1,1,26,0,0.411383," ","integrate(2/(3-cos(4+6*x)),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*sin(6*x + 4)/(cos(6*x + 4) + 1))","A",0
2,1,26,0,0.643154," ","integrate(2*csc(4+6*x)/(-cot(4+6*x)+3*csc(4+6*x)),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*sin(6*x + 4)/(cos(6*x + 4) + 1))","A",0
3,1,16,0,0.890323," ","integrate(1/(1+sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*tan(3*x + 2))","A",0
4,1,16,0,0.410849," ","integrate(1/(2-cos(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*tan(3*x + 2))","A",0
5,1,16,0,0.565305," ","integrate(1/(cos(2+3*x)^2+2*sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*tan(3*x + 2))","A",0
6,1,16,0,0.441772," ","integrate(sec(2+3*x)^2/(1+2*tan(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*tan(3*x + 2))","A",0
7,1,16,0,0.614325," ","integrate(csc(2+3*x)^2/(2+cot(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*tan(3*x + 2))","A",0
8,1,54,0,0.567942," ","integrate(2/(1-3*cos(4+6*x)),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{2 \, \sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}{\sqrt{2} + \frac{2 \, \sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*sin(6*x + 4)/(cos(6*x + 4) + 1))/(sqrt(2) + 2*sin(6*x + 4)/(cos(6*x + 4) + 1)))","A",0
9,1,54,0,0.489755," ","integrate(2*csc(4+6*x)/(-3*cot(4+6*x)+csc(4+6*x)),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{2 \, \sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}{\sqrt{2} + \frac{2 \, \sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*sin(6*x + 4)/(cos(6*x + 4) + 1))/(sqrt(2) + 2*sin(6*x + 4)/(cos(6*x + 4) + 1)))","A",0
10,1,34,0,0.409391," ","integrate(1/(-1+3*sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - 2 \, \tan\left(3 \, x + 2\right)}{\sqrt{2} + 2 \, \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*tan(3*x + 2))/(sqrt(2) + 2*tan(3*x + 2)))","A",0
11,1,34,0,0.496693," ","integrate(1/(2-3*cos(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - 2 \, \tan\left(3 \, x + 2\right)}{\sqrt{2} + 2 \, \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*tan(3*x + 2))/(sqrt(2) + 2*tan(3*x + 2)))","A",0
12,1,34,0,0.412717," ","integrate(1/(-cos(2+3*x)^2+2*sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - 2 \, \tan\left(3 \, x + 2\right)}{\sqrt{2} + 2 \, \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*tan(3*x + 2))/(sqrt(2) + 2*tan(3*x + 2)))","A",0
13,1,34,0,1.031788," ","integrate(sec(2+3*x)^2/(-1+2*tan(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - 2 \, \tan\left(3 \, x + 2\right)}{\sqrt{2} + 2 \, \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*tan(3*x + 2))/(sqrt(2) + 2*tan(3*x + 2)))","A",0
14,1,34,0,0.412793," ","integrate(csc(2+3*x)^2/(2-cot(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - 2 \, \tan\left(3 \, x + 2\right)}{\sqrt{2} + 2 \, \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - 2*tan(3*x + 2))/(sqrt(2) + 2*tan(3*x + 2)))","A",0
15,1,27,0,0.419855," ","integrate(2/(3+cos(4+6*x)),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sin\left(6 \, x + 4\right)}{2 \, {\left(\cos\left(6 \, x + 4\right) + 1\right)}}\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*sin(6*x + 4)/(cos(6*x + 4) + 1))","A",0
16,1,27,0,0.432251," ","integrate(2*csc(4+6*x)/(cot(4+6*x)+3*csc(4+6*x)),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sin\left(6 \, x + 4\right)}{2 \, {\left(\cos\left(6 \, x + 4\right) + 1\right)}}\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*sin(6*x + 4)/(cos(6*x + 4) + 1))","A",0
17,1,17,0,0.443358," ","integrate(1/(2-sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(3*x + 2))","A",0
18,1,17,0,0.442753," ","integrate(1/(1+cos(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(3*x + 2))","A",0
19,1,17,0,0.444134," ","integrate(1/(2*cos(2+3*x)^2+sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(3*x + 2))","A",0
20,1,17,0,1.180762," ","integrate(sec(2+3*x)^2/(2+tan(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(3*x + 2))","A",0
21,1,17,0,0.744569," ","integrate(csc(2+3*x)^2/(1+2*cot(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(3*x + 2))","A",0
22,1,53,0,0.433089," ","integrate(-2/(1+3*cos(4+6*x)),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{\sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}{\sqrt{2} + \frac{\sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - sin(6*x + 4)/(cos(6*x + 4) + 1))/(sqrt(2) + sin(6*x + 4)/(cos(6*x + 4) + 1)))","A",0
23,1,53,0,0.525634," ","integrate(-2*csc(4+6*x)/(3*cot(4+6*x)+csc(4+6*x)),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{\sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}{\sqrt{2} + \frac{\sin\left(6 \, x + 4\right)}{\cos\left(6 \, x + 4\right) + 1}}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - sin(6*x + 4)/(cos(6*x + 4) + 1))/(sqrt(2) + sin(6*x + 4)/(cos(6*x + 4) + 1)))","A",0
24,1,32,0,0.501234," ","integrate(1/(-2+3*sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \tan\left(3 \, x + 2\right)}{\sqrt{2} + \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - tan(3*x + 2))/(sqrt(2) + tan(3*x + 2)))","A",0
25,1,32,0,0.516190," ","integrate(1/(1-3*cos(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \tan\left(3 \, x + 2\right)}{\sqrt{2} + \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - tan(3*x + 2))/(sqrt(2) + tan(3*x + 2)))","A",0
26,1,32,0,0.535870," ","integrate(1/(-2*cos(2+3*x)^2+sin(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \tan\left(3 \, x + 2\right)}{\sqrt{2} + \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - tan(3*x + 2))/(sqrt(2) + tan(3*x + 2)))","A",0
27,1,32,0,1.341721," ","integrate(sec(2+3*x)^2/(-2+tan(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \tan\left(3 \, x + 2\right)}{\sqrt{2} + \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - tan(3*x + 2))/(sqrt(2) + tan(3*x + 2)))","A",0
28,1,32,0,1.181615," ","integrate(csc(2+3*x)^2/(1-2*cot(2+3*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \tan\left(3 \, x + 2\right)}{\sqrt{2} + \tan\left(3 \, x + 2\right)}\right)"," ",0,"1/12*sqrt(2)*log(-(sqrt(2) - tan(3*x + 2))/(sqrt(2) + tan(3*x + 2)))","A",0
29,1,24,0,0.326401," ","integrate((x+sin(x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} - 2 \, x \cos\left(x\right) + \frac{1}{2} \, x - \frac{1}{4} \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right)"," ",0,"1/3*x^3 - 2*x*cos(x) + 1/2*x - 1/4*sin(2*x) + 2*sin(x)","A",0
30,1,48,0,0.517087," ","integrate((x+sin(x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} + \frac{1}{3} \, \cos\left(x\right)^{3} + \frac{3}{4} \, x^{2} - 3 \, {\left(x^{2} - 2\right)} \cos\left(x\right) - \frac{3}{4} \, x \sin\left(2 \, x\right) + 6 \, x \sin\left(x\right) - \frac{3}{8} \, \cos\left(2 \, x\right) - \cos\left(x\right)"," ",0,"1/4*x^4 + 1/3*cos(x)^3 + 3/4*x^2 - 3*(x^2 - 2)*cos(x) - 3/4*x*sin(2*x) + 6*x*sin(x) - 3/8*cos(2*x) - cos(x)","A",0
31,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(sin(b*x + a)/(d*x^2 + c), x)","F",0
32,0,0,0,0.000000," ","integrate(sin(b*x+a)/(e*x^2+d*x+c),x, algorithm=""maxima"")","\int \frac{\sin\left(b x + a\right)}{e x^{2} + d x + c}\,{d x}"," ",0,"integrate(sin(b*x + a)/(e*x^2 + d*x + c), x)","F",0
33,1,8,0,0.309495," ","integrate(sin((-7+x)^(1/2))/(-7+x)^(1/2),x, algorithm=""maxima"")","-2 \, \cos\left(\sqrt{x - 7}\right)"," ",0,"-2*cos(sqrt(x - 7))","A",0
34,0,0,0,0.000000," ","integrate(sin(x)*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b - \frac{a}{x^{2}}} \sin\left(x\right)}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(b - a/x^2)*sin(x)/sqrt(-b*x^2 + a), x)","F",0
35,1,17,0,0.305949," ","integrate(1/x/(1+sin(log(x))),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(\log\left(x\right)\right)}{\cos\left(\log\left(x\right)\right) + 1} + 1}"," ",0,"-2/(sin(log(x))/(cos(log(x)) + 1) + 1)","A",0
36,0,0,0,0.000000," ","integrate(sin((b*x+a)/(d*x+c)),x, algorithm=""maxima"")","\int \sin\left(\frac{b x + a}{d x + c}\right)\,{d x}"," ",0,"integrate(sin((b*x + a)/(d*x + c)), x)","F",0
37,0,0,0,0.000000," ","integrate(sin((b*x+a)/(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, x - \frac{1}{2} \, \int \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right)\,{d x}"," ",0,"1/2*x - 1/2*integrate(cos(2*(b*x + a)/(d*x + c)), x)","F",0
38,0,0,0,0.000000," ","integrate(sin((b*x+a)/(d*x+c))^3,x, algorithm=""maxima"")","\int \sin\left(\frac{b x + a}{d x + c}\right)^{3}\,{d x}"," ",0,"integrate(sin((b*x + a)/(d*x + c))^3, x)","F",0
39,0,0,0,0.000000," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(sin(sqrt(-a*x + 1)/sqrt(a*x + 1))^3/(a^2*x^2 - 1), x)","F",0
40,0,0,0,0.000000," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x, algorithm=""maxima"")","\frac{a \int \frac{\cos\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}\,{d x} + a \int \frac{\cos\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \sin\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}\,{d x} + \log\left(a x + 1\right) - \log\left(a x - 1\right)}{4 \, a}"," ",0,"1/4*(4*a*integrate(1/4*cos(2*sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x) + 4*a*integrate(1/4*cos(2*sqrt(-a*x + 1)/sqrt(a*x + 1))/((a^2*x^2 - 1)*cos(2*sqrt(-a*x + 1)/sqrt(a*x + 1))^2 + (a^2*x^2 - 1)*sin(2*sqrt(-a*x + 1)/sqrt(a*x + 1))^2), x) + log(a*x + 1) - log(a*x - 1))/a","F",0
41,0,0,0,0.000000," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(sin(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} x^{2} - 1\right)} \sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}\,{d x}"," ",0,"-integrate(1/((a^2*x^2 - 1)*sin(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
43,-1,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,1,24,0,0.305689," ","integrate((x+cos(x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} + 2 \, x \sin\left(x\right) + \frac{1}{2} \, x + 2 \, \cos\left(x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/3*x^3 + 2*x*sin(x) + 1/2*x + 2*cos(x) + 1/4*sin(2*x)","A",0
45,1,46,0,0.313838," ","integrate((x+cos(x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} - \frac{1}{3} \, \sin\left(x\right)^{3} + \frac{3}{4} \, x^{2} + 6 \, x \cos\left(x\right) + \frac{3}{4} \, x \sin\left(2 \, x\right) + 3 \, {\left(x^{2} - 2\right)} \sin\left(x\right) + \frac{3}{8} \, \cos\left(2 \, x\right) + \sin\left(x\right)"," ",0,"1/4*x^4 - 1/3*sin(x)^3 + 3/4*x^2 + 6*x*cos(x) + 3/4*x*sin(2*x) + 3*(x^2 - 2)*sin(x) + 3/8*cos(2*x) + sin(x)","A",0
46,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x^2 + c), x)","F",0
47,0,0,0,0.000000," ","integrate(cos(b*x+a)/(e*x^2+d*x+c),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)}{e x^{2} + d x + c}\,{d x}"," ",0,"integrate(cos(b*x + a)/(e*x^2 + d*x + c), x)","F",0
48,1,8,0,0.350363," ","integrate(x*cos((x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""maxima"")","\sin\left(\sqrt{x^{2} + 1}\right)"," ",0,"sin(sqrt(x^2 + 1))","A",0
49,1,17,0,0.410833," ","integrate(x*cos(3^(1/2)*(x^2+2)^(1/2))/(x^2+2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \sqrt{3} \sin\left(\sqrt{3} \sqrt{x^{2} + 2}\right)"," ",0,"1/3*sqrt(3)*sin(sqrt(3)*sqrt(x^2 + 2))","A",0
50,1,16,0,0.305654," ","integrate((-1+2*x)*cos((6+3*(-1+2*x)^2)^(1/2))/(6+3*(-1+2*x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, \sin\left(\sqrt{3 \, {\left(2 \, x - 1\right)}^{2} + 6}\right)"," ",0,"1/6*sin(sqrt(3*(2*x - 1)^2 + 6))","A",0
51,0,0,0,0.000000," ","integrate(cos((b*x+a)/(d*x+c)),x, algorithm=""maxima"")","\int \cos\left(\frac{b x + a}{d x + c}\right)\,{d x}"," ",0,"integrate(cos((b*x + a)/(d*x + c)), x)","F",0
