8a cos(x) - 8a cos(x) - 8a cos(x)) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 2a cos(x) - 8a cos(x) - 10a cos(x) + 16a cos(x) + 16a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R Type: Expression Integer +--E 398 + +--S 399 of 528 +t0376:= (a+b*csc(c+d*x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (361) b csc(d x + c) + 3a b csc(d x + c) + 3a b csc(d x + c) + a +--R Type: Expression Integer +--E 399 + +--S 400 of 528 +r0376:= a^3*x-3*a^2*b*atanh(cos(c+d*x))/d-1/2*b^3*atanh(cos(c+d*x))/d-3*a*b^2*cot(c+d*x)/d-1/2*b^3*cot(c+d*x)*csc(c+d*x)/d +--R +--R +--R (362) +--R 3 2 3 +--R (- b - 6a b)atanh(cos(d x + c)) - b cot(d x + c)csc(d x + c) +--R + +--R 2 3 +--R - 6a b cot(d x + c) + 2a d x +--R / +--R 2d +--R Type: Expression Integer +--E 400 + +--S 401 of 528 +a0376:= integrate(t0376,x) +--R +--R +--R (363) +--R 3 2 2 3 2 sin(d x + c) +--R ((b + 6a b)cos(d x + c) - b - 6a b)log(----------------) +--R cos(d x + c) + 1 +--R + +--R 2 3 2 3 +--R 6a b cos(d x + c)sin(d x + c) + 2a d x cos(d x + c) + b cos(d x + c) +--R + +--R 3 +--R - 2a d x +--R / +--R 2 +--R 2d cos(d x + c) - 2d +--R Type: Union(Expression Integer,...) +--E 401 + +--S 402 of 528 +m0376:= a0376-r0376 +--R +--R +--R (364) +--R 3 2 2 3 2 sin(d x + c) +--R ((b + 6a b)cos(d x + c) - b - 6a b)log(----------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 3 2 +--R ((b + 6a b)cos(d x + c) - b - 6a b)atanh(cos(d x + c)) +--R + +--R 2 +--R 6a b cos(d x + c)sin(d x + c) +--R + +--R 3 2 3 +--R (b cos(d x + c) - b )cot(d x + c)csc(d x + c) +--R + +--R 2 2 2 3 +--R (6a b cos(d x + c) - 6a b )cot(d x + c) + b cos(d x + c) +--R / +--R 2 +--R 2d cos(d x + c) - 2d +--R Type: Expression Integer +--E 402 + +--S 403 of 528 +d0376:= D(m0376,x) +--R +--R +--R (365) +--R 2 2 2 3 +--R (6a b cos(d x + c) + 6a b )sin(d x + c) +--R + +--R 3 2 3 3 2 +--R (b + 6a b)cos(d x + c) + b cos(d x + c) +--R + +--R 3 2 3 +--R (- b - 6a b)cos(d x + c) + b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 4 3 2 3 2 +--R (- 2b cos(d x + c) + 4b cos(d x + c) - 2b )cot(d x + c) +--R + +--R 3 4 3 2 3 +--R - b cos(d x + c) + 2b cos(d x + c) - b +--R * +--R csc(d x + c) +--R + +--R 2 4 2 2 2 2 +--R (- 6a b cos(d x + c) + 12a b cos(d x + c) - 6a b )cot(d x + c) +--R + +--R 2 2 2 +--R 6a b cos(d x + c) - 6a b +--R * +--R sin(d x + c) +--R + +--R 3 2 5 3 2 3 +--R (b + 6a b)cos(d x + c) + (- 2b - 12a b)cos(d x + c) +--R + +--R 3 2 +--R (b + 6a b)cos(d x + c) +--R / +--R 4 2 +--R (2cos(d x + c) - 4cos(d x + c) + 2)sin(d x + c) +--R Type: Expression Integer +--E 403 + +--S 404 of 528 +t0377:= (a+b*csc(c+d*x))^2 +--R +--R +--R 2 2 2 +--R (366) b csc(d x + c) + 2a b csc(d x + c) + a +--R Type: Expression Integer +--E 404 + +--S 405 of 528 +r0377:= a^2*x-2*a*b*atanh(cos(c+d*x))/d-b^2*cot(c+d*x)/d +--R +--R +--R 2 2 +--R - 2a b atanh(cos(d x + c)) - b cot(d x + c) + a d x +--R (367) --------------------------------------------------- +--R d +--R Type: Expression Integer +--E 405 + +--S 406 of 528 +a0377:= integrate(t0377,x) +--R +--R +--R (368) +--R sin(d x + c) 2 2 +--R 2a b sin(d x + c)log(----------------) + a d x sin(d x + c) - b cos(d x + c) +--R cos(d x + c) + 1 +--R ---------------------------------------------------------------------------- +--R d sin(d x + c) +--R Type: Union(Expression Integer,...) +--E 406 + +--S 407 of 528 +m0377:= a0377-r0377 +--R +--R +--R (369) +--R sin(d x + c) +--R 2a b sin(d x + c)log(----------------) +--R cos(d x + c) + 1 +--R + +--R 2 +--R 2a b sin(d x + c)atanh(cos(d x + c)) + b cot(d x + c)sin(d x + c) +--R + +--R 2 +--R - b cos(d x + c) +--R / +--R d sin(d x + c) +--R Type: Expression Integer +--E 407 + +--S 408 of 528 +d0377:= D(m0377,x) +--R +--R +--R (370) +--R 3 +--R 2a b cos(d x + c)sin(d x + c) +--R + +--R 2 2 2 2 2 +--R (- b cos(d x + c) + b )cot(d x + c) sin(d x + c) +--R + +--R 3 2 4 +--R (2a b cos(d x + c) - 2a b cos(d x + c))sin(d x + c) + b cos(d x + c) +--R + +--R 2 2 +--R - b cos(d x + c) +--R / +--R 2 2 +--R (cos(d x + c) - 1)sin(d x + c) +--R Type: Expression Integer +--E 408 + +--S 409 of 528 +t0378:= 1/(3+5*csc(c+d*x)) +--R +--R +--R 1 +--R (371) ----------------- +--R 5csc(d x + c) + 3 +--R Type: Expression Integer +--E 409 + +--S 410 of 528 +r0378:= 1/3*x-5/6*atan(3/4+5/4*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R 5tan(-------) + 3 +--R 2 +--R - 5atan(-----------------) + 2d x +--R 4 +--R (372) --------------------------------- +--R 6d +--R Type: Expression Integer +--E 410 + +--S 411 of 528 +a0378:= integrate(t0378,x) +--R +--R +--R 5sin(d x + c) + 3cos(d x + c) + 3 +--R - 5atan(---------------------------------) + 2d x +--R 4cos(d x + c) + 4 +--R (373) ------------------------------------------------- +--R 6d +--R Type: Union(Expression Integer,...) +--E 411 + +--S 412 of 528 +m0378:= a0378-r0378 +--R +--R +--R d x + c +--R 5tan(-------) + 3 +--R 2 5sin(d x + c) + 3cos(d x + c) + 3 +--R 5atan(-----------------) - 5atan(---------------------------------) +--R 4 4cos(d x + c) + 4 +--R (374) ------------------------------------------------------------------- +--R 6d +--R Type: Expression Integer +--E 412 + +--S 413 of 528 +d0378:= D(m0378,x) +--R +--R +--R (375) +--R 2 +--R - 25sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) +--R + +--R 2 +--R - 25cos(d x + c) + 25 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 d x + c +--R (- 60sin(d x + c) - 60cos(d x + c) - 60cos(d x + c))tan(-------) +--R 2 +--R + +--R 2 2 +--R - 25sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) - 25cos(d x + c) +--R + +--R 25 +--R / +--R 2 2 +--R 75sin(d x + c) + (90cos(d x + c) + 90)sin(d x + c) + 75cos(d x + c) +--R + +--R 150cos(d x + c) + 75 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 +--R 90sin(d x + c) + (108cos(d x + c) + 108)sin(d x + c) +--R + +--R 2 +--R 90cos(d x + c) + 180cos(d x + c) + 90 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R 75sin(d x + c) + (90cos(d x + c) + 90)sin(d x + c) + 75cos(d x + c) +--R + +--R 150cos(d x + c) + 75 +--R Type: Expression Integer +--E 413 + +--S 414 of 528 +t0379:= 1/(5+3*csc(c+d*x)) +--R +--R +--R 1 +--R (376) ----------------- +--R 3csc(d x + c) + 5 +--R Type: Expression Integer +--E 414 + +--S 415 of 528 +r0379:= 1/5*x+3/10*atanh(5/4+3/4*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R 3tan(-------) + 5 +--R 2 +--R 3atanh(-----------------) + 2d x +--R 4 +--R (377) -------------------------------- +--R 10d +--R Type: Expression Integer +--E 415 + +--S 416 of 528 +a0379:= integrate(t0379,x) +--R +--R +--R (378) +--R 3sin(d x + c) + cos(d x + c) + 1 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) + 3cos(d x + c) + 3 +--R 3log(--------------------------------) + 4d x +--R cos(d x + c) + 1 +--R / +--R 20d +--R Type: Union(Expression Integer,...) +--E 416 + +--S 417 of 528 +m0379:= a0379-r0379 +--R +--R +--R (379) +--R 3sin(d x + c) + cos(d x + c) + 1 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R d x + c +--R 3tan(-------) + 5 +--R sin(d x + c) + 3cos(d x + c) + 3 2 +--R 3log(--------------------------------) - 6atanh(-----------------) +--R cos(d x + c) + 1 4 +--R / +--R 20d +--R Type: Expression Integer +--E 417 + +--S 418 of 528 +d0379:= D(m0379,x) +--R +--R +--R (380) +--R 2 2 +--R - 9sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) - 9cos(d x + c) +--R + +--R 9 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 d x + c +--R (- 60sin(d x + c) - 60cos(d x + c) - 60cos(d x + c))tan(-------) +--R 2 +--R + +--R 2 2 +--R - 9sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) - 9cos(d x + c) + 9 +--R / +--R 2 +--R 45sin(d x + c) + (150cos(d x + c) + 150)sin(d x + c) +--R + +--R 2 +--R 45cos(d x + c) + 90cos(d x + c) + 45 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 +--R 150sin(d x + c) + (500cos(d x + c) + 500)sin(d x + c) +--R + +--R 2 +--R 150cos(d x + c) + 300cos(d x + c) + 150 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R 45sin(d x + c) + (150cos(d x + c) + 150)sin(d x + c) + 45cos(d x + c) +--R + +--R 90cos(d x + c) + 45 +--R Type: Expression Integer +--E 418 + +--S 419 of 528 +t0380:= 1/(a+b*csc(c+d*x)) +--R +--R +--R 1 +--R (381) ------------------ +--R b csc(d x + c) + a +--R Type: Expression Integer +--E 419 + +--S 420 of 528 +r0380:= x/a+2*b*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2)/d +--R +--R +--R d x + c +--R b tan(-------) + a +---------+ +--R 2 | 2 2 +--R 2b atanh(------------------) + d x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (382) ---------------------------------------------- +--R +---------+ +--R | 2 2 +--R a d\|- b + a +--R Type: Expression Integer +--E 420 + +--S 421 of 528 +a0380:= integrate(t0380,x) +--R +--R +--R (383) +--R [ +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R +---------+ +--R | 2 2 +--R d x\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R a d\|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a | 2 2 +--R - 2b atan(-----------------------------------------------) + d x\|b - a +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R --------------------------------------------------------------------------] +--R +-------+ +--R | 2 2 +--R a d\|b - a +--R Type: Union(List Expression Integer,...) +--E 421 + +--S 422 of 528 +m0380a:= a0380.1-r0380 +--R +--R +--R (384) +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R d x + c +--R b tan(-------) + a +--R 2 +--R - 2b atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R a d\|- b + a +--R Type: Expression Integer +--E 422 + +--S 423 of 528 +d0380a:= D(m0380a,x) +--R +--R +--R (385) +--R 3 2 2 2 2 +--R ((- b + a b)cos(d x + c) + a b)sin(d x + c) - a b cos(d x + c) +--R + +--R 2 +--R a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 2 2 2 +--R - 2a b sin(d x + c) - 2a b sin(d x + c) - 2a b cos(d x + c) +--R + +--R 3 2 +--R (2b - 2a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 2 2 2 2 2 +--R ((- b + a b)cos(d x + c) + a b)sin(d x + c) - a b cos(d x + c) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) - a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(d x + c) - b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 2 4 2 2 +--R (2a b - 2a b)sin(d x + c) + (2b - 2a b )sin(d x + c) +--R + +--R 3 3 2 3 3 +--R (2a b - 2a b)cos(d x + c) + (2a b - 2a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) - a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(d x + c) - b + a b +--R / +--R 2 2 2 +--R a b sin(d x + c) +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) + a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 2 +--R (- b + a b )cos(d x + c) + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 2 +--R 2a b sin(d x + c) +--R + +--R 2 2 4 2 2 4 +--R ((- 2a b + 2a )cos(d x + c) + 2a b + 2a )sin(d x + c) +--R + +--R 3 3 3 +--R (- 2a b + 2a b)cos(d x + c) + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 2 +--R a b sin(d x + c) +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) + a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 2 +--R (- b + a b )cos(d x + c) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 +--R (- a b + a b )sin(d x + c) +--R + +--R 2 3 4 5 4 +--R ((- a b + a b)cos(d x + c) - b + a b)sin(d x + c) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(d x + c) - a b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 3 4 2 +--R (- 2a b + 2a b)sin(d x + c) +--R + +--R 3 2 5 4 5 +--R ((- 2a b + 2a )cos(d x + c) - 2a b + 2a )sin(d x + c) +--R + +--R 2 3 4 2 3 4 +--R (- 2a b + 2a b)cos(d x + c) - 2a b + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 +--R (- a b + a b )sin(d x + c) +--R + +--R 2 3 4 5 4 +--R ((- a b + a b)cos(d x + c) - b + a b)sin(d x + c) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(d x + c) - a b + a b +--R Type: Expression Integer +--E 423 + +--S 424 of 528 +m0380b:= a0380.2-r0380 +--R +--R +--R (386) +--R d x + c +--R +-------+ b tan(-------) + a +--R | 2 2 2 +--R - 2b\|b - a atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R - 2b\|- b + a atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a d\|- b + a \|b - a +--R Type: Expression Integer +--E 424 + +--S 425 of 528 +d0380b:= D(m0380b,x) +--R +--R +--R (387) +--R 2 2 +--R - b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 +--R - b cos(d x + c) + b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R (- 4a b sin(d x + c) - 4a b cos(d x + c) - 4a b cos(d x + c)) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R - b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 +--R - b cos(d x + c) + b +--R / +--R 2 2 2 2 +--R a b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 2 +--R a b cos(d x + c) + 2a b cos(d x + c) + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 3 3 +--R 2a b sin(d x + c) + (4a cos(d x + c) + 4a )sin(d x + c) +--R + +--R 2 2 2 2 +--R 2a b cos(d x + c) + 4a b cos(d x + c) + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 2 2 +--R a b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 2 +--R a b cos(d x + c) + 2a b cos(d x + c) + a b +--R Type: Expression Integer +--E 425 + +--S 426 of 528 +t0381:= 1/(a+b*csc(c+d*x))^2 +--R +--R +--R 1 +--R (388) ---------------------------------------- +--R 2 2 2 +--R b csc(d x + c) + 2a b csc(d x + c) + a +--R Type: Expression Integer +--E 426 + +--S 427 of 528 +r0381:= x/a^2+2*b^3*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(3/2)/d+4*b*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)/d-b^2*cos(c+d*x)/a/(a^2-b^2)/d/(b+a*sin(c+d*x)) +--R +--R +--R (389) +--R d x + c +--R b tan(-------) + a +--R 3 3 4 2 2 2 +--R ((2a b - 4a b)sin(d x + c) + 2b - 4a b )atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 2 +--R ((a b - a )d x sin(d x + c) + a b cos(d x + c) + (b - a b)d x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d sin(d x + c) + (a b - a b)d)\|- b + a +--R Type: Expression Integer +--E 427 + +--S 428 of 528 +a0381:= integrate(t0381,x) +--R +--R +--R (390) +--R [ +--R 3 3 4 2 2 +--R ((a b - 2a b)sin(d x + c) + b - 2a b ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R 2 3 2 2 +--R ((a b - a )d x + a b)sin(d x + c) + a b cos(d x + c) +--R + +--R 3 2 2 +--R (b - a b)d x + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d sin(d x + c) + (a b - a b)d)\|- b + a +--R , +--R +--R 3 3 4 2 2 +--R ((- 2a b + 4a b)sin(d x + c) - 2b + 4a b ) +--R * +--R +-------+ +--R | 2 2 +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 2 3 2 2 +--R ((a b - a )d x + a b)sin(d x + c) + a b cos(d x + c) +--R + +--R 3 2 2 +--R (b - a b)d x + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d sin(d x + c) + (a b - a b)d)\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 428 + +--S 429 of 528 +m0381a:= a0381.1-r0381 +--R +--R +--R (391) +--R 3 2 +--R (b - 2a b) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R d x + c +--R b tan(-------) + a +---------+ +--R 3 2 2 | 2 2 +--R (- 2b + 4a b)atanh(------------------) + a b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 4 | 2 2 +--R (a b - a )d\|- b + a +--R Type: Expression Integer +--E 429 + +--S 430 of 528 +d0381a:= D(m0381a,x) +--R +--R +--R (392) +--R 5 2 3 4 2 3 4 +--R ((- b + 3a b - 2a b)cos(d x + c) + a b - 2a b)sin(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (- a b + 2a b )cos(d x + c) + a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 3 4 2 4 3 2 +--R (- 2a b + 4a b)sin(d x + c) + (- 2a b + 4a b )sin(d x + c) +--R + +--R 2 3 4 2 5 2 3 4 +--R (- 2a b + 4a b)cos(d x + c) + (2b - 6a b + 4a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 5 2 3 4 2 3 4 +--R ((- b + 3a b - 2a b)cos(d x + c) + a b - 2a b)sin(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (- a b + 2a b )cos(d x + c) + a b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 3 3 5 5 3 3 5 +--R ((- a b + 3a b - 2a b)cos(d x + c) - a b + 3a b - 2a b) +--R * +--R sin(d x + c) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (b - 3a b + 2a b )cos(d x + c) - b + 3a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 3 3 5 2 +--R (2a b - 6a b + 4a b)sin(d x + c) +--R + +--R 6 2 4 4 2 +--R (2b - 6a b + 4a b )sin(d x + c) +--R + +--R 5 3 3 5 2 +--R (2a b - 6a b + 4a b)cos(d x + c) +--R + +--R 5 3 3 5 +--R (2a b - 6a b + 4a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 5 3 3 5 5 3 3 5 +--R ((- a b + 3a b - 2a b)cos(d x + c) - a b + 3a b - 2a b)sin(d x + c) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (b - 3a b + 2a b )cos(d x + c) - b + 3a b - 2a b +--R / +--R 3 4 5 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 5 6 +--R ((- a b + 2a b - a b)cos(d x + c) + a b - a b)sin(d x + c) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- a b + 2a b - a b )cos(d x + c) + a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 6 2 +--R (2a b - 2a b)sin(d x + c) +--R + +--R 3 4 5 2 7 3 4 7 +--R ((- 2a b + 4a b - 2a )cos(d x + c) + 2a b - 2a )sin(d x + c) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 2a b + 4a b - 2a b)cos(d x + c) + 2a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 4 5 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 5 6 +--R ((- a b + 2a b - a b)cos(d x + c) + a b - a b)sin(d x + c) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- a b + 2a b - a b )cos(d x + c) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )sin(d x + c) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 +--R ((- a b + 2a b - a b)cos(d x + c) - a b + a b + a b - a b) +--R * +--R sin(d x + c) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (- a b + 2a b - a b )cos(d x + c) - a b + 2a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 5 5 3 7 2 +--R (- 2a b + 4a b - 2a b)sin(d x + c) +--R + +--R 4 4 6 2 8 2 6 4 4 6 2 8 +--R ((- 2a b + 4a b - 2a )cos(d x + c) - 2a b + 2a b + 2a b - 2a ) +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (- 2a b + 4a b - 2a b)cos(d x + c) - 2a b + 4a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )sin(d x + c) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 +--R ((- a b + 2a b - a b)cos(d x + c) - a b + a b + a b - a b) +--R * +--R sin(d x + c) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (- a b + 2a b - a b )cos(d x + c) - a b + 2a b - a b +--R Type: Expression