diff --git a/changelog b/changelog index 7b25e3f..7219234 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100610 tpd src/axiom-website/patches.html 20100610.02.tpd.patch +20100610 tpd src/input/Makefile rule-based trig integration +20100610 tpd src/input/richtrig400-499.input rule-based trig integration 20100610 tpd src/axiom-website/patches.html 20100610.01.tpd.patch 20100610 tpd books/bookvolbib Golub [GL89], Higham [Hig02], Householder [Hou81] 20100610 tpd books/bookvol10.5 start of numeric analysis of BLAS/LAPACK diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index a275cca..b4cfca1 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2874,6 +2874,8 @@ src/input/richtrig200-299.input rule-based trig integration
src/input/richtrig300-399.input rule-based trig integration
20100610.01.tpd.patch books/bookvol10.5 start of numeric analysis of BLAS/LAPACK
+20100610.02.tpd.patch +src/input/richtrig400-499.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 0c340e8..55b758c 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -380,6 +380,7 @@ REGRES= ackermann.regress \ richtrig100-199.regress \ richtrig200-299.regress \ richtrig300-399.regress \ + richtrig400-499.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -703,6 +704,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richtrig100-199.input \ ${OUT}/richtrig200-299.input \ ${OUT}/richtrig300-399.input \ + ${OUT}/richtrig400-499.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1055,6 +1057,7 @@ DOCFILES= \ ${DOC}/richtrig100-199.input.dvi \ ${DOC}/richtrig200-299.input.dvi \ ${DOC}/richtrig300-399.input.dvi \ + ${DOC}/richtrig400-499.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/richtrig400-499.input.pamphlet b/src/input/richtrig400-499.input.pamphlet new file mode 100644 index 0000000..32dcb69 --- /dev/null +++ b/src/input/richtrig400-499.input.pamphlet @@ -0,0 +1,32959 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig400-499.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig400-499.output +)spool richtrig400-499.output +)set message auto off +)clear all + +--S 1 of 546 +t0400:= x/csc(x)^(7/2)-5/21*x*csc(x)^(1/2) +--R +--R +--R 4 +--R - 5x csc(x) + 21x +--R (1) ------------------ +--R 3 +------+ +--R 21csc(x) \|csc(x) +--R Type: Expression Integer +--E 1 + +--S 2 of 546 +r0400:= 2/441*(88*sin(x)-18*sin(x)*cos(x)^2-168*x*cos(x)+63*x*cos(x)^3)/(1/sin(x))^(1/2) +--R +--R +--R 2 3 +--R (- 36cos(x) + 176)sin(x) + 126x cos(x) - 336x cos(x) +--R (2) ------------------------------------------------------ +--R +------+ +--R | 1 +--R 441 |------ +--R \|sin(x) +--R Type: Expression Integer +--E 2 + +--S 3 of 546 +a0400:= integrate(t0400,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 3 + +--S 4 of 546 +m0400:= a0400-r0400 +--R +--R +--R (3) +--R +------+ +--R | 1 2 3 +--R 441a0400 |------ + (36cos(x) - 176)sin(x) - 126x cos(x) + 336x cos(x) +--R \|sin(x) +--R ------------------------------------------------------------------------ +--R +------+ +--R | 1 +--R 441 |------ +--R \|sin(x) +--R Type: Expression Integer +--E 4 + +--S 5 of 546 +d0400:= D(m0400,x) +--R +--R +--R (4) +--R 3 2 2 +--R - 24cos(x)sin(x) + (126x cos(x) - 112x)sin(x) +--R + +--R 3 4 2 +--R (- 24cos(x) + 24cos(x))sin(x) - 21x cos(x) + 56x cos(x) +--R / +--R +------+ +--R | 1 +--R 147sin(x) |------ +--R \|sin(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 546 +t0401:= x^2/csc(x)^(3/2)-1/3*x^2*csc(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x csc(x) + 3x +--R (5) ----------------- +--R +------+ +--R 3csc(x)\|csc(x) +--R Type: Expression Integer +--E 6 + +--S 7 of 546 +r0401:= -2/27*(-12*x*sin(x)^(3/2)-8*cos(x)*sin(x)^(1/2)+9*x^2*cos(x)*sin(x)^(1/2)+8*EllipticF(-1/4*%pi+1/2*x,2))/sin(x)^(1/2)/(1/sin(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 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 7 + +--S 8 of 546 +a0401:= integrate(t0401,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 8 + +--S 9 of 546 +m0401:= a0401-r0401 +--R +--R +--R (6) - r0401 + a0401 +--R Type: Polynomial Integer +--E 9 + +--S 10 of 546 +d0401:= D(m0401,x) +--R +--R +--R (7) 0 +--R Type: Polynomial Integer +--E 10 + +--S 11 of 546 +t0402:= csc(x^(1/2))^3/x^(1/2) +--R +--R +--R +-+ 3 +--R csc(\|x ) +--R (8) ---------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 11 + +--S 12 of 546 +r0402:= -atanh(cos(x^(1/2)))-cot(x^(1/2))*csc(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R (9) - atanh(cos(\|x )) - cot(\|x )csc(\|x ) +--R Type: Expression Integer +--E 12 + +--S 13 of 546 +a0402:= integrate(t0402,x) +--R +--R +--R (10) +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- cos(\|x ) + 1)log(cos(\|x ) + 1) + (cos(\|x ) - 1)log(cos(\|x ) - 1) +--R + +--R +-+ +--R 2cos(\|x ) +--R / +--R +-+ 2 +--R 2cos(\|x ) - 2 +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 546 +m0402:= a0402-r0402 +--R +--R +--R (11) +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- cos(\|x ) + 1)log(cos(\|x ) + 1) + (cos(\|x ) - 1)log(cos(\|x ) - 1) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +-+ +--R (2cos(\|x ) - 2)atanh(cos(\|x )) + (2cos(\|x ) - 2)cot(\|x )csc(\|x ) +--R + +--R +-+ +--R 2cos(\|x ) +--R / +--R +-+ 2 +--R 2cos(\|x ) - 2 +--R Type: Expression Integer +--E 14 + +--S 15 of 546 +d0402:= D(m0402,x) +--R +--R +--R (12) +--R +-+ 2 +-+ +--R (cos(\|x ) + 1)sin(\|x ) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +-+ 4 +--R (- 2cos(\|x ) + 4cos(\|x ) - 2)cot(\|x ) - cos(\|x ) +--R + +--R +-+ 2 +--R 2cos(\|x ) - 1 +--R * +--R +-+ +--R csc(\|x ) +--R / +--R +-+ +-+ 4 +-+ +-+ 2 +-+ +--R 2\|x cos(\|x ) - 4\|x cos(\|x ) + 2\|x +--R Type: Expression Integer +--E 15 + +--S 16 of 546 +t0403:= sin(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R sin(x) +--R (13) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 16 + +--S 17 of 546 +r0403:= -a*x/b^2+2*a^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)-cos(x)/b +--R +--R +--R x +--R a tan(-) + b +---------+ +--R 2 2 | 2 2 +--R 2a atan(------------) + (- b cos(x) - a x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (14) ------------------------------------------------------ +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 17 + +--S 18 of 546 +a0403:= integrate(t0403,x) +--R +--R +--R (15) +--R [ +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R | 2 2 +--R (- b cos(x) - a x)\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R - 2a atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R (- b cos(x) - a x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 18 + +--S 19 of 546 +m0403a:= a0403.1-r0403 +--R +--R +--R (16) +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 2 | 2 2 2 +--R - 2a \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression Integer +--E 19 + +--S 20 of 546 +d0403a:= D(m0403a,x) +--R +--R +--R (17) +--R 2 2 4 2 2 3 2 3 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 3 2 2 2 2 2 4 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 3 2 3 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 2 3 4 3 2 5 2 3 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 5 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 3 2 5 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 3 4 3 2 5 2 3 2 5 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression Integer +--E 20 + +--S 21 of 546 +m0403b:= a0403.2-r0403 +--R +--R +--R (18) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 2 (a sin(x) + b cos(x) + b)\|- b + a 2 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R ------------------------------------------------------------------------ +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 21 + +--S 22 of 546 +d0403b:= D(m0403b,x) +--R +--R +--R (19) +--R 3 2 2 2 3 2 3 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x 3 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 2 2 3 2 3 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression Integer +--E 22 + +--S 23 of 546 +t0404:= sin(x)^3/(a+b*sin(x)) +--R +--R +--R 3 +--R sin(x) +--R (20) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 23 + +--S 24 of 546 +r0404:= a^2*x/b^3+1/2*x/b-2*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)+a*cos(x)/b^2-1/2*cos(x)*sin(x)/b +--R +--R +--R (21) +--R x +--R a tan(-) + b +--R 3 2 +--R - 4a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) + 2a b cos(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression Integer +--E 24 + +--S 25 of 546 +a0404:= integrate(t0404,x) +--R +--R +--R (22) +--R [ +--R 3 +--R 2a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) + 2a b cos(x) + (b + 2a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 3 (a sin(x) + b cos(x) + b)\|- b + a +--R 4a atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) + 2a b cos(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 25 + +--S 26 of 546 +m0404a:= a0404.1-r0404 +--R +--R +--R (23) +--R +---------+ +--R 3 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 3 | 2 2 2 +--R 2a \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression Integer +--E 26 + +--S 27 of 546 +d0404a:= D(m0404a,x) +--R +--R +--R (24) +--R 3 2 5 3 2 4 2 4 x 2 +--R (((a b - a )cos(x) + a b )sin(x) - a b cos(x) + a b)tan(-) +--R 2 +--R + +--R 3 2 2 4 3 2 2 +--R - 2a b sin(x) - 2a b sin(x) - 2a b cos(x) +--R + +--R 3 2 5 +--R (- 2a b + 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 3 2 4 2 4 +--R ((a b - a )cos(x) + a b )sin(x) - a b cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 3 5 3 3 5 4 2 6 2 4 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 6 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 4 2 6 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 5 3 3 5 4 2 6 2 4 2 6 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 4 2 5 3 3 5 3 3 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 4 2 2 4 +--R (a b - a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 2 4 6 2 4 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 5 3 3 5 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 3 3 5 3 3 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 4 2 2 4 +--R (a b - a b )cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 2 6 3 4 6 5 2 +--R (a b - a b )sin(x) + ((a b - a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 7 2 5 7 4 3 +--R (2a b - 2a b )sin(x) + ((2b - 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 6 3 4 6 5 2 +--R (a b - a b )sin(x) + ((a b - a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + a b - a b +--R Type: Expression Integer +--E 27 + +--S 28 of 546 +m0404b:= a0404.2-r0404 +--R +--R +--R (25) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 3 (a sin(x) + b cos(x) + b)\|- b + a 3 2 +--R 2a atan(-------------------------------------) + 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 28 + +--S 29 of 546 +d0404b:= D(m0404b,x) +--R +--R +--R (26) +--R 4 2 3 3 4 2 4 x 2 +--R (- a sin(x) + (2a b cos(x) + 2a b)sin(x) - a cos(x) + a )tan(-) +--R 2 +--R + +--R 3 2 3 2 3 x 4 2 +--R (- 4a b sin(x) - 4a b cos(x) - 4a b cos(x))tan(-) - a sin(x) +--R 2 +--R + +--R 3 3 4 2 4 +--R (2a b cos(x) + 2a b)sin(x) - a cos(x) + a +--R / +--R 2 3 2 4 4 2 3 2 2 3 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 3 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 4 2 4 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 4 2 3 2 2 3 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 3 +--R a b +--R Type: Expression Integer +--E 29 + +--S 30 of 546 +t0405:= sin(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R sin(x) +--R (27) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 30 + +--S 31 of 546 +r0405:= -a^3*x/b^4-1/2*a*x/b^2+2*a^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(1/2)-a^2*cos(x)/b^3-cos(x)/b+1/3*cos(x)^3/b+1/2*a*cos(x)*sin(x)/b^2 +--R +--R +--R (28) +--R x +--R a tan(-) + b +--R 4 2 +--R 12a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 3 2 +--R 3a b cos(x)sin(x) + 2b cos(x) + (- 6b - 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R Type: Expression Integer +--E 31 + +--S 32 of 546 +a0405:= integrate(t0405,x) +--R +--R +--R (29) +--R [ +--R 4 +--R 6a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 3 3 3 2 +--R 3a b cos(x)sin(x) + 2b cos(x) + (- 6b - 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b - 6a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 (a sin(x) + b cos(x) + b)\|- b + a +--R - 12a atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 3 3 2 +--R 3a b cos(x)sin(x) + 2b cos(x) + (- 6b - 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 32 + +--S 33 of 546 +m0405a:= a0405.1-r0405 +--R +--R +--R (30) +--R +---------+ +--R 4 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 4 | 2 2 2 +--R - 2a \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression Integer +--E 33 + +--S 34 of 546 +d0405a:= D(m0405a,x) +--R +--R +--R (31) +--R 4 2 6 4 2 5 2 5 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 4 2 2 5 4 2 2 4 2 6 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 4 2 5 2 5 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 6 4 3 6 5 2 7 2 5 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 7 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 5 2 7 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 4 3 6 2 4 3 6 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 6 4 3 6 5 2 7 2 5 2 7 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 5 2 6 3 4 6 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (a b - a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 2 5 7 2 5 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 6 3 4 6 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 2 6 3 4 6 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (a b - a b )cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 4 4 2 7 3 5 7 5 3 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 8 2 6 8 4 4 7 3 5 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 7 3 5 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 2 7 3 5 7 5 3 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression Integer +--E 34 + +--S 35 of 546 +m0405b:= a0405.2-r0405 +--R +--R +--R (32) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 4 (a sin(x) + b cos(x) + b)\|- b + a 4 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R ------------------------------------------------------------------------ +--R +---------+ +--R 4 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 35 + +--S 36 of 546 +d0405b:= D(m0405b,x) +--R +--R +--R (33) +--R 5 2 4 4 5 2 5 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 4 2 4 2 4 x 5 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 4 4 5 2 5 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 5 2 5 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R Type: Expression Integer +--E 36 + +--S 37 of 546 +t0406:= sin(x)/(a+a*sin(x)) +--R +--R +--R sin(x) +--R (34) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 37 + +--S 38 of 546 +r0406:= x/a+cos(x)/a/(1+sin(x)) +--R +--R +--R x sin(x) + cos(x) + x +--R (35) --------------------- +--R a sin(x) + a +--R Type: Expression Integer +--E 38 + +--S 39 of 546 +a0406:= integrate(t0406,x) +--R +--R +--R x sin(x) + (x + 2)cos(x) + x + 2 +--R (36) -------------------------------- +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 39 + +--S 40 of 546 +m0406:= a0406-r0406 +--R +--R +--R 2 +--R (cos(x) + 2)sin(x) - cos(x) + cos(x) + 2 +--R (37) ------------------------------------------------ +--R 2 +--R a sin(x) + (a cos(x) + 2a)sin(x) + a cos(x) + a +--R Type: Expression Integer +--E 40 + +--S 41 of 546 +d0406:= D(m0406,x) +--R +--R +--R (38) +--R 4 3 2 +--R - sin(x) + (2cos(x) - 1)sin(x) + (2cos(x) + 1)sin(x) +--R + +--R 3 2 4 3 2 +--R (2cos(x) - cos(x) - 2cos(x) + 1)sin(x) + cos(x) + 2cos(x) - cos(x) +--R + +--R - 2cos(x) +--R / +--R 4 3 2 2 +--R a sin(x) + (2a cos(x) + 4a)sin(x) + (a cos(x) + 6a cos(x) + 6a)sin(x) +--R + +--R 2 2 +--R (2a cos(x) + 6a cos(x) + 4a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression Integer +--E 41 + +--S 42 of 546 +t0407:= sin(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R sin(x) +--R (39) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 42 + +--S 43 of 546 +r0407:= -(cos(x)^2+x*cos(x)-sin(x)+1)/a/cos(x) +--R +--R +--R 2 +--R sin(x) - cos(x) - x cos(x) - 1 +--R (40) ------------------------------- +--R a cos(x) +--R Type: Expression Integer +--E 43 + +--S 44 of 546 +a0407:= integrate(t0407,x) +--R +--R +--R 2 +--R (- cos(x) - x - 1)sin(x) - cos(x) + (- x - 4)cos(x) - x - 3 +--R (41) ------------------------------------------------------------ +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 44 + +--S 45 of 546 +m0407:= a0407-r0407 +--R +--R +--R 2 2 +--R - sin(x) - 2cos(x)sin(x) - 3cos(x) - 2cos(x) + 1 +--R (42) -------------------------------------------------- +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression Integer +--E 45 + +--S 46 of 546 +d0407:= D(m0407,x) +--R +--R +--R (43) +--R 4 3 2 +--R - sin(x) + (- 2cos(x) - 1)sin(x) + sin(x) +--R + +--R 3 2 4 2 +--R (- 2cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 3 2 4 +--R a cos(x) sin(x) + (2a cos(x) + 2a cos(x) )sin(x) + a cos(x) +--R + +--R 3 2 +--R 2a cos(x) + a cos(x) +--R Type: Expression Integer +--E 46 + +--S 47 of 546 +t0408:= sin(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R sin(x) +--R (44) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 47 + +--S 48 of 546 +r0408:= -1/2*(cos(x)^2*sin(x)-2*cos(x)^2-3*x*cos(x)-2+2*sin(x))/a/cos(x) +--R +--R +--R 2 2 +--R (- cos(x) - 2)sin(x) + 2cos(x) + 3x cos(x) + 2 +--R (45) ------------------------------------------------ +--R 2a cos(x) +--R Type: Expression Integer +--E 48 + +--S 49 of 546 +a0408:= integrate(t0408,x) +--R +--R +--R (46) +--R 2 3 2 +--R (- cos(x) + cos(x) + 3x + 2)sin(x) + cos(x) + 2cos(x) + (3x + 7)cos(x) +--R + +--R 3x + 6 +--R / +--R 2a sin(x) + 2a cos(x) + 2a +--R Type: Union(Expression Integer,...) +--E 49 + +--S 50 of 546 +m0408:= a0408-r0408 +--R +--R +--R (47) +--R 2 2 4 2 +--R (cos(x) + 2)sin(x) + 4cos(x)sin(x) + cos(x) + 5cos(x) + 4cos(x) - 2 +--R ----------------------------------------------------------------------- +--R 2 +--R 2a cos(x)sin(x) + 2a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 50 + +--S 51 of 546 +d0408:= D(m0408,x) +--R +--R +--R (48) +--R 2 4 2 3 +--R (- cos(x) + 2)sin(x) + (- cos(x) + 4cos(x) + 2)sin(x) +--R + +--R 4 2 2 +--R (- 2cos(x) + cos(x) - 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (- cos(x) + 4cos(x) + 3cos(x) - 4cos(x) - 2)sin(x) - cos(x) - cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 51 + +--S 52 of 546 +t0409:= sin(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R sin(x) +--R (49) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 52 + +--S 53 of 546 +r0409:= 1/6*(2*cos(x)^4+3*cos(x)^2*sin(x)-12*cos(x)^2-9*x*cos(x)-6+6*sin(x))/a/cos(x) +--R +--R +--R 2 4 2 +--R (3cos(x) + 6)sin(x) + 2cos(x) - 12cos(x) - 9x cos(x) - 6 +--R (50) ----------------------------------------------------------- +--R 6a cos(x) +--R Type: Expression Integer +--E 53 + +--S 54 of 546 +a0409:= integrate(t0409,x) +--R +--R +--R (51) +--R 3 2 4 3 +--R (2cos(x) + 3cos(x) - 9cos(x) - 9x - 10)sin(x) + 2cos(x) - cos(x) +--R + +--R 2 +--R - 12cos(x) + (- 9x - 31)cos(x) - 9x - 22 +--R / +--R 6a sin(x) + 6a cos(x) + 6a +--R Type: Union(Expression Integer,...) +--E 54 + +--S 55 of 546 +m0409:= a0409-r0409 +--R +--R +--R (52) +--R 2 2 4 2 +--R (- 3cos(x) - 6)sin(x) - 16cos(x)sin(x) - 3cos(x) - 19cos(x) +--R + +--R - 16cos(x) + 6 +--R / +--R 2 +--R 6a cos(x)sin(x) + 6a cos(x) + 6a cos(x) +--R Type: Expression Integer +--E 55 + +--S 56 of 546 +d0409:= D(m0409,x) +--R +--R +--R (53) +--R 2 4 2 3 +--R (cos(x) - 2)sin(x) + (cos(x) - 4cos(x) - 2)sin(x) +--R + +--R 4 2 2 +--R (2cos(x) - cos(x) + 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (cos(x) - 4cos(x) - 3cos(x) + 4cos(x) + 2)sin(x) + cos(x) + cos(x) +--R + +--R 2 +--R - 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 56 + +--S 57 of 546 +t0410:= cos(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R cos(x) +--R (54) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 57 + +--S 58 of 546 +r0410:= a*x/b^2-2*(a^2-b^2)^(1/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2+cos(x)/b +--R +--R +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R - 2\|- b + a atan(------------) + b cos(x) + a x +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (55) -------------------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 58 + +--S 59 of 546 +a0410:= integrate(t0410,x) +--R +--R +--R (56) +--R [ +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R b cos(x) + a x +--R / +--R 2 +--R b +--R , +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R 2\|- b + a atan(------------------------) + b cos(x) + a x +--R a sin(x) + b cos(x) + b +--R ------------------------------------------------------------] +--R 2 +--R b +--R Type: Union(List Expression Integer,...) +--E 59 + +--S 60 of 546 +m0410a:= a0410.1-r0410 +--R +--R +--R (57) +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R 2\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 +--R b +--R Type: Expression Integer +--E 60 + +--S 61 of 546 +d0410a:= D(m0410a,x) +--R +--R +--R (58) +--R 3 2 3 2 2 3 2 2 +--R ((- b + a b)cos(x) - b + a b)sin(x) + (a b - a )cos(x) - a b +--R + +--R 3 +--R a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 3 2 2 +--R (2b - 2a b)sin(x) + (2a b - 2a )sin(x) + (2b - 2a b)cos(x) +--R + +--R 3 2 +--R (2b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 2 3 2 2 3 +--R ((- b + a b)cos(x) - b + a b)sin(x) + (a b - a )cos(x) - a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 2 4 4 2 2 3 3 2 +--R ((b - 2a b + a )cos(x) + b - a b )sin(x) + (- a b + a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 3 3 +--R (- 2b + 2a b )sin(x) + (- 2a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R (- 2b + 2a b )cos(x) + (- 2b + 4a b - 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 4 2 2 3 3 2 +--R ((b - 2a b + a )cos(x) + b - a b )sin(x) + (- a b + a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R / +--R 2 2 2 3 3 3 2 2 2 2 +--R (a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 2 3 +--R 2a b sin(x) + (2b cos(x) + 2b + 2a b )sin(x) + 2a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 3 2 2 2 2 +--R a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 4 3 2 4 3 2 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (- a b + a b)cos(x) - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R - 2a b sin(x) + ((- 2b + 2a b )cos(x) - 2b - 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (- a b + a b)cos(x) - a b +--R Type: Expression Integer +--E 61 + +--S 62 of 546 +m0410b:= a0410.2-r0410 +--R +--R +--R (59) +--R +---------+ x +--R +---------+ | 2 2 +---------+ a tan(-) + b +--R | 2 2 (cos(x) + 1)\|- b + a | 2 2 2 +--R 2\|- b + a atan(------------------------) + 2\|- b + a atan(------------) +--R a sin(x) + b cos(x) + b +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 62 + +--S 63 of 546 +d0410b:= D(m0410b,x) +--R +--R +--R (60) +--R 2 3 2 3 2 3 2 +--R (a b - a )sin(x) + ((- 2b + 2a b)cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cos(x) - a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 3 2 x +--R ((4b - 4a b)sin(x) + (4b - 4a b)cos(x) + (4b - 4a b)cos(x))tan(-) +--R 2 +--R + +--R 2 3 2 3 2 3 2 +--R (a b - a )sin(x) + ((- 2b + 2a b)cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cos(x) - a b + a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression Integer +--E 63 + +--S 64 of 546 +t0411:= cos(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R cos(x) +--R (61) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 64 + +--S 65 of 546 +r0411:= -a^3*x/b^4+3/2*a*x/b^2+2*(a^2-b^2)^(3/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4-a^2*cos(x)/b^3+cos(x)/b+1/3*cos(x)^3/b+1/2*a*cos(x)*sin(x)/b^2 +--R +--R +--R (62) +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 2 2 +--R (- 12b + 12a )\|- b + a atan(------------) + 3a b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 2 2 3 +--R 2b cos(x) + (6b - 6a b)cos(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R Type: Expression Integer +--E 65 + +--S 66 of 546 +a0411:= integrate(t0411,x) +--R +--R +--R (63) +--R [ +--R +-------+ +--R 2 2 | 2 2 +--R (6b - 6a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 2 3 3 3 2 2 3 +--R 3a b cos(x)sin(x) + 2b cos(x) + (6b - 6a b)cos(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (12b - 12a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R 2 3 3 3 2 2 3 +--R 3a b cos(x)sin(x) + 2b cos(x) + (6b - 6a b)cos(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R ] +--R Type: Union(List Expression Integer,...) +--E 66 + +--S 67 of 546 +m0411a:= a0411.1-r0411 +--R +--R +--R (64) +--R +-------+ +--R 2 2 | 2 2 +--R (b - a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 2 +--R (2b - 2a )\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 +--R b +--R Type: Expression Integer +--E 67 + +--S 68 of 546 +d0411a:= D(m0411a,x) +--R +--R +--R (65) +--R 5 2 3 4 5 2 3 4 +--R ((- b + 2a b - a b)cos(x) - b + 2a b - a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (2b - 4a b + 2a b)sin(x) + (2a b - 4a b + 2a )sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (2b - 4a b + 2a b)cos(x) + (2b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- b + 2a b - a b)cos(x) - b + 2a b - a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 +--R ((b - 3a b + 3a b - a )cos(x) + b - 2a b + a b )sin(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b + 2a b - a b)cos(x) + a b - 2a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 +--R (- 2b + 4a b - 2a b )sin(x) + (- 2a b + 4a b - 2a b)sin(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 6 +--R (- 2b + 4a b - 2a b )cos(x) + (- 2b + 6a b - 6a b + 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 +--R ((b - 3a b + 3a b - a )cos(x) + b - 2a b + a b )sin(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b + 2a b - a b)cos(x) + a b - 2a b + a b +--R / +--R 2 4 2 5 5 3 3 2 4 +--R a b sin(x) + (a b cos(x) + a b + a b )sin(x) + a b cos(x) +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 2 4 5 +--R 2a b sin(x) + (2b cos(x) + 2b + 2a b )sin(x) + 2a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 5 3 3 2 4 2 4 +--R a b sin(x) + (a b cos(x) + a b + a b )sin(x) + a b cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 2 6 3 4 6 3 4 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (- a b + a b )cos(x) - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 2 5 7 2 5 +--R - 2a b sin(x) + ((- 2b + 2a b )cos(x) - 2b - 2a b )sin(x) +--R + +--R 6 3 4 6 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 2 6 3 4 6 3 4 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (- a b + a b )cos(x) - a b +--R Type: Expression Integer +--E 68 + +--S 69 of 546 +m0411b:= a0411.2-r0411 +--R +--R +--R (66) +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (2b - 2a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 2 +--R (2b - 2a )\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 +--R b +--R Type: Expression Integer +--E 69 + +--S 70 of 546 +d0411b:= D(m0411b,x) +--R +--R +--R (67) +--R 4 3 2 5 2 +--R (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- 2b + 4a b - 2a b)cos(x) - 2b + 4a b - 2a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 5 2 3 4 2 +--R (4b - 8a b + 4a b)sin(x) + (4b - 8a b + 4a b)cos(x) +--R + +--R 5 2 3 4 +--R (4b - 8a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 2 +--R (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- 2b + 4a b - 2a b)cos(x) - 2b + 4a b - 2a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R / +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 5 2 5 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R Type: Expression Integer +--E 70 + +--S 71 of 546 +t0412:= cos(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R cos(x) +--R (68) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 71 + +--S 72 of 546 +r0412:= (x+cos(x))/a +--R +--R +--R cos(x) + x +--R (69) ---------- +--R a +--R Type: Expression Integer +--E 72 + +--S 73 of 546 +a0412:= integrate(t0412,x) +--R +--R +--R cos(x) + x +--R (70) ---------- +--R a +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 546 +m0412:= a0412-r0412 +--R +--R +--R (71) 0 +--R Type: Expression Integer +--E 74 + +--S 75 of 546 +d0412:= D(m0412,x) +--R +--R +--R (72) 0 +--R Type: Expression Integer +--E 75 + +--S 76 of 546 +t0413:= tan(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R tan(x) +--R (73) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 76 + +--S 77 of 546 +r0413:= 2*a^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+1/12*cos(x)/(a+b)/(1-sin(x))^2+1/12*cos(x)/(a+b)/(1-sin(x))-1/4*(3*a+2*b)*cos(x)/(a+b)^2/(1-sin(x))-1/12*cos(x)/(a-b)/(1+sin(x))^2+1/4*(3*a-2*b)*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (74) +--R x +--R a tan(-) + b +--R 4 4 4 2 4 2 +--R (6a sin(x) - 12a sin(x) + 6a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 3 2 2 +--R (- a b + 4a )cos(x)sin(x) + (3b - 6a b)cos(x)sin(x) +--R + +--R 3 3 2 +--R - 3a cos(x)sin(x) + (- 2b + 5a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (3b - 6a b + 3a )sin(x) + (- 6b + 12a b - 6a )sin(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 77 + +--S 78 of 546 +a0413:= integrate(t0413,x) +--R +--R +--R (75) +--R [ +--R 4 3 +--R 3a cos(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b - 4a )cos(x) - a b + a )sin(x) + (- 2b + 5a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3b + 6a b)cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 3 (a sin(x) + b cos(x) + b)\|- b + a +--R - 6a cos(x) atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b - 4a )cos(x) - a b + a )sin(x) + (- 2b + 5a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3b + 6a b)cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 78 + +--S 79 of 546 +m0413a:= a0413.1-r0413 +--R +--R +--R (76) +--R +---------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (3a cos(x) sin(x) - 6a cos(x) sin(x) + 3a cos(x) )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (- 6a cos(x) sin(x) + 12a cos(x) sin(x) - 6a cos(x) )\|b - a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 2 3 2 4 +--R ((- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b - 4a )cos(x) + (- 2a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 3 2 3 +--R (- 3b + 6a b)cos(x) + (4b - 10a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (6b - 12a b)cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (3a cos(x) + (a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2b - 5a b)cos(x) + (- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) +--R + +--R 3 2 +--R b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 79 + +--S 80 of 546 +d0413a:= D(m0413a,x) +--R +--R +--R (77) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (a b - 5a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 2a b + 3a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 3a b + 10a b - 11a b + 4a )cos(x) +--R + +--R 6 5 2 2 +--R (- 3a b + 15a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (3a b - 9a b + 9a b - 3a )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 2 5 4 3 4 +--R (- 3a b + 3a b)cos(x) + (3a b - 9a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 7a b + 26a b - 19a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (2a b - 3a b + 13a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b + 7a b )cos(x) + (3a b - 9a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (3a b - 5a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 31a b + 35a b - 13a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - 7a b - 20a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- a b + 5a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (5a b - 9a b + 4a b)cos(x) + (a b + 7a b - 8a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 4a b + 17a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (15a b - 48a b + 33a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (6a b - 9a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (6a b - 19a b + 17a b - 4a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (6a b - 10a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 5a b + 14a b - 4a b - 5a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 5a b + 7a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 33a b - 39a b + 15a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b + 11a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (3a b - 12a b + 9a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 2a b - 5a b + 7a b)cos(x) + (- 9a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 13a b + 38a b - 25a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b + 15a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 2a b + 7a b - 2a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 2a b + 3a b + 17a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b - 4a b - 7a b + 9a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - a b - 19a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (3a b - 13a b + 17a b - 7a )cos(x) +--R + +--R 6 3 4 2 +--R (3a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 2a b + 7a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (- 2a b + 5a b - 3a b)cos(x) + (a b + a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b + a b + 4a b)cos(x) + (4a b - 11a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (4a b - 6a b - a b)cos(x) + (- 3a b + 6a b - 3a b)cos(x) +--R + +--R 2 5 4 3 +--R - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 2 7 7 5 2 6 +--R (- 3a b + 3a )cos(x) - 6a b cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- a b + 5a b - 4a )cos(x) + (- a b + 7a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 10 +--R ((2a b - 8a b )cos(x) - 6a b + 6a b )sin(x) +--R + +--R 6 3 4 5 2 3 +--R (2a b - 10a b + 8a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b + 6a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 4 7 2 5 4 3 6 3 +--R 6a b cos(x) + (- 6b + 20a b - 22a b + 8a b)cos(x) +--R + +--R 7 4 3 2 +--R (- 6b + 30a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 18a b - 6a b)cos(x) + 6b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 14a b + 52a b - 38a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (4a b - 6a b + 26a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 6a b + 12a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 6 +--R (- 2a b + 14a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (6b - 10a b - 20a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 62a b + 70a b - 26a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (18b - 14a b - 40a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 18b + 54a b - 54a b + 18a b)cos(x) - 18b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 2a b + 10a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (10a b - 18a b + 8a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (30a b - 96a b + 66a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b - 18a b - 30a b )cos(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R (- 36a b + 72a b - 36a b )cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (12b - 38a b + 34a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (12b - 20a b - 28a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 10b + 28a b - 26a b + 8a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 10b + 14a b + 32a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 66a b - 78a b + 30a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (- 18b + 22a b + 20a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (18b - 54a b + 54a b - 18a b)cos(x) + 18b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (6a b - 24a b + 18a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (2a b - 8a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 26a b + 76a b - 50a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 20a b + 30a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 18a b - 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 4b + 14a b - 4a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 4b + 6a b + 34a b )cos(x) +--R + +--R 7 2 5 4 3 5 7 2 5 4 3 4 +--R (4b - 8a b + 4a b )cos(x) + (4b - 2a b - 26a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b - 26a b + 34a b - 14a b)cos(x) +--R + +--R 7 2 5 2 +--R (6b - 12a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 +--R (- 6b + 18a b - 18a b + 6a b)cos(x) - 6b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 4a b + 14a b - 10a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 4a b + 10a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (8a b - 22a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (8a b - 12a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 3 6 7 4 3 6 +--R (- 6a b + 6a b)cos(x) - 12a b cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (a b - 5a b + 4a b)cos(x) + (- 2a b + 3a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 3a b + 10a b - 11a b + 4a )cos(x) +--R + +--R 6 5 2 2 6 3 4 5 2 7 +--R (- 3a b + 15a b )cos(x) + (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 +--R 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 2 5 4 3 4 +--R (- 3a b + 3a b)cos(x) + (3a b - 9a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 7a b + 26a b - 19a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (2a b - 3a b + 13a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 +--R 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b + 7a b )cos(x) + (3a b - 9a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (3a b - 5a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 31a b + 35a b - 13a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - 7a b - 20a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (- a b + 5a b - 4a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (a b + 7a b - 8a b)cos(x) + (- 4a b + 17a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (15a b - 48a b + 33a b)cos(x) + (6a b - 9a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (6a b - 19a b + 17a b - 4a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (6a b - 10a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 5a b + 14a b - 4a b - 5a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 5a b + 7a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 33a b - 39a b + 15a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b + 11a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (3a b - 12a b + 9a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 2a b - 5a b + 7a b)cos(x) + (- 9a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 13a b + 38a b - 25a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b + 15a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 2a b + 7a b - 2a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 2a b + 3a b + 17a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b - 4a b - 7a b + 9a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - a b - 19a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 3 4 2 +--R (3a b - 13a b + 17a b - 7a )cos(x) + (3a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (- 2a b + 7a b - 5a b)cos(x) + (- 2a b + 5a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (a b + a b - 2a b)cos(x) + (a b + a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (4a b - 11a b + 7a b)cos(x) + (4a b - 6a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 2 7 7 5 2 6 3 4 5 2 7 5 +--R (- 3a b + 3a )cos(x) - 6a b cos(x) + (- a b + 5a b - 4a )cos(x) +--R + +--R 3 4 5 2 4 3 4 5 2 7 3 +--R (- a b + 7a b )cos(x) + (a b - 2a b + a )cos(x) +--R + +--R 3 4 5 2 2 +--R (a b - a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- a b + 5a b - 4a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 5a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (2a b - 5a b + 7a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (3a b - 10a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (3a b - 3a b - 15a b + 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3a b - 3a b )cos(x) + (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (7a b - 26a b + 19a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b + 5a b - 16a b + 13a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 3 5 5 3 7 6 7 3 5 5 3 5 +--R (a b - 8a b + 7a b)cos(x) + (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 8a b - a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 31a b - 35a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 16a b + 13a b - 20a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b +--R + +--R 7 +--R 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (a b - 5a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 5a b + 14a b - 13a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- a b - 7a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (4a b - 21a b + 12a b + 5a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 15a b + 48a b - 33a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 6a b + 15a b + 6a b - 15a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 6a b + 19a b - 17a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 6a b + 16a b + 4a b - 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5a b - 14a b + 17a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 4a b + 7a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 3a b + 18a b - 19a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 13a b - 17a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (2a b - 7a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (2a b - 7a b + 8a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 6 2 8 4 +--R (- a b - a b + 2a b )cos(x) + (- a b - 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 4a b + 11a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 4a b + 10a b - 5a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 5 3 7 7 5 3 7 6 +--R (3a b - 3a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (a b - 5a b + 4a b)cos(x) + (a b - 8a b + 7a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- 2a b + 10a b - 8a b )cos(x) + 6a b - 12a b + 6a b )sin(x) +--R + +--R 7 3 5 5 3 3 +--R (- 2a b + 10a b - 8a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b - 10a b + 14a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 7 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 4 6 2 4 8 2 6 4 4 6 2 3 +--R (- 6a b + 6a b )cos(x) + (6b - 20a b + 22a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (6b - 6a b - 30a b + 30a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) - 6b - 6a b + 30a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (14a b - 52a b + 38a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 4a b + 10a b - 32a b + 26a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 6a b - 6a b + 30a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 +--R (2a b - 16a b + 14a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 16a b + 10a b - 20a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 18b + 62a b - 70a b + 26a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 18b + 32a b + 26a b - 40a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (18b - 54a b + 54a b - 18a b )cos(x) + 18b - 18a b - 18a b +--R + +--R 6 2 +--R 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (2a b - 10a b + 8a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 10a b + 28a b - 26a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (8a b - 24a b + 24a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 30a b + 96a b - 66a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b + 30a b + 12a b - 30a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (36a b - 72a b + 36a b )cos(x) + 18a b - 18a b - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 12b + 38a b - 34a b + 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 12b + 32a b + 8a b - 28a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (10b - 28a b + 26a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (10b - 24a b - 18a b + 32a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (18b - 66a b + 78a b - 30a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (18b - 40a b + 2a b + 20a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) - 18b + 30a b - 6a b +--R + +--R 6 2 +--R - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 6a b + 24a b - 18a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 2a b + 10a b - 14a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (26a b - 76a b + 50a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (20a b - 50a b + 16a b + 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 18a b + 30a b - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (4b - 14a b + 4a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (4b - 10a b - 28a b + 34a b )cos(x) +--R + +--R 8 2 6 4 4 5 +--R (- 4b + 8a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 4b + 6a b + 24a b - 26a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 6b + 26a b - 34a b + 14a b )cos(x) +--R + +--R 8 2 6 4 4 2 +--R (- 6b + 18a b - 12a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (6b - 18a b + 18a b - 6a b )cos(x) + 6b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (4a b - 14a b + 10a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (4a b - 14a b + 16a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 6a b - 6a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 8a b + 22a b - 14a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 8a b + 20a b - 10a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 7 4 4 6 2 6 +--R (6a b - 6a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 10a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- a b + 5a b - 4a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 5a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 2 6 4 4 6 2 +--R (2a b - 5a b + 7a b - 4a )cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 4 4 6 2 8 +--R 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (3a b - 10a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (3a b - 3a b - 15a b + 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3a b - 3a b )cos(x) + (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (7a b - 26a b + 19a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b + 5a b - 16a b + 13a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 3 5 5 3 7 6 7 3 5 5 3 5 +--R (a b - 8a b + 7a b)cos(x) + (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 8a b - a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 31a b - 35a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 16a b + 13a b - 20a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (a b - 5a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 5a b + 14a b - 13a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- a b - 7a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (4a b - 21a b + 12a b + 5a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 15a b + 48a b - 33a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 6a b + 15a b + 6a b - 15a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 6a b + 19a b - 17a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 6a b + 16a b + 4a b - 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (5a b - 14a b + 4a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (5a b - 12a b - 9a b + 16a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 33a b + 39a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 20a b + a b + 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 8 4 +--R (2a b + 5a b - 7a b )cos(x) + (9a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (13a b - 38a b + 25a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (10a b - 25a b + 8a b + 7a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (2a b - 7a b + 2a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 5a b - 14a b + 17a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 4a b + 7a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 3a b + 18a b - 19a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 13a b - 17a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 8 6 +--R (2a b - 7a b + 5a b )cos(x) + (2a b - 7a b + 8a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 6 2 8 4 +--R (- a b - a b + 2a b )cos(x) + (- a b - 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 4a b + 11a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 4a b + 10a b - 5a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 5 3 7 7 5 3 7 6 +--R (3a b - 3a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (a b - 5a b + 4a b)cos(x) + (a b - 8a b + 7a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 4 8 +--R (6a b - 12a b + 6a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b - 6a b - 6a b + 6a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 12a b + 24a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 18b + 18a b + 18a b - 18a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (18b - 18a b - 18a b + 18a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (18a b - 54a b + 54a b - 18a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (12a b - 24a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 6a b + 6a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 6b + 12a b - 12a b + 6a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (12a b - 36a b + 36a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (18b - 36a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (18a b - 54a b + 54a b - 18a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 18b + 36a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 18a b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 12a b + 36a b - 36a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (6b - 12a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R Type: Expression Integer +--E 80 + +--S 81 of 546 +m0413b:= a0413.2-r0413 +--R +--R +--R (78) +--R 4 3 4 4 3 2 4 3 +--R (- 6a cos(x) sin(x) + 12a cos(x) sin(x) - 6a cos(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 4 3 4 4 3 2 4 3 2 +--R (- 6a cos(x) sin(x) + 12a cos(x) sin(x) - 6a cos(x) )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 2 3 2 4 +--R ((- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b - 4a )cos(x) + (- 2a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 3 2 3 +--R (- 3b + 6a b)cos(x) + (4b - 10a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (6b - 12a b)cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (3a cos(x) + (a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2b - 5a b)cos(x) + (- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) +--R + +--R 3 2 +--R b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 81 + +--S 82 of 546 +d0413b:= D(m0413b,x) +--R +--R +--R (79) +--R 3 2 5 2 3 2 5 10 +--R ((a b - 4a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b - 8a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (a b - a )cos(x) + (- 6a b + 14a b - 8a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b + 12a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 4 5 +--R 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R - 6a b cos(x) - 6a b cos(x) + (- 14a b + 38a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (a b + 11a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 +--R (- a b + 7a )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (6a b - 18a b + 6a )cos(x) + (18a b - 44a b + 26a )cos(x) +--R + +--R 4 3 2 5 2 +--R (18a b - 25a b - 11a )cos(x) +--R + +--R 4 3 2 5 4 3 2 +--R (- 18a b + 36a b - 18a )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b + 8a b)cos(x) + (7a b - 10a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 16a b)cos(x) + (3a b + 15a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (30a b - 66a b)cos(x) + (3a b - 21a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- a b + 4a )cos(x) + (12a b - 26a b + 8a )cos(x) +--R + +--R 4 3 2 5 6 +--R (12a b - 30a b + 3a )cos(x) +--R + +--R 4 3 2 5 5 +--R (- 10a b + 18a b + 10a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 10a b + 29a b - a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 18a b + 48a b - 30a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 18a b + 29a b + a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 12a b)cos(x) + (6a b - 18a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 7a b + 13a b)cos(x) + (- 4a b - 14a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 6a b - 12a b)cos(x) + (- 26a b + 50a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 5a b + 17a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (- 4a b + 10a b + 6a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 4a b + 16a b )cos(x) + (4a b - 4a b - 18a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (4a b - 12a b - 10a )cos(x) + (6a b - 20a b + 14a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 12a b + 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 4 6 +--R (- 2a b + 8a b)cos(x) + (- 4a b + 10a b)cos(x) - 3a b cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 4a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (8a b - 14a b)cos(x) + (2a b - 5a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 8 5 7 3 2 5 6 +--R - 3a cos(x) - 6a cos(x) + (- a b - 2a )cos(x) +--R + +--R 3 2 5 5 5 4 3 2 5 3 +--R (- 2a b + 8a )cos(x) + 6a cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 2 +--R (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 10 +--R ((2a b - 8a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (4a b - 16a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (2a b + 4a b)cos(x) + (- 12b + 28a b - 16a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 12b + 12a b + 24a b)cos(x) + (12b - 24a b + 12a b)cos(x) +--R + +--R 5 4 +--R 12b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 28a b + 76a b )cos(x) + (2a b + 22a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (48a b - 48a b )cos(x) + 24a b - 24a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 4 6 5 2 3 4 5 +--R (- 2a b + 20a b)cos(x) + (12b - 24a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R (12b - 36a b )cos(x) + (36b - 88a b + 52a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (36b - 50a b - 22a b)cos(x) + (- 36b + 72a b - 36a b)cos(x) +--R + +--R 5 2 3 +--R - 36b + 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 4a b + 16a b )cos(x) + (14a b - 20a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (4a b - 4a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (60a b - 132a b )cos(x) + (6a b - 42a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 72a b + 72a b )cos(x) - 36a b + 36a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (- 2a b + 8a b)cos(x) + (24b - 52a b + 16a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (24b - 60a b - 12a b)cos(x) + (- 20b + 36a b - 16a b)cos(x) +--R + +--R 5 2 3 4 4 +--R (- 20b + 58a b - 2a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 36b + 96a b - 60a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 36b + 58a b + 2a b)cos(x) + (36b - 72a b + 36a b)cos(x) +--R + +--R 5 2 3 4 +--R 36b - 48a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (12a b - 24a b )cos(x) + (12a b - 36a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 14a b + 26a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 12a b + 12a b )cos(x) + (- 52a b + 100a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- 10a b + 34a b )cos(x) + (48a b - 48a b )cos(x) + 24a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (- 8b + 20a b + 12a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 5 +--R (- 8b + 32a b + 18a b)cos(x) + (8b - 8a b )cos(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (8b - 24a b - 8a b)cos(x) + (12b - 40a b + 28a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (12b - 24a b + 6a b)cos(x) + (- 12b + 24a b - 12a b)cos(x) +--R + +--R 5 2 3 4 +--R - 12b + 18a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 4a b + 16a b )cos(x) + (- 8a b + 20a b )cos(x) +--R + +--R 3 2 6 4 3 2 5 4 3 2 4 +--R - 6a b cos(x) + (4a b - 4a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (16a b - 28a b )cos(x) + (4a b - 10a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 8 4 7 2 3 4 6 +--R - 6a b cos(x) - 12a b cos(x) + (- 2a b - 10a b)cos(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + 6a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 3 2 5 10 +--R ((a b - 4a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b - 8a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (a b - a )cos(x) + (- 6a b + 14a b - 8a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b + 12a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 4 5 +--R 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R - 6a b cos(x) - 6a b cos(x) + (- 14a b + 38a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (a b + 11a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 +--R (- a b + 7a )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (6a b - 18a b + 6a )cos(x) + (18a b - 44a b + 26a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 25a b - 11a )cos(x) + (- 18a b + 36a b - 18a )cos(x) +--R + +--R 4 3 2 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b + 8a b)cos(x) + (7a b - 10a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 16a b)cos(x) + (3a b + 15a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (30a b - 66a b)cos(x) + (3a b - 21a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- a b + 4a )cos(x) + (12a b - 26a b + 8a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (12a b - 30a b + 3a )cos(x) + (- 10a b + 18a b + 10a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 10a b + 29a b - a )cos(x) + (- 18a b + 48a b - 30a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 18a b + 29a b + a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 12a b)cos(x) + (6a b - 18a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 7a b + 13a b)cos(x) + (- 4a b - 14a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 6a b - 12a b)cos(x) + (- 26a b + 50a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 5a b + 17a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (- 4a b + 10a b + 6a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 4a b + 16a b )cos(x) + (4a b - 4a b - 18a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (4a b - 12a b - 10a )cos(x) + (6a b - 20a b + 14a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 12a b + 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 4 6 +--R (- 2a b + 8a b)cos(x) + (- 4a b + 10a b)cos(x) - 3a b cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 4a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (8a b - 14a b)cos(x) + (2a b - 5a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 8 5 7 3 2 5 6 +--R - 3a cos(x) - 6a cos(x) + (- a b - 2a )cos(x) +--R + +--R 3 2 5 5 5 4 3 2 5 3 +--R (- 2a b + 8a )cos(x) + 6a cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 2 +--R (a b - a )cos(x) +--R / +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 +--R (- 9a b + 18a b - 9a )cos(x) +--R + +--R 2 4 4 2 6 5 +--R (- 18a b + 36a b - 18a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((12b - 24a b + 12a b )cos(x) + (12b - 24a b + 12a b )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 36b + 72a b - 36a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 36b + 72a b - 36a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((36b - 72a b + 36a b )cos(x) + (36b - 72a b + 36a b )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 12b + 24a b - 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R ((- 9a b + 18a b - 9a )cos(x) + (- 18a b + 36a b - 18a )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R Type: Expression Integer +--E 82 + +--S 83 of 546 +t0414:= tan(x)/(a+a*sin(x)) +--R +--R +--R tan(x) +--R (80) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 83 + +--S 84 of 546 +r0414:= 1/2*atanh(sin(x))/a+1/2/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(sin(x)) + 1 +--R (81) ----------------------------- +--R 2a sin(x) + 2a +--R Type: Expression Integer +--E 84 + +--S 85 of 546 +a0414:= integrate(t0414,x) +--R +--R +--R (82) +--R sin(x) + cos(x) + 1 +--R (sin(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- sin(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R 2a sin(x) + 2a +--R Type: Union(Expression Integer,...) +--E 85 + +--S 86 of 546 +m0414:= a0414-r0414 +--R +--R +--R (83) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) - 1 +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------- +--R 2a +--R Type: Expression Integer +--E 86 + +--S 87 of 546 +d0414:= D(m0414,x) +--R +--R +--R (84) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R / +--R 4 2 2 2 +--R 2a sin(x) + (- 2a cos(x) - 4a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R Type: Expression Integer +--E 87 + +--S 88 of 546 +t0415:= tan(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R tan(x) +--R (85) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 88 + +--S 89 of 546 +r0415:= 1/3*(1+2*sin(x)+cos(x)^2)/cos(x)/a/(1+sin(x)) +--R +--R +--R 2 +--R 2sin(x) + cos(x) + 1 +--R (86) --------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Expression Integer +--E 89 + +--S 90 of 546 +a0415:= integrate(t0415,x) +--R +--R +--R 2 +--R (2cos(x) + 2)sin(x) + cos(x) + 2cos(x) + 1 +--R (87) ------------------------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Union(Expression Integer,...) +--E 90 + +--S 91 of 546 +m0415:= a0415-r0415 +--R +--R +--R 2 +--R (88) -- +--R 3a +--R Type: Expression Integer +--E 91 + +--S 92 of 546 +d0415:= D(m0415,x) +--R +--R +--R (89) 0 +--R Type: Expression Integer +--E 92 + +--S 93 of 546 +t0416:= tan(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R tan(x) +--R (90) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 93 + +--S 94 of 546 +r0416:= -1/8/cos(x)^4*(3*atanh(sin(x))*cos(x)^4+2*sin(x)-2-5*sin(x)*cos(x)^2+4*cos(x)^2)/a +--R +--R +--R 4 2 2 +--R - 3cos(x) atanh(sin(x)) + (5cos(x) - 2)sin(x) - 4cos(x) + 2 +--R (91) ------------------------------------------------------------- +--R 4 +--R 8a cos(x) +--R Type: Expression Integer +--E 94 + +--S 95 of 546 +a0416:= integrate(t0416,x) +--R +--R +--R (92) +--R 2 2 sin(x) + cos(x) + 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2cos(x) + 1)sin(x) - 3cos(x) + 3 +--R / +--R 2 2 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Union(Expression Integer,...) +--E 95 + +--S 96 of 546 +m0416:= a0416-r0416 +--R +--R +--R (93) +--R 4 4 sin(x) + cos(x) + 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 sin(x) - cos(x) - 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 2 2 +--R (3cos(x) sin(x) + 3cos(x) )atanh(sin(x)) + (- 5cos(x) + 2)sin(x) +--R + +--R 4 4 2 +--R 2cos(x) sin(x) - 3cos(x) + 7cos(x) - 2 +--R / +--R 4 4 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Expression