52,0,0,0,0.000000," ","integrate(cos((b*x+a)/(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, x + \frac{1}{2} \, \int \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right)\,{d x}"," ",0,"1/2*x + 1/2*integrate(cos(2*(b*x + a)/(d*x + c)), x)","F",0
53,0,0,0,0.000000," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^3/(a^2*x^2 - 1), x)","F",0
54,0,0,0,0.000000," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x, algorithm=""maxima"")","-\frac{a \int \frac{\cos\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}\,{d x} + a \int \frac{\cos\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \sin\left(\frac{2 \, \sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}\,{d x} - \log\left(a x + 1\right) + \log\left(a x - 1\right)}{4 \, a}"," ",0,"-1/4*(4*a*integrate(1/4*cos(2*sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x) + 4*a*integrate(1/4*cos(2*sqrt(-a*x + 1)/sqrt(a*x + 1))/((a^2*x^2 - 1)*cos(2*sqrt(-a*x + 1)/sqrt(a*x + 1))^2 + (a^2*x^2 - 1)*sin(2*sqrt(-a*x + 1)/sqrt(a*x + 1))^2), x) - log(a*x + 1) + log(a*x - 1))/a","F",0
55,0,0,0,0.000000," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate(cos(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}\,{d x}"," ",0,"-integrate(1/((a^2*x^2 - 1)*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
57,-1,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,1,7,0,0.302121," ","integrate(tan(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","2 \, \log\left(\sec\left(\sqrt{x}\right)\right)"," ",0,"2*log(sec(sqrt(x)))","A",0
59,1,12,0,0.536711," ","integrate(tan(x^(1/2))^2/x^(1/2),x, algorithm=""maxima"")","-2 \, \sqrt{x} + 2 \, \tan\left(\sqrt{x}\right)"," ",0,"-2*sqrt(x) + 2*tan(sqrt(x))","A",0
60,1,80,0,0.414185," ","integrate(x^(1/2)*tan(x^(1/2)),x, algorithm=""maxima"")","-2 i \, x \arctan\left(\sin\left(2 \, \sqrt{x}\right), \cos\left(2 \, \sqrt{x}\right) + 1\right) - x \log\left(\cos\left(2 \, \sqrt{x}\right)^{2} + \sin\left(2 \, \sqrt{x}\right)^{2} + 2 \, \cos\left(2 \, \sqrt{x}\right) + 1\right) + \frac{2}{3} i \, x^{\frac{3}{2}} + 2 i \, \sqrt{x} {\rm Li}_2\left(-e^{\left(2 i \, \sqrt{x}\right)}\right) - {\rm Li}_{3}(-e^{\left(2 i \, \sqrt{x}\right)})"," ",0,"-2*I*x*arctan2(sin(2*sqrt(x)), cos(2*sqrt(x)) + 1) - x*log(cos(2*sqrt(x))^2 + sin(2*sqrt(x))^2 + 2*cos(2*sqrt(x)) + 1) + 2/3*I*x^(3/2) + 2*I*sqrt(x)*dilog(-e^(2*I*sqrt(x))) - polylog(3, -e^(2*I*sqrt(x)))","A",0
61,1,83,0,0.376432," ","integrate(1/2*b*tan(c*x^2+b*x+a)/c+x*tan(c*x^2+b*x+a),x, algorithm=""maxima"")","-\frac{\log\left(\cos\left(2 \, c x^{2}\right)^{2} + 2 \, \cos\left(2 \, c x^{2}\right) \cos\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, c x^{2}\right)^{2} - 2 \, \sin\left(2 \, c x^{2}\right) \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)}{4 \, c}"," ",0,"-1/4*log(cos(2*c*x^2)^2 + 2*cos(2*c*x^2)*cos(2*b*x + 2*a) + cos(2*b*x + 2*a)^2 + sin(2*c*x^2)^2 - 2*sin(2*c*x^2)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2)/c","B",0
62,1,14,0,0.481488," ","integrate(cot(x^(1/2))^2/x^(1/2),x, algorithm=""maxima"")","-2 \, \sqrt{x} - \frac{2}{\tan\left(\sqrt{x}\right)}"," ",0,"-2*sqrt(x) - 2/tan(sqrt(x))","A",0
63,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/(1+cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right) + 1}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/(cos(d*x + c) + 1), x)","F",0
64,1,6257,0,108.038057," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(a\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(b x\right) + \sqrt{2} \cos\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(2 \, b x\right) + \cos\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right), \sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(2 \, b x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sin\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 1\right) - 2 \, {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(a\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(-\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(b x\right) - \sqrt{2} \cos\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(2 \, b x\right) + \cos\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right), -\sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(2 \, b x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sin\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 1\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(-\frac{2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}, \frac{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(-\frac{2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}, \frac{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) + {\left(\sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + 2 \, \sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - 2 \, \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(2 \, b x\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(2 \, b x\right) + 1\right) - {\left(\sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - 2 \, \sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 2 \, \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(2 \, b x\right) + 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(2 \, b x\right) + 1\right) - {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left(\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) - {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left(\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) - 4 \, \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right)}{8 \, b}"," ",0,"-1/8*(2*(sqrt(2)*cos(3*a)*cos(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(a)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(b*x) + sqrt(2)*cos(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(2*b*x) + cos(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))), sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(2*b*x)*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sin(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + 1) - 2*(sqrt(2)*cos(3*a)*cos(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(a)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(-sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(b*x) - sqrt(2)*cos(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(2*b*x) + cos(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))), -sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(2*b*x)*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sin(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + 1) - 2*((sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(-2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2), (2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 - 2*(sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) - 2*((sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(-2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2), (2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 - 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) + (sqrt(2)*cos(3/4*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(a) - sqrt(2)*cos(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*log((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + 2*sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - 2*sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + 2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + cos(1/2*arctan2(sin(4*a), cos(4*a))))*cos(2*b*x) - 2*((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(2*b*x) + 1) - (sqrt(2)*cos(3/4*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(a) - sqrt(2)*cos(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*log((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - 2*sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + 2*sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) - 2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - cos(1/2*arctan2(sin(4*a), cos(4*a))))*cos(2*b*x) + 2*((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(2*b*x) + 1) - ((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*log(((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) - ((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*log(((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) - 4*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)))/b","B",0
65,1,6257,0,116.999374," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(a\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(b x\right) + \sqrt{2} \cos\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(2 \, b x\right) + \cos\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right), \sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(2 \, b x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sin\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 1\right) - 2 \, {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(a\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(-\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(b x\right) - \sqrt{2} \cos\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(2 \, b x\right) + \cos\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right), -\sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(2 \, b x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sin\left(2 \, b x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 1\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(-\frac{2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}, \frac{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \arctan\left(-\frac{2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}, \frac{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - 2 \, \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - 2 \, \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) + {\left(\sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + 2 \, \sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - 2 \, \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(2 \, b x\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(2 \, b x\right) + 1\right) - {\left(\sqrt{2} \cos\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{3}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(2 \, b x\right)^{2} + 2 \, {\left(\cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - 2 \, \sqrt{2} \cos\left(b x\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + 2 \, \sqrt{2} \sin\left(b x\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(2 \, b x\right) + 2 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) - \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(2 \, b x\right) + 1\right) - {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left(\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) - {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) \sin\left(3 \, a\right) - \sqrt{2} \cos\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(a\right)\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(3 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(3 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \cos\left(a\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \log\left(\frac{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}{{\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \cos\left(b x\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}\right)} \sin\left(b x\right)^{2} - {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(b x\right) + \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2} + {\left({\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) - \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + {\left(\sqrt{2} \cos\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right) + \sqrt{2} \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)\right)} \sin\left(b