diff --git a/changelog b/changelog index b8fd57d..fc101e5 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100612 tpd src/axiom-website/patches.html 20100612.02.tpd.patch +20100612 tpd src/input/Makefile rule-based trig integration +20100612 tpd src/input/richtrig900-920.input rule-based trig integration 20100612 tpd src/axiom-website/patches.html 20100612.01.tpd.patch 20100612 tpd src/input/Makefile rule-based trig integration 20100612 tpd src/input/richtrig800-899.input rule-based trig integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index a62f79c..a8ca385 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2884,6 +2884,8 @@ src/input/richtrig600-699.input rule-based trig integration
src/input/richtrig700-799.input rule-based trig integration
20100612.01.tpd.patch src/input/richtrig800-899.input rule-based trig integration
+20100612.02.tpd.patch +src/input/richtrig900-920.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index a9dab57..a8ad4d6 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -385,6 +385,7 @@ REGRES= ackermann.regress \ richtrig600-699.regress \ richtrig700-799.regress \ richtrig800-899.regress \ + richtrig900-920.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -713,6 +714,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richtrig600-699.input \ ${OUT}/richtrig700-799.input \ ${OUT}/richtrig800-899.input \ + ${OUT}/richtrig900-920.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1070,6 +1072,7 @@ DOCFILES= \ ${DOC}/richtrig600-699.input.dvi \ ${DOC}/richtrig700-799.input.dvi \ ${DOC}/richtrig800-899.input.dvi \ + ${DOC}/richtrig900-920.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/richtrig900-920.input.pamphlet b/src/input/richtrig900-920.input.pamphlet new file mode 100644 index 0000000..4ca7240 --- /dev/null +++ b/src/input/richtrig900-920.input.pamphlet @@ -0,0 +1,6029 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig900-920.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig900-920.output +)spool richtrig900-920.output +)set message auto off +)clear all + +--S 1 of 105 +t0900:= cot(x)^n*csc(x)^4 +--R +--R +--R 4 n +--R (1) csc(x) cot(x) +--R Type: Expression Integer +--E 1 + +--S 2 of 105 +r0900:= -cot(x)^(1+n)/(1+n)-cot(x)^(3+n)/(3+n) +--R +--R +--R n + 3 n + 1 +--R (- n - 1)cot(x) + (- n - 3)cot(x) +--R (2) ------------------------------------------- +--R 2 +--R n + 4n + 3 +--R Type: Expression Integer +--E 2 + +--S 3 of 105 +a0900:= integrate(t0900,x) +--R +--R +--R cos(x) +--R n log(------) +--R 3 sin(x) +--R (- 2cos(x) + (n + 3)cos(x))%e +--R (3) ------------------------------------------- +--R 2 2 2 +--R ((n + 4n + 3)cos(x) - n - 4n - 3)sin(x) +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 105 +m0900:= a0900-r0900 +--R +--R +--R (4) +--R cos(x) +--R n log(------) +--R 3 sin(x) +--R (- 2cos(x) + (n + 3)cos(x))%e +--R + +--R 2 n + 3 +--R ((n + 1)cos(x) - n - 1)sin(x)cot(x) +--R + +--R 2 n + 1 +--R ((n + 3)cos(x) - n - 3)sin(x)cot(x) +--R / +--R 2 2 2 +--R ((n + 4n + 3)cos(x) - n - 4n - 3)sin(x) +--R Type: Expression Integer +--E 4 + +--S 5 of 105 +d0900:= D(m0900,x) +--R +--R +--R (5) +--R 4 2 2 6 +--R (2cos(x) + (- n - 3)cos(x) + n + 3)sin(x) + 2cos(x) +--R + +--R 4 2 +--R (- n - 5)cos(x) + (n + 3)cos(x) +--R * +--R cos(x) +--R n log(------) +--R sin(x) +--R %e +--R + +--R 4 2 2 +--R ((- n - 3)cos(x) + (2n + 6)cos(x) - n - 3)cot(x) +--R + +--R 4 2 +--R (- n - 3)cos(x) + (2n + 6)cos(x) - n - 3 +--R * +--R 2 n + 2 +--R sin(x) cot(x) +--R + +--R 4 2 2 +--R ((- n - 3)cos(x) + (2n + 6)cos(x) - n - 3)cot(x) +--R + +--R 4 2 +--R (- n - 3)cos(x) + (2n + 6)cos(x) - n - 3 +--R * +--R 2 n +--R sin(x) cot(x) +--R / +--R 4 2 2 +--R ((n + 3)cos(x) + (- 2n - 6)cos(x) + n + 3)sin(x) +--R Type: Expression Integer +--E 5 + +--S 6 of 105 +t0901:= sec(x)*tan(x)/(sec(x)+sec(x)^2) +--R +--R +--R tan(x) +--R (6) ---------- +--R sec(x) + 1 +--R Type: Expression Integer +--E 6 + +--S 7 of 105 +r0901:= -log(cos(x)+1) +--R +--R +--R (7) - log(cos(x) + 1) +--R Type: Expression Integer +--E 7 + +--S 8 of 105 +a0901:= integrate(t0901,x) +--R +--R +--R 2 +--R (8) log(----------) +--R cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 105 +m0901:= a0901-r0901 +--R +--R +--R 2 +--R (9) log(cos(x) + 1) + log(----------) +--R cos(x) + 1 +--R Type: Expression Integer +--E 9 + +--S 10 of 105 +d0901:= D(m0901,x) +--R +--R +--R (10) 0 +--R Type: Expression Integer +--E 10 + +--S 11 of 105 +t0902:= cos(x)*sec(sin(x)) +--R +--R +--R (11) cos(x)sec(sin(x)) +--R Type: Expression Integer +--E 11 + +--S 12 of 105 +r0902:= atanh(sin(sin(x))) +--R +--R +--R (12) atanh(sin(sin(x))) +--R Type: Expression Integer +--E 12 + +--S 13 of 105 +a0902:= integrate(t0902,x) +--R +--R +--R log(sin(sin(x)) + 1) - log(sin(sin(x)) - 1) +--R (13) ------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 105 +m0902:= a0902-r0902 +--R +--R +--R log(sin(sin(x)) + 1) - log(sin(sin(x)) - 1) - 2atanh(sin(sin(x))) +--R (14) ----------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 14 + +--S 15 of 105 +d0902:= D(m0902,x) +--R +--R +--R (15) 0 +--R Type: Expression Integer +--E 15 + +--S 16 of 105 +t0903:= sec(x)*(1-sin(x)) +--R +--R +--R (16) - sec(x)sin(x) + sec(x) +--R Type: Expression Integer +--E 16 + +--S 17 of 105 +r0903:= log(1+sin(x)) +--R +--R +--R (17) log(sin(x) + 1) +--R Type: Expression Integer +--E 17 + +--S 18 of 105 +a0903:= integrate(t0903,x) +--R +--R +--R sin(x) + cos(x) + 1 2 +--R (18) 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 105 +m0903:= a0903-r0903 +--R +--R +--R sin(x) + cos(x) + 1 2 +--R (19) - log(sin(x) + 1) + 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Integer +--E 19 + +--S 20 of 105 +d0903:= D(m0903,x) +--R +--R +--R (20) +--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 (cos(x) + 1)sin(x) + (cos(x) + 3cos(x) + 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression Integer +--E 20 + +--S 21 of 105 +t0904:= (cos(x)+1)*csc(x) +--R +--R +--R (21) (cos(x) + 1)csc(x) +--R Type: Expression Integer +--E 21 + +--S 22 of 105 +r0904:= log(1-cos(x)) +--R +--R +--R (22) log(- cos(x) + 