Integer +--E 96 + +--S 97 of 546 +d0416:= D(m0416,x) +--R +--R +--R (94) +--R 2 7 +--R (- 10cos(x) + 8)sin(x) +--R + +--R 5 4 3 2 5 +--R (6cos(x) + 5cos(x) + 20cos(x) + 28cos(x) - 16cos(x) - 24)sin(x) +--R + +--R 5 4 2 4 +--R (6cos(x) - 5cos(x) + 2cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R 6cos(x) + 13cos(x) + 4cos(x) - 18cos(x) - 52cos(x) - 26cos(x) +--R + +--R 32cos(x) + 24 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 2 +--R (6cos(x) + 3cos(x) + 4cos(x) + 10cos(x) - 4cos(x) - 4cos(x) )sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 2cos(x) - 10cos(x) - 11cos(x) - 6cos(x) + 13cos(x) + 32cos(x) +--R + +--R 2 +--R 8cos(x) - 16cos(x) - 8 +--R * +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R 8cos(x) + 10cos(x) - 5cos(x) - 14cos(x) - 5cos(x) + 4cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 5 5 5 4 +--R 8a cos(x) sin(x) + 8a cos(x) sin(x) +--R + +--R 7 6 5 3 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 2 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 7 6 +--R (8a cos(x) + 16a cos(x) + 8a cos(x) )sin(x) + 8a cos(x) + 16a cos(x) +--R + +--R 5 +--R 8a cos(x) +--R Type: Expression Integer +--E 97 + +--S 98 of 546 +t0417:= tan(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R tan(x) +--R (95) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 98 + +--S 99 of 546 +r0417:= -1/15*(-1-4*sin(x)+12*sin(x)*cos(x)^2+6*cos(x)^2+3*cos(x)^4)/cos(x)^3/a/(1+sin(x)) +--R +--R +--R 2 4 2 +--R (- 12cos(x) + 4)sin(x) - 3cos(x) - 6cos(x) + 1 +--R (96) ------------------------------------------------- +--R 3 3 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Expression Integer +--E 99 + +--S 100 of 546 +a0417:= integrate(t0417,x) +--R +--R +--R (97) +--R 3 2 4 3 2 +--R (- 8cos(x) - 12cos(x) + 4)sin(x) - 3cos(x) - 8cos(x) - 6cos(x) + 1 +--R ----------------------------------------------------------------------- +--R 3 3 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Union(Expression Integer,...) +--E 100 + +--S 101 of 546 +m0417:= a0417-r0417 +--R +--R +--R 8 +--R (98) - --- +--R 15a +--R Type: Expression Integer +--E 101 + +--S 102 of 546 +d0417:= D(m0417,x) +--R +--R +--R (99) 0 +--R Type: Expression Integer +--E 102 + +--S 103 of 546 +t0418:= cot(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R cot(x) +--R (100) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 103 + +--S 104 of 546 +r0418:= -2*(a^2-b^2)^(1/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2+b*atanh(cos(x))/a^2-cot(x)/a +--R +--R +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R b atanh(cos(x)) - 2\|- b + a atan(------------) - a cot(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (101) ------------------------------------------------------------ +--R 2 +--R a +--R Type: Expression Integer +--E 104 + +--S 105 of 546 +a0418:= integrate(t0418,x) +--R +--R +--R (102) +--R [ +--R sin(x) +--R - b sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R - a cos(x) +--R / +--R 2 +--R a sin(x) +--R , +--R +--R sin(x) +--R - b sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R 2sin(x)\|- b + a atan(------------------------) - a cos(x) +--R a sin(x) + b cos(x) + b +--R / +--R 2 +--R a sin(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 105 + +--S 106 of 546 +m0418a:= a0418.1-r0418 +--R +--R +--R (103) +--R sin(x) +--R - b sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R - b sin(x)atanh(cos(x)) + 2sin(x)\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R a cot(x)sin(x) - a cos(x) +--R / +--R 2 +--R a sin(x) +--R Type: Expression Integer +--E 106 + +--S 107 of 546 +d0418a:= D(m0418a,x) +--R +--R +--R (104) +--R 2 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 3 2 +--R (- a b cos(x) + a b)cot(x) - a b cos(x) +--R + +--R 3 3 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 2 2 4 2 2 2 2 2 +--R - a b cos(x) + (- a b - a )cos(x) + a b cos(x) + a b +--R + +--R 4 +--R a +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 4 2 4 2 2 4 2 2 +--R - b cos(x) - b cos(x) + (b - a b )cos(x) + b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 3 2 3 3 2 +--R (- a b cos(x) - a b cos(x) + a b cos(x) + a b)cot(x) +--R + +--R 3 3 3 3 3 2 +--R (- a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 +--R (a b + a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 4 4 2 2 3 4 2 +--R a b cos(x) + a cos(x) - 2a b cos(x) - a cos(x) +--R + +--R 2 2 +--R a b cos(x) +--R * +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b cos(x) + 2a b )cot(x) - 2a b cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2b - 2a b )cos(x) - 2b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 3 3 2 3 +--R - 2a b cos(x) + (- 2a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 3 3 +--R 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 3 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b )cot(x) +--R + +--R 2 2 3 2 2 +--R - 4a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R + +--R 3 +--R 2a b cos(x) +--R * +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 3 2 3 3 +--R ((- a b cos(x) + a b)cot(x) - a b cos(x) + (- a b - a b)cos(x)) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 2 2 4 2 2 2 2 2 4 +--R (- a b cos(x) + (- a b - a )cos(x) + a b cos(x) + a b + a ) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 4 2 4 2 2 4 2 2 +--R - b cos(x) - b cos(x) + (b - a b )cos(x) + b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 3 2 3 3 2 +--R (- a b cos(x) - a b cos(x) + a b cos(x) + a b)cot(x) +--R + +--R 3 3 3 3 3 2 +--R (- a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 +--R (a b + a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 4 4 2 2 3 4 2 2 2 +--R (a b cos(x) + a cos(x) - 2a b cos(x) - a cos(x) + a b cos(x)) +--R * +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 5 +--R a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (a b cos(x) - a b )cot(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R (a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (a b - a b)cos(x) + (a b + a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 3 5 4 2 +--R (b - a b + a b)cos(x) + (b - a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (- b + 2a b - a b)cos(x) - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 4 2 +--R - a b cos(x) + (a b + a b )cos(x) + a b cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b - a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- a b + a b)cos(x) - 2a b cos(x) + (2a b - a b)cos(x) +--R + +--R 4 2 2 3 +--R 2a b cos(x) - a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 3 2 2 +--R (- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R 2a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 5 2 3 5 2 3 +--R ((2a b cos(x) - 2a b )cot(x) + (2b + 2a b )cos(x) + 2b - 2a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 2a b + 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 4 3 2 +--R 2a b cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 3 2 3 2 2 3 4 +--R (2a b - 2a b)cos(x) + 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 3 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 2 3 2 +--R - 2a b cos(x) + (6a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) - 4a b cos(x) + (4a b - 2a b )cos(x) +--R + +--R 3 2 2 4 +--R 4a b cos(x) - 2a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 2 3 4 3 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 3 2 +--R 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 +--R a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (a b cos(x) - a b )cot(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R (a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 2 3 4 +--R (a b - a b)cos(x) + (a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 2 3 4 +--R - a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 3 5 4 2 +--R (b - a b + a b)cos(x) + (b - a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (- b + 2a b - a b)cos(x) - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 4 2 +--R - a b cos(x) + (a b + a b )cos(x) + a b cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b - a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- a b + a b)cos(x) - 2a b cos(x) + (2a b - a b)cos(x) +--R + +--R 4 2 2 3 +--R 2a b cos(x) - a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 3 2 2 +--R (- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b cos(x) +--R / +--R 4 2 4 4 +--R (a b cos(x) - a b)sin(x) +--R + +--R 3 2 3 3 2 5 2 3 2 3 2 5 +--R (a b cos(x) + (a b + a )cos(x) - a b cos(x) - a b - a ) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 4 2 4 4 2 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b)sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 3 3 2 3 4 2 2 3 2 3 +--R 2a b cos(x) + (2a b + 2a b)cos(x) - 2a b cos(x) - 2a b +--R + +--R 4 +--R - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (a b cos(x) - a b)sin(x) +--R + +--R 3 2 3 3 2 5 2 3 2 3 2 5 3 +--R (a b cos(x) + (a b + a )cos(x) - a b cos(x) - a b - a )sin(x) +--R + +--R 4 3 4 2 4 4 2 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b)sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 2 4 2 4 +--R (- a b cos(x) + a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (a b - a b)cos(x) + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (- 2a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 4 +--R (- a b cos(x) + a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 +--R a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b )sin(x) +--R Type: Expression Integer +--E 107 + +--S 108 of 546 +m0418b:= a0418.2-r0418 +--R +--R +--R (105) +--R sin(x) +--R - b sin(x)log(----------) - b sin(x)atanh(cos(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R 2sin(x)\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R 2sin(x)\|- b + a atan(------------) + a cot(x)sin(x) - a cos(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 +--R a sin(x) +--R Type: Expression Integer +--E 108 + +--S 109 of 546 +d0418b:= D(m0418b,x) +--R +--R +--R (106) +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 3 2 2 +--R (- a cos(x) + a )cot(x) + (- a b - a )cos(x) - 2a b cos(x) +--R + +--R 2 3 +--R - a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 3 3 2 3 2 3 2 +--R - 2b cos(x) - 2b cos(x) + (2b - 2a b)cos(x) + 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 2 4 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) - a b cos(x) +--R + +--R 2 3 3 2 2 2 3 +--R - 2a b cos(x) + a cos(x) + 2a b cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2a cos(x) - 2a cos(x) - a cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 2 3 3 +--R (- 2a b cos(x) + 2a b)cot(x) - 4a b cos(x) - 4b cos(x) - 4b +--R + +--R 2 +--R 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4a b cos(x) - 4a b cos(x) + 4a b cos(x) + 4a b )cot(x) +--R + +--R 2 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (- 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b)cot(x) +--R + +--R 2 4 2 3 2 2 2 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 2 6 +--R (2a b cos(x) - 4a b cos(x) + 2a b cos(x))sin(x) + 2a b cos(x) +--R + +--R 2 5 2 3 2 2 +--R 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 3 2 2 2 +--R (- a cos(x) + a )cot(x) + (- a b - a )cos(x) - 2a b cos(x) - a b +--R + +--R 3 +--R a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 3 3 2 3 2 3 2 +--R - 2b cos(x) - 2b cos(x) + (2b - 2a b)cos(x) + 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 2 4 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) - a b cos(x) +--R + +--R 2 3 3 2 2 2 3 +--R - 2a b cos(x) + a cos(x) + 2a b cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 3 5 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) + 2a cos(x) +--R + +--R 3 3 3 2 +--R - 2a cos(x) - a cos(x) +--R / +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b)sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R Type: Expression Integer +--E 109 + +--S 110 of 546 +t0419:= cot(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R cot(x) +--R (107) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 110 + +--S 111 of 546 +r0419:= 2*(a^2-b^2)^(3/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^4-3/2*b*atanh(cos(x))/a^2+b^3*atanh(cos(x))/a^4+cot(x)/a-b^2*cot(x)/a^3-1/3*cot(x)^3/a+1/2*b*cot(x)*csc(x)/a^2 +--R +--R +--R (108) +--R x +--R +---------+ a tan(-) + b +--R 3 2 2 2 | 2 2 2 +--R (6b - 9a b)atanh(cos(x)) + (- 12b + 12a )\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 3 +--R 3a b cot(x)csc(x) - 2a cot(x) + (- 6a b + 6a )cot(x) +--R / +--R 4 +--R 6a +--R Type: Expression Integer +--E 111 + +--S 112 of 546 +a0419:= integrate(t0419,x) +--R +--R +--R (109) +--R [ +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R ((6b - 6a )cos(x) - 6b + 6a )sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 3 2 3 +--R - 3a b cos(x)sin(x) + (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R , +--R +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R (cos(x) + 1)\|- b + a +--R atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R 2 2 3 3 2 3 +--R - 3a b cos(x)sin(x) + (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 112 + +--S 113 of 546 +m0419a:= a0419.1-r0419 +--R +--R +--R (110) +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R ((6b - 6a )cos(x) - 6b + 6a )sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 3 2 2 3 2 +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)atanh(cos(x)) +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 2 2 2 | 2 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b - 6a )cos(x) - 6a b + 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R Type: Expression Integer +--E 113 + +--S 114 of 546 +d0419a:= D(m0419a,x) +--R +--R +--R (111) +--R 2 4 4 2 3 4 2 2 +--R (- 6a b + 9a b )cos(x) - 3a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (6a b - 9a b )cos(x) - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 4 2 4 4 2 2 4 2 +--R 3a b cos(x) - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b)cot(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 6a b + 9a b - 2a b)cos(x) + (- 6a b + 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (6a b - 12a b + 3a b)cos(x) + (6a b - 6a b - 9a b)cos(x) +--R + +--R 3 3 5 +--R - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 6a b cos(x) + (6a b + 6a b)cos(x) - 12a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 12a b - 12a b)cos(x) + 6a b cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 3a b cos(x) + (3a b + 3a b)cos(x) - 6a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 6a b - 6a b)cos(x) + 3a b cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 2 5 4 2 6 4 4 2 3 +--R - 6a b cos(x) + (- 6a b - 6a )cos(x) + 12a b cos(x) +--R + +--R 4 2 6 2 4 2 4 2 6 +--R (12a b + 12a )cos(x) - 6a b cos(x) - 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 2 4 3 +--R - 6a b cos(x) + (- 6a b - 6a b )cos(x) + 12a b cos(x) +--R + +--R 2 4 4 2 2 2 4 2 4 4 2 +--R (12a b + 12a b )cos(x) - 6a b cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 5 +--R (- 6b + 6a b + a b )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 6b + 6a b + a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (12b - 18a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (12b - 18a b + 6a b + 6a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- 6b + 12a b - 9a b )cos(x) - 6b + 12a b - 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) +--R + +--R 4 2 2 4 2 4 2 +--R - 12a b cos(x) + 6a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 3a b cos(x) + 3a b cos(x) - 6a b cos(x) - 6a b cos(x) +--R + +--R 4 2 4 2 +--R 3a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 5 5 4 5 3 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) +--R + +--R 5 2 5 5 +--R 12a b cos(x) - 6a b cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 3 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R 12a b cos(x) - 6a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (3a b - 2a b)cos(x) + (- 6a b + 3a b + 7a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 6a b - 6a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (12a b - 6a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (12a b - 21a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 6a b + 3a b + 9a b)cos(x) - 6a b + 12a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 4 2 6 6 +--R (6a b - 8a b )cos(x) + (7a b - 8a )cos(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- 18a b + 23a b )cos(x) + (- 16a b + 14a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 +--R (18a b - 24a b )cos(x) + (9a b - 6a )cos(x) +--R + +--R 2 4 4 2 +--R (- 6a b + 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (6a b - 8a b)cos(x) + (6a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 12a b + 14a b)cos(x) + (- 12a b + 14a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 3 3 3 2 +--R (- 12a b + 18a b )cos(x) - 6a b cos(x) +--R + +--R 5 3 3 3 3 +--R (12a b - 18a b )cos(x) - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 2 4 4 2 2 4 2 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 4 4 2 4 2 2 4 2 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 4 4 2 4 6 4 2 3 +--R (- 6a b + 8a b )cos(x) + (- 12b + 18a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (- 12b + 24a b - 18a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (12b - 12a b - 18a b )cos(x) + 12b - 30a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 5 2 4 4 2 4 +--R 12a b cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 4 3 2 4 4 2 2 +--R - 24a b cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 2 4 2 4 4 2 +--R 12a b cos(x) + 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 2 4 3 +--R 6a b cos(x) + (6a b + 6a b )cos(x) - 12a b cos(x) +--R + +--R 2 4 4 2 2 2 4 2 4 4 2 +--R (- 12a b - 12a b )cos(x) + 6a b cos(x) + 6a b + 6a b +--R * +--R csc(x) +--R + +--R 3 3 5 3 3 5 4 +--R - 12a b cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 3 3 3 3 3 5 2 3 3 +--R 24a b cos(x) + (24a b + 24a b)cos(x) - 12a b cos(x) +--R + +--R 3 3 5 +--R - 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 5 5 5 3 3 4 +--R - 12a b cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 5 3 5 3 3 2 5 +--R 24a b cos(x) + (24a b + 24a b )cos(x) - 12a b cos(x) +--R + +--R 5 3 3 +--R - 12a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 12a b + 14a b )cos(x) + (- 10a b + 8a b)cos(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (12a b - 12a b )cos(x) + (- 12a b + 36a b - 12a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R - 6a b cos(x) + 12a b - 30a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 4 3 3 3 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R - 24a b cos(x) + 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 3 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R - 12a b cos(x) + 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 4 2 2 4 2 4 2 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 2 4 2 2 4 2 4 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (6a b - 4a b )cos(x) + (- 18a b + 26a b )cos(x) +--R + +--R 2 4 4 2 4 4 2 3 +--R - 12a b cos(x) + (36a b - 48a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (6a b + 12a b )cos(x) + (- 18a b + 30a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 3 3 5 6 +--R (12a b - 16a b )cos(x) + (14a b - 16a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 36a b + 46a b )cos(x) + (- 32a b + 28a b)cos(x) +--R + +--R 5 3 3 3 3 3 5 2 +--R (36a b - 48a b )cos(x) + (18a b - 12a b)cos(x) +--R + +--R 5 3 3 +--R (- 12a b + 18a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (12a b - 16a b )cos(x) + (12a b - 16a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 24a b + 28a b )cos(x) + (- 24a b + 28a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 3 4 2 2 2 4 4 2 +--R (- 6a b + 9a b )cos(x) - 3a b cos(x) + (6a b - 9a b )cos(x) +--R + +--R 4 2 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 4 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) + 3a b cos(x) +--R + +--R 4 2 2 4 2 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b)cot(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 6a b + 9a b - 2a b)cos(x) + (- 6a b + 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (6a b - 12a b + 3a b)cos(x) + (6a b - 6a b - 9a b)cos(x) +--R + +--R 3 3 5 +--R - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 6a b cos(x) + (6a b + 6a b)cos(x) - 12a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 12a b - 12a b)cos(x) + 6a b cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 3a b cos(x) + (3a b + 3a b)cos(x) - 6a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 6a b - 6a b)cos(x) + 3a b cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 2 5 4 2 6 4 4 2 3 +--R - 6a b cos(x) + (- 6a b - 6a )cos(x) + 12a b cos(x) +--R + +--R 4 2 6 2 4 2 4 2 6 +--R (12a b + 12a )cos(x) - 6a b cos(x) - 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 2 4 3 +--R - 6a b cos(x) + (- 6a b - 6a b )cos(x) + 12a b cos(x) +--R + +--R 2 4 4 2 2 2 4 2 4 4 2 +--R (12a b + 12a b )cos(x) - 6a b cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 5 +--R (- 6b + 6a b + a b )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 6b + 6a b + a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (12b - 18a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (12b - 18a b + 6a b + 6a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- 6b + 12a b - 9a b )cos(x) - 6b + 12a b - 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) +--R + +--R 4 2 2 4 2 4 2 +--R - 12a b cos(x) + 6a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 3a b cos(x) + 3a b cos(x) - 6a b cos(x) - 6a b cos(x) +--R + +--R 4 2 4 2 +--R 3a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) + 12a b cos(x) +--R + +--R 5 5 +--R - 6a b cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 3 3 3 2 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) + 12a b cos(x) +--R + +--R 3 3 3 3 +--R - 6a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (3a b - 2a b)cos(x) + (- 6a b + 3a b + 7a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 6a b + 6a b - 6a b)cos(x) + (12a b - 6a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (12a b - 21a b + 18a b)cos(x) + (- 6a b + 3a b + 9a b)cos(x) +--R + +--R 5 3 3 5 +--R - 6a b + 12a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 4 2 6 6 +--R (6a b - 8a b )cos(x) + (7a b - 8a )cos(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- 18a b + 23a b )cos(x) + (- 16a b + 14a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 +--R (18a b - 24a b )cos(x) + (9a b - 6a )cos(x) +--R + +--R 2 4 4 2 +--R (- 6a b + 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (6a b - 8a b)cos(x) + (6a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 12a b + 14a b)cos(x) + (- 12a b + 14a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 3 4 3 2 2 5 4 3 +--R (6a b - 9a b )cos(x) + 3a b cos(x) + (- 6a b + 9a b )cos(x) +--R + +--R 4 3 +--R 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 4 3 4 4 3 2 4 3 +--R - 3a b cos(x) + 6a b cos(x) - 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 3 +--R (6a b - 15a b + 11a b )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 6a b + 18a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- 6a b + 6a b + 6a b )cos(x) + 3a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 6a b + 6a b )cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b - 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 3a b + 3a b )cos(x) - 3a b - 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 12a b + 11a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (6b - 6a b - 7a b + 11a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 12b + 30a b - 30a b + 15a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (- 12b + 18a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 21a b - 9a b)cos(x) + 6b - 12a b + 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (- 6a b + 6a b)cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 3a b + 3a b)cos(x) - 3a b cos(x) +--R + +--R 4 3 6 3 4 3 2 4 3 6 +--R (6a b - 6a b)cos(x) + 6a b cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 4 3 +--R - 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 +--R (6a b - 6a )cos(x) + 6a b cos(x) +--R + +--R 5 2 7 3 5 2 2 +--R (- 12a b + 12a )cos(x) - 12a b cos(x) +--R + +--R 5 2 7 5 2 +--R (6a b - 6a )cos(x) + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (- 9a b + 11a b )cos(x) + (6a b - 3a b - 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 12a b + 6a b + 12a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 12a b + 15a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (6a b - 3a b - 9a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (- 6a b + 14a b - 8a b)cos(x) + (- 13a b + 17a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (18a b - 35a b + 14a b)cos(x) + (28a b - 32a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (- 18a b + 30a b - 6a b)cos(x) + (- 15a b + 15a b)cos(x) +--R + +--R 2 5 4 3 +--R (6a b - 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (- 6a b + 14a b - 8a )cos(x) + (- 6a b + 8a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (12a b - 26a b + 14a )cos(x) + (12a b - 14a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a )cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 3 3 4 2 +--R (12a b - 18a b )cos(x) + 6a b cos(x) +--R + +--R 6 3 4 3 4 +--R (- 12a b + 18a b )cos(x) + 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 +--R - 6a b cos(x) + 12a b cos(x) - 6a b +--R * +--R csc(x) +--R + +--R 4 3 4 4 3 2 4 3 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 2 5 4 2 5 2 2 5 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 2 5 4 3 4 7 4 3 3 +--R (- 6a b + 10a b )cos(x) + (12b - 24a b )cos(x) +--R + +--R 7 2 5 2 7 2 5 4 3 7 +--R (12b - 12a b )cos(x) + (- 12b + 12a b + 12a b )cos(x) - 12b +--R + +--R 2 5 4 3 +--R 30a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (24a b - 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 12a b + 12a b )cos(x) - 12a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 6a b + 6a b )cos(x) - 6a b - 6a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (12a b - 12a b )cos(x) + 12a b + 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (12a b - 12a b )cos(x) + 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (12a b - 14a b - 4a b )cos(x) + (- 2a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 12a b + 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 3 4 5 2 6 +--R (12a b - 24a b - 6a b )cos(x) + (6a b - 6a b )cos(x) - 12a b +--R + +--R 3 4 5 2 +--R 30a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (24a b - 24a b )cos(x) + 24a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (- 12a b + 12a b )cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (- 6a b + 6a b )cos(x) - 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (- 6a b + 6a b )cos(x) - 6a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 4 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 24a b + 24a b)cos(x) - 24a b cos(x) +--R + +--R 4 3 6 4 3 +--R (12a b - 12a b)cos(x) + 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 2 5 4 3 3 2 5 2 +--R (- 24a b + 24a b )cos(x) - 24a b cos(x) +--R + +--R 2 5 4 3 2 5 +--R (12a b - 12a b )cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 5 +--R (- 18a b + 22a b )cos(x) + (30a b - 50a b + 8a b)cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (36a b - 36a b )cos(x) + (- 60a b + 96a b - 12a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 +--R (- 18a b + 6a b )cos(x) + (30a b - 54a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (- 12a b + 28a b - 16a b )cos(x) + (- 26a b + 34a b )cos(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (36a b - 70a b + 28a b )cos(x) + (56a b - 64a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 36a b + 60a b - 12a b )cos(x) + (- 30a b + 30a b )cos(x) +--R + +--R 6 3 4 +--R (12a b - 18a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 +--R (- 12a b + 28a b - 16a b)cos(x) + (- 12a b + 16a b )cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (24a b - 52a b + 28a b)cos(x) + (24a b - 28a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 2 +--R (- 12a b + 24a b - 12a b)cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 3 4 3 2 2 5 4 3 +--R (6a b - 9a b )cos(x) + 3a b cos(x) + (- 6a b + 9a b )cos(x) +--R + +--R 4 3 +--R 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 4 3 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) - 3a b cos(x) +--R + +--R 4 3 2 4 3 +--R 6a b cos(x) - 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 3 +--R (6a b - 15a b + 11a b )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 6a b + 18a b - 12a b )cos(x) + (- 6a b + 6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 +--R 3a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 6a b + 6a b )cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b - 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 3a b + 3a b )cos(x) - 3a b - 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 12a b + 11a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (6b - 6a b - 7a b + 11a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 12b + 30a b - 30a b + 15a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (- 12b + 18a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 21a b - 9a b)cos(x) + 6b - 12a b + 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (- 6a b + 6a b)cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 4 3 6 3 +--R (- 3a b + 3a b)cos(x) - 3a b cos(x) + (6a b - 6a b)cos(x) +--R + +--R 4 3 2 4 3 6 4 3 +--R 6a b cos(x) + (- 3a b + 3a b)cos(x) - 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 5 2 7 3 +--R (6a b - 6a )cos(x) + 6a b cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 5 2 2 5 2 7 5 2 +--R - 12a b cos(x) + (6a b - 6a )cos(x) + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (- 9a b + 11a b )cos(x) + (6a b - 3a b - 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 12a b + 6a b + 12a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 12a b + 15a b - 9a b )cos(x) + (6a b - 3a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 6a b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (- 6a b + 14a b - 8a b)cos(x) + (- 13a b + 17a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (18a b - 35a b + 14a b)cos(x) + (28a b - 32a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (- 18a b + 30a b - 6a b)cos(x) + (- 15a b + 15a b)cos(x) +--R + +--R 2 5 4 3 +--R (6a b - 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (- 6a b + 14a b - 8a )cos(x) + (- 6a b + 8a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (12a b - 26a b + 14a )cos(x) + (12a b - 14a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a )cos(x) + (- 6a b + 6a b )cos(x) +--R / +--R 6 4 6 2 6 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)sin(x) +--R + +--R 5 2 5 5 2 7 4 5 2 3 +--R 6a b cos(x) + (6a b + 6a )cos(x) - 12a b cos(x) +--R + +--R 5 2 7 2 5 2 5 2 7 +--R (- 12a b - 12a )cos(x) + 6a b cos(x) + 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 6 6 +--R 6a b cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b )sin(x) +--R + +--R 4 3 5 4 3 6 4 4 3 3 +--R 12a b cos(x) + (12a b + 12a b)cos(x) - 24a b cos(x) +--R + +--R 4 3 6 2 4 3 4 3 6 +--R (- 24a b - 24a b)cos(x) + 12a b cos(x) + 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 5 5 2 4 5 2 3 5 2 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 2 5 2 +--R 12a b cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 6 2 6 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)sin(x) +--R + +--R 5 2 5 5 2 7 4 5 2 3 +--R 6a b cos(x) + (6a b + 6a )cos(x) - 12a b cos(x) +--R + +--R 5 2 7 2 5 2 5 2 7 +--R (- 12a b - 12a )cos(x) + 6a b cos(x) + 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 6 6 +--R 6a b cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 2 4 6 2 2 6 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 6 2 8 3 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) + (12a b - 12a )cos(x) +--R + +--R 6 2 2 6 2 8 6 2 +--R 12a b cos(x) + (- 6a b + 6a )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 4 5 3 2 5 3 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (24a b - 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 12a b + 12a b )cos(x) - 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 7 5 5 3 4 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 5 3 7 3 5 3 2 +--R (24a b - 24a b)cos(x) + 24a b cos(x) +--R + +--R 5 3 7 5 3 +--R (- 12a b + 12a b)cos(x) - 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 6 2 2 6 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 6 2 8 3 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) + (12a b - 12a )cos(x) +--R + +--R 6 2 2 6 2 8 6 2 +--R 12a b cos(x) + (- 6a b + 6a )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 114 + +--S 115 of 546 +m0419b:= a0419.2-r0419 +--R +--R +--R (112) +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)atanh(cos(x)) +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R (cos(x) + 1)\|- b + a +--R atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 2 2 2 | 2 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b - 6a )cos(x) - 6a b + 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R Type: Expression Integer +--E 115 + +--S 116 of 546 +d0419b:= D(m0419b,x) +--R +--R +--R (113) +--R 2 3 4 3 4 2 2 3 4 +--R (- 6a b + 9a b)cos(x) - 3a b cos(x) + (6a b - 9a b)cos(x) +--R + +--R 4 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b + 6a b + 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 5 2 4 3 2 4 3 2 5 +--R - 6a cos(x) + (12a b - 24a b )cos(x) + 6a b - 18a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 24a b cos(x) + 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 4 2 4 4 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 12b + 12a b + 2a b)cos(x) + (- 12b + 12a b - a b)cos(x) +--R + +--R 5 2 3 4 3 5 2 3 4 2 +--R (24b - 36a b + 12a b)cos(x) + (24b - 36a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (- 12b + 24a b - 18a b)cos(x) - 12b + 24a b - 15a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R - 24a b cos(x) - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R - 6a b cos(x) - 12a b cos(x) + 6a b cos(x) + 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 6a b cos(x) - 12a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 6 +--R (- 6a b + 12a b - 4a )cos(x) +--R + +--R 4 3 2 5 5 4 3 2 4 +--R (- 12a b + 18a b - 4a )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (24a b - 36a b + 12a )cos(x) + (6a b - 12a b + 18a )cos(x) +--R + +--R 4 3 2 4 3 2 5 +--R (- 12a b + 18a b )cos(x) - 6a b + 12a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b - 7a b)cos(x) + 2a b cos(x) + (- 18a b + 19a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b - 21a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 9a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (6a b - 8a )cos(x) + (12a b - 16a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 6a b + 6a )cos(x) + (- 24a b + 28a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 3 2 5 2 +--R (- 6a b + 8a )cos(x) + (12a b - 12a )cos(x) + (6a b - 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 3 2 2 +--R (- 12a b + 18a b )cos(x) - 6a b cos(x) +--R + +--R 4 3 2 3 2 +--R (12a b - 18a b )cos(x) - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 4 4 2 4 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b)cot(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 3 4 4 5 2 3 3 +--R (- 12a b + 20a b)cos(x) + (- 24b + 24a b )cos(x) +--R + +--R 5 2 3 4 2 5 2 3 5 +--R (- 24b + 48a b - 36a b)cos(x) + (24b - 48a b )cos(x) + 24b +--R + +--R 2 3 4 +--R - 60a b + 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 48a b cos(x) + 24a b cos(x) + 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 2 3 2 3 +--R 12a b cos(x) + 12a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R - 24a b cos(x) - 24a b cos(x) + 48a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 48a b cos(x) - 24a b cos(x) - 24a b +--R * +--R 4 +--R cot(x) +--R + +--R 4 5 4 4 4 3 +--R - 24a b cos(x) - 24a b cos(x) + 48a b cos(x) +--R + +--R 4 2 4 4 +--R 48a b cos(x) - 24a b cos(x) - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 24a b + 28a b )cos(x) + (- 24a b + 22a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 2 3 2 +--R - 12a b cos(x) - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 5 3 2 4 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R - 48a b cos(x) - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 6 4 5 4 4 +--R - 12a b cos(x) - 24a b cos(x) + 12a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R 48a b cos(x) + 12a b cos(x) - 24a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R - 12a b cos(x) - 24a b cos(x) + 12a b cos(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 +--R 48a b cos(x) + 12a b cos(x) - 24a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 2 3 4 5 4 4 +--R 4a b cos(x) + (- 12a b + 16a b)cos(x) - 12a b cos(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (24a b - 24a b)cos(x) + 24a b cos(x) + (- 12a b + 24a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 3 2 6 +--R (12a b - 14a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 5 3 2 4 +--R (- 36a b + 38a b )cos(x) - 16a b cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (36a b - 42a b )cos(x) + 12a b cos(x) +--R + +--R 4 3 2 +--R (- 12a b + 18a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (12a b - 16a b)cos(x) + (24a b - 32a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b + 12a b)cos(x) + (- 48a b + 56a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 12a b + 16a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 4 2 +--R (12a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 4 2 2 3 4 4 +--R ((- 6a b + 9a b)cos(x) - 3a b cos(x) + (6a b - 9a b)cos(x) - 3a b) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b + 6a b + 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 5 2 4 3 2 4 3 2 5 +--R - 6a cos(x) + (12a b - 24a b )cos(x) + 6a b - 18a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 3 2 3 2 +--R 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) + 24a b cos(x) +--R + +--R 4 4 +--R - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) + 24a b cos(x) +--R + +--R 2 3 2 3 +--R - 12a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 12b + 12a b + 2a b)cos(x) + (- 12b + 12a b - a b)cos(x) +--R + +--R 5 2 3 4 3 5 2 3 4 2 +--R (24b - 36a b + 12a b)cos(x) + (24b - 36a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (- 12b + 24a b - 18a b)cos(x) - 12b + 24a b - 15a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 4 2 4 4 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R - 6a b cos(x) - 12a b cos(x) + 6a b cos(x) + 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 6a b cos(x) - 12a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (- 6a b + 12a b - 4a )cos(x) + (- 12a b + 18a b - 4a )cos(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (6a b - 12a b )cos(x) + (24a b - 36a b + 12a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 4 +--R (6a b - 12a b + 18a )cos(x) + (- 12a b + 18a b )cos(x) - 6a b +--R + +--R 3 2 5 +--R 12a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b - 7a b)cos(x) + 2a b cos(x) + (- 18a b + 19a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b - 21a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 9a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (6a b - 8a )cos(x) + (12a b - 16a )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 24a b + 28a )cos(x) + (- 6a b + 8a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (12a b - 12a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b)sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) - 48a b cos(x) +--R + +--R 4 2 4 2 +--R 24a b cos(x) + 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) - 48a b cos(x) +--R + +--R 5 2 5 5 +--R - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 116 + +--S 117 of 546 +t0420:= cot(x)/(a+a*sin(x)) +--R +--R +--R cot(x) +--R (114) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 117 + +--S 118 of 546 +r0420:= -2*atanh(1+2*sin(x))/a +--R +--R +--R 2atanh(2sin(x) + 1) +--R (115) - ------------------- +--R a +--R Type: Expression Integer +--E 118 + +--S 119 of 546 +a0420:= integrate(t0420,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) +--R - 2log(-------------------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (116) --------------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 119 + +--S 120 of 546 +m0420:= a0420-r0420 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) +--R - 2log(-------------------) + log(----------) + 2atanh(2sin(x) + 1) +--R cos(x) + 1 cos(x) + 1 +--R (117) ------------------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 120 + +--S 121 of 546 +d0420:= D(m0420,x) +--R +--R +--R (118) +--R 3 2 2 3 +--R - sin(x) + cos(x)sin(x) + (- cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (a cos(x) + 3a cos(x) + 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R Type: Expression Integer +--E 121 + +--S 122 of 546 +t0421:= cot(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R cot(x) +--R (119) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 122 + +--S 123 of 546 +r0421:= atanh(cos(x))/a-cot(x)/a +--R +--R +--R atanh(cos(x)) - cot(x) +--R (120) ---------------------- +--R a +--R Type: Expression Integer +--E 123 + +--S 124 of 546 +a0421:= integrate(t0421,x) +--R +--R +--R sin(x) +--R - sin(x)log(----------) - cos(x) +--R cos(x) + 1 +--R (121) -------------------------------- +--R a sin(x) +--R Type: Union(Expression Integer,...) +--E 124 + +--S 125 of 546 +m0421:= a0421-r0421 +--R +--R +--R (122) +--R sin(x) +--R - sin(x)log(----------) - sin(x)atanh(cos(x)) + cot(x)sin(x) - cos(x) +--R cos(x) + 1 +--R --------------------------------------------------------------------- +--R a sin(x) +--R Type: Expression Integer +--E 125 + +--S 126 of 546 +d0421:= D(m0421,x) +--R +--R +--R (123) +--R 3 2 2 2 +--R - cos(x)sin(x) + (- cos(x) + 1)cot(x) sin(x) +--R + +--R 3 4 2 +--R (- cos(x) + cos(x))sin(x) + cos(x) - cos(x) +--R / +--R 2 2 +--R (a cos(x) - a)sin(x) +--R Type: Expression Integer +--E 126 + +--S 127 of 546 +t0422:= cot(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R cot(x) +--R (124) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 127 + +--S 128 of 546 +r0422:= -1/2*atanh(cos(x))/a-1/3*cot(x)^3/a+1/2*cot(x)*csc(x)/a +--R +--R +--R 3 +--R - 3atanh(cos(x)) + 3cot(x)csc(x) - 2cot(x) +--R (125) ------------------------------------------- +--R 6a +--R Type: Expression Integer +--E 128 + +--S 129 of 546 +a0422:= integrate(t0422,x) +--R +--R +--R 2 sin(x) 3 +--R (3cos(x) - 3)sin(x)log(----------) - 3cos(x)sin(x) + 2cos(x) +--R cos(x) + 1 +--R (126) -------------------------------------------------------------- +--R 2 +--R (6a cos(x) - 6a)sin(x) +--R Type: Union(Expression Integer,...) +--E 129 + +--S 130 of 546 +m0422:= a0422-r0422 +--R +--R +--R (127) +--R 2 sin(x) 2 +--R (3cos(x) - 3)sin(x)log(----------) + (3cos(x) - 3)sin(x)atanh(cos(x)) +--R cos(x) + 1 +--R + +--R 2 2 3 +--R ((- 3cos(x) + 3)cot(x)csc(x) + (2cos(x) - 2)cot(x) - 3cos(x))sin(x) +--R + +--R 3 +--R 2cos(x) +--R / +--R 2 +--R (6a cos(x) - 6a)sin(x) +--R Type: Expression Integer +--E 130 + +--S 131 of 546 +d0422:= D(m0422,x) +--R +--R +--R (128) +--R 3 2 3 +--R (3cos(x) - 3cos(x) - 3cos(x) - 3)sin(x) +--R + +--R 4 2 2 4 2 +--R ((6cos(x) - 12cos(x) + 6)cot(x) + 3cos(x) - 6cos(x) + 3)csc(x) +--R + +--R 4 2 4 +--R (- 6cos(x) + 12cos(x) - 6)cot(x) +--R + +--R 4 2 2 4 2 +--R (- 6cos(x) + 12cos(x) - 6)cot(x) - 2cos(x) + 6cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 6 4 +--R (3cos(x) - 6cos(x) + 3cos(x))sin(x) - 2cos(x) + 2cos(x) +--R / +--R 4 2 2 +--R (6a cos(x) - 12a cos(x) + 6a)sin(x) +--R Type: Expression Integer +--E 131 + +--S 132 of 546 +t0423:= sec(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R sec(x) +--R (129) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 132 + +--S 133 of 546 +r0423:= 2*b^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+1/12*cos(x)/(a+b)/(1-sin(x))^2+1/12*cos(x)/(a+b)/(1-sin(x))+1/4*(a+2*b)*cos(x)/(a+b)^2/(1-sin(x))-1/12*cos(x)/(a-b)/(1+sin(x))^2-1/4*(a-2*b)*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (130) +--R x +--R a tan(-) + b +--R 4 4 4 2 4 2 +--R (6b sin(x) - 12b sin(x) + 6b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 3 2 +--R (5a b - 2a )cos(x)sin(x) - 3b cos(x)sin(x) +--R + +--R 2 3 3 2 +--R (- 6a b + 3a )cos(x)sin(x) + (4b - a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (3b - 6a b + 3a )sin(x) + (- 6b + 12a b - 6a )sin(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 133 + +--S 134 of 546 +a0423:= integrate(t0423,x) +--R +--R +--R (131) +--R [ +--R 4 3 +--R 3b cos(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) + (4b - a b)cos(x) +--R + +--R 3 2 3 2 +--R 3b cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 3 (a sin(x) + b cos(x) + b)\|- b + a +--R - 6b cos(x) atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) + (4b - a b)cos(x) +--R + +--R 3 2 3 2 +--R 3b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 134 + +--S 135 of 546 +m0423a:= a0423.1-r0423 +--R +--R +--R (132) +--R +---------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (3b cos(x) sin(x) - 6b cos(x) sin(x) + 3b cos(x) )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )\|b - a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 3 2 4 +--R ((4b - a b)cos(x) + 3b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((- 5a b + 2a )cos(x) + (10a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 4 3 2 3 3 2 3 2 2 +--R (3b cos(x) + (- 8b + 2a b)cos(x) - 6b cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((6a b - 3a )cos(x) + (- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 3 2 +--R (- 4b + a b)cos(x) + (4b - a b)cos(x) + 3b cos(x) + b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 135 + +--S 136 of 546 +d0423a:= D(m0423a,x) +--R +--R +--R (133) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((- 5a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 5a b + 7a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 2a b - 3a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (3a b - 8a b + 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (3a b + 12a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (3a b - 9a b + 9a b - 3a )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 7 2 5 4 +--R (- 3b + 3a b )cos(x) + (- 3b - 3a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (17a b - 22a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (8a b + 9a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 +--R (3a b + 5a b - 2a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 23a b - 19a b + 5a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b - 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (5a b - 7a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- a b + 3a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (9b - 8a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (9b + 8a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 21a b + 24a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 12a b - 9a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 6a b + 11a b - 7a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 15a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (7a b - 4a b - 4a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (16a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 21a b + 15a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 9a b + 12a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 9b + 7a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 9b - 6a b - 6a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (11a b - 10a b - a b)cos(x) + (8a b + 3a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (10a b - 17a b + 10a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (19a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 4a b - 4a b + 11a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 13a b - 7a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 2 +--R (- 3a b + 5a b - a b - a )cos(x) - 3a b cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (4a b - 5a b + a b)cos(x) + (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b - 2a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (3b + a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- 2a b + a b + a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a )cos(x) + (- 3a b - 6a b + 3a b )cos(x) +--R + +--R 3 4 5 2 7 5 6 3 4 5 2 4 +--R (5a b - 7a b + 2a )cos(x) + (3a b + 5a b - 2a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 10 +--R ((- 10a b + 4a b )cos(x) - 6a b + 6a b )sin(x) +--R + +--R 6 3 4 5 2 3 +--R (- 10a b + 14a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b - 6a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 7 4 7 2 5 4 3 6 3 +--R 6b cos(x) + (6b - 16a b + 14a b - 4a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (6b + 24a b - 6a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 18a b - 6a b)cos(x) + 6b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 6 3 4 5 2 3 +--R (34a b - 44a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (16a b + 18a b - 10a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 6a b + 12a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 7 2 5 4 3 6 +--R (6b + 10a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 24b + 2a b - 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 46a b - 38a b + 10a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (- 18b - 14a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 18b + 54a b - 54a b + 18a b)cos(x) - 18b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (10a b - 14a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 2a b + 6a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 42a b + 48a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 24a b - 18a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R (- 36a b + 72a b - 36a b )cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 12b + 22a b - 14a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 30b - 8a b + 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 4b + 10a b - 8a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (32b + 2a b + 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 42a b + 30a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (18b - 2a b + 8a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (18b - 54a b + 54a b - 18a b)cos(x) + 18b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 18a b + 24a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (2a b - 8a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (22a b - 20a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (16a b + 6a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 18a b - 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (20b - 34a b + 20a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (38b - 6a b + 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (10b - 26a b + 22a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 14b - 14a b + 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 7 2 +--R (- 6b + 10a b - 2a b - 2a b)cos(x) - 6b cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 +--R (- 6b + 18a b - 18a b + 6a b)cos(x) - 6b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (8a b - 10a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (8a b - 14a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 6 5 2 2 +--R (- 4a b + 2a b + 2a b )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 12a b + 18a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 6b - 12a b + 6a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 2 5 4 3 4 +--R (- 6b + 16a b - 14a b + 4a b)cos(x) + (10a b - 4a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((- 5a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 5a b + 7a b - 2a b)cos(x) + (- 2a b - 3a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (3a b - 8a b + 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (3a b + 12a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (3a b - 9a b + 9a b - 3a )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 7 2 5 4 +--R (- 3b + 3a b )cos(x) + (- 3b - 3a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (17a b - 22a b + 5a b)cos(x) + (8a b + 9a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 +--R (3a b + 5a b - 2a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 23a b - 19a b + 5a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b - 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (5a b - 7a b + 2a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (9b - 8a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (9b + 8a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 21a b + 24a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 12a b - 9a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 6a b + 11a b - 7a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 15a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (7a b - 4a b - 4a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (16a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 21a b + 15a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (- 9a b + 12a b - 3a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 9b + 7a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 9b - 6a b - 6a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (11a b - 10a b - a b)cos(x) + (8a b + 3a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (10a b - 17a b + 10a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (19a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 4a b - 4a b + 11a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 13a b - 7a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 2 +--R (- 3a b + 5a b - a b - a )cos(x) - 3a b cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (4a b - 5a b + a b)cos(x) + (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b - 2a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (3b + a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- 2a b + a b + a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a )cos(x) + (- 3a b - 6a b + 3a b )cos(x) +--R + +--R 3 4 5 2 7 5 6 3 4 5 2 4 +--R (5a b - 7a b + 2a )cos(x) + (3a b + 5a b - 2a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((5a b - 7a b + 2a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (5a b - 7a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (2a b + a b - 5a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 8a b - 7a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b - 9a b + 15a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 2 6 5 8 4 4 4 +--R (3b - 3a b )cos(x) + (3b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 17a b + 22a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b - a b + 14a b - 5a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 6 7 3 5 5 +--R (- 3a b - 2a b + 7a b - 2a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 7a b + 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 23a b + 19a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 2a b - 5a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b +--R + +--R 7 +--R 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 8a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 9b + a b + 6a b + 3a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (21a b - 24a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (12a b - 3a b - 12a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (6a b - 11a b + 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (15a b - 11a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 7a b + 4a b + 4a b - a b)cos(x) +--R + +--R 7 3 5 7 4 +--R (- 16a b + 15a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 21a b - 15a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 10a b - 5a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (9a b - 12a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (9b - 7a b - 4a b + 2a b )cos(x) +--R + +--R 8 2 6 6 2 8 4 +--R (9b - 3a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 11a b + 10a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b + 5a b + 2a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 10a b + 17a b - 10a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 19a b + 22a b - 5a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (4a b + 4a b - 11a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (13a b - 6a b - 9a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 2 +--R (3a b - 5a b + a b + a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 4a b + 5a b - a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 4a b + 11a b - 10a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 2a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 3b + 2a b - 3a b + 6a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 8 2 +--R (2a b - a b - a b )cos(x) + (2a b - 2a b + a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 7 3 5 5 3 7 6 +--R (6a b - 9a b + 3a b)cos(x) + (3a b + 3a b - 9a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- 5a b + 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b - 2a b + 7a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((10a b - 14a b + 4a b )cos(x) + 6a b - 12a b + 6a b )sin(x) +--R + +--R 7 3 5 5 3 3 +--R (10a b - 14a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b + 2a b - 10a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 7 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 8 2 6 4 8 2 6 4 4 6 2 3 +--R (- 6b + 6a b )cos(x) + (- 6b + 16a b - 14a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 6b - 18a b + 30a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) - 6b - 6a b + 30a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 3 3 +--R (- 34a b + 44a b - 10a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 16a b - 2a b + 28a b - 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 6a b - 6a b + 30a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 6b - 4a b + 14a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (24b - 26a b + 4a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (18b - 46a b + 38a b - 10a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (18b - 4a b - 10a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (18b - 54a b + 54a b - 18a b )cos(x) + 18b - 18a b - 18a b +--R + +--R 6 2 +--R 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 10a b + 14a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 8a b + 10a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (42a b - 48a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (24a b - 6a b - 24a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (36a b - 72a b + 36a b )cos(x) + 18a b - 18a b - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (12b - 22a b + 14a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (30b - 22a b - 10a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (4b - 10a b + 8a b - 2a b )cos(x) +--R + +--R 8 2 6 6 2 4 +--R (- 32b + 30a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 18b + 42a b - 30a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 18b + 20a b - 10a b + 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) - 18b + 30a b - 6a b +--R + +--R 6 2 +--R - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (18a b - 24a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 2a b + 10a b - 14a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 22a b + 20a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 16a b + 10a b + 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 18a b + 30a b - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 20b + 34a b - 20a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 38b + 44a b - 10a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 10b + 26a b - 22a b + 6a b )cos(x) +--R + +--R 8 4 4 6 2 4 +--R (14b - 18a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 8 2 6 2 +--R (6b - 10a b + 2a b + 2a b )cos(x) + (6b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (6b - 18a b + 18a b - 6a b )cos(x) + 6b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 8a b + 22a b - 20a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (4a b - 12a b + 12a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (4a b - 2a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b - 4a b + 2a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (12a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (6b + 6a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b - 16a b + 14a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (- 10a b + 14a b - 4a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 2a b + 4a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((5a b - 7a b + 2a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 8 2 +--R (5a b - 7a b + 2a b )cos(x) + (2a b + a b - 5a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 8a b - 7a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b - 9a b + 15a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 2 6 5 8 4 4 4 +--R (3b - 3a b )cos(x) + (3b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 17a b + 22a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b - a b + 14a b - 5a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 6 7 3 5 5 +--R (- 3a b - 2a b + 7a b - 2a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 7a b + 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 23a b + 19a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 2a b - 5a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 8a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 9b + a b + 6a b + 3a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (21a b - 24a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (12a b - 3a b - 12a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (6a b - 11a b + 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (15a b - 11a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 7a b + 4a b + 4a b - a b)cos(x) +--R + +--R 7 3 5 7 4 +--R (- 16a b + 15a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 21a b - 15a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 10a b - 5a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (9a b - 12a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (9b - 7a b - 4a b + 2a b )cos(x) +--R + +--R 8 2 6 6 2 8 4 +--R (9b - 3a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 11a b + 10a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b + 5a b + 2a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 10a b + 17a b - 10a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 19a b + 22a b - 5a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (4a b + 4a b - 11a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (13a