x\right) + \sin\left(\frac{1}{4} \, \arctan\left(\sin\left(4 \, a\right), \cos\left(4 \, a\right)\right)\right)^{2}}\right) - 4 \, \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right)}{8 \, b}"," ",0,"-1/8*(2*(sqrt(2)*cos(3*a)*cos(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(a)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(b*x) + sqrt(2)*cos(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(2*b*x) + cos(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))), sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(2*b*x)*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sin(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + 1) - 2*(sqrt(2)*cos(3*a)*cos(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(a)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(-sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(b*x) - sqrt(2)*cos(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(2*b*x) + cos(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))), -sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + cos(2*b*x)*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sin(2*b*x)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + 1) - 2*((sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(-2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2), (2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 - 2*(sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) - 2*((sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*arctan2(-2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2), (2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 - 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/(2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + 2*(cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - 2*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))^2 + 2*(sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - 2*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) + (sqrt(2)*cos(3/4*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(a) - sqrt(2)*cos(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*log((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + 2*sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - 2*sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) + 2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + cos(1/2*arctan2(sin(4*a), cos(4*a))))*cos(2*b*x) - 2*((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(2*b*x) + 1) - (sqrt(2)*cos(3/4*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(a) - sqrt(2)*cos(3*a)*sin(3/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*log((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(2*b*x)^2 + 2*(cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - 2*sqrt(2)*cos(b*x)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + 2*sqrt(2)*sin(b*x)*sin(1/4*arctan2(sin(4*a), cos(4*a))) - 2*((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - cos(1/2*arctan2(sin(4*a), cos(4*a))))*cos(2*b*x) + 2*((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a)))*sin(1/2*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(b*x) - (sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/2*arctan2(sin(4*a), cos(4*a)))*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(b*x) - sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(2*b*x) + 1) - ((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*log(((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) - ((sqrt(2)*cos(1/2*arctan2(sin(4*a), cos(4*a)))*sin(3*a) - sqrt(2)*cos(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(a))*cos(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(3*a)*cos(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(3*a)*sin(1/2*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*cos(a))*sin(1/2*pi + 1/4*arctan2(sin(4*a), cos(4*a))))*log(((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)/((cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*cos(b*x)^2 + (cos(1/2*arctan2(sin(4*a), cos(4*a)))^2 + sin(1/2*arctan2(sin(4*a), cos(4*a)))^2)*sin(b*x)^2 - ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) - (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*cos(b*x) + cos(1/4*arctan2(sin(4*a), cos(4*a)))^2 + ((sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) - sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*cos(1/2*arctan2(sin(4*a), cos(4*a))) + (sqrt(2)*cos(1/4*arctan2(sin(4*a), cos(4*a))) + sqrt(2)*sin(1/4*arctan2(sin(4*a), cos(4*a))))*sin(1/2*arctan2(sin(4*a), cos(4*a))))*sin(b*x) + sin(1/4*arctan2(sin(4*a), cos(4*a)))^2)) - 4*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)))/b","B",0
66,1,11,0,0.306917," ","integrate(sin(x)*sin(2*x),x, algorithm=""maxima"")","-\frac{1}{6} \, \sin\left(3 \, x\right) + \frac{1}{2} \, \sin\left(x\right)"," ",0,"-1/6*sin(3*x) + 1/2*sin(x)","A",0
67,1,13,0,0.307591," ","integrate(sin(x)*sin(3*x),x, algorithm=""maxima"")","-\frac{1}{8} \, \sin\left(4 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-1/8*sin(4*x) + 1/4*sin(2*x)","A",0
68,1,13,0,0.305040," ","integrate(sin(x)*sin(4*x),x, algorithm=""maxima"")","-\frac{1}{10} \, \sin\left(5 \, x\right) + \frac{1}{6} \, \sin\left(3 \, x\right)"," ",0,"-1/10*sin(5*x) + 1/6*sin(3*x)","A",0
69,1,28,0,0.306062," ","integrate(sin(x)*sin(m*x),x, algorithm=""maxima"")","-\frac{\sin\left({\left(m + 1\right)} x\right)}{2 \, {\left(m + 1\right)}} - \frac{\sin\left(-{\left(m - 1\right)} x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"-1/2*sin((m + 1)*x)/(m + 1) - 1/2*sin(-(m - 1)*x)/(m - 1)","A",0
70,1,11,0,0.307342," ","integrate(cos(2*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{6} \, \cos\left(3 \, x\right) + \frac{1}{2} \, \cos\left(x\right)"," ",0,"-1/6*cos(3*x) + 1/2*cos(x)","A",0
71,1,13,0,0.538084," ","integrate(cos(3*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{8} \, \cos\left(4 \, x\right) + \frac{1}{4} \, \cos\left(2 \, x\right)"," ",0,"-1/8*cos(4*x) + 1/4*cos(2*x)","A",0
72,1,13,0,0.505250," ","integrate(cos(4*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{10} \, \cos\left(5 \, x\right) + \frac{1}{6} \, \cos\left(3 \, x\right)"," ",0,"-1/10*cos(5*x) + 1/6*cos(3*x)","A",0
73,1,28,0,0.317140," ","integrate(cos(m*x)*sin(x),x, algorithm=""maxima"")","-\frac{\cos\left({\left(m + 1\right)} x\right)}{2 \, {\left(m + 1\right)}} + \frac{\cos\left(-{\left(m - 1\right)} x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"-1/2*cos((m + 1)*x)/(m + 1) + 1/2*cos(-(m - 1)*x)/(m - 1)","A",0
74,1,141,0,0.436228," ","integrate(sin(x)*tan(2*x),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \sin\left(x\right)"," ",0,"1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - sin(x)","B",0
75,0,0,0,0.000000," ","integrate(sin(x)*tan(3*x),x, algorithm=""maxima"")","\int -\frac{{\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - \cos\left(2 \, x\right) \cos\left(x\right) + {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(3 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right) \sin\left(x\right) + \cos\left(x\right)}{3 \, {\left(2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1\right)}}\,{d x} + \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"integrate(-1/3*((cos(3*x) + cos(x))*cos(4*x) - (cos(2*x) - 1)*cos(3*x) - cos(2*x)*cos(x) + (sin(3*x) + sin(x))*sin(4*x) - sin(3*x)*sin(2*x) - sin(2*x)*sin(x) + cos(x))/(2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) + 1/6*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 1/6*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - sin(x)","F",0
76,0,0,0,0.000000," ","integrate(sin(x)*tan(4*x),x, algorithm=""maxima"")","\int \frac{{\left(\cos\left(7 \, x\right) + \cos\left(x\right)\right)} \cos\left(8 \, x\right) + {\left(\sin\left(7 \, x\right) + \sin\left(x\right)\right)} \sin\left(8 \, x\right) + \cos\left(7 \, x\right) + \cos\left(x\right)}{\cos\left(8 \, x\right)^{2} + \sin\left(8 \, x\right)^{2} + 2 \, \cos\left(8 \, x\right) + 1}\,{d x} - \sin\left(x\right)"," ",0,"integrate(((cos(7*x) + cos(x))*cos(8*x) + (sin(7*x) + sin(x))*sin(8*x) + cos(7*x) + cos(x))/(cos(8*x)^2 + sin(8*x)^2 + 2*cos(8*x) + 1), x) - sin(x)","F",0
77,0,0,0,0.000000," ","integrate(sin(x)*tan(5*x),x, algorithm=""maxima"")","\int -\frac{{\left(3 \, \cos\left(7 \, x\right) - \cos\left(5 \, x\right) - \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \cos\left(8 \, x\right) - 3 \, {\left(\cos\left(6 \, x\right) - \cos\left(4 \, x\right) + \cos\left(2 \, x\right) - 1\right)} \cos\left(7 \, x\right) + {\left(\cos\left(5 \, x\right) + \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \cos\left(6 \, x\right) - {\left(\cos\left(4 \, x\right) - \cos\left(2 \, x\right) + 1\right)} \cos\left(5 \, x\right) - {\left(\cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 3 \, \cos\left(2 \, x\right) \cos\left(x\right) + {\left(3 \, \sin\left(7 \, x\right) - \sin\left(5 \, x\right) - \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \sin\left(8 \, x\right) - 3 \, {\left(\sin\left(6 \, x\right) - \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(7 \, x\right) + {\left(\sin\left(5 \, x\right) + \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \sin\left(6 \, x\right) - {\left(\sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \sin\left(5 \, x\right) - {\left(\sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 3 \, \sin\left(2 \, x\right) \sin\left(x\right) + 3 \, \cos\left(x\right)}{5 \, {\left(2 \, {\left(\cos\left(6 \, x\right) - \cos\left(4 \, x\right) + \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) - \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - \cos\left(6 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} + 2 \, {\left(\sin\left(6 \, x\right) - \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - \sin\left(6 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1\right)}}\,{d x} + \frac{1}{10} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \frac{1}{10} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"integrate(-1/5*((3*cos(7*x) - cos(5*x) - cos(3*x) + 3*cos(x))*cos(8*x) - 3*(cos(6*x) - cos(4*x) + cos(2*x) - 1)*cos(7*x) + (cos(5*x) + cos(3*x) - 3*cos(x))*cos(6*x) - (cos(4*x) - cos(2*x) + 1)*cos(5*x) - (cos(3*x) - 3*cos(x))*cos(4*x) + (cos(2*x) - 1)*cos(3*x) - 3*cos(2*x)*cos(x) + (3*sin(7*x) - sin(5*x) - sin(3*x) + 3*sin(x))*sin(8*x) - 3*(sin(6*x) - sin(4*x) + sin(2*x))*sin(7*x) + (sin(5*x) + sin(3*x) - 3*sin(x))*sin(6*x) - (sin(4*x) - sin(2*x))*sin(5*x) - (sin(3*x) - 3*sin(x))*sin(4*x) + sin(3*x)*sin(2*x) - 3*sin(2*x)*sin(x) + 3*cos(x))/(2*(cos(6*x) - cos(4*x) + cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 2*(cos(4*x) - cos(2*x) + 1)*cos(6*x) - cos(6*x)^2 + 2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 + 2*(sin(6*x) - sin(4*x) + sin(2*x))*sin(8*x) - sin(8*x)^2 + 2*(sin(4*x) - sin(2*x))*sin(6*x) - sin(6*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) + 1/10*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 1/10*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - sin(x)","F",0