1) +--R Type: Expression Integer +--E 22 + +--S 23 of 105 +a0904:= integrate(t0904,x) +--R +--R +--R sin(x) 2 +--R (23) 2log(----------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 105 +m0904:= a0904-r0904 +--R +--R +--R sin(x) 2 +--R (24) 2log(----------) - log(----------) - log(- cos(x) + 1) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Integer +--E 24 + +--S 25 of 105 +d0904:= D(m0904,x) +--R +--R +--R 2 3 +--R 2cos(x)sin(x) + 2cos(x) - 2cos(x) +--R (25) ----------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression Integer +--E 25 + +--S 26 of 105 +t0905:= csc(2*x)*(cos(x)+sin(x)) +--R +--R +--R (26) csc(2x)sin(x) + cos(x)csc(2x) +--R Type: Expression Integer +--E 26 + +--S 27 of 105 +r0905:= -1/2*atanh(cos(x))+1/2*atanh(sin(x)) +--R +--R +--R atanh(sin(x)) - atanh(cos(x)) +--R (27) ----------------------------- +--R 2 +--R Type: Expression Integer +--E 27 + +--S 28 of 105 +a0905:= integrate(t0905,x) +--R +--R +--R sin(x) - cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (28) --------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 105 +m0905:= a0905-r0905 +--R +--R +--R (29) +--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 + +--R atanh(cos(x)) +--R / +--R 2 +--R Type: Expression Integer +--E 29 + +--S 30 of 105 +d0905:= D(m0905,x) +--R +--R +--R (30) +--R 5 4 2 3 3 2 +--R sin(x) - 2cos(x)sin(x) - cos(x) sin(x) + (- cos(x) + 3cos(x))sin(x) +--R + +--R 4 2 5 +--R (- 2cos(x) + 3cos(x) - 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 3 3 +--R (2cos(x) - 2)sin(x) + (- 4cos(x) + 4cos(x))sin(x) +--R + +--R 4 2 2 3 4 +--R (2cos(x) - 6cos(x) + 4)sin(x) + (4cos(x) - 4cos(x))sin(x) - 2cos(x) +--R + +--R 2 +--R 4cos(x) - 2 +--R Type: Expression Integer +--E 30 + +--S 31 of 105 +t0906:= 2*cot(2*x)-3*sin(3*x) +--R +--R +--R (31) - 3sin(3x) + 2cot(2x) +--R Type: Expression Integer +--E 31 + +--S 32 of 105 +r0906:= cos(3*x)+log(sin(2*x)) +--R +--R +--R (32) log(sin(2x)) + cos(3x) +--R Type: Expression Integer +--E 32 + +--S 33 of 105 +a0906:= integrate(t0906,x) +--R +--R +--R (33) +--R 2 2cos(x)sin(x) 3 +--R - 2log(----------) + log(- ---------------------) + 4cos(x) - 3cos(x) +--R cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 105 +m0906:= a0906-r0906 +--R +--R +--R (34) +--R 2 2cos(x)sin(x) +--R - log(sin(2x)) - 2log(----------) + log(- ---------------------) - cos(3x) +--R cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R 4cos(x) - 3cos(x) +--R Type: Expression Integer +--E 34 + +--S 35 of 105 +d0906:= D(m0906,x) +--R +--R +--R (35) +--R 3cos(x)sin(x)sin(2x)sin(3x) +--R + +--R 3 2 2 +--R ((- 12cos(x) + 3cos(x) - 1)sin(x) + cos(x) )sin(2x) +--R + +--R - 2cos(x)cos(2x)sin(x) +--R / +--R cos(x)sin(x)sin(2x) +--R Type: Expression Integer +--E 35 + +--S 36 of 105 +t0907:= x*sec(-5+x^2) +--R +--R +--R 2 +--R (36) x sec(x - 5) +--R Type: Expression Integer +--E 36 + +--S 37 of 105 +r0907:= 1/2*atanh(sin(-5+x^2)) +--R +--R +--R 2 +--R atanh(sin(x - 5)) +--R (37) ------------------ +--R 2 +--R Type: Expression Integer +--E 37 + +--S 38 of 105 +a0907:= integrate(t0907,x) +--R +--R +--R (38) +--R 2 2 2 2 +--R sin(x - 5) + cos(x - 5) + 1 sin(x - 5) - cos(x - 5) - 1 +--R log(-----------------------------) - log(-----------------------------) +--R 2 2 +--R cos(x - 5) + 1 cos(x - 5) + 1 +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 105 +m0907:= a0907-r0907 +--R +--R +--R (39) +--R 2 2 2 2 +--R sin(x - 5) + cos(x - 5) + 1 sin(x - 5) - cos(x - 5) - 1 +--R log(-----------------------------) - log(-----------------------------) +--R 2 2 +--R cos(x - 5) + 1 cos(x - 5) + 1 +--R + +--R 2 +--R - atanh(sin(x - 5)) +--R / +--R 2 +--R Type: Expression Integer +--E 39 + +--S 40 of 105 +d0907:= D(m0907,x) +--R +--R +--R (40) +--R 2 4 2 2 2 2 2 +--R - 2x sin(x - 5) + (- 2x cos(x - 5) - x cos(x - 5) + 2x)sin(x - 5) +--R + +--R 2 3 2 +--R - x cos(x - 5) + x cos(x - 5) +--R / +--R 2 4 2 2 2 2 2 +--R sin(x - 5) + (- cos(x - 5) - 2cos(x - 5) - 2)sin(x - 5) +--R + +--R 2 2 2 +--R cos(x - 5) + 2cos(x - 5) + 1 +--R Type: Expression Integer +--E 40 + +--S 41 of 105 +t0908:= csc(1/x)/x^2 +--R +--R +--R 1 +--R csc(-) +--R x +--R (41) ------ +--R 2 +--R x +--R Type: Expression Integer +--E 41 + +--S 42 of 105 +r0908:= atanh(cos(1/x)) +--R +--R +--R 1 +--R (42) atanh(cos(-)) +--R x +--R Type: Expression Integer +--E 42 + +--S 43 of 105 +a0908:= integrate(t0908,x) +--R +--R +--R 1 +--R sin(-) +--R x +--R (43) - log(----------) +--R 1 +--R cos(-) + 1 +--R x +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 105 +m0908:= a0908-r0908 +--R +--R +--R 1 +--R sin(-) +--R x 1 +--R (44) - log(----------) - atanh(cos(-)) +--R 1 x +--R cos(-) + 1 +--R x +--R Type: Expression Integer +--E 44 + +--S 45 of 105 +d0908:= D(m0908,x) +--R +--R +--R 1 1 2 1 3 1 +--R cos(-)sin(-) + cos(-) - cos(-) +--R x x x x +--R (45) -------------------------------- +--R 2 1 2 2 1 +--R (x cos(-) - x )sin(-) +--R x x +--R Type: Expression Integer +--E 45 + +--S 46 of 105 +t0909:= cos(x)/(-sin(x)+sin(x)^3) +--R +--R +--R cos(x) +--R (46) ---------------- +--R 3 +--R sin(x) - sin(x) +--R Type: Expression Integer +--E 46 + +--S 47 of 105 +r0909:= -log(tan(x)) +--R +--R +--R (47) - log(tan(x)) +--R Type: Expression Integer +--E 47 + +--S 48 of 105 +a0909:= integrate(t0909,x) +--R +--R +--R sin(x) 2cos(x) +--R (48) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 105 +m0909:= a0909-r0909 +--R +--R +--R sin(x) 2cos(x) +--R (49) log(tan(x)) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Integer +--E 49 + +--S 50 of 105 +d0909:= D(m0909,x) +--R +--R +--R 2 2 2 +--R cos(x)sin(x)tan(x) + (- sin(x) - cos(x) )tan(x) + cos(x)sin(x) +--R (50) ---------------------------------------------------------------- +--R cos(x)sin(x)tan(x) +--R Type: Expression Integer +--E 50 + +--S 51 of 105 +t0910:= 1/(4+3*cos(x)+4*sin(x)) +--R +--R +--R 1 +--R (51) --------------------- +--R 4sin(x) + 3cos(x) + 4 +--R Type: Expression Integer +--E 51 + +--S 52 of 105 +r0910:= -2/3*atanh(4/3+1/3*tan(1/2*x)) +--R +--R +--R x +--R tan(-) + 4 +--R 2 +--R 2atanh(----------) +--R 3 +--R (52) - ------------------ +--R 3 +--R Type: Expression Integer +--E 52 + +--S 53 of 105 +a0910:= integrate(t0910,x) +--R +--R +--R sin(x) + 7cos(x) + 7 sin(x) + cos(x) + 1 +--R - log(--------------------) + log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (53) ------------------------------------------------------ +--R 3 +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 105 +m0910:= a0910-r0910 +--R +--R +--R (54) +--R x +--R tan(-) + 4 +--R sin(x) + 7cos(x) + 7 sin(x) + cos(x) + 1 2 +--R - log(--------------------) + log(-------------------) + 2atanh(----------) +--R cos(x) + 1 cos(x) + 1 3 +--R --------------------------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 54 + +--S 55 of 105 +d0910:= D(m0910,x) +--R +--R +--R (55) +--R 2 2 x 2 +--R (sin(x) + (- 8cos(x) - 8)sin(x) - 5cos(x) - 12cos(x) - 7)tan(-) +--R 2 +--R + +--R 2 2 x 2 +--R (16sin(x) + 16cos(x) + 16cos(x))tan(-) + 13sin(x) +--R 2 +--R + +--R 2 +--R (- 8cos(x) - 8)sin(x) + 7cos(x) - 7 +--R / +--R 2 2 x 2 +--R (sin(x) + (8cos(x) + 8)sin(x) + 7cos(x) + 14cos(x) + 7)tan(-) +--R 2 +--R + +--R 2 2 x +--R (8sin(x) + (64cos(x) + 64)sin(x) + 56cos(x) + 112cos(x) + 56)tan(-) +--R 2 +--R + +--R 2 2 +--R 7sin(x) + (56cos(x) + 56)sin(x) + 49cos(x) + 98cos(x) + 49 +--R Type: Expression Integer +--E 55 + +--S 56 of 105 +t0911:= (sin(x)-cos(x))*(cos(x)+sin(x))^5 +--R +--R +--R (56) +--R 6 5 2 4 4 2 +--R sin(x) + 4cos(x)sin(x) + 5cos(x) sin(x) - 5cos(x) sin(x) +--R + +--R 5 6 +--R - 4cos(x) sin(x) - cos(x) +--R Type: Expression Integer +--E 56 + +--S 57 of 105 +r0911:= -1/6*(cos(x)+sin(x))^6 +--R +--R +--R (57) +--R 6 5 2 4 3 3 +--R - sin(x) - 6cos(x)sin(x) - 15cos(x) sin(x) - 20cos(x) sin(x) +--R + +--R 4 2 5 6 +--R - 15cos(x) sin(x) - 6cos(x) sin(x) - cos(x) +--R / +--R 6 +--R Type: Expression Integer +--E 57 + +--S 58 of 105 +a0911:= integrate(t0911,x) +--R +--R +--R 5 3 4 2 +--R (4cos(x) - 4cos(x) - 3cos(x))sin(x) + 6cos(x) - 6cos(x) +--R (58) ----------------------------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 105 +m0911:= a0911-r0911 +--R +--R +--R (59) +--R 6 5 2 4 3 3 +--R sin(x) + 6cos(x)sin(x) + 15cos(x) sin(x) + 20cos(x) sin(x) +--R + +--R 4 2 5 3 6 +--R 15cos(x) sin(x) + (14cos(x) - 8cos(x) - 6cos(x))sin(x) + cos(x) +--R + +--R 4 2 +--R 12cos(x) - 12cos(x) +--R / +--R 6 +--R Type: Expression Integer +--E 59 + +--S 60 of 105 +d0911:= D(m0911,x) +--R +--R +--R (60) +--R 6 5 2 4 +--R - 3sin(x) - 12cos(x)sin(x) - 15cos(x) sin(x) +--R + +--R 4 2 2 +--R (- 5cos(x) + 12cos(x) + 3)sin(x) +--R + +--R 5 3 6 4 2 +--R (12cos(x) - 24cos(x) + 12cos(x))sin(x) + 7cos(x) - 4cos(x) - 3cos(x) +--R / +--R 3 +--R Type: Expression Integer +--E 60 + +--S 61 of 105 +t0912:= sin(x)/(cos(x)^3-cos(x)^5) +--R +--R +--R sin(x) +--R (61) - ----------------- +--R 5 3 +--R cos(x) - cos(x) +--R Type: Expression Integer +--E 61 + +--S 62 of 105 +r0912:= log(tan(x))+1/2*tan(x)^2 +--R +--R +--R 2 +--R 2log(tan(x)) + tan(x) +--R (62) ---------------------- +--R 2 +--R Type: Expression Integer +--E 62 + +--S 63 of 105 +a0912:= integrate(t0912,x) +--R +--R +--R 2 sin(x) 2 2cos(x) 2 +--R 2cos(x) log(----------) - 2cos(x) log(- ----------) - cos(x) + 1 +--R cos(x) + 1 cos(x) + 1 +--R (63) ----------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 105 +m0912:= a0912-r0912 +--R +--R +--R (64) +--R 2 2 sin(x) +--R - 2cos(x) log(tan(x)) + 2cos(x) log(----------) +--R cos(x) + 1 +--R + +--R 2 2cos(x) 2 2 2 +--R - 2cos(x) log(- ----------) - cos(x) tan(x) - cos(x) + 1 +--R cos(x) + 1 +--R / +--R 2 +--R 2cos(x) +--R Type: Expression Integer +--E 64 + +--S 65 of 105 +d0912:= D(m0912,x) +--R +--R +--R (65) +--R 3 4 3 2 +--R - cos(x) sin(x)tan(x) - 2cos(x) sin(x)tan(x) +--R + +--R 2 2 4 3 +--R ((cos(x) + 1)sin(x) + cos(x) )tan(x) - cos(x) sin(x) +--R / +--R 3 +--R cos(x) sin(x)tan(x) +--R Type: Expression Integer +--E 65 + +--S 66 of 105 +t0913:= sin(x)*tan(x)^5 +--R +--R +--R 5 +--R (66) sin(x)tan(x) +--R Type: Expression Integer +--E 66 + +--S 67 of 105 +r0913:= 15/8*atanh(sin(x))-15/8*sin(x)-5/8*sin(x)*tan(x)^2+1/4*sin(x)*tan(x)^4 +--R +--R +--R 4 2 +--R 15atanh(sin(x)) + 2sin(x)tan(x) - 5sin(x)tan(x) - 15sin(x) +--R (67) ------------------------------------------------------------ +--R 8 +--R Type: Expression Integer +--E 67 + +--S 68 of 105 +a0913:= integrate(t0913,x) +--R +--R +--R (68) +--R 4 sin(x) + cos(x) + 1 4 sin(x) - cos(x) - 1 +--R 15cos(x) log(-------------------) - 15cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 4 2 +--R (- 8cos(x) - 9cos(x) + 2)sin(x) +--R / +--R 4 +--R 8cos(x) +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 105 +m0913:= a0913-r0913 +--R +--R +--R (69) +--R 4 sin(x) + cos(x) + 1 4 sin(x) - cos(x) - 1 +--R 15cos(x) log(-------------------) - 15cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 4 4 4 4 2 +--R - 15cos(x) atanh(sin(x)) - 2cos(x) sin(x)tan(x) + 5cos(x) sin(x)tan(x) +--R + +--R 4 2 +--R (7cos(x) - 9cos(x) + 2)sin(x) +--R / +--R 4 +--R 8cos(x) +--R Type: Expression Integer +--E 69 + +--S 70 of 105 +d0913:= D(m0913,x) +--R +--R +--R (70) +--R 5 5 7 6 5 3 +--R - 8cos(x) sin(x) + (8cos(x) + 16cos(x) + 16cos(x) )sin(x) +--R + +--R 7 6 5 +--R (- 8cos(x) - 16cos(x) - 8cos(x) )sin(x) +--R * +--R 5 +--R tan(x) +--R + +--R 6 4 8 7 6 2 +--R - 2cos(x) sin(x) + (2cos(x) + 4cos(x) + 4cos(x) )sin(x) +--R + +--R 8 7 6 +--R - 2cos(x) - 4cos(x) - 2cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 5 5 7 6 5 3 +--R 2cos(x) sin(x) + (- 2cos(x) - 4cos(x) - 4cos(x) )sin(x) +--R + +--R 7 6 5 +--R (2cos(x) + 4cos(x) + 2cos(x) )sin(x) +--R * +--R 3 +--R tan(x) +--R + +--R 6 4 8 7 6 2 +--R 5cos(x) sin(x) + (- 5cos(x) - 10cos(x) - 10cos(x) )sin(x) +--R + +--R 8 7 6 +--R 5cos(x) + 10cos(x) + 5cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 5 7 6 5 3 +--R 10cos(x) sin(x) + (- 10cos(x) - 20cos(x) - 20cos(x) )sin(x) +--R + +--R 7 6 5 +--R (10cos(x) + 20cos(x) + 10cos(x) )sin(x) +--R * +--R tan(x) +--R + +--R 2 6 +--R (- 18cos(x) + 8)sin(x) +--R + +--R 6 5 4 3 2 +--R 7cos(x) - 30cos(x) + 9cos(x) + 36cos(x) + 30cos(x) - 16cos(x) +--R + +--R - 16 +--R * +--R 4 +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 