b - 6a b - 9a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 2 +--R (3a b - 5a b + a b + a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 4a b + 5a b - a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 4a b + 11a b - 10a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 2a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 3b + 2a b - 3a b + 6a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 8 2 +--R (2a b - a b - a b )cos(x) + (2a b - 2a b + a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 7 3 5 5 3 7 6 +--R (6a b - 9a b + 3a b)cos(x) + (3a b + 3a b - 9a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 5 7 3 5 5 3 7 4 +--R (- 5a b + 7a b - 2a b)cos(x) + (- 3a b - 2a b + 7a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 4 8 +--R (6a b - 12a b + 6a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b - 6a b - 6a b + 6a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 12a b + 24a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 18b + 18a b + 18a b - 18a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (18b - 18a b - 18a b + 18a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (18a b - 54a b + 54a b - 18a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (12a b - 24a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 6a b + 6a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 6b + 12a b - 12a b + 6a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (12a b - 36a b + 36a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (18b - 36a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (18a b - 54a b + 54a b - 18a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 18b + 36a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 18a b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 12a b + 36a b - 36a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (6b - 12a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R Type: Expression Integer +--E 136 + +--S 137 of 546 +m0423b:= a0423.2-r0423 +--R +--R +--R (134) +--R 4 3 4 4 3 2 4 3 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 4 3 4 4 3 2 4 3 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 3 2 4 +--R ((4b - a b)cos(x) + 3b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((- 5a b + 2a )cos(x) + (10a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 4 3 2 3 3 2 3 2 2 +--R (3b cos(x) + (- 8b + 2a b)cos(x) - 6b cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((6a b - 3a )cos(x) + (- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 3 2 +--R (- 4b + a b)cos(x) + (4b - a b)cos(x) + 3b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 137 + +--S 138 of 546 +d0423b:= D(m0423b,x) +--R +--R +--R (135) +--R 3 2 5 2 3 2 5 10 +--R ((- 5a b + 2a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 10a b + 4a b)cos(x) + (- 7a b + 4a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (3a b - 5a b + 2a )cos(x) + (6a b - 10a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 3 2 5 4 5 +--R (6a b + 6a b )cos(x) + (6a b - 12a b + 6a )cos(x) + 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 2 3 4 3 +--R - 6b cos(x) - 6b cos(x) + (34a b - 10a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (25a b - 13a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 5 6 4 5 +--R (3a b + 5a b - 2a )cos(x) - 6a b cos(x) +--R + +--R 4 3 2 5 4 +--R (- 18a b + 18a b - 6a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 18a b + 28a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 +--R (- 18a b + 11a b - 11a )cos(x) +--R + +--R 4 3 2 5 4 3 2 +--R (- 18a b + 36a b - 18a )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (10a b - 4a b)cos(x) + (a b - 4a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (18b + 2a b - 2a b)cos(x) + (18b + 3a b - 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 42a b + 6a b)cos(x) + (- 33a b + 15a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (5a b - 2a )cos(x) + (- 12a b + 10a b - 4a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 21a b + 6a b )cos(x) + (14a b + 6a b - 2a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (32a b - 19a b + 5a )cos(x) + (18a b - 24a b + 6a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 19a b + 13a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 2 3 4 6 +--R - 6a b cos(x) + (- 18a b + 6a b)cos(x) + (5a b + a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 18b - 4a b + 4a b)cos(x) + (- 18b - 6a b + 6a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (22a b + 2a b)cos(x) + (19a b - 7a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (20a b - 14a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (29a b - 26a b + 9a )cos(x) + (- 8a b - 16a b + 6a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 20a b + 2a )cos(x) + (- 6a b + 4a b + 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (10a b - 4a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 2 3 4 6 5 2 3 4 5 +--R (- 6a b + 3a b)cos(x) + (6b + 2a b - 2a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b + 3a b - 3a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 4a b + a b)cos(x) + (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 3a )cos(x) + (- 12a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 3 2 5 5 +--R (- 3a b - a b + a )cos(x) + (10a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 3 +--R (3a b + 6a b - 3a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 2 +--R (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 10 +--R ((- 10a b + 4a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 20a b + 8a b )cos(x) + (- 14a b + 8a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (12b - 10a b + 4a b)cos(x) + (12b - 20a b + 8a b)cos(x) +--R + +--R 5 2 3 2 5 2 3 4 5 +--R (12b + 12a b )cos(x) + (12b - 24a b + 12a b)cos(x) + 12b +--R + +--R 4 +--R - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (68a b - 20a b )cos(x) + (50a b - 26a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (48a b - 48a b )cos(x) + 24a b - 24a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 4 +--R (12b + 10a b - 4a b)cos(x) + (- 48b + 36a b - 12a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 36b + 56a b - 20a b)cos(x) +--R + +--R 5 2 3 4 2 +--R (- 36b + 22a b - 22a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (- 36b + 72a b - 36a b)cos(x) - 36b + 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (20a b - 8a b )cos(x) + (2a b - 8a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (4a b - 4a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 84a b + 12a b )cos(x) + (- 66a b + 30a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 72a b + 72a b )cos(x) - 36a b + 36a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (10a b - 4a b)cos(x) + (- 24b + 20a b - 8a b)cos(x) +--R + +--R 5 2 3 6 5 2 3 4 5 +--R (- 60b + 12a b )cos(x) + (- 8b + 12a b - 4a b)cos(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (64b - 38a b + 10a b)cos(x) + (36b - 48a b + 12a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (36b - 38a b + 26a b)cos(x) + (36b - 72a b + 36a b)cos(x) +--R + +--R 5 2 3 4 +--R 36b - 48a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 8 4 3 2 7 +--R - 12a b cos(x) + (- 36a b + 12a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (10a b + 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 12a b + 12a b )cos(x) + (44a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (38a b - 14a b )cos(x) + (48a b - 48a b )cos(x) + 24a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (40b - 28a b + 12a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (76b - 52a b + 18a b)cos(x) + (20b - 32a b + 12a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (- 28b + 4a b)cos(x) + (- 12b + 8a b + 4a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 12b + 12a b - 6a b)cos(x) + (- 12b + 24a b - 12a b)cos(x) +--R + +--R 5 2 3 4 +--R - 12b + 18a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (20a b - 8a b )cos(x) + (16a b - 4a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 12a b + 6a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (6a b - 6a b )cos(x) + (- 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- 8a b + 2a b )cos(x) + (- 12a b + 12a b )cos(x) - 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 12a b + 6a b)cos(x) + (- 24a b + 12a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (- 12b - 2a b + 2a b)cos(x) + (- 12b + 20a b - 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 2 3 4 2 +--R (12a b - 6a b)cos(x) + (4a b - 4a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 3 2 5 10 +--R ((- 5a b + 2a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 10a b + 4a b)cos(x) + (- 7a b + 4a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (3a b - 5a b + 2a )cos(x) + (6a b - 10a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 3 2 5 4 5 +--R (6a b + 6a b )cos(x) + (6a b - 12a b + 6a )cos(x) + 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 2 3 4 3 +--R - 6b cos(x) - 6b cos(x) + (34a b - 10a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (25a b - 13a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 5 6 4 5 +--R (3a b + 5a b - 2a )cos(x) - 6a b cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 18a b + 18a b - 6a )cos(x) + (- 18a b + 28a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 18a b + 11a b - 11a )cos(x) + (- 18a b + 36a b - 18a )cos(x) +--R + +--R 4 3 2 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (10a b - 4a b)cos(x) + (a b - 4a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (18b + 2a b - 2a b)cos(x) + (18b + 3a b - 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 42a b + 6a b)cos(x) + (- 33a b + 15a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (5a b - 2a )cos(x) + (- 12a b + 10a b - 4a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 21a b + 6a b )cos(x) + (14a b + 6a b - 2a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (32a b - 19a b + 5a )cos(x) + (18a b - 24a b + 6a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 19a b + 13a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 2 3 4 6 +--R - 6a b cos(x) + (- 18a b + 6a b)cos(x) + (5a b + a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 18b - 4a b + 4a b)cos(x) + (- 18b - 6a b + 6a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (22a b + 2a b)cos(x) + (19a b - 7a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (20a b - 14a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (29a b - 26a b + 9a )cos(x) + (- 8a b - 16a b + 6a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 20a b + 2a )cos(x) + (- 6a b + 4a b + 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (10a b - 4a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 2 3 4 6 5 2 3 4 5 +--R (- 6a b + 3a b)cos(x) + (6b + 2a b - 2a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b + 3a b - 3a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 4a b + a b)cos(x) + (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 3a )cos(x) + (- 12a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 3 2 5 5 +--R (- 3a b - a b + a )cos(x) + (10a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 3 3 2 5 2 +--R (3a b + 6a b - 3a )cos(x) + (2a b - 2a )cos(x) + (a b - a )cos(x) +--R / +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 +--R (- 9a b + 18a b - 9a )cos(x) +--R + +--R 2 4 4 2 6 5 +--R (- 18a b + 36a b - 18a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((12b - 24a b + 12a b )cos(x) + (12b - 24a b + 12a b )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 36b + 72a b - 36a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 36b + 72a b - 36a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((36b - 72a b + 36a b )cos(x) + (36b - 72a b + 36a b )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 12b + 24a b - 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R ((- 9a b + 18a b - 9a )cos(x) + (- 18a b + 36a b - 18a )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R Type: Expression Integer +--E 138 + +--S 139 of 546 +t0424:= sec(x)/(a+a*sin(x)) +--R +--R +--R sec(x) +--R (136) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 139 + +--S 140 of 546 +r0424:= 1/2/a*(atanh(sin(x))*cos(x)^2+sin(x)-1)/cos(x)^2 +--R +--R +--R 2 +--R cos(x) atanh(sin(x)) + sin(x) - 1 +--R (137) --------------------------------- +--R 2 +--R 2a cos(x) +--R Type: Expression Integer +--E 140 + +--S 141 of 546 +a0424:= integrate(t0424,x) +--R +--R +--R (138) +--R sin(x) + cos(x) + 1 +--R (sin(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- sin(x) - 1)log(-------------------) + sin(x) +--R cos(x) + 1 +--R / +--R 2a sin(x) + 2a +--R Type: Union(Expression Integer,...) +--E 141 + +--S 142 of 546 +m0424:= a0424-r0424 +--R +--R +--R (139) +--R 2 2 sin(x) + cos(x) + 1 +--R (cos(x) sin(x) + cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (- cos(x) sin(x) - cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R (- cos(x) sin(x) - cos(x) )atanh(sin(x)) - sin(x) + cos(x) sin(x) + 1 +--R / +--R 2 2 +--R 2a cos(x) sin(x) + 2a cos(x) +--R Type: Expression Integer +--E 142 + +--S 143 of 546 +d0424:= D(m0424,x) +--R +--R +--R (140) +--R 7 3 2 5 +--R - 2sin(x) + (- 2cos(x) + cos(x) + 4cos(x) + 6)sin(x) +--R + +--R 3 2 4 +--R (- 2cos(x) - cos(x) )sin(x) +--R + +--R 5 4 3 2 3 +--R (- 2cos(x) + cos(x) + 4cos(x) - 2cos(x) - 8cos(x) - 6)sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) - cos(x) + 4cos(x) + 2cos(x) )sin(x) +--R + +--R 6 5 4 3 2 +--R (- 2cos(x) - 2cos(x) - cos(x) - 2cos(x) + cos(x) + 4cos(x) + 2) +--R * +--R sin(x) +--R + +--R 5 4 3 2 +--R 2cos(x) + cos(x) - 2cos(x) - cos(x) +--R / +--R 3 5 3 4 +--R 2a cos(x) sin(x) + 2a cos(x) sin(x) +--R + +--R 5 4 3 3 +--R (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 2 +--R (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2a cos(x) + 4a cos(x) + 2a cos(x) )sin(x) + 2a cos(x) + 4a cos(x) +--R + +--R 3 +--R 2a cos(x) +--R Type: Expression Integer +--E 143 + +--S 144 of 546 +t0425:= sec(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R sec(x) +--R (141) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 144 + +--S 145 of 546 +r0425:= 1/8/cos(x)^4*(3*atanh(sin(x))*cos(x)^4+2*sin(x)-2+3*sin(x)*cos(x)^2)/a +--R +--R +--R 4 2 +--R 3cos(x) atanh(sin(x)) + (3cos(x) + 2)sin(x) - 2 +--R (142) ------------------------------------------------ +--R 4 +--R 8a cos(x) +--R Type: Expression Integer +--E 145 + +--S 146 of 546 +a0425:= integrate(t0425,x) +--R +--R +--R (143) +--R 2 2 sin(x) + cos(x) + 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2cos(x) + 3)sin(x) - cos(x) + 1 +--R / +--R 2 2 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Union(Expression Integer,...) +--E 146 + +--S 147 of 546 +m0425:= a0425-r0425 +--R +--R +--R (144) +--R 4 4 sin(x) + cos(x) + 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 sin(x) - cos(x) - 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 2 2 +--R (- 3cos(x) sin(x) - 3cos(x) )atanh(sin(x)) + (- 3cos(x) - 2)sin(x) +--R + +--R 4 4 2 +--R 2cos(x) sin(x) - cos(x) + cos(x) + 2 +--R / +--R 4 4 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Expression Integer +--E 147 + +--S 148 of 546 +d0425:= D(m0425,x) +--R +--R +--R (145) +--R 2 7 +--R (- 6cos(x) - 8)sin(x) +--R + +--R 5 4 3 2 5 +--R (- 6cos(x) + 3cos(x) + 12cos(x) + 20cos(x) + 16cos(x) + 24)sin(x) +--R + +--R 5 4 2 4 +--R (- 6cos(x) - 3cos(x) - 2cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 6cos(x) + 3cos(x) + 12cos(x) + 2cos(x) - 12cos(x) - 22cos(x) +--R + +--R - 32cos(x) - 24 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R (- 6cos(x) - 3cos(x) + 12cos(x) + 6cos(x) + 4cos(x) + 4cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 8 7 6 5 4 2 +--R - 6cos(x) - 6cos(x) - 5cos(x) - 10cos(x) - 5cos(x) + 8cos(x) +--R + +--R 16cos(x) + 8 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 6cos(x) + 5cos(x) - 2cos(x) - 3cos(x) - 4cos(x) - 2cos(x) +--R / +--R 5 5 5 4 +--R 8a cos(x) sin(x) + 8a cos(x) sin(x) +--R + +--R 7 6 5 3 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 2 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 7 6 +--R (8a cos(x) + 16a cos(x) + 8a cos(x) )sin(x) + 8a cos(x) + 16a cos(x) +--R + +--R 5 +--R 8a cos(x) +--R Type: Expression Integer +--E 148 + +--S 149 of 546 +t0426:= csc(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R csc(x) +--R (146) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 149 + +--S 150 of 546 +r0426:= 2*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)+b*atanh(cos(x))/a^2-cot(x)/a +--R +--R +--R (147) +--R x +--R +---------+ a tan(-) + b +---------+ +--R | 2 2 2 2 | 2 2 +--R b\|- b + a atanh(cos(x)) + 2b atan(------------) - a cot(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 150 + +--S 151 of 546 +a0426:= integrate(t0426,x) +--R +--R +--R (148) +--R [ +--R 2 +--R b sin(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) | 2 2 +--R - b sin(x)\|b - a log(----------) - a cos(x)\|b - a +--R cos(x) + 1 +--R / +--R +-------+ +--R 2 | 2 2 +--R a sin(x)\|b - a +--R , +--R +--R +---------+ +--R | 2 2 sin(x) +--R - b sin(x)\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R - 2b sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R - a cos(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a sin(x)\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 151 + +--S 152 of 546 +m0426a:= a0426.1-r0426 +--R +--R +--R (149) +--R +---------+ +--R 2 | 2 2 +--R b sin(x)\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R - b sin(x)\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - b sin(x)\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +--R 2 | 2 2 2 +--R - 2b sin(x)\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (a cot(x)sin(x) - a cos(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a sin(x)\|- b + a \|b - a +--R Type: Expression Integer +--E 152 + +--S 153 of 546 +d0426a:= D(m0426a,x) +--R +--R +--R (150) +--R 2 3 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (- a b cos(x) + a b )cot(x) + (- a b + a b )cos(x) +--R + +--R 4 3 2 +--R (- a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (a b - a b)cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 5 2 3 4 2 5 2 3 +--R - b cos(x) + (- b - a b + a b)cos(x) + (b - a b )cos(x) +--R + +--R 5 +--R b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 +--R (- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) +--R + +--R 3 2 +--R a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 +--R 2a b cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- a b - 2a b )cos(x) + (a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (a b - a b)cos(x) + 2a b cos(x) + (- 2a b + a b)cos(x) +--R + +--R 4 2 2 3 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 +--R (a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) +--R + +--R 3 2 2 +--R - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 2 +--R (- 2a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 5 2 3 5 +--R (- 2b - 2a b )cos(x) - 2b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 3 2 2 4 +--R - 2a b cos(x) + 2a b cos(x) - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) +--R + +--R 2 3 4 2 3 +--R (2a b - 2a b)cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 3 2 3 2 2 3 +--R 4a b cos(x) - 4a b cos(x) - 4a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 +--R (2a b - 2a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 3 3 2 2 4 +--R (- 4a b + 2a b )cos(x) - 4a b cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 2 3 4 3 +--R (2a b - 2a b)cos(x) + 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 3 2 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (- a b cos(x) + a b )cot(x) + (- a b + a b )cos(x) +--R + +--R 4 3 2 +--R (- a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (a b - a b)cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 5 2 3 4 2 5 2 3 5 +--R - b cos(x) + (- b - a b + a b)cos(x) + (b - a b )cos(x) + b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 4 3 2 2 +--R 2a b cos(x) + (- a b - a b )cos(x) + (- a b - 2a b )cos(x) +--R + +--R 4 3 2 4 +--R (a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (a b - a b)cos(x) + 2a b cos(x) + (- 2a b + a b)cos(x) +--R + +--R 4 2 2 3 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 3 2 2 +--R (a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 5 +--R (a b - a b )cos(x)sin(x) +--R + +--R 3 3 5 2 3 3 5 2 5 3 3 2 +--R ((a b - a b)cos(x) - a b + a b)cot(x) + (a b - a b )cos(x) +--R + +--R 5 5 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 +--R (a b - a b )cos(x) + (a b - a )cos(x) +--R + +--R 2 4 4 2 2 4 6 +--R (- a b + a b )cos(x) - a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 3 6 4 2 2 6 2 4 +--R (b - a b )cos(x) + (b - a b )cos(x) + (- b + a b )cos(x) +--R + +--R 6 2 4 +--R - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 4 5 5 3 5 5 2 +--R (- a b + a b)cos(x) + (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 5 5 5 3 3 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + (a b - a )cos(x) + (- a b + a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 3 3 5 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 +--R (2a b - 2a b )cos(x)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )cot(x) +--R + +--R 6 4 2 6 2 4 +--R (2b - 2a b )cos(x) + 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 3 5 5 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 3 5 3 3 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 5 3 3 3 3 3 5 2 +--R (4a b - 4a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 5 +--R (a b - a b )cos(x)sin(x) +--R + +--R 3 3 5 2 3 3 5 2 5 3 3 2 +--R ((a b - a b)cos(x) - a b + a b)cot(x) + (a b - a b )cos(x) +--R + +--R 5 5 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 2 4 4 2 +--R (a b - a b )cos(x) + (a b - a )cos(x) + (- a b + a b )cos(x) +--R + +--R 2 4 6 +--R - a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 3 6 4 2 2 6 2 4 6 +--R (b - a b )cos(x) + (b - a b )cos(x) + (- b + a b )cos(x) - b +--R + +--R 2 4 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (a b - a b)cos(x) + (a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 5 +--R - a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 4 5 5 3 5 5 2 +--R (- a b + a b)cos(x) + (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 5 5 5 3 3 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + (a b - a )cos(x) + (- a b + a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 3 3 5 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 2 +--R (a b - a b)cos(x) +--R / +--R 4 2 2 4 2 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (a b - a b)cos(x) + (a b + a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b ) +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (2a b - 2a b)cos(x) + 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 3 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (a b - a b)cos(x) + (a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 5 +--R - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b )sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 6 2 4 3 6 4 +--R ((- a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (a b - a b )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 4 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 4 3 6 4 +--R ((- a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 3 4 5 2 3 3 4 7 2 3 4 5 2 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) + (a b - a b )cos(x) +--R + +--R 3 4 7 +--R a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 3 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 4 3 6 +--R a b - a b +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 153 + +--S 154 of 546 +m0426b:= a0426.2-r0426 +--R +--R +--R (151) +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R - b sin(x)\|- b + a log(----------) - b sin(x)\|- b + a atanh(cos(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R - 2b sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 2 2 | 2 2 +--R - 2b sin(x)atan(------------) + (a cot(x)sin(x) - a cos(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a sin(x)\|- b + a +--R Type: Expression Integer +--E 154 + +--S 155 of 546 +d0426b:= D(m0426b,x) +--R +--R +--R (152) +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- a cos(x) + a )cot(x) - a b cos(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 2 3 3 2 2 3 3 +--R (- 2b - 2a b)cos(x) + (- 2b - 2a b)cos(x) + 2b cos(x) + 2b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) +--R + +--R 2 3 4 2 3 3 2 2 +--R (- a b + a )cos(x) - 2a b cos(x) - a cos(x) + 2a b cos(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2a cos(x) - 2a cos(x) - a cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 3 3 4 +--R ((- 2a b cos(x) + 2a b)cot(x) - 4b cos(x) - 4b )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4a b cos(x) - 4a b cos(x) + 4a b cos(x) + 4a b )cot(x) +--R + +--R 2 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (- 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b)cot(x) +--R + +--R 2 4 2 2 +--R 2a b cos(x) - 2a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 2 6 +--R (2a b cos(x) - 4a b cos(x) + 2a b cos(x))sin(x) + 2a b cos(x) +--R + +--R 2 5 2 3 2 2 +--R 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- a cos(x) + a )cot(x) - a b cos(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 2 3 3 2 2 3 3 +--R (- 2b - 2a b)cos(x) + (- 2b - 2a b)cos(x) + 2b cos(x) + 2b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) +--R + +--R 2 3 4 2 3 3 2 2 2 +--R (- a b + a )cos(x) - 2a b cos(x) - a cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 3 5 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) + 2a cos(x) +--R + +--R 3 3 3 2 +--R - 2a cos(x) - a cos(x) +--R / +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b)sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R Type: Expression Integer +--E 155 + +--S 156 of 546 +t0427:= csc(x)^3/(a+b*sin(x)) +--R +--R +--R 3 +--R csc(x) +--R (153) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 156 + +--S 157 of 546 +r0427:= -2*b^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)-1/2*atanh(cos(x))/a-b^2*atanh(cos(x))/a^3+b*cot(x)/a^2-1/2*cot(x)*csc(x)/a +--R +--R +--R (154) +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 3 2 +--R (- 2b - a )\|- b + a atanh(cos(x)) - 4b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- a cot(x)csc(x) + 2a b cot(x))\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression Integer +--E 157 + +--S 158 of 546 +a0427:= integrate(t0427,x) +--R +--R +--R (155) +--R [ +--R 3 2 3 +--R (2b cos(x) - 2b ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + a cos(x))\|b - a +--R / +--R +-------+ +--R 3 2 3 | 2 2 +--R (2a cos(x) - 2a )\|b - a +--R , +--R +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 3 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (4b cos(x) - 4b )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + a cos(x))\|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2a cos(x) - 2a )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 158 + +--S 159 of 546 +m0427a:= a0427.1-r0427 +--R +--R +--R (156) +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 +--R ((2b + a )cos(x) - 2b - a )\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +--R 3 2 3 | 2 2 2 +--R (4b cos(x) - 4b )\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (a cos(x) - a )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 +--R (2a cos(x) - 2a )\|- b + a \|b - a +--R Type: Expression Integer +--E 159 + +--S 160 of 546 +d0427a:= D(m0427a,x) +--R +--R +--R (157) +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 3 2 4 4 2 2 +--R 3a b cos(x) + (- 2a b - a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + a b )cos(x) - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 4 2 4 4 2 2 4 2 +--R - a b cos(x) + 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - a b - a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 +--R (- 2a b - 2a b + 2a b)cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 3 3 5 +--R a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (4a b - 4a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 5 6 2 4 4 2 6 4 +--R (2b + a b )cos(x) + (2b + 2a b - a b - a )cos(x) +--R + +--R 6 4 2 6 3 6 2 4 6 2 +--R (- 4b + 2a b - a )cos(x) + (- 4b - 4a b + a )cos(x) +--R + +--R 6 4 2 6 6 2 4 4 2 +--R (2b - a b - a )cos(x) + 2b + 2a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 4 2 4 +--R (- 2a b + 2a )cos(x) - 2a b cos(x) +--R + +--R 4 2 6 3 4 2 2 +--R (4a b - 4a )cos(x) + 4a b cos(x) +--R + +--R 4 2 6 4 2 +--R (- 2a b + 2a )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 6 5 4 2 4 4 2 6 3 +--R (- a b + a )cos(x) - a b cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 2 2 4 2 6 4 2 +--R 2a b cos(x) + (- a b + a )cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 3 3 5 3 3 3 2 +--R (- 4a b + 4a b)cos(x) - 4a b cos(x) +--R + +--R 3 3 5 3 3 +--R (2a b - 2a b)cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- a b - a b)cos(x) + (2a b + 3a b + a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b + 2a b + 2a b)cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 4a b - 3a b - a b)cos(x) + (2a b + 5a b - a b)cos(x) +--R + +--R 5 3 3 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 3 +--R (- 4a b + 2a b + 2a )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 4 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 5 3 3 2 +--R 6a b cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 8a b + 2a b )cos(x) - 4a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 4 2 2 4 2 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 2a b - 2a b )cos(x) + (4b + 4a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 6 +--R (4b - 4a b + 4a b )cos(x) + (- 4b - 8a b )cos(x) - 4b +--R + +--R 2 4 4 2 +--R 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (8a b - 8a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) - 2a b - 2a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (4a b - 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (4a b - 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (4a b + 2a b )cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 5 2 +--R (- 8a b + 4a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 5 3 3 5 3 3 +--R (4a b - 2a b - 2a b)cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 3 3 4 +--R (- 4a b + 4a b)cos(x) - 4a b cos(x) +--R + +--R 3 3 5 3 3 3 2 +--R (8a b - 8a b)cos(x) + 8a b cos(x) +--R + +--R 3 3 5 3 3 +--R (- 4a b + 4a b)cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 3 3 4 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) +--R + +--R 3 3 5 3 3 3 2 +--R (4a b - 4a b)cos(x) + 4a b cos(x) +--R + +--R 3 3 5 3 3 +--R (- 2a b + 2a b)cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 +--R (4a b - 4a b )cos(x) + 4a b cos(x) +--R + +--R 2 4 4 2 3 2 4 2 +--R (- 8a b + 8a b )cos(x) - 8a b cos(x) +--R + +--R 2 4 4 2 2 4 +--R (4a b - 4a b )cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 2a b - 2a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 2 4 4 2 4 2 4 3 +--R (4a b + 4a b )cos(x) - 24a b cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 +--R (- 6a b - 2a b )cos(x) + (14a b - 2a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 +--R (4a b - 2a b - 2a b)cos(x) + (4a b + 2a b )cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (- 8a b + 4a b + 4a b)cos(x) + (- 8a b - 4a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 +--R (4a b - 2a b - 2a b)cos(x) + (4a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 3 2 4 4 2 2 2 4 4 2 +--R 3a b cos(x) + (- 2a b - a b )cos(x) + (- 4a b + a b )cos(x) +--R + +--R 2 4 4 2 +--R - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 4 2 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 2 4 2 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - a b - a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 3 3 +--R (- 2a b - 2a b + 2a b)cos(x) + (- 2a b - 4a b )cos(x) + a b +--R + +--R 5 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (4a b - 4a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 5 6 2 4 4 2 6 4 +--R (2b + a b )cos(x) + (2b + 2a b - a b - a )cos(x) +--R + +--R 6 4 2 6 3 6 2 4 6 2 +--R (- 4b + 2a b - a )cos(x) + (- 4b - 4a b + a )cos(x) +--R + +--R 6 4 2 6 6 2 4 4 2 +--R (2b - a b - a )cos(x) + 2b + 2a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 4 2 4 +--R (- 2a b + 2a )cos(x) - 2a b cos(x) +--R + +--R 4 2 6 3 4 2 2 +--R (4a b - 4a )cos(x) + 4a b cos(x) +--R + +--R 4 2 6 4 2 +--R (- 2a b + 2a )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 6 5 4 2 4 4 2 6 3 +--R (- a b + a )cos(x) - a b cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 2 2 4 2 6 4 2 +--R 2a b cos(x) + (- a b + a )cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (- 4a b + 4a b)cos(x) - 4a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- a b - a b)cos(x) + (2a b + 3a b + a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b + 2a b + 2a b)cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 4a b - 3a b - a b)cos(x) + (2a b + 5a b - a b)cos(x) +--R + +--R 5 3 3 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 3 +--R (- 4a b + 2a b + 2a )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 4 5 2 2 3 4 5 2 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 4 3 6 3 2 5 4 3 6 2 +--R (a b - a b)cos(x) + (- 2a b + a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 4a b + 3a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 +--R (- 2a b + 2a b)cos(x) + (4a b - 4a b)cos(x) - 2a b +--R + +--R 6 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + (2a b - 2a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b +--R + +--R 5 2 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 7 3 +--R (2a b - a b - a b )cos(x) + (2a b - a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b - 2a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (- 2a b - 2a b + 3a b + a )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- a b + a b )cos(x) - a b + a +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 7 4 3 6 4 +--R (2b - a b - a b)cos(x) + (2b - a b - a b)cos(x) +--R + +--R 7 4 3 3 7 4 3 6 2 +--R (- 4b + 4a b )cos(x) + (- 4b + 2a b + 2a b)cos(x) +--R + +--R 7 4 3 6 7 4 3 6 +--R (2b - a b - a b)cos(x) + 2b + a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (a b - a b )cos(x) + (2a b + a b - 2a b - a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 4a b - 4a b + 6a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b + 3a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (2a b + 3a b - 4a b - a )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 5 +--R ((- 4a b + 4a b )cos(x) - 4a b + 4a b )sin(x) +--R + +--R 3 4 5 2 3 6 3 4 5 2 2 +--R (2a b - 2a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 8a b + 6a b + 2a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) - 4a b +--R + +--R 5 2 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 5 2 +--R 2a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 2 5 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 4 3 +--R - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 4 7 4 3 6 3 +--R (2a b - 2a b )cos(x) + (4b - 2a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (4b - 12a b + 10a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 6 +--R (- 4b - 4a b + 6a b + 2a b)cos(x) - 4b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 6 3 4 5 6 5 2 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 6 3 4 3 6 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 6 3 4 6 5 2 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (4a b - 2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 3 4 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (4a b - 2a b - 2a b )cos(x) + 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 5 +--R (2a b - 2a b )cos(x) + (6a b - 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (- 4a b + 4a b )cos(x) + (- 16a b + 12a b + 4a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (- 2a b + 2a b )cos(x) + (10a b - 8a b - 2a b)cos(x) + 4a b +--R + +--R 4 3 +--R - 4a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (4a b - 2a b - 2a b )cos(x) + (4a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (- 8a b + 4a b + 4a b )cos(x) + (- 8a b + 4a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (4a b - 2a b - 2a b )cos(x) + (4a b - 2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 4 3 6 3 2 5 4 3 6 2 +--R (a b - a b)cos(x) + (- 2a b + a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 4a b + 3a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 +--R (- 2a b + 2a b)cos(x) + (4a b - 4a b)cos(x) - 2a b +--R + +--R 6 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + (2a b - 2a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 5 2 +--R ((2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b - 2a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 7 3 +--R (2a b - a b - a b )cos(x) + (2a b - a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b - 2a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (- 2a b - 2a b + 3a b + a )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- a b + a b )cos(x) - a b + a +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 7 4 3 6 4 +--R (2b - a b - a b)cos(x) + (2b - a b - a b)cos(x) +--R + +--R 7 4 3 3 7 4 3 6 2 +--R (- 4b + 4a b )cos(x) + (- 4b + 2a b + 2a b)cos(x) +--R + +--R 7 4 3 6 7 4 3 6 +--R (2b - a b - a b)cos(x) + 2b + a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (a b - a b )cos(x) + (2a b + a b - 2a b - a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 4a b - 4a b + 6a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 7 +--R (- 4a b + 3a b + a b )cos(x) + (2a b + 3a b - 4a b - a )cos(x) +--R + +--R 6 5 2 +--R 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R / +--R 5 2 4 5 2 2 5 2 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (2a b - 2a b)cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 4 5 2 7 3 +--R (2a b - 2a )cos(x) + 2a b cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 5 2 2 5 2 7 5 2 +--R - 4a b cos(x) + (2a b - 2a )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 4 4 3 2 4 3 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (4a b - 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (4a b - 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (4a b - 4a b)cos(x) + 4a b cos(x) +--R + +--R 4 3 6 3 4 3 2 4 3 6 +--R (- 8a b + 8a b)cos(x) - 8a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 3 +--R 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 2 2 5 2 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (2a b - 2a b)cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 4 5 2 7 3 +--R (2a b - 2a )cos(x) + 2a b cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 5 2 2 5 2 7 5 2 +--R - 4a b cos(x) + (2a b - 2a )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 3 7 4 5 3 7 2 5 3 7 +--R ((2a b - 2a b)cos(x) + (- 4a b + 4a b)cos(x) + 2a b - 2a b) +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (2a b - 2a b )cos(x) + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R ((4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b - 4a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 7 4 5 3 7 2 5 3 7 3 +--R ((2a b - 2a b)cos(x) + (- 4a b + 4a b)cos(x) + 2a b - 2a b)sin(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (2a b - 2a b )cos(x) + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R Type: Expression Integer +--E 160 + +--S 161 of 546 +m0427b:= a0427.2-r0427 +--R +--R +--R (158) +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((2b + a )cos(x) - 2b - a )\|- b + a atanh(cos(x)) +--R + +--R +---------+ +--R | 2 2 +--R 3 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (4b cos(x) - 4b )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 3 2 3 2 +--R (4b cos(x) - 4b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (a cos(x) - a )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2a cos(x) - 2a )\|- b + a +--R Type: Expression Integer +--E 161 + +--S 162 of 546 +d0427b:= D(m0427b,x) +--R +--R +--R (159) +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R (- 2a b + a )cos(x) + (- 4a b + a )cos(x) +--R + +--R 2 2 4 2 2 4 +--R (- 6a b - a )cos(x) - 4a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a cos(x) + 4a cos(x) - 2a )cot(x) - a cos(x) +--R + +--R 4 2 4 +--R 2a cos(x) - a +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b)cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (4b + 4a b + 2a )cos(x) + (4b + 4a b + 3a )cos(x) +--R + +--R 4 2 2 3 4 2 2 2 +--R (- 8b - 8a b )cos(x) + (- 8b - 8a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (4b + 4a b + 2a )cos(x) + 4b + 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2a cos(x) - 4a cos(x) + 2a cos(x) + 8a cos(x) +--R + +--R 4 2 4 4 +--R 2a cos(x) - 4a cos(x) - 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - a cos(x) - 2a cos(x) + a cos(x) + 4a cos(x) + a cos(x) +--R + +--R 4 4 +--R - 2a cos(x) - a +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (4a b + 2a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 2a b - 6a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (- 2a b + 2a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 2 2 4 5 +--R (2a b + a )cos(x) + (4a b + 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 8a b - 4a )cos(x) + (- 2a b - a )cos(x) + (4a b + 2a )cos(x) +--R + +--R 2 2 4 +--R (2a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 3 3 2 +--R (- 4a b + 2a b)cos(x) + (- 8a b + 2a b)cos(x) +--R + +--R 3 3 3 3 +--R (- 12a b - 2a b)cos(x) - 8a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b)cot(x) - 2a b cos(x) +--R + +--R 3 2 3 +--R 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 4 2 2 2 2 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) + 8b cos(x) +--R + +--R 4 2 2 2 4 2 2 4 2 2 +--R (8b - 12a b )cos(x) + (- 8b - 8a b )cos(x) - 8b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R - 8a b cos(x) - 8a b cos(x) + 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 16a b cos(x) - 8a b cos(x) - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 2 2 2 2 +--R - 4a b cos(x) - 4a b +--R * +--R csc(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 +--R (8a b + 4a b)cos(x) + (8a b + 6a b)cos(x) - 16a b cos(x) +--R + +--R 3 2 3 3 3 3 +--R - 16a b cos(x) + (8a b + 4a b)cos(x) + 8a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 5 3 4 +--R - 4a b cos(x) - 8a b cos(x) + 4a b cos(x) +--R + +--R 3 3 3 2 3 3 +--R 16a b cos(x) + 4a b cos(x) - 8a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 4a b cos(x) - 12a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 4a b cos(x) + 12a b cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 3 7 3 3 6 +--R (4a b + 2a b)cos(x) + (8a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (- 4a b - 2a b)cos(x) + (- 16a b - 8a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (- 4a b - 2a b)cos(x) + (8a b + 4a b)cos(x) + (4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 4 3 2 2 4 2 2 2 4 +--R (- 2a b + a )cos(x) + (- 4a b + a )cos(x) + (- 6a b - a )cos(x) +--R + +--R 2 2 4 +--R - 4a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 4 2 +--R (- 2a cos(x) + 4a cos(x) - 2a )cot(x) - a cos(x) + 2a cos(x) +--R + +--R 4 +--R - a +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b)cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (4b + 4a b + 2a )cos(x) + (4b + 4a b + 3a )cos(x) +--R + +--R 4 2 2 3 4 2 2 2 +--R (- 8b - 8a b )cos(x) + (- 8b - 8a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (4b + 4a b + 2a )cos(x) + 4b + 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2a cos(x) - 4a cos(x) + 2a cos(x) + 8a cos(x) +--R + +--R 4 2 4 4 +--R 2a cos(x) - 4a cos(x) - 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - a cos(x) - 2a cos(x) + a cos(x) + 4a cos(x) + a cos(x) +--R + +--R 4 4 +--R - 2a cos(x) - a +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (4a b + 2a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 2a b - 6a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (- 2a b + 2a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 2 2 4 5 +--R (2a b + a )cos(x) + (4a b + 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 8a b - 4a )cos(x) + (- 2a b - a )cos(x) + (4a b + 2a )cos(x) +--R + +--R 2 2 4 +--R (2a b + a )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2a cos(x) - 4a cos(x) + 2a )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 5 5 +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 4 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b)sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 2 3 2 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 4 2 4 4 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2a cos(x) - 4a cos(x) + 2a )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 5 5 +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R Type: Expression Integer +--E 162 + +--S 163 of 546 +t0428:= csc(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R csc(x) +--R (160) ------------ +--R b sin(x) + a +--R Type: Expression Integer +--E 163 + +--S 164 of 546 +r0428:= 2*b^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+1/2*b*atanh(cos(x))/a^2+b^3*atanh(cos(x))/a^4-cot(x)/a-b^2*cot(x)/a^3-1/3*cot(x)^3/a+1/2*b*cot(x)*csc(x)/a^2 +--R +--R +--R (161) +--R x +--R +---------+ a tan(-) + b +--R 3 2 | 2 2 4 2 +--R (6b + 3a b)\|- b + a atanh(cos(x)) + 12b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 3 3 2 3 | 2 2 +--R (3a b cot(x)csc(x) - 2a cot(x) + (- 6a b - 6a )cot(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression Integer +--E 164 + +--S 165 of 546 +a0428:= integrate(t0428,x) +--R +--R +--R (162) +--R [ +--R 4 2 4 +--R (6b cos(x) - 6b )sin(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 3 2 2 3 2 | 2 2 sin(x) +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|b - a log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 3 2 3 +--R (- 3a b cos(x)sin(x) + (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 4 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|b - a +--R , +--R +--R +---------+ +--R 3 2 2 3 2 | 2 2 sin(x) +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 4 2 4 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 12b cos(x) + 12b )sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 3 3 2 3 +--R (- 3a b cos(x)sin(x) + (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 4 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 165 + +--S 166 of 546 +m0428a:= a0428.1-r0428 +--R +--R +--R (163) +--R +---------+ +--R 4 2 4 | 2 2 +--R (6b cos(x) - 6b )sin(x)\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R 3 2 2 3 2 | 2 2 | 2 2 +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a \|b - a +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 3 2 2 3 2 | 2 2 | 2 2 +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a \|b - a +--R * +--R atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +--R 4 2 4 | 2 2 2 +--R (- 12b cos(x) + 12b )sin(x)\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b + 6a )cos(x) - 6a b - 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 2 4 | 2 2 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|- b + a \|b - a +--R Type: Expression Integer +--E 166 + +--S 167 of 546 +d0428a:= D(m0428a,x) +--R +--R +--R (164) +--R 2 5 4 3 3 4 3 2 +--R (- 6a b - 3a b )cos(x) - 3a b cos(x) +--R + +--R 2 5 4 3 4 3 +--R (6a b + 3a b )cos(x) - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 4 3 4 4 3 2 4 3 +--R 3a b cos(x) - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 +--R (- 6a b - 12a b )cos(x) + (12a b + 24a b )cos(x) +--R + +--R 3 4 5 2 +--R - 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 3 4 3 +--R (- 6a b + 3a b + a b )cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 6 3 4 2 6 3 4 5 2 +--R (6a b - 6a b )cos(x) + (6a b + 6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 +--R - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 +--R (- 12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 2 3 4 5 2 +--R (- 12a b - 12a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 +--R 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (3a b - 3a b )cos(x) + (3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (3a b - 3a b )cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b - 6a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b - 18a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (12a b + 12a b - 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b + 36a b + 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 6a b - 6a b + 12a b)cos(x) - 6a b - 18a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 +--R (- 6b - 5a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 6b - 6a b + a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (12b - 6a b + 6a b - 3a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (12b + 6a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 6b + 6a b - 3a b + 3a b)cos(x) - 6b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (6a b - 6a b)cos(x) + 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (6a b - 6a b)cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 +--R (3a b - 3a b)cos(x) + 3a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) +--R + +--R 4 3 6 4 3 +--R (3a b - 3a b)cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) +--R + +--R 5 2 7 3 5 2 2 +--R (12a b - 12a )cos(x) + 12a b cos(x) +--R + +--R 5 2 7 5 2 +--R (- 6a b + 6a )cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 7 5 +--R (- 6a b - 6a b + 12a )cos(x) +--R + +--R 3 4 5 2 4 +--R (- 6a b - 12a b )cos(x) +--R + +--R 3 4 5 2 7 3 +--R (12a b + 12a b - 24a )cos(x) +--R + +--R 3 4 5 2 2 3 4 5 2 7 +--R (12a b + 24a b )cos(x) + (- 6a b - 6a b + 12a )cos(x) +--R + +--R 3 4 5 2 +--R - 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 +--R (9a b + 7a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 6a b - 9a b - 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b - 18a b - 18a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (12a b + 18a b + 12a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b + 9a b + 15a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 6a b - 9a b - 3a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (6a b - 2a b - 4a b)cos(x) + (13a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 18a b - a b + 10a b)cos(x) + (- 28a b - 16a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (18a b + 6a b - 6a b)cos(x) + (15a b + 9a b)cos(x) +--R + +--R 2 5 4 3 +--R (- 6a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (6a b - 2a b - 4a )cos(x) + (6a b + 4a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- 12a b + 2a b + 10a )cos(x) + (- 12a b - 10a b )cos(x) +--R + +--R 3 4 7 3 3 4 5 2 2 +--R (6a b - 6a )cos(x) + (6a b + 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 3 3 4 2 +--R (- 12a b - 6a b )cos(x) - 6a b cos(x) +--R + +--R 6 3 4 3 4 +--R (12a b + 6a b )cos(x) - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 3 4 4 3 2 4 3 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 +--R (- 12a b - 24a b )cos(x) + (24a b + 48a b )cos(x) +--R + +--R 2 5 4 3 +--R - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 4 7 2 5 3 +--R (6a b + 2a b )cos(x) + (- 12b - 24a b )cos(x) +--R + +--R 7 2 5 2 7 2 5 4 3 +--R (- 12b - 12a b )cos(x) + (12b + 12a b + 12a b )cos(x) +--R + +--R 7 2 5 4 3 +--R 12b - 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 5 4 3 3 +--R (- 24a b + 24a b )cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 +--R (- 24a b - 24a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 +--R 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (24a b - 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 12a b + 12a b )cos(x) - 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 6 3 4 5 2 5 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 12a b - 36a b - 24a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (24a b + 24a b - 48a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b + 72a b + 48a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 12a b - 12a b + 24a b )cos(x) - 12a b - 36a b +--R + +--R 5 2 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (- 12a b - 10a b + 4a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 6 5 2 2 +--R (12a b + 12a b - 6a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 3 4 5 2 6 3 4 +--R (- 6a b + 6a b )cos(x) + 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 24a b + 24a b )cos(x) - 24a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (12a b - 12a b )cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (24a b - 24a b)cos(x) + 24a b cos(x) +--R + +--R 4 3 6 4 3 +--R (- 12a b + 12a b)cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 6 5 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 2 5 4 3 4 +--R (- 12a b - 24a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (24a b + 24a b - 48a b)cos(x) +--R + +--R 2 5 4 3 2 +--R (24a b + 48a b )cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 12a b - 12a b + 24a b)cos(x) - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 5 +--R (18a b + 14a b )cos(x) + (- 30a b - 10a b + 4a b)cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (- 36a b - 36a b )cos(x) + (60a b + 24a b - 12a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 +--R (18a b + 30a b )cos(x) + (- 30a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (12a b - 4a b - 8a b )cos(x) + (26a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 36a b - 2a b + 20a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (- 56a b - 32a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (36a b + 12a b - 12a b )cos(x) + (30a b + 18a b )cos(x) +--R + +--R 6 3 4 +--R (- 12a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 +--R (12a b - 4a b - 8a b)cos(x) + (12a b + 8a b )cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (- 24a b + 4a b + 20a b)cos(x) + (- 24a b - 20a b )cos(x) +--R + +--R 2 5 6 3 2 5 4 3 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 3 4 3 2 2 5 4 3 +--R (- 6a b - 3a b )cos(x) - 3a b cos(x) + (6a b + 3a b )cos(x) +--R + +--R 4 3 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 4 3 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) + 3a b cos(x) +--R + +--R 4 3 2 4 3 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 6a b - 12a b )cos(x) + (12a b + 24a b )cos(x) - 6a b +--R + +--R 5 2 +--R - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 3 4 3 +--R (- 6a b + 3a b + a b )cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 6 3 4 2 6 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b + 6a b )cos(x) - 3a b +--R + +--R 5 2 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (3a b - 3a b )cos(x) + (3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (3a b - 3a b )cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b - 6a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b - 18a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (12a b + 12a b - 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b + 36a b + 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 6a b - 6a b + 12a b)cos(x) - 6a b - 18a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 +--R (- 6b - 5a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 6b - 6a b + a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (12b - 6a b + 6a b - 3a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (12b + 6a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 6b + 6a b - 3a b + 3a b)cos(x) - 6b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (6a b - 6a b)cos(x) + 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (6a b - 6a b)cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 +--R (3a b - 3a b)cos(x) + 3a b cos(x) +--R + +--R 4 3 6 3 4 3 2 4 3 6 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) + (3a b - 3a b)cos(x) +--R + +--R 4 3 +--R 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) +--R + +--R 5 2 7 3 5 2 2 +--R (12a b - 12a )cos(x) + 12a b cos(x) +--R + +--R 5 2 7 5 2 +--R (- 6a b + 6a )cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- 6a b - 6a b + 12a )cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (12a b + 12a b - 24a )cos(x) + (12a b + 24a b )cos(x) +--R + +--R 3 4 5 2 7 3 4 5 2 +--R (- 6a b - 6a b + 12a )cos(x) - 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (9a b + 7a b )cos(x) + (- 6a b - 9a b - 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b - 18a b - 18a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (12a b + 18a b + 12a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b + 9a b + 15a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 6a b - 9a b - 3a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (6a b - 2a b - 4a b)cos(x) + (13a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 18a b - a b + 10a b)cos(x) + (- 28a b - 16a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (18a b + 6a b - 6a b)cos(x) + (15a b + 9a b)cos(x) +--R + +--R 2 5 4 3 +--R (- 6a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (6a b - 2a b - 4a )cos(x) + (6a b + 4a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- 12a b + 2a b + 10a )cos(x) + (- 12a b - 10a b )cos(x) +--R + +--R 3 4 7 3 3 4 5 2 2 +--R (6a b - 6a )cos(x) + (6a b + 6a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b + 3a b + 3a b )cos(x) + 3a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 +--R (- 6a b + 6a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 +--R - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 +--R (- 3a b + 3a b )cos(x) + (6a b - 6a b )cos(x) - 3a b +--R + +--R 6 2 +--R 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 4 5 3 7 2 5 3 +--R (6a b - 6a b)cos(x) + (- 12a b + 12a b)cos(x) + 6a b +--R + +--R 7 +--R - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 +--R (- 12a b - 12a b + 24a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 3a b - a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 6a b - 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 6a b - 3a b + 3a b)cos(x) +--R + +--R 7 5 3 7 3 5 7 +--R (- 6a b + 3a b + 3a b)cos(x) + 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (6a b - 6a b )cos(x) + (6a b - 6a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (6a b - 6a b )cos(x) + 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 5 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b + 12a b - 6a b - 12a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 12a b - 24a b + 12a b + 24a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (6a b + 6a b - 12a b )cos(x) + 6a b + 12a b - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 8 4 4 6 2 5 8 4 4 6 2 8 4 +--R (6b - a b - 5a b )cos(x) + (6b - a b - 3a b - 2a )cos(x) +--R + +--R 8 2 6 6 2 3 8 2 6 8 2 +--R (- 12b + 6a b + 6a b )cos(x) + (- 12b + 6a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (6b - 6a b + 3a b - 3a b )cos(x) + 6b - 6a b + 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 5 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (6a b + 6a b - 12a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 7 6 +--R (- 3a b - a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b + 3a b - 4a b - 5a b)cos(x) +--R + +--R 7 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b + 9a b - 9a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (6a b + 3a b - 6a b - 3a b)cos(x) + 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 4 4 6 2 8 6 +--R (- 6a b + 2a b + 4a b )cos(x) + (- 7a b + 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 6 2 8 4 +--R (18a b - 5a b - 13a b )cos(x) + (16a b - 6a b - 10a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 18a b + 6a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 2 2 6 4 4 6 2 +--R (- 9a b + 3a b + 6a )cos(x) + (6a b - 3a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 6 +--R (- 6a b + 2a b + 4a b)cos(x) + (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (12a b - 2a b - 10a b)cos(x) + (12a b - 2a b - 10a b)cos(x) +--R + +--R 3 5 7 3 3 5 7 2 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 3 3 5 5 3 2 +--R (12a b - 6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 +--R (- 12a b + 6a b + 6a b )cos(x) + 6a b - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 +--R (- 12a b + 12a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 +--R - 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 3 5 +--R (- 6a b + 6a b )cos(x) + (12a b - 12a b )cos(x) - 6a b +--R + +--R 5 3 +--R 6a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 +--R (12a b - 12a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 +--R 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (- 24a b - 24a b + 48a b )cos(x) + 12a b + 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 2a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (12b + 12a b - 18a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (12b - 12a b - 6a b + 6a b )cos(x) +--R + +--R 8 4 4 6 2 8 2 6 6 2 +--R (- 12b + 6a b + 6a b )cos(x) - 12b + 18a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R csc(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (12a b - 12a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 7 3 5 5 3 5 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (12a b + 24a b - 12a b - 24a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 24a b - 24a b + 48a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b - 48a b + 24a b + 48a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (12a b + 12a b - 24a b )cos(x) + 12a b + 24a b - 12a b +--R + +--R 7 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 5 3 5 5 3 7 4 +--R (12a b - 2a b - 10a b )cos(x) + (10a b - 6a b - 4a b)cos(x) +--R + +--R 7 5 3 3 7 3 5 7 2 +--R (- 12a b + 12a b )cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 +--R (6a b - 6a b )cos(x) - 12a b + 18a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 5 3 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 3 5 5 3 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 5 3 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 3 5 5 3 3 5 5 3 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (12a b - 12a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 5 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 24a b - 24a b + 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 24a b - 24a b + 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (12a b + 12a b - 24a b )cos(x) + 12a b + 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 6 +--R (- 6a b - 2a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (18a b - 8a b - 10a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 36a b + 12a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 6a b - 18a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R (18a b - 12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 12a b + 4a b + 8a b )cos(x) +--R + +--R 3 5 5 3 7 6 +--R (- 14a b + 