Integer +--E 430 + +--S 431 of 528 +m0381b:= a0381.2-r0381 +--R +--R +--R (393) +--R d x + c +--R +-------+ b tan(-------) + a +--R 3 2 | 2 2 2 +--R (- 2b + 4a b)\|b - a atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 | 2 2 +--R (- 2b + 4a b)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a b\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 4 | 2 2 | 2 2 +--R (a b - a )d\|- b + a \|b - a +--R Type: Expression Integer +--E 431 + +--S 432 of 528 +d0381b:= D(m0381b,x) +--R +--R +--R (394) +--R 4 2 2 2 +--R (- b + 2a b )sin(d x + c) +--R + +--R 3 3 3 3 +--R ((2a b - 4a b)cos(d x + c) + 2a b - 4a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (- b + 2a b )cos(d x + c) + b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 2 3 3 2 +--R (- 4a b + 8a b)sin(d x + c) + (- 4a b + 8a b)cos(d x + c) +--R + +--R 3 3 +--R (- 4a b + 8a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 2 2 2 +--R (- b + 2a b )sin(d x + c) +--R + +--R 3 3 3 3 +--R ((2a b - 4a b)cos(d x + c) + 2a b - 4a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (- b + 2a b )cos(d x + c) + b - 2a b +--R / +--R 2 4 4 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 3 3 5 3 3 5 +--R ((2a b - 2a b)cos(d x + c) + 2a b - 2a b)sin(d x + c) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(d x + c) + (2a b - 2a b )cos(d x + c) + a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 5 2 +--R (2a b - 2a b)sin(d x + c) +--R + +--R 4 2 6 4 2 6 +--R ((4a b - 4a )cos(d x + c) + 4a b - 4a )sin(d x + c) +--R + +--R 3 3 5 2 3 3 5 3 3 5 +--R (2a b - 2a b)cos(d x + c) + (4a b - 4a b)cos(d x + c) + 2a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 4 4 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 3 3 5 3 3 5 +--R ((2a b - 2a b)cos(d x + c) + 2a b - 2a b)sin(d x + c) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(d x + c) + (2a b - 2a b )cos(d x + c) + a b - a b +--R Type: Expression Integer +--E 432 + +--S 433 of 528 +t0382:= 1/(a+b*csc(c+d*x))^3 +--R +--R +--R 1 +--R (395) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b csc(d x + c) + 3a b csc(d x + c) + 3a b csc(d x + c) + a +--R Type: Expression Integer +--E 433 + +--S 434 of 528 +r0382:= x/a^3+6*b^3*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(3/2)/d+6*b*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)/d+b^3*(a^2+2*b^2)*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(5/2)/d+1/2*b^3*cos(c+d*x)/a^2/(a^2-b^2)/d/(b+a*sin(c+d*x))^2-3/2*b^4*cos(c+d*x)/a^2/(a^2-b^2)^2/d/(b+a*sin(c+d*x))-3*b^2*cos(c+d*x)/a^2/(a^2-b^2)/d/(b+a*sin(c+d*x)) +--R +--R +--R (396) +--R 2 5 4 3 6 2 +--R (4a b - 10a b + 12a b)sin(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (8a b - 20a b + 24a b )sin(d x + c) + 4b - 10a b + 12a b +--R * +--R d x + c +--R b tan(-------) + a +--R 2 +--R atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x sin(d x + c) +--R + +--R 2 4 4 2 5 3 3 5 +--R ((3a b - 6a b )cos(d x + c) + (4a b - 8a b + 4a b)d x)sin(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 +--R (2a b - 5a b )cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d sin(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d sin(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 434 + +--S 435 of 528 +a0382:= integrate(t0382,x) +--R +--R +--R (397) +--R [ +--R 6 3 4 5 2 +--R (4a b - 10a b + 12a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 6 +--R (- 2a b + 5a b - 6a b)cos(d x + c) + 2b - 3a b + a b + 6a b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R 2 4 4 2 5 3 3 5 2 4 +--R (3a b - 6a b )cos(d x + c) + (4a b - 8a b + 4a b)d x + 4a b +--R + +--R 4 2 +--R - 10a b +--R * +--R sin(d x + c) +--R + +--R 2 4 4 2 6 3 3 5 2 +--R ((- 2a b + 4a b - 2a )d x - 2a b + 5a b)cos(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 6 +--R (2a b - 5a b )cos(d x + c) + (2b - 2a b - 2a b + 2a )d x +--R + +--R 5 3 3 5 +--R 2a b - 3a b - 5a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 5 6 3 8 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 5 4 7 2 9 2 3 6 5 4 7 2 9 +--R (- 2a b + 4a b - 2a )d cos(d x + c) + (2a b - 2a b - 2a b + 2a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 6 3 4 5 2 +--R (- 8a b + 20a b - 24a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 6 +--R (4a b - 10a b + 12a b)cos(d x + c) - 4b + 6a b - 2a b - 12a b +--R * +--R +-------+ +--R | 2 2 +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 2 4 4 2 5 3 3 5 2 4 +--R (3a b - 6a b )cos(d x + c) + (4a b - 8a b + 4a b)d x + 4a b +--R + +--R 4 2 +--R - 10a b +--R * +--R sin(d x + c) +--R + +--R 2 4 4 2 6 3 3 5 2 +--R ((- 2a b + 4a b - 2a )d x - 2a b + 5a b)cos(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 6 +--R (2a b - 5a b )cos(d x + c) + (2b - 2a b - 2a b + 2a )d x +--R + +--R 5 3 3 5 +--R 2a b - 3a b - 5a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 5 6 3 8 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 5 4 7 2 9 2 3 6 5 4 7 2 9 +--R (- 2a b + 4a b - 2a )d cos(d x + c) + (2a b - 2a b - 2a b + 2a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 435 + +--S 436 of 528 +m0382a:= a0382.1-r0382 +--R +--R +--R (398) +--R 3 6 5 4 7 2 3 +--R (4a b - 10a b + 12a b )sin(d x + c) +--R + +--R 4 5 6 3 8 2 2 7 4 5 6 3 +--R (- 2a b + 5a b - 6a b)cos(d x + c) + 10a b - 23a b + 25a b +--R + +--R 8 +--R 6a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 6 5 4 7 2 2 8 3 6 +--R (- 4a b + 10a b - 12a b )cos(d x + c) + 8a b - 16a b +--R + +--R 5 4 7 2 +--R 14a b + 12a b +--R * +--R sin(d x + c) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 6 3 +--R (- 2a b + 5a b - 6a b )cos(d x + c) + 2b - 3a b + a b + 6a b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R 3 6 5 4 7 2 3 +--R (- 8a b + 20a b - 24a b )sin(d x + c) +--R + +--R 4 5 6 3 8 2 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b)cos(d x + c) - 20a b + 46a b - 50a b +--R + +--R 8 +--R - 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 6 5 4 7 2 2 8 3 6 5 4 +--R (8a b - 20a b + 24a b )cos(d x + c) - 16a b + 32a b - 28a b +--R + +--R 7 2 +--R - 24a b +--R * +--R sin(d x + c) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b )cos(d x + c) - 4b + 6a b - 2a b - 12a b +--R * +--R d x + c +--R b tan(-------) + a +--R 2 +--R atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 4 4 6 2 3 +--R ((3a b - 6a b )cos(d x + c) + 4a b - 10a b )sin(d x + c) +--R + +--R 5 3 7 2 3 5 5 3 +--R (- 2a b + 5a b)cos(d x + c) + (2a b - 5a b )cos(d x + c) +--R + +--R 3 5 5 3 7 +--R 10a b - 23a b - 5a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (3a b - 6a b )cos(d x + c) + (- 4a b + 10a b )cos(d x + c) +--R + +--R 4 4 6 2 2 6 4 4 6 2 +--R (- 3a b + 6a b )cos(d x + c) + 8a b - 16a b - 10a b +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (2a b - 5a b )cos(d x + c) + (- 2a b + 5a b )cos(d x + c) +--R + +--R 3 5 5 3 7 3 5 5 3 +--R (- 2a b + 5a b )cos(d x + c) + 2a b - 3a b - 5a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 6 5 8 3 10 3 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 7 4 9 2 11 2 +--R (- 2a b + 4a b - 2a )d cos(d x + c) +--R + +--R 5 6 7 4 9 2 11 +--R (10a b - 18a b + 6a b + 2a )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 5 8 3 10 2 +--R (- 4a b + 8a b - 4a b)d cos(d x + c) +--R + +--R 4 7 6 5 10 +--R (8a b - 12a