7cos(x) - 44cos(x) - 20cos(x) + 48cos(x) - 2cos(x) - 40cos(x) +--R + +--R 2 +--R - 14cos(x) + 16cos(x) + 8 +--R * +--R 2 +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 8cos(x) + 14cos(x) + 13cos(x) - 18cos(x) - 7cos(x) + 4cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 5 4 7 6 5 2 7 +--R 8cos(x) sin(x) + (- 8cos(x) - 16cos(x) - 16cos(x) )sin(x) + 8cos(x) +--R + +--R 6 5 +--R 16cos(x) + 8cos(x) +--R Type: Expression Integer +--E 70 + +--S 71 of 105 +t0914:= sec(x)*tan(x)^2/(4+3*sec(x)) +--R +--R +--R 2 +--R sec(x)tan(x) +--R (71) ------------- +--R 3sec(x) + 4 +--R Type: Expression Integer +--E 71 + +--S 72 of 105 +r0914:= -4/9*atanh(sin(x))+2/9*7^(1/2)*atanh(1/7*tan(1/2*x)*7^(1/2))+1/3*tan(x) +--R +--R +--R +-+ x +--R \|7 tan(-) +--R +-+ 2 +--R 2\|7 atanh(----------) - 4atanh(sin(x)) + 3tan(x) +--R 7 +--R (72) ------------------------------------------------- +--R 9 +--R Type: Expression Integer +--E 72 + +--S 73 of 105 +a0914:= integrate(t0914,x) +--R +--R +--R (73) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - 4cos(x)log(-------------------) + 4cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ +--R +-+ - \|7 sin(x) - 3cos(x) - 4 +--R \|7 cos(x)log(--------------------------) + 3sin(x) +--R 4cos(x) + 3 +--R / +--R 9cos(x) +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 105 +m0914:= a0914-r0914 +--R +--R +--R (74) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - 4cos(x)log(-------------------) + 4cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ x +--R +-+ \|7 tan(-) +--R +-+ - \|7 sin(x) - 3cos(x) - 4 +-+ 2 +--R \|7 cos(x)log(--------------------------) - 2\|7 cos(x)atanh(----------) +--R 4cos(x) + 3 7 +--R + +--R 4cos(x)atanh(sin(x)) - 3cos(x)tan(x) + 3sin(x) +--R / +--R 9cos(x) +--R Type: Expression Integer +--E 74 + +--S 75 of 105 +d0914:= D(m0914,x) +--R +--R +--R (75) +--R +-+ 3 +-+ 2 5 +--R (- 12\|7 cos(x) - 9\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (- 36cos(x) - 75cos(x) - 36cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (12\|7 cos(x) + 33\|7 cos(x) + 42\|7 cos(x) + 18\|7 cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (36cos(x) + 147cos(x) + 258cos(x) + 222cos(x) + 72cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 12\|7 cos(x) - 33\|7 cos(x) - 30\|7 cos(x) +--R + +--R +-+ 2 +--R - 9\|7 cos(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 36cos(x) - 147cos(x) - 222cos(x) - 147cos(x) - 36cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R +-+ 3 +-+ 2 5 +--R (84\|7 cos(x) + 63\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (252cos(x) + 525cos(x) + 252cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 84\|7 cos(x) - 231\|7 cos(x) - 294\|7 cos(x) +--R + +--R +-+ 2 +--R - 126\|7 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 252cos(x) - 1029cos(x) - 1806cos(x) - 1554cos(x) +--R + +--R 2 +--R - 504cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (84\|7 cos(x) + 231\|7 cos(x) + 210\|7 cos(x) + 63\|7 cos(x) ) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 252cos(x) + 1029cos(x) + 1554cos(x) + 1029cos(x) + 252cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ +-+ 7 2 6 +--R (12\|7 cos(x) + 9\|7 )sin(x) + (64cos(x) + 75cos(x) + 36)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ 5 +--R (48\|7 cos(x) + 19\|7 cos(x) - 42\|7 cos(x) - 18\|7 )sin(x) +--R + +--R 4 3 2 4 +--R (144cos(x) + 193cos(x) - 134cos(x) - 222cos(x) - 72)sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R 4\|7 cos(x) - 44\|7 cos(x) - 120\|7 cos(x) - 47\|7 cos(x) +--R + +--R +-+ +-+ +--R 30\|7 cos(x) + 9\|7 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) - 172cos(x) - 536cos(x) - 509cos(x) - 14cos(x) +--R + +--R 147cos(x) + 36 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 16\|7 cos(x) + 40\|7 cos(x) + 68\|7 cos(x) + 72\|7 cos(x) +--R + +--R +-+ 2 +--R 28\|7 cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 48cos(x) + 212cos(x) + 420cos(x) + 488cos(x) + 316cos(x) +--R + +--R 2 +--R 84cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R +-+ +-+ 7 +--R (- 84\|7 cos(x) - 63\|7 )sin(x) +--R + +--R 2 6 +--R (- 448cos(x) - 525cos(x) - 252)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ 5 +--R (- 112\|7 cos(x) + 35\|7 cos(x) + 294\|7 cos(x) + 126\|7 )sin(x) +--R + +--R 4 3 2 4 +--R (- 336cos(x) + 49cos(x) + 1610cos(x) + 1554cos(x) + 504)sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 252\|7 cos(x) - 308\|7 cos(x) + 56\|7 cos(x) - 7\|7 cos(x) +--R + +--R +-+ +-+ +--R - 210\|7 cos(x) - 63\|7 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 560cos(x) - 1540cos(x) - 1064cos(x) - 581cos(x) - 1246cos(x) +--R + +--R - 1029cos(x) - 252 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R - 112\|7 cos(x) - 56\|7 cos(x) + 140\|7 cos(x) + 56\|7 cos(x) +--R + +--R +-+ 2 +--R - 28\|7 cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 336cos(x) - 812cos(x) - 196cos(x) + 728cos(x) + 532cos(x) +--R + +--R 2 +--R 84cos(x) +--R / +--R +-+ 3 +-+ 2 5 +--R (36\|7 cos(x) + 27\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (108cos(x) + 225cos(x) + 108cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (- 36\|7 cos(x) - 99\|7 cos(x) - 126\|7 cos(x) - 54\|7 cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (- 108cos(x) - 441cos(x) - 774cos(x) - 666cos(x) - 216cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (36\|7 cos(x) + 99\|7 cos(x) + 90\|7 cos(x) + 27\|7 cos(x) )sin(x) +--R + +--R 6 5 4 3 2 +--R 108cos(x) + 441cos(x) + 666cos(x) + 441cos(x) + 108cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R +-+ 3 +-+ 2 5 +--R (- 252\|7 cos(x) - 189\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (- 756cos(x) - 1575cos(x) - 756cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (252\|7 cos(x) + 693\|7 cos(x) + 882\|7 cos(x) + 378\|7 cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (756cos(x) + 3087cos(x) + 5418cos(x) + 4662cos(x) + 1512cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (- 252\|7 cos(x) - 693\|7 cos(x) - 630\|7 cos(x) - 189\|7 cos(x) ) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 756cos(x) - 