78,0,0,0,0.000000," ","integrate(sin(x)*tan(6*x),x, algorithm=""maxima"")","\frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \int -\frac{{\left(2 \, \cos\left(7 \, x\right) - \cos\left(5 \, x\right) - \cos\left(3 \, x\right) + 2 \, \cos\left(x\right)\right)} \cos\left(8 \, x\right) - 2 \, {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(7 \, x\right) + {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(5 \, x\right) + {\left(\cos\left(3 \, x\right) - 2 \, \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(2 \, \sin\left(7 \, x\right) - \sin\left(5 \, x\right) - \sin\left(3 \, x\right) + 2 \, \sin\left(x\right)\right)} \sin\left(8 \, x\right) + {\left(\sin\left(3 \, x\right) - 2 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 2 \, \sin\left(7 \, x\right) \sin\left(4 \, x\right) + \sin\left(5 \, x\right) \sin\left(4 \, x\right) - \cos\left(3 \, x\right) + 2 \, \cos\left(x\right)}{3 \, {\left(2 \, {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} - \cos\left(4 \, x\right)^{2} - \sin\left(8 \, x\right)^{2} + 2 \, \sin\left(8 \, x\right) \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) - 1\right)}}\,{d x} - \sin\left(x\right)"," ",0,"1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + integrate(-1/3*((2*cos(7*x) - cos(5*x) - cos(3*x) + 2*cos(x))*cos(8*x) - 2*(cos(4*x) - 1)*cos(7*x) + (cos(4*x) - 1)*cos(5*x) + (cos(3*x) - 2*cos(x))*cos(4*x) + (2*sin(7*x) - sin(5*x) - sin(3*x) + 2*sin(x))*sin(8*x) + (sin(3*x) - 2*sin(x))*sin(4*x) - 2*sin(7*x)*sin(4*x) + sin(5*x)*sin(4*x) - cos(3*x) + 2*cos(x))/(2*(cos(4*x) - 1)*cos(8*x) - cos(8*x)^2 - cos(4*x)^2 - sin(8*x)^2 + 2*sin(8*x)*sin(4*x) - sin(4*x)^2 + 2*cos(4*x) - 1), x) - sin(x)","F",0
79,0,0,0,0.000000," ","integrate(sin(x)*tan(n*x),x, algorithm=""maxima"")","\int \sin\left(x\right) \tan\left(n x\right)\,{d x}"," ",0,"integrate(sin(x)*tan(n*x), x)","F",0
80,1,37,0,0.408258," ","integrate(cot(2*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-1/4*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/4*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + sin(x)","B",0
81,1,127,0,0.444361," ","integrate(cot(3*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) - \frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \sin\left(x\right)"," ",0,"-1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) - 1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) + 1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) + 1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) + sin(x)","B",0
82,1,173,0,0.543934," ","integrate(cot(4*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) + 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) + 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/8*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/8*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + sin(x)","B",0
83,0,0,0,0.000000," ","integrate(cot(5*x)*sin(x),x, algorithm=""maxima"")","-\int \frac{{\left(\cos\left(3 \, x\right) + \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(2 \, \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + {\left(2 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + {\left(\sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(\sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + \cos\left(x\right)}{2 \, {\left(2 \, {\left(\cos\left(3 \, x\right) + \cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}}\,{d x} - \int -\frac{{\left(\cos\left(3 \, x\right) - \cos\left(2 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(2 \, \cos\left(2 \, x\right) - 2 \, \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} + {\left(2 \, \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + {\left(\sin\left(3 \, x\right) - \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, {\left(\sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2} + \cos\left(x\right)}{2 \, {\left(2 \, {\left(\cos\left(3 \, x\right) - \cos\left(2 \, x\right) + \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1\right)}}\,{d x} + \sin\left(x\right)"," ",0,"-integrate(1/2*((cos(3*x) + cos(2*x) + cos(x))*cos(4*x) + (2*cos(2*x) + 2*cos(x) + 1)*cos(3*x) + cos(3*x)^2 + (2*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + (sin(3*x) + sin(2*x) + sin(x))*sin(4*x) + 2*(sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + cos(x))/(2*(cos(3*x) + cos(2*x) + cos(x) + 1)*cos(4*x) + cos(4*x)^2 + 2*(cos(2*x) + cos(x) + 1)*cos(3*x) + cos(3*x)^2 + 2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + 2*(sin(3*x) + sin(2*x) + sin(x))*sin(4*x) + sin(4*x)^2 + 2*(sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1), x) - integrate(-1/2*((cos(3*x) - cos(2*x) + cos(x))*cos(4*x) + (2*cos(2*x) - 2*cos(x) + 1)*cos(3*x) - cos(3*x)^2 + (2*cos(x) - 1)*cos(2*x) - cos(2*x)^2 - cos(x)^2 + (sin(3*x) - sin(2*x) + sin(x))*sin(4*x) + 2*(sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - sin(2*x)^2 + 2*sin(2*x)*sin(x) - sin(x)^2 + cos(x))/(2*(cos(3*x) - cos(2*x) + cos(x) - 1)*cos(4*x) - cos(4*x)^2 + 2*(cos(2*x) - cos(x) + 1)*cos(3*x) - cos(3*x)^2 + 2*(cos(x) - 1)*cos(2*x) - cos(2*x)^2 - cos(x)^2 + 2*(sin(3*x) - sin(2*x) + sin(x))*sin(4*x) - sin(4*x)^2 + 2*(sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - sin(2*x)^2 + 2*sin(2*x)*sin(x) - sin(x)^2 + 2*cos(x) - 1), x) + sin(x)","F",0
84,0,0,0,0.000000," ","integrate(cot(6*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) - \frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) - \int -\frac{{\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - \cos\left(2 \, x\right) \cos\left(x\right) + {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(3 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right) \sin\left(x\right) + \cos\left(x\right)}{6 \, {\left(2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1\right)}}\,{d x} - \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) - 1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) + 1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) + 1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) - integrate(-1/6*((cos(3*x) + cos(x))*cos(4*x) - (cos(2*x) - 1)*cos(3*x) - cos(2*x)*cos(x) + (sin(3*x) + sin(x))*sin(4*x) - sin(3*x)*sin(2*x) - sin(2*x)*sin(x) + cos(x))/(2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) - 1/12*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/12*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + sin(x)","F",0
85,1,129,0,0.426618," ","integrate(sec(2*x)*sin(x),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right)"," ",0,"1/8*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) - 1/8*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1)","B",0
86,1,81,0,0.418488," ","integrate(sec(3*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{12} \, \log\left(-2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} - 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)"," ",0,"-1/12*log(-2*(cos(2*x) - 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 + sin(4*x)^2 - 2*sin(4*x)*sin(2*x) + sin(2*x)^2 - 2*cos(2*x) + 1) + 1/6*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
87,0,0,0,0.000000," ","integrate(sec(4*x)*sin(x),x, algorithm=""maxima"")","\int \sec\left(4 \, x\right) \sin\left(x\right)\,{d x}"," ",0,"integrate(sec(4*x)*sin(x), x)","F",0
88,0,0,0,0.000000," ","integrate(sec(5*x)*sin(x),x, algorithm=""maxima"")","\frac{1}{5} \, \int -\frac{\cos\left(4 \, x\right) \sin\left(8 \, x\right) - \cos\left(8 \, x\right) \sin\left(4 \, x\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) \sin\left(4 \, x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) \sin\left(4 \, x\right) - \cos\left(4 \, x\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) - \cos\left(4 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) - \sin\left(4 \, x\right)}{2 \, {\left(\cos\left(4 \, x\right) + 1\right)} \cos\left(8 \, x\right) + \cos\left(8 \, x\right)^{2} + \cos\left(4 \, x\right)^{2} - 2 \, {\left(\cos\left(8 \, x\right) + \cos\left(4 \, x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} - 2 \, {\left(\cos\left(8 \, x\right) + \cos\left(4 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + \sin\left(8 \, x\right)^{2} + 2 \, \sin\left(8 \, x\right) \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} - 2 \, {\left(\sin\left(8 \, x\right) + \sin\left(4 \, x\right) - \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} - 2 \, {\left(\sin\left(8 \, x\right) + \sin\left(4 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right)\right)\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1}\,{d x} + \frac{4}{5} \, \int -\frac{\cos\left(2 \, x\right) \sin\left(8 \, x\right) - \cos\left(2 \, x\right) \sin\left(6 \, x\right) + \cos\left(2 \, x\right) \sin\left(4 \, x\right) - \cos\left(8 \, x\right) \sin\left(2 \, x\right) + \cos\left(6 \, x\right) \sin\left(2 \, x\right) - \cos\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(6 \, x\right) - \cos\left(4 \, x\right) + \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) - \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - \cos\left(6 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} + 2 \, {\left(\sin\left(6 \, x\right) - \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - \sin\left(6 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1}\,{d x} - \frac{2}{5} \, \int -\frac{\cos\left(\frac{4}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) \sin\left(6 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) \sin\left(6 \, x\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) \sin\left(6 \, x\right) - \cos\left(6 \, x\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) - \cos\left(6 \, x\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \cos\left(6 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \sin\left(6 \, x\right)}{\cos\left(6 \, x\right)^{2} - 2 \, {\left(\cos\left(6 \, x\right) - \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) - 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)^{2} - 2 \, {\left(\cos\left(6 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(6 \, x\right) - 1\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)^{2} + \sin\left(6 \, x\right)^{2} - 2 \, {\left(\sin\left(6 \, x\right) - \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)^{2} - 2 \, {\left(\sin\left(6 \, x\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)^{2} + 2 \, \sin\left(6 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, x\right), \cos\left(6 \, x\right)\right)\right)^{2} - 2 \, \cos\left(6 \, x\right) + 1}\,{d x} - \frac{2}{5} \, \int -\frac{\sin\left(8 \, x\right) - \sin\left(6 \, x\right) + \sin\left(4 \, x\right) - \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(6 \, x\right) - \cos\left(4 \, x\right) + \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) - \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - \cos\left(6 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} + 2 \, {\left(\sin\left(6 \, x\right) - \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - \sin\left(6 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1}\,{d x} - \frac{1}{10} \, \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)"," ",0,"1/5*integrate(-(cos(4*x)*sin(8*x) - cos(8*x)*sin(4*x) + cos(3/2*arctan2(sin(4*x), cos(4*x)))*sin(4*x) + cos(1/2*arctan2(sin(4*x), cos(4*x)))*sin(4*x) - cos(4*x)*sin(3/2*arctan2(sin(4*x), cos(4*x))) - cos(4*x)*sin(1/2*arctan2(sin(4*x), cos(4*x))) - sin(4*x))/(2*(cos(4*x) + 1)*cos(8*x) + cos(8*x)^2 + cos(4*x)^2 - 2*(cos(8*x) + cos(4*x) - cos(1/2*arctan2(sin(4*x), cos(4*x))) + 1)*cos(3/2*arctan2(sin(4*x), cos(4*x))) + cos(3/2*arctan2(sin(4*x), cos(4*x)))^2 - 2*(cos(8*x) + cos(4*x) + 1)*cos(1/2*arctan2(sin(4*x), cos(4*x))) + cos(1/2*arctan2(sin(4*x), cos(4*x)))^2 + sin(8*x)^2 + 2*sin(8*x)*sin(4*x) + sin(4*x)^2 - 2*(sin(8*x) + sin(4*x) - sin(1/2*arctan2(sin(4*x), cos(4*x))))*sin(3/2*arctan2(sin(4*x), cos(4*x))) + sin(3/2*arctan2(sin(4*x), cos(4*x)))^2 - 2*(sin(8*x) + sin(4*x))*sin(1/2*arctan2(sin(4*x), cos(4*x))) + sin(1/2*arctan2(sin(4*x), cos(4*x)))^2 + 2*cos(4*x) + 1), x) + 4/5*integrate(-(cos(2*x)*sin(8*x) - cos(2*x)*sin(6*x) + cos(2*x)*sin(4*x) - cos(8*x)*sin(2*x) + cos(6*x)*sin(2*x) - cos(4*x)*sin(2*x) - sin(2*x))/(2*(cos(6*x) - cos(4*x) + cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 