b + 4a b)d +--R * +--R sin(d x + c) +--R + +--R 5 6 7 4 9 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 +--R (2a b - 2a b - 2a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 436 + +--S 437 of 528 +d0382a:= D(m0382a,x) +--R +--R +--R (399) +--R 6 7 8 5 7 +--R (- 6a b + 12a b )sin(d x + c) +--R + +--R 7 6 9 4 2 +--R (- 3a b + 6a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 8 7 6 +--R (6a b - 18a b + 12a b )cos(d x + c) - 13a b + 19a b +--R + +--R 9 4 +--R 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 3 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 2 +--R (- 23a b + 44a b + 6a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 9 +--R (5a b - 10a b - 25a b + 30a b )cos(d x + c) - 9a b +--R + +--R 6 7 8 5 10 3 +--R 17a b + 4a b + 30a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (31a b - 98a b + 91a b - 24a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 38a b + 55a b + 49a b - 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 15a b + 45a b - 81a b + 27a b + 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R - 2a b + 39a b - 70a b + 69a b + 24a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 12 5 +--R (- 2a b + 7a b - 11a b + 6a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 8a b + 13a b + 19a b + 6a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 3 +--R (50a b - 162a b + 156a b - 32a b - 12a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 38a b + 40a b + 60a b - 92a b - 12a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R (- 24a b + 53a b - 39a b - 39a b + 43a b + 6a b) +--R * +--R cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 57a b - 97a b + 51a b + 73a b + 6a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (a b - a b - 6a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 5 +--R (12a b - 33a b + 9a b + 12a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (3a b - 21a b + 78a b + 30a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 +--R (30a b - 108a b + 126a b - 24a b - 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 28a b + 15a b + 61a b - 159a b - 42a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R (- 12a b + 17a b + 11a b - 43a b + 15a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 40a b - 53a b + 9a b + 82a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 7 +--R (- 3a b + 9a b - 6a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 3a b + 9a b - 18a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (15a b - 45a b + 12a b + 18a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (11a b - 31a b + 56a b + 54a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 +--R (6a b - 32a b + 61a b - 17a b - 18a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 12a b - 3a b + 45a b - 105a b - 54a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R (- 2b + a b + 6a b - 7a b - 4a b + 6a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 14a b - 13a b - 5a b + 40a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 7 +--R (- a b + 5a b - 4a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (- 2a b + 6a b - 10a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 5 +--R (5a b - 17a b + 4a b + 8a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (4a b - 9a b + 9a b + 26a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 5a b + 18a b - 9a b - 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 2a b - 3a b + 13a b - 22a b - 22a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R 2a b - a b - 2a b + 7a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 7 6 9 4 7 +--R (- 12a b + 24a b )sin(d x + c) +--R + +--R