3087cos(x) - 4662cos(x) - 3087cos(x) - 756cos(x) +--R Type: Expression Integer +--E 75 + +--S 76 of 105 +t0915:= x*sec(1+x)*tan(1+x) +--R +--R +--R (76) x sec(x + 1)tan(x + 1) +--R Type: Expression Integer +--E 76 + +--S 77 of 105 +r0915:= -atanh(sin(1+x))+x*sec(1+x) +--R +--R +--R (77) - atanh(sin(x + 1)) + x sec(x + 1) +--R Type: Expression Integer +--E 77 + +--S 78 of 105 +a0915:= integrate(t0915,x) +--R +--R +--R (78) +--R sin(x + 1) + cos(x + 1) + 1 +--R - cos(x + 1)log(---------------------------) +--R cos(x + 1) + 1 +--R + +--R sin(x + 1) - cos(x + 1) - 1 +--R cos(x + 1)log(---------------------------) + x +--R cos(x + 1) + 1 +--R / +--R cos(x + 1) +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 105 +m0915:= a0915-r0915 +--R +--R +--R (79) +--R sin(x + 1) + cos(x + 1) + 1 +--R - cos(x + 1)log(---------------------------) +--R cos(x + 1) + 1 +--R + +--R sin(x + 1) - cos(x + 1) - 1 +--R cos(x + 1)log(---------------------------) + cos(x + 1)atanh(sin(x + 1)) +--R cos(x + 1) + 1 +--R + +--R - x cos(x + 1)sec(x + 1) + x +--R / +--R cos(x + 1) +--R Type: Expression Integer +--E 79 + +--S 80 of 105 +d0915:= D(m0915,x) +--R +--R +--R (80) +--R 2 4 +--R - x cos(x + 1) sec(x + 1)sin(x + 1) +--R + +--R 4 3 2 +--R (x cos(x + 1) + 2x cos(x + 1) + 2x cos(x + 1) )sec(x + 1) +--R * +--R 2 +--R sin(x + 1) +--R + +--R 4 3 2 +--R (- x cos(x + 1) - 2x cos(x + 1) - x cos(x + 1) )sec(x + 1) +--R * +--R tan(x + 1) +--R + +--R 5 +--R x sin(x + 1) +--R + +--R 2 2 4 +--R (- cos(x + 1) sec(x + 1) + 2cos(x + 1) + cos(x + 1))sin(x + 1) +--R + +--R 2 3 +--R (- x cos(x + 1) - 2x cos(x + 1) - 2x)sin(x + 1) +--R + +--R 4 3 2 4 +--R (cos(x + 1) + 2cos(x + 1) + 2cos(x + 1) )sec(x + 1) + 2cos(x + 1) +--R + +--R 2 +--R - 4cos(x + 1) - 2cos(x + 1) +--R * +--R 2 +--R sin(x + 1) +--R + +--R 2 +--R (x cos(x + 1) + 2x cos(x + 1) + x)sin(x + 1) +--R + +--R 4 3 2 5 +--R (- cos(x + 1) - 2cos(x + 1) - cos(x + 1) )sec(x + 1) + cos(x + 1) +--R + +--R 2 +--R 2cos(x + 1) + cos(x + 1) +--R / +--R 2 4 +--R cos(x + 1) sin(x + 1) +--R + +--R 4 3 2 2 4 +--R (- cos(x + 1) - 2cos(x + 1) - 2cos(x + 1) )sin(x + 1) + cos(x + 1) +--R + +--R 3 2 +--R 2cos(x + 1) + cos(x + 1) +--R Type: Expression Integer +--E 80 + +--S 81 of 105 +t0916:= cos(x)/(sin(x)+sin(x)^(2^(1/2))) +--R +--R +--R cos(x) +--R (81) ------------------- +--R +-+ +--R \|2 +--R sin(x) + sin(x) +--R Type: Expression Integer +--E 81 + +--S 82 of 105 +r0916:= -log(1+sin(x)^(-2^(1/2)+1))/(2^(1/2)-1) +--R +--R +--R +-+ +--R - \|2 + 1 +--R log(sin(x) + 1) +--R (82) - ------------------------- +--R +-+ +--R \|2 - 1 +--R Type: Expression Integer +--E 82 + +--S 83 of 105 +a0916:= integrate(t0916,x) +--R +--R +--R +-+ +--R \|2 log(sin(x)) +-+ 2 +--R - 2log(%e + sin(x)) + \|2 log(cos(x) - 1) +--R (83) --------------------------------------------------------- +--R +-+ +--R 2\|2 - 2 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 105 +m0916:= a0916-r0916 +--R +--R +--R (84) +--R +-+ +-+ +--R \|2 log(sin(x)) - \|2 + 1 +--R - 2log(%e + sin(x)) + 2log(sin(x) + 1) +--R + +--R +-+ 2 +--R \|2 log(cos(x) - 1) +--R / +--R +-+ +--R 2\|2 - 2 +--R Type: Expression Integer +--E 84 + +--S 85 of 105 +d0916:= D(m0916,x) +--R +--R +--R (85) +--R +-+ 2 +-+ 3 +--R (- \|2 + 2)cos(x)sin(x) + (- \|2 + 2)cos(x) +--R + +--R +-+ +--R (\|2 - 2)cos(x) +--R * +--R +-+ +--R - \|2 + 1 +--R sin(x) +--R + +--R +-+ +--R +-+ 3 +-+ - \|2 +--R ((- 2\|2 + 3)cos(x) + (2\|2 - 3)cos(x))sin(x)sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +--R (- \|2 + 2)cos(x)sin(x) + (- \|2 + 2)cos(x) + (\|2 - 2)cos(x) +--R * +--R +-+ +--R \|2 log(sin(x)) +--R %e +--R + +--R +-+ 3 +--R (- \|2 + 2)cos(x)sin(x) +--R + +--R +-+ 3 +-+ +--R ((\|2 - 1)cos(x) + (- \|2 + 1)cos(x))sin(x) +--R * +--R +-+ +--R - \|2 + 1 +--R sin(x) +--R + +--R +-+ +--R +-+ 3 +-+ 2 - \|2 +--R ((- 2\|2 + 3)cos(x) + (2\|2 - 3)cos(x))sin(x) sin(x) +--R + +--R +-+ 3 +-+ 3 +-+ +--R (- \|2 + 2)cos(x)sin(x) + ((\|2 - 1)cos(x) + (- \|2 + 1)cos(x))sin(x) +--R / +--R +-+ +--R +-+ 2 +-+ - \|2 + 1 +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x)sin(x) +--R + +--R +-+ 2 +-+ +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x) +--R * +--R +-+ +--R \|2 log(sin(x)) +--R %e +--R + +--R +-+ +--R +-+ 2 +-+ 2 - \|2 + 1 +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x) sin(x) +--R + +--R +-+ 2 +-+ 2 +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x) +--R Type: Expression Integer +--E 85 + +--S 86 of 105 +t0917:= (-1+sec(x))/(1-tan(x)) +--R +--R +--R - sec(x) + 1 +--R (86) ------------ +--R tan(x) - 1 +--R Type: Expression Integer +--E 86 + +--S 87 of 105 +r0917:= -1/2*x+1/2*atanh(1/2*(cos(x)+sin(x))*2^(1/2))*2^(1/2)+1/2*log(cos(x)-sin(x)) +--R +--R +--R +-+ +-+ +--R +-+ \|2 sin(x) + \|2 cos(x) +--R log(- sin(x) + cos(x)) + \|2 atanh(-----------------------) - x +--R 2 +--R (87) --------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 87 + +--S 88 of 105 +a0917:= integrate(t0917,x) +--R +--R +--R (88) +--R 2sin(x) - 2cos(x) +--R log(-----------------) +--R cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 + 1)sin(x) + (\|2 + 1)cos(x) + \|2 + 2 2 +--R \|2 log(----------------------------------------------) - log(----------) +--R sin(x) - cos(x) cos(x) + 1 +--R + +--R - x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 105 +m0917:= a0917-r0917 +--R +--R +--R (89) +--R 2sin(x) - 2cos(x) +--R log(-----------------) +--R cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 + 1)sin(x) + (\|2 + 1)cos(x) + \|2 + 2 2 +--R \|2 log(----------------------------------------------) - log(----------) +--R sin(x) - cos(x) cos(x) + 1 +--R + +--R +-+ +-+ +--R +-+ \|2 sin(x) + \|2 cos(x) +--R - log(- sin(x) + cos(x)) - \|2 atanh(-----------------------) +--R 2 +--R / +--R 2 +--R Type: Expression Integer +--E 89 + +--S 90 of 105 +d0917:= D(m0917,x) +--R +--R +--R (90) +--R +-+ 4 +-+ +-+ 3 +--R (- \|2 - 2)sin(x) + ((- 2\|2 - 4)cos(x) - 2\|2 - 2)sin(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R ((- 2\|2 - 4)cos(x) + (- 2\|2 - 2)cos(x) + \|2 + 2)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 2\|2 - 4)cos(x) + (- 