6a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (36a b - 10a b - 26a b )cos(x) +--R + +--R 3 5 5 3 7 4 +--R (32a b - 12a b - 20a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 36a b + 12a b + 24a b )cos(x) +--R + +--R 3 5 5 3 7 2 7 3 5 5 3 +--R (- 18a b + 6a b + 12a b)cos(x) + (12a b - 6a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (- 12a b + 4a b + 8a b )cos(x) + (- 12a b + 4a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (24a b - 4a b - 20a b )cos(x) + (24a b - 4a b - 20a b )cos(x) +--R + +--R 2 6 6 2 3 2 6 6 2 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b + 3a b + 3a b )cos(x) + 3a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 +--R (- 6a b + 6a b )cos(x) + (12a b - 12a b )cos(x) - 6a b +--R + +--R 6 2 +--R 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R (- 3a b + 3a b )cos(x) + (6a b - 6a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 4 5 3 7 2 5 3 7 +--R ((6a b - 6a b)cos(x) + (- 12a b + 12a b)cos(x) + 6a b - 6a b) +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 +--R (- 12a b - 12a b + 24a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 3a b - a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 6a b - 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 6a b - 3a b + 3a b)cos(x) +--R + +--R 7 5 3 7 3 5 7 +--R (- 6a b + 3a b + 3a b)cos(x) + 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (6a b - 6a b )cos(x) + (6a b - 6a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (6a b - 6a b )cos(x) + 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 5 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b + 12a b - 6a b - 12a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 12a b - 24a b + 12a b + 24a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (6a b + 6a b - 12a b )cos(x) + 6a b + 12a b - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 8 4 4 6 2 5 8 4 4 6 2 8 4 +--R (6b - a b - 5a b )cos(x) + (6b - a b - 3a b - 2a )cos(x) +--R + +--R 8 2 6 6 2 3 8 2 6 8 2 +--R (- 12b + 6a b + 6a b )cos(x) + (- 12b + 6a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (6b - 6a b + 3a b - 3a b )cos(x) + 6b - 6a b + 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) + (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (6a b + 6a b - 12a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 7 6 +--R (- 3a b - a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b + 3a b - 4a b - 5a b)cos(x) +--R + +--R 7 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b + 9a b - 9a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (6a b + 3a b - 6a b - 3a b)cos(x) + 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 4 4 6 2 8 6 +--R (- 6a b + 2a b + 4a b )cos(x) + (- 7a b + 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 6 2 8 4 +--R (18a b - 5a b - 13a b )cos(x) + (16a b - 6a b - 10a )cos(x) +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 8 2 +--R (- 18a b + 6a b + 12a b )cos(x) + (- 9a b + 3a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 +--R (6a b - 3a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 6 +--R (- 6a b + 2a b + 4a b)cos(x) + (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (12a b - 2a b - 10a b)cos(x) + (12a b - 2a b - 10a b)cos(x) +--R + +--R 3 5 7 3 3 5 7 2 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R / +--R 6 2 4 6 2 2 6 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 +--R (6a b - 6a )cos(x) + 6a b cos(x) +--R + +--R 6 2 8 3 6 2 2 +--R (- 12a b + 12a )cos(x) - 12a b cos(x) +--R + +--R 6 2 8 6 2 +--R (6a b - 6a )cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 4 5 3 2 5 3 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b )sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (12a b - 12a b )cos(x) + 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 7 5 5 3 4 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 5 3 7 3 5 3 2 +--R (- 24a b + 24a b)cos(x) - 24a b cos(x) +--R + +--R 5 3 7 5 3 +--R (12a b - 12a b)cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 6 2 2 6 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 6 2 8 3 +--R (6a b - 6a )cos(x) + 6a b cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 6 2 2 6 2 8 6 2 +--R - 12a b cos(x) + (6a b - 6a )cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 3 8 4 6 3 8 2 6 3 8 +--R ((- 6a b + 6a b)cos(x) + (12a b - 12a b)cos(x) - 6a b + 6a b) +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 7 2 5 5 4 9 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 5 4 7 2 3 5 4 9 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a )cos(x) +--R + +--R 5 4 7 2 5 4 9 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 8 5 6 3 8 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 6 3 8 3 6 3 8 2 +--R (12a b - 12a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 6 3 8 6 3 8 +--R (- 6a b + 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 7 2 4 5 4 7 2 2 5 4 +--R (- 12a b + 12a b )cos(x) + (24a b - 24a b )cos(x) - 12a b +--R + +--R 7 2 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 6 3 5 4 5 8 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 4 5 6 3 3 4 5 8 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b)cos(x) +--R + +--R 4 5 6 3 4 5 8 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 7 2 5 5 4 7 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 8 4 6 3 8 2 6 3 8 4 +--R ((- 6a b + 6a b)cos(x) + (12a b - 12a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 5 4 7 2 5 5 4 9 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 5 4 7 2 3 5 4 9 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a )cos(x) +--R + +--R 5 4 7 2 5 4 9 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 8 5 6 3 8 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 6 3 8 3 6 3 8 2 +--R (12a b - 12a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 6 3 8 6 3 8 +--R (- 6a b + 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 167 + +--S 168 of 546 +m0428b:= a0428.2-r0428 +--R +--R +--R (165) +--R +---------+ +--R 3 2 2 3 2 | 2 2 sin(x) +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 2 3 2 | 2 2 +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a atanh(cos(x)) +--R + +--R +---------+ +--R | 2 2 +--R 4 2 4 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 12b cos(x) + 12b )sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 4 2 4 2 +--R (- 12b cos(x) + 12b )sin(x)atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b + 6a )cos(x) - 6a b - 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 4 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|- b + a +--R Type: Expression Integer +--E 168 + +--S 169 of 546 +d0428b:= D(m0428b,x) +--R +--R +--R (166) +--R 2 3 4 3 4 2 2 3 4 +--R (- 6a b - 3a b)cos(x) - 3a b cos(x) + (6a b + 3a b)cos(x) +--R + +--R 4 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 +--R (- 6a b - 12a )cos(x) + (12a b + 24a )cos(x) - 6a b +--R + +--R 5 +--R - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b - 6a b - 2a )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 5 2 4 4 3 2 +--R 6a cos(x) + 12a b cos(x) + 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 24a b cos(x) + 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 4 2 4 4 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 12a b - 24a b)cos(x) + (- 12a b - 24a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (24a b + 48a b)cos(x) + (24a b + 48a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 12a b - 24a b)cos(x) - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 +--R (- 12b - 12a b - 10a b)cos(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (- 12b - 12a b - 13a b)cos(x) + (24b + 12a b + 12a b)cos(x) +--R + +--R 5 2 3 4 2 5 4 5 +--R (24b + 12a b + 12a b)cos(x) + (- 12b - 6a b)cos(x) - 12b +--R + +--R 4 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R - 24a b cos(x) - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 6a b - 12a )cos(x) + (- 12a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (6a b + 12a )cos(x) + (24a b + 48a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (6a b + 12a )cos(x) + (- 12a b - 24a )cos(x) - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (- 6a b + 2a )cos(x) + (- 12a b - 6a b - 4a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (6a b - 6a )cos(x) + (24a b + 12a b + 12a )cos(x) +--R + +--R 4 5 2 4 3 2 4 +--R (6a b + 12a )cos(x) + (- 12a b - 6a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b + 5a b)cos(x) + 2a b cos(x) + (- 18a b - 17a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b + 15a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (6a b + 4a )cos(x) + (12a b + 8a )cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 24a b - 20a )cos(x) + (- 6a b - 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (12a b + 12a )cos(x) + (6a b + 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R (- 12a b - 6a b )cos(x) - 6a b cos(x) + (12a b + 6a b )cos(x) +--R + +--R 3 2 +--R - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 4 4 2 4 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b)cot(x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 +--R (- 12a b - 24a b)cos(x) + (24a b + 48a b)cos(x) - 12a b +--R + +--R 4 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 4 5 2 3 3 +--R (- 12a b - 4a b)cos(x) + (- 24b - 24a b )cos(x) +--R + +--R 5 4 2 5 5 2 3 +--R (- 24b + 12a b)cos(x) + 24b cos(x) + 24b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 48a b cos(x) + 24a b cos(x) + 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 2 3 2 3 +--R 12a b cos(x) + 12a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R - 24a b cos(x) - 24a b cos(x) + 48a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 48a b cos(x) - 24a b cos(x) - 24a b +--R * +--R 4 +--R cot(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 24a b - 48a b )cos(x) + (- 24a b - 48a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (48a b + 96a b )cos(x) + (48a b + 96a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 24a b - 48a b )cos(x) - 24a b - 48a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 24a b - 20a b )cos(x) + (- 24a b - 26a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (24a b + 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 3 2 3 2 +--R - 12a b cos(x) - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 5 3 2 4 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R - 48a b cos(x) - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 6 4 5 4 4 +--R - 12a b cos(x) - 24a b cos(x) + 12a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R 48a b cos(x) + 12a b cos(x) - 24a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b - 24a b)cos(x) + (- 24a b - 48a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (12a b + 24a b)cos(x) + (48a b + 96a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (12a b + 24a b)cos(x) + (- 24a b - 48a b)cos(x) - 12a b +--R + +--R 4 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 2 3 4 5 4 4 +--R 4a b cos(x) + (- 12a b - 8a b)cos(x) - 12a b cos(x) +--R + +--R 2 3 4 3 4 2 2 3 +--R (24a b + 24a b)cos(x) + 24a b cos(x) - 12a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 3 2 6 +--R (12a b + 10a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 5 3 2 4 +--R (- 36a b - 34a b )cos(x) - 16a b cos(x) +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R (36a b + 30a b )cos(x) + 12a b cos(x) + (- 12a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (12a b + 8a b)cos(x) + (24a b + 16a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b - 12a b)cos(x) + (- 48a b - 40a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 12a b - 8a b)cos(x) + (24a b + 24a b)cos(x) +--R + +--R 2 3 4 2 +--R (12a b + 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 4 2 2 3 4 4 +--R ((- 6a b - 3a b)cos(x) - 3a b cos(x) + (6a b + 3a b)cos(x) - 3a b) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R ((- 6a b - 12a )cos(x) + (12a b + 24a )cos(x) - 6a b - 12a ) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b - 6a b - 2a )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 5 2 4 4 3 2 +--R 6a cos(x) + 12a b cos(x) + 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 3 2 3 2 +--R 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) + 24a b cos(x) +--R + +--R 4 4 +--R - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 12a b - 24a b)cos(x) + (- 12a b - 24a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (24a b + 48a b)cos(x) + (24a b + 48a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 12a b - 24a b)cos(x) - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 12b - 12a b - 10a b)cos(x) + (- 12b - 12a b - 13a b)cos(x) +--R + +--R 5 2 3 4 3 5 2 3 4 2 +--R (24b + 12a b + 12a b)cos(x) + (24b + 12a b + 12a b)cos(x) +--R + +--R 5 4 5 4 +--R (- 12b - 6a b)cos(x) - 12b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 4 2 4 4 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 6a b - 12a )cos(x) + (- 12a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (6a b + 12a )cos(x) + (24a b + 48a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (6a b + 12a )cos(x) + (- 12a b - 24a )cos(x) - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (- 6a b + 2a )cos(x) + (- 12a b - 6a b - 4a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (6a b - 6a )cos(x) + (24a b + 12a b + 12a )cos(x) +--R + +--R 4 5 2 4 3 2 4 +--R (6a b + 12a )cos(x) + (- 12a b - 6a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b + 5a b)cos(x) + 2a b cos(x) + (- 18a b - 17a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b + 15a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (6a b + 4a )cos(x) + (12a b + 8a )cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 24a b - 20a )cos(x) + (- 6a b - 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (12a b + 12a )cos(x) + (6a b + 6a )cos(x) +--R / +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b)sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) - 48a b cos(x) +--R + +--R 4 2 4 2 +--R 24a b cos(x) + 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) - 48a b cos(x) +--R + +--R 5 2 5 5 +--R - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 169 + +--S 170 of 546 +t0429:= csc(x)/(a+a*sin(x)) +--R +--R +--R csc(x) +--R (167) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 170 + +--S 171 of 546 +r0429:= -1/a/cos(x)*(atanh(cos(x))*cos(x)+sin(x)-1) +--R +--R +--R - cos(x)atanh(cos(x)) - sin(x) + 1 +--R (168) ---------------------------------- +--R a cos(x) +--R Type: Expression Integer +--E 171 + +--S 172 of 546 +a0429:= integrate(t0429,x) +--R +--R +--R sin(x) +--R (sin(x) + cos(x) + 1)log(----------) + 2cos(x) + 2 +--R cos(x) + 1 +--R (169) -------------------------------------------------- +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 172 + +--S 173 of 546 +m0429:= a0429-r0429 +--R +--R +--R (170) +--R 2 sin(x) +--R (cos(x)sin(x) + cos(x) + cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (cos(x)sin(x) + cos(x) + cos(x))atanh(cos(x)) + sin(x) + cos(x)sin(x) +--R + +--R 2 +--R 2cos(x) + cos(x) - 1 +--R / +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression Integer +--E 173 + +--S 174 of 546 +d0429:= D(m0429,x) +--R +--R +--R (171) +--R 2 5 3 2 4 +--R (cos(x) - 1)sin(x) + (3cos(x) + cos(x) - 2cos(x) - 1)sin(x) +--R + +--R 4 3 2 3 +--R (2cos(x) + 2cos(x) - cos(x) + 1)sin(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 3cos(x) - 4cos(x) - 2cos(x) + 2cos(x) + 1)sin(x) +--R + +--R 6 5 3 2 7 6 +--R (cos(x) + 2cos(x) - 2cos(x) - cos(x) )sin(x) + cos(x) + 2cos(x) +--R + +--R 4 3 +--R - 2cos(x) - cos(x) +--R / +--R 4 2 3 +--R (a cos(x) - a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (2a cos(x) + 2a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 6 5 3 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a cos(x) )sin(x) +--R Type: Expression Integer +--E 174 + +--S 175 of 546 +t0430:= csc(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R csc(x) +--R (172) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 175 + +--S 176 of 546 +r0430:= atanh(cos(x))/a-cot(x)/a-cos(x)/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(cos(x)) - cot(x)sin(x) - cot(x) - cos(x) +--R (173) ---------------------------------------------------------- +--R a sin(x) + a +--R Type: Expression Integer +--E 176 + +--S 177 of 546 +a0430:= integrate(t0430,x) +--R +--R +--R (174) +--R 2 sin(x) +--R ((- cos(x) - 1)sin(x) + cos(x) - 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 3cos(x) - 2)sin(x) - cos(x) - cos(x) +--R / +--R 2 +--R (a cos(x) + a)sin(x) - a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 177 + +--S 178 of 546 +m0430:= a0430-r0430 +--R +--R +--R (175) +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R atanh(cos(x)) +--R + +--R 2 +--R ((cos(x) + 1)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 +--R ((- cos(x) + cos(x) + 2)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 3 2 +--R (- cos(x) + 1)cot(x) - cos(x) - cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (- a cos(x) + a cos(x) + 2a)sin(x) - a cos(x) + a +--R Type: Expression Integer +--E 178 + +--S 179 of 546 +d0430:= D(m0430,x) +--R +--R +--R (176) +--R 2 6 +--R (- cos(x) - 1)sin(x) +--R + +--R 3 2 2 3 2 +--R (- cos(x) - cos(x) + cos(x) + 1)cot(x) + 4cos(x) - 2cos(x) +--R + +--R - 2cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (2cos(x) - 2cos(x) - 6cos(x) + 2cos(x) + 4)cot(x) + 2cos(x) +--R + +--R 3 2 +--R 10cos(x) - 5cos(x) - 6cos(x) - 3 +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 2 5 +--R (- cos(x) + 5cos(x) + cos(x) - 11cos(x) + 6)cot(x) + 3cos(x) +--R + +--R 4 3 2 +--R 3cos(x) + 2cos(x) - 8cos(x) - 3cos(x) + 3 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) + 4cos(x) + 4cos(x) - 8cos(x) - 2cos(x) + 4)cot(x) +--R + +--R 6 5 4 3 2 +--R cos(x) + 10cos(x) + cos(x) - 15cos(x) - 6cos(x) + 5cos(x) + 4 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + 1)cot(x) +--R + +--R 7 6 5 4 3 2 +--R - cos(x) - cos(x) + 9cos(x) + 3cos(x) - 13cos(x) - 3cos(x) +--R + +--R 5cos(x) + 1 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + cos(x) +--R / +--R 3 2 5 +--R (a cos(x) + a cos(x) - a cos(x) - a)sin(x) +--R + +--R 4 3 2 4 +--R (- 2a cos(x) + 2a cos(x) + 6a cos(x) - 2a cos(x) - 4a)sin(x) +--R + +--R 5 4 3 2 3 +--R (a cos(x) - 5a cos(x) - a cos(x) + 11a cos(x) - 6a)sin(x) +--R + +--R 5 4 3 2 +--R (2a cos(x) - 4a cos(x) - 4a cos(x) + 8a cos(x) + 2a cos(x) - 4a) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (a cos(x) - a cos(x) - 2a cos(x) + 2a cos(x) + a cos(x) - a)sin(x) +--R Type: Expression Integer +--E 179 + +--S 180 of 546 +t0431:= csc(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R csc(x) +--R (177) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 180 + +--S 181 of 546 +r0431:= -3/2*atanh(cos(x))/a+cot(x)/a-1/2*cot(x)*csc(x)/a+cos(x)/a/(1+sin(x)) +--R +--R +--R (178) +--R (- 3sin(x) - 3)atanh(cos(x)) + (- cot(x)csc(x) + 2cot(x))sin(x) +--R + +--R - cot(x)csc(x) + 2cot(x) + 2cos(x) +--R / +--R 2a sin(x) + 2a +--R Type: Expression Integer +--E 181 + +--S 182 of 546 +a0431:= integrate(t0431,x) +--R +--R +--R (179) +--R 2 3 2 sin(x) +--R ((3cos(x) - 3)sin(x) + 3cos(x) + 3cos(x) - 3cos(x) - 3)log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (- 2cos(x) - cos(x))sin(x) + 6cos(x) + 5cos(x) - 5cos(x) - 4 +--R / +--R 2 3 2 +--R (2a cos(x) - 2a)sin(x) + 2a cos(x) + 2a cos(x) - 2a cos(x) - 2a +--R Type: Union(Expression Integer,...) +--E 182 + +--S 183 of 546 +m0431:= a0431-r0431 +--R +--R +--R (180) +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R atanh(cos(x)) +--R + +--R 2 2 2 +--R (cos(x) - 1)cot(x)csc(x) + (- 2cos(x) + 2)cot(x) - 2cos(x) +--R + +--R - cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + 2cos(x) - cos(x) - 2)cot(x)csc(x) +--R + +--R 3 2 3 2 +--R (- 2cos(x) - 4cos(x) + 2cos(x) + 4)cot(x) + 4cos(x) + 3cos(x) +--R + +--R - 4cos(x) - 4 +--R * +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + cos(x) - cos(x) - 1)cot(x)csc(x) +--R + +--R 3 2 4 3 +--R (- 2cos(x) - 2cos(x) + 2cos(x) + 2)cot(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R 7cos(x) - 3cos(x) - 4 +--R / +--R 2 2 +--R (2a cos(x) - 2a)sin(x) +--R + +--R 3 2 3 +--R (2a cos(x) + 4a cos(x) - 2a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 2 +--R 2a cos(x) - 2a cos(x) - 2a +--R Type: Expression Integer +--E 183 + +--S 184 of 546 +d0431:= D(m0431,x) +--R +--R +--R (181) +--R 3 2 6 +--R (3cos(x) - cos(x) - 7cos(x) - 1)sin(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1)csc(x) +--R + +--R 4 2 2 4 3 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) + 2cos(x) + 10cos(x) - 6cos(x) +--R + +--R - 22cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 3 2 +--R (- 4cos(x) - 8cos(x) + 8cos(x) + 16cos(x) - 4cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 4cos(x) + 8cos(x) - 2cos(x) - 4 +--R * +--R csc(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 8cos(x) - 8cos(x) - 16cos(x) + 4cos(x) + 8)cot(x) +--R + +--R 5 4 3 2 +--R 14cos(x) + 15cos(x) - 9cos(x) - 21cos(x) - 13cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 12cos(x) - 8cos(x) + 24cos(x) + 22cos(x) +--R + +--R - 12cos(x) - 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 6cos(x) - 4cos(x) + 12cos(x) + 11cos(x) - 6cos(x) +--R + +--R - 6 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 12cos(x) + 8cos(x) - 24cos(x) - 22cos(x) +--R + +--R 12cos(x) + 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) + 30cos(x) + 14cos(x) - 44cos(x) - 24cos(x) + 18cos(x) +--R + +--R 10 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R (- 4cos(x) - 12cos(x) + 24cos(x) + 12cos(x) - 12cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 3 2 +--R - 2cos(x) - 6cos(x) + 12cos(x) + 6cos(x) - 6cos(x) - 4 +--R * +--R csc(x) +--R + +--R 6 5 3 2 2 +--R (4cos(x) + 12cos(x) - 24cos(x) - 12cos(x) + 12cos(x) + 8)cot(x) +--R + +--R 7 6 5 4 3 +--R 7cos(x) + 12cos(x) + 7cos(x) - 17cos(x) - 35cos(x) + 25cos(x) + 9 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 2cos(x) + 8cos(x) + 2cos(x) +--R + +--R - 4cos(x) - 2 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 2cos(x) + cos(x) + 4cos(x) + cos(x) - 2cos(x) - 1 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 4cos(x) - 2cos(x) - 8cos(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 3 +--R 2cos(x) + 10cos(x) + 10cos(x) - 12cos(x) - 28cos(x) - 10cos(x) +--R + +--R 2 +--R 14cos(x) + 12cos(x) + 2 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) + 6cos(x) - 3cos(x) - 12cos(x) - 3cos(x) + 6cos(x) + 3cos(x) +--R / +--R 4 2 5 +--R (2a cos(x) - 4a cos(x) + 2a)sin(x) +--R + +--R 5 4 3 2 +--R (4a cos(x) + 8a cos(x) - 8a cos(x) - 16a cos(x) + 4a cos(x) + 8a) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 12a cos(x) + 8a cos(x) - 24a cos(x) - 22a cos(x) +--R + +--R 12a cos(x) + 12a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R 4a cos(x) + 12a cos(x) - 24a cos(x) - 12a cos(x) + 12a cos(x) +--R + +--R 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R Type: Expression Integer +--E 184 + +--S 185 of 546 +t0432:= csc(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R csc(x) +--R (182) ------------ +--R a sin(x) + a +--R Type: Expression Integer +--E 185 + +--S 186 of 546 +r0432:= 3/2*atanh(cos(x))/a-2*cot(x)/a-1/3*cot(x)^3/a+1/2*cot(x)*csc(x)/a-cos(x)/a/(1+sin(x)) +--R +--R +--R (183) +--R 3 +--R (9sin(x) + 9)atanh(cos(x)) + (3cot(x)csc(x) - 2cot(x) - 12cot(x))sin(x) +--R + +--R 3 +--R 3cot(x)csc(x) - 2cot(x) - 12cot(x) - 6cos(x) +--R / +--R 6a sin(x) + 6a +--R Type: Expression Integer +--E 186 + +--S 187 of 546 +a0432:= integrate(t0432,x) +--R +--R +--R (184) +--R 3 2 4 2 +--R (- 9cos(x) - 9cos(x) + 9cos(x) + 9)sin(x) + 9cos(x) - 18cos(x) +--R + +--R 9 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 4 3 +--R (- 22cos(x) - 15cos(x) + 21cos(x) + 12)sin(x) - 10cos(x) - 7cos(x) +--R + +--R 2 +--R 12cos(x) + 9cos(x) +--R / +--R 3 2 4 +--R (6a cos(x) + 6a cos(x) - 6a cos(x) - 6a)sin(x) - 6a cos(x) +--R + +--R 2 +--R 12a cos(x) - 6a +--R Type: Union(Expression Integer,...) +--E 187 + +--S 188 of 546 +m0432:= a0432-r0432 +--R +--R +--R (185) +--R 3 2 2 +--R (- 9cos(x) - 9cos(x) + 9cos(x) + 9)sin(x) +--R + +--R 4 3 2 4 +--R (9cos(x) - 9cos(x) - 27cos(x) + 9cos(x) + 18)sin(x) + 9cos(x) +--R + +--R 2 +--R - 18cos(x) + 9 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 +--R (- 9cos(x) - 9cos(x) + 9cos(x) + 9)sin(x) +--R + +--R 4 3 2 4 +--R (9cos(x) - 9cos(x) - 27cos(x) + 9cos(x) + 18)sin(x) + 9cos(x) +--R + +--R 2 +--R - 18cos(x) + 9 +--R * +--R atanh(cos(x)) +--R + +--R 3 2 +--R (- 3cos(x) - 3cos(x) + 3cos(x) + 3)cot(x)csc(x) +--R + +--R 3 2 3 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2)cot(x) +--R + +--R 3 2 3 2 +--R (12cos(x) + 12cos(x) - 12cos(x) - 12)cot(x) - 22cos(x) - 15cos(x) +--R + +--R 21cos(x) + 12 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (3cos(x) - 3cos(x) - 9cos(x) + 3cos(x) + 6)cot(x)csc(x) +--R + +--R 4 3 2 3 +--R (- 2cos(x) + 2cos(x) + 6cos(x) - 2cos(x) - 4)cot(x) +--R + +--R 4 3 2 +--R (- 12cos(x) + 12cos(x) + 36cos(x) - 12cos(x) - 24)cot(x) +--R + +--R 4 3 2 +--R - 4cos(x) - 23cos(x) - 9cos(x) + 24cos(x) + 12 +--R * +--R sin(x) +--R + +--R 4 2 +--R (3cos(x) - 6cos(x) + 3)cot(x)csc(x) +--R + +--R 4 2 3 4 2 +--R (- 2cos(x) + 4cos(x) - 2)cot(x) + (- 12cos(x) + 24cos(x) - 12)cot(x) +--R + +--R 5 4 3 2 +--R - 6cos(x) - 10cos(x) + 5cos(x) + 12cos(x) + 3cos(x) +--R / +--R 3 2 2 +--R (6a cos(x) + 6a cos(x) - 6a cos(x) - 6a)sin(x) +--R + +--R 4 3 2 +--R (- 6a cos(x) + 6a cos(x) + 18a cos(x) - 6a cos(x) - 12a)sin(x) +--R + +--R 4 2 +--R - 6a cos(x) + 12a cos(x) - 6a +--R Type: Expression Integer +--E 188 + +--S 189 of 546 +d0432:= D(m0432,x) +--R +--R +--R (186) +--R 4 3 6 +--R (- 9cos(x) - 2cos(x) - 6cos(x) + 9)sin(x) +--R + +--R 5 4 3 2 +--R (6cos(x) + 6cos(x) - 12cos(x) - 12cos(x) + 6cos(x) + 6) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 2 +--R 3cos(x) + 3cos(x) - 6cos(x) - 6cos(x) + 3cos(x) + 3 +--R * +--R csc(x) +--R + +--R 5 4 3 2 4 +--R (- 6cos(x) - 6cos(x) + 12cos(x) + 12cos(x) - 6cos(x) - 6)cot(x) +--R + +--R 5 4 3 2 +--R (- 18cos(x) - 18cos(x) + 36cos(x) + 36cos(x) - 18cos(x) - 18) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 +--R 32cos(x) - 18cos(x) - 52cos(x) + 30 +--R * +--R 5 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 12cos(x) + 12cos(x) + 48cos(x) - 24cos(x) - 60cos(x) +--R + +--R 12cos(x) + 24 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - 6cos(x) + 6cos(x) + 24cos(x) - 12cos(x) - 30cos(x) +--R + +--R 6cos(x) + 12 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 12cos(x) - 12cos(x) - 48cos(x) + 24cos(x) + 60cos(x) +--R + +--R - 12cos(x) - 24 +--R * +--R 4 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 36cos(x) - 36cos(x) - 144cos(x) + 72cos(x) + 180cos(x) +--R + +--R - 36cos(x) - 72 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 18cos(x) + 77cos(x) - 66cos(x) - 132cos(x) + 60cos(x) + 39cos(x) +--R + +--R 12 +--R * +--R 4 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 30cos(x) - 12cos(x) + 96cos(x) + 6cos(x) +--R + +--R 2 +--R - 102cos(x) + 36 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 3cos(x) - 15cos(x) - 6cos(x) + 48cos(x) + 3cos(x) +--R + +--R 2 +--R - 51cos(x) + 18 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 6cos(x) + 30cos(x) + 12cos(x) - 96cos(x) - 6cos(x) +--R + +--R 2 +--R 102cos(x) - 36 +--R * +--R 4 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 18cos(x) + 90cos(x) + 36cos(x) - 288cos(x) - 18cos(x) +--R + +--R 2 +--R 306cos(x) - 108 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 26cos(x) + 36cos(x) - 16cos(x) - 126cos(x) - 50cos(x) +--R + +--R 2 +--R 144cos(x) + 36cos(x) - 42 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 12cos(x) - 24cos(x) - 36cos(x) + 72cos(x) + 36cos(x) +--R + +--R 2 +--R - 72cos(x) - 12cos(x) + 24 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 12cos(x) - 18cos(x) + 36cos(x) + 18cos(x) +--R + +--R 2 +--R - 36cos(x) - 6cos(x) + 12 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 12cos(x) + 24cos(x) + 36cos(x) - 72cos(x) - 36cos(x) +--R + +--R 2 +--R 72cos(x) + 12cos(x) - 24 +--R * +--R 4 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 36cos(x) + 72cos(x) + 108cos(x) - 216cos(x) - 108cos(x) +--R + +--R 2 +--R 216cos(x) + 36cos(x) - 72 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R 3cos(x) + 79cos(x) + 27cos(x) - 198cos(x) - 108cos(x) +--R + +--R 3 2 +--R 143cos(x) + 123cos(x) - 24cos(x) - 45 +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 6cos(x) - 18cos(x) + 18cos(x) + 18cos(x) +--R + +--R 2 +--R - 18cos(x) - 6cos(x) + 6 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) - 3cos(x) - 9cos(x) + 9cos(x) + 9cos(x) - 9cos(x) +--R + +--R - 3cos(x) + 3 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 6cos(x) + 6cos(x) + 18cos(x) - 18cos(x) - 18cos(x) +--R + +--R 2 +--R 18cos(x) + 6cos(x) - 6 +--R * +--R 4 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 18cos(x) + 18cos(x) + 54cos(x) - 54cos(x) - 54cos(x) +--R + +--R 2 +--R 54cos(x) + 18cos(x) - 18 +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R - 6cos(x) - 12cos(x) + 74cos(x) + 48cos(x) - 170cos(x) +--R + +--R 4 3 2 +--R - 72cos(x) + 138cos(x) + 48cos(x) - 36cos(x) - 12 +--R * +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 9cos(x) + 9cos(x) + 27cos(x) - 27cos(x) - 27cos(x) + 27cos(x) +--R + +--R 2 +--R 9cos(x) - 9cos(x) +--R / +--R 5 4 3 2 +--R (6a cos(x) + 6a cos(x) - 12a cos(x) - 12a cos(x) + 6a cos(x) + 6a) +--R * +--R 5 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 12a cos(x) + 12a cos(x) + 48a cos(x) - 24a cos(x) - 60a cos(x) +--R + +--R 12a cos(x) + 24a +--R * +--R 4 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6a cos(x) - 30a cos(x) - 12a cos(x) + 96a cos(x) + 6a cos(x) +--R + +--R 2 +--R - 102a cos(x) + 36a +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 12a cos(x) - 24a cos(x) - 36a cos(x) + 72a cos(x) + 36a cos(x) +--R + +--R 2 +--R - 72a cos(x) - 12a cos(x) + 24a +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6a cos(x) - 6a cos(x) - 18a cos(x) + 18a cos(x) + 18a cos(x) +--R + +--R 2 +--R - 18a cos(x) - 6a cos(x) + 6a +--R * +--R sin(x) +--R Type: Expression Integer +--E 189 + +--S 190 of 546 +t0433:= sin(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R sin(x) +--R (187) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 190 + +--S 191 of 546 +r0433:= 1/b^2*(a*x+2*(a^2-b^2)^(1/2)*atan((a-b)/(a^2-b^2)^(1/2)*(-1+cos(x))/sin(x))-b*sin(x)) +--R +--R +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R - 2\|- b + a atan(---------------------) - b sin(x) + a x +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R (188) ----------------------------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 191 + +--S 192 of 546 +a0433:= integrate(t0433,x) +--R +--R +--R (189) +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R \|b - a log(---------------------------------) - b sin(x) + a x +--R b cos(x) + a +--R [-----------------------------------------------------------------, +--R 2 +--R b +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R - 2\|- b + a atan(------------------------) - b sin(x) + a x +--R (b - a)sin(x) +--R --------------------------------------------------------------] +--R 2 +--R b +--R Type: Union(List Expression Integer,...) +--E 192 + +--S 193 of 546 +m0433a:= a0433.1-r0433 +--R +--R +--R (190) +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R \|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atan(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R 2 +--R b +--R Type: Expression Integer +--E 193 + +--S 194 of 546 +d0433a:= D(m0433a,x) +--R +--R +--R (191) +--R 3 2 3 2 2 3 3 +--R ((- 2b + 2a b)cos(x) + b - a b - a b + a )sin(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 2b + 2a b)cos(x) + (b - a b - a b + a )cos(x) +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)cos(x) - b + a b + a b - a +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 2 2 3 4 +--R (b + a b - a b - a b)sin(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 2 +--R ((- a b - a b + a b + a )cos(x) - b - a b + a b + a b)sin(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 4 3 +--R (- b - a b + a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 3 2 2 3 4 +--R (b + a b - a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R / +--R 4 3 3 2 2 3 +--R ((b + a b )cos(x) + a b + a b )sin(x) +--R + +--R 4 3 3 4 3 2 2 2 +--R (- b + a b )cos(x) + (2b - 3a b + a b )cos(x) +--R + +--R 4 3 2 2 3 2 2 +--R (- b + 3a b - 2a b )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 2 5 4 2 3 3 2 4 2 3 +--R ((a b + a b )cos(x) + (b + a b + a b + a b )cos(x) + a b + a b ) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 4 5 4 2 3 3 2 3 +--R (- a b + a b )cos(x) + (- b + 3a b - 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (2b - 4a b + 4a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 3 +--R (- b + 3a b - 3a b + a b )cos(x) - a b + a b +--R Type: Expression Integer +--E 194 + +--S 195 of 546 +m0433b:= a0433.2-r0433 +--R +--R +--R (192) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R - 2\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atan(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R 2 +--R b +--R Type: Expression Integer +--E 195 + +--S 196 of 546 +d0433b:= D(m0433b,x) +--R +--R +--R (193) +--R 3 2 4 2 3 3 2 2 +--R (- 4b + 4a b)sin(x) + ((4a b - 4a )cos(x) + 4b - 4a b)sin(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R (4b - 4a b)cos(x) + (4a b - 4a )cos(x) + (- 4b + 4a b)cos(x) +--R + +--R 2 3 +--R (- 4a b + 4a )cos(x) +--R / +--R 4 2 2 4 +--R (b - a b )sin(x) +--R + +--R 4 2 2 2 3 4 2 2 2 +--R ((- 2b - 2a b )cos(x) - 8a b cos(x) - 2b - 2a b )sin(x) +--R + +--R 4 2 2 4 4 2 2 2 4 2 2 +--R (b - a b )cos(x) + (- 2b + 2a b )cos(x) + b - a b +--R Type: Expression Integer +--E 196 + +--S 197 of 546 +t0434:= sin(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R sin(x) +--R (194) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 197 + +--S 198 of 546 +r0434:= -a^3*x/b^4+3/2*a*x/b^2+2*(a^2-b^2)^(3/2)*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^4+a^2*sin(x)/b^3-sin(x)/b-1/2*a*cos(x)*sin(x)/b^2-1/3*sin(x)^3/b +--R +--R +--R (195) +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (12b - 12a )\|- b + a atan(-------------) - 2b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 +--R (- 3a b cos(x) - 6b + 6a b)sin(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R Type: Expression Integer +--E 198 + +--S 199 of 546 +a0434:= integrate(t0434,x) +--R +--R +--R (196) +--R [ +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (6b - 6a )\|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R 3 2 2 3 2 2 3 +--R (2b cos(x) - 3a b cos(x) - 8b + 6a b)sin(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (- 12b + 12a )\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R 3 2 2 3 2 2 3 +--R (2b cos(x) - 3a b cos(x) - 8b + 6a b)sin(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R ] +--R Type: Union(List Expression Integer,...) +--E 199 + +--S 200 of 546 +m0434a:= a0434.1-r0434 +--R +--R +--R (197) +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (3b - 3a )\|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (- 6b + 6a )\|- b + a atan(-------------) + b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 +--R (b cos(x) - b )sin(x) +--R / +--R 4 +--R 3b +--R Type: Expression Integer +--E 200 + +--S 201 of 546 +d0434a:= D(m0434a,x) +--R +--R +--R (198) +--R 4 3 2 3 2 2 3 +--R ((b - a b )cos(x) + (a b - a b )cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 3 +--R (b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 2 4 4 +--R (- b + a b )cos(x) + (3b - a b - 5a b + 3a )cos(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 2 3 +--R ((- b - a b )cos(x) + (- a b - a b )cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 3 +--R (- b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 2 4 4 +--R (b + a b )cos(x) + (3b + a b - 5a b + 3a )cos(x) - 3b +--R + +--R 2 2 4 +--R 6a b - 3a +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 4 2 3 5 4 2 3 3 2 4 5 +--R (a b - a b )cos(x) + 3b - 3a b - 6a b + 6a b + 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (2b + a b - 7a b + a b + 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 3 2 5 +--R (3b + 2a b - 5a b - 6a b + 3a b + 3a )cos(x) + 3a b - 6a b + 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 5 4 2 3 3 2 4 5 +--R (- a b - a b )cos(x) - 3b - 3a b + 6a b + 6a b - 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 2b + a b + 7a b + a b - 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 3 2 5 +--R (3b - 2a b - 5a b + 6a b + 3a b - 3a )cos(x) + 3a b - 6a b + 3a +--R / +--R 5 4 4 2 3 x 2 +--R ((3b - 3a b )cos(x) + 3a b - 3a b )sin(x)tan(-) +--R 2 +--R + +--R 5 4 4 2 3 +--R ((- 3b - 3a b )cos(x) - 3a b - 3a b )sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 2 4 2 6 5 2 4 3 3 5 +--R (3a b - 3a b )cos(x) + (3b - 3a b + 3a b - 3a b )cos(x) + 3a b +--R + +--R 2 4 +--R - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 5 2 4 3 3 5 +--R (- 3a b - 3a b )cos(x) + (- 3b - 3a b - 3a b - 3a b )cos(x) - 3a b +--R + +--R 2 4 +--R - 3a b +--R Type: Expression Integer +--E 201 + +--S 202 of 546 +m0434b:= a0434.2-r0434 +--R +--R +--R (199) +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (- 6b + 6a )\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (- 6b + 6a )\|- b + a atan(-------------) + b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 +--R (b cos(x) - b )sin(x) +--R / +--R 4 +--R 3b +--R Type: Expression Integer +--E 202 + +--S 203 of 546 +d0434b:= D(m0434b,x) +--R +--R +--R (200) +--R 5 4 2 3 4 +--R (b - 2a b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 2 3 2 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 4 5 4 2 3 3 2 4 5 +--R (- 2b + 2a b )cos(x) - 3b + 3a b + 6a b - 6a b - 3a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 5 5 2 3 4 +--R (- b + a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 7b + 3a b + 16a b - 6a b - 9a b + 3a )cos(x) +--R + +--R 5 2 3 4 5 4 2 3 3 2 4 +--R (- 11b + 23a b - 12a b)cos(x) - 3b - 3a b + 6a b + 6a b - 3a b +--R + +--R 5 +--R - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R (- b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 4 2 3 2 +--R (2a b + 2a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 5 4 2 3 3 2 4 5 +--R (2b + 2a b )cos(x) + 9b + 3a b - 18a b - 6a b + 9a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (b + 2a b + a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (b - a b - 8a b - 6a b + 3a b + 3a )cos(x) +--R + +--R 5 4 2 3 5 4 2 3 3 2 4 5 +--R (- b - 2a b - a b )cos(x) - 3b - 3a b + 6a b + 6a b - 3a b - 3a +--R / +--R 6 5 2 4 2 6 2 4 2 +--R (3b - 6a b + 3a b )sin(x) + (- 3b + 3a b )cos(x) +--R + +--R 6 2 4 6 2 4 +--R (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 4 2 6 5 2 4 2 +--R (- 3b + 3a b )sin(x) + (3b + 6a b + 3a b )cos(x) +--R + +--R 6 5 2 4 6 5 2 4 +--R (6b + 12a b + 6a b )cos(x) + 3b + 6a b + 3a b +--R Type: Expression Integer +--E 203 + +--S 204 of 546 +t0435:= sin(2*x)/(1+cos(2*x)) +--R +--R +--R sin(2x) +--R (201) ----------- +--R cos(2x) + 1 +--R Type: Expression Integer +--E 204 + +--S 205 of 546 +r0435:= -log(cos(x)) +--R +--R +--R (202) - log(cos(x)) +--R Type: Expression Integer +--E 205 + +--S 206 of 546 +a0435:= integrate(t0435,x) +--R +--R +--R 2 +--R log(-----------) +--R cos(2x) + 1 +--R (203) ---------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 206 + +--S 207 of 546 +m0435:= a0435-r0435 +--R +--R +--R 2 +--R 2log(cos(x)) + log(-----------) +--R cos(2x) + 1 +--R (204) ------------------------------- +--R 2 +--R Type: Expression Integer +--E 207 + +--S 208 of 546 +d0435:= D(m0435,x) +--R +--R +--R cos(x)sin(2x) + (- cos(2x) - 1)sin(x) +--R (205) ------------------------------------- +--R cos(x)cos(2x) + cos(x) +--R Type: Expression Integer +--E 208 + +--S 209 of 546 +t0436:= sin(2*x)/(1-cos(2*x)) +--R +--R +--R sin(2x) +--R (206) - ----------- +--R cos(2x) - 1 +--R Type: Expression Integer +--E 209 + +--S 210 of 546 +r0436:= log(sin(x)) +--R +--R +--R (207) log(sin(x)) +--R Type: Expression Integer +--E 210 + +--S 211 of 546 +a0436:= integrate(t0436,x) +--R +--R +--R sin(2x) 2 +--R 2log(-----------) - log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R (208) ------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 211 + +--S 212 of 546 +m0436:= a0436-r0436 +--R +--R +--R sin(2x) 2 +--R 2log(-----------) - 2log(sin(x)) - log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R (209) --------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 212 + +--S 213 of 546 +d0436:= D(m0436,x) +--R +--R +--R (210) +--R 2 +--R sin(x)sin(2x) + (- cos(x)cos(2x) - cos(x))sin(2x) +--R + +--R 2 +--R (2cos(2x) + 2cos(2x))sin(x) +--R / +--R (cos(2x) + 1)sin(x)sin(2x) +--R Type: Expression Integer +--E 213 + +--S 214 of 546 +t0437:= sin(x)^2/(a+a*cos(x)) +--R +--R +--R 2 +--R sin(x) +--R (211) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 214 + +--S 215 of 546 +r0437:= -(-x+sin(x))/a +--R +--R +--R - sin(x) + x +--R (212) ------------ +--R a +--R Type: Expression Integer +--E 215 + +--S 216 of 546 +a0437:= integrate(t0437,x) +--R +--R +--R - sin(x) + x +--R (213) ------------ +--R a +--R Type: Union(Expression Integer,...) +--E 216 + +--S 217 of 546 +m0437:= a0437-r0437 +--R +--R +--R (214) 0 +--R Type: Expression Integer +--E 217 + +--S 218 of 546 +d0437:= D(m0437,x) +--R +--R +--R (215) 0 +--R Type: Expression Integer +--E 218 + +--S 219 of 546 +t0438:= cos(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R cos(x) +--R (216) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 219 + +--S 220 of 546 +r0438:= -a*x/b^2+2*a^2*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)+sin(x)/b +--R +--R +--R x +--R (b - a)tan(-) +---------+ +--R 2 2 | 2 2 +--R - 2a atan(-------------) + (b sin(x) - a x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (217) ------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 220 + +--S 221 of 546 +a0438:= integrate(t0438,x) +--R +--R +--R (218) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) - a x)\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R b \|b - a +--R , +--R +---------+ +--R | 2 2 +---------+ +--R 2 sin(x)\|- b + a | 2 2 +--R 2a atan(---------------------) + (b sin(x) - a x)\|- b + a +--R (b + a)cos(x) + b + a +--R -------------------------------------------------------------] +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Union(List Expression Integer,...) +--E 221 + +--S 222 of 546 +m0438a:= a0438.1-r0438 +--R +--R +--R (219) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 2 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R a \|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2a \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression Integer +--E 222 + +--S 223 of 546 +d0438a:= D(m0438a,x) +--R +--R +--R (220) +--R 2 3 2 2 2 2 3 3 x 2 +--R ((a b - a )sin(x) + a b cos(x) + (a b + a )cos(x) + a )tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 3 3 +--R (- a b - a )sin(x) - a b cos(x) + (a b - a )cos(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 4 2 2 4 x 2 +--R ((a b - a )cos(x) + a b - a )sin(x)tan(-) +--R 2 +--R + +--R 2 2 4 2 2 4 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R / +--R 3 2 2 2 4 3 2 2 3 3 +--R (a b - a b )cos(x) + (b - a b + a b - a b)cos(x) + a b +--R + +--R 2 2 +--R - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 3 2 2 3 3 2 2 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b)cos(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 x 2 +--R ((b - a b - a b + a b )cos(x) + a b - a b - a b + a b)sin(x)tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 +--R ((- b - a b + a b + a b )cos(x) - a b - a b + a b + a b)sin(x) +--R Type: Expression Integer +--E 223 + +--S 224 of 546 +m0438b:= a0438.2-r0438 +--R +--R +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 2 sin(x)\|- b + a 2 2 +--R 2a atan(---------------------) + 2a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R (221) ------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 224 + +--S 225 of 546 +d0438b:= D(m0438b,x) +--R +--R +--R (222) +--R 2 3 2 2 3 2 2 2 3 +--R ((- a b + a )sin(x) + (- 3a b + a )cos(x) - 4a b cos(x) - a b - a ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 2 2 3 +--R (3a b + a )sin(x) + (a b + a )cos(x) - a b - a +--R / +--R 4 3 2 2 2 4 2 2 2 +--R (b - 2a b + a b )sin(x) + (- b + a b )cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2b + 2a b )cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 4 3 2 2 2 +--R (- b + a b )sin(x) + (b + 2a b + a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R (2b + 4a b + 2a b )cos(x) + b + 2a b + a b +--R Type: Expression Integer +--E 225 + +--S 226 of 546 +t0439:= cos(x)^3/(a+b*cos(x)) +--R +--R +--R 3 +--R cos(x) +--R (223) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 226 + +--S 227 of 546 +r0439:= a^2*x/b^3+1/2*x/b-2*a^3*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)-a*sin(x)/b^2+1/2*cos(x)*sin(x)/b +--R +--R +--R (224) +--R x +--R (b - a)tan(-) +---------+ +--R 3 2 2 2 2 | 2 2 +--R 4a atan(-------------) + ((b cos(x) - 2a b)sin(x) + (b + 2a )x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression Integer +--E 227 + +--S 228 of 546 +a0439:= integrate(t0439,x) +--R +--R +--R (225) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 3 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R 2a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R ((b cos(x) - 2a b)sin(x) + (b + 2a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 3 sin(x)\|- b + a +--R - 4a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((b cos(x) - 2a b)sin(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 228 + +--S 229 of 546 +m0439a:= a0439.1-r0439 +--R +--R +--R (226) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 3 | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R a \|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 3 | 2 2 2 +--R - 2a \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression Integer +--E 229 + +--S 230 of 546 +d0439a:= D(m0439a,x) +--R +--R +--R (227) +--R 3 4 2 3 2 3 4 4 x 2 +--R ((- a b + a )sin(x) - a b cos(x) + (- a b - a )cos(x) - a )tan(-) +--R 2 +--R + +--R 3 4 2 3 2 3 4 4 +--R (a b + a )sin(x) + a b cos(x) + (- a b + a )cos(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 2 5 3 2 5 x 2 +--R ((a b - a )cos(x) + a b - a )sin(x)tan(-) +--R 2 +--R + +--R 3 2 5 3 2 5 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R / +--R 4 2 3 2 5 4 2 3 3 2 4 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) + a b +--R + +--R 2 3 +--R - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) - a b +--R + +--R 2 3 +--R - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 5 2 4 3 3 5 2 4 3 3 4 2 +--R ((- b + a b + a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 5 2 4 3 3 4 2 +--R ((b + a b - a b - a b )cos(x) + a b + a b - a b - a b )sin(x) +--R Type: Expression Integer +--E 230 + +--S 231 of 546 +m0439b:= a0439.2-r0439 +--R +--R +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 3 sin(x)\|- b + a 3 2 +--R - 2a atan(---------------------) - 2a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R (228) --------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 231 + +--S 232 of 546 +d0439b:= D(m0439b,x) +--R +--R +--R (229) +--R 3 4 2 3 4 2 3 3 4 x 2 +--R ((a b - a )sin(x) + (3a b - a )cos(x) + 4a b cos(x) + a b + a )tan(-) +--R 2 +--R + +--R 3 4 2 3 4 2 3 4 +--R (- 3a b - a )sin(x) + (- a b - a )cos(x) + a b + a +--R / +--R 5 4 2 3 2 5 2 3 2 +--R (b - 2a b + a b )sin(x) + (- b + a b )cos(x) +--R + +--R 5 2 3 5 2 3 +--R (- 2b + 2a b )cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 5 4 2 3 2 +--R (- b + a b )sin(x) + (b + 2a b + a b )cos(x) +--R + +--R 5 4 2 3 5 4 2 3 +--R (2b + 4a b + 2a b )cos(x) + b + 2a b + a b +--R Type: Expression Integer +--E 232 + +--S 233 of 546 +t0440:= cos(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R cos(x) +--R (230) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 233 + +--S 234 of 546 +r0440:= -a^3*x/b^4-1/2*a*x/b^2+2*a^4*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(1/2)+a^2*sin(x)/b^3+sin(x)/b-1/2*a*cos(x)*sin(x)/b^2-1/3*sin(x)^3/b +--R +--R +--R (231) +--R x +--R (b - a)tan(-) +--R 4 2 +--R - 12a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 3 2 2 3 +--R (- 2b sin(x) + (- 3a b cos(x) + 6b + 6a b)sin(x) + (- 3a b - 6a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R Type: Expression Integer +--E 234 + +--S 235 of 546 +a0440:= integrate(t0440,x) +--R +--R +--R (232) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 4 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 6a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R 3 2 2 3 2 2 3 +--R ((2b cos(x) - 3a b cos(x) + 4b + 6a b)sin(x) + (- 3a b - 6a )x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 sin(x)\|- b + a +--R 12a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 3 2 2 3 2 2 3 +--R ((2b cos(x) - 3a b cos(x) + 4b + 6a b)sin(x) + (- 3a b - 6a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 235 + +--S 236 of 546 +m0440a:= a0440.1-r0440 +--R +--R +--R (233) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 4 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 3a \|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 4 | 2 2 2 +--R 6a \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 3 3 3 2 3 | 2 2 | 2 2 +--R (b sin(x) + (b cos(x) - b )sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R 3b \|- b + a \|b - a +--R Type: Expression Integer +--E 236 + +--S 237 of 546 +d0440a:= D(m0440a,x) +--R +--R +--R (234) +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 4 2 3 4 5 +--R (a b - a b )cos(x) + 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- b + a b - a b + a b + 3a b)cos(x) +--R + +--R 4 2 3 4 5 5 +--R (- a b + a b + 3a b + 3a )cos(x) + 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 4 5 +--R (- a b - a b )cos(x) - 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (b + a b + a b + a b - 3a b)cos(x) +--R + +--R 4 2 3 4 5 5 +--R (a b + a b + 3a b - 3a )cos(x) + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 5 2 4 3 3 2 +--R (b - a b - a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 +--R (a b - a b - a b + a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 2 4 3 3 4 +--R (b - a b - a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (a b - a b - a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b + a b + a b - a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 4 2 6 +--R (- a b + a b + a b + 2a b - 3a )cos(x) + 3a b - 3a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- a b - a b + a b + a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- b - a b + a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 4 2 6 +--R (a b + a b - a b + 2a b - 3a )cos(x) - 3a b + 3a +--R * +--R sin(x) +--R / +--R 5 2 4 2 6 5 2 4 3 3 +--R (3a b - 3a b )cos(x) + (3b - 3a b + 3a b - 3a b )cos(x) +--R + +--R 5 2 4 +--R 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 5 2 4 3 3 +--R (- 3a b - 3a b )cos(x) + (- 3b - 3a b - 3a b - 3a b )cos(x) +--R + +--R 5 2 4 +--R - 3a b - 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 7 6 2 5 3 4 6 2 5 3 4 4 3 +--R ((3b - 3a b - 3a b + 3a b )cos(x) + 3a b - 3a b - 3a b + 3a b ) +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 7 6 2 5 3 4 6 2 5 3 4 4 3 +--R ((- 3b - 3a b + 3a b + 3a b )cos(x) - 3a b - 3a b + 3a b + 3a b ) +--R * +--R sin(x) +--R Type: Expression Integer +--E 237 + +--S 238 of 546 +m0440b:= a0440.2-r0440 +--R +--R +--R (235) +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 4 sin(x)\|- b + a 4 2 +--R 6a atan(---------------------) + 6a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 3 2 3 | 2 2 +--R (b sin(x) + (b cos(x) - b )sin(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 3b \|- b + a +--R Type: Expression Integer +--E 238 + +--S 239 of 546 +d0440b:= D(m0440b,x) +--R +--R +--R (236) +--R 5 4 2 3 4 +--R (b - 2a b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 2 3 2 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 4 4 5 +--R (- 2b + 2a b )cos(x) - 3a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 5 5 2 3 4 +--R (- b + a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 2 3 4 5 2 5 2 3 4 4 +--R (2b - 2a b - 9a b + 3a )cos(x) + (b - a b - 12a b)cos(x) - 3a b +--R + +--R 5 +--R - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R (- b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 4 2 3 2 +--R (2a b + 2a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 4 5 +--R (2b + 2a b )cos(x) + 9a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (b + 2a b + a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 2 3 4 5 2 5 4 2 3 +--R (- 2b - 4a b - 2a b + 3a b + 3a )cos(x) + (- b - 2a b - a b )cos(x) +--R + +--R 4 5 +--R - 3a b - 3a +--R / +--R 6 5 2 4 2 6 2 4 2 +--R (3b - 6a b + 3a b )sin(x) + (- 3b + 3a b )cos(x) +--R + +--R 6 2 4 6 2 4 +--R (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 4 2 6 5 2 4 2 +--R (- 3b + 3a b )sin(x) + (3b + 6a b + 3a b )cos(x) +--R + +--R 6 5 2 4 6 5 2 4 +--R (6b + 12a b + 6a b )cos(x) + 3b + 6a b + 3a b +--R Type: Expression Integer +--E 239 + +--S 240 of 546 +t0441:= tan(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R tan(x) +--R (237) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 240 + +--S 241 of 546 +r0441:= -2*(a^2-b^2)^(1/2)*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2-b*atanh(sin(x))/a^2+tan(x)/a +--R +--R +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R - b atanh(sin(x)) + 2\|- b + a atan(-------------) + a tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (238) --------------------------------------------------------------- +--R 2 +--R a +--R Type: Expression Integer +--E 241 + +--S 242 of 546 +a0441:= integrate(t0441,x) +--R +--R +--R (239) +--R [ +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R cos(x)\|b - a log(---------------------------------) + a sin(x) +--R b cos(x) + a +--R / +--R 2 +--R a cos(x) +--R , +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R - 2cos(x)\|- b + a atan(------------------------) + a sin(x) +--R (b - a)sin(x) +--R / +--R 2 +--R a cos(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 242 + +--S 243 of 546 +m0441a:= a0441.1-r0441 +--R +--R +--R (240) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R cos(x)\|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R b cos(x)atanh(sin(x)) - 2cos(x)\|- b + a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R - a cos(x)tan(x) + a sin(x) +--R / +--R 2 +--R a cos(x) +--R Type: Expression Integer +--E 243 + +--S 244 of 546 +d0441a:= D(m0441a,x) +--R +--R +--R (241) +--R 2 2 3 2 3 2 5 +--R ((- a b + a b)cos(x) + (- a b + a )cos(x) )sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (a b - a b)cos(x) + (2a b - a b - a )cos(x) +--R + +--R 2 3 3 2 3 2 +--R (2a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- a b + a b)cos(x) + (- 2a b + a b + a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- a b - a b + 2a )cos(x) + (- a b + a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 5 +--R ((a b + a b)cos(x) + (a b + a )cos(x) )sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- a b - a b)cos(x) + (- 2a b - 3a b - a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- 2a b - 4a b - 2a )cos(x) + (- 2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (a b + a b)cos(x) + (2a b + 3a b + a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (a b + 3a b + 2a )cos(x) + (a b + a )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 3 7 +--R ((a b - a b)cos(x) + a b - a )sin(x) +--R + +--R 3 2 3 3 2 3 2 +--R (3b - 3a b )cos(x) + (b - 2a b + a )cos(x) +--R + +--R 2 3 2 3 +--R (- 2a b + 2a )cos(x) - 2a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (b - 2a b + a b)cos(x) + (- 2b + a b + a b)cos(x) +--R + +--R 3 2 2 3 3 2 3 2 +--R (- 6b + 4a b + 2a b)cos(x) + (- 2b + 3a b - a )cos(x) +--R + +--R 2 2 3 2 3 +--R (a b + a b - 2a )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 2 5 +--R (b - a b )cos(x) + (b + a b - 2a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2b + a b - 3a b)cos(x) + (3b - a b - 2a b)cos(x) +--R + +--R 3 2 2 +--R (b - a b)cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 7 +--R ((- a b - a b)cos(x) - a b - a )sin(x) +--R + +--R 3 2 3 3 2 3 2 +--R (- b - a b )cos(x) + (- b + 2a b + a )cos(x) +--R + +--R 2 2 3 2 3 +--R (2a b + 4a b + 2a )cos(x) + 2a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 3b - 2a b + a b)cos(x) + (- 2b - 3a b - a b)cos(x) +--R + +--R 3 2 3 3 2 3 2 +--R (2b - 2a b)cos(x) + (2b - 3a b - a )cos(x) +--R + +--R 2 2 3 2 3 +--R (- a b - 3a b - 2a )cos(x) - a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- b - a b )cos(x) + (b - a b - 2a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2b + a b - a b)cos(x) + (- b + a b + 2a b)cos(x) +--R + +--R 3 2 2 +--R (- b + a b)cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b + a b)cos(x) + (- a b + a b - a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 3 4 3 +--R (2a b + a b - a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 3 2 +--R (2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 4 4 3 2 2 3 4 3 +--R (- 2a b + 2a )cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 2a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (a b + 3a b + 3a b + a )cos(x) + (a b + a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 3 2 2 3 4 2 2 3 +--R ((b - a b )cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 4 4 2 2 3 4 3 +--R (3a b - 3a b )cos(x) + (b + 2a b - 4a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b + 3a b - a b - 2a b + 2a )cos(x) +--R + +--R 3 4 2 2 3 +--R (- 2a b + 2a )cos(x) - 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- b + 2a b - a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - 2a b + 4a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 5a b + 5a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b - 2a b + 7a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b - 3a b + a b + 3a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (a b + a b - a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 3 6 +--R (a b - a b )cos(x) + (2b - a b - a b)cos(x) +--R + +--R 4 3 2 2 3 5 +--R (3b + a b - 3a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 3 +--R (2b + 4a b - 4a b - 2a b)cos(x) + (b + 2a b - 3a b)cos(x) +--R + +--R 3 3 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 2 3 4 2 2 3 +--R ((- b - a b )cos(x) + (- a b - a b - a b - a )cos(x) - a b - a b) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 4 4 2 2 4 3 +--R (- a b - a b )cos(x) + (b - 2a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b + a b + 2a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2a b + 4a b + 4a b + 2a )cos(x) + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 5 +--R (b - 2a b - 3a b )cos(x) + (- b - 2a b - 4a b - 3a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - a b - a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b + 2a b + a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 3a b - a b - a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 3 6 +--R (- a b - a b )cos(x) + (- 2b - a b - a b)cos(x) +--R + +--R 4 3 2 2 3 5 4 3 4 +--R (- b - a b + a b + a b)cos(x) + (2b + 2a b)cos(x) +--R + +--R 4 3 3 3 3 3 2 +--R (b + 2a b - a b)cos(x) + (a b - a b)cos(x) +--R / +--R 2 2 3 3 3 4 2 5 +--R ((a b - a b)cos(x) + (a b - a )cos(x) )sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (- a b + a b)cos(x) + (- 2a b + a b + a )cos(x) +--R + +--R 2 2 4 3 3 4 2 +--R (- 2a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (a b - a b)cos(x) + (2a b - a b - a )cos(x) +--R + +--R 2 2 3 4 3 3 4 2 +--R (a b + a b - 2a )cos(x) + (a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 3 3 4 2 5 +--R ((- a b - a b)cos(x) + (- a b - a )cos(x) )sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (a b + a b)cos(x) + (2a b + 3a b + a )cos(x) +--R + +--R 2 2 3 4 3 3 4 2 +--R (2a b + 4a b + 2a )cos(x) + (2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (- a b - a b)cos(x) + (- 2a b - 3a b - a )cos(x) +--R + +--R 2 2 3 4 3 3 4 2 +--R (- a b - 3a b - 2a )cos(x) + (- a b - a )cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 2 3 5 3 +--R (- 2a b - a b + a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 2 3 5 4 2 3 3 2 4 5 3 +--R (2a b - 2a )cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (2a b + 5a b + 5a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (2a b + 4a b + 4a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- a b - 3a b - 3a b - a )cos(x) + (- a b - a b)cos(x) +--R Type: Expression Integer +--E 244 + +--S 245 of 546 +m0441b:= a0441.2-r0441 +--R +--R +--R (242) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R b cos(x)atanh(sin(x)) - 2cos(x)\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R - 2cos(x)\|- b + a atan(-------------) - a cos(x)tan(x) + a sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 +--R a cos(x) +--R Type: Expression Integer +--E 245 + +--S 246 of 546 +d0441b:= D(m0441b,x) +--R +--R +--R (243) +--R 2 2 3 2 6 +--R (- a b + 2a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (3a b - 4a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 2 3 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 8a b + 2a b + 6a )cos(x) + (- 8a b + 4a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b + 2a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (6a b - 6a )cos(x) +--R + +--R 2 3 3 2 3 2 +--R (4a b - 4a )cos(x) + (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 6 +--R (a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b - 2a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (8a b + 14a b + 6a )cos(x) + (8a b + 12a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (3a b + 4a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 6a b - 12a b - 6a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b - 2a b - a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 8 +--R (a b - 2a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 2 2 +--R (b - 5a b + 5a b - a )cos(x) + (- 4a b + 4a b)cos(x) - 3a b +--R + +--R 2 3 +--R 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 3 2 3 3 +--R (- 2b - 3a b + 6a b - a )cos(x) + (- 5b + 7a b - 2a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b + 9a b - 3a b - 3a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 +--R 3a b - 2a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 6 3 2 2 3 5 +--R (b - a b - a b + a )cos(x) + (6b - 4a b - 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (12b - a b - 12a b + a )cos(x) + (10b + 2a b - 12a b)cos(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (3b - 3a b - 3a b + 3a )cos(x) + (- 4a b + 4a )cos(x) - a b +--R + +--R 3 