2*(cos(4*x) - cos(2*x) + 1)*cos(6*x) - cos(6*x)^2 + 2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 + 2*(sin(6*x) - sin(4*x) + sin(2*x))*sin(8*x) - sin(8*x)^2 + 2*(sin(4*x) - sin(2*x))*sin(6*x) - sin(6*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) - 2/5*integrate(-(cos(4/3*arctan2(sin(6*x), cos(6*x)))*sin(6*x) + cos(2/3*arctan2(sin(6*x), cos(6*x)))*sin(6*x) - cos(1/3*arctan2(sin(6*x), cos(6*x)))*sin(6*x) - cos(6*x)*sin(4/3*arctan2(sin(6*x), cos(6*x))) - cos(6*x)*sin(2/3*arctan2(sin(6*x), cos(6*x))) + cos(6*x)*sin(1/3*arctan2(sin(6*x), cos(6*x))) + sin(6*x))/(cos(6*x)^2 - 2*(cos(6*x) - cos(2/3*arctan2(sin(6*x), cos(6*x))) + cos(1/3*arctan2(sin(6*x), cos(6*x))) - 1)*cos(4/3*arctan2(sin(6*x), cos(6*x))) + cos(4/3*arctan2(sin(6*x), cos(6*x)))^2 - 2*(cos(6*x) + cos(1/3*arctan2(sin(6*x), cos(6*x))) - 1)*cos(2/3*arctan2(sin(6*x), cos(6*x))) + cos(2/3*arctan2(sin(6*x), cos(6*x)))^2 + 2*(cos(6*x) - 1)*cos(1/3*arctan2(sin(6*x), cos(6*x))) + cos(1/3*arctan2(sin(6*x), cos(6*x)))^2 + sin(6*x)^2 - 2*(sin(6*x) - sin(2/3*arctan2(sin(6*x), cos(6*x))) + sin(1/3*arctan2(sin(6*x), cos(6*x))))*sin(4/3*arctan2(sin(6*x), cos(6*x))) + sin(4/3*arctan2(sin(6*x), cos(6*x)))^2 - 2*(sin(6*x) + sin(1/3*arctan2(sin(6*x), cos(6*x))))*sin(2/3*arctan2(sin(6*x), cos(6*x))) + sin(2/3*arctan2(sin(6*x), cos(6*x)))^2 + 2*sin(6*x)*sin(1/3*arctan2(sin(6*x), cos(6*x))) + sin(1/3*arctan2(sin(6*x), cos(6*x)))^2 - 2*cos(6*x) + 1), x) - 2/5*integrate(-(sin(8*x) - sin(6*x) + sin(4*x) - sin(2*x))/(2*(cos(6*x) - cos(4*x) + cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 2*(cos(4*x) - cos(2*x) + 1)*cos(6*x) - cos(6*x)^2 + 2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 + 2*(sin(6*x) - sin(4*x) + sin(2*x))*sin(8*x) - sin(8*x)^2 + 2*(sin(4*x) - sin(2*x))*sin(6*x) - sin(6*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) - 1/10*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","F",0
89,0,0,0,0.000000," ","integrate(sec(6*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{24} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) + \frac{1}{24} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \int \frac{{\left(\sin\left(7 \, x\right) - \sin\left(5 \, x\right) + \sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(8 \, x\right) - {\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(7 \, x\right) - \cos\left(5 \, x\right) + \cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(8 \, x\right) - {\left(\cos\left(4 \, x\right) - 1\right)} \sin\left(7 \, x\right) + {\left(\cos\left(4 \, x\right) - 1\right)} \sin\left(5 \, x\right) + {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) + \cos\left(7 \, x\right) \sin\left(4 \, x\right) - \cos\left(5 \, x\right) \sin\left(4 \, x\right) + \sin\left(3 \, x\right) - \sin\left(x\right)}{3 \, {\left(2 \, {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} - \cos\left(4 \, x\right)^{2} - \sin\left(8 \, x\right)^{2} + 2 \, \sin\left(8 \, x\right) \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) - 1\right)}}\,{d x}"," ",0,"-1/24*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) + 1/24*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1) - integrate(1/3*((sin(7*x) - sin(5*x) + sin(3*x) - sin(x))*cos(8*x) - (sin(3*x) - sin(x))*cos(4*x) - (cos(7*x) - cos(5*x) + cos(3*x) - cos(x))*sin(8*x) - (cos(4*x) - 1)*sin(7*x) + (cos(4*x) - 1)*sin(5*x) + (cos(3*x) - cos(x))*sin(4*x) + cos(7*x)*sin(4*x) - cos(5*x)*sin(4*x) + sin(3*x) - sin(x))/(2*(cos(4*x) - 1)*cos(8*x) - cos(8*x)^2 - cos(4*x)^2 - sin(8*x)^2 + 2*sin(8*x)*sin(4*x) - sin(4*x)^2 + 2*cos(4*x) - 1), x)","F",0
90,1,35,0,0.420522," ","integrate(csc(2*x)*sin(x),x, algorithm=""maxima"")","\frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"1/4*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 1/4*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","B",0
91,1,125,0,0.440795," ","integrate(csc(3*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) - \frac{1}{12} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right)"," ",0,"-1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) + 1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) + 1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) - 1/12*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3)","B",0
92,1,171,0,0.433133," ","integrate(csc(4*x)*sin(x),x, algorithm=""maxima"")","\frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{16} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/16*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/8*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + 1/8*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","B",0
93,0,0,0,0.000000," ","integrate(csc(5*x)*sin(x),x, algorithm=""maxima"")","\int \csc\left(5 \, x\right) \sin\left(x\right)\,{d x}"," ",0,"integrate(csc(5*x)*sin(x), x)","F",0
94,0,0,0,0.000000," ","integrate(csc(6*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) - \frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) + \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \frac{1}{24} \, \sqrt{3} \log\left(\frac{4}{3} \, \cos\left(x\right)^{2} + \frac{4}{3} \, \sin\left(x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(x\right) - \frac{4}{3} \, \cos\left(x\right) + \frac{4}{3}\right) + \int -\frac{{\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - \cos\left(2 \, x\right) \cos\left(x\right) + {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(3 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right) \sin\left(x\right) + \cos\left(x\right)}{6 \, {\left(2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1\right)}}\,{d x} + \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"-1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) - 1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 + 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) + 1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) + 4/3*cos(x) + 4/3) + 1/24*sqrt(3)*log(4/3*cos(x)^2 + 4/3*sin(x)^2 - 4/3*sqrt(3)*sin(x) - 4/3*cos(x) + 4/3) + integrate(-1/6*((cos(3*x) + cos(x))*cos(4*x) - (cos(2*x) - 1)*cos(3*x) - cos(2*x)*cos(x) + (sin(3*x) + sin(x))*sin(4*x) - sin(3*x)*sin(2*x) - sin(2*x)*sin(x) + cos(x))/(2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) + 1/12*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 1/12*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","F",0
95,1,6,0,0.308776," ","integrate(csc(x)*sin(3*x),x, algorithm=""maxima"")","x + \sin\left(2 \, x\right)"," ",0,"x + sin(2*x)","A",0
96,1,6,0,0.319953," ","integrate(csc(3*x)*sin(6*x),x, algorithm=""maxima"")","\frac{2}{3} \, \sin\left(3 \, x\right)"," ",0,"2/3*sin(3*x)","A",0
97,1,11,0,0.307626," ","integrate(cos(x)*sin(2*x),x, algorithm=""maxima"")","-\frac{1}{6} \, \cos\left(3 \, x\right) - \frac{1}{2} \, \cos\left(x\right)"," ",0,"-1/6*cos(3*x) - 1/2*cos(x)","A",0
98,1,13,0,0.306878," ","integrate(cos(x)*sin(3*x),x, algorithm=""maxima"")","-\frac{1}{8} \, \cos\left(4 \, x\right) - \frac{1}{4} \, \cos\left(2 \, x\right)"," ",0,"-1/8*cos(4*x) - 1/4*cos(2*x)","A",0
99,1,13,0,0.312576," ","integrate(cos(x)*sin(4*x),x, algorithm=""maxima"")","-\frac{1}{10} \, \cos\left(5 \, x\right) - \frac{1}{6} \, \cos\left(3 \, x\right)"," ",0,"-1/10*cos(5*x) - 1/6*cos(3*x)","A",0
100,1,27,0,0.316314," ","integrate(cos(x)*sin(m*x),x, algorithm=""maxima"")","-\frac{\cos\left({\left(m + 1\right)} x\right)}{2 \, {\left(m + 1\right)}} - \frac{\cos\left({\left(m - 1\right)} x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"-1/2*cos((m + 1)*x)/(m + 1) - 1/2*cos((m - 1)*x)/(m - 1)","A",0
101,1,11,0,0.304950," ","integrate(cos(x)*cos(2*x),x, algorithm=""maxima"")","\frac{1}{6} \, \sin\left(3 \, x\right) + \frac{1}{2} \, \sin\left(x\right)"," ",0,"1/6*sin(3*x) + 1/2*sin(x)","A",0
102,1,13,0,0.321795," ","integrate(cos(x)*cos(3*x),x, algorithm=""maxima"")","\frac{1}{8} \, \sin\left(4 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/8*sin(4*x) + 1/4*sin(2*x)","A",0
103,1,13,0,0.314377," ","integrate(cos(x)*cos(4*x),x, algorithm=""maxima"")","\frac{1}{10} \, \sin\left(5 \, x\right) + \frac{1}{6} \, \sin\left(3 \, x\right)"," ",0,"1/10*sin(5*x) + 1/6*sin(3*x)","A",0
104,1,28,0,0.317404," ","integrate(cos(x)*cos(m*x),x, algorithm=""maxima"")","\frac{\sin\left({\left(m + 1\right)} x\right)}{2 \, {\left(m + 1\right)}} - \frac{\sin\left(-{\left(m - 1\right)} x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"1/2*sin((m + 1)*x)/(m + 1) - 1/2*sin(-(m - 1)*x)/(m - 1)","A",0
105,1,133,0,0.434036," ","integrate(cos(x)*tan(2*x),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \cos\left(x\right)"," ",0,"1/8*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) - 1/8*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1) - cos(x)","B",0
106,0,0,0,0.000000," ","integrate(cos(x)*tan(3*x),x, algorithm=""maxima"")","-\cos\left(x\right) - \int \frac{{\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + \cos\left(3 \, x\right) \sin\left(2 \, x\right) - \cos\left(x\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1}\,{d x}"," ",0,"-cos(x) - integrate(((sin(3*x) - sin(x))*cos(4*x) - (cos(3*x) - cos(x))*sin(4*x) - (cos(2*x) - 1)*sin(3*x) + cos(3*x)*sin(2*x) - cos(x)*sin(2*x) + cos(2*x)*sin(x) - sin(x))/(2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x)","F",0
107,0,0,0,0.000000," ","integrate(cos(x)*tan(4*x),x, algorithm=""maxima"")","-\cos\left(x\right) - \int -\frac{{\left(\sin\left(7 \, x\right) - \sin\left(x\right)\right)} \cos\left(8 \, x\right) - {\left(\cos\left(7 \, x\right) - \cos\left(x\right)\right)} \sin\left(8 \, x\right) + \sin\left(7 \, x\right) - \sin\left(x\right)}{\cos\left(8 \, x\right)^{2} + \sin\left(8 \, x\right)^{2} + 2 \, \cos\left(8 \, x\right) + 1}\,{d x}"," ",0,"-cos(x) - integrate(-((sin(7*x) - sin(x))*cos(8*x) - (cos(7*x) - cos(x))*sin(8*x) + sin(7*x) - sin(x))/(cos(8*x)^2 + sin(8*x)^2 + 2*cos(8*x) + 1), x)","F",0
108,0,0,0,0.000000," ","integrate(cos(x)*tan(5*x),x, algorithm=""maxima"")","-\cos\left(x\right) - \int \frac{{\left(\sin\left(7 \, x\right) - \sin\left(5 \, x\right) + \sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(8 \, x\right) + {\left(\sin\left(6 \, x\right) - \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) + {\left(\sin\left(5 \, x\right) - \sin\left(3 \, x\right) + \sin\left(x\right)\right)} \cos\left(6 \, x\right) + {\left(\sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) + {\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(7 \, x\right) - \cos\left(5 \, x\right) + \cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(8 \, x\right) - {\left(\cos\left(6 \, x\right) - \cos\left(4 \, x\right) + \cos\left(2 \, x\right) - 1\right)} \sin\left(7 \, x\right) - {\left(\cos\left(5 \, x\right) - \cos\left(3 \, x\right) + \cos\left(x\right)\right)} \sin\left(6 \, x\right) - {\left(\cos\left(4 \, x\right) - \cos\left(2 \, x\right) + 1\right)} \sin\left(5 \, x\right) - {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + \cos\left(3 \, x\right) \sin\left(2 \, x\right) - \cos\left(x\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(6 \, x\right) - \cos\left(4 \, x\right) + \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) - \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - \cos\left(6 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} + 2 \, {\left(\sin\left(6 \, x\right) - \sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - \sin\left(6 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1}\,{d x}"," ",0,"-cos(x) - integrate(((sin(7*x) - sin(5*x) + sin(3*x) - sin(x))*cos(8*x) + (sin(6*x) - sin(4*x) + sin(2*x))*cos(7*x) + (sin(5*x) - sin(3*x) + sin(x))*cos(6*x) + (sin(4*x) - sin(2*x))*cos(5*x) + (sin(3*x) - sin(x))*cos(4*x) - (cos(7*x) - cos(5*x) + cos(3*x) - cos(x))*sin(8*x) - (cos(6*x) - cos(4*x) + cos(2*x) - 1)*sin(7*x) - (cos(5*x) - cos(3*x) + cos(x))*sin(6*x) - (cos(4*x) - cos(2*x) + 1)*sin(5*x) - (cos(3*x) - cos(x))*sin(4*x) - (cos(2*x) - 1)*sin(3*x) + cos(3*x)*sin(2*x) - cos(x)*sin(2*x) + cos(2*x)*sin(x) - sin(x))/(2*(cos(6*x) - cos(4*x) + cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 2*(cos(4*x) - cos(2*x) + 1)*cos(6*x) - cos(6*x)^2 + 2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 + 2*(sin(6*x) - sin(4*x) + sin(2*x))*sin(8*x) - sin(8*x)^2 + 2*(sin(4*x) - sin(2*x))*sin(6*x) - sin(6*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x)","F",0