2\|2 - 2)cos(x) + (2\|2 + 4)cos(x) +--R + +--R +-+ +--R 2\|2 + 2 +--R * +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (- \|2 - 2)cos(x) + (- 2\|2 - 2)cos(x) + (\|2 + 2)cos(x) +--R + +--R +-+ +--R (2\|2 + 2)cos(x) +--R / +--R +-+ 4 +-+ +-+ 3 +--R (\|2 + 1)sin(x) + ((2\|2 + 2)cos(x) + \|2 + 2)sin(x) +--R + +--R +-+ +-+ 2 +--R ((\|2 + 2)cos(x) - 2\|2 - 2)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R ((- 2\|2 - 2)cos(x) + (- \|2 - 2)cos(x) - 2\|2 - 4)sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (- \|2 - 1)cos(x) + (- \|2 - 2)cos(x) + (2\|2 + 2)cos(x) +--R + +--R +-+ +--R (2\|2 + 4)cos(x) +--R Type: Expression Integer +--E 90 + +--S 91 of 105 +t0918:= cos(x)^2*tan(x)^(1/2) +--R +--R +--R 2 +------+ +--R (91) cos(x) \|tan(x) +--R Type: Expression Integer +--E 91 + +--S 92 of 105 +r0918:= 1/8*2^(1/2)*atan(-1+2^(1/2)*tan(x)^(1/2))+1/8*2^(1/2)*atan(1+2^(1/2)*tan(x)^(1/2))+1/16*log(1-2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)-1/16*log(1+2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)+1/2*cos(x)^2*tan(x)^(3/2) +--R +--R +--R (92) +--R +-+ +-+ +------+ +--R - \|2 log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +-+ +-+ +------+ +-+ +-+ +------+ +--R \|2 log(- \|2 \|tan(x) + tan(x) + 1) + 2\|2 atan(\|2 \|tan(x) + 1) +--R + +--R +-+ +-+ +------+ 2 +------+ +--R 2\|2 atan(\|2 \|tan(x) - 1) + 8cos(x) tan(x)\|tan(x) +--R / +--R 16 +--R Type: Expression Integer +--E 92 + +--S 93 of 105 +a0918:= integrate(t0918,x) +--R +--R +--R (93) +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------ + 4cos(x)sin(x) + 1) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 4\|2 cos(x)sin(x) - 4\|2 cos(x) ) |------ + 8cos(x)sin(x) + 2) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((64cos(x) + 16cos(x))sin(x) - 64cos(x) + 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 32\|2 cos(x)sin(x) + 64\|2 cos(x) - 64\|2 cos(x) - 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) - \|2 +--R \|cos(x) +--R atan(--------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x)sin(x) |------ - 2\|2 cos(x)sin(x) + 2\|2 cos(x) - \|2 +--R \|cos(x) +--R atan(----------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x) |------ - 2\|2 cos(x)sin(x) - 2\|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) +--R \|cos(x) +--R atan(---------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R 5 3 +--R (512cos(x) + (- 32log(2) - 448)cos(x) - 8log(2)cos(x))sin(x) +--R + +--R 4 2 +--R (32log(2) + 192)cos(x) + (- 40log(2) - 176)cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 256\|2 cos(x) + 192\|2 cos(x) + (16log(2) + 32)\|2 cos(x))sin(x) +--R + +--R +-+ 6 +-+ 4 +--R 256\|2 cos(x) + (- 32log(2) - 512)\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R (32log(2) + 256)\|2 cos(x) + (log(2) - 2)\|2 +--R / +--R +-+ 3 +-+ +-+ 4 +--R (512\|2 cos(x) + 128\|2 cos(x))sin(x) - 512\|2 cos(x) +--R + +--R +-+ 2 +--R 640\|2 cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R 4 2 +--R - 512cos(x)sin(x) + 1024cos(x) - 1024cos(x) - 32 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 105 +m0918:= a0918-r0918 +--R +--R +--R (94) +--R +------+ +--R 3 4 2 |sin(x) +--R ((64cos(x) + 16cos(x))sin(x) - 64cos(x) + 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 32\|2 cos(x)sin(x) + 64\|2 cos(x) - 64\|2 cos(x) - 2\|2 +--R * +--R +-+ +------+ +--R log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------ + 4cos(x)sin(x) + 1) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 4\|2 cos(x)sin(x) - 4\|2 cos(x) ) |------ + 8cos(x)sin(x) + 2) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +-+ +------+ +--R log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 128cos(x) - 32cos(x))sin(x) + 128cos(x) - 160cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 64\|2 cos(x)sin(x) - 128\|2 cos(x) + 128\|2 cos(x) + 4\|2 +--R * +--R +-+ +------+ +--R atan(\|2 \|tan(x) + 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 128cos(x) - 32cos(x))sin(x) + 128cos(x) - 160cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 64\|2 cos(x)sin(x) - 128\|2 cos(x) + 128\|2 cos(x) + 4\|2 +--R * +--R +-+ +------+ +--R atan(\|2 \|tan(x) - 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((64cos(x) + 16cos(x))sin(x) - 64cos(x) + 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 32\|2 cos(x)sin(x) + 64\|2 cos(x) - 64\|2 cos(x) - 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) - \|2 +--R \|cos(x) +--R atan(--------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x)sin(x) |------ - 2\|2 cos(x)sin(x) + 2\|2 cos(x) - \|2 +--R \|cos(x) +--R atan(----------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x) |------ - 2\|2 cos(x)sin(x) - 2\|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) +--R \|cos(x) +--R atan(---------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ 6 +--R (- 256\|2 cos(x) - 64\|2 cos(x) )sin(x) + 256\|2 cos(x) +--R + +--R +-+ 4 +--R - 320\|2 cos(x) +--R * +--R +------+ +--R |sin(x) +--R tan(x) |------ +--R \|cos(x) +--R + +--R 3 6 4 2 +--R (256cos(x) sin(x) - 512cos(x) + 512cos(x) + 16cos(x) )tan(x) +--R * +--R +------+ +--R \|tan(x) +--R + +--R 5 3 +--R (512cos(x) + (- 32log(2) - 448)cos(x) - 8log(2)cos(x))sin(x) +--R + +--R 4 2 +--R (32log(2) + 192)cos(x) + (- 40log(2) - 176)cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 256\|2 cos(x) + 192\|2 cos(x) + (16log(2) + 32)\|2 cos(x))sin(x) +--R + +--R +-+ 6 +-+ 4 +--R 256\|2 cos(x) + (- 32log(2) - 512)\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R (32log(2) + 256)\|2 cos(x) + (log(2) - 2)\|2 +--R / +--R +-+ 3 +-+ +-+ 4 +--R (512\|2 cos(x) + 128\|2 cos(x))sin(x) - 512\|2 cos(x) +--R + +--R +-+ 2 +--R 640\|2 cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R 4 2 +--R - 512cos(x)sin(x) + 1024cos(x) - 1024cos(x) - 32 +--R Type: Expression Integer +--E 94 + +--S 95 of 105 +d0918:= D(m0918,x) +--R +--R +--R (95) +--R +-+ 14 +-+ 12 +--R - 2097152\|2 cos(x) - 1114112\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R 425984\|2 cos(x) - 4096\|2 cos(x) +--R * +--R 22 +--R sin(x) +--R + +--R +-+ 15 +-+ 13 +--R - 281542656\|2 cos(x) - 