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 3 2 2 3 6 +--R (- b + a b)cos(x) + (- 5b + a b + 5a b - a )cos(x) +--R + +--R 3 2 2 3 5 3 2 4 +--R (- 10b + 2a b + 10a b - 2a )cos(x) + (- 10b + 10a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (- 5b - 2a b + 5a b + 2a )cos(x) + (- b - a b + a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 8 +--R (- a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (b + 3a b + a b - a )cos(x) + (4a b + 4a b)cos(x) + 3a b + 2a b +--R + +--R 3 +--R - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 3a b + 4a b - a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 3b + 2a b + 3a b - 2a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b - 7a b - 7a b - 3a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 +--R - 3a b - 4a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 6 3 2 2 3 5 +--R (b + 3a b + 3a b + a )cos(x) + (2b + 8a b + 8a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (4b + 5a b + 2a b + a )cos(x) + (6b + 2a b - 4a b)cos(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3b + 5a b + 5a b + 3a )cos(x) + (4a b + 8a b + 4a )cos(x) + a b +--R + +--R 2 3 +--R 2a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 3 2 2 3 6 +--R (b + 2a b + a b)cos(x) + (3b + 5a b + a b - a )cos(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (2b + 2a b - 2a b - 2a )cos(x) + (- 2b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (- 3b - 4a b + a b + 2a )cos(x) + (- b - a b + a b + a )cos(x) +--R / +--R 2 2 3 4 2 6 +--R (a b - 2a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b + 4a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (8a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b - 2a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 6a b + 6a )cos(x) + (- 4a b + 4a )cos(x) + (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 6 +--R (- a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b + 2a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (- 8a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b - 4a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (6a b + 12a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (a b + 2a b + a )cos(x) +--R Type: Expression Integer +--E 246 + +--S 247 of 546 +t0442:= tan(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R tan(x) +--R (244) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 247 + +--S 248 of 546 +r0442:= 2*(a^2-b^2)^(3/2)*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^4+3/2*b*atanh(sin(x))/a^2-b^3*atanh(sin(x))/a^4-tan(x)/a+b^2*tan(x)/a^3-1/2*b*sec(x)*tan(x)/a^2+1/3*tan(x)^3/a +--R +--R +--R (245) +--R 3 2 +--R (- 6b + 9a b)atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (12b - 12a )\|- b + a atan(-------------) + 2a tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 +--R (- 3a b sec(x) + 6a b - 6a )tan(x) +--R / +--R 4 +--R 6a +--R Type: Expression Integer +--E 248 + +--S 249 of 546 +a0442:= integrate(t0442,x) +--R +--R +--R (246) +--R [ +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 3 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (6b - 6a )cos(x) \|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R , +--R +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (- 12b + 12a )cos(x) \|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 249 + +--S 250 of 546 +m0442a:= a0442.1-r0442 +--R +--R +--R (247) +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 3 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (6b - 6a )cos(x) \|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R 3 2 3 +--R (6b - 9a b)cos(x) atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 3 | 2 2 2 3 3 3 +--R (- 12b + 12a )cos(x) \|- b + a atan(-------------) - 2a cos(x) tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b + 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R Type: Expression Integer +--E 250 + +--S 251 of 546 +d0442a:= D(m0442a,x) +--R +--R +--R (248) +--R 3 2 4 5 4 5 4 5 +--R ((- 6a b + 6a b)cos(x) + (- 6a b + 6a )cos(x) )sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (6a b - 6a b)cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 3 2 5 5 4 5 4 +--R (12a b - 12a )cos(x) + (12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (- 6a b + 6a b)cos(x) + (- 12a b + 6a b + 6a )cos(x) +--R + +--R 3 2 4 5 5 4 5 4 +--R (- 6a b - 6a b + 12a )cos(x) + (- 6a b + 6a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 5 4 5 4 5 +--R ((6a b + 6a b)cos(x) + (6a b + 6a )cos(x) )sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (- 6a b - 6a b)cos(x) + (- 12a b - 18a b - 6a )cos(x) +--R + +--R 3 2 4 5 5 4 5 4 +--R (- 12a b - 24a b - 12a )cos(x) + (- 12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (6a b + 6a b)cos(x) + (12a b + 18a b + 6a )cos(x) +--R + +--R 3 2 4 5 5 4 5 4 +--R (6a b + 18a b + 12a )cos(x) + (6a b + 6a )cos(x) +--R * +--R sin(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((6a b - 6a b )cos(x) + (6a b - 6a b)cos(x) )sec(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (- 6a b + 6a b )cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 12a b + 6a b + 6a b)cos(x) +--R + +--R 2 3 4 5 3 2 4 4 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 4 2 3 3 2 6 +--R (6a b - 6a b )cos(x) + (12a b - 6a b - 6a b )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (6a b - 6a b )cos(x) +--R + +--R 2 3 3 2 4 6 +--R (12a b - 6a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (6a b + 6a b - 12a b)cos(x) + (6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 +--R (- 6a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 12a b + 6a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 6a b - 6a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 +--R (- 6a b + 6a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((- 6a b - 6a b )cos(x) + (- 6a b - 6a b)cos(x) )sec(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (6a b + 6a b )cos(x) + (6a b + 6a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (6a b + 6a b )cos(x) + (12a b + 18a b + 6a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (12a b + 24a b + 12a b)cos(x) + (12a b + 12a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 4 2 3 3 2 6 +--R (- 6a b - 6a b )cos(x) + (- 12a b - 18a b - 6a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 12a b - 24a b - 12a b )cos(x) +--R + +--R 2 3 3 2 4 +--R (- 12a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 12a b - 18a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (- 6a b - 18a b - 12a b)cos(x) + (- 6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 4 2 3 3 2 6 +--R (6a b + 6a b )cos(x) + (12a b + 18a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 5 2 3 3 2 4 +--R (6a b + 18a b + 12a b )cos(x) + (6a b + 6a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 3 4 5 2 +--R (6a b - 6a b - 8a b + 8a b)cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 4 5 +--R 6a b - 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((3a b - 3a b )cos(x) + (3a b - 3a b)cos(x) )sec(x) +--R + +--R 5 4 2 3 3 2 5 +--R (18b - 18a b - 24a b + 24a b )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (6b - 15a b + a b + 14a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b + 12a b + 15a b + a b - 16a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (12a b - 12a )cos(x) + (- 12a b + 12a )cos(x) - 12a b + 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (- 3a b + 3a b )cos(x) +--R + +--R 2 3 3 2 4 6 2 3 4 5 +--R (- 6a b + 3a b + 3a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 3 2 4 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (6b - 12a b - 6a b + 20a b - 8a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b + 6a b + 18a b - 8a b - 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 36b + 24a b + 60a b - 36a b - 8a b - 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 12b + 30a b - 2a b - 22a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (6a b - 6a b - 6a b - 14a b + 20a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (- 6a b + 6a )cos(x) + (12a b - 12a )cos(x) + 6a b - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (3a b - 3a b )cos(x) + (6a b - 3a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (3a b + 3a b - 6a b)cos(x) + (3a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 8 +--R (6b - 6a b - 9a b + 9a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (6b + 6a b - 18a b - 11a b + 17a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (12b + 6a b - 30a b - 10a b + 20a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (18b - 6a b - 36a b + 12a b + 8a b + 4a )cos(x) +--R + +--R 5 2 3 3 2 4 4 +--R (6b - 15a b + a b + 8a b)cos(x) +--R + +--R 3 2 4 5 3 4 5 2 +--R (- a b + 5a b - 4a )cos(x) + (2a b - 2a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 4 5 2 +--R (- 6a b - 6a b + 8a b + 8a b)cos(x) + (8a b + 8a )cos(x) +--R + +--R 4 5 +--R - 6a b - 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((- 3a b - 3a b )cos(x) + (- 3a b - 3a b)cos(x) )sec(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 6b - 6a b + 12a b + 12a b )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 6b + 15a b + 5a b - 10a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (12a b + 12a b - 15a b - 31a b - 16a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (- 12a b - 12a )cos(x) + (12a b + 12a )cos(x) + 12a b + 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (3a b + 3a b )cos(x) + (6a b + 9a b + 3a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (6a b + 12a b + 6a b)cos(x) + (6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 18b - 12a b + 30a b + 16a b - 8a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 18a b + 6a b + 20a b + 6a b - 2a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (12b - 36a b - 12a b + 8a b - 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (12b - 30a b - 10a b + 14a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 6a b - 6a b + 6a b + 26a b + 20a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (6a b + 6a )cos(x) + (- 12a b - 12a )cos(x) - 6a b - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (- 3a b - 3a b )cos(x) + (- 6a b - 9a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (- 3a b - 9a b - 6a b)cos(x) + (- 3a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 6b - 6a b + 9a b + 9a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (6b - 6a b - 18a b + 11a b + 17a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (12b + 6a b - 18a b - 2a b + 12a b + 2a )cos(x) +--R + +--R 5 4 2 3 4 5 5 +--R (- 6b + 6a b + 24a b - 8a b + 4a )cos(x) +--R + +--R 5 2 3 3 2 4 4 +--R (- 6b + 15a b + 5a b - 4a b)cos(x) +--R + +--R 3 2 4 5 3 4 5 2 +--R (a b - 3a b - 4a )cos(x) + (- 2a b - 2a )cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 5 6 +--R (- 6a b + 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (- 6a b + 6a b - 6a b + 6a )cos(x) + (- 6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (6a b - 6a b)cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 6a b - 6a b - 12a )cos(x) +--R + +--R 3 3 6 5 4 2 5 4 +--R (12a b - 12a )cos(x) + (12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 3 3 6 6 3 3 4 2 5 6 5 +--R (- 12a b + 12a )cos(x) + (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 6 3 3 4 2 5 6 5 +--R (6a b + 6a b)cos(x) + (6a b + 6a b + 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 12a b - 30a b - 30a b - 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 2 5 4 +--R (- 12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 24a b + 24a b + 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (6a b + 18a b + 18a b + 6a )cos(x) + (6a b + 6a b)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 3 4 2 6 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b - 6a b + 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 6 +--R (- 6a b + 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 6a b + 6a b - 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 +--R (- 6a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 +--R (6a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (6a b + 6a b - 6a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (12a b + 6a b - 6a b - 12a b )cos(x) +--R + +--R 5 4 2 5 2 4 3 3 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 2 4 5 6 +--R (12a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (6a b + 6a b - 6a b - 6a b)cos(x) + (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 +--R (- 6a b + 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) +--R + +--R 5 4 2 6 +--R (- 12a b + 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 4 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 6 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 6a b - 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 6 5 2 4 3 3 4 2 5 +--R (6a b + 6a b )cos(x) + (6a b + 6a b + 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 +--R (6a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (12a b + 30a b + 30a b + 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (12a b + 24a b + 24a b + 12a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 +--R (- 6a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 6a b - 18a b - 18a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 12a b - 30a b - 30a b - 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 12a b - 24a b - 24a b - 12a b )cos(x) +--R + +--R 2 4 3 3 4 +--R (- 12a b - 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 18a b - 18a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 24a b - 24a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 18a b - 18a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 5 2 4 3 3 4 2 7 +--R (6a b + 6a b )cos(x) + (6a b + 18a b + 18a b + 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (12a b + 24a b + 24a b + 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 4 +--R (6a b + 18a b + 18a b + 6a b )cos(x) + (6a b + 6a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (6b - 6a b - 6a b + 6a b - 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b - 8a b + 8a b - 8a b + 8a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (- 8a b + 8a b)cos(x) + (6a b - 6a )cos(x) + 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (3a b - 3a b + 3a b - 3a b)cos(x) + (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (18a b - 18a b - 24a b + 24a b )cos(x) +--R + +--R 6 3 3 4 2 5 6 5 +--R (6b - 15a b - 11a b + 26a b - 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b + 18a b + 9a b - 23a b + 11a b + 13a b - 16a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 12a b + 12a b + 15a b + a b - 4a b - 12a )cos(x) +--R + +--R 4 2 5 6 2 4 2 6 4 2 +--R (12a b - 24a b + 12a )cos(x) + (- 12a b + 12a )cos(x) - 12a b +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 3a b + 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b - 3a b + 3a b + 6a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 3 3 4 2 5 8 +--R (- 6b + 12a b - 18a b + 14a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- 6b - 12a b + 24a b + 14a b - 28a b + 10a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 12b - 30a b + 42a b + 52a b - 38a b - 10a b - 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 12b - 12a b + 12a b + 42a b + 14a b - 50a b + 6a )cos(x) +--R + +--R 6 5 3 3 4 2 5 6 4 +--R (6b - 18a b + 28a b - 10a b - 26a b + 20a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b - 6a b - 14a b + 14a b + 6a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 +--R (- 6a b + 18a b - 12a )cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 4 2 5 +--R 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 2 4 3 3 4 2 5 7 +--R (3a b - 3a b )cos(x) + (3a b + 3a b - 3a b - 3a b)cos(x) +--R + +--R 2 4 5 6 2 4 3 3 4 2 5 5 +--R (6a b - 6a b)cos(x) + (3a b + 3a b - 3a b - 3a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (6a b - 6a b - 9a b + 9a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (12b - 6a b - 15a b + 3a b - 5a b + 11a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (18b + 6a b - 36a b - 17a b + 19a b + 8a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (12b + 24a b - 36a b - 46a b + 32a b + 10a b + 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (6b + 12a b - 12a b - 27a b - 3a b + 24a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6a b - 3a b - 11a b + a b + 11a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 4 2 5 2 +--R (- a b + 5a b - 2a b - 2a )cos(x) + (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 6b - 6a b + 6a b + 6a b + 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6a b - 6a b + 8a b + 8a b + 8a b + 8a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (8a b + 8a b)cos(x) + (- 6a b - 6a )cos(x) - 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (- 3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (- 3a b - 3a b - 3a b - 3a b)cos(x) + (- 3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 6a b - 6a b + 12a b + 12a b )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 5 +--R (6b - 12a b + 3a b + 17a b + 2a b - 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (12b + 18a b - 9a b - 19a b - 7a b - 19a b - 16a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (12a b + 12a b - 15a b - 31a b - 28a b - 12a )cos(x) +--R + +--R 4 2 6 2 4 2 5 6 4 2 +--R (- 12a b + 12a )cos(x) + (12a b + 24a b + 12a )cos(x) + 12a b +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 2 4 3 3 4 2 5 7 +--R (3a b + 3a b )cos(x) + (3a b + 9a b + 9a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (6a b + 15a b + 15a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (6a b + 12a b + 12a b + 6a b)cos(x) + (6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (6b - 12a b - 24a b + 18a b + 22a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- 6b - 12a b - 12a b - 2a b + 24a b + 18a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 12b - 6a b + 6a b - 16a b - 6a b + 6a b - 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 12b - 12a b + 12a b + 6a b - 26a b - 14a b + 6a )cos(x) +--R + +--R 6 5 3 3 4 2 5 6 4 +--R (- 6b - 18a b + 20a b + 2a b + 14a b + 20a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6a b - 6a b + 6a b + 26a b + 26a b + 6a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 4 2 +--R (6a b - 6a b - 12a )cos(x) + (- 12a b - 18a b - 6a )cos(x) - 6a b +--R + +--R 5 +--R - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 2 4 3 3 4 2 5 7 +--R (- 3a b - 3a b )cos(x) + (- 3a b - 9a b - 9a b - 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b - 12a b - 12a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (- 3a b - 9a b - 9a b - 3a b)cos(x) + (- 3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (- 6a b - 6a b + 9a b + 9a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (- 12b - 6a b + 15a b + 3a b + 5a b + 11a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 7 +--R (- 6b - 6a b + 12a b + 17a b + 3a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 6 +--R (12b - 12a b + 22a b + 12a b - 6a b + 4a )cos(x) +--R + +--R 6 5 3 3 4 2 5 5 +--R (6b + 12a b - 9a b + 9a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6a b + 3a b - 7a b + 3a b + 3a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 4 2 5 2 +--R (a b - 3a b - 6a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R / +--R 4 2 5 5 5 6 4 5 +--R ((6a b - 6a b)cos(x) + (6a b - 6a )cos(x) )sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (- 6a b + 6a b)cos(x) + (- 12a b + 6a b + 6a )cos(x) +--R + +--R 4 2 6 5 5 6 4 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (6a b - 6a b)cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 4 2 5 6 5 5 6 4 +--R (6a b + 6a b - 12a )cos(x) + (6a b - 6a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 5 6 4 5 +--R ((- 6a b - 6a b)cos(x) + (- 6a b - 6a )cos(x) )sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (6a b + 6a b)cos(x) + (12a b + 18a b + 6a )cos(x) +--R + +--R 4 2 5 6 5 5 6 4 +--R (12a b + 24a b + 12a )cos(x) + (12a b + 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (- 6a b - 6a b)cos(x) + (- 12a b - 18a b - 6a )cos(x) +--R + +--R 4 2 5 6 5 5 6 4 +--R (- 6a b - 18a b - 12a )cos(x) + (- 6a b - 6a )cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (6a b - 6a b)cos(x) + (6a b - 6a b + 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 6a b + 6a b + 12a )cos(x) +--R + +--R 4 3 7 5 5 2 6 4 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b - 6a b)cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 4 3 7 6 4 3 5 2 6 7 5 +--R (12a b - 12a )cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (- 6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (12a b + 30a b + 30a b + 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (12a b + 24a b + 24a b + 12a )cos(x) + (12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (- 6a b - 18a b - 18a b - 6a )cos(x) + (- 6a b - 6a b)cos(x) +--R Type: Expression Integer +--E 251 + +--S 252 of 546 +m0442b:= a0442.2-r0442 +--R +--R +--R (249) +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 +--R (6b - 9a b)cos(x) atanh(sin(x)) +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (- 12b + 12a )cos(x) \|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 3 | 2 2 2 3 3 3 +--R (- 12b + 12a )cos(x) \|- b + a atan(-------------) - 2a cos(x) tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b + 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R Type: Expression Integer +--E 252 + +--S 253 of 546 +d0442b:= D(m0442b,x) +--R +--R +--R (250) +--R 3 2 4 5 4 6 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (12a b - 12a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b - 24a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 +--R (- 48a b + 12a b + 36a )cos(x) +--R + +--R 3 2 4 5 5 +--R (- 48a b + 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b + 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (36a b - 36a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 4 +--R (6a b - 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 4 6 +--R (6a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 12a b - 12a b)cos(x) + (- 24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b - 12a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (48a b + 84a b + 36a )cos(x) + (48a b + 72a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b + 24a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (- 36a b - 72a b - 36a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 6a b - 12a b - 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 3 2 4 4 +--R (6a b - 12a b + 6a b)cos(x) sec(x) +--R + +--R 4 2 3 3 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 12a b + 12a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b + 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 6 4 2 3 5 +--R (12a b - 12a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (18a b - 24a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 6a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (48a b - 12a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (48a b - 24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b - 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 6a b + 6a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 48a b + 12a b + 36a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 48a b + 24a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 18a b + 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 36a b + 36a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (6a b - 6a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (36a b - 36a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 3 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 4 3 2 4 6 +--R ((- 6a b + 6a b)cos(x) sec(x) + (6a b - 6a b )cos(x) )sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (12a b + 12a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b + 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 6 4 2 3 5 +--R (- 12a b - 12a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 18a b - 12a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 6a b - 12a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 24a b - 48a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 48a b - 84a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 48a b - 72a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b - 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 8 +--R (6a b + 12a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 7 +--R (24a b + 48a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (48a b + 84a b + 36a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (48a b + 72a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (18a b + 24a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (6a b + 12a b + 6a b)cos(x) + (24a b + 48a b + 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (36a b + 72a b + 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 4 +--R (24a b + 48a b + 24a b)cos(x) + (6a b + 12a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 8 +--R (- 6a b - 12a b - 6a b )cos(x) +--R + +--R 4 2 3 3 2 7 +--R (- 24a b - 48a b - 24a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 36a b - 72a b - 36a b )cos(x) +--R + +--R 4 2 3 3 2 5 4 2 3 3 2 4 +--R (- 24a b - 48a b - 24a b )cos(x) + (- 6a b - 12a b - 6a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b - 2a b + 16a b - 8a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 6a b + 12a b - 6a b)cos(x) + 6a b - 12a b + 6a +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b - 6a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b - 30a b + 18a b + 38a b - 36a b + 4a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 24a b + 33a b + 26a b - 35a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 48a b - 16a b - 24a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (18a b - 48a b + 30a b)cos(x) - 18a b + 24a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 6a b + 6a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b + 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 18a b + 48a b + 26a b - 52a b + 8a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 30b + 81a b - 12a b - 59a b + 20a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 18b + 54a b - 104a b + 42a b + 26a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (48a b - 63a b - 72a b + 79a b + 8a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 60a b + 36a b + 36a b - 30a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 18a b + 60a b - 18a b - 24a )cos(x) + 18a b - 12a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (3a b - 3a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (24a b - 6a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (24a b - 12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b - 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 5 8 +--R (6b - 6a b - 6a b + 10a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (36b - 24a b - 51a b + 34a b + 9a b - 4a )cos(x) +--R + +--R 5 4 2 3 4 5 6 +--R (72b - 6a b - 150a b + 82a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (60b + 12a b - 156a b - 12a b + 104a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b - 18a b - 42a b + 64a b + 12a b - 34a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 24a b + 27a b + 54a b - 41a b - 16a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 6a b + 24a b - 16a b - 28a b + 26a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 5 +--R (6a b - 24a b - 6a b + 24a )cos(x) - 6a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 3a b + 3a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 18a b + 18a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 2 3 4 9 +--R (- 6b + 15a b - 9a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 30b + 6a b + 66a b - 10a b - 36a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 60b + 12a b + 123a b - 16a b - 63a b + 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (- 60b + 126a b + 10a b - 66a b - 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 30b - 12a b + 75a b + 24a b - 45a b - 12a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 6b - 6a b + 24a b + 2a b - 18a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 5 2 +--R (3a b - 8a b - 3a b + 8a )cos(x) + (- 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R ((- 6a b + 14a b - 8a )cos(x) + (6a b - 6a b)cos(x) - 6a b + 6a ) +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b + 18a b + 6a b - 26a b - 16a b + 4a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (24a b + 15a b - 44a b - 35a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 12a b - 44a b - 4a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 18a b + 12a b + 30a b)cos(x) + 18a b + 12a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (6a b + 6a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b + 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b + 18a b + 36a b - 38a b - 36a b + 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 18b + 12a b + 27a b - 42a b - 19a b + 20a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b - 42a b - 24a b + 56a b + 82a b + 26a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 48a b - 33a b + 102a b + 95a b + 8a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 24a b + 48a b - 24a b - 30a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (18a b - 24a b - 66a b - 24a )cos(x) - 18a b - 24a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 3a b - 6a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 12a b - 24a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 24a b - 42a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 24a b - 36a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b - 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (6b + 18a b + 6a b - 22a b - 20a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 48a b + 27a b - 52a b - 47a b - 4a )cos(x) +--R + +--R 5 4 2 3 4 5 6 +--R (24b + 30a b - 6a b + 14a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (36b + 12a b - 36a b + 36a b + 40a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b + 30a b + 18a b - 28a b - 68a b - 34a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (24a b + 21a b - 60a b - 73a b - 16a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b - 20a b + 24a b + 26a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 6a b + 12a b + 42a b + 24a )cos(x) + 6a b + 12a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (3a b + 6a b + 3a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (18a b + 36a b + 18a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b + 6a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (6b + 12a b - 3a b - 18a b - 9a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (18b + 30a b - 18a b - 50a b - 16a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 12a b - 27a b - 38a b - 7a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 24a b - 6a b + 2a b - 14a b - 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 18b - 24a b + 9a b + 6a b - 21a b - 12a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 6b - 6a b - 2a b + 2a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 5 2 +--R (- 3a b + 2a b + 13a b + 8a )cos(x) + (2a b + 4a b + 2a )cos(x) +--R / +--R 4 2 5 6 4 6 +--R (6a b - 12a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (- 12a b + 12a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b + 24a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (48a b - 12a b - 36a )cos(x) + (48a b - 24a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b - 12a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 36a b + 36a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 4 +--R (- 6a b + 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 6 4 6 +--R (- 6a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (12a b + 12a b)cos(x) + (24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b + 12a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (- 48a b - 84a b - 36a )cos(x) + (- 48a b - 72a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b - 24a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (36a b + 72a b + 36a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (6a b + 12a b + 6a )cos(x) +--R Type: Expression Integer +--E 253 + +--S 254 of 546 +t0443:= tan(x)^2/(a+a*cos(x)) +--R +--R +--R 2 +--R tan(x) +--R (251) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 254 + +--S 255 of 546 +r0443:= -atanh(sin(x))/a+tan(x)/a +--R +--R +--R - atanh(sin(x)) + tan(x) +--R (252) ------------------------ +--R a +--R Type: Expression Integer +--E 255 + +--S 256 of 546 +a0443:= integrate(t0443,x) +--R +--R +--R (253) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) + sin(x) +--R cos(x) + 1 cos(x) + 1 +--R -------------------------------------------------------------------------- +--R a cos(x) +--R Type: Union(Expression Integer,...) +--E 256 + +--S 257 of 546 +m0443:= a0443-r0443 +--R +--R +--R (254) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R cos(x)atanh(sin(x)) - cos(x)tan(x) + sin(x) +--R / +--R a cos(x) +--R Type: Expression Integer +--E 257 + +--S 258 of 546 +d0443:= D(m0443,x) +--R +--R +--R (255) +--R 2 4 4 3 2 2 4 +--R - cos(x) sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sin(x) - cos(x) +--R + +--R 3 2 +--R - 2cos(x) - cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 4 +--R sin(x) + (cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 5 3 +--R (2cos(x) + cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 4 3 2 2 +--R a cos(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 4 3 2 +--R a cos(x) + 2a cos(x) + a cos(x) +--R Type: Expression Integer +--E 258 + +--S 259 of 546 +t0444:= tan(x)^4/(a+a*cos(x)) +--R +--R +--R 4 +--R tan(x) +--R (256) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 259 + +--S 260 of 546 +r0444:= 1/2*atanh(sin(x))/a-1/2*sec(x)*tan(x)/a+1/3*tan(x)^3/a +--R +--R +--R 3 +--R 3atanh(sin(x)) + 2tan(x) - 3sec(x)tan(x) +--R (257) ----------------------------------------- +--R 6a +--R Type: Expression Integer +--E 260 + +--S 261 of 546 +a0444:= integrate(t0444,x) +--R +--R +--R (258) +--R 3 sin(x) + cos(x) + 1 3 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 +--R (- 2cos(x) - 3cos(x) + 2)sin(x) +--R / +--R 3 +--R 6a cos(x) +--R Type: Union(Expression Integer,...) +--E 261 + +--S 262 of 546 +m0444:= a0444-r0444 +--R +--R +--R (259) +--R 3 sin(x) + cos(x) + 1 3 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 3 3 3 +--R - 3cos(x) atanh(sin(x)) - 2cos(x) tan(x) + 3cos(x) sec(x)tan(x) +--R + +--R 2 +--R (- 2cos(x) - 3cos(x) + 2)sin(x) +--R / +--R 3 +--R 6a cos(x) +--R Type: Expression Integer +--E 262 + +--S 263 of 546 +d0444:= D(m0444,x) +--R +--R +--R (260) +--R 4 4 6 5 4 2 +--R - 6cos(x) sin(x) + (6cos(x) + 12cos(x) + 12cos(x) )sin(x) +--R + +--R 6 5 4 +--R - 6cos(x) - 12cos(x) - 6cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 4 4 4 +--R (6cos(x) sec(x) - 6cos(x) )sin(x) +--R + +--R 6 5 4 6 5 +--R (- 6cos(x) - 12cos(x) - 12cos(x) )sec(x) + 6cos(x) + 12cos(x) +--R + +--R 4 +--R 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 6 5 +--R (6cos(x) + 12cos(x) + 6cos(x) )sec(x) - 6cos(x) - 12cos(x) +--R + +--R 4 +--R - 6cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 +--R (- 2cos(x) - 6cos(x) + 6)sin(x) +--R + +--R 4 4 3 2 4 +--R (3cos(x) sec(x) - 6cos(x) + 7cos(x) + 12cos(x) - 12)sin(x) +--R + +--R 6 5 4 6 5 +--R (- 3cos(x) - 6cos(x) - 6cos(x) )sec(x) - 4cos(x) + 4cos(x) +--R + +--R 4 3 2 +--R 12cos(x) - 8cos(x) - 12cos(x) + 6cos(x) + 6 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 7 6 5 +--R (3cos(x) + 6cos(x) + 3cos(x) )sec(x) - 3cos(x) - 2cos(x) - 4cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) + cos(x) + 2cos(x) +--R / +--R 4 4 6 5 4 2 +--R 6a cos(x) sin(x) + (- 6a cos(x) - 12a cos(x) - 12a cos(x) )sin(x) +--R + +--R 6 5 4 +--R 6a cos(x) + 12a cos(x) + 6a cos(x) +--R Type: Expression Integer +--E 263 + +--S 264 of 546 +t0445:= cot(x)/(a+a*cos(x)) +--R +--R +--R cot(x) +--R (261) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 264 + +--S 265 of 546 +r0445:= -1/2*atanh(cos(x))/a-1/2/a/(cos(x)+1) +--R +--R +--R (- cos(x) - 1)atanh(cos(x)) - 1 +--R (262) ------------------------------- +--R 2a cos(x) + 2a +--R Type: Expression Integer +--E 265 + +--S 266 of 546 +a0445:= integrate(t0445,x) +--R +--R +--R sin(x) +--R (2cos(x) + 2)log(----------) + cos(x) - 1 +--R cos(x) + 1 +--R (263) ----------------------------------------- +--R 4a cos(x) + 4a +--R Type: Union(Expression Integer,...) +--E 266 + +--S 267 of 546 +m0445:= a0445-r0445 +--R +--R +--R sin(x) +--R 2log(----------) + 2atanh(cos(x)) + 1 +--R cos(x) + 1 +--R (264) ------------------------------------- +--R 4a +--R Type: Expression Integer +--E 267 + +--S 268 of 546 +d0445:= D(m0445,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (265) -------------------------------- +--R 2 +--R (2a cos(x) - 2a)sin(x) +--R Type: Expression Integer +--E 268 + +--S 269 of 546 +t0446:= sec(x)/(a+b*cos(x)) +--R +--R +--R sec(x) +--R (266) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 269 + +--S 270 of 546 +r0446:= -2*b*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2)+atanh(sin(x))/a +--R +--R +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R \|- b + a atanh(sin(x)) + 2b atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (267) -------------------------------------------------- +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression Integer +--E 270 + +--S 271 of 546 +a0446:= integrate(t0446,x) +--R +--R +--R (268) +--R [ +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b - a log(-------------------) - \|b - a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R b log(--------------------------------------------) +--R b cos(x) + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b - a +--R , +--R +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x) - cos(x) - 1 sin(x)\|- b + a +--R - \|- b + a log(-------------------) - 2b atan(---------------------) +--R cos(x) + 1 (b + a)cos(x) + b + a +--R / +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 271 + +--S 272 of 546 +m0446a:= a0446.1-r0446 +--R +--R +--R (269) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R b\|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +---------+ +-------+ +-------+ (b - a)tan(-) +--R | 2 2 | 2 2 | 2 2 2 +--R - \|- b + a \|b - a atanh(sin(x)) - 2b\|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a\|- b + a \|b - a +--R Type: Expression Integer +--E 272 + +--S 273 of 546 +d0446a:= D(m0446a,x) +--R +--R +--R (270) +--R 3 2 6 +--R (- b + a b )sin(x) +--R + +--R 2 2 2 3 2 2 3 +--R (- 3a b + 2a b)cos(x) + (- b - a b - 2a b + 2a )cos(x) +--R + +--R 3 2 2 +--R 2b - 5a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 3 +--R (b - 2a b + 2a b)cos(x) + (b + 2a b - a b + 2a )cos(x) +--R + +--R 3 2 2 3 2 +--R (2b + 5a b - a b + a )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (2b + 3a b + 3a b - 2a )cos(x) - b + 5a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- a b + a b)cos(x) + (- 2b + a b - a b + a )cos(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3b - a b )cos(x) + (- 2b - 4a b + a b - a )cos(x) +--R + +--R 3 2 2 2 +--R (- b - 2a b - a b)cos(x) - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 6 +--R (b + a b )sin(x) +--R + +--R 2 2 2 3 2 2 3 3 +--R (a b + 2a b)cos(x) + (- b + a b + 2a b + 2a )cos(x) - 2b +--R + +--R 2 2 +--R - a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 3 +--R (- b + 2a b + 2a b)cos(x) + (b + 2a b + 3a b + 2a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + a b + a b + a )cos(x) + (2b + a b - a b - 2a )cos(x) +--R + +--R 3 2 2 +--R b + a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (a b + a b)cos(x) + (2b + a b + a b + a )cos(x) +--R + +--R 3 2 3 3 2 3 2 +--R (b + a b )cos(x) + (- 2b - a b - a )cos(x) +--R + +--R 3 2 2 2 +--R (- b - 2a b - a b)cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (3b - 2a b - 3a b + 2a b)cos(x) + b + 2a b - 3a b - 2a b +--R + +--R 4 +--R 2a +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (b - 2a b - a b + 2a b)cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b + a b - a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (- 6b + 3a b + 5a b - 3a b + a )cos(x) - 2b - 2a b + 4a b +--R + +--R 3 4 +--R 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 3 4 +--R (b - a b - a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + a b - 2a b - a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b + a b - 2a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 2 2 +--R (3b - a b - 2a b + a b - a )cos(x) + b - a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 4 3 2 2 3 4 +--R ((- b - 2a b + a b + 2a b)cos(x) - b - 2a b - a b + 2a b + 2a ) +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (- 3b - 2a b + 3a b + 2a b)cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b - 3a b + 3a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 4 +--R (2b + a b - 3a b - a b + a )cos(x) + 2b + 2a b - 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - a b + a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b - a b - 2a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b + a b - 2a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 2 2 +--R (- b + a b + 2a b - a b - a )cos(x) - b + a b +--R * +--R sin(x) +--R / +--R 2 2 3 2 3 2 2 3 4 2 2 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b +--R + +--R 3 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 2 2 3 4 2 3 4 +--R (- 2a b - a b + a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 2 2 3 +--R - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 4 2 3 2 2 3 4 2 2 3 +--R (2a b - 2a )cos(x) + (a b + a b - a b - a )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 2 3 4 2 2 +--R (- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) - a b +--R + +--R 3 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (2a b + 5a b + 5a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2a b + 4a b + 4a b + 2a )cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 5 +--R ((- a b + a b + a b - a b)cos(x) - a b + a b + a b - a )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 5 +--R (2a b - 4a b + 2a )cos(x) + 2a b - 2a b - 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (- a b - a b + 3a b + a b - 2a )cos(x) - a b + a b + a b - a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 5 +--R ((a b + a b - a b - a b)cos(x) + a b + a b - a b - a )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 4 2 3 4 5 2 3 3 2 4 5 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) - 2a b - 2a b + 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (a b + 3a b + a b - 3a b - 2a )cos(x) + a b + a b - a b - a +--R * +--R sin(x) +--R Type: Expression Integer +--E 273 + +--S 274 of 546 +m0446b:= a0446.2-r0446 +--R +--R +--R (271) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) - cos(x) - 1 | 2 2 +--R - \|- b + a log(-------------------) - \|- b + a atanh(sin(x)) +--R cos(x) + 1 +--R + +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R sin(x)\|- b + a 2 +--R - 2b atan(---------------------) - 2b atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression Integer +--E 274 + +--S 275 of 546 +d0446b:= D(m0446b,x) +--R +--R +--R (272) +--R 2 2 6 +--R (- b + 3a b - 2a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R ((2b + 4a b - 4a )cos(x) + (5b + 4a b - 5a )cos(x) + 3b - a b) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- b + a b - 2a )cos(x) + (- 6b + 4a b - 6a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 12b - 2a )cos(x) + (- 10b - 6a b + 4a )cos(x) - 3b - 3a b +--R + +--R 2 +--R 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 3 +--R (b - a )cos(x) + (5b - a b - 2a )cos(x) + (10b - 2a b)cos(x) +--R + +--R 2 2 2 2 2 2 +--R (10b + 2a )cos(x) + (5b + 2a b + a )cos(x) + b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 6 +--R (- b - a b - 2a )sin(x) +--R + +--R 2 2 2 2 2 2 4 +--R ((2b - 4a b - 4a )cos(x) + (3b - 6a b - 5a )cos(x) + 3b - a b)sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- b - 3a b - 2a )cos(x) + (- 2b - 8a b - 6a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 4b - 4a b - 2a )cos(x) + (- 6b + 2a b + 4a )cos(x) - 3b + a b +--R + +--R 2 +--R 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (- b - 2a b - a )cos(x) + (- 3b - 5a b - 2a )cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2b - 2a b)cos(x) + (2b + 4a b + 2a )cos(x) +--R + +--R 2 2 2 +--R (3b + 4a b + a )cos(x) + b + a b +--R / +--R 2 2 3 6 +--R (a b - 2a b + a )sin(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) - 3a b + 4a b +--R + +--R 3 +--R - a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 3 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 2 2 3 2 2 2 3 2 +--R (8a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) + 3a b +--R + +--R 2 3 +--R - 2a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 6a b + 6a )cos(x) + (- 4a b + 4a )cos(x) - a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 6 +--R (- a b + a )sin(x) +--R + +--R 2 2 2 2 2 2 2 3 4 +--R ((2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) + 3a b + 2a b - a )sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 8a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 +--R - 3a b - 4a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 2 2 2 3 2 2 +--R (6a b + 12a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) + a b + 2a b +--R + +--R 3 +--R a +--R Type: Expression Integer +--E 275 + +--S 276 of 546 +t0447:= sec(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R sec(x) +--R (273) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 276 + +--S 277 of 546 +r0447:= 2*b^2*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)-b*atanh(sin(x))/a^2+tan(x)/a +--R +--R +--R (274) +--R x +--R +---------+ (b - a)tan(-) +---------+ +--R | 2 2 2 2 | 2 2 +--R - b\|- b + a atanh(sin(x)) - 2b atan(-------------) + a tan(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 277 + +--S 278 of 546 +a0447:= integrate(t0447,x) +--R +--R +--R (275) +--R [ +--R +-------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R b cos(x)log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R | 2 2 +--R a sin(x)\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R a cos(x)\|b - a +--R , +--R +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +---------+ +--R 2 sin(x)\|- b + a | 2 2 +--R 2b cos(x)atan(---------------------) + a sin(x)\|- b + a +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a cos(x)\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 278 + +--S 279 of 546 +m0447a:= a0447.1-r0447 +--R +--R +--R (276) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 2 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R b cos(x)\|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b cos(x)\|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2b cos(x)\|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (- a cos(x)tan(x) + a sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a cos(x)\|- b + a \|b - a +--R Type: Expression Integer +--E 279 + +--S 280 of 546 +d0447a:= D(m0447a,x) +--R +--R +--R (277) +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b + a b)cos(x) + (- a b + a b - a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 3 4 3 +--R (2a b + a b - a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 3 2 +--R (2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 4 4 3 2 2 3 4 3 +--R (- 2a b + 2a )cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 2a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (a b + 3a b + 3a b + a )cos(x) + (a b + a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 3 2 +--R (b - a b + a b - a b)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (a b - a b + a b - a )cos(x) + a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 2 2 3 4 3 +--R (3a b - 3a b + a b)cos(x) + (b + a b - a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b + 3a b - 3a b + a b + 2a )cos(x) +--R + +--R 3 4 2 2 3 +--R (- 2a b + 2a )cos(x) - 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- b + 2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - 2a b + a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 5a b + 2a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b - 2a b + a b - a )cos(x) +--R + +--R 4 3 2 2 4 2 +--R (b - 3a b + 2a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (a b + a b - a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 2 2 3 6 +--R (a b - a b )cos(x) + (2b - a b + a b - a b)cos(x) +--R + +--R 4 3 5 4 3 2 2 3 4 +--R (3b + a b )cos(x) + (2b + 4a b - a b + a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 +--R (b + 2a b + a b )cos(x) + a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b - a b - a b - a b)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - a b - a b - a )cos(x) - a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 2 2 3 4 3 +--R (- a b - a b + a b)cos(x) + (b + a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b + 3a b + 5a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2a b + 4a b + 4a b + 2a )cos(x) + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (b - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - 2a b - 3a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - a b - 2a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b - 2a b - a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 3a b - 2a b - 4a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 2 2 3 6 +--R (- a b - a b )cos(x) + (- 2b - a b - a b - a b)cos(x) +--R + +--R 4 3 5 4 2 2 3 4 +--R (- b - a b )cos(x) + (2b + a b + a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 +--R (b + 2a b + a b )cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 3 2 4 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- a b + a b + a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 4 3 2 5 3 +--R (2a b - 4a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- a b - a b + 3a b + a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- a b + a b + a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (a b + a b - a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 4 2 3 4 5 3 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (a b + 3a b + a b - 3a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (a b + a b - a b - a )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 7 +--R ((a b - a b - a b + a b)cos(x) + a b - a b - a b + a )sin(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (3b - 3a b - 2a b + 3a b - a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (b - 2a b + a b + a b - a )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 5 +--R (- 2a b + 4a b - 2a )cos(x) - 2a b + 2a b + 2a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 2 3 3 2 5 +--R (b - 2a b - a b + 2a b )cos(x) +--R + +--R 5 4 3 2 4 4 +--R (- 2b + a b - a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 6b + 4a b + 4a b - 4a b + 2a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- 2b + 3a b - a b - a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (a b + a b - 3a b - a b + 2a )cos(x) + a b - a b - a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 2 3 3 2 6 +--R (b - a b - a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b + a b - 2a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + a b - 2a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 5 2 3 2 +--R (3b - a b - 2a b + a b - a b)cos(x) + (b - a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 7 +--R ((- a b - a b + a b + a b)cos(x) - a b - a b + a b + a )sin(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- b - a b + 2a b + a b - a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- b + 2a b + a b - a b - a )cos(x) +--R + +--R 4 2 3 4 5 2 3 3 2 4 5 +--R (2a b + 4a b - 4a b - 2a )cos(x) + 2a b + 2a b - 2a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 3b - 2a b + 3a b + 2a b )cos(x) +--R + +--R 5 4 3 2 4 4 5 2 3 4 3 +--R (- 2b - 3a b + 3a b + 2a b)cos(x) + (2b - 4a b + 2a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (2b - 3a b - a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (- a b - 3a b - a b + 3a b + 2a )cos(x) - a b - a b + a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- b - a b + a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + a b - 2a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 5 2 3 2 +--R (- b + a b + 2a b - a b - a b)cos(x) + (- b + a b )cos(x) +--R * +--R sin(x) +--R / +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 2 3 5 3 +--R (- 2a b - a b + a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 2 3 5 4 2 3 3 2 4 5 3 +--R (2a b - 2a )cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (2a b + 5a b + 5a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (2a b + 4a b + 4a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- a b - 3a b - 3a b - a )cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 3 3 4 2 5 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b - a b - a b + a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (a b + a b - 3a b - a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b - a b - a b + a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 3 3 4 2 5 3 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 2 4 3 3 5 6 3 +--R (2a b + 4a b - 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- a b - 3a b - a b + 3a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a )cos(x) +--R * +--R sin(x) +--R Type: Expression Integer +--E 280 + +--S 281 of 546 +m0447b:= a0447.2-r0447 +--R +--R +--R (278) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 2 sin(x)\|- b + a +--R b cos(x)\|- b + a atanh(sin(x)) + 2b cos(x)atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R x +--R (b - a)tan(-) +---------+ +--R 2 2 | 2 2 +--R 2b cos(x)atan(-------------) + (- a cos(x)tan(x) + a sin(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a cos(x)\|- b + a +--R Type: Expression Integer +--E 281 + +--S 282 of 546 +d0447b:= D(m0447b,x) +--R +--R +--R (279) +--R 2 2 3 2 6 +--R (- a b + 2a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (3a b - 4a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 2 3 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 8a b + 2a b + 6a )cos(x) + (- 8a b + 4a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b + 2a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (6a b - 6a )cos(x) +--R + +--R 2 3 3 2 3 2 +--R (4a b - 4a )cos(x) + (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 6 +--R (a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b - 2a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (8a b + 14a b + 6a )cos(x) + (8a b + 12a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (3a b + 4a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 6a b - 12a b - 6a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b - 2a b - a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 8 +--R (a b - 2a b + a )sin(x) +--R + +--R 3 2 2 2 2 2 2 +--R (b - 5a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) - 3a b +--R + +--R 2 3 +--R 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 3 2 3 3 +--R (- 2b - 3a b + 4a b - a )cos(x) + (- 5b + 5a b - 4a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b + 9a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 +--R 3a b - 2a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (b - a b + 2a b)cos(x) + (6b - 4a b + 6a b)cos(x) +--R + +--R 3 2 2 3 4 +--R (12b - a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 3 +--R (10b + 2a b - 4a b + 4a )cos(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (3b - 3a b - 2a b + 6a )cos(x) + (- 4a b + 4a )cos(x) - a b +--R + +--R 3 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 3 2 2 6 +--R (- b + a b)cos(x) + (- 5b + a b + 2a b)cos(x) +--R + +--R 3 2 5 3 2 4 +--R (- 10b + 2a b )cos(x) + (- 10b - 2a b)cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 5b - 2a b - a b)cos(x) + (- b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 8 +--R (- a b + a )sin(x) +--R + +--R 3 2 2 2 2 2 2 2 3 +--R ((b + 3a b + 4a b)cos(x) + (4a b + 4a b)cos(x) + 3a b + 2a b - a ) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 3a b + 2a b - a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 3b + 2a b - 3a b - 4a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b - 7a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 +--R - 3a b - 4a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (b + 3a b + 2a b)cos(x) + (2b + 8a b + 6a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (4b + 5a b + 4a b + a )cos(x) + (6b + 2a b + 4a b + 4a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (3b + 5a b + 10a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 +--R a b + 2a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 3 2 2 6 +--R (b + 2a b + a b)cos(x) + (3b + 5a b + 2a b)cos(x) +--R + +--R 3 2 5 3 2 2 4 +--R (2b + 2a b )cos(x) + (- 2b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 3b - 4a b - a b)cos(x) + (- b - a b )cos(x) +--R / +--R 2 2 3 4 2 6 +--R (a b - 2a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b + 4a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (8a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b - 2a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 6a b + 6a )cos(x) + (- 4a b + 4a )cos(x) + (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 6 +--R (- a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b + 2a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (- 8a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b - 4a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (6a b + 12a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (a b + 2a b + a )cos(x) +--R Type: Expression Integer +--E 282 + +--S 283 of 546 +t0448:= sec(x)^3/(a+b*cos(x)) +--R +--R +--R 3 +--R sec(x) +--R (280) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 283 + +--S 284 of 546 +r0448:= -2*b^3*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)+1/2*atanh(sin(x))/a+b^2*atanh(sin(x))/a^3-b*tan(x)/a^2+1/2*sec(x)*tan(x)/a +--R +--R +--R (281) +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 3 2 +--R (2b + a )\|- b + a atanh(sin(x)) + 4b atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (a sec(x) - 2a b)tan(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression Integer +--E 284 + +--S 285 of 546 +a0448:= integrate(t0448,x) +--R +--R +--R (282) +--R [ +--R +-------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 3 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R 2b cos(x) log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + a )sin(x)\|b - a +--R / +--R +-------+ +--R 3 2 | 2 2 +--R 2a cos(x) \|b - a +--R , +--R +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 3 2 sin(x)\|- b + a +--R - 4b cos(x) atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + a )sin(x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2a cos(x) \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 285 + +--S 286 of 546 +m0448a:= a0448.1-r0448 +--R +--R +--R (283) +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 3 2 | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R 2b cos(x) \|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 +--R (- 2b - a )cos(x) \|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R - 4b cos(x) \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R ((- a cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a )sin(x)) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R 2a cos(x) \|- b + a \|b - a +--R Type: Expression Integer +--E 286 + +--S 287 of 546 +d0448a:= D(m0448a,x) +--R +--R +--R (284) +--R 3 2 4 5 +--R (- 2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 3 2 4 3 +--R (- 2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (2a b - 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 +--R (2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (4a b + 2a b - 2a b - 4a )cos(x) +--R + +--R 2 3 5 4 3 2 4 3 +--R (4a b - 4a )cos(x) + (4a b - 4a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 2a b + 2a b + 4a b)cos(x) +--R + +--R 4 4 4 2 3 3 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 +--R (- 2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 2 3 5 5 +--R (- 4a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 3 2 4 3 +--R (- 2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 4 4 5 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 5 +--R (2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (2a b + 2a b + 2a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 2a b - 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 +--R (- 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 2a b - 6a b - 6a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 4a b - 10a b - 10a b - 4a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 4a b - 8a b - 8a b - 4a )cos(x) +--R + +--R 3 2 4 3 +--R (- 4a b - 4a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (2a b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b + 10a b + 10a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (4a b + 8a b + 8a b + 4a b)cos(x) + (4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (2a b + 2a b)cos(x) + (2a b + 6a b + 6a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (4a b + 8a b + 8a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (2a b + 6a b + 6a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 8a b - 8a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 2b + 2a b - 2a b + 2a b )cos(x) +--R + +--R 4 2 3 2 4 5 3 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a )cos(x) + 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (- a b + a b)cos(x) + (- a b + a b - a b + a )cos(x) +--R + +--R 3 2 4 3 +--R (- a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 6a b + 6a b - 4a b + 2a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 2b - 4a b + 3a b - 3a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (4b - 6a b + 5a b - 7a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (4a b - 4a b - a b - 3a b + 4a )cos(x) +--R + +--R 3 2 5 3 2 4 +--R (- 4a b + 4a )cos(x) - 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 5 2 3 5 4 +--R (2a b + a b - a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 4 3 +--R (2a b - 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (2b - 4a b + 4a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (2b + 4a b - 4a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (4b + 10a b - 6a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (4b + 4a b + 4a b - 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 2b + 6a b - 4a b + 4a b )cos(x) +--R + +--R 4 2 3 4 5 2 +--R (- 2a b + 2a b + 4a b - 4a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (4a b - 2a b - 2a )cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 3 5 5 2 3 3 2 4 5 4 +--R (- 2a b + 2a )cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 2 4 3 +--R (- a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (- 