109,0,0,0,0.000000," ","integrate(cos(x)*tan(6*x),x, algorithm=""maxima"")","\frac{1}{24} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \frac{1}{24} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \cos\left(x\right) - \int \frac{{\left(2 \, \sin\left(7 \, x\right) + \sin\left(5 \, x\right) - \sin\left(3 \, x\right) - 2 \, \sin\left(x\right)\right)} \cos\left(8 \, x\right) + {\left(\sin\left(3 \, x\right) + 2 \, \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(2 \, \cos\left(7 \, x\right) + \cos\left(5 \, x\right) - \cos\left(3 \, x\right) - 2 \, \cos\left(x\right)\right)} \sin\left(8 \, x\right) - 2 \, {\left(\cos\left(4 \, x\right) - 1\right)} \sin\left(7 \, x\right) - {\left(\cos\left(4 \, x\right) - 1\right)} \sin\left(5 \, x\right) - {\left(\cos\left(3 \, x\right) + 2 \, \cos\left(x\right)\right)} \sin\left(4 \, x\right) + 2 \, \cos\left(7 \, x\right) \sin\left(4 \, x\right) + \cos\left(5 \, x\right) \sin\left(4 \, x\right) - \sin\left(3 \, x\right) - 2 \, \sin\left(x\right)}{3 \, {\left(2 \, {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} - \cos\left(4 \, x\right)^{2} - \sin\left(8 \, x\right)^{2} + 2 \, \sin\left(8 \, x\right) \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) - 1\right)}}\,{d x}"," ",0,"1/24*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) - 1/24*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1) - cos(x) - integrate(1/3*((2*sin(7*x) + sin(5*x) - sin(3*x) - 2*sin(x))*cos(8*x) + (sin(3*x) + 2*sin(x))*cos(4*x) - (2*cos(7*x) + cos(5*x) - cos(3*x) - 2*cos(x))*sin(8*x) - 2*(cos(4*x) - 1)*sin(7*x) - (cos(4*x) - 1)*sin(5*x) - (cos(3*x) + 2*cos(x))*sin(4*x) + 2*cos(7*x)*sin(4*x) + cos(5*x)*sin(4*x) - sin(3*x) - 2*sin(x))/(2*(cos(4*x) - 1)*cos(8*x) - cos(8*x)^2 - cos(4*x)^2 - sin(8*x)^2 + 2*sin(8*x)*sin(4*x) - sin(4*x)^2 + 2*cos(4*x) - 1), x)","F",0
110,1,37,0,0.328641," ","integrate(cos(x)*cot(2*x),x, algorithm=""maxima"")","\cos\left(x\right) - \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"cos(x) - 1/4*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/4*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
111,1,131,0,0.416315," ","integrate(cos(x)*cot(3*x),x, algorithm=""maxima"")","\cos\left(x\right) - \frac{1}{12} \, \log\left(2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(-2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"cos(x) - 1/12*log(2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1) + 1/12*log(-2*(cos(x) - 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 - 2*sin(2*x)*sin(x) + sin(x)^2 - 2*cos(x) + 1) - 1/6*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/6*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
112,1,165,0,0.424757," ","integrate(cos(x)*cot(4*x),x, algorithm=""maxima"")","-\frac{1}{16} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) + \frac{1}{16} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right) + \cos\left(x\right) - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/16*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) + 1/16*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1) + cos(x) - 1/8*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/8*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
113,0,0,0,0.000000," ","integrate(cos(x)*cot(5*x),x, algorithm=""maxima"")","\cos\left(x\right) + \frac{1}{10} \, \int -\frac{\cos\left(2 \, x\right) \sin\left(4 \, x\right) - \cos\left(4 \, x\right) \sin\left(2 \, x\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) - \cos\left(2 \, x\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) - \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) - \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} - 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right) - \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} - 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x} + \frac{1}{10} \, \int \frac{\cos\left(2 \, x\right) \sin\left(4 \, x\right) - \cos\left(4 \, x\right) \sin\left(2 \, x\right) - \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) - \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x} - \frac{1}{10} \, \int \frac{\cos\left(x\right) \sin\left(4 \, x\right) + \cos\left(x\right) \sin\left(3 \, x\right) + \cos\left(x\right) \sin\left(2 \, x\right) - \cos\left(4 \, x\right) \sin\left(x\right) - \cos\left(3 \, x\right) \sin\left(x\right) - \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) + \cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\,{d x} - \frac{1}{10} \, \int -\frac{\cos\left(x\right) \sin\left(4 \, x\right) - \cos\left(x\right) \sin\left(3 \, x\right) + \cos\left(x\right) \sin\left(2 \, x\right) - \cos\left(4 \, x\right) \sin\left(x\right) + \cos\left(3 \, x\right) \sin\left(x\right) - \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) - \cos\left(2 \, x\right) + \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1}\,{d x} + \frac{3}{10} \, \int -\frac{\cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) - \cos\left(3 \, x\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - \cos\left(3 \, x\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - \cos\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(3 \, x\right)}{\cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) + 1\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + \sin\left(3 \, x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \sin\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \cos\left(3 \, x\right) + 1}\,{d x} + \frac{3}{10} \, \int -\frac{\cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) - \cos\left(3 \, x\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - \cos\left(3 \, x\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(3 \, x\right)}{\cos\left(3 \, x\right)^{2} - 2 \, {\left(\cos\left(3 \, x\right) - \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) - 1\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + \sin\left(3 \, x\right)^{2} - 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \sin\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, \cos\left(3 \, x\right) + 1}\,{d x} + \frac{1}{5} \, \int \frac{\sin\left(4 \, x\right) + \sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) + \cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\,{d x} - \frac{1}{5} \, \int -\frac{\sin\left(4 \, x\right) - \sin\left(3 \, x\right) + \sin\left(2 \, x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) - \cos\left(2 \, x\right) + \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1}\,{d x} - \frac{1}{10} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{10} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"cos(x) + 1/10*integrate(-(cos(2*x)*sin(4*x) - cos(4*x)*sin(2*x) + cos(3/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) + cos(1/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) - cos(2*x)*sin(3/2*arctan2(sin(2*x), cos(2*x))) - cos(2*x)*sin(1/2*arctan2(sin(2*x), cos(2*x))) - sin(2*x))/(2*(cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 - 2*(cos(4*x) + cos(2*x) - cos(1/2*arctan2(sin(2*x), cos(2*x))) + 1)*cos(3/2*arctan2(sin(2*x), cos(2*x))) + cos(3/2*arctan2(sin(2*x), cos(2*x)))^2 - 2*(cos(4*x) + cos(2*x) + 1)*cos(1/2*arctan2(sin(2*x), cos(2*x))) + cos(1/2*arctan2(sin(2*x), cos(2*x)))^2 + sin(4*x)^2 + 2*sin(4*x)*sin(2*x) + sin(2*x)^2 - 2*(sin(4*x) + sin(2*x) - sin(1/2*arctan2(sin(2*x), cos(2*x))))*sin(3/2*arctan2(sin(2*x), cos(2*x))) + sin(3/2*arctan2(sin(2*x), cos(2*x)))^2 - 2*(sin(4*x) + sin(2*x))*sin(1/2*arctan2(sin(2*x), cos(2*x))) + sin(1/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*cos(2*x) + 1), x) + 1/10*integrate((cos(2*x)*sin(4*x) - cos(4*x)*sin(2*x) - cos(3/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) - cos(1/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) + cos(2*x)*sin(3/2*arctan2(sin(2*x), cos(2*x))) + cos(2*x)*sin(1/2*arctan2(sin(2*x), cos(2*x))) - sin(2*x))/(2*(cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 + 2*(cos(4*x) + cos(2*x) + cos(1/2*arctan2(sin(2*x), cos(2*x))) + 1)*cos(3/2*arctan2(sin(2*x), cos(2*x))) + cos(3/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*(cos(4*x) + cos(2*x) + 1)*cos(1/2*arctan2(sin(2*x), cos(2*x))) + cos(1/2*arctan2(sin(2*x), cos(2*x)))^2 + sin(4*x)^2 + 2*sin(4*x)*sin(2*x) + sin(2*x)^2 + 2*(sin(4*x) + sin(2*x) + sin(1/2*arctan2(sin(2*x), cos(2*x))))*sin(3/2*arctan2(sin(2*x), cos(2*x))) + sin(3/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*(sin(4*x) + sin(2*x))*sin(1/2*arctan2(sin(2*x), cos(2*x))) + sin(1/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*cos(2*x) + 1), x) - 1/10*integrate((cos(x)*sin(4*x) + cos(x)*sin(3*x) + cos(x)*sin(2*x) - cos(4*x)*sin(x) - cos(3*x)*sin(x) - cos(2*x)*sin(x) - sin(x))/(2*(cos(3*x) + cos(2*x) + cos(x) + 1)*cos(4*x) + cos(4*x)^2 + 2*(cos(2*x) + cos(x) + 1)*cos(3*x) + cos(3*x)^2 + 2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + 2*(sin(3*x) + sin(2*x) + sin(x))*sin(4*x) + sin(4*x)^2 + 2*(sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1), x) - 1/10*integrate(-(cos(x)*sin(4*x) - cos(x)*sin(3*x) + cos(x)*sin(2*x) - cos(4*x)*sin(x) + cos(3*x)*sin(x) - cos(2*x)*sin(x) - sin(x))/(2*(cos(3*x) - cos(2*x) + cos(x) - 1)*cos(4*x) - cos(4*x)^2 + 2*(cos(2*x) - cos(x) + 1)*cos(3*x) - cos(3*x)^2 + 2*(cos(x) - 1)*cos(2*x) - cos(2*x)^2 - cos(x)^2 + 2*(sin(3*x) - sin(2*x) + sin(x))*sin(4*x) - sin(4*x)^2 + 2*(sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - sin(2*x)^2 + 2*sin(2*x)*sin(x) - sin(x)^2 + 2*cos(x) - 1), x) + 3/10*integrate(-(cos(4/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) + cos(2/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) + cos(1/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) - cos(3*x)*sin(4/3*arctan2(sin(3*x), cos(3*x))) - cos(3*x)*sin(2/3*arctan2(sin(3*x), cos(3*x))) - cos(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(3*x))/(cos(3*x)^2 + 2*(cos(3*x) + cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x))) + 1)*cos(4/3*arctan2(sin(3*x), cos(3*x))) + cos(4/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(cos(3*x) + cos(1/3*arctan2(sin(3*x), cos(3*x))) + 1)*cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(cos(3*x) + 1)*cos(1/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x)))^2 + sin(3*x)^2 + 2*(sin(3*x) + sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(4/3*arctan2(sin(3*x), cos(3*x))) + sin(4/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(sin(3*x) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*sin(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*cos(3*x) + 1), x) + 3/10*integrate(-(cos(4/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) + cos(2/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) - cos(1/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) - cos(3*x)*sin(4/3*arctan2(sin(3*x), cos(3*x))) - cos(3*x)*sin(2/3*arctan2(sin(3*x), cos(3*x))) + cos(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(3*x))/(cos(3*x)^2 - 2*(cos(3*x) - cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x))) - 1)*cos(4/3*arctan2(sin(3*x), cos(3*x))) + cos(4/3*arctan2(sin(3*x), cos(3*x)))^2 - 2*(cos(3*x) + cos(1/3*arctan2(sin(3*x), cos(3*x))) - 1)*cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(cos(3*x) - 1)*cos(1/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x)))^2 + sin(3*x)^2 - 2*(sin(3*x) - sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(4/3*arctan2(sin(3*x), cos(3*x))) + sin(4/3*arctan2(sin(3*x), cos(3*x)))^2 - 2*(sin(3*x) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*sin(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x)))^2 - 2*cos(3*x) + 1), x) + 1/5*integrate((sin(4*x) + sin(3*x) + sin(2*x) + sin(x))/(2*(cos(3*x) + cos(2*x) + cos(x) + 1)*cos(4*x) + cos(4*x)^2 + 2*(cos(2*x) + cos(x) + 1)*cos(3*x) + cos(3*x)^2 + 2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + 2*(sin(3*x) + sin(2*x) + sin(x))*sin(4*x) + sin(4*x)^2 + 2*(sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1), x) - 1/5*integrate(-(sin(4*x) - sin(3*x) + sin(2*x) - sin(x))/(2*(cos(3*x) - cos(2*x) + cos(x) - 1)*cos(4*x) - cos(4*x)^2 + 2*(cos(2*x) - cos(x) + 1)*cos(3*x) - cos(3*x)^2 + 2*(cos(x) - 1)*cos(2*x) - cos(2*x)^2 - cos(x)^2 + 2*(sin(3*x) - sin(2*x) + sin(x))*sin(4*x) - sin(4*x)^2 + 2*(sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - sin(2*x)^2 + 2*sin(2*x)*sin(x) - sin(x)^2 + 2*cos(x) - 1), x) - 1/10*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/10*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