185139200\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 71663616\|2 cos(x) - 2125824\|2 cos(x) + 12288\|2 cos(x) +--R * +--R 21 +--R sin(x) +--R + +--R +-+ 16 +-+ 14 +--R - 5922357248\|2 cos(x) - 4811784192\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 2164424704\|2 cos(x) - 183029760\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +--R 3291136\|2 cos(x) - 13312\|2 cos(x) +--R * +--R 20 +--R sin(x) +--R + +--R +-+ 17 +-+ 15 +--R - 44349521920\|2 cos(x) - 49788485632\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 24705859584\|2 cos(x) - 3421900800\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 144923648\|2 cos(x) - 1888384\|2 cos(x) + 6144\|2 cos(x) +--R * +--R 19 +--R sin(x) +--R + +--R +-+ 18 +-+ 16 +--R - 153987579904\|2 cos(x) - 274652659712\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R 137678946304\|2 cos(x) - 23697547264\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R 1290334208\|2 cos(x) - 18452864\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 167296\|2 cos(x) - 1024\|2 cos(x) +--R * +--R 18 +--R sin(x) +--R + +--R +-+ 19 +-+ 17 +--R - 302523088896\|2 cos(x) - 899057123328\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 438689202176\|2 cos(x) - 79881003008\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R 2782665728\|2 cos(x) + 373268864\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +--R - 18033920\|2 cos(x) + 146016\|2 cos(x) +--R * +--R 17 +--R sin(x) +--R + +--R +-+ 20 +-+ 18 +--R - 453085495296\|2 cos(x) - 1862692110336\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 934049742848\|2 cos(x) - 189419495424\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 5531232256\|2 cos(x) + 2489199744\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 149855232\|2 cos(x) + 2158464\|2 cos(x) - 11584\|2 cos(x) +--R * +--R 16 +--R sin(x) +--R + +--R +-+ 21 +-+ 19 +--R - 639685885952\|2 cos(x) - 2739569426432\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R 1641249898496\|2 cos(x) - 462687387648\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 50612662272\|2 cos(x) + 2606540288\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +--R 95881728\|2 cos(x) - 55188768\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +--R 1521728\|2 cos(x) - 6688\|2 cos(x) +--R * +--R 15 +--R sin(x) +--R + +--R +-+ 22 +-+ 20 +--R - 830157619200\|2 cos(x) - 3121456218112\|2 cos(x) +--R + +--R +-+ 18 +-+ 16 +--R 2469378850816\|2 cos(x) - 915660496896\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R 140313673728\|2 cos(x) + 11607306752\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R - 1719996928\|2 cos(x) - 102631264\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 3649856\|2 cos(x) - 15608\|2 cos(x) +--R * +--R 14 +--R sin(x) +--R + +--R +-+ 23 +-+ 21 +--R - 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615168\|2 cos(x) +--R * +--R 11 +--R sin(x) +--R + +--R +-+ 24 +-+ 22 +--R - 1873444601856\|2 cos(x) + 10099015811072\|2 cos(x) +--R + +--R +-+ 20 +-+ 18 +--R - 17874731401216\|2 cos(x) + 13026922790912\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R - 3989367726080\|2 cos(x) + 422778062848\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R - 30427530240\|2 cos(x) + 15872553728\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 2653555712\|2 cos(x) + 143437248\|2 cos(x) - 1473088\|2 cos(x) +--R + +--R +-+ 2 +--R - 53056\|2 cos(x) +--R * +--R 10 +--R sin(x) +--R + +--R +-+ 25 +-+ 23 +--R - 2047147507712\|2 cos(x) + 10210496217088\|2 cos(x) +--R + +--R +-+ 21 +-+ 19 +--R - 18356108787712\|2 cos(x) + 15225812156416\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R - 6304780288000\|2 cos(x) + 1375523555328\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R - 216658208256\|2 cos(x) + 36821313792\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +--R - 2824994688\|2 cos(x) - 249719488\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +--R 38368064\|2 cos(x) - 1130528\|2 cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R +-+ 26 +-+ 24 +--R - 1680808607744\|2 cos(x) + 8177705811968\|2 cos(x) +--R + +--R +-+ 22 +-+ 20 +--R - 15180674629632\|2 cos(x) + 13895431225344\|2 cos(x) +--R + +--R +-+ 18 +-+ 16 +--R - 6798093811712\|2 cos(x) + 1795529771008\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R - 244448361472\|2 cos(x) + 5829399552\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R 6795280384\|2 cos(x) - 1598287488\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 107781888\|2 cos(x) + 510400\|2 cos(x) - 149184\|2 cos(x) +--R * +--R 8 +--R sin(x) +--R + +--R +-+ 27 +-+ 25 +--R - 1093899649024\|2 cos(x) + 5353567682560\|2 cos(x) +--R + +--R +-+ 23 +-+ 21 +--R - 10497186856960\|2 cos(x) + 10793919709184\|2 cos(x) +--R + +--R +-+ 19 +-+ 17 +--R - 6438125633536\|2 cos(x) + 2356560013312\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R - 569976827392\|2 cos(x) + 103685773312\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R - 16007406080\|2 cos(x) + 2426208384\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 374494464\|2 cos(x) + 34711360\|2 cos(x) - 1015264\|2 cos(x) +--R + +--R +-+ +--R - 6560\|2 cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R +-+ 28 +-+ 26 +--R - 549554487296\|2 cos(x) + 2785563115520\|2 cos(x) +--R + +--R +-+ 24 +-+ 22 +--R - 5932676808704\|2 cos(x) + 7047240351744\|2 cos(x) +--R + +--R +-+ 20 +-+ 18 +--R - 5272981159936\|2 cos(x) + 2700850411520\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R - 1022326303744\|2 cos(x) + 301380123392\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R - 68237679616\|2 cos(x) + 11060377472\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 1156883840\|2 cos(x) + 57648320\|2 cos(x) + 877248\|2 cos(x) +--R + +--R +-+ 2 +--R - 134400\|2 cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R +-+ 29 +-+ 27 +--R - 179254067200\|2 cos(x) + 947110543360\|2 cos(x) +--R + +--R +-+ 25 +-+ 23 +--R - 2163420823552\|2 cos(x) + 2838778347520\|2 cos(x) +--R + +--R +-+ 21 +-+ 19 +--R - 2405754208256\|2 cos(x) + 1406353528832\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R - 588822379008\|2 cos(x) + 176400677120\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R - 34833939328\|2 cos(x) + 3170855552\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 318197632\|2 cos(x) - 127436160\|2 cos(x) + 13766368\|2 cos(x) +--R + +--R +-+ 3 +-+ +--R - 449024\|2 cos(x) - 6688\|2 cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 30 +-+ 28 +--R - 31339839488\|2 cos(x) + 167999700992\|2 cos(x) +--R + +--R +-+ 26 +-+ 24 +--R - 388160684032\|2 cos(x) + 504411422720\|2 cos(x) +--R + +--R +-+ 22 +-+ 20 +--R - 397088817152\|2 cos(x) + 178820245504\|2 cos(x) +--R + +--R +-+ 18 +-+ 16 +--R - 21533588480\|2 cos(x) - 28914678272\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R 22940360704\|2 cos(x) - 8982026560\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 2115989248\|2 cos(x) - 289734848\|2 cos(x) + 18565568\|2 cos(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 26368\|2 cos(x) - 42016\|2 cos(x) - 128\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 31 +-+ 29 +--R - 2371878912\|2 cos(x) + 11792285696\|2 cos(x) +--R + +--R +-+ 27 +-+ 25 +--R - 22705733632\|2 cos(x) + 16496984064\|2 cos(x) +--R + +--R +-+ 23 +-+ 21 +--R 11655184384\|2 cos(x) - 39280244736\|2 cos(x) +--R + +--R +-+ 19 +-+ 17 +--R 44639345152\|2 cos(x) - 30808709632\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 14189916416\|2 cos(x) - 4358633920\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 823319040\|2 cos(x) - 68399424\|2 cos(x) - 4878496\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 1455840\|2 cos(x) - 73696\|2 cos(x) - 1328\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 32 +-+ 30 +--R - 50331648\|2 cos(x) + 132120576\|2 cos(x) +--R + +--R +-+ 28 +-+ 26 +--R 313655296\|2 cos(x) - 2038005760\|2 cos(x) +--R + +--R +-+ 24 +-+ 22 +--R 4439543808\|2 cos(x) - 5541152768\|2 cos(x) +--R + +--R +-+ 20 +-+ 18 +--R 4355552256\|2 cos(x) - 2070590208\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 386927616\|2 cos(x) + 199519936\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R - 182637120\|2 cos(x) + 67859328\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 13844416\|2 cos(x) + 1424384\|2 cos(x) - 39072\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 2560\|2 cos(x) - 16\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 2097152\|2 cos(x) + 11534336\|2 cos(x) - 22020096\|2 cos(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 704512\|2 cos(x) + 78899200\|2 cos(x) - 182747648\|2 cos(x) +--R + +--R +-+ 19 +-+ 17 +--R 235505408\|2 cos(x) - 203157632\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 123476032\|2 cos(x) - 53190848\|2 cos(x) + 15809440\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 3013984\|2 cos(x) + 304960\|2 cos(x) - 5440\|2 cos(x) +--R + +--R +-+ 3 +-+ +--R - 1072\|2 cos(x) - 16\|2 cos(x) +--R * +--R sin(x) +--R * +--R +------+ +--R \|tan(x) +--R Type: Expression Integer +--E 95 + +--S 96 of 105 +t0919:= cos(a+b*x)^n*sin(a+b*x)^(-2-n) +--R +--R +--R n - n - 2 +--R (96) cos(b x + a) sin(b x + a) +--R Type: Expression Integer +--E 96 + +--S 97 of 105 +r0919:= -cos(a+b*x)^(1+n)*sin(a+b*x)^(-1-n)/b/(1+n) +--R +--R +--R n + 1 - n - 1 +--R cos(b x + a) sin(b x + a) +--R (97) - ------------------------------------ +--R b n + b +--R Type: Expression Integer +--E 97 + +--S 98 of 105 +a0919:= integrate(t0919,x) +--R +--R +--R x +--R ++ n - n - 2 +--R (98) | cos(%I b + a) sin(%I b + a) d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 105 +m0919:= a0919-r0919 +--R +--R +--R (99) +--R x +--R ++ n - n - 2 +--R (b n + b) | cos(%I b + a) sin(%I b + a) d%I +--R ++ +--R + +--R n + 1 - n - 1 +--R cos(b x + a) sin(b x + a) +--R / +--R b n + b +--R Type: Expression Integer +--E 99 + +--S 100 of 105 +d0919:= D(m0919,x) +--R +--R +--R (100) +--R n - n - 1 +--R - sin(b x + a)cos(b x + a) sin(b x + a) +--R + +--R n + 1 n - n - 2 +--R (- cos(b x + a)cos(b x + a) + cos(b x + a) )sin(b x + a) +--R Type: Expression Integer +--E 100 + +--S 101 of 105 +t0920:= x^5*sec(a+b*x^3)^7*tan(a+b*x^3) +--R +--R +--R 5 3 7 3 +--R (101) x sec(b x + a) tan(b x + a) +--R Type: Expression Integer +--E 101 + +--S 102 of 105 +r0920:= -1/1008*(15*atanh(sin(a+b*x^3))*cos(a+b*x^3)^7-48*b*x^3+15*cos(a+b*x^3)^5*sin(a+b*x^3)+10*cos(a+b*x^3)^3*sin(a+b*x^3)+8*cos(a+b*x^3)*sin(a+b*x^3))/cos(a+b*x^3)^7/b^2 +--R +--R +--R (102) +--R 3 7 3 +--R - 15cos(b x + a) atanh(sin(b x + a)) +--R + +--R 3 5 3 3 3 3 +--R (- 15cos(b x + a) - 10cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 3 +--R 48b x +--R / +--R 2 3 7 +--R 1008b cos(b x + a) +--R Type: Expression Integer +--E 102 + +--S 103 of 105 +a0920:= integrate(t0920,x) +--R +--R +--R (103) +--R 3 3 +--R 3 7 sin(b x + a) + cos(b x + a) + 1 +--R - 15cos(b x + a) log(---------------------------------) +--R 3 +--R cos(b x + a) + 1 +--R + +--R 3 3 +--R 3 7 sin(b x + a) - cos(b x + a) - 1 +--R 15cos(b x + a) log(---------------------------------) +--R 3 +--R cos(b x + a) + 1 +--R + +--R 3 5 3 3 3 3 +--R (- 15cos(b x + a) - 10cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 3 +--R 48b x +--R / +--R 2 3 7 +--R 1008b cos(b x + a) +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 105 +m0920:= a0920-r0920 +--R +--R +--R (104) +--R 3 3 +--R sin(b x + a) + cos(b x + a) + 1 +--R - 5log(---------------------------------) +--R 3 +--R cos(b x + a) + 1 +--R + +--R 3 3 +--R sin(b x + a) - cos(b x + a) - 1 3 +--R 5log(---------------------------------) + 5atanh(sin(b x + a)) +--R 3 +--R cos(b x + a) + 1 +--R / +--R 2 +--R 336b +--R Type: Expression Integer +--E 104 + +--S 105 of 105 +d0920:= D(m0920,x) +--R +--R +--R (105) +--R 2 3 4 +--R 10x sin(b x + a) +--R + +--R 2 3 2 2 3 2 3 2 +--R (10x cos(b x + a) + 5x cos(b x + a) - 10x )sin(b x + a) +--R + +--R 2 3 3 2 3 +--R 5x cos(b x + a) - 5x cos(b x + a) +--R / +--R 3 4 +--R 112b sin(b x + a) +--R + +--R 3 2 3 3 2 +--R (- 112b cos(b x + a) - 224b cos(b x + a) - 224b)sin(b x + a) +--R + +--R 3 2 3 +--R 112b cos(b x + a) + 224b cos(b x + a) + 112b +--R Type: Expression Integer +--E 105 + +)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}