2a b + 2a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 4b + 2a b - 3a b + 3a b - a b + a )cos(x) +--R + +--R 5 4 3 2 4 6 +--R (- 6b - 2a b + a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (- 4b - 8a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 2b - 4a b + a b - a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 4 2 +--R (- 2a b + a b + a b - a b - a )cos(x) + (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 3 4 2 3 2 +--R (2b + 2a b + 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 4 5 3 2 4 +--R (- 2a b - 2a )cos(x) - 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 3 2 4 3 +--R (a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 4 5 5 3 2 4 5 4 +--R (2a b + 2a b + 2a b)cos(x) + (- 2b + a b + a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4b - 6a b - 5a b - 3a b + 3a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 4a b - 4a b + a b + 5a b + 4a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (4a b + 8a b + 4a )cos(x) + 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 2a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 2b + 4a b + 4a b + 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (2b + 4a b + 8a b + 8a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b + 2a b + 6a b + 8a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (4b + 4a b + 4a b + 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (2b + 6a b + 4a b + 4a b )cos(x) +--R + +--R 4 2 3 4 5 2 +--R (2a b + 2a b - 4a b - 4a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (- 4a b - 6a b - 2a )cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (a b + 3a b + 3a b + a )cos(x) + (a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (2a b + 2a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (4b + 2a b + 3a b + 3a b + a b + a )cos(x) +--R + +--R 5 4 3 2 4 6 +--R (2b + 2a b - a b - a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 4b - 4a b - 6a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 2b - 4a b - 4a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 4 2 +--R (- 2a b - a b - 3a b - 3a b - a )cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 3 3 4 2 5 4 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 4a b + 2a b + 6a b - 2a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 4a b + 8a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 4a b + 4a b + 4a b - 4a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (4a b - 2a b - 6a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (4a b - 8a b + 4a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (4a b - 4a b - 4a b + 4a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (4a b - 2a b - 6a b + 2a b + 2a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2a b + 2a b - 6a b - 2a b + 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 4a b + 2a b + 6a b - 2a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 2a b - 2a b + 6a b + 2a b - 4a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (4a b + 6a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 2 4 3 3 5 6 4 +--R (4a b + 8a b - 8a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (4a b + 4a b - 4a b - 4a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 4a b - 6a b + 2a b + 6a b + 2a b)cos(x) +--R + +--R 5 2 4 4 2 5 4 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 4a b - 4a b + 4a b + 4a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 4a b - 6a b + 2a b + 6a b + 2a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2a b - 6a b - 2a b + 6a b + 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (4a b + 6a b - 2a b - 6a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (2a b + 6a b + 2a b - 6a b - 4a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 2 4 3 3 4 2 2 3 3 4 2 5 +--R (2a b - 2a b - 2a b + 2a b )cos(x) - 2a b + 2a b + 2a b +--R + +--R 6 +--R - 2a +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (a b - a b - a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (6b - 6a b - 2a b + 4a b - 4a b + 2a b)cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (2b - 3a b + 3a b - a b - 3a b + 2a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 4a b + 4a b + 5a b - 5a b - a b + a )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (4a b - 4a b - 4a b + 4a )cos(x) + 4a b - 4a b - 4a b + 4a +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 3 3 4 2 5 6 +--R (2b - 4a b + 2a b - 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 +--R (- 4b + 2a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b + 8a b + 8a b - 6a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 3 +--R (- 4b + 6a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (- 4a b + 4a b + 4a b - 4a )cos(x) - 2a b + 2a b + 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (a b + a b - 3a b - a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (a b - a b - a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (2b - 2a b - a b + a b - a b + a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b + 2a b - 4a b - a b + a b - a b + a )cos(x) +--R + +--R 6 5 2 4 4 2 5 5 +--R (4b + 2a b - 6a b + 2a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 4 +--R (6b - 2a b - 6a b + 2a b + 2a b - 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (2b - 3a b - a b + 3a b + a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- a b + a b + a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 3 3 4 2 2 3 3 4 2 5 6 +--R ((- 2a b - 2a b + 2a b + 2a b )cos(x) + 2a b + 2a b - 2a b - 2a ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- a b - a b + a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 5 4 +--R (- 2b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (- 2b + 3a b - a b - 3a b + a b + 2a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (4a b + 4a b - 5a b - 5a b + a b + a )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (- 4a b - 4a b + 4a b + 4a )cos(x) - 4a b - 4a b + 4a b + 4a +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 2 4 3 3 5 6 4 +--R (2a b + 4a b - 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b - 4a b + 4a b + 2a b + 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 4b - 6a b - 2a b + 2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b - 2a b + 2a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 3 +--R (4b - 6a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (4a b + 4a b - 4a b - 4a )cos(x) + 2a b + 2a b - 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- a b - 3a b - a b + 3a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- a b - a b + a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 2b - 2a b + a b + a b + a b + a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b - 2a b - 4a b + a b + a b + a b + a )cos(x) +--R + +--R 6 5 2 4 4 2 5 5 +--R (4b + 2a b - 2a b - 2a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b + 2a b + 6a b + 2a b - 2a b - 4a b - 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (- 2b + 3a b + 3a b + a b - 3a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b + a b - a b - a )cos(x) +--R * +--R sin(x) +--R / +--R 4 2 5 5 3 3 4 2 5 6 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b + 2a b - 2a )cos(x) +--R + +--R 4 2 5 3 +--R (2a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 7 +--R (- 2a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 4a b - 2a b + 2a b + 4a )cos(x) +--R + +--R 3 3 6 4 4 2 5 3 +--R (- 4a b + 4a )cos(x) + (- 4a b + 4a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 7 3 3 4 2 5 6 6 +--R (2a b - 2a b)cos(x) + (2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 3 3 6 5 3 3 4 2 5 6 4 +--R (4a b - 4a )cos(x) + (2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 4 2 5 3 +--R (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 3 3 4 2 5 6 4 +--R (- 2a b - 2a b)cos(x) + (- 2a b - 2a b - 2a b - 2a )cos(x) +--R + +--R 4 2 5 3 +--R (- 2a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 7 3 3 4 2 5 6 6 +--R (2a b + 2a b)cos(x) + (2a b + 6a b + 6a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (4a b + 10a b + 10a b + 4a )cos(x) +--R + +--R 3 3 4 2 5 6 4 4 2 5 3 +--R (4a b + 8a b + 8a b + 4a )cos(x) + (4a b + 4a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 7 3 3 4 2 5 6 6 +--R (- 2a b - 2a b)cos(x) + (- 2a b - 6a b - 6a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 4a b - 8a b - 8a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 4 4 2 5 3 +--R (- 2a b - 6a b - 6a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (4a b - 2a b - 6a b + 2a b + 2a )cos(x) +--R + +--R 3 4 5 2 7 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 4a )cos(x) + (4a b - 4a b - 4a b + 4a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (- 4a b + 2a b + 6a b - 2a b - 2a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 2a b - 2a b + 6a b + 2a b - 4a )cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 5 2 6 4 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (- 4a b - 6a b + 2a b + 6a b + 2a )cos(x) +--R + +--R 3 4 4 3 6 7 4 +--R (- 4a b - 8a b + 8a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 4a b - 4a b + 4a b + 4a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (4a b + 6a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (2a b + 6a b + 2a b - 6a b - 4a )cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R sin(x) +--R Type: Expression Integer +--E 287 + +--S 288 of 546 +m0448b:= a0448.2-r0448 +--R +--R +--R (285) +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- 2b - a )cos(x) \|- b + a atanh(sin(x)) +--R + +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 3 2 sin(x)\|- b + a 3 2 2 +--R - 4b cos(x) atan(---------------------) - 4b cos(x) atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R ((- a cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a )sin(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2a cos(x) \|- b + a +--R Type: Expression Integer +--E 288 + +--S 289 of 546 +d0448b:= D(m0448b,x) +--R +--R +--R (286) +--R 2 2 3 4 3 +--R (- 2a b + 4a b - 2a )cos(x) sec(x) +--R + +--R 3 2 2 3 3 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (6a b - 8a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 6a b + 8a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 +--R (- 2a b + 2a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 16a b + 4a b + 12a )cos(x) +--R + +--R 2 2 3 4 4 +--R (- 16a b + 8a b + 8a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- 6a b + 4a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (16a b - 4a b - 12a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (16a b - 8a b - 8a b)cos(x) + (6a b - 4a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 +--R (2a b - 2a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 2 2 4 5 2 2 4 4 +--R (12a b - 12a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 2 2 4 3 +--R (2a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (- 12a b + 12a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 3 3 +--R (- 2a b + 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 3 3 3 6 +--R ((2a b - 2a )cos(x) sec(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (- 4a b - 4a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (- 6a b - 4a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (4a b + 4a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 3 2 2 3 3 +--R (6a b + 4a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (2a b + 4a b + 2a )cos(x) + (8a b + 16a b + 8a )cos(x) +--R + +--R 2 2 3 4 5 +--R (16a b + 28a b + 12a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (16a b + 24a b + 8a )cos(x) + (6a b + 8a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 +--R (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8a b - 16a b - 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 16a b - 28a b - 12a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (- 16a b - 24a b - 8a b)cos(x) + (- 6a b - 8a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (- 2a b - 4a b - 2a )cos(x) + (- 8a b - 16a b - 8a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (- 12a b - 24a b - 12a )cos(x) + (- 8a b - 16a b - 8a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- 2a b - 4a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 3 2 2 3 6 +--R (2a b + 4a b + 2a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 5 3 2 2 3 4 +--R (12a b + 24a b + 12a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 2 3 4 8 +--R ((- 2a b + 4a b - 2a b)cos(x) + 2a b - 4a b + 2a )sin(x) +--R + +--R 2 2 3 4 3 +--R (- a b + 2a b - a )cos(x) sec(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b + 10a b - 10a b + 4a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (8a b - 11a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R (6a b - 16a b + 10a b)cos(x) - 6a b + 8a b - 2a +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (3a b - 4a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b + 6a b - 8a b + 6a b - 4a )cos(x) +--R + +--R 4 2 2 3 4 4 +--R (10b - 7a b + 12a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b - 18a b + 12a b + 12a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 16a b + 21a b + 8a b - 13a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 4 +--R (- 6a b + 20a b - 6a b - 8a )cos(x) + 6a b - 4a b - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (- 8a b + 2a b + 6a )cos(x) + (- 8a b + 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- 3a b + 2a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 4 7 +--R (- 2b + 2a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 12b + 8a b - 7a b + 2a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 24b + 2a b + 2a b - 2a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 20b - 4a b + 12a b - 12a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 6b + 6a b + 2a b - 16a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (8a b - 9a b - 10a b + 11a )cos(x) +--R + +--R 3 2 2 3 4 2 2 4 +--R (2a b - 8a b - 2a b + 8a )cos(x) - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 2 2 4 5 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (6a b - 6a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 +--R (4a b - 4a )cos(x) + (a b - a )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 2 4 8 4 3 2 2 4 7 +--R (2b - a b - a )cos(x) + (10b - 2a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 4 6 4 2 2 4 5 +--R (20b - 4a b - a b + a )cos(x) + (20b - 2a b + 6a )cos(x) +--R + +--R 4 3 2 2 4 4 +--R (10b + 4a b - 5a b + 7a )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 4 2 +--R (2b + 2a b - 4a b + 4a )cos(x) + (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 4 8 +--R ((2a b - 2a b)cos(x) - 2a b + 2a )sin(x) +--R + +--R 2 2 4 3 4 3 2 2 4 3 +--R (a b - a )cos(x) sec(x) + (- 2b - 6a b - 6a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 8a b - 5a b + 4a b + a )cos(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R (- 6a b + 4a b + 10a b)cos(x) + 6a b + 4a b - 2a +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (- 3a b - 2a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b - 6a b - 4a b - 2a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b - 4a b + 3a b - 2a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b + 14a b + 20a b - 4a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (16a b + 11a b - 18a b - 13a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 4 +--R (6a b - 8a b - 22a b - 8a )cos(x) - 6a b - 8a b - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (8a b + 14a b + 6a )cos(x) + (8a b + 12a b + 4a )cos(x) +--R + +--R 2 2 3 4 3 +--R (3a b + 4a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 2b - 6a b - 6a b - 4a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 16a b - 17a b - 12a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 8b - 10a b - 14a b - 14a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 12b - 4a b - 12a b - 12a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 6b - 10a b - 18a b - 4a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 8a b - 7a b + 12a b + 11a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 4 +--R (- 2a b + 4a b + 14a b + 8a )cos(x) + 2a b + 4a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (- 6a b - 12a b - 6a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- a b - 2a b - a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b - 4a b - 3a b - 2a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 6b - 10a b - 6a b - 4a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 4a b + a b + 2a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b + 8a b + 10a b + 12a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b + 8a b + 9a b + 14a b + 7a )cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 4 2 +--R (2b + 2a b + 4a b + 8a b + 4a )cos(x) + (a b + 2a b + a )cos(x) +--R / +--R 3 2 4 5 3 6 +--R (2a b - 4a b + 2a )cos(x) sin(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (- 4a b + 4a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 2 4 5 3 +--R (- 6a b + 8a b - 2a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 7 3 2 5 6 +--R (2a b - 2a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (16a b - 4a b - 12a )cos(x) + (16a b - 8a b - 8a )cos(x) +--R + +--R 3 2 4 5 3 +--R (6a b - 4a b - 2a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 7 3 2 5 6 +--R (- 2a b + 2a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 12a b + 12a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 3 2 5 3 +--R (- 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 3 6 +--R (- 2a b + 2a )cos(x) sin(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (4a b + 4a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 3 2 4 5 3 +--R (6a b + 4a b - 2a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 5 7 3 2 4 5 6 +--R (- 2a b - 4a b - 2a )cos(x) + (- 8a b - 16a b - 8a )cos(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (- 16a b - 28a b - 12a )cos(x) + (- 16a b - 24a b - 8a )cos(x) +--R + +--R 3 2 4 5 3 +--R (- 6a b - 8a b - 2a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 7 3 2 4 5 6 +--R (2a b + 4a b + 2a )cos(x) + (8a b + 16a b + 8a )cos(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (12a b + 24a b + 12a )cos(x) + (8a b + 16a b + 8a )cos(x) +--R + +--R 3 2 4 5 3 +--R (2a b + 4a b + 2a )cos(x) +--R Type: Expression Integer +--E 289 + +--S 290 of 546 +t0449:= sec(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R sec(x) +--R (287) ------------ +--R b cos(x) + a +--R Type: Expression Integer +--E 290 + +--S 291 of 546 +r0449:= 2*b^4*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)-1/2*b*atanh(sin(x))/a^2-b^3*atanh(sin(x))/a^4+tan(x)/a+b^2*tan(x)/a^3-1/2*b*sec(x)*tan(x)/a^2+1/3*tan(x)^3/a +--R +--R +--R (288) +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 4 2 +--R (- 6b - 3a b)\|- b + a atanh(sin(x)) - 12b atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 2 2 3 | 2 2 +--R (2a tan(x) + (- 3a b sec(x) + 6a b + 6a )tan(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression Integer +--E 291 + +--S 292 of 546 +a0449:= integrate(t0449,x) +--R +--R +--R (289) +--R [ +--R +-------+ +--R 3 2 3 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 3 2 3 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 4 3 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 6b cos(x) log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 3 2 2 3 | 2 2 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x)\|b - a +--R / +--R +-------+ +--R 4 3 | 2 2 +--R 6a cos(x) \|b - a +--R , +--R +--R +---------+ +--R 3 2 3 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 3 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 4 3 sin(x)\|- b + a +--R 12b cos(x) atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x)\|- b + a +--R / +--R +---------+ +--R 4 3 | 2 2 +--R 6a cos(x) \|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 292 + +--S 293 of 546 +m0449a:= a0449.1-r0449 +--R +--R +--R (290) +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 4 3 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 6b cos(x) \|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 +--R (6b + 3a b)cos(x) \|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 4 3 | 2 2 2 +--R 12b cos(x) \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 +--R - 2a cos(x) tan(x) +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b - 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 3 | 2 2 | 2 2 +--R 6a cos(x) \|- b + a \|b - a +--R Type: Expression Integer +--E 293 + +--S 294 of 546 +d0449a:= D(m0449a,x) +--R +--R +--R (291) +--R 4 2 5 6 +--R (- 6a b + 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 6a b + 6a b - 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 +--R (6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 6a b - 6a b - 12a )cos(x) +--R + +--R 3 3 6 5 4 2 5 4 +--R (12a b - 12a )cos(x) + (12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 +--R (- 6a b + 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 3 3 6 6 +--R (- 12a b + 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) + (- 6a b + 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 6 3 3 4 2 5 6 5 +--R (6a b + 6a b)cos(x) + (6a b + 6a b + 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 +--R (- 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 12a b - 30a b - 30a b - 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 2 5 4 +--R (- 12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 24a b + 24a b + 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (6a b + 18a b + 18a b + 6a )cos(x) + (6a b + 6a b)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 3 4 2 6 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b - 6a b + 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b + 6a b - 18a b + 18a b - 12a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (6a b - 6a b + 12a b - 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a )cos(x) +--R + +--R 5 2 4 3 3 5 6 6 +--R (12a b + 6a b + 18a b - 12a b - 24a )cos(x) +--R + +--R 5 3 3 4 2 6 5 +--R (12a b + 24a b - 12a b - 24a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (12a b - 12a b + 24a b - 24a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 2 4 5 6 +--R (12a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (- 6a b - 6a b - 6a b - 6a b + 12a b + 12a )cos(x) +--R + +--R 5 3 3 4 2 6 6 +--R (- 12a b - 24a b + 12a b + 24a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 6a b - 6a b - 6a b + 12a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 6 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 6a b - 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (6a b + 6a b + 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (6a b + 6a b + 18a b + 18a b + 12a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (6a b + 6a b + 12a b + 12a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (12a b + 30a b + 30a b + 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (12a b + 24a b + 24a b + 12a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (- 6a b - 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6a b + 6a b - 6a b + 4a b - 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b + 4a b - 4a b + 4a b - 4a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (4a b - 4a b)cos(x) + (6a b - 6a )cos(x) + 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (3a b - 3a b + 3a b - 3a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (18a b - 18a b + 12a b - 12a b + 6a b)cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 5 +--R (6b + 12a b - 15a b + 7a b - 4a b + 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 18a b - 15a b + 13a b - 13a b + 7a b + 8a ) +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 12a b + 12a b - 9a b + a b - 4a b + 12a )cos(x) +--R + +--R 4 2 6 2 4 2 6 4 2 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a )cos(x) - 12a b +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 3a b + 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b - 3a b + 3a b + 6a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (- 6b + 12a b - 12a b + 6a b - 4a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b - 12a b + 12a b - 10a b + 2a b - 8a b - 2a ) +--R * +--R 7 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b - 30a b + 18a b - 8a b + 4a b - 10a b - 4a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b - 12a b - 12a b + 18a b - 10a b - 2a b - 6a ) +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b - 18a b + 12a b - 8a b + 8a b - 8a b - 4a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b + 6a b - 2a b + 2a b - 6a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 +--R (6a b + 6a b - 12a )cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 4 2 5 +--R 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 2 4 5 6 +--R (3a b + 3a b - 3a b - 3a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (3a b + 3a b - 3a b - 3a b)cos(x) + (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (6a b - 6a b + 3a b - 3a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (12b - 6a b + 9a b - 9a b + a b - a b)cos(x) +--R + +--R 6 5 3 3 4 2 5 6 7 +--R (18b + 6a b - 5a b + a b + 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (12b + 24a b - 12a b + 2a b + 2a b + 4a b + 4a )cos(x) +--R + +--R 6 5 3 3 4 2 5 5 +--R (6b + 12a b - 3a b + 3a b + 6a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6a b - 3a b + a b + a b + 5a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 4 2 5 2 +--R (- a b + 5a b - 2a b - 2a )cos(x) + (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 6b - 6a b - 6a b - 6a b - 4a b - 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6a b - 6a b - 4a b - 4a b - 4a b - 4a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (- 4a b - 4a b)cos(x) + (- 6a b - 6a )cos(x) - 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (- 3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 3a b - 3a b - 3a b - 3a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 5 6 +--R (- 6a b - 6a b + 6a b)cos(x) +--R + +--R 6 3 3 4 2 5 6 5 +--R (6b + 3a b + 11a b + 8a b + 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (12b + 18a b + 15a b + 17a b + 17a b + 23a b + 8a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (12a b + 12a b + 9a b + 17a b + 20a b + 12a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 +--R (12a b + 24a b + 12a )cos(x) + (12a b + 24a b + 12a )cos(x) +--R + +--R 4 2 5 +--R 12a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (3a b + 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (3a b + 9a b + 9a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (6a b + 15a b + 15a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b + 12a b + 12a b + 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (6b - 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36a b + 24a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (12a b - 12a b + 12a b - 12a b - 24a b + 24a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (6a b - 6a b - 6a b + 6a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (12a b - 6a b - 18a b + 6a b + 6a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (6a b + 6a b - 18a b - 6a b + 12a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (6a b - 6a b - 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 6a b + 6a b - 6a b + 6a b + 12a b - 12a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12a b + 6a b - 6a b + 6a b + 30a b - 12a b - 12a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 6a b - 6a b + 6a b - 6a b + 24a b + 12a b - 24a ) +--R * +--R 5 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (- 6a b + 6a b - 6a b + 6a b + 12a b - 12a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 5 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (6a b + 6a b - 6a b - 6a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (12a b + 18a b - 6a b - 18a b - 6a b)cos(x) +--R + +--R 2 5 3 4 5 2 6 5 +--R (12a b + 24a b - 24a b - 12a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (12a b + 12a b - 12a b - 12a b)cos(x) +--R * +--R sec(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 6a b - 6a b - 6a b - 6a b + 12a b + 12a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12a b - 18a b - 18a b - 18a b + 18a b + 36a b + 12a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12a b - 24a b - 24a b - 24a b + 12a b + 48a b + 24a ) +--R * +--R 5 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (- 12a b - 12a b - 12a b - 12a b + 24a b + 24a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 12a b - 18a b + 6a b + 18a b + 6a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (- 6a b - 18a b - 6a b + 18a b + 12a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (12a b + 18a b + 18a b + 18a b - 18a b - 36a b - 12a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 6 7 5 +--R (6a b + 18a b + 18a b + 18a b - 36a b - 24a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (6a b - 6a b - 2a b + 2a b - 4a b + 4a b)cos(x) +--R + +--R 4 3 5 2 6 7 2 4 3 5 2 6 7 +--R (4a b - 4a b - 4a b + 4a )cos(x) + 6a b - 6a b - 6a b + 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (3a b - 3a b - 3a b + 3a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 5 +--R (18b - 18a b - 6a b + 6a b - 6a b + 12a b - 6a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (6b - 9a b + a b - a b + 5a b + 4a b - 6a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (- 12a b + 12a b + 3a b - 11a b + 17a b - a b - 8a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (- 12a b + 12a b + 12a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 +--R (- 12a b + 12a b + 12a b - 12a )cos(x) - 12a b + 12a b +--R + +--R 6 7 +--R 12a b - 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (- 3a b + 3a b + 3a b - 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 6a b + 3a b + 9a b - 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 6a b + 6a b + 6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 3 4 4 3 5 2 6 7 +--R (6b - 12a b + 8a b - 8a b + 4a b + 2a b)cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12b + 6a b + 6a b - 2a b - 2a b - 6a b + 8a b + 2a ) +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 36b + 24a b + 24a b - 12a b + 4a b - 16a b + 8a b +--R + +--R 7 +--R 4a +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (- 12b + 18a b - 2a b - 4a b - 4a b - 2a b + 6a )cos(x) +--R + +--R 6 2 5 4 3 5 2 6 7 3 +--R (6a b - 6a b + 4a b - 10a b + 2a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (12a b - 12a b - 12a b + 12a )cos(x) + 6a b - 6a b - 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (3a b - 3a b - 3a b + 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (6a b - 3a b - 9a b + 3a b + 3a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (3a b + 3a b - 9a b - 3a b + 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 8 +--R (6b - 6a b - 3a b + 3a b - 3a b + 3a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (6b + 6a b - 12a b - 5a b + 5a b - a b + a b)cos(x) +--R + +--R 7 6 2 5 3 4 4 3 6 7 6 +--R (12b + 6a b - 18a b - 4a b + 8a b - 2a b - 2a )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (18b - 6a b - 18a b + 6a b + 2a b + 4a b - 2a b - 4a ) +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 4 +--R (6b - 9a b + a b + 5a b - a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- a b + 5a b - 3a b - 5a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (- 6a b - 6a b + 2a b + 2a b + 4a b + 4a b)cos(x) +--R + +--R 4 3 5 2 6 7 2 4 3 5 2 6 7 +--R (- 4a b - 4a b + 4a b + 4a )cos(x) - 6a b - 6a b + 6a b + 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 3a b - 3a b + 3a b + 3a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 6 5 +--R (- 6b - 6a b + 6a b + 6a b + 6a b - 6a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (- 6b + 9a b + 5a b + 5a b + a b - 8a b - 6a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (12a b + 12a b - 3a b + 5a b - a b - 17a b - 8a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (12a b + 12a b - 12a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (12a b + 12a b - 12a b - 12a )cos(x) + 12a b + 12a b - 12a b - 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (3a b + 3a b - 3a b - 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (6a b + 9a b - 3a b - 9a b - 3a b)cos(x) +--R + +--R 2 5 3 4 5 2 6 5 +--R (6a b + 12a b - 12a b - 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 18b - 12a b + 12a b + 4a b + 4a b + 8a b + 2a b)cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12b - 18a b - 6a b + 2a b + 6a b + 14a b + 12a b + 2a ) +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (12b - 24a b - 12a b - 4a b + 8a b + 16a b + 4a )cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (12b - 18a b - 10a b - 4a b + 4a b + 10a b + 6a )cos(x) +--R + +--R 6 2 5 4 3 5 2 6 7 3 +--R (- 6a b - 6a b - 4a b + 2a b + 10a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (- 12a b - 12a b + 12a b + 12a )cos(x) - 6a b - 6a b + 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (- 3a b - 3a b + 3a b + 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 6a b - 9a b + 3a b + 9a b + 3a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (- 3a b - 9a b - 3a b + 9a b + 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 8 +--R (- 6b - 6a b + 3a b + 3a b + 3a b + 3a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (6b - 6a b - 12a b + 5a b + 5a b + a b + a b)cos(x) +--R + +--R 7 6 2 5 3 4 5 2 6 7 6 +--R (12b + 6a b - 6a b + 4a b - 8a b - 6a b - 2a )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 5 +--R (- 6b + 6a b + 18a b + 6a b - 2a b - 8a b - 10a b - 4a )cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 4 +--R (- 6b + 9a b + 5a b - a b - 5a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (a b - 3a b - 5a b + 3a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R sin(x) +--R / +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (6a b - 6a b)cos(x) + (6a b - 6a b + 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 +--R (- 6a b + 6a b)cos(x) +--R + +--R 4 3 5 2 6 7 7 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 6a b + 6a b + 12a )cos(x) +--R + +--R 4 3 7 5 5 2 6 4 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b - 6a b)cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 4 3 7 6 4 3 5 2 6 7 5 +--R (12a b - 12a )cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (- 6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (12a b + 30a b + 30a b + 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (12a b + 24a b + 24a b + 12a )cos(x) + (12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (- 6a b - 18a b - 18a b - 6a )cos(x) + (- 6a b - 6a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 4 5 3 6 2 7 5 +--R (6a b - 6a b - 6a b + 6a b)cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (- 6a b + 6a b + 6a b - 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (- 12a b + 6a b + 18a b - 6a b - 6a )cos(x) +--R + +--R 4 4 6 2 8 5 +--R (- 12a b + 24a b - 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 12a b + 12a b + 12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (6a b - 6a b - 6a b + 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (12a b - 6a b - 18a b + 6a b + 6a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 5 +--R (6a b + 6a b - 18a b - 6a b + 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (12a b + 18a b - 6a b - 18a b - 6a )cos(x) +--R + +--R 4 4 5 3 7 8 5 +--R (12a b + 24a b - 24a b - 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (12a b + 12a b - 12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (- 12a b - 18a b + 6a b + 18a b + 6a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 5 +--R (- 6a b - 18a b - 6a b + 18a b + 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R * +--R sin(x) +--R Type: Expression Integer +--E 294 + +--S 295 of 546 +m0449b:= a0449.2-r0449 +--R +--R +--R (292) +--R +---------+ +--R 3 2 3 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 3 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 3 | 2 2 +--R (6b + 3a b)cos(x) \|- b + a atanh(sin(x)) +--R + +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 4 3 sin(x)\|- b + a 4 3 2 +--R 12b cos(x) atan(---------------------) + 12b cos(x) atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 +--R - 2a cos(x) tan(x) +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b - 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 3 | 2 2 +--R 6a cos(x) \|- b + a +--R Type: Expression Integer +--E 295 + +--S 296 of 546 +d0449b:= D(m0449b,x) +--R +--R +--R (293) +--R 3 2 4 5 4 6 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (12a b - 12a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b - 24a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 +--R (- 48a b + 12a b + 36a )cos(x) +--R + +--R 3 2 4 5 5 +--R (- 48a b + 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b + 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (36a b - 36a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 4 +--R (6a b - 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 4 6 +--R (6a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 12a b - 12a b)cos(x) + (- 24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b - 12a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (48a b + 84a b + 36a )cos(x) + (48a b + 72a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b + 24a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (- 36a b - 72a b - 36a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 6a b - 12a b - 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 3 2 4 4 +--R (6a b - 12a b + 6a b)cos(x) sec(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 6a b + 12a b - 18a b + 24a b - 12a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 12a b + 12a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b + 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 6 +--R (12a b - 12a b + 24a b - 24a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (24a b - 24a b + 48a b - 48a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (18a b - 24a b + 42a b - 48a b + 12a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 6a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (48a b - 12a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (48a b - 24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b - 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 5 8 +--R (- 6a b - 6a b + 12a )cos(x) +--R + +--R 4 3 2 5 7 +--R (- 24a b - 24a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 48a b + 12a b - 60a b + 24a b + 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 48a b + 24a b - 72a b + 48a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 18a b + 12a b - 30a b + 24a b + 12a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 36a b + 36a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 5 8 4 3 2 5 7 +--R (6a b + 6a b - 12a )cos(x) + (24a b + 24a b - 48a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (36a b + 36a b - 72a )cos(x) + (24a b + 24a b - 48a )cos(x) +--R + +--R 4 3 2 5 4 +--R (6a b + 6a b - 12a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 4 3 2 5 4 +--R ((- 6a b + 6a b)cos(x) sec(x) + (6a b + 6a b - 12a )cos(x) ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (12a b + 12a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b + 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 12a b - 12a b - 24a b - 24a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 24a b - 24a b - 48a b - 48a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 18a b - 12a b - 30a b - 24a b + 12a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 6a b - 12a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 24a b - 48a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 48a b - 84a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 48a b - 72a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b - 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (6a b + 12a b + 18a b + 24a b + 12a )cos(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (24a b + 48a b + 72a b + 96a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (48a b + 84a b + 132a b + 168a b + 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (48a b + 72a b + 120a b + 144a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (18a b + 24a b + 42a b + 48a b + 12a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (6a b + 12a b + 6a b)cos(x) + (24a b + 48a b + 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (36a b + 72a b + 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 4 +--R (24a b + 48a b + 24a b)cos(x) + (6a b + 12a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 6a b - 12a b - 18a b - 24a b - 12a )cos(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 24a b - 48a b - 72a b - 96a b - 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 36a b - 72a b - 108a b - 144a b - 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 24a b - 48a b - 72a b - 96a b - 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 6a b - 12a b - 18a b - 24a b - 12a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b + 10a b - 8a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 6a b + 12a b - 6a b)cos(x) + 6a b - 12a b + 6a +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b - 6a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b - 30a b + 30a b - 22a b + 18a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 24a b + 33a b - 22a b + 13a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 48a b - 52a b + 24a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (18a b - 48a b + 30a b)cos(x) - 18a b + 24a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 6a b + 6a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b + 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 18a b + 24a b - 10a b + 8a b - 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 30b + 21a b - 12a b + 13a b - 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b + 54a b - 36a b + 4a b + 12a b - 28a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (48a b - 63a b + 24a b + 31a b - 40a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 60a b + 72a b + 12a b - 42a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 18a b + 60a b - 18a b - 24a )cos(x) + 18a b - 12a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (3a b - 3a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (24a b - 6a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (24a b - 12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b - 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (6b - 6a b + 6a b - 2a b + 6a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (36b - 24a b + 21a b - 14a b + 21a b + 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (72b - 6a b - 6a b - 12a b + 22a b + 14a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (60b + 12a b - 36a b + 12a b + 8a b + 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b - 18a b - 6a b + 28a b - 18a b + 20a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 24a b + 27a b + 6a b - 41a b + 32a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 6a b + 24a b - 28a b - 28a b + 38a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 5 +--R (6a b - 24a b - 6a b + 24a )cos(x) - 6a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 3a b + 3a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 18a b + 18a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 2 3 4 9 +--R (- 6b + 3a b + 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 30b + 6a b + 6a b + 2a b + 6a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 60b + 12a b + 3a b + 8a b - 3a b - 8a )cos(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (- 60b + 6a b + 10a b - 18a b - 10a )cos(x) +--R + +--R 5 4 2 3 4 5 +--R (- 30b - 12a b + 15a b - 21a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 6b - 6a b + 12a b - 10a b - 12a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 5 2 +--R (3a b - 8a b - 3a b + 8a )cos(x) + (- 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R ((- 6a b + 2a b + 4a )cos(x) + (6a b - 6a b)cos(x) - 6a b + 6a ) +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b + 18a b + 18a b + 10a b + 14a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (24a b + 15a b + 4a b + 13a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 12a b - 8a b + 20a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 18a b + 12a b + 30a b)cos(x) + 18a b + 12a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (6a b + 6a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b + 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (- 12b + 18a b + 12a b - 2a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 18b + 12a b - 9a b - 18a b - 19a b - 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b - 42a b - 60a b - 28a b - 44a b - 28a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 48a b - 33a b + 6a b - 49a b - 40a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 24a b + 12a b - 72a b - 42a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (18a b - 24a b - 66a b - 24a )cos(x) - 18a b - 24a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 3a b - 6a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 12a b - 24a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 24a b - 42a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 24a b - 36a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b - 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (6b + 18a b + 18a b + 14a b + 10a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 48a b + 51a b + 44a b + 37a b + 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (24b + 30a b + 42a b + 60a b + 50a b + 14a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (36b + 12a b + 36a b + 60a b + 40a b + 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b + 30a b + 54a b + 32a b + 22a b + 20a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (24a b + 21a b - 12a b + 23a b + 32a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b - 8a b + 48a b + 38a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 6a b + 12a b + 42a b + 24a )cos(x) + 6a b + 12a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (3a b + 6a b + 3a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (18a b + 36a b + 18a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b + 6a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (6b + 12a b + 9a b + 6a b + 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (18b + 30a b + 18a b + 10a b + 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 12a b - 3a b - 14a b - 19a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 24a b - 30a b - 46a b - 38a b - 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 18b - 24a b - 27a b - 42a b - 21a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 6b - 6a b - 12a b - 14a b + 8a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 5 2 +--R (- 3a b + 2a b + 13a b + 8a )cos(x) + (2a b + 4a b + 2a )cos(x) +--R / +--R 4 2 5 6 4 6 +--R (6a b - 12a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (- 12a b + 12a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b + 24a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (48a b - 12a b - 36a )cos(x) + (48a b - 24a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b - 12a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 36a b + 36a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 4 +--R (- 6a b + 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 6 4 6 +--R (- 6a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (12a b + 12a b)cos(x) + (24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b + 12a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (- 48a b - 84a b - 36a )cos(x) + (- 48a b - 72a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b - 24a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (36a b + 72a b + 36a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (6a b + 12a b + 6a )cos(x) +--R Type: Expression Integer +--E 296 + +--S 297 of 546 +t0450:= sec(x)/(a+a*cos(x)) +--R +--R +--R sec(x) +--R (294) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 297 + +--S 298 of 546 +r0450:= atanh(sin(x))/a-sin(x)/a/(cos(x)+1) +--R +--R +--R (cos(x) + 1)atanh(sin(x)) - sin(x) +--R (295) ---------------------------------- +--R a cos(x) + a +--R Type: Expression Integer +--E 298 + +--S 299 of 546 +a0450:= integrate(t0450,x) +--R +--R +--R (296) +--R sin(x) + cos(x) + 1 +--R (cos(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- cos(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 299 + +--S 300 of 546 +m0450:= a0450-r0450 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (297) ------------------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 300 + +--S 301 of 546 +d0450:= D(m0450,x) +--R +--R +--R (298) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression Integer +--E 301 + +--S 302 of 546 +t0451:= sec(x)^2/(a+a*cos(x)) +--R +--R +--R 2 +--R sec(x) +--R (299) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 302 + +--S 303 of 546 +r0451:= -atanh(sin(x))/a+sin(x)/a/(cos(x)+1)+tan(x)/a +--R +--R +--R (- cos(x) - 1)atanh(sin(x)) + (cos(x) + 1)tan(x) + sin(x) +--R (300) --------------------------------------------------------- +--R a cos(x) + a +--R Type: Expression Integer +--E 303 + +--S 304 of 546 +a0451:= integrate(t0451,x) +--R +--R +--R (301) +--R 2 sin(x) + cos(x) + 1 +--R (- cos(x) - cos(x))log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 +--R (cos(x) + cos(x))log(-------------------) + (2cos(x) + 1)sin(x) +--R cos(x) + 1 +--R / +--R 2 +--R a cos(x) + a cos(x) +--R Type: Union(Expression Integer,...) +--E 304 + +--S 305 of 546 +m0451:= a0451-r0451 +--R +--R +--R (302) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R cos(x)atanh(sin(x)) - cos(x)tan(x) + sin(x) +--R / +--R a cos(x) +--R Type: Expression Integer +--E 305 + +--S 306 of 546 +d0451:= D(m0451,x) +--R +--R +--R (303) +--R 2 4 4 3 2 2 4 +--R - cos(x) sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sin(x) - cos(x) +--R + +--R 3 2 +--R - 2cos(x) - cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 4 +--R sin(x) + (cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 5 3 +--R (2cos(x) + cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 4 3 2 2 +--R a cos(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 4 3 2 +--R a cos(x) + 2a cos(x) + a cos(x) +--R Type: Expression Integer +--E 306 + +--S 307 of 546 +t0452:= sec(x)^3/(a+a*cos(x)) +--R +--R +--R 3 +--R sec(x) +--R (304) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 307 + +--S 308 of 546 +r0452:= 3/2*atanh(sin(x))/a-sin(x)/a/(cos(x)+1)-tan(x)/a+1/2*sec(x)*tan(x)/a +--R +--R +--R (305) +--R (3cos(x) + 3)atanh(sin(x)) + ((cos(x) + 1)sec(x) - 2cos(x) - 2)tan(x) +--R + +--R - 2sin(x) +--R / +--R 2a cos(x) + 2a +--R Type: Expression Integer +--E 308 + +--S 309 of 546 +a0452:= integrate(t0452,x) +--R +--R +--R (306) +--R 3 2 sin(x) + cos(x) + 1 +--R (3cos(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 sin(x) - cos(x) - 1 +--R (- 3cos(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 4cos(x) - cos(x) + 1)sin(x) +--R / +--R 3 2 +--R 2a cos(x) + 2a cos(x) +--R Type: Union(Expression Integer,...) +--E 309 + +--S 310 of 546 +m0452:= a0452-r0452 +--R +--R +--R (307) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 2 2 +--R - 3cos(x) atanh(sin(x)) + (- cos(x) sec(x) + 2cos(x) )tan(x) +--R + +--R (- 2cos(x) + 1)sin(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Expression Integer +--E 310 + +--S 311 of 546 +d0452:= D(m0452,x) +--R +--R +--R (308) +--R 3 3 4 +--R (- 2cos(x) sec(x) + 2cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2cos(x) + 4cos(x) + 4cos(x) )sec(x) - 2cos(x) - 4cos(x) +--R + +--R 3 +--R - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 5 4 +--R (- 2cos(x) - 4cos(x) - 2cos(x) )sec(x) + 2cos(x) + 4cos(x) +--R + +--R 3 +--R 2cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 +--R (- 2cos(x) + 2)sin(x) +--R + +--R 3 3 2 4 +--R (- cos(x) sec(x) - 4cos(x) + 3cos(x) - 4)sin(x) +--R + +--R 5 4 3 5 4 +--R (cos(x) + 2cos(x) + 2cos(x) )sec(x) - 6cos(x) - 4cos(x) +--R + +--R 3 2 +--R 2cos(x) - 4cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 6 4 3 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) - 3cos(x) + 4cos(x) + 2cos(x) +--R + +--R 2 +--R cos(x) +--R / +--R 3 4 5 4 3 2 +--R 2a cos(x) sin(x) + (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 +--R 2a cos(x) + 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 311 + +--S 312 of 546 +t0453:= sec(x)^4/(a+a*cos(x)) +--R +--R +--R 4 +--R sec(x) +--R (309) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 312 + +--S 313 of 546 +r0453:= -3/2*atanh(sin(x))/a+sin(x)/a/(cos(x)+1)+2*tan(x)/a-1/2*sec(x)*tan(x)/a+1/3*tan(x)^3/a +--R +--R +--R (310) +--R 3 +--R (- 9cos(x) - 9)atanh(sin(x)) + (2cos(x) + 2)tan(x) +--R + +--R ((- 3cos(x) - 3)sec(x) + 12cos(x) + 12)tan(x) + 6sin(x) +--R / +--R 6a cos(x) + 6a +--R Type: Expression Integer +--E 313 + +--S 314 of 546 +a0453:= integrate(t0453,x) +--R +--R +--R (311) +--R 4 3 sin(x) + cos(x) + 1 +--R (- 9cos(x) - 9cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 3 sin(x) - cos(x) - 1 +--R (9cos(x) + 9cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 +--R (16cos(x) + 7cos(x) - cos(x) + 2)sin(x) +--R / +--R 4 3 +--R 6a cos(x) + 6a cos(x) +--R Type: Union(Expression Integer,...) +--E 314 + +--S 315 of 546 +m0453:= a0453-r0453 +--R +--R +--R (312) +--R 3 sin(x) + cos(x) + 1 3 sin(x) - cos(x) - 1 +--R - 9cos(x) log(-------------------) + 9cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 3 3 +--R 9cos(x) atanh(sin(x)) - 2cos(x) tan(x) +--R + +--R 3 3 2 +--R (3cos(x) sec(x) - 12cos(x) )tan(x) + (10cos(x) - 3cos(x) + 2)sin(x) +--R / +--R 3 +--R 6a cos(x) +--R Type: Expression Integer +--E 315 + +--S 316 of 546 +d0453:= D(m0453,x) +--R +--R +--R (313) +--R 4 4 6 5 4 2 +--R - 6cos(x) sin(x) + (6cos(x) + 12cos(x) + 12cos(x) )sin(x) +--R + +--R 6 5 4 +--R - 6cos(x) - 12cos(x) - 6cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 4 4 4 +--R (6cos(x) sec(x) - 18cos(x) )sin(x) +--R + +--R 6 5 4 6 +--R (- 6cos(x) - 12cos(x) - 12cos(x) )sec(x) + 18cos(x) +--R + +--R 5 4 +--R 36cos(x) + 36cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 6 5 +--R (6cos(x) + 12cos(x) + 6cos(x) )sec(x) - 18cos(x) - 36cos(x) +--R + +--R 4 +--R - 18cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 +--R (10cos(x) - 6cos(x) + 6)sin(x) +--R + +--R 4 4 3 2 4 +--R (3cos(x) sec(x) + 6cos(x) - 17cos(x) - 12cos(x) - 12)sin(x) +--R + +--R 6 5 4 6 5 +--R (- 3cos(x) - 6cos(x) - 6cos(x) )sec(x) + 20cos(x) + 16cos(x) +--R + +--R 3 +--R 16cos(x) + 6cos(x) + 6 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 7 6 5 +--R (3cos(x) + 6cos(x) + 3cos(x) )sec(x) + 9cos(x) - 2cos(x) - 16cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) + cos(x) + 2cos(x) +--R / +--R 4 4 6 5 4 2 +--R 6a cos(x) sin(x) + (- 6a cos(x) - 12a cos(x) - 12a cos(x) )sin(x) +--R + +--R 6 5 4 +--R 6a cos(x) + 12a cos(x) + 6a cos(x) +--R Type: Expression Integer +--E 316 + +--S 317 of 546 +t0454:= csc(x)/(a+a*cos(x)) +--R +--R +--R csc(x) +--R (314) ------------ +--R a cos(x) + a +--R Type: Expression Integer +--E 317 + +--S 318 of 546 +r0454:= -1/2*atanh(cos(x))/a+1/2/a/(cos(x)+1) +--R +--R +--R (- cos(x) - 1)atanh(cos(x)) + 1 +--R (315) ------------------------------- +--R 2a cos(x) + 2a +--R Type: Expression Integer +--E 318 + +--S 319 of 546 +a0454:= integrate(t0454,x) +--R +--R +--R sin(x) +--R (2cos(x) + 2)log(----------) - cos(x) + 1 +--R cos(x) + 1 +--R (316) ----------------------------------------- +--R 4a cos(x) + 4a +--R Type: Union(Expression Integer,...) +--E 319 + +--S 320 of 546 +m0454:= a0454-r0454 +--R +--R +--R sin(x) +--R 2log(----------) + 2atanh(cos(x)) - 1 +--R cos(x) + 1 +--R (317) ------------------------------------- +--R 4a +--R Type: Expression Integer +--E 320 + +--S 321 of 546 +d0454:= D(m0454,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (318) -------------------------------- +--R 2 +--R (2a cos(x) - 2a)sin(x) +--R Type: Expression Integer +--E 321 + +--S 322 of 546 +t0455:= sin(x)/(a+b*tan(x)) +--R +--R +--R sin(x) +--R (319) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 322 + +--S 323 of 546 +r0455:= a*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-a*cos(x)/(a^2+b^2)+b*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - a b atanh(-------------------) + (b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (320) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 323 + +--S 324 of 546 +a0455:= integrate(t0455,x) +--R +--R +--R (321) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) - a cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 324 + +--S 325 of 546 +m0455:= a0455-r0455 +--R +--R +--R (322) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R a sin(x) - b cos(x) +--R a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 325 + +--S 326 of 546 +d0455:= D(m0455,x) +--R +--R +--R (323) +--R 2 3 2 2 2 2 2 +--R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 +--R - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 326 + +--S 327 of 546 +t0456:= sin(x)^2/(a+b*tan(x)) +--R +--R +--R 2 +--R sin(x) +--R (324) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 327 + +--S 328 of 546 +r0456:= -1/2*(-a^3*x+a*b^2*x-2*a^2*b*log(a*cos(x)+b*sin(x))+sin(x)*a^3*cos(x)+sin(x)*a*b^2*cos(x)-a^2*b+a^2*b*cos(x)^2-b^3+b^3*cos(x)^2)/(a^2+b^2)^2 +--R +--R +--R (325) +--R 2 2 3 +--R 2a b log(b sin(x) + a cos(x)) + (- a b - a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cos(x) + (- a b + a )x + b + a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 328 + +--S 329 of 546 +a0456:= integrate(t0456,x) +--R +--R +--R (326) +--R 2 2 2 - 2b sin(x) - 2a cos(x) +--R - 2a b log(----------) + 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (- a b - a )cos(x)sin(x) + (- b - a b)cos(x) + (- a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 329 + +--S 330 of 546 +m0456:= a0456-r0456 +--R +--R +--R (327) +--R 2 2 2 +--R - 2a b log(b sin(x) + a cos(x)) - 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2b sin(x) - 2a cos(x) 3 2 +--R 2a b log(-----------------------) - b - a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 330 + +--S 331 of 546 +d0456:= D(m0456,x) +--R +--R +--R (328) 0 +--R Type: Expression Integer +--E 331 + +--S 332 of 546 +t0457:= sin(x)^3/(a+b*tan(x)) +--R +--R +--R 3 +--R sin(x) +--R (329) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 332 + +--S 333 of 546 +r0457:= 2/3*(3*a^3*b*atanh(1/(a^2+b^2)^(1/2)*(a*cos(x)-a+b*sin(x))/sin(x))-6*a^3*cos(1/2*x)^4*(a^2+b^2)^(1/2)+4*a^3*cos(1/2*x)^6*(a^2+b^2)^(1/2)+4*b*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2-4*b*cos(1/2*x)^5*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2+3*b*cos(1/2*x)*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2+3*a*cos(1/2*x)^2*(a^2+b^2)^(1/2)*b^2+4*a*cos(1/2*x)^6*(a^2+b^2)^(1/2)*b^2-6*a*cos(1/2*x)^4*(a^2+b^2)^(1/2)*b^2+4*b^3*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2)-4*b^3*cos(1/2*x)^5*sin(1/2*x)*(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2) +--R +--R +--R (330) +--R 3 b sin(x) + a cos(x) - a +--R 6a b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 x 5 3 2 x 3 2 x x +--R ((- 8b - 8a b)cos(-) + (8b + 8a b)cos(-) + 6a b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 x 6 2 3 x 4 2 x 2 +--R (8a b + 8a )cos(-) + (- 12a b - 12a )cos(-) + 6a b cos(-) +--R 2 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 333 + +--S 334 of 546 +a0457:= integrate(t0457,x) +--R +--R +--R (331) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((- b - a b)cos(x) + b + 4a b)sin(x) + (a b + a )cos(x) +--R + +--R 3 +--R - 3a cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression Integer,...) +--E 334 + +--S 335 of 546 +m0457:= a0457-r0457 +--R +--R +--R (332) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 b sin(x) + a cos(x) - a +--R - 6a b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 2 3 2 +--R ((- b - a b)cos(x) + b + 4a b)sin(x) +--R + +--R 3 2 x 5 3 2 x 3 2 x x +--R ((8b + 8a b)cos(-) + (- 8b - 8a b)cos(-) - 6a b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 3 3 2 3 x 6 +--R (a b + a )cos(x) - 3a cos(x) + (- 8a b - 8a )cos(-) +--R 2 +--R + +--R 2 3 x 4 2 x 2 +--R (12a b + 12a )cos(-) - 6a b cos(-) +--R 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 335 + +--S 336 of 546 +d0457:= D(m0457,x) +--R +--R +--R (333) +--R 2 5 4 3 6 +--R (2a b + 2a b )cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 5 2 5 2 +--R ((- 6a b - 7a b - a b )cos(x) + (2a b - 2a b )cos(x) + 3a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 4 3 +--R ((- 20a b - 20a b )cos(-) + (12a b + 12a b )cos(-) + 3a b ) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R 6a b cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 4a b - 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (7a b + 8a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 x 6 +--R (- 4b - 9a b - 11a b + 3a b)cos(x) + (4a b + 4a b )cos(-) +--R 2 +--R + +--R 2 5 4 3 x 4 4 3 x 2 4 3 +--R (- 4a b - 4a b )cos(-) - 3a b cos(-) + 12a b +--R 2 2 +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (60a b + 40a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (- 36a b - 24a b + 12a b )cos(-) - 9a b + 3a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 5 2 x 4 6 5 2 x 2 3 4 +--R (- 20a b + 20a b )cos(-) + (12a b - 12a b )cos(-) + 3a b +--R 2 2 +--R + +--R 5 2 +--R - 3a b +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (- 72a b - 48a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (72a b + 48a b - 24a b)cos(-) + (- 18a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 2 5 6 x 5 2 5 6 x 3 +--R (24a b - 24a b)cos(-) + (- 24a b + 24a b)cos(-) +--R 2 2 +--R + +--R 2 5 4 3 x +--R (6a b - 6a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 4 +--R (3a b + 12a b + 9a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 3a b - 7a b - a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 3a b - 6a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 12a b - 8a b + 4a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (12a b + 8a b - 4a b )cos(-) + (9a b - 3a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 7 +--R 3a b - 5a b + 13a b - 3a +--R * +--R cos(x) +--R + +--R 6 5 2 x 6 6 5 2 x 4 +--R (4a b - 4a b )cos(-) + (- 4a b + 4a b )cos(-) +--R 2 2 +--R + +--R 3 4 5 2 x 2 3 4 5 2 +--R (- 3a b + 3a b )cos(-) - 6a b - 12a b +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 x 4 +--R (- 40b + 40a b + 80a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 2 5 4 3 +--R (24b - 24a b - 48a b )cos(-) + 6a b - 12a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 100a b - 80a b + 20a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 4 3 6 +--R (60a b + 48a b - 12a b)cos(-) + 15a b - 3a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (40b + 100a b + 60a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 2 5 4 3 +--R (- 24b - 60a b - 36a b )cos(-) - 6a b - 9a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 x 5 +--R (48a b - 48a b - 96a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 +--R (- 48a b + 48a b + 96a b )cos(-) +--R 2 +--R + +--R 6 3 4 x +--R (12a b - 24a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (120a b + 96a b - 24a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (- 120a b - 96a b + 24a )cos(-) + (30a b - 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (- 48a b - 120a b - 72a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (48a b + 120a b + 72a b )cos(-) + (- 12a b - 18a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 2 5 6 5 2 5 4 3 6 4 +--R (- 2b - 5a b + 3a b)cos(x) + (- 4a b - 16a b - 12a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 16a b + 14a b + 8a b)cos(x) +--R + +--R 7 2 5 4 3 x 6 +--R (8b - 8a b - 16a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 4 2 5 4 3 x 2 +--R (- 8b + 8a b + 16a b )cos(-) + (- 6a b + 12a b )cos(-) +--R 2 2 +--R + +--R 2 5 4 3 6 +--R 4a b + 14a b + 10a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 +--R (20a b + 16a b - 4a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 4 4 3 6 x 2 +--R (- 20a b - 16a b + 4a b)cos(-) + (- 15a b + 3a b)cos(-) +--R 2 2 +--R + +--R 7 2 5 4 3 6 +--R - 2b - 11a b - 18a b - 15a b +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 7 2 5 4 3 x 4 +--R (- 8b - 20a b - 12a b )cos(-) + (8b + 20a b + 12a b )cos(-) +--R 2 2 +--R + +--R 2 5 4 3 x 2 4 3 +--R (6a b + 9a b )cos(-) - 6a b +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 60a b - 40a b + 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (36a b + 24a b - 12a b )cos(-) + 9a b - 3a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (20a b - 80a b - 100a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (- 12a b + 48a b + 60a b )cos(-) - 3a b + 15a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (60a b + 160a b + 100a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (- 36a b - 96a b - 60a b )cos(-) - 9a b - 15a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (72a b + 48a b - 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (- 72a b - 48a b + 24a b)cos(-) + (18a b - 6a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (- 24a b + 96a b + 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (24a b - 96a b - 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 6a b + 30a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (- 72a b - 192a b - 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (72a b + 192a b + 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 18a b - 30a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 6 +--R (- 3a b - 5a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (a b - a b - 5a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (6a b + 22a b + 13a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (12a b + 8a b - 4a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (- 12a b - 8a b + 4a b )cos(-) + (- 9a b + 3a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 +--R - 2a b - 16a b + 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 4a b + 16a b + 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (4a b - 16a b - 20a b )cos(-) + (3a b - 15a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 7 +--R - 3a b - 17a b - 26a b - 6a +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 12a b - 32a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (12a b + 32a b + 20a b )cos(-) + (9a b + 15a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 7 +--R a b + 17a b + 7a b + 3a +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 6 3 4 5 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 3 4 5 2 x 2 5 2 +--R (- 3a b - 3a b )cos(-) + 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 4 3 +--R ((- 20a b - 20a b )cos(-) + (12a b + 12a b )cos(-) + 3a b ) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 6 x 4 2 5 6 x 2 4 3 +--R (20a b - 20a b)cos(-) + (- 12a b + 12a b)cos(-) - 3a b +--R 2 2 +--R + +--R 6 +--R 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 4 +--R (20a b + 60a b + 40a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 4 3 6 +--R (- 12a b - 36a b - 24a b)cos(-) - 3a b - 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 20a b - 40a b - 20a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 4 3 6 +--R (12a b + 24a b + 12a b)cos(-) + 3a b + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R 6a b cos(-) +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 3 4 7 x 5 3 4 7 x 3 +--R (- 24a b + 24a )cos(-) + (24a b - 24a )cos(-) +--R 2 2 +--R + +--R 3 4 5 2 x +--R (- 6a b + 6a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (- 24a b - 72a b - 48a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (24a b + 72a b + 48a )cos(-) + (- 6a b - 12a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (24a b + 48a b + 24a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (- 24a b - 48a b - 24a )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 7 2 5 6 6 +--R (- a b - a b )cos(x) + (a b - a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (2a b + 7a b + 2a b)cos(x) +--R + +--R 2 5 4 3 x 6 2 5 4 3 x 4 4 3 x 2 +--R (4a b + 4a b )cos(-) + (- 4a b - 4a b )cos(-) - 3a b cos(-) +--R 2 2 2 +--R + +--R 2 5 4 3 +--R - 2a b - 14a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 6 x 6 2 5 6 x 4 +--R (- 4a b + 4a b)cos(-) + (4a b - 4a b)cos(-) +--R 2 2 +--R + +--R 4 3 6 x 2 2 5 4 3 6 +--R (3a b - 3a b)cos(-) - a b - 3a b - 8a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 2 5 4 3 6 x 4 +--R (- 4a b - 12a b - 8a b)cos(-) + (4a b + 12a b + 8a b)cos(-) +--R 2 2 +--R + +--R 4 3 6 x 2 2 5 4 3 6 +--R (3a b + 6a b)cos(-) + a b + 14a b + 7a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 2 5 4 3 6 x 4 +--R (4a b + 8a b + 4a b)cos(-) + (- 4a b - 8a b - 4a b)cos(-) +--R 2 2 +--R + +--R 4 3 6 x 2 4 3 +--R (- 3a b - 3a b)cos(-) - 3a b +--R 2 +--R * +--R cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 6 4 4 6 2 6 +--R (2a b + 4a b + 2a b )cos(x)sin(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b - 13a b - 8a b - a b)cos(x) +--R + +--R 7 3 5 5 3 5 3 7 +--R (2a b + 4a b + 2a b )cos(x) + 3a b + 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 5 5 3 7 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (4b + 8a b + a b - 6a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (3a b + 6a b + 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 4b - 9a b - 12a b - 4a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 4 4 6 2 +--R (- 3a b - 3a b )cos(-) + 12a b + 12a b +--R 2 +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (60a b + 100a b + 20a b - 20a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 3 5 5 3 +--R (- 36a b - 60a b - 12a b + 12a b)cos(-) - 9a b - 6a b +--R 2 +--R + +--R 7 +--R 3a b +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 3 5 5 3 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (- 72a b - 120a b - 24a b + 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (72a b + 120a b + 24a b - 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 18a b - 12a b + 6a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 4 +--R (3a b + 15a b + 21a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b - 11a b - 13a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b - 7a b - 11a b - 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (- 12a b - 20a b - 4a b + 4a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (12a b + 20a b + 4a b - 4a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (9a b + 6a b - 3a b)cos(-) + 3a b - 3a b + 9a b + 15a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 3 5 5 3 x 2 3 5 5 3 7 +--R (- 3a b - 3a b )cos(-) - 6a b - 12a b - 6a b +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 8 4 4 6 2 x 4 +--R (- 40b + 120a b + 80a b )cos(-) +--R 2 +--R + +--R 8 4 4 6 2 x 2 2 6 4 4 6 2 +--R (24b - 72a b - 48a b )cos(-) + 6a b - 6a b - 12a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 60a b - 120a b - 60a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (36a b + 72a b + 36a b )cos(-) + 9a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (40b + 100a b + 80a b + 20a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 2 6 4 4 6 2 +--R (- 24b - 60a b - 48a b - 12a b )cos(-) - 6a b - 9a b - 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 7 5 3 7 x 5 +--R (48a b - 144a b - 96a b)cos(-) +--R 2 +--R + +--R 7 5 3 7 x 3 +--R (- 48a b + 144a b + 96a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (12a b - 12a b - 24a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (72a b + 144a b + 72a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 72a b - 144a b - 72a b)cos(-) + (18a b + 18a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 5 +--R (- 48a b - 120a b - 96a b - 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (48a b + 120a b + 96a b + 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (- 12a b - 18a b - 6a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 5 +--R (- 2b - 7a b - 5a b + 3a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b - 10a b - 14a b - 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b + 18a b + 18a b + 4a b )cos(x) +--R + +--R 8 4 4 6 2 x 6 8 4 4 6 2 x 4 +--R (8b - 24a b - 16a b )cos(-) + (- 8b + 24a b + 16a b )cos(-) +--R 2 2 +--R + +--R 2 6 4 4 6 2 x 2 2 6 4 4 6 2 8 +--R (- 6a b + 6a b + 12a b )cos(-) + 2a b + 10a b + 14a b + 6a +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 +--R (12a b + 24a b + 12a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 4 4 4 6 2 x 2 +--R (- 12a b - 24a b - 12a b )cos(-) + (- 9a b - 9a b )cos(-) +--R 2 2 +--R + +--R 8 2 6 4 4 6 2 8 +--R - 2b - 11a b - 19a b - 13a b - 3a +--R * +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (- 8b - 20a b - 16a b - 4a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (8b + 20a b + 16a b + 4a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (6a b + 9a b + 3a b )cos(-) - 6a b - 6a b +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (- 60a b - 100a b - 20a b + 20a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 3 5 5 3 +--R (36a b + 60a b + 12a b - 12a b)cos(-) + 9a b + 6a b +--R 2 +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 5 3 7 x 4 +--R (20a b - 60a b - 40a b)cos(-) +--R 2 +--R + +--R 7 5 3 7 x 2 3 5 5 3 7 +--R (- 12a b + 36a b + 24a b)cos(-) - 3a b + 3a b + 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (60a b + 140a b + 100a b + 20a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 3 5 5 3 +--R (- 36a b - 84a b - 60a b - 12a b)cos(-) - 9a b - 12a b +--R 2 +--R + +--R 7 +--R - 3a b +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 3 5 5 3 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (72a b + 120a b + 24a b - 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (- 72a b - 120a b - 24a b + 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (18a b + 12a b - 6a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 6 2 8 x 5 +--R (- 24a b + 72a b + 48a )cos(-) +--R 2 +--R + +--R 2 6 6 2 8 x 3 +--R (24a b - 72a b - 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 6a b + 6a b + 12a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (- 72a b - 168a b - 120a b - 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (72a b + 168a b + 120a b + 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 18a b - 24a b - 6a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 6 +--R (- 3a b - 8a b - 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (a b + 3a b + 3a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b + 24a b + 21a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (12a b + 20a b + 4a b - 4a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (- 12a b - 20a b - 4a b + 4a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (- 9a b - 6a b + 3a b)cos(-) - 2a b - 20a b - 10a b + 8a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 5 3 7 x 6 7 5 3 7 x 4 +--R (- 4a b + 12a b + 8a b)cos(-) + (4a b - 12a b - 8a b)cos(-) +--R 2 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (3a b - 3a b - 6a b)cos(-) - 3a b - 16a b - 23a b - 10a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (- 12a b - 28a b - 20a b - 4a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (12a b + 28a b + 20a b + 4a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (9a b + 12a b + 3a b)cos(-) + a b + 17a b + 13a b - 3a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 3 5 5 3 x 2 5 3 7 +--R (- 3a b - 3a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 5 5 3 7 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (- a b - 2a b - a b )cos(x) + (a b + 2a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (2a b + 7a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 2 6 4 4 6 2 +--R (- 3a b - 3a b )cos(-) - 2a b - 16a b - 14a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 2 6 4 4 6 2 +--R (3a b + 3a b )cos(-) - a b - 2a b - a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 2 6 4 4 6 2 +--R (3a b + 3a b )cos(-) + a b + 14a b + 13a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 4 4 6 2 +--R (- 3a b - 3a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R cos(x) +--R / +--R 2 6 4 4 6 2 4 +--R (3a b + 6a b + 3a b )sin(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b - 15a b - 3a b + 3a b)cos(x) + 3a b + 3a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 4 4 6 2 2 +--R (6b - 18a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 8 2 6 4 4 +--R (15a b + 27a b + 9a b - 3a )cos(x) - 6b - 21a b - 24a b +--R + +--R 6 2 +--R - 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b + 15a b + 3a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b + 9a b + 27a b + 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b - 33a b - 39a b - 15a b)cos(x) + 3a b + 9a b + 9a b +--R + +--R 7 +--R 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (3a b + 6a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 3a b - 3a b + 3a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 3a b - 12a b - 15a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 +--R (3a b + 9a b + 9a b + 3a )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b + 9a b + 9a b + 3a b)sin(x) +--R + +--R 8 3 6 5 4 9 8 3 6 5 4 +--R (- 9a b - 24a b - 18a b + 3a )cos(x) + 3a b + 9a b + 9a b +--R + +--R 7 2 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (6b + 6a b - 18a b - 30a b - 12a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 9 2 7 4 5 +--R (9a b + 27a b + 27a b + 9a b)cos(x) - 6b - 21a b - 27a b +--R + +--R 6 3 8 +--R - 15a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 9 3 +--R (9a b + 24a b + 18a b - 3a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (- 3a b - 3a b + 9a b + 15a b + 6a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 8 3 6 +--R (- 9a b - 30a b - 36a b - 18a b - 3a )cos(x) + 3a b + 9a b +--R + +--R 5 4 7 2 +--R 9a b + 3a b +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b + 9a b + 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 3a b - 9a b - 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b - 9a b - 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 +--R (3a b + 9a b + 9a b + 3a b)cos(x) +--R Type: Expression Integer +--E 336 + +--S 337 of 546 +t0458:= cos(x)/(a+b*tan(x)) +--R +--R +--R cos(x) +--R (334) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 337 + +--S 338 of 546 +r0458:= -b^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R b atanh(-------------------) + (a sin(x) + b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (335) -------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 338 + +--S 339 of 546 +a0458:= integrate(t0458,x) +--R +--R +--R (336) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) + b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 339 + +--S 340 of 546 +m0458:= a0458-r0458 +--R +--R +--R (337) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 a sin(x) - b cos(x) +--R - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 340 + +--S 341 of 546 +d0458:= D(m0458,x) +--R +--R +--R (338) +--R 2 3 3 2 2 2 2 3 3 +--R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b )sin(x) - b cos(x) +--R + +--R 3 +--R b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression Integer +--E 341 + +--S 342 of 546 +t0459:= cos(x)^2/(a+b*tan(x)) +--R +--R +--R 2 +--R cos(x) +--R (339) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 342 + +--S 343 of 546 +r0459:= 1/2/(a^2+b^2)^2*(3*a*b^2*x+a^3*x+2*b^3*log(a*cos(x)+b*sin(x))+a^3*cos(x)*sin(x)+a*cos(x)*sin(x)*b^2-a^2*b+a^2*b*cos(x)^2-b^3+b^3*cos(x)^2) +--R +--R +--R (340) +--R 3 2 3 3 2 2 +--R 2b log(b sin(x) + a cos(x)) + (a b + a )cos(x)sin(x) + (b + a b)cos(x) +--R + +--R 2 3 3 2 +--R (3a b + a )x - b - a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 343 + +--S 344 of 546 +a0459:= integrate(t0459,x) +--R +--R +--R (341) +--R 3 2 3 - 2b sin(x) - 2a cos(x) +--R - 2b log(----------) + 2b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (a b + a )cos(x)sin(x) + (b + a b)cos(x) + (3a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 344 + +--S 345 of 546 +m0459:= a0459-r0459 +--R +--R +--R (342) +--R 3 3 2 +--R - 2b log(b sin(x) + a cos(x)) - 2b log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2b sin(x) - 2a cos(x) 3 2 +--R 2b log(-----------------------) + b + a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 345 + +--S 346 of 546 +d0459:= D(m0459,x) +--R +--R +--R (343) 0 +--R Type: Expression Integer +--E 346 + +--S 347 of 546 +t0460:= tan(x)/(a+b*tan(x)) +--R +--R +--R tan(x) +--R (344) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 347 + +--S 348 of 546 +r0460:= -(-b*x+a*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R - a log(b sin(x) + a cos(x)) + b x +--R (345) ---------------------------------- +--R 2 2 +--R b + a +--R Type: Expression Integer +--E 348 + +--S 349 of 546 +a0460:= integrate(t0460,x) +--R +--R +--R 2 +--R a log(tan(x) + 1) - 2a log(b tan(x) + a) + 2b x +--R (346) ------------------------------------------------ +--R 2 2 +--R 2b + 2a +--R Type: Union(Expression Integer,...) +--E 349 + +--S 350 of 546 +m0460:= a0460-r0460 +--R +--R +--R (347) +--R 2 +--R a log(tan(x) + 1) - 2a log(b tan(x) + a) + 2a log(b sin(x) + a cos(x)) +--R ----------------------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Expression Integer +--E 350 + +--S 351 of 546 +d0460:= D(m0460,x) +--R +--R +--R a cos(x)tan(x) - a sin(x) +--R (348) ----------------------------------------------------- +--R 2 2 +--R (b sin(x) + a b cos(x))tan(x) + a b sin(x) + a cos(x) +--R Type: Expression Integer +--E 351 + +--S 352 of 546 +t0461:= cot(x)/(a+b*tan(x)) +--R +--R +--R cot(x) +--R (349) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 352 + +--S 353 of 546 +r0461:= -b*x/(a^2+b^2)+log(sin(x))/a-b^2*log(a*cos(x)+b*sin(x))/a/(a^2+b^2) +--R +--R +--R 2 2 2 +--R - b log(b sin(x) + a cos(x)) + (b + a )log(sin(x)) - a b x +--R (350) ----------------------------------------------------------- +--R 2 3 +--R a b + a +--R Type: Expression Integer +--E 353 + +--S 354 of 546 +a0461:= integrate(t0461,x) +--R +--R +--R (351) +--R 2 2 2 2 2 +--R - a log(tan(x) + 1) - 2b log(b tan(x) + a) + (2b + 2a )log(tan(x)) - 2a b x +--R ----------------------------------------------------------------------------- +--R 2 3 +--R 2a b + 2a +--R Type: Union(Expression Integer,...) +--E 354 + +--S 355 of 546 +m0461:= a0461-r0461 +--R +--R +--R (352) +--R 2 2 2 2 2 +--R - a log(tan(x) + 1) - 2b log(b tan(x) + a) + (2b + 2a )log(tan(x)) +--R + +--R 2 2 2 +--R 2b log(b sin(x) + a cos(x)) + (- 2b - 2a )log(sin(x)) +--R / +--R 2 3 +--R 2a b + 2a +--R Type: Expression Integer +--E 355 + +--S 356 of 546 +d0461:= D(m0461,x) +--R +--R +--R (353) +--R 2 2 2 2 +--R - b cos(x) tan(x) - a cos(x) tan(x) + b sin(x) + a cos(x)sin(x) +--R ---------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R (b sin(x) + a b cos(x)sin(x))tan(x) + (a b sin(x) + a cos(x)sin(x))tan(x) +--R Type: Expression Integer +--E 356 + +--S 357 of 546 +t0462:= sec(x)^3/(a+b*tan(x)) +--R +--R +--R 3 +--R sec(x) +--R (354) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 357 + +--S 358 of 546 +r0462:= 1/b^2*(-2*(a^2+b^2)^(1/2)*atanh(1/(a^2+b^2)^(1/2)*(a*cos(x)-a+b*sin(x))/sin(x))*cos(x)+2*a*atanh((-1+cos(x))/sin(x))*cos(x)+b*cos(x)+b)/cos(x) +--R +--R +--R (355) +--R cos(x) - 1 +--R 2a cos(x)atanh(----------) +--R sin(x) +--R + +--R +-------+ +--R | 2 2 b sin(x) + a cos(x) - a +--R - 2cos(x)\|b + a atanh(-----------------------) + b cos(x) + b +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R / +--R 2 +--R b cos(x) +--R Type: Expression Integer +--E 358 + +--S 359 of 546 +a0462:= integrate(t0462,x) +--R +--R +--R (356) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - a cos(x)log(-------------------) + a cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R cos(x)\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 +--R (- a sin(x) + b cos(x) + b)\|b + a + a b sin(x) - b cos(x) +--R + +--R 2 2 +--R - b - a +--R / +--R b sin(x) + a cos(x) +--R + +--R b cos(x) + b +--R / +--R 2 +--R b cos(x) +--R Type: Union(Expression Integer,...) +--E 359 + +--S 360 of 546 +m0462:= a0462-r0462 +--R +--R +--R (357) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - a log(-------------------) + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 +--R (- a sin(x) + b cos(x) + b)\|b + a + a b sin(x) - b cos(x) +--R + +--R 2 2 +--R - b - a +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R cos(x) - 1 | 2 2 b sin(x) + a cos(x) - a +--R - 2a atanh(----------) + 2\|b + a atanh(-----------------------) +--R sin(x) +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R / +--R 2 +--R b +--R Type: Expression Integer +--E 360 + +--S 361 of 546 +d0462:= D(m0462,x) +--R +--R +--R (358) +--R 3 3 8 +--R (- 3a b + a b)sin(x) +--R + +--R 4 2 2 4 2 2 4 7 +--R ((4b - 10a b + 2a )cos(x) + 5a b + a )sin(x) +--R + +--R 3 3 2 3 3 3 3 +--R ((14a b - 10a b)cos(x) + (- a b + 11a b)cos(x) + a b + a b) +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 2 4 3 2 2 4 2 +--R (- 4b + 10a b - 2a )cos(x) + (- 5a b + 7a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 12b - 6a b - 2a )cos(x) - 3a b - 3a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 3 3 3 2 +--R (a b - 3a b)cos(x) + (- 11a b + 13a b)cos(x) +--R + +--R 3 3 3 3 +--R (3a b - 5a b)cos(x) - a b - 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 4 5 2 2 4 4 +--R (- 4b + 10a b - 2a )cos(x) + (- 5a b - a )cos(x) +--R + +--R 4 2 2 4 3 2 2 4 2 +--R (- 8b - 28a b + 12a )cos(x) + (6a b - 10a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (12b + 18a b - 2a )cos(x) - a b + 3a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 6 3 3 5 +--R (- 14a b + 10a b)cos(x) + (a b - 11a b)cos(x) +--R + +--R 3 3 4 3 3 3 3 2 +--R (19a b - 13a b)cos(x) + (2a b + 18a b)cos(x) - 8a b cos(x) +--R + +--R 3 3 3 3 +--R (- 3a b - 7a b)cos(x) + 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 4 7 2 2 4 6 +--R (4b - 10a b + 2a )cos(x) + (5a b - 7a )cos(x) +--R + +--R 4 2 2 4 5 2 2 4 4 +--R (- 12b + 18a b + 6a )cos(x) + (- 11a b + 5a )cos(x) +--R + +--R 4 2 2 4 3 2 2 4 2 +--R (12b - 6a b - 10a )cos(x) + (7a b + 3a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 4b - 2a b + 2a )cos(x) - a b - a +--R * +--R sin(x) +--R + +--R 3 3 8 3 3 7 +--R (3a b - a b)cos(x) + (- a b + 3a b)cos(x) +--R + +--R 3 3 6 3 3 5 +--R (- 9a b - a b)cos(x) + (3a b - 5a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (9a b + 5a b)cos(x) + (- 3a b + a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 3a b - 3a b)cos(x) + (a b + a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 5 8 +--R (3a b + a )sin(x) +--R + +--R 5 2 3 4 2 3 4 7 +--R ((- 4b + 8a b - 4a b)cos(x) - 5a b + 3a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (- 14a b + 8a b - 2a )cos(x) + (a b - 19a b + 4a )cos(x) - a b +--R + +--R 3 2 5 +--R 4a b - 3a +--R * +--R 6 +--R sin(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (4b - 8a b + 4a b)cos(x) + (5a b - 19a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (12b + 12a b + 24a b)cos(x) + 3a b - 5a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (- a b + 3a b - 4a )cos(x) + (11a b - 12a b + 9a )cos(x) +--R + +--R 4 3 2 5 4 5 +--R (- 3a b + 13a b - 8a )cos(x) + a b + 3a +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (4b - 8a b + 4a b)cos(x) + (5a b - 3a b)cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (8b + 32a b - 8a b)cos(x) + (- 6a b + 26a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (- 12b - 24a b - 20a b)cos(x) + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (14a b - 8a b + 2a )cos(x) + (- a b + 19a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 19a b + 4a b - a )cos(x) + (- 2a b - 26a b + 8a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (8a b + 8a b - 8a )cos(x) + (3a b + 7a b + 4a )cos(x) - 3a b +--R + +--R 3 2 5 +--R - 4a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 7 2 3 4 6 +--R (- 4b + 8a b - 4a b)cos(x) + (- 5a b + 19a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (12b - 12a b - 16a b)cos(x) + (11a b - 13a b)cos(x) +--R + +--R 5 4 3 2 3 4 2 +--R (- 12b + 20a b)cos(x) + (- 7a b - 7a b)cos(x) +--R + +--R 5 2 3 2 3 4 +--R (4b + 4a b )cos(x) + a b + a b +--R * +--R sin(x) +--R + +--R 4 5 8 4 3 2 5 7 +--R (- 3a b - a )cos(x) + (a b - 3a b + 4a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 +--R (9a b + 4a b - 5a )cos(x) + (- 3a b + 5a b )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 9a b - 8a b + 5a )cos(x) + (3a b - a b - 4a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 +--R (3a b + 4a b + a )cos(x) + (- a b - a b )cos(x) +--R / +--R 2 3 8 4 3 2 4 7 +--R a b sin(x) + ((- 3a b + a b )cos(x) + a b )sin(x) +--R + +--R 5 2 3 2 2 3 5 2 3 6 +--R ((2b - 6a b )cos(x) + 3a b cos(x) - 2b - 3a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (9a b - 3a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 +--R (3a b - 3a b )cos(x) - a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 3 4 2 3 3 2 3 2 +--R (- 4b + 10a b )cos(x) - 7a b cos(x) + 7a b cos(x) +--R + +--R 2 3 5 2 3 +--R - 5a b cos(x) + 4b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 9a b + 3a b )cos(x) + (3a b - 4a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (6a b + 2a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 4 3 2 4 +--R (3a b + 3a b )cos(x) - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 6 2 3 5 5 2 3 4 +--R (2b - 6a b )cos(x) + 5a b cos(x) + (- 6b + 7a b )cos(x) +--R + +--R 2 3 3 5 2 2 3 5 2 3 +--R - 6a b cos(x) + 6b cos(x) + a b cos(x) - 2b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (3a b - a b )cos(x) + (- a b + 2a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 9a b + a b )cos(x) + (3a b - 4a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (9a b + a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 +--R (- 3a b - a b )cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 3 8 2 3 7 2 3 6 2 3 5 +--R a b cos(x) - a b cos(x) - 3a b cos(x) + 3a b cos(x) +--R + +--R 2 3 4 2 3 3 2 3 2 2 3 +--R 3a b cos(x) - 3a b cos(x) - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 8 5 3 3 5 3 3 7 +--R - a b sin(x) + ((3a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 6 2 4 2 2 4 4 2 6 2 4 6 +--R ((- 2b + 6a b )cos(x) + (- 5a b + a b )cos(x) + 2b + 5a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 9a b + 3a b )cos(x) + (3a b - 7a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 3a b + 7a b )cos(x) + a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 4 4 2 4 4 2 3 +--R (4b - 10a b )cos(x) + (11a b - 3a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (- 11a b + 2a b )cos(x) + (9a b - 3a b )cos(x) - 4b - 7a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (9a b - 3a b )cos(x) + (- 3a b + 11a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 6a b - 10a b )cos(x) + (2a b + 10a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 3a b - 11a b )cos(x) + a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 6 2 4 4 2 5 +--R (- 2b + 6a b )cos(x) + (- 7a b + 3a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (6b - 5a b - 4a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 2 4 +--R (- 6b - 4a b - 4a b )cos(x) + (- 3a b + 3a b )cos(x) + 2b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (- 3a b + a b )cos(x) + (a b - 5a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (9a b + 3a b )cos(x) + (- 3a b + 9a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 9a b - 9a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (3a b + 5a b )cos(x) - a b - a b +--R * +--R sin(x) +--R + +--R 2 4 8 2 4 4 2 7 2 4 4 2 6 +--R - a b cos(x) + (a b - a b )cos(x) + (3a b + 2a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 3a b + a b )cos(x) + (- 3a b - 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 2 4 4 2 +--R (3a b + a b )cos(x) + (a b + 2a b )cos(x) + (- a b - a b )cos(x) +--R Type: Expression Integer +--E 361 + +--S 362 of 546 +t0463:= csc(x)^2/(a+b*tan(x)) +--R +--R +--R 2 +--R csc(x) +--R (359) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 362 + +--S 363 of 546 +r0463:= (-a*cot(x)+b*log(b+a*cot(x)))/a^2 +--R +--R +--R b log(a cot(x) + b) - a cot(x) +--R (360) ------------------------------ +--R 2 +--R a +--R Type: Expression Integer +--E 363 + +--S 364 of 546 +a0463:= integrate(t0463,x) +--R +--R +--R (361) +--R sin(x) - 2b sin(x) - 2a cos(x) +--R - b sin(x)log(----------) + b sin(x)log(-----------------------) - a cos(x) +--R cos(x) + 1 cos(x) + 1 +--R --------------------------------------------------------------------------- +--R 2 +--R a sin(x) +--R Type: Union(Expression Integer,...) +--E 364 + +--S 365 of 546 +m0463:= a0463-r0463 +--R +--R +--R (362) +--R sin(x) +--R - b sin(x)log(----------) - b sin(x)log(a cot(x) + b) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R b sin(x)log(-----------------------) + a cot(x)sin(x) - a cos(x) +--R cos(x) + 1 +--R / +--R 2 +--R a sin(x) +--R Type: Expression Integer +--E 365 + +--S 366 of 546 +d0463:= D(m0463,x) +--R +--R +--R (363) +--R 3 3 3 2 +--R (- b cot(x) - b cot(x))sin(x) + (- a cos(x)cot(x) + b cos(x))sin(x) +--R + +--R 3 3 +--R a cos(x) cot(x) + b cos(x) +--R / +--R 2 3 2 2 +--R (a b cot(x) + b )sin(x) + (a cos(x)cot(x) + a b cos(x))sin(x) +--R Type: Expression Integer +--E 366 + +--S 367 of 546 +t0464:= csc(x)^4/(a+b*tan(x)) +--R +--R +--R 4 +--R csc(x) +--R (364) ------------ +--R b tan(x) + a +--R Type: Expression Integer +--E 367 + +--S 368 of 546 +r0464:= -(a^2+b^2)*cot(x)/a^3+1/2*b*cot(x)^2/a^2-1/3*cot(x)^3/a+b*(a^2+b^2)*log(b+a*cot(x))/a^4 +--R +--R +--R (365) +--R 3 2 3 3 2 2 +--R (6b + 6a b)log(a cot(x) + b) - 2a cot(x) + 3a b cot(x) +--R + +--R 2 3 +--R (- 6a b - 6a )cot(x) +--R / +--R 4 +--R 6a +--R Type: Expression Integer +--E 368 + +--S 369 of 546 +a0464:= integrate(t0464,x) +--R +--R +--R (366) +--R 3 2 2 3 2 sin(x) +--R ((- 12b - 12a b)cos(x) + 12b + 12a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 - 2b sin(x) - 2a cos(x) +--R ((12b + 12a b)cos(x) - 12b - 12a b)sin(x)log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 3 3 +--R (- 3a b cos(x) - 3a b)sin(x) + (- 12a b - 8a )cos(x) +--R + +--R 2 3 +--R (12a b + 12a )cos(x) +--R / +--R 4 2 4 +--R (12a cos(x) - 12a )sin(x) +--R Type: Union(Expression Integer,...) +--E 369 + +--S 370 of 546 +m0464:= a0464-r0464 +--R +--R +--R (367) +--R 3 2 2 3 2 sin(x) +--R ((- 12b - 12a b)cos(x) + 12b + 12a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 +--R ((- 12b - 12a b)cos(x) + 12b + 12a b)sin(x)log(a cot(x) + b) +--R + +--R 3 2 2 3 2 - 2b sin(x) - 2a cos(x) +--R ((12b + 12a b)cos(x) - 12b - 12a b)sin(x)log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 3 2 2 2 2 +--R (4a cos(x) - 4a )cot(x) + (- 6a b cos(x) + 6a b)cot(x) +--R + +--R 2 3 2 2 3 2 2 2 +--R ((12a b + 12a )cos(x) - 12a b - 12a )cot(x) - 3a b cos(x) - 3a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 12a b - 8a )cos(x) + (12a b + 12a )cos(x) +--R / +--R 4 2 4 +--R (12a cos(x) - 12a )sin(x) +--R Type: Expression Integer +--E 370 + +--S 371 of 546 +d0464:= D(m0464,x) +--R +--R +--R (368) +--R 2 3 4 +--R (- 3a b cos(x)cot(x) - 3b cos(x))sin(x) +--R + +--R 2 4 2 2 2 5 +--R (- 3a b cos(x) + 6a b cos(x) - 3a b)cot(x) +--R + +--R 2 4 2 2 2 3 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b)cot(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- 4a b cos(x) + 6a b cos(x) - 3a b)cot(x) - a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 3 3 5 +--R (- 3a cos(x) + 6a cos(x) - 3a cos(x))cot(x) +--R + +--R 3 5 3 3 3 3 +--R (- 6a cos(x) + 12a cos(x) - 6a cos(x))cot(x) +--R + +--R 2 3 5 2 3 3 2 +--R ((3a b - a )cos(x) + (- 6a b + 3a )cos(x) + 3a b cos(x))cot(x) +--R + +--R 3 2 5 3 2 3 3 2 +--R (3b + 2a b)cos(x) + (- 6b - 3a b)cos(x) + (3b + 3a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 4 2 6 2 4 +--R ((- a b cos(x) + a b cos(x) )cot(x) - a b cos(x) + a b cos(x) )sin(x) +--R + +--R 2 3 7 2 3 5 2 3 3 +--R ((3a b + 2a )cos(x) + (- 6a b - 5a )cos(x) + (3a b + 3a )cos(x) ) +--R * +--R cot(x) +--R + +--R 3 2 7 3 2 5 3 2 3 +--R (3b + 2a b)cos(x) + (- 6b - 5a b)cos(x) + (3b + 3a b)cos(x) +--R / +--R 3 4 3 2 3 2 2 4 +--R (3a b cos(x) - 6a b cos(x) + 3a b)cot(x) + 3a b cos(x) +--R + +--R 2 2 2 2 2 +--R - 6a b cos(x) + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 3 4 3 5 +--R (3a cos(x) - 6a cos(x) + 3a cos(x))cot(x) + 3a b cos(x) +--R + +--R 3 3 3 +--R - 6a b cos(x) + 3a b cos(x) +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 371 + +--S 372 of 546 +t0465:= sin(x)/(%i+tan(x)) +--R +--R +--R sin(x) +--R (369) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 372 + +--S 373 of 546 +r0465:= 1/3*%i*cos(x)^3+1/3*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (370) - sin(x) + - %i cos(x) +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 373 + +--S 374 of 546 +--a0465:= integrate(t0465,x) +--E 374 + +--S 375 of 546 +--m0465:= a0465-r0465 +--E 375 + +--S 376 of 546 +--d0465:= D(m0465,x) +--E 376 + +--S 377 of 546 +t0466:= sin(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R sin(x) +--R (371) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 377 + +--S 378 of 546 +r0466:= -1/8*%i*x-1/8*%i*cos(x)*sin(x)+1/4*%i*cos(x)^3*sin(x)+1/4*sin(x)^4 +--R +--R +--R 1 4 1 3 1 1 +--R (372) - sin(x) + (- %i cos(x) - - %i cos(x))sin(x) - - %i x +--R 4 4 8 8 +--R Type: Expression Complex Fraction Integer +--E 378 + +--S 379 of 546 +--a0466:= integrate(t0466,x) +--E 379 + +--S 380 of 546 +--m0466:= a0466-r0466 +--E 380 + +--S 381 of 546 +--d0466:= D(m0466,x) +--E 381 + +--S 382 of 546 +t0467:= sin(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R sin(x) +--R (373) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 382 + +--S 383 of 546 +r0467:= 1/3*%i*cos(x)^3-1/5*%i*cos(x)^5+1/5*sin(x)^5 +--R +--R +--R 1 5 1 5 1 3 +--R (374) - sin(x) - - %i cos(x) + - %i cos(x) +--R 5 5 3 +--R Type: Expression Complex Fraction Integer +--E 383 + +--S 384 of 546 +--a0467:= integrate(t0467,x) +--E 384 + +--S 385 of 546 +--m0467:= a0467-r0467 +--E 385 + +--S 386 of 546 +--d0467:= D(m0467,x) +--E 386 + +--S 387 of 546 +t0468:= sin(x)^4/(%i+tan(x)) +--R +--R +--R 4 +--R sin(x) +--R (375) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 387 + +--S 388 of 546 +r0468:= -1/16*%i*x-1/16*%i*cos(x)*sin(x)+1/8*%i*cos(x)^3*sin(x)+1/6*%i*cos(x)^3*sin(x)^3+1/6*sin(x)^6 +--R +--R +--R (376) +--R 1 6 1 3 3 1 3 1 +--R - sin(x) + - %i cos(x) sin(x) + (- %i cos(x) - -- %i cos(x))sin(x) +--R 6 6 8 16 +--R + +--R 1 +--R - -- %i x +--R 16 +--R Type: Expression Complex Fraction Integer +--E 388 + +--S 389 of 546 +--a0468:= integrate(t0468,x) +--E 389 + +--S 390 of 546 +--m0468:= a0468-r0468 +--E 390 + +--S 391 of 546 +--d0468:= D(m0468,x) +--E 391 + +--S 392 of 546 +t0469:= cos(x)/(%i+tan(x)) +--R +--R +--R cos(x) +--R (377) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 392 + +--S 393 of 546 +r0469:= -1/3*cos(x)^3-%i*sin(x)+1/3*%i*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (378) - %i sin(x) - %i sin(x) - - cos(x) +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 393 + +--S 394 of 546 +--a0469:= integrate(t0469,x) +--E 394 + +--S 395 of 546 +--m0469:= a0469-r0469 +--E 395 + +--S 396 of 546 +--d0469:= D(m0469,x) +--E 396 + +--S 397 of 546 +t0470:= cos(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R cos(x) +--R (379) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 397 + +--S 398 of 546 +r0470:= -3/8*%i*x-1/4*cos(x)^4-3/8*%i*cos(x)*sin(x)-1/4*%i*cos(x)^3*sin(x) +--R +--R +--R 1 3 3 1 4 3 +--R (380) (- - %i cos(x) - - %i cos(x))sin(x) - - cos(x) - - %i x +--R 4 8 4 8 +--R Type: Expression Complex Fraction Integer +--E 398 + +--S 399 of 546 +--a0470:= integrate(t0470,x) +--E 399 + +--S 400 of 546 +--m0470:= a0470-r0470 +--E 400 + +--S 401 of 546 +--d0470:= D(m0470,x) +--E 401 + +--S 402 of 546 +t0471:= cos(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R cos(x) +--R (381) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 402 + +--S 403 of 546 +r0471:= -1/5*cos(x)^5-%i*sin(x)+2/3*%i*sin(x)^3-1/5*%i*sin(x)^5 +--R +--R +--R 1 5 2 3 1 5 +--R (382) - - %i sin(x) + - %i sin(x) - %i sin(x) - - cos(x) +--R 5 3 5 +--R Type: Expression Complex Fraction Integer +--E 403 + +--S 404 of 546 +--a0471:= integrate(t0471,x) +--E 404 + +--S 405 of 546 +--m0471:= a0471-r0471 +--E 405 + +--S 406 of 546 +--d0471:= D(m0471,x) +--E 406 + +--S 407 of 546 +t0472:= cos(x)^4/(%i+tan(x)) +--R +--R +--R 4 +--R cos(x) +--R (383) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 407 + +--S 408 of 546 +r0472:= -5/16*%i*x-1/6*cos(x)^6-5/16*%i*cos(x)*sin(x)-5/24*%i*cos(x)^3*sin(x)-1/6*%i*cos(x)^5*sin(x) +--R +--R +--R (384) +--R 1 5 5 3 5 1 6 5 +--R (- - %i cos(x) - -- %i cos(x) - -- %i cos(x))sin(x) - - cos(x) - -- %i x +--R 6 24 16 6 16 +--R Type: Expression Complex Fraction Integer +--E 408 + +--S 409 of 546 +--a0472:= integrate(t0472,x) +--E 409 + +--S 410 of 546 +--m0472:= a0472-r0472 +--E 410 + +--S 411 of 546 +--d0472:= D(m0472,x) +--E 411 + +--S 412 of 546 +t0473:= tan(x)/(%i+tan(x)) +--R +--R +--R tan(x) +--R (385) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 412 + +--S 413 of 546 +r0473:= 1/2*x-%i/(2+2*%i*cot(x)) +--R +--R +--R x cot(x) - %i x - 1 +--R (386) ------------------- +--R 2cot(x) - 2%i +--R Type: Expression Complex Integer +--E 413 + +--S 414 of 546 +a0473:= integrate(t0473,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 414 + +--S 415 of 546 +m0473:= a0473-r0473 +--R +--R +--R (- x + 2a0473)cot(x) + %i x - 2%i a0473 + 1 +--R (387) ------------------------------------------- +--R 2cot(x) - 2%i +--R Type: Expression Complex Integer +--E 415 + +--S 416 of 546 +d0473:= D(m0473,x) +--R +--R +--R %i +--R (388) ----------- +--R cot(x) - %i +--R Type: Expression Complex Integer +--E 416 + +--S 417 of 546 +t0474:= tan(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R tan(x) +--R (389) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 417 + +--S 418 of 546 +r0474:= -1/2*%i*x-log(cos(x))+%i/(2*%i+2*tan(x)) +--R +--R +--R %i (- 2tan(x) - 2%i)log(cos(x)) + %i +--R (390) - -- x + --------------------------------- +--R 2 2tan(x) + 2%i +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 418 + +--S 419 of 546 +a0474:= integrate(t0474,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 419 + +--S 420 of 546 +m0474:= a0474-r0474 +--R +--R +--R %i (2tan(x) + 2%i)log(cos(x)) + 2a0474 tan(x) + 2%i a0474 - %i +--R (391) -- x + ----------------------------------------------------------- +--R 2 2tan(x) + 2%i +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 420 + +--S 421 of 546 +d0474:= D(m0474,x) +--R +--R +--R (- sin(x) + %i cos(x))tan(x) - %i sin(x) +--R (392) ---------------------------------------- +--R cos(x)tan(x) + %i cos(x) +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 421 + +--S 422 of 546 +t0475:= cot(x)/(%i+tan(x)) +--R +--R +--R cot(x) +--R (393) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 422 + +--S 423 of 546 +r0475:= 1/2*x-%i*log(sin(x))+1/(2*%i+2*tan(x)) +--R +--R +--R (- 2%i tan(x) + 2)log(sin(x)) + x tan(x) + %i x + 1 +--R (394) --------------------------------------------------- +--R 2tan(x) + 2%i +--R Type: Expression Complex Integer +--E 423 + +--S 424 of 546 +a0475:= integrate(t0475,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 424 + +--S 425 of 546 +m0475:= a0475-r0475 +--R +--R +--R (395) +--R (2%i tan(x) - 2)log(sin(x)) + (- x + 2a0475)tan(x) - %i x + 2%i a0475 - 1 +--R ------------------------------------------------------------------------- +--R 2tan(x) + 2%i +--R Type: Expression Complex Integer +--E 425 + +--S 426 of 546 +d0475:= D(m0475,x) +--R +--R +--R %i cos(x)tan(x) - %i sin(x) - cos(x) +--R (396) ------------------------------------ +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression Complex Integer +--E 426 + +--S 427 of 546 +t0476:= cot(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R cot(x) +--R (397) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 427 + +--S 428 of 546 +r0476:= 3/2*%i*x+%i*cot(x)+log(sin(x))+%i/(2*%i+2*tan(x)) +--R +--R +--R (398) +--R (2tan(x) + 2%i)log(sin(x)) + (2%i cot(x) + 3%i x)tan(x) - 2cot(x) - 3x + %i +--R --------------------------------------------------------------------------- +--R 2tan(x) + 2%i +--R Type: Expression Complex Integer +--E 428 + +--S 429 of 546 +a0476:= integrate(t0476,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 429 + +--S 430 of 546 +m0476:= a0476-r0476 +--R +--R +--R (399) +--R (- 2tan(x) - 2%i)log(sin(x)) + (- 2%i cot(x) - 3%i x + 2a0476)tan(x) +--R + +--R 2cot(x) + 3x + 2%i a0476 - %i +--R / +--R 2tan(x) + 2%i +--R Type: Expression Complex Integer +--E 430 + +--S 431 of 546 +d0476:= D(m0476,x) +--R +--R +--R (400) +--R 2 2 +--R (%i cot(x) sin(x) - cos(x))tan(x) + (- cot(x) + 1)sin(x) - %i cos(x) +--R --------------------------------------------------------------------- +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression Complex Integer +--E 431 + +--S 432 of 546 +t0477:= cot(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R cot(x) +--R (401) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 432 + +--S 433 of 546 +r0477:= -3/2*x-cot(x)+1/2*%i*cot(x)^2+2*%i*log(sin(x))-1/(2*%i+2*tan(x)) +--R +--R +--R (402) +--R 1 2 3 +--R (2%i tan(x) - 2)log(sin(x)) + (- %i cot(x) - cot(x) - - x)tan(x) +--R 2 2 +--R + +--R 1 2 3 1 +--R - - cot(x) - %i cot(x) - - %i x - - +--R 2 2 2 +--R / +--R tan(x) + %i +--R Type: Expression Complex Fraction Integer +--E 433 + +--S 434 of 546 +a0477:= integrate(t0477,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 434 + +--S 435 of 546 +m0477:= a0477-r0477 +--R +--R +--R (403) +--R (- 2%i tan(x) + 2)log(sin(x)) +--R + +--R 1 2 3 1 2 +--R (- - %i cot(x) + cot(x) + - x + a0477)tan(x) + - cot(x) + %i cot(x) +--R 2 2 2 +--R + +--R 3 1 +--R - %i x + %i a0477 + - +--R 2 2 +--R / +--R tan(x) + %i +--R Type: Expression Complex Fraction Integer +--E 435 + +--S 436 of 546 +d0477:= D(m0477,x) +--R +--R +--R (404) +--R 3 2 +--R ((%i cot(x) - cot(x) + %i cot(x))sin(x) - 2%i cos(x))tan(x) +--R + +--R 3 2 +--R (- cot(x) - %i cot(x) - cot(x) + %i)sin(x) + 2cos(x) +--R / +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression Complex Fraction Integer +--E 436 + +--S 437 of 546 +t0478:= cot(x)^4/(%i+tan(x)) +--R +--R +--R 4 +--R cot(x) +--R (405) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 437 + +--S 438 of 546 +r0478:= -5/2*%i*x-2*%i*cot(x)-1/2*cot(x)^2+1/3*%i*cot(x)^3-2*log(sin(x))-%i/(2*%i+2*tan(x)) +--R +--R +--R (406) +--R (- 2tan(x) - 2%i)log(sin(x)) +--R + +--R 1 3 1 2 5 1 3 +--R (- %i cot(x) - - cot(x) - 2%i cot(x) - - %i x)tan(x) - - cot(x) +--R 3 2 2 3 +--R + +--R 1 2 5 1 +--R - - %i cot(x) + 2cot(x) + - x - - %i +--R 2 2 2 +--R / +--R tan(x) + %i +--R Type: Expression Complex Fraction Integer +--E 438 + +--S 439 of 546 +a0478:= integrate(t0478,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 439 + +--S 440 of 546 +m0478:= a0478-r0478 +--R +--R +--R (407) +--R (2tan(x) + 2%i)log(sin(x)) +--R + +--R 1 3 1 2 5 +--R (- - %i cot(x) + - cot(x) + 2%i cot(x) + - %i x + a0478)tan(x) +--R 3 2 2 +--R + +--R 1 3 1 2 5 1 +--R - cot(x) + - %i cot(x) - 2cot(x) - - x + %i a0478 + - %i +--R 3 2 2 2 +--R / +--R tan(x) + %i +--R Type: Expression Complex Fraction Integer +--E 440 + +--S 441 of 546 +d0478:= D(m0478,x) +--R +--R +--R (408) +--R 4 3 2 +--R ((%i cot(x) - cot(x) - %i cot(x) - cot(x))sin(x) + 2cos(x))tan(x) +--R + +--R 4 3 2 +--R (- cot(x) - %i cot(x) + cot(x) - %i cot(x) - 1)sin(x) + 2%i cos(x) +--R / +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression Complex Fraction Integer +--E 441 + +--S 442 of 546 +t0479:= sec(x)/(%i+tan(x)) +--R +--R +--R sec(x) +--R (409) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 442 + +--S 443 of 546 +r0479:= -cos(x)-%i*sin(x) +--R +--R +--R (410) - %i sin(x) - cos(x) +--R Type: Expression Complex Integer +--E 443 + +--S 444 of 546 +a0479:= integrate(t0479,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 444 + +--S 445 of 546 +m0479:= a0479-r0479 +--R +--R +--R (411) %i sin(x) + cos(x) + a0479 +--R Type: Expression Complex Integer +--E 445 + +--S 446 of 546 +d0479:= D(m0479,x) +--R +--R +--R (412) - sin(x) + %i cos(x) +--R Type: Expression Complex Integer +--E 446 + +--S 447 of 546 +t0480:= sec(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R sec(x) +--R (413) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 447 + +--S 448 of 546 +r0480:= -%i*atanh(sin(x))+sec(x) +--R +--R +--R (414) - %i atanh(sin(x)) + sec(x) +--R Type: Expression Complex Integer +--E 448 + +--S 449 of 546 +a0480:= integrate(t0480,x) +--R +--R +--R sin(x) - cos(x) - 1 +--R %i cos(x)log(-------------------) + cos(x) + 1 +--R sin(x) + cos(x) + 1 +--R (415) ---------------------------------------------- +--R cos(x) +--R Type: Union(Expression Complex Integer,...) +--E 449 + +--S 450 of 546 +m0480:= a0480-r0480 +--R +--R +--R (416) +--R sin(x) - cos(x) - 1 +--R %i cos(x)log(-------------------) + %i cos(x)atanh(sin(x)) - cos(x)sec(x) +--R sin(x) + cos(x) + 1 +--R + +--R cos(x) + 1 +--R / +--R cos(x) +--R Type: Expression Complex Integer +--E 450 + +--S 451 of 546 +d0480:= D(m0480,x) +--R +--R +--R (417) +--R 2 4 4 3 2 2 +--R - cos(x) sec(x)sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sec(x)sin(x) +--R + +--R 4 3 2 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) +--R * +--R tan(x) +--R + +--R 5 2 4 2 3 +--R sin(x) + 2%i cos(x) sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 +--R (2%i cos(x) + %i cos(x) - 2%i cos(x) )sin(x) +--R + +--R 2 5 3 +--R (cos(x) + 2cos(x) + 1)sin(x) + %i cos(x) - %i cos(x) +--R / +--R 2 4 4 3 2 2 4 +--R cos(x) sin(x) + (- cos(x) - 2cos(x) - 2cos(x) )sin(x) + cos(x) +--R + +--R 3 2 +--R 2cos(x) + cos(x) +--R Type: Expression Complex Integer +--E 451 + +--S 452 of 546 +t0481:= csc(x)/(%i+tan(x)) +--R +--R +--R csc(x) +--R (418) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 452 + +--S 453 of 546 +r0481:= %i*atanh(cos(x))-%i*cos(x)+sin(x) +--R +--R +--R (419) %i atanh(cos(x)) + sin(x) - %i cos(x) +--R Type: Expression Complex Integer +--E 453 + +--S 454 of 546 +a0481:= integrate(t0481,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 454 + +--S 455 of 546 +m0481:= a0481-r0481 +--R +--R +--R (420) - %i atanh(cos(x)) - sin(x) + %i cos(x) + a0481 +--R Type: Expression Complex Integer +--E 455 + +--S 456 of 546 +d0481:= D(m0481,x) +--R +--R +--R 2 3 +--R - %i cos(x) sin(x) - cos(x) + cos(x) +--R (421) ------------------------------------- +--R 2 +--R cos(x) - 1 +--R Type: Expression Complex Integer +--E 456 + +--S 457 of 546 +t0482:= csc(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R csc(x) +--R (422) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 457 + +--S 458 of 546 +r0482:= %i*cot(x)-log(-%i+cot(x)) +--R +--R +--R (423) - log(cot(x) - %i) + %i cot(x) +--R Type: Expression Complex Integer +--E 458 + +--S 459 of 546 +a0482:= integrate(t0482,x) +--R +--R +--R (424) +--R sin(x) 2 +--R sin(x)log(----------) - sin(x)log(----------) + %i x sin(x) + %i cos(x) +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------- +--R sin(x) +--R Type: Union(Expression Complex Integer,...) +--E 459 + +--S 460 of 546 +m0482:= a0482-r0482 +--R +--R +--R (425) +--R sin(x) 2 +--R sin(x)log(----------) + sin(x)log(cot(x) - %i) - sin(x)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R (- %i cot(x) + %i x)sin(x) + %i cos(x) +--R / +--R sin(x) +--R Type: Expression Complex Integer +--E 460 + +--S 461 of 546 +d0482:= D(m0482,x) +--R +--R +--R 2 2 2 +--R (%i cot(x) - cot(x))sin(x) + cos(x)sin(x) - %i cos(x) +--R (426) -------------------------------------------------------- +--R 2 +--R sin(x) +--R Type: Expression Complex Integer +--E 461 + +--S 462 of 546 +t0483:= csc(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R csc(x) +--R (427) ----------- +--R tan(x) + %i +--R Type: Expression Complex Integer +--E 462 + +--S 463 of 546 +r0483:= -1/2*%i*atanh(cos(x))-csc(x)+1/2*%i*cot(x)*csc(x) +--R +--R +--R 1 1 +--R (428) - - %i atanh(cos(x)) + (- %i cot(x) - 1)csc(x) +--R 2 2 +--R Type: Expression Complex Fraction Integer +--E 463 + +--S 464 of 546 +a0483:= integrate(t0483,x) +--R +--R +--R 2 sin(x) +--R (%i cos(x) - %i)log(----------) + 2sin(x) - %i cos(x) +--R cos(x) + 1 +--R (429) ------------------------------------------------------ +--R 2 +--R 2cos(x) - 2 +--R Type: Union(Expression Complex Integer,...) +--E 464 + +--S 465 of 546 +m0483:= a0483-r0483 +--R +--R +--R (430) +--R 1 2 1 sin(x) 1 2 1 +--R (- %i cos(x) - - %i)log(----------) + (- %i cos(x) - - %i)atanh(cos(x)) +--R 2 2 cos(x) + 1 2 2 +--R + +--R 1 2 1 2 1 +--R sin(x) + ((- - %i cos(x) + - %i)cot(x) + cos(x) - 1)csc(x) - - %i cos(x) +--R 2 2 2 +--R / +--R 2 +--R cos(x) - 1 +--R Type: Expression Complex Fraction Integer +--E 465 + +--S 466 of 546 +d0483:= D(m0483,x) +--R +--R +--R (431) +--R 3 +--R 2cos(x)sin(x) +--R + +--R 1 3 1 2 1 1 2 +--R (- %i cos(x) - - %i cos(x) - - %i cos(x) - - %i)sin(x) +--R 2 2 2 2 +--R + +--R 4 2 2 +--R (%i cos(x) - 2%i cos(x) + %i)cot(x) +--R + +--R 4 2 1 4 2 1 +--R (- cos(x) + 2cos(x) - 1)cot(x) + - %i cos(x) - %i cos(x) + - %i +--R 2 2 +--R * +--R csc(x) +--R + +--R 3 +--R cos(x) - cos(x) +--R * +--R sin(x) +--R + +--R 1 5 3 1 +--R - %i cos(x) - %i cos(x) + - %i cos(x) +--R 2 2 +--R / +--R 4 2 +--R (cos(x) - 2cos(x) + 1)sin(x) +--R Type: Expression Complex Fraction Integer +--E 466 + +--S 467 of 546 +t0484:= sin(x)/(a+b*cot(x)) +--R +--R +--R sin(x) +--R (432) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 467 + +--S 468 of 546 +r0484:= -b^2*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-a*cos(x)/(a^2+b^2)-b*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 b sin(x) - a cos(x) | 2 2 +--R b atanh(-------------------) + (- b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (433) ---------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 468 + +--S 469 of 546 +a0484:= integrate(t0484,x) +--R +--R +--R (434) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (- b sin(x) - a cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 469 + +--S 470 of 546 +m0484:= a0484-r0484 +--R +--R +--R (435) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R 2 b sin(x) - a cos(x) +--R - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 470 + +--S 471 of 546 +d0484:= D(m0484,x) +--R +--R +--R (436) +--R 3 3 2 2 3 2 3 2 3 +--R b sin(x) - a b cos(x)sin(x) + (b cos(x) - b )sin(x) - a b cos(x) +--R + +--R 2 +--R a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 3 5 2 3 4 2 +--R (a b + a b )sin(x) + (b - a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R ((- 2a b - a b + a )cos(x) - a b - 2a b - a )sin(x) +--R + +--R 2 3 4 3 5 2 3 4 +--R (a b + a b)cos(x) + (- b - 2a b - a b)cos(x) +--R Type: Expression Integer +--E 471 + +--S 472 of 546 +t0485:= sin(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R sin(x) +--R (437) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 472 + +--S 473 of 546 +r0485:= -1/2*(-a^3*x-3*a*b^2*x+2*b^3*log(b*cos(x)+a*sin(x))+a^3*sin(x)*cos(x)+b^2*a*sin(x)*cos(x)+a^2*b-a^2*b*cos(x)^2+b^3-b^3*cos(x)^2)/(a^2+b^2)^2 +--R +--R +--R (438) +--R 3 2 3 +--R - 2b log(a sin(x) + b cos(x)) + (- a b - a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b + a b)cos(x) + (3a b + a )x - b - a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 473 + +--S 474 of 546 +a0485:= integrate(t0485,x) +--R +--R +--R (439) +--R 3 2 3 - 2a sin(x) - 2b cos(x) +--R 2b log(----------) - 2b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (- a b - a )cos(x)sin(x) + (b + a b)cos(x) + (3a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 474 + +--S 475 of 546 +m0485:= a0485-r0485 +--R +--R +--R (440) +--R 3 3 2 +--R 2b log(a sin(x) + b cos(x)) + 2b log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2a sin(x) - 2b cos(x) 3 2 +--R - 2b log(-----------------------) + b + a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 475 + +--S 476 of 546 +d0485:= D(m0485,x) +--R +--R +--R (441) 0 +--R Type: Expression Integer +--E 476 + +--S 477 of 546 +t0486:= sin(x)^3/(a+b*cot(x)) +--R +--R +--R 3 +--R sin(x) +--R (442) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 477 + +--S 478 of 546 +r0486:= 2/3*(-6*a^3*cos(1/2*x)^4*(a^2+b^2)^(1/2)+4*a^3*cos(1/2*x)^6*(a^2+b^2)^(1/2)+4*b*cos(1/2*x)^5*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2-4*b*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2-6*a*cos(1/2*x)^4*(a^2+b^2)^(1/2)*b^2+4*a*cos(1/2*x)^6*(a^2+b^2)^(1/2)*b^2-3*a*cos(1/2*x)^2*(a^2+b^2)^(1/2)*b^2-3*b^4*atanh(1/(a^2+b^2)^(1/2)*(b*cos(x)-b+a*sin(x))/sin(x))+4*b^3*cos(1/2*x)^5*sin(1/2*x)*(a^2+b^2)^(1/2)-3*b^3*cos(1/2*x)*sin(1/2*x)*(a^2+b^2)^(1/2)-4*b^3*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2) +--R +--R +--R (443) +--R 4 a sin(x) + b cos(x) - b +--R - 6b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 x 5 3 2 x 3 3 x x +--R ((8b + 8a b)cos(-) + (- 8b - 8a b)cos(-) - 6b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 x 6 2 3 x 4 2 x 2 +--R (8a b + 8a )cos(-) + (- 12a b - 12a )cos(-) - 6a b cos(-) +--R 2 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 478 + +--S 479 of 546 +a0486:= integrate(t0486,x) +--R +--R +--R (444) +--R 4 +--R 3b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((b + a b)cos(x) - 4b - a b)sin(x) + (a b + a )cos(x) +--R + +--R 2 3 +--R (- 6a b - 3a )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression Integer,...) +--E 479 + +--S 480 of 546 +m0486:= a0486-r0486 +--R +--R +--R (445) +--R 4 +--R 3b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R 4 a sin(x) + b cos(x) - b +--R 6b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 2 3 2 +--R ((b + a b)cos(x) - 4b - a b)sin(x) +--R + +--R 3 2 x 5 3 2 x 3 3 x x +--R ((- 8b - 8a b)cos(-) + (8b + 8a b)cos(-) + 6b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 3 2 3 2 3 x 6 +--R (a b + a )cos(x) + (- 6a b - 3a )cos(x) + (- 8a b - 8a )cos(-) +--R 2 +--R + +--R 2 3 x 4 2 x 2 +--R (12a b + 12a )cos(-) + 6a b cos(-) +--R 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression Integer +--E 480 + +--S 481 of 546 +d0486:= D(m0486,x) +--R +--R +--R (446) +--R 2 5 4 3 6 +--R (- 2a b - 2a b )cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 5 2 3 4 +--R (- 2a b + a b + 3a b )cos(x) + (2a b - 2a b )cos(x) + 6a b +--R + +--R 5 2 +--R 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 2 5 +--R ((20a b + 20a b )cos(-) + (- 12a b - 12a b )cos(-) - 3a b ) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R - 6a b cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 3 +--R (6a b + 11a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (2b - 5a b - 10a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 x 6 +--R (8a b - 6a b - 5a b)cos(x) + (- 4a b - 4a b )cos(-) +--R 2 +--R + +--R 2 5 4 3 x 4 2 5 x 2 7 2 5 4 3 6 +--R (4a b + 4a b )cos(-) + 3a b cos(-) - 3b - 15a b + 3a b + 3a b +--R 2 2 +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (20a b - 40a b - 60a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (- 12a b + 24a b + 36a b )cos(-) - 3a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 5 2 x 4 6 5 2 x 2 6 +--R (- 20a b + 20a b )cos(-) + (12a b - 12a b )cos(-) + 3a b +--R 2 2 +--R + +--R 3 4 +--R - 3a b +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (24a b - 48a b - 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (- 24a b + 48a b + 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 6a b + 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 6 x 5 2 5 6 x 3 +--R (- 24a b + 24a b)cos(-) + (24a b - 24a b)cos(-) +--R 2 2 +--R + +--R 2 5 4 3 x +--R (6a b - 6a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 7 4 +--R (3a b + 6a b - 3a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 8a b - 20a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (6a b + 12a b + 24a b + 12a )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 4a b + 8a b + 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 6 3 4 x 2 +--R (4a b - 8a b - 12a b )cos(-) + (3a b - 9a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 +--R - 4a b + 32a b + 12a b +--R * +--R cos(x) +--R + +--R 6 5 2 x 6 6 5 2 x 4 +--R (4a b - 4a b )cos(-) + (- 4a b + 4a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 x 2 6 3 4 5 2 7 +--R (- 3a b + 3a b )cos(-) + 3a b - 18a b - 21a b - 6a +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 80a b - 40a b + 40a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 2 5 4 3 +--R (48a b + 24a b - 24a b)cos(-) + 12a b - 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (- 20b + 80a b + 100a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 7 2 5 +--R (12b - 48a b - 60a b )cos(-) + 3b - 15a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 60a b - 100a b - 40a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 2 5 4 3 +--R (36a b + 60a b + 24a b)cos(-) + 9a b + 6a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 7 x 5 +--R (- 96a b - 48a b + 48a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (96a b + 48a b - 48a )cos(-) + (24a b - 12a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (- 24a b + 96a b + 120a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (24a b - 96a b - 120a b )cos(-) + (6a b - 30a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (- 72a b - 120a b - 48a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (72a b + 120a b + 48a )cos(-) + (18a b + 12a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 5 +--R (- 3a b - 10a b - 7a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 3b - 11a b - 5a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 28a b + 32a b + 14a b)cos(x) +--R + +--R 2 5 4 3 6 x 6 +--R (16a b + 8a b - 8a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 4 2 5 4 3 x 2 +--R (- 16a b - 8a b + 8a b)cos(-) + (- 12a b + 6a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 4 3 6 +--R 2b + 4a b - 4a b - 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 +--R (4b - 16a b - 20a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 4 7 2 5 x 2 +--R (- 4b + 16a b + 20a b )cos(-) + (- 3b + 15a b )cos(-) +--R 2 2 +--R + +--R 2 5 4 3 6 +--R - 21a b - 22a b - 7a b +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 +--R (12a b + 20a b + 8a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 4 2 5 4 3 x 2 +--R (- 12a b - 20a b - 8a b)cos(-) + (- 9a b - 6a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 4 3 6 +--R 3b + 15a b + 9a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 20a b + 40a b + 60a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (12a b - 24a b - 36a b )cos(-) + 3a b - 9a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (100a b + 80a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (- 60a b - 48a b + 12a b )cos(-) - 15a b + 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 100a b - 160a b - 60a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (60a b + 96a b + 36a b )cos(-) + 15a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (- 24a b + 48a b + 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (24a b - 48a b - 72a b)cos(-) + (6a b - 18a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (120a b + 96a b - 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (- 120a b - 96a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 30a b + 6a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (- 120a b - 192a b - 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (120a b + 192a b + 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (30a b + 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 6 6 3 4 5 2 5 +--R (- a b - a b )cos(x) + (2a b + 4a b + 2a b )cos(x) +--R + +--R 6 3 4 4 +--R (5a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (4a b - 8a b - 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 6 3 4 x 2 +--R (- 4a b + 8a b + 12a b )cos(-) + (- 3a b + 9a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 +--R - 16a b + 4a b - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 20a b - 16a b + 4a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 6 3 4 x 2 +--R (20a b + 16a b - 4a b )cos(-) + (15a b - 3a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 +--R 11a b + 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (20a b + 32a b + 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 +--R (- 20a b - 32a b - 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 x 2 6 3 4 5 2 +--R (- 15a b - 9a b )cos(-) + 2a b - 8a b + 2a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 6 3 4 5 2 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 x 2 6 +--R (3a b + 3a b )cos(-) - 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 2 5 +--R ((20a b + 20a b )cos(-) + (- 12a b - 12a b )cos(-) - 3a b ) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 7 4 3 x 4 7 4 3 x 2 7 +--R (20b - 20a b )cos(-) + (- 12b + 12a b )cos(-) - 3b +--R 2 2 +--R + +--R 2 5 +--R 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (- 40b - 60a b - 20a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 7 2 5 +--R (24b + 36a b + 12a b )cos(-) + 6b + 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (20b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 7 2 5 +--R (- 12b - 24a b - 12a b )cos(-) - 3b - 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R - 6a b cos(-) +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 x 5 6 5 2 x 3 +--R (24a b - 24a b )cos(-) + (- 24a b + 24a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 x +--R (- 6a b + 6a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (- 48a b - 72a b - 24a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (48a b + 72a b + 24a b )cos(-) + (12a b + 6a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 7 7 4 3 6 +--R (a b + a b )cos(x) + (b - a b )cos(x) +--R + +--R 7 2 5 4 3 5 +--R (- 2b - 7a b - 2a b )cos(x) +--R + +--R 2 5 4 3 x 6 2 5 4 3 x 4 2 5 x 2 +--R (- 4a b - 4a b )cos(-) + (4a b + 4a b )cos(-) + 3a b cos(-) +--R 2 2 2 +--R + +--R 2 5 4 3 +--R 14a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 4 3 x 6 7 4 3 x 4 +--R (- 4b + 4a b )cos(-) + (4b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 x 2 7 2 5 4 3 +--R (3b - 3a b )cos(-) + 8b + 3a b + a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 7 2 5 4 3 x 4 +--R (8b + 12a b + 4a b )cos(-) + (- 8b - 12a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 x 2 7 2 5 4 3 +--R (- 6b - 3a b )cos(-) - 7b - 14a b - a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 7 2 5 4 3 x 4 +--R (- 4b - 8a b - 4a b )cos(-) + (4b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 x 2 2 5 +--R (3b + 3a b )cos(-) + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 7 3 5 5 3 6 +--R (2a b + 4a b + 2a b )cos(x)sin(x) +--R + +--R 8 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (2b + a b - 4a b - 3a b )cos(x) + (2a b + 4a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R - 6a b - 9a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 24a b - 48a b - 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (24a b + 48a b + 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 3 +--R (- 6a b - 17a b - 16a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b + 15a b + 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 +--R (- 4a b + 6a b + 15a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 7 +--R (- 3a b - 3a b )cos(-) + 9a b + 3a b - 9a b - 3a b +--R 2 +--R * +--R 4 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (- 20b + 20a b + 100a b + 60a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 8 2 6 4 4 +--R (12b - 12a b - 60a b - 36a b )cos(-) + 3b - 6a b - 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 2 6 4 4 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 5 +--R (- 24a b + 24a b + 120a b + 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (24a b - 24a b - 120a b - 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (6a b - 12a b - 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 3b - 9a b - 3a b + 9a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b + 14a b + 16a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (2b + 4a b - 16a b - 30a b - 12a )cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (4b - 4a b - 20a b - 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (- 4b + 4a b + 20a b + 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 6 2 +--R (- 3b + 6a b + 9a b )cos(-) + 6b - 18a b - 30a b - 6a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 2 6 4 4 x 2 8 2 6 4 4 6 2 8 +--R (- 3a b - 3a b )cos(-) - 3b + 3a b + 21a b + 21a b + 6a +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 7 x 4 +--R (80a b + 120a b - 40a b)cos(-) +--R 2 +--R + +--R 7 3 5 7 x 2 7 3 5 5 3 +--R (- 48a b - 72a b + 24a b)cos(-) - 12a b - 6a b + 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 60a b - 120a b - 60a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (36a b + 72a b + 36a b )cos(-) + 9a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (20a b + 80a b + 100a b + 40a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 7 3 5 5 3 +--R (- 12a b - 48a b - 60a b - 24a b)cos(-) - 3a b - 9a b - 6a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 8 x 5 +--R (96a b + 144a b - 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 8 x 3 +--R (- 96a b - 144a b + 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 24a b - 12a b + 12a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 72a b - 144a b - 72a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (72a b + 144a b + 72a b )cos(-) + (18a b + 18a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (24a b + 96a b + 120a b + 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (- 24a b - 96a b - 120a b - 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 6a b - 18a b - 12a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 5 +--R (3a b + 13a b + 17a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b - a b - 5a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 14a b - 36a b - 36a b - 14a b)cos(x) +--R + +--R 7 3 5 7 x 6 +--R (- 16a b - 24a b + 8a b)cos(-) +--R 2 +--R + +--R 7 3 5 7 x 4 7 3 5 5 3 x 2 +--R (16a b + 24a b - 8a b)cos(-) + (12a b + 6a b - 6a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 5 3 7 +--R 2a b + 10a b + 14a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 +--R (12a b + 24a b + 12a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 4 7 3 5 x 2 +--R (- 12a b - 24a b - 12a b )cos(-) + (- 9a b - 9a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 5 3 7 +--R 5a b + 17a b + 19a b + 7a b +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (- 4a b - 16a b - 20a b - 8a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (4a b + 16a b + 20a b + 8a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 5 3 7 +--R (3a b + 9a b + 6a b )cos(-) - 9a b - 15a b - 9a b - 3a b +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (20b - 20a b - 100a b - 60a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 8 2 6 +--R (- 12b + 12a b + 60a b + 36a b )cos(-) - 3b + 6a b +--R 2 +--R + +--R 4 4 +--R 9a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 6 6 2 x 4 +--R (- 40b - 60a b + 20a b )cos(-) +--R 2 +--R + +--R 8 2 6 6 2 x 2 8 2 6 4 4 +--R (24b + 36a b - 12a b )cos(-) + 6b + 3a b - 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (20b + 100a b + 140a b + 60a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 8 2 6 +--R (- 12b - 60a b - 84a b - 36a b )cos(-) - 3b - 12a b +--R 2 +--R + +--R 4 4 +--R - 9a b +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 2 6 4 4 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 5 +--R (24a b - 24a b - 120a b - 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (- 24a b + 24a b + 120a b + 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (- 6a b + 12a b + 18a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 3 5 7 x 5 +--R (- 48a b - 72a b + 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 7 x 3 +--R (48a b + 72a b - 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (12a b + 6a b - 6a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 5 +--R (24a b + 120a b + 168a b + 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (- 24a b - 120a b - 168a b - 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (- 6a b - 24a b - 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 8 2 6 4 4 6 2 5 +--R (b + 2a b + a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 4 +--R (- 3b + 3a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (- 4b + 4a b + 20a b + 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (4b - 4a b - 20a b - 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 6 2 +--R (3b - 6a b - 9a b )cos(-) + 14b + 8a b - 2a b + 4a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 6 6 2 x 6 8 2 6 6 2 x 4 +--R (8b + 12a b - 4a b )cos(-) + (- 8b - 12a b + 4a b )cos(-) +--R 2 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 +--R (- 6b - 3a b + 3a b )cos(-) - 7b - 14a b - 7a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (- 4b - 20a b - 28a b - 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (4b + 20a b + 28a b + 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 6 2 +--R (3b + 12a b + 9a b )cos(-) - 6b + 4a b + 8a b - 2a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 2 6 4 4 x 2 8 2 6 +--R (- 3a b - 3a b )cos(-) + 3b + 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 24a b - 48a b - 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (24a b + 48a b + 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 24a b - 48a b - 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (24a b + 48a b + 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 6 +--R (- a b - 2a b - a b )cos(x) + (a b + 2a b + a b )cos(x) +--R + +--R 7 3 5 5 3 5 +--R (5a b + 7a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 +--R (- 3a b - 3a b )cos(-) - 14a b - 16a b - 2a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 +--R (3a b + 3a b )cos(-) - a b - 2a b - a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 +--R (3a b + 3a b )cos(-) + 13a b + 14a b + a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 +--R (- 3a b - 3a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R cos(x) +--R / +--R 2 6 4 4 6 2 4 +--R (3a b + 6a b + 3a b )sin(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 3a b - 15a b - 9a b)cos(x) - 3a b - 3a b + 3a b +--R + +--R 7 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 8 2 +--R (- 12a b - 18a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 6 4 4 6 2 +--R (- 3b + 9a b + 27a b + 15a b )cos(x) - 9a b - 24a b - 21a b +--R + +--R 8 +--R - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 3a b + 15a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (15a b + 27a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 15a b - 39a b - 33a b - 9a b)cos(x) + 3a b + 9a b + 9a b +--R + +--R 7 +--R 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 8 2 6 4 4 6 2 3 +--R (3a b + 6a b + 3a b )cos(x) + (3b + 3a b - 3a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 6b - 15a b - 12a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 +--R (3b + 9a b + 9a b + 3a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 3a b - 9a b - 9a b - 3a b )sin(x) +--R + +--R 9 4 5 6 3 8 2 7 4 5 6 3 8 +--R ((- 3b + 18a b + 24a b + 9a b)cos(x) - 3a b - 9a b - 9a b - 3a b) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (12a b + 30a b + 18a b - 6a b - 6a )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 9a b - 27a b - 27a b - 9a b )cos(x) + 3a b + 15a b + 27a b +--R + +--R 7 2 9 +--R 21a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 9 4 5 6 3 8 3 +--R (3b - 18a b - 24a b - 9a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 6b - 15a b - 9a b + 3a b + 3a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (3b + 18a b + 36a b + 30a b + 9a b)cos(x) - 3a b - 9a b - 9a b +--R + +--R 8 +--R - 3a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 3a b - 9a b - 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (3a b + 9a b + 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (3a b + 9a b + 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R (- 3a b - 9a b - 9a b - 3a b )cos(x) +--R Type: Expression Integer +--E 481 + +--S 482 of 546 +t0487:= cos(x)/(a+b*cot(x)) +--R +--R +--R cos(x) +--R (447) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 482 + +--S 483 of 546 +r0487:= a*b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R b sin(x) - a cos(x) | 2 2 +--R - a b atanh(-------------------) + (a sin(x) - b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (448) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 483 + +--S 484 of 546 +a0487:= integrate(t0487,x) +--R +--R +--R (449) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) - b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression Integer,...) +--E 484 + +--S 485 of 546 +m0487:= a0487-r0487 +--R +--R +--R (450) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R b sin(x) - a cos(x) +--R a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression Integer +--E 485 + +--S 486 of 546 +d0487:= D(m0487,x) +--R +--R +--R (451) +--R 2 3 2 2 2 2 2 +--R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b )sin(x) +--R + +--R 2 3 2 +--R - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 3 5 2 3 4 2 +--R (a b + a b )sin(x) + (b - a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R ((- 2a b - a b + a )cos(x) - a b - 2a b - a )sin(x) +--R + +--R 2 3 4 3 5 2 3 4 +--R (a b + a b)cos(x) + (- b - 2a b - a b)cos(x) +--R Type: Expression Integer +--E 486 + +--S 487 of 546 +t0488:= cos(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R cos(x) +--R (452) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 487 + +--S 488 of 546 +r0488:= -1/2*(a*b^2*x-a^3*x+2*a^2*b*log(b*cos(x)+a*sin(x))-a^3*sin(x)*cos(x)-b^2*a*sin(x)*cos(x)-a^2*b+a^2*b*cos(x)^2-b^3+b^3*cos(x)^2)/(a^2+b^2)^2 +--R +--R +--R (453) +--R 2 2 3 +--R - 2a b log(a sin(x) + b cos(x)) + (a b + a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cos(x) + (- a b + a )x + b + a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 488 + +--S 489 of 546 +a0488:= integrate(t0488,x) +--R +--R +--R (454) +--R 2 2 2 - 2a sin(x) - 2b cos(x) +--R 2a b log(----------) - 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (a b + a )cos(x)sin(x) + (- b - a b)cos(x) + (- a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression Integer,...) +--E 489 + +--S 490 of 546 +m0488:= a0488-r0488 +--R +--R +--R (455) +--R 2 2 2 +--R 2a b log(a sin(x) + b cos(x)) + 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2a sin(x) - 2b cos(x) 3 2 +--R - 2a b log(-----------------------) - b - a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression Integer +--E 490 + +--S 491 of 546 +d0488:= D(m0488,x) +--R +--R +--R (456) 0 +--R Type: Expression Integer +--E 491 + +--S 492 of 546 +t0489:= cot(x)/(a+b*cot(x)) +--R +--R +--R cot(x) +--R (457) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 492 + +--S 493 of 546 +r0489:= (b*x+a*log(b*cos(x)+a*sin(x)))/(a^2+b^2) +--R +--R +--R a log(a sin(x) + b cos(x)) + b x +--R (458) -------------------------------- +--R 2 2 +--R b + a +--R Type: Expression Integer +--E 493 + +--S 494 of 546 +a0489:= integrate(t0489,x) +--R +--R +--R a sin(2x) + b cos(2x) + b 2 +--R 2a log(-------------------------) - a log(-----------) + 2b x +--R cos(2x) + 1 cos(2x) + 1 +--R (459) ------------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Union(Expression Integer,...) +--E 494 + +--S 495 of 546 +m0489:= a0489-r0489 +--R +--R +--R (460) +--R a sin(2x) + b cos(2x) + b +--R 2a log(-------------------------) - 2a log(a sin(x) + b cos(x)) +--R cos(2x) + 1 +--R + +--R 2 +--R - a log(-----------) +--R cos(2x) + 1 +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression Integer +--E 495 + +--S 496 of 546 +d0489:= D(m0489,x) +--R +--R +--R (461) +--R 3 2 2 +--R (a sin(x) + a b cos(x))sin(2x) +--R + +--R 2 3 2 3 +--R ((- a b - a )cos(x)cos(2x) + (- a b - a )cos(x))sin(2x) +--R + +--R 2 3 2 2 3 2 +--R ((a b + 2a )cos(2x) + (2a b + 2a )cos(2x) + a b )sin(x) +--R + +--R 2 2 2 +--R a b cos(x)cos(2x) - a b cos(x) +--R / +--R 2 2 4 2 2 4 3 3 +--R ((a b + a )cos(2x) + a b + a )sin(x) + (a b + a b)cos(x)cos(2x) +--R + +--R 3 3 +--R (a b + a b)cos(x) +--R * +--R sin(2x) +--R + +--R 3 3 2 3 3 3 3 +--R ((a b + a b)cos(2x) + (2a b + 2a b)cos(2x) + a b + a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 2 2 +--R (b + a b )cos(x)cos(2x) + (2b + 2a b )cos(x)cos(2x) + (b + a b )cos(x) +--R Type: Expression Integer +--E 496 + +--S 497 of 546 +t0490:= sec(x)/(a+b*cot(x)) +--R +--R +--R sec(x) +--R (462) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 497 + +--S 498 of 546 +r0490:= atanh(sin(x))/a+b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/a/(a^2+b^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R \|b + a atanh(sin(x)) - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (463) ------------------------------------------------------ +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression Integer +--E 498 + +--S 499 of 546 +a0490:= integrate(t0490,x) +--R +--R +--R (464) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Union(Expression Integer,...) +--E 499 + +--S 500 of 546 +m0490:= a0490-r0490 +--R +--R +--R (465) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R - \|b + a atanh(sin(x)) + b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression Integer +--E 500 + +--S 501 of 546 +d0490:= D(m0490,x) +--R +--R +--R (466) +--R 5 2 3 8 4 3 2 4 3 2 7 +--R (b - a b )sin(x) + ((- 4a b + 4a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 5 2 3 +--R (5a b - 5a b)cos(x) + (- 4a b - 3a b)cos(x) - 3b + a b +--R + +--R 4 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 3 4 3 2 5 2 +--R (- 2a b + 2a )cos(x) + (a b + 7a b + 2a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (13a b + 3a b - 2a )cos(x) - a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 4a b)cos(x) + (- 2a b - 7a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 5 2 3 4 +--R (b - 12a b - a b)cos(x) + a b cos(x) + 3b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 5 3 2 5 4 +--R (2a b - 4a b + 2a )cos(x) + (3a b + 3a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (3a b + 8a b - 3a )cos(x) + (- 4a b - 13a b - 5a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (- 14a b - 13a b + a )cos(x) - a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- a b + a b)cos(x) + (2a b - 3a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (2b - 3a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 2 3 +--R (- 2b + 8a b + 10a b)cos(x) + (4a b + 4a b)cos(x) - b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 5 +--R (- 3a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 4a b - 2a b - 2a )cos(x) + (- a b - 3a b - 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (3a b + 4a b + a )cos(x) + (5a b + 6a b + a )cos(x) + a b +--R + +--R 3 2 +--R a b +--R * +--R sin(x) +--R + +--R 4 7 2 3 4 6 2 3 4 5 +--R a b cos(x) + (2a b + 2a b)cos(x) + (2a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 3 +--R (- b - a b )cos(x) + (- a b - a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (b - a b - 2a b)cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 3 3 8 +--R (- a b - a b )sin(x) +--R + +--R 6 2 4 4 2 6 4 2 7 +--R ((- 2b + 2a b + 4a b )cos(x) - b + a b )sin(x) +--R + +--R 5 3 3 5 2 3 3 5 5 3 3 +--R (4a b - a b - 5a b)cos(x) + (- 3a b - 3a b)cos(x) + a b + 3a b +--R + +--R 5 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 2b - 2a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- b + 4a b + 7a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (6b + 9a b + a b - 2a )cos(x) + 3b + 2a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b + a b - 4a b)cos(x) + (2a b - 5a b - 7a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 3 3 +--R (- 7a b - 8a b - a b)cos(x) + (- a b - a b )cos(x) + a b - a b +--R + +--R 5 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (- 4a b - 2a b + 2a )cos(x) + (a b + 4a b + 3a )cos(x) +--R + +--R 6 2 4 4 2 6 3 +--R (4b + 11a b + 4a b - 3a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (2b - 7a b - 14a b - 5a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (- 6b - 18a b - 11a b + a )cos(x) - 3b - 4a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (a b + a b)cos(x) + (2a b - a b - 3a b)cos(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 2a b - 9a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 5 +--R (4a b + 14a b + 10a b)cos(x) + (2a b + 6a b + 4a b)cos(x) - a b +--R + +--R 3 3 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b - 2a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 2 4 4 2 6 4 6 2 4 4 2 6 3 +--R (- 2a b - 4a b - 2a )cos(x) + (- 2b - 3a b - 3a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- b + 3a b + 5a b + a )cos(x) + (2b + 7a b + 6a b + a )cos(x) +--R + +--R 6 2 4 4 2 +--R b + 2a b + a b +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 3 3 5 5 +--R (a b + a b)cos(x) + (2a b + 2a b)cos(x) + (a b + a b)cos(x) +--R + +--R 5 3 3 4 5 5 3 +--R (a b + a b )cos(x) + (a b - a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b - 3a b - 2a b)cos(x) + (- a b - 2a b - a b)cos(x) +--R / +--R 3 3 8 2 4 4 2 2 4 4 2 7 +--R a b sin(x) + ((a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 3 3 5 2 5 3 3 5 3 3 +--R (- 4a b + 3a b)cos(x) + (- a b - a b + 2a b)cos(x) - 3a b +--R + +--R 5 +--R - a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- a b + 6a b - a )cos(x) + (a b + 8a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b + 8a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (3a b - 4a b)cos(x) + (a b + 4a b - 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (2a b + 7a b - 8a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 3 3 5 +--R 3a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (- 3a b + a )cos(x) + (- 2a b - 7a b + 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- 2a b - 11a b + 3a )cos(x) + (- 2a b - 11a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b - 9a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R a b cos(x) + (a b + 3a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (- 2a b - 7a b + 7a b)cos(x) + (- 4a b - 8a b + 2a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- 3a b - 5a b - 2a b)cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (3a b - a )cos(x) + (2a b + 7a b - 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (3a b + 5a b - 2a )cos(x) + (a b + 3a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (a b + 4a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R - a b cos(x) + (- a b - 3a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (a b + 3a b + 2a b)cos(x) + (2a b + 5a b + 3a b)cos(x) +--R + +--R 5 3 3 5 +--R (a b + 2a b + a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 5 4 3 8 +--R (a b + a b )sin(x) +--R + +--R 6 3 4 5 2 3 4 5 2 7 +--R ((a b - 2a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 4a b - a b + 3a b)cos(x) + (- 3a b - a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - 3a b - 4a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 5a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + 7a b + 8a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 3a b + 5a b + 9a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (3a b - a b - 4a b)cos(x) + (7a b - 2a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 2 5 +--R (11a b + 3a b - 8a b)cos(x) + (7a b + 6a b - a b)cos(x) + 3a b +--R + +--R 4 3 6 +--R 5a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (- 3a b - 2a b + a )cos(x) + (- 8a b - 5a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (2a b - 11a b - 10a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (4a b - 8a b - 13a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (3a b - 4a b - 11a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (a b + a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 6a b)cos(x) + (- 10a b - 3a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 10a b - 8a b + 2a b)cos(x) + (- 5a b - 7a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - a b - 2a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (3a b + 2a b - a )cos(x) + (8a b + 5a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 6a b + 5a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + a b + 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- a b + a b + 5a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- a b - a b)cos(x) + (- 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b - a b - 2a b)cos(x) + (3a b + 5a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (3a b + 6a b + 3a b)cos(x) + (a b + 2a b + a b)cos(x) +--R Type: Expression Integer +--E 501 + +--S 502 of 546 +t0491:= sec(x)^3/(a+b*cot(x)) +--R +--R +--R 3 +--R sec(x) +--R (467) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 502 + +--S 503 of 546 +r0491:= (a^2+2*b^2)*atanh(tan(1/2*x))/a^3+2*b*(a^2+b^2)^(1/2)*atanh((a-b*tan(1/2*x))/(a^2+b^2)^(1/2))/a^3+1/2/a/(1-tan(1/2*x))^2-1/2*(a+2*b)/a^2/(1-tan(1/2*x))-1/2/a/(1+tan(1/2*x))^2+1/2*(a-2*b)/a^2/(1+tan(1/2*x)) +--R +--R +--R (468) +--R 2 2 x 4 2 2 x 2 2 2 x +--R ((2b + a )tan(-) + (- 4b - 2a )tan(-) + 2b + a )atanh(tan(-)) +--R 2 2 2 +--R + +--R x +--R +-------+ b tan(-) - a +--R x 4 x 2 | 2 2 2 2 x 3 +--R (- 2b tan(-) + 4b tan(-) - 2b)\|b + a atanh(------------) + a tan(-) +--R 2 2 +-------+ 2 +--R | 2 2 +--R \|b + a +--R + +--R x 2 2 x +--R 2a b tan(-) + a tan(-) - 2a b +--R 2 2 +--R / +--R 3 x 4 3 x 2 3 +--R a tan(-) - 2a tan(-) + a +--R 2 2 +--R Type: Expression Integer +--E 503 + +--S 504 of 546 +a0491:= integrate(t0491,x) +--R +--R +--R (469) +--R +-------+ +--R 2 | 2 2 +--R 2b cos(x) \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (b sin(x) - a cos(x) - a)\|b + a + a b sin(x) - a cos(x) - b +--R + +--R 2 +--R - a +--R / +--R a sin(x) + b cos(x) +--R + +--R 2 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 sin(x) - cos(x) - 1 2 2 +--R (- 2b - a )cos(x) log(-------------------) + a sin(x) - 2a b cos(x) +--R cos(x) + 1 +--R + +--R - 2a b cos(x) +--R / +--R 3 2 +--R 2a cos(x) +--R Type: Union(Expression Integer,...) +--E 504 + +--S 505 of 546 +m0491:= a0491-r0491 +--R +--R +--R (470) +--R +-------+ +--R 2 x 4 2 x 2 2 | 2 2 +--R (2b cos(x) tan(-) - 4b cos(x) tan(-) + 2b cos(x) )\|b + a +--R 2 2 +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (b sin(x) - a cos(x) - a)\|b + a + a b sin(x) - a cos(x) - b +--R + +--R 2 +--R - a +--R / +--R a sin(x) + b cos(x) +--R + +--R 2 2 2 x 4 2 2 2 x 2 +--R (2b + a )cos(x) tan(-) + (- 4b - 2a )cos(x) tan(-) +--R 2 2 +--R + +--R 2 2 2 +--R (2b + a )cos(x) +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 x 4 2 2 2 x 2 +--R (- 2b - a )cos(x) tan(-) + (4b + 2a )cos(x) tan(-) +--R 2 2 +--R + +--R 2 2 2 +--R (- 2b - a )cos(x) +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 x 4 2 2 2 x 2 +--R (- 4b - 2a )cos(x) tan(-) + (8b + 4a )cos(x) tan(-) +--R 2 2 +--R + +--R 2 2 2 +--R (- 4b - 2a )cos(x) +--R * +--R x +--R atanh(tan(-)) +--R 2 +--R + +--R +-------+ +--R 2 x 4 2 x 2 2 | 2 2 +--R (4b cos(x) tan(-) - 8b cos(x) tan(-) + 4b cos(x) )\|b + a +--R 2 2 +--R * +--R x +--R b tan(-) - a +--R 2 +--R atanh(------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 x 4 2 2 x 3 +--R (a sin(x) - 2a b cos(x) - 2a b cos(x))tan(-) - 2a cos(x) tan(-) +--R 2 2 +--R + +--R 2 x 2 2 2 x 2 +--R (- 2a sin(x) + 4a b cos(x))tan(-) - 2a cos(x) tan(-) + a sin(x) +--R 2 2 +--R + +--R 2 +--R 2a b cos(x) - 2a b cos(x) +--R / +--R 3 2 x 4 3 2 x 2 3 2 +--R 2a cos(x) tan(-) - 4a cos(x) tan(-) + 2a cos(x) +--R 2 2 +--R Type: Expression Integer +--E 505 + +--S 506 of 546 +d0491:= D(m0491,x) +--R +--R +--R (471) +--R 3 2 6 4 4 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) +--R + +--R 3 2 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (2a b + 5a b)cos(x) + 6a b cos(x) + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R - 4a b cos(x) + (2a b - 5a b )cos(x) +--R + +--R 4 3 2 2 +--R (2a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 5a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (4b + 5a b)cos(x) + (2b - 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 4 3 2 5 +--R 2a b cos(x) + (2a b - a b )cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 3 +--R (- 2a b + a b )cos(x) + a b cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R - 4a b sin(x) + (4a cos(x) + 4a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 4 +--R (4a b - 4a b)cos(x) + (4a b + 2a b)cos(x) + 8a b cos(x) +--R + +--R 4 +--R 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (8a b - 8a b )cos(x) + (4a b - 10a b - 2a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (- 4a b - 10a )cos(x) - 12a cos(x) - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 8a b cos(x) + 20a b cos(x) + (- 4a b + 14a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 4a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (8a b - 8a )cos(x) + (4a b - 2a b - 22a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 8a b + 4a b - 22a )cos(x) +--R + +--R 4 3 2 5 3 3 2 5 2 +--R (- 4a b + 10a b - 10a )cos(x) + (4a b - 2a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 4a b - 4a b)cos(x) + (- 4a b - 10a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (4a b - 10a b)cos(x) + (4a b - 6a b)cos(x) - 2a b cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 3 2 +--R (8a b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (- 8a b - 20a b)cos(x) - 24a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R 16a b cos(x) + (- 8a b + 20a b )cos(x) +--R + +--R 4 3 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 20a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (- 16b - 20a b)cos(x) + (- 8b + 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 +--R (8a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 +--R - 8a b cos(x) + (- 8a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 3 2 3 +--R (8a b + 4a b )cos(x) + (8a b - 4a b )cos(x) - 4a b cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R 12a b sin(x) + (- 12a cos(x) - 12a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 12a b - 12a b)cos(x) + (- 12a b - 6a b)cos(x) +--R + +--R 4 4 +--R - 24a b cos(x) - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 24a b + 24a )cos(x) + (- 12a b + 30a b + 30a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (12a b + 30a )cos(x) + 36a cos(x) + 12a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 24a b cos(x) + 12a b cos(x) + (12a b - 18a b)cos(x) +--R + +--R 2 3 4 2 +--R (12a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 24a b + 24a b )cos(x) + (- 12a b + 54a b - 6a )cos(x) +--R + +--R 4 3 2 5 4 +--R (24a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 3 3 2 5 2 +--R (12a b - 30a b + 6a )cos(x) + (- 12a b + 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (12a b - 12a b)cos(x) + (12a b - 42a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (- 12a b - 42a b)cos(x) + (- 12a b - 6a b)cos(x) + 6a b cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R 12a b sin(x) + (- 12a b cos(x) - 12a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 +--R - 12a b cos(x) + (- 12a b - 6a b )cos(x) - 24a b cos(x) +--R + +--R 3 2 +--R - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 +--R (- 24b + 12a b + 12a b)cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (- 12b + 30a b + 18a b)cos(x) + (12a b + 30a b)cos(x) +--R + +--R 4 4 +--R 36a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R - 24a b cos(x) + (12a b - 30a b )cos(x) +--R + +--R 4 3 2 2 +--R (12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 +--R (- 24b + 12a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 5 4 4 +--R (- 12b + 30a b + 30a b)cos(x) + (24b + 30a b)cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (12b - 30a b + 18a b)cos(x) + (- 12a b + 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 +--R 12a b cos(x) + (12a b - 6a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 12a b - 6a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 3 2 3 +--R 6a b cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R - 12a b sin(x) + (12a cos(x) + 12a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (12a b - 12a b)cos(x) + (12a b + 6a b)cos(x) +--R + +--R 4 4 +--R 24a b cos(x) + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (24a b - 24a b )cos(x) + (12a b - 30a b - 6a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (- 12a b - 30a )cos(x) - 36a cos(x) - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 24a b cos(x) + 60a b cos(x) + (- 12a b + 42a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 12a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (24a b - 24a )cos(x) + (12a b - 6a b - 66a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 24a b + 12a b - 66a )cos(x) +--R + +--R 4 3 2 5 3 3 2 5 2 +--R (- 12a b + 30a b - 30a )cos(x) + (12a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 12a b - 12a b)cos(x) + (- 12a b - 30a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (12a b - 30a b)cos(x) + (12a b - 18a b)cos(x) - 6a b cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 3 2 +--R (8a b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (- 8a b - 20a b)cos(x) - 24a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R 16a b cos(x) + (- 8a b + 20a b )cos(x) +--R + +--R 4 3 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 20a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (- 16b - 20a b)cos(x) + (- 8b + 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 +--R (8a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 +--R - 8a b cos(x) + (- 8a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 3 2 3 +--R (8a b + 4a b )cos(x) + (8a b - 4a b )cos(x) - 4a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R 4a b sin(x) + (- 4a cos(x) - 4a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 4a b - 4a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 4 4 +--R - 8a b cos(x) - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 8a b + 8a )cos(x) + (- 4a b + 10a b + 10a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (4a b + 10a )cos(x) + 12a cos(x) + 4a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 8a b cos(x) + 4a b cos(x) + (4a b - 6a b)cos(x) +--R + +--R 2 3 4 2 +--R (4a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 8a b + 8a b )cos(x) + (- 4a b + 18a b - 2a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (8a b + 4a b - 2a )cos(x) + (4a b - 10a b + 2a )cos(x) +--R + +--R 3 2 5 2 +--R (- 4a b + 2a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (4a b - 4a b)cos(x) + (4a b - 14a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (- 4a b - 14a b)cos(x) + (- 4a b - 2a b)cos(x) + 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 3 2 +--R (- 2a b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) - 2a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (2a b + 5a b)cos(x) + 6a b cos(x) + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 4 3 2 2 +--R (- 4a b cos(x) + (2a b - 5a b )cos(x) + (2a b - a b )cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 5a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (4b + 5a b)cos(x) + (2b - 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 4 3 2 5 +--R 2a b cos(x) + (2a b - a b )cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 3 +--R (- 2a b + a b )cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 2 6 5 3 3 5 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b - 2a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (2b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) - 2a b )sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 5 +--R (2a b + 3a b + 5a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 2a b - 4a b )cos(x) + (- 2b - a b - 5a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (2a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 5a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (6a b + 3a b + 5a b)cos(x) + (- 2a b - 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 2a b - a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 4 2 4 +--R - 2b cos(x) - a b cos(x) + (2b - a b - a b )cos(x) + a b cos(x) +--R + +--R 2 4 4 2 3 +--R (a b + a b )cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R - 4a b sin(x) + (4a cos(x) + 4a b + 4a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (- 4a b - 4a b)cos(x) + (4a b + 2a b)cos(x) + 8a b cos(x) +--R + +--R 5 +--R 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (8a b - 8a b )cos(x) + (- 4a b - 10a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 4 2 +--R (- 4a b - 6a b - 10a )cos(x) + (- 8a b - 12a )cos(x) - 4a b +--R + +--R 6 +--R - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 3 3 5 4 +--R 8a b cos(x) + (8a b + 20a b)cos(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (4a b + 2a b + 14a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 6 2 4 4 2 6 5 +--R (8a b - 8a )cos(x) + (- 4a b - 10a b - 22a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 12a b - 10a b - 22a )cos(x) + (4a b + 2a b - 10a )cos(x) +--R + +--R 2 4 4 2 6 2 +--R (4a b + 2a b - 2a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (4a b - 4a b)cos(x) + (- 4a b - 10a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (- 4a b - 6a b - 10a b)cos(x) + (- 4a b - 6a b)cos(x) +--R + +--R 3 3 5 3 +--R (- 2a b - 2a b)cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b + 8a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (- 8b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b )sin(x) +--R + +--R 5 3 3 5 4 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 8a b - 28a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 8a b - 12a b - 20a b)cos(x) + (- 16a b - 24a b)cos(x) +--R + +--R 3 3 5 +--R - 8a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (8a b + 16a b )cos(x) + (8b + 4a b + 20a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 8a b - 28a b - 20a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 24a b - 12a b - 20a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (8a b + 12a b - 12a b)cos(x) + (8a b + 4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 +--R 8b cos(x) + 4a b cos(x) + (- 8b + 4a b + 4a b )cos(x) +--R + +--R 4 2 4 2 4 4 2 3 +--R - 4a b cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R 12a b sin(x) + (- 12a cos(x) - 12a b - 12a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (12a b - 12a b)cos(x) + (- 12a b - 6a b)cos(x) - 24a b cos(x) +--R + +--R 5 +--R - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 6 4 2 4 4 2 6 3 +--R (- 24a b + 24a )cos(x) + (12a b + 54a b + 30a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 4 2 +--R (12a b + 18a b + 30a )cos(x) + (24a b + 36a )cos(x) + 12a b +--R + +--R 6 +--R 12a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 24a b cos(x) + 12a b cos(x) + (- 12a b - 6a b - 18a b)cos(x) +--R + +--R 3 3 5 2 +--R (12a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 5 +--R (- 24a b + 24a b )cos(x) + (12a b + 54a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (36a b + 6a b - 6a )cos(x) + (- 12a b - 30a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 2 +--R (- 12a b - 6a b + 6a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (- 12a b - 12a b)cos(x) + (- 12a b - 42a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (12a b - 30a b - 42a b)cos(x) + (- 12a b - 6a b)cos(x) +--R + +--R 3 3 5 3 +--R (6a b + 6a b)cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R 12a b sin(x) + (- 12a b cos(x) - 12a b - 12a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 +--R (12b cos(x) + (- 12a b - 6a b )cos(x) - 24a b cos(x) - 12a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 4 +--R (- 24a b + 12a b + 12a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (12a b + 42a b + 18a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (12a b + 18a b + 30a b)cos(x) + (24a b + 36a b)cos(x) +--R + +--R 3 3 5 +--R 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 12a b - 24a b )cos(x) + (- 12b - 6a b - 30a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 24a b + 12a b + 12a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (12a b + 42a b + 30a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (36a b + 18a b + 30a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 12a b - 18a b + 18a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 12a b - 6a b + 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 +--R - 12b cos(x) - 6a b cos(x) + (12b - 6a b - 6a b )cos(x) +--R + +--R 4 2 4 2 4 4 2 3 +--R 6a b cos(x) + (6a b + 6a b )cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R - 12a b sin(x) + (12a cos(x) + 12a b + 12a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (- 12a b - 12a b)cos(x) + (12a b + 6a b)cos(x) + 24a b cos(x) +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (24a b - 24a b )cos(x) + (- 12a b - 30a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (- 12a b - 18a b - 30a )cos(x) + (- 24a b - 36a )cos(x) +--R + +--R 4 2 6 +--R - 12a b - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 3 3 5 4 +--R 24a b cos(x) + (24a b + 60a b)cos(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (12a b + 6a b + 42a b)cos(x) + (- 12a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 6 2 4 4 2 6 5 +--R (24a b - 24a )cos(x) + (- 12a b - 30a b - 66a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 36a b - 30a b - 66a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (12a b + 6a b - 30a )cos(x) + (12a b + 6a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (12a b - 12a b)cos(x) + (- 12a b - 30a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (- 12a b - 18a b - 30a b)cos(x) + (- 12a b - 18a b)cos(x) +--R + +--R 3 3 5 3 +--R (- 6a b - 6a b)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b + 8a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (- 8b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b )sin(x) +--R + +--R 5 3 3 5 4 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 8a b - 28a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 8a b - 12a b - 20a b)cos(x) + (- 16a b - 24a b)cos(x) +--R + +--R 3 3 5 +--R - 8a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (8a b + 16a b )cos(x) + (8b + 4a b + 20a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 8a b - 28a b - 20a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 24a b - 12a b - 20a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (8a b + 12a b - 12a b)cos(x) + (8a b + 4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 +--R 8b cos(x) + 4a b cos(x) + (- 8b + 4a b + 4a b )cos(x) +--R + +--R 4 2 4 2 4 4 2 3 +--R - 4a b cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R 4a b sin(x) + (- 4a cos(x) - 4a b - 4a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (4a b - 4a b)cos(x) + (- 4a b - 2a b)cos(x) - 8a b cos(x) +--R + +--R 5 +--R - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 6 4 2 4 4 2 6 3 +--R (- 8a b + 8a )cos(x) + (4a b + 18a b + 10a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 4 2 6 +--R (4a b + 6a b + 10a )cos(x) + (8a b + 12a )cos(x) + 4a b + 4a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 8a b cos(x) + 4a b cos(x) + (- 4a b - 2a b - 6a b)cos(x) +--R + +--R 3 3 5 2 +--R (4a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 5 +--R (- 8a b + 8a b )cos(x) + (4a b + 18a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (12a b + 2a b - 2a )cos(x) + (- 4a b - 10a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 2 +--R (- 4a b - 2a b + 2a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (- 4a b - 4a b)cos(x) + (- 4a b - 14a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (4a b - 10a b - 14a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 3 3 5 3 +--R (2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b - 2a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (2b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) - 2a b )sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 5 +--R (2a b + 3a b + 5a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 2a b - 4a b )cos(x) + (- 2b - a b - 5a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (2a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 5a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (6a b + 3a b + 5a b)cos(x) + (- 2a b - 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 2a b - a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 4 2 4 +--R - 2b cos(x) - a b cos(x) + (2b - a b - a b )cos(x) + a b cos(x) +--R + +--R 2 4 4 2 3 +--R (a b + a b )cos(x) +--R / +--R 4 2 3 4 +--R 2a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((2a b - 2a b)cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (- 4a b cos(x) - 6a b cos(x) - 2a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 6a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (- 2a b + 6a b)cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R 2a b cos(x) + 6a b cos(x) + 6a b cos(x) + 2a b cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 5 3 4 +--R - 4a b cos(x) sin(x) +--R + +--R 4 2 6 4 6 3 3 +--R ((- 4a b + 4a )cos(x) + 4a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (8a b cos(x) + 12a b cos(x) + 4a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (4a b - 4a )cos(x) + (8a b - 12a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (4a b - 12a )cos(x) - 4a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R - 4a b cos(x) - 12a b cos(x) - 12a b cos(x) - 4a b cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (16a b cos(x) + 24a b cos(x) + 8a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (8a b - 8a b)cos(x) + (16a b - 24a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (8a b - 24a b)cos(x) - 8a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R - 8a b cos(x) - 24a b cos(x) - 24a b cos(x) - 8a b cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 5 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 4 2 6 4 6 3 3 +--R ((12a b - 12a )cos(x) - 12a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (- 24a b cos(x) - 36a b cos(x) - 12a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 12a b + 12a )cos(x) + (- 24a b + 36a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (- 12a b + 36a )cos(x) + 12a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R 12a b cos(x) + 36a b cos(x) + 36a b cos(x) + 12a b cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((12a b - 12a b)cos(x) - 12a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (- 24a b cos(x) - 36a b cos(x) - 12a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (- 12a b + 12a b)cos(x) + (- 24a b + 36a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (- 12a b + 36a b)cos(x) + 12a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R 12a b cos(x) + 36a b cos(x) + 36a b cos(x) + 12a b cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 5 3 4 +--R - 12a b cos(x) sin(x) +--R + +--R 4 2 6 4 6 3 3 +--R ((- 12a b + 12a )cos(x) + 12a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (24a b cos(x) + 36a b cos(x) + 12a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (12a b - 12a )cos(x) + (24a b - 36a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (12a b - 36a )cos(x) - 12a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R - 12a b cos(x) - 36a b cos(x) - 36a b cos(x) - 12a b cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (16a b cos(x) + 24a b cos(x) + 8a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (8a b - 8a b)cos(x) + (16a b - 24a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (8a b - 24a b)cos(x) - 8a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R - 8a b cos(x) - 24a b cos(x) - 24a b cos(x) - 8a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 4 4 2 6 4 6 3 3 +--R 4a b cos(x) sin(x) + ((4a b - 4a )cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (- 8a b cos(x) - 12a b cos(x) - 4a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 4a b + 4a )cos(x) + (- 8a b + 12a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (- 4a b + 12a )cos(x) + 4a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R 4a b cos(x) + 12a b cos(x) + 12a b cos(x) + 4a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 3 3 5 4 5 3 3 +--R 2a b cos(x) sin(x) + ((2a b - 2a b)cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (- 4a b cos(x) - 6a b cos(x) - 2a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 6a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (- 2a b + 6a b)cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R 2a b cos(x) + 6a b cos(x) + 6a b cos(x) + 2a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 2 3 4 +--R 2a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((2a b - 2a b)cos(x) + (- 2a b - 2a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (- 4a b cos(x) + (- 2a b - 6a b )cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (2a b + 6a b)cos(x) + (2a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 3 4 5 2 5 +--R 2a b cos(x) + (2a b + 6a b )cos(x) + (4a b + 6a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R - 4a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((- 4a b + 4a )cos(x) + (4a b + 4a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (8a b cos(x) + (4a b + 12a b)cos(x) + 4a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (4a b - 4a )cos(x) + (4a b - 12a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (- 4a b - 12a )cos(x) + (- 4a b - 4a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 4 3 6 5 +--R - 4a b cos(x) + (- 4a b - 12a b)cos(x) + (- 8a b - 12a b)cos(x) +--R + +--R 4 3 6 4 +--R (- 4a b - 4a b)cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((- 8a b + 8a b)cos(x) + (8a b + 8a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (16a b cos(x) + (8a b + 24a b )cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (8a b - 8a b)cos(x) + (8a b - 24a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (- 8a b - 24a b)cos(x) + (- 8a b - 8a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 +--R - 8a b cos(x) + (- 8a b - 24a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 16a b - 24a b )cos(x) + (- 8a b - 8a b )cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((12a b - 12a )cos(x) + (- 12a b - 12a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (- 24a b cos(x) + (- 12a b - 36a b)cos(x) - 12a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (- 12a b + 12a )cos(x) + (- 12a b + 36a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (12a b + 36a )cos(x) + (12a b + 12a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 4 3 6 5 +--R 12a b cos(x) + (12a b + 36a b)cos(x) + (24a b + 36a b)cos(x) +--R + +--R 4 3 6 4 +--R (12a b + 12a b)cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((12a b - 12a b)cos(x) + (- 12a b - 12a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (- 24a b cos(x) + (- 12a b - 36a b )cos(x) - 12a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 36a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (12a b + 36a b)cos(x) + (12a b + 12a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 3 4 5 2 5 +--R 12a b cos(x) + (12a b + 36a b )cos(x) + (24a b + 36a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (12a b + 12a b )cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R - 12a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((- 12a b + 12a )cos(x) + (12a b + 12a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (24a b cos(x) + (12a b + 36a b)cos(x) + 12a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (12a b - 12a )cos(x) + (12a b - 36a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (- 12a b - 36a )cos(x) + (- 12a b - 12a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 +--R - 12a b cos(x) + (- 12a b - 36a b)cos(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 24a b - 36a b)cos(x) + (- 12a b - 12a b)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((- 8a b + 8a b)cos(x) + (8a b + 8a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (16a b cos(x) + (8a b + 24a b )cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (8a b - 8a b)cos(x) + (8a b - 24a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (- 8a b - 24a b)cos(x) + (- 8a b - 8a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 +--R - 8a b cos(x) + (- 8a b - 24a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 16a b - 24a b )cos(x) + (- 8a b - 8a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R 4a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((4a b - 4a )cos(x) + (- 4a b - 4a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (- 8a b cos(x) + (- 4a b - 12a b)cos(x) - 4a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (- 4a b + 4a )cos(x) + (- 4a b + 12a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (4a b + 12a )cos(x) + (4a b + 4a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 4 3 6 5 +--R 4a b cos(x) + (4a b + 12a b)cos(x) + (8a b + 12a b)cos(x) +--R + +--R 4 3 6 4 +--R (4a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R 2a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((2a b - 2a b)cos(x) + (- 2a b - 2a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (- 4a b cos(x) + (- 2a b - 6a b )cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (2a b + 6a b)cos(x) + (2a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 3 4 5 2 5 +--R 2a b cos(x) + (2a b + 6a b )cos(x) + (4a b + 6a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )cos(x) +--R Type: Expression Integer +--E 506 + +--S 507 of 546 +t0492:= sec(x)/(1+2*cot(x)) +--R +--R +--R sec(x) +--R (472) ----------- +--R 2cot(x) + 1 +--R Type: Expression Integer +--E 507 + +--S 508 of 546 +r0492:= 2/5*atanh(1/5*(cos(x)-2*sin(x))*5^(1/2))*5^(1/2)+atanh(sin(x)) +--R +--R +--R +-+ +-+ +--R +-+ 2\|5 sin(x) - \|5 cos(x) +--R - 2\|5 atanh(------------------------) + 5atanh(sin(x)) +--R 5 +--R (473) ------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 508 + +--S 509 of 546 +a0492:= integrate(t0492,x) +--R +--R +--R (474) +--R +-+ sin(x) + cos(x) + 1 +-+ sin(x) - cos(x) - 1 +--R \|5 log(-------------------) - \|5 log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R (2\|5 + 10)sin(x) + (- \|5 - 5)cos(x) - 5\|5 - 5 +--R 2log(---------------------------------------------------) +--R sin(x) + 2cos(x) +--R / +--R +-+ +--R \|5 +--R Type: Union(Expression Integer,...) +--E 509 + +--S 510 of 546 +m0492:= a0492-r0492 +--R +--R +--R (475) +--R +-+ sin(x) + cos(x) + 1 +-+ sin(x) - cos(x) - 1 +--R \|5 log(-------------------) - \|5 log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R (2\|5 + 10)sin(x) + (- \|5 - 5)cos(x) - 5\|5 - 5 +--R 2log(---------------------------------------------------) +--R sin(x) + 2cos(x) +--R + +--R +-+ +-+ +--R 2\|5 sin(x) - \|5 cos(x) +-+ +--R 2atanh(------------------------) - \|5 atanh(sin(x)) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression Integer +--E 510 + +--S 511 of 546 +d0492:= D(m0492,x) +--R +--R +--R (476) +--R +-+ 8 +-+ +-+ 7 +--R (24\|5 - 40)sin(x) + ((- 48\|5 - 80)cos(x) + 20\|5 - 60)sin(x) +--R + +--R +-+ 2 +-+ +-+ 6 +--R ((30\|5 + 110)cos(x) + (- 38\|5 - 30)cos(x) - 84\|5 + 60)sin(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 30\|5 - 150)cos(x) + (46\|5 + 30)cos(x) +--R + +--R +-+ +-+ +--R (218\|5 + 530)cos(x) - 30\|5 + 210 +--R * +--R 5 +--R sin(x) +--R + +--R 4 +-+ 3 +-+ 2 +--R 160cos(x) + (- 30\|5 + 10)cos(x) + (- 66\|5 - 290)cos(x) +--R + +--R +-+ +-+ +--R (8\|5 - 40)cos(x) + 100\|5 + 20 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R (18\|5 - 70)cos(x) + (15\|5 + 35)cos(x) + (77\|5 + 445)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 121\|5 - 45)cos(x) + (- 275\|5 - 715)cos(x) - 10\|5 - 250 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R (- 6\|5 + 10)cos(x) + (10\|5 + 50)cos(x) + (26\|5 - 150)cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 18\|5 - 90)cos(x) + (20\|5 + 260)cos(x) + (40\|5 + 120)cos(x) +--R + +--R +-+ +--R - 40\|5 - 40 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +--R (- 11\|5 - 55)cos(x) + (- 75\|5 - 75)cos(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 74\|5 - 50)cos(x) + (- 30\|5 - 190)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (65\|5 + 5)cos(x) + (105\|5 + 265)cos(x) + 20\|5 + 100 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R (2\|5 + 10)cos(x) + (20\|5 + 20)cos(x) + (18\|5 + 10)cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (- 40\|5 + 40)cos(x) + (- 10\|5 + 30)cos(x) + (20\|5 - 60)cos(x) +--R + +--R +-+ +--R (- 10\|5 - 50)cos(x) +--R / +--R +-+ 8 +-+ +-+ 7 +--R (8\|5 + 40)sin(x) + ((4\|5 + 20)cos(x) - 20\|5 - 20)sin(x) +--R + +--R +-+ 2 +-+ +-+ 6 +--R ((- 26\|5 - 130)cos(x) + (- 36\|5 - 100)cos(x) - 26\|5 - 130)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (7\|5 + 35)cos(x) + (47\|5 + 15)cos(x) + (17\|5 - 75)cos(x) +--R + +--R +-+ +--R 65\|5 + 65 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (16\|5 + 80)cos(x) + (46\|5 + 190)cos(x) + (104\|5 + 360)cos(x) +--R + +--R +-+ +-+ +--R (126\|5 + 270)cos(x) + 28\|5 + 140 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +--R (- 11\|5 - 55)cos(x) + (- 57\|5 - 145)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 73\|5 - 85)cos(x) + (- 77\|5 + 75)cos(x) +--R + +--R +-+ +-+ +--R (- 56\|5 + 80)cos(x) - 70\|5 - 70 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R (2\|5 + 10)cos(x) + (14\|5 + 30)cos(x) + (- 4\|5 - 100)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 106\|5 - 330)cos(x) + (- 188\|5 - 380)cos(x) +--R + +--R +-+ +-+ +--R (- 140\|5 - 220)cos(x) - 10\|5 - 50 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R (11\|5 + 55)cos(x) + (57\|5 + 145)cos(x) + (66\|5 + 50)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (30\|5 - 90)cos(x) + (35\|5 - 25)cos(x) + 25\|5 + 25 +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R (- 2\|5 - 10)cos(x) + (- 14\|5 - 30)cos(x) + (- 12\|5 + 20)cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (60\|5 + 140)cos(x) + (110\|5 + 150)cos(x) + (50\|5 + 50)cos(x) +--R Type: Expression Integer +--E 511 + +--S 512 of 546 +t0493:= csc(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R csc(x) +--R (477) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 512 + +--S 513 of 546 +r0493:= -log(a+b*cot(x))/b +--R +--R +--R log(b cot(x) + a) +--R (478) - ----------------- +--R b +--R Type: Expression Integer +--E 513 + +--S 514 of 546 +a0493:= integrate(t0493,x) +--R +--R +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (479) ---------------------------------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 514 + +--S 515 of 546 +m0493:= a0493-r0493 +--R +--R +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) + log(b cot(x) + a) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (480) ------------------------------------------------------------------ +--R b +--R Type: Expression Integer +--E 515 + +--S 516 of 546 +d0493:= D(m0493,x) +--R +--R +--R (481) +--R 2 2 2 +--R (- a cot(x) + b cot(x))sin(x) + (- b cos(x)cot(x) - b cos(x))sin(x) +--R + +--R 2 2 +--R b cos(x) cot(x) + a cos(x) +--R / +--R 2 2 2 +--R (a b cot(x) + a )sin(x) + (b cos(x)cot(x) + a b cos(x))sin(x) +--R Type: Expression Integer +--E 516 + +--S 517 of 546 +t0494:= csc(x)^4/(a+b*cot(x)) +--R +--R +--R 4 +--R csc(x) +--R (482) ------------ +--R b cot(x) + a +--R Type: Expression Integer +--E 517 + +--S 518 of 546 +r0494:= a*cot(x)/b^2-1/2*cot(x)^2/b-(a^2+b^2)*log(a+b*cot(x))/b^3 +--R +--R +--R 2 2 2 2 +--R (- 2b - 2a )log(b cot(x) + a) - b cot(x) + 2a b cot(x) +--R (483) -------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression Integer +--E 518 + +--S 519 of 546 +a0494:= integrate(t0494,x) +--R +--R +--R (484) +--R 2 2 2 2 2 sin(x) +--R ((4b + 4a )cos(x) - 4b - 4a )log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 - 2a sin(x) - 2b cos(x) +--R ((- 4b - 4a )cos(x) + 4b + 4a )log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R - 4a b cos(x)sin(x) + b cos(x) + b +--R / +--R 3 2 3 +--R 4b cos(x) - 4b +--R Type: Union(Expression Integer,...) +--E 519 + +--S 520 of 546 +m0494:= a0494-r0494 +--R +--R +--R (485) +--R 2 2 2 2 2 sin(x) +--R ((4b + 4a )cos(x) - 4b - 4a )log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 +--R ((4b + 4a )cos(x) - 4b - 4a )log(b cot(x) + a) +--R + +--R 2 2 2 2 2 - 2a sin(x) - 2b cos(x) +--R ((- 4b - 4a )cos(x) + 4b + 4a )log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R - 4a b cos(x)sin(x) + (2b cos(x) - 2b )cot(x) +--R + +--R 2 2 2 2 +--R (- 4a b cos(x) + 4a b)cot(x) + b cos(x) + b +--R / +--R 3 2 3 +--R 4b cos(x) - 4b +--R Type: Expression Integer +--E 520 + +--S 521 of 546 +d0494:= D(m0494,x) +--R +--R +--R (486) +--R 2 2 2 3 2 3 4 +--R ((- a b cos(x) - a b)cot(x) - a cos(x) - a )sin(x) +--R + +--R 2 3 2 3 3 +--R (- a b cos(x) cot(x) - a b cos(x) )sin(x) +--R + +--R 2 4 2 2 2 4 +--R (- a b cos(x) + 2a b cos(x) - a b )cot(x) +--R + +--R 2 4 2 2 2 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 3 4 3 2 2 3 2 +--R (b cos(x) + (- b - a b)cos(x) + b + a b)cot(x) +--R + +--R 2 3 2 3 +--R (a b - a )cos(x) + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 3 3 3 4 +--R (- b cos(x) + 2b cos(x) - b cos(x))cot(x) +--R + +--R 3 5 3 3 3 2 +--R (- 2b cos(x) + 4b cos(x) - 2b cos(x))cot(x) +--R + +--R 2 5 2 3 3 2 5 +--R (- a b cos(x) + a b cos(x) )cot(x) + (- b - a b)cos(x) +--R + +--R 3 2 3 3 +--R (2b + a b)cos(x) - b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R ((b + a b)cos(x) + (- 2b - 2a b)cos(x) + (b + a b)cos(x) )cot(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (a b + a )cos(x) + (- 2a b - 2a )cos(x) + (a b + a )cos(x) +--R / +--R 3 4 3 2 3 2 2 4 +--R (a b cos(x) - 2a b cos(x) + a b )cot(x) + a b cos(x) +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 3 4 3 5 +--R (b cos(x) - 2b cos(x) + b cos(x))cot(x) + a b cos(x) +--R + +--R 3 3 3 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R Type: Expression Integer +--E 521 + +--S 522 of 546 +t0495:= sin(x)/(%i+cot(x)) +--R +--R +--R sin(x) +--R (487) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 522 + +--S 523 of 546 +r0495:= %i*cos(x)-1/3*%i*cos(x)^3+1/3*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (488) - sin(x) - - %i cos(x) + %i cos(x) +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 523 + +--S 524 of 546 +--a0495:= integrate(t0495,x) +--E 524 + +--S 525 of 546 +--m0495:= a0495-r0495 +--E 525 + +--S 526 of 546 +--d0495:= D(m0495,x) +--E 526 + +--S 527 of 546 +t0496:= sin(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R sin(x) +--R (489) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 527 + +--S 528 of 546 +r0496:= -3/8*%i*x+3/8*%i*cos(x)*sin(x)+1/4*%i*cos(x)*sin(x)^3+1/4*sin(x)^4 +--R +--R +--R 1 4 1 3 3 3 +--R (490) - sin(x) + - %i cos(x)sin(x) + - %i cos(x)sin(x) - - %i x +--R 4 4 8 8 +--R Type: Expression Complex Fraction Integer +--E 528 + +--S 529 of 546 +--a0496:= integrate(t0496,x) +--E 529 + +--S 530 of 546 +--m0496:= a0496-r0496 +--E 530 + +--S 531 of 546 +--d0496:= D(m0496,x) +--E 531 + +--S 532 of 546 +t0497:= sin(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R sin(x) +--R (491) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 532 + +--S 533 of 546 +r0497:= %i*cos(x)-2/3*%i*cos(x)^3+1/5*%i*cos(x)^5+1/5*sin(x)^5 +--R +--R +--R 1 5 1 5 2 3 +--R (492) - sin(x) + - %i cos(x) - - %i cos(x) + %i cos(x) +--R 5 5 3 +--R Type: Expression Complex Fraction Integer +--E 533 + +--S 534 of 546 +--a0497:= integrate(t0497,x) +--E 534 + +--S 535 of 546 +--m0497:= a0497-r0497 +--E 535 + +--S 536 of 546 +--d0497:= D(m0497,x) +--E 536 + +--S 537 of 546 +t0498:= sin(x)^4/(%i+cot(x)) +--R +--R +--R 4 +--R sin(x) +--R (493) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 537 + +--S 538 of 546 +r0498:= -5/16*%i*x+5/16*%i*cos(x)*sin(x)+5/24*%i*cos(x)*sin(x)^3+1/6*%i*cos(x)*sin(x)^5+1/6*sin(x)^6 +--R +--R +--R (494) +--R 1 6 1 5 5 3 5 +--R - sin(x) + - %i cos(x)sin(x) + -- %i cos(x)sin(x) + -- %i cos(x)sin(x) +--R 6 6 24 16 +--R + +--R 5 +--R - -- %i x +--R 16 +--R Type: Expression Complex Fraction Integer +--E 538 + +--S 539 of 546 +--a0498:= integrate(t0498,x) +--E 539 + +--S 540 of 546 +--m0498:= a0498-r0498 +--E 540 + +--S 541 of 546 +--d0498:= D(m0498,x) +--E 541 + +--S 542 of 546 +t0499:= cos(x)/(%i+cot(x)) +--R +--R +--R cos(x) +--R (495) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 542 + +--S 543 of 546 +r0499:= -1/3*cos(x)^3-1/3*%i*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (496) - - %i sin(x) - - cos(x) +--R 3 3 +--R Type: Expression Complex Fraction Integer +--E 543 + +--S 544 of 546 +--a0499:= integrate(t0499,x) +--E 544 + +--S 545 of 546 +--m0499:= a0499-r0499 +--E 545 + +--S 546 of 546 +--d0499:= D(m0499,x) +--E 546 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}