114,0,0,0,0.000000," ","integrate(cos(x)*cot(6*x),x, algorithm=""maxima"")","\cos\left(x\right) + \int \frac{{\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + \cos\left(3 \, x\right) \sin\left(2 \, x\right) - \cos\left(x\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1\right)}}\,{d x} - \frac{1}{24} \, \log\left(2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{24} \, \log\left(-2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"cos(x) + integrate(1/2*((sin(3*x) - sin(x))*cos(4*x) - (cos(3*x) - cos(x))*sin(4*x) - (cos(2*x) - 1)*sin(3*x) + cos(3*x)*sin(2*x) - cos(x)*sin(2*x) + cos(2*x)*sin(x) - sin(x))/(2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) - 1/24*log(2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1) + 1/24*log(-2*(cos(x) - 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 - 2*sin(2*x)*sin(x) + sin(x)^2 - 2*cos(x) + 1) - 1/12*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/12*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
115,0,0,0,0.000000," ","integrate(cos(x)*cot(n*x),x, algorithm=""maxima"")","\int \cos\left(x\right) \cot\left(n x\right)\,{d x}"," ",0,"integrate(cos(x)*cot(n*x), x)","F",0
116,1,137,0,1.075961," ","integrate(cos(x)*sec(2*x),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{8} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right)"," ",0,"1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + 1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/8*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2)","B",0
117,1,76,0,0.429585," ","integrate(cos(x)*sec(3*x),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{3} {\left(\log\left(\frac{4}{3} \, \cos\left(2 \, x\right)^{2} + \frac{4}{3} \, \sin\left(2 \, x\right)^{2} + \frac{4}{3} \, \sqrt{3} \sin\left(2 \, x\right) - \frac{4}{3} \, \cos\left(2 \, x\right) + \frac{4}{3}\right) - \log\left(\frac{4}{3} \, \cos\left(2 \, x\right)^{2} + \frac{4}{3} \, \sin\left(2 \, x\right)^{2} - \frac{4}{3} \, \sqrt{3} \sin\left(2 \, x\right) - \frac{4}{3} \, \cos\left(2 \, x\right) + \frac{4}{3}\right)\right)}"," ",0,"1/12*sqrt(3)*(log(4/3*cos(2*x)^2 + 4/3*sin(2*x)^2 + 4/3*sqrt(3)*sin(2*x) - 4/3*cos(2*x) + 4/3) - log(4/3*cos(2*x)^2 + 4/3*sin(2*x)^2 - 4/3*sqrt(3)*sin(2*x) - 4/3*cos(2*x) + 4/3))","B",0
118,0,0,0,0.000000," ","integrate(cos(x)*sec(4*x),x, algorithm=""maxima"")","\int \cos\left(x\right) \sec\left(4 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*sec(4*x), x)","F",0
119,0,0,0,0.000000," ","integrate(cos(x)*sec(5*x),x, algorithm=""maxima"")","\int \cos\left(x\right) \sec\left(5 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*sec(5*x), x)","F",0
120,0,0,0,0.000000," ","integrate(cos(x)*sec(6*x),x, algorithm=""maxima"")","-\frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{24} \, \sqrt{2} \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \int -\frac{{\left(\cos\left(7 \, x\right) + \cos\left(5 \, x\right) + \cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(8 \, x\right) - {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(7 \, x\right) - {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(5 \, x\right) - {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) + {\left(\sin\left(7 \, x\right) + \sin\left(5 \, x\right) + \sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(8 \, x\right) - {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(7 \, x\right) \sin\left(4 \, x\right) - \sin\left(5 \, x\right) \sin\left(4 \, x\right) + \cos\left(3 \, x\right) + \cos\left(x\right)}{3 \, {\left(2 \, {\left(\cos\left(4 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} - \cos\left(4 \, x\right)^{2} - \sin\left(8 \, x\right)^{2} + 2 \, \sin\left(8 \, x\right) \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) - 1\right)}}\,{d x}"," ",0,"-1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) + 1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) + 1/24*sqrt(2)*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + integrate(-1/3*((cos(7*x) + cos(5*x) + cos(3*x) + cos(x))*cos(8*x) - (cos(4*x) - 1)*cos(7*x) - (cos(4*x) - 1)*cos(5*x) - (cos(3*x) + cos(x))*cos(4*x) + (sin(7*x) + sin(5*x) + sin(3*x) + sin(x))*sin(8*x) - (sin(3*x) + sin(x))*sin(4*x) - sin(7*x)*sin(4*x) - sin(5*x)*sin(4*x) + cos(3*x) + cos(x))/(2*(cos(4*x) - 1)*cos(8*x) - cos(8*x)^2 - cos(4*x)^2 - sin(8*x)^2 + 2*sin(8*x)*sin(4*x) - sin(4*x)^2 + 2*cos(4*x) - 1), x)","F",0
121,1,19,0,0.312837," ","integrate(cos(2*x)*sec(x),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\sin\left(x\right) - 1\right) + 2 \, \sin\left(x\right)"," ",0,"-1/2*log(sin(x) + 1) + 1/2*log(sin(x) - 1) + 2*sin(x)","A",0
122,1,129,0,0.477733," ","integrate(cos(4*x)*sec(2*x),x, algorithm=""maxima"")","\frac{1}{4} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{4} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) - \frac{1}{4} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \frac{1}{4} \, \log\left(2 \, \cos\left(x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2} \sin\left(x\right) + 2\right) + \sin\left(2 \, x\right)"," ",0,"1/4*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) - 1/4*log(2*cos(x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) - 1/4*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 2*sqrt(2)*sin(x) + 2) + 1/4*log(2*cos(x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) - 2*sqrt(2)*sin(x) + 2) + sin(2*x)","B",0
123,1,35,0,0.315132," ","integrate(cos(x)*csc(2*x),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/4*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/4*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
124,1,129,0,0.426326," ","integrate(cos(x)*csc(3*x),x, algorithm=""maxima"")","-\frac{1}{12} \, \log\left(2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/12*log(2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1) - 1/12*log(-2*(cos(x) - 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 - 2*sin(2*x)*sin(x) + sin(x)^2 - 2*cos(x) + 1) + 1/6*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/6*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
125,1,163,0,0.442112," ","integrate(cos(x)*csc(4*x),x, algorithm=""maxima"")","\frac{1}{16} \, \sqrt{2} \log\left(2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(\sqrt{2} \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} + 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(-2 \, \sqrt{2} \sin\left(2 \, x\right) \sin\left(x\right) - 2 \, {\left(\sqrt{2} \cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 2 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(x\right)^{2} - 2 \, \sqrt{2} \cos\left(x\right) + 1\right) - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"1/16*sqrt(2)*log(2*sqrt(2)*sin(2*x)*sin(x) + 2*(sqrt(2)*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 + 2*sqrt(2)*cos(x) + 1) - 1/16*sqrt(2)*log(-2*sqrt(2)*sin(2*x)*sin(x) - 2*(sqrt(2)*cos(x) - 1)*cos(2*x) + cos(2*x)^2 + 2*cos(x)^2 + sin(2*x)^2 + 2*sin(x)^2 - 2*sqrt(2)*cos(x) + 1) - 1/8*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/8*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
126,0,0,0,0.000000," ","integrate(cos(x)*csc(5*x),x, algorithm=""maxima"")","-\frac{1}{10} \, \int -\frac{\cos\left(2 \, x\right) \sin\left(4 \, x\right) - \cos\left(4 \, x\right) \sin\left(2 \, x\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) - \cos\left(2 \, x\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) - \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) - \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} - 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} - 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right) - \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} - 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x} + \frac{1}{10} \, \int \frac{\cos\left(2 \, x\right) \sin\left(4 \, x\right) - \cos\left(4 \, x\right) \sin\left(2 \, x\right) - \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) - \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + \cos\left(2 \, x\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, x\right) + \cos\left(2 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + \sin\left(2 \, x\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, {\left(\sin\left(4 \, x\right) + \sin\left(2 \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right) + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right)\right)\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x} - \frac{1}{10} \, \int \frac{\cos\left(x\right) \sin\left(4 \, x\right) + \cos\left(x\right) \sin\left(3 \, x\right) + \cos\left(x\right) \sin\left(2 \, x\right) - \cos\left(4 \, x\right) \sin\left(x\right) - \cos\left(3 \, x\right) \sin\left(x\right) - \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) + \cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\,{d x} + \frac{1}{10} \, \int -\frac{\cos\left(x\right) \sin\left(4 \, x\right) - \cos\left(x\right) \sin\left(3 \, x\right) + \cos\left(x\right) \sin\left(2 \, x\right) - \cos\left(4 \, x\right) \sin\left(x\right) + \cos\left(3 \, x\right) \sin\left(x\right) - \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) - \cos\left(2 \, x\right) + \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1}\,{d x} + \frac{3}{10} \, \int -\frac{\cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) - \cos\left(3 \, x\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - \cos\left(3 \, x\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - \cos\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(3 \, x\right)}{\cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) + 1\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + \sin\left(3 \, x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \sin\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \cos\left(3 \, x\right) + 1}\,{d x} - \frac{3}{10} \, \int -\frac{\cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) - \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) \sin\left(3 \, x\right) - \cos\left(3 \, x\right) \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - \cos\left(3 \, x\right) \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(3 \, x\right)}{\cos\left(3 \, x\right)^{2} - 2 \, {\left(\cos\left(3 \, x\right) - \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - 1\right)} \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) - 1\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, {\left(\cos\left(3 \, x\right) - 1\right)} \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + \sin\left(3 \, x\right)^{2} - 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{4}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} + 2 \, \sin\left(3 \, x\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right) + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, x\right), \cos\left(3 \, x\right)\right)\right)^{2} - 2 \, \cos\left(3 \, x\right) + 1}\,{d x} + \frac{1}{5} \, \int \frac{\sin\left(4 \, x\right) + \sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) + \cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) + \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) + \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(3 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1}\,{d x} + \frac{1}{5} \, \int -\frac{\sin\left(4 \, x\right) - \sin\left(3 \, x\right) + \sin\left(2 \, x\right) - \sin\left(x\right)}{2 \, {\left(\cos\left(3 \, x\right) - \cos\left(2 \, x\right) + \cos\left(x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right) - \cos\left(x\right) + 1\right)} \cos\left(3 \, x\right) - \cos\left(3 \, x\right)^{2} + 2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + 2 \, {\left(\sin\left(3 \, x\right) - \sin\left(2 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - \sin\left(4 \, x\right)^{2} + 2 \, {\left(\sin\left(2 \, x\right) - \sin\left(x\right)\right)} \sin\left(3 \, x\right) - \sin\left(3 \, x\right)^{2} - \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1}\,{d x} + \frac{1}{10} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{10} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/10*integrate(-(cos(2*x)*sin(4*x) - cos(4*x)*sin(2*x) + cos(3/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) + cos(1/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) - cos(2*x)*sin(3/2*arctan2(sin(2*x), cos(2*x))) - cos(2*x)*sin(1/2*arctan2(sin(2*x), cos(2*x))) - sin(2*x))/(2*(cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 - 2*(cos(4*x) + cos(2*x) - cos(1/2*arctan2(sin(2*x), cos(2*x))) + 1)*cos(3/2*arctan2(sin(2*x), cos(2*x))) + cos(3/2*arctan2(sin(2*x), cos(2*x)))^2 - 2*(cos(4*x) + cos(2*x) + 1)*cos(1/2*arctan2(sin(2*x), cos(2*x))) + cos(1/2*arctan2(sin(2*x), cos(2*x)))^2 + sin(4*x)^2 + 2*sin(4*x)*sin(2*x) + sin(2*x)^2 - 2*(sin(4*x) + sin(2*x) - sin(1/2*arctan2(sin(2*x), cos(2*x))))*sin(3/2*arctan2(sin(2*x), cos(2*x))) + sin(3/2*arctan2(sin(2*x), cos(2*x)))^2 - 2*(sin(4*x) + sin(2*x))*sin(1/2*arctan2(sin(2*x), cos(2*x))) + sin(1/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*cos(2*x) + 1), x) + 1/10*integrate((cos(2*x)*sin(4*x) - cos(4*x)*sin(2*x) - cos(3/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) - cos(1/2*arctan2(sin(2*x), cos(2*x)))*sin(2*x) + cos(2*x)*sin(3/2*arctan2(sin(2*x), cos(2*x))) + cos(2*x)*sin(1/2*arctan2(sin(2*x), cos(2*x))) - sin(2*x))/(2*(cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + cos(2*x)^2 + 2*(cos(4*x) + cos(2*x) + cos(1/2*arctan2(sin(2*x), cos(2*x))) + 1)*cos(3/2*arctan2(sin(2*x), cos(2*x))) + cos(3/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*(cos(4*x) + cos(2*x) + 1)*cos(1/2*arctan2(sin(2*x), cos(2*x))) + cos(1/2*arctan2(sin(2*x), cos(2*x)))^2 + sin(4*x)^2 + 2*sin(4*x)*sin(2*x) + sin(2*x)^2 + 2*(sin(4*x) + sin(2*x) + sin(1/2*arctan2(sin(2*x), cos(2*x))))*sin(3/2*arctan2(sin(2*x), cos(2*x))) + sin(3/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*(sin(4*x) + sin(2*x))*sin(1/2*arctan2(sin(2*x), cos(2*x))) + sin(1/2*arctan2(sin(2*x), cos(2*x)))^2 + 2*cos(2*x) + 1), x) - 1/10*integrate((cos(x)*sin(4*x) + cos(x)*sin(3*x) + cos(x)*sin(2*x) - cos(4*x)*sin(x) - cos(3*x)*sin(x) - cos(2*x)*sin(x) - sin(x))/(2*(cos(3*x) + cos(2*x) + cos(x) + 1)*cos(4*x) + cos(4*x)^2 + 2*(cos(2*x) + cos(x) + 1)*cos(3*x) + cos(3*x)^2 + 2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + 2*(sin(3*x) + sin(2*x) + sin(x))*sin(4*x) + sin(4*x)^2 + 2*(sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1), x) + 1/10*integrate(-(cos(x)*sin(4*x) - cos(x)*sin(3*x) + cos(x)*sin(2*x) - cos(4*x)*sin(x) + cos(3*x)*sin(x) - cos(2*x)*sin(x) - sin(x))/(2*(cos(3*x) - cos(2*x) + cos(x) - 1)*cos(4*x) - cos(4*x)^2 + 2*(cos(2*x) - cos(x) + 1)*cos(3*x) - cos(3*x)^2 + 2*(cos(x) - 1)*cos(2*x) - cos(2*x)^2 - cos(x)^2 + 2*(sin(3*x) - sin(2*x) + sin(x))*sin(4*x) - sin(4*x)^2 + 2*(sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - sin(2*x)^2 + 2*sin(2*x)*sin(x) - sin(x)^2 + 2*cos(x) - 1), x) + 3/10*integrate(-(cos(4/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) + cos(2/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) + cos(1/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) - cos(3*x)*sin(4/3*arctan2(sin(3*x), cos(3*x))) - cos(3*x)*sin(2/3*arctan2(sin(3*x), cos(3*x))) - cos(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(3*x))/(cos(3*x)^2 + 2*(cos(3*x) + cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x))) + 1)*cos(4/3*arctan2(sin(3*x), cos(3*x))) + cos(4/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(cos(3*x) + cos(1/3*arctan2(sin(3*x), cos(3*x))) + 1)*cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(cos(3*x) + 1)*cos(1/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x)))^2 + sin(3*x)^2 + 2*(sin(3*x) + sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(4/3*arctan2(sin(3*x), cos(3*x))) + sin(4/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(sin(3*x) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*sin(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*cos(3*x) + 1), x) - 3/10*integrate(-(cos(4/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) + cos(2/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) - cos(1/3*arctan2(sin(3*x), cos(3*x)))*sin(3*x) - cos(3*x)*sin(4/3*arctan2(sin(3*x), cos(3*x))) - cos(3*x)*sin(2/3*arctan2(sin(3*x), cos(3*x))) + cos(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(3*x))/(cos(3*x)^2 - 2*(cos(3*x) - cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x))) - 1)*cos(4/3*arctan2(sin(3*x), cos(3*x))) + cos(4/3*arctan2(sin(3*x), cos(3*x)))^2 - 2*(cos(3*x) + cos(1/3*arctan2(sin(3*x), cos(3*x))) - 1)*cos(2/3*arctan2(sin(3*x), cos(3*x))) + cos(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*(cos(3*x) - 1)*cos(1/3*arctan2(sin(3*x), cos(3*x))) + cos(1/3*arctan2(sin(3*x), cos(3*x)))^2 + sin(3*x)^2 - 2*(sin(3*x) - sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(4/3*arctan2(sin(3*x), cos(3*x))) + sin(4/3*arctan2(sin(3*x), cos(3*x)))^2 - 2*(sin(3*x) + sin(1/3*arctan2(sin(3*x), cos(3*x))))*sin(2/3*arctan2(sin(3*x), cos(3*x))) + sin(2/3*arctan2(sin(3*x), cos(3*x)))^2 + 2*sin(3*x)*sin(1/3*arctan2(sin(3*x), cos(3*x))) + sin(1/3*arctan2(sin(3*x), cos(3*x)))^2 - 2*cos(3*x) + 1), x) + 1/5*integrate((sin(4*x) + sin(3*x) + sin(2*x) + sin(x))/(2*(cos(3*x) + cos(2*x) + cos(x) + 1)*cos(4*x) + cos(4*x)^2 + 2*(cos(2*x) + cos(x) + 1)*cos(3*x) + cos(3*x)^2 + 2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + 2*(sin(3*x) + sin(2*x) + sin(x))*sin(4*x) + sin(4*x)^2 + 2*(sin(2*x) + sin(x))*sin(3*x) + sin(3*x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1), x) + 1/5*integrate(-(sin(4*x) - sin(3*x) + sin(2*x) - sin(x))/(2*(cos(3*x) - cos(2*x) + cos(x) - 1)*cos(4*x) - cos(4*x)^2 + 2*(cos(2*x) - cos(x) + 1)*cos(3*x) - cos(3*x)^2 + 2*(cos(x) - 1)*cos(2*x) - cos(2*x)^2 - cos(x)^2 + 2*(sin(3*x) - sin(2*x) + sin(x))*sin(4*x) - sin(4*x)^2 + 2*(sin(2*x) - sin(x))*sin(3*x) - sin(3*x)^2 - sin(2*x)^2 + 2*sin(2*x)*sin(x) - sin(x)^2 + 2*cos(x) - 1), x) + 1/10*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/10*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
127,0,0,0,0.000000," ","integrate(cos(x)*csc(6*x),x, algorithm=""maxima"")","-\int \frac{{\left(\sin\left(3 \, x\right) - \sin\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(\cos\left(3 \, x\right) - \cos\left(x\right)\right)} \sin\left(4 \, x\right) - {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + \cos\left(3 \, x\right) \sin\left(2 \, x\right) - \cos\left(x\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(x\right) - \sin\left(x\right)}{2 \, {\left(2 \, {\left(\cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 2 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) - 1\right)}}\,{d x} - \frac{1}{24} \, \log\left(2 \, {\left(\cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{24} \, \log\left(-2 \, {\left(\cos\left(x\right) - 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \sin\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-integrate(1/2*((sin(3*x) - sin(x))*cos(4*x) - (cos(3*x) - cos(x))*sin(4*x) - (cos(2*x) - 1)*sin(3*x) + cos(3*x)*sin(2*x) - cos(x)*sin(2*x) + cos(2*x)*sin(x) - sin(x))/(2*(cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - cos(2*x)^2 - sin(4*x)^2 + 2*sin(4*x)*sin(2*x) - sin(2*x)^2 + 2*cos(2*x) - 1), x) - 1/24*log(2*(cos(x) + 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 + 2*sin(2*x)*sin(x) + sin(x)^2 + 2*cos(x) + 1) + 1/24*log(-2*(cos(x) - 1)*cos(2*x) + cos(2*x)^2 + cos(x)^2 + sin(2*x)^2 - 2*sin(2*x)*sin(x) + sin(x)^2 - 2*cos(x) + 1) - 1/12*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/12*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","F",0
128,1,25,0,0.453835," ","integrate(cos(6*x)^3*sin(x),x, algorithm=""maxima"")","-\frac{1}{152} \, \cos\left(19 \, x\right) + \frac{1}{136} \, \cos\left(17 \, x\right) - \frac{3}{56} \, \cos\left(7 \, x\right) + \frac{3}{40} \, \cos\left(5 \, x\right)"," ",0,"-1/152*cos(19*x) + 1/136*cos(17*x) - 3/56*cos(7*x) + 3/40*cos(5*x)","A",0
129,1,25,0,0.312316," ","integrate(cos(6*x)^3*sin(9*x),x, algorithm=""maxima"")","-\frac{1}{216} \, \cos\left(27 \, x\right) - \frac{1}{40} \, \cos\left(15 \, x\right) + \frac{1}{72} \, \cos\left(9 \, x\right) - \frac{1}{8} \, \cos\left(3 \, x\right)"," ",0,"-1/216*cos(27*x) - 1/40*cos(15*x) + 1/72*cos(9*x) - 1/8*cos(3*x)","A",0
130,1,19,0,0.319243," ","integrate(cos(2*x)*sin(6*x)^2,x, algorithm=""maxima"")","-\frac{1}{56} \, \sin\left(14 \, x\right) - \frac{1}{40} \, \sin\left(10 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-1/56*sin(14*x) - 1/40*sin(10*x) + 1/4*sin(2*x)","A",0
131,1,17,0,0.310987," ","integrate(cos(x)*sin(6*x)^2,x, algorithm=""maxima"")","-\frac{1}{52} \, \sin\left(13 \, x\right) - \frac{1}{44} \, \sin\left(11 \, x\right) + \frac{1}{2} \, \sin\left(x\right)"," ",0,"-1/52*sin(13*x) - 1/44*sin(11*x) + 1/2*sin(x)","A",0
132,1,25,0,0.560666," ","integrate(cos(x)*sin(6*x)^3,x, algorithm=""maxima"")","\frac{1}{152} \, \cos\left(19 \, x\right) + \frac{1}{136} \, \cos\left(17 \, x\right) - \frac{3}{56} \, \cos\left(7 \, x\right) - \frac{3}{40} \, \cos\left(5 \, x\right)"," ",0,"1/152*cos(19*x) + 1/136*cos(17*x) - 3/56*cos(7*x) - 3/40*cos(5*x)","A",0
133,1,23,0,0.726835," ","integrate(cos(7*x)*sin(6*x)^3,x, algorithm=""maxima"")","\frac{1}{200} \, \cos\left(25 \, x\right) - \frac{3}{104} \, \cos\left(13 \, x\right) + \frac{1}{88} \, \cos\left(11 \, x\right) + \frac{3}{8} \, \cos\left(x\right)"," ",0,"1/200*cos(25*x) - 3/104*cos(13*x) + 1/88*cos(11*x) + 3/8*cos(x)","A",0
134,1,31,0,0.354713," ","integrate(cos(3*x)^2*sin(2*x)^3,x, algorithm=""maxima"")","\frac{1}{192} \, \cos\left(12 \, x\right) - \frac{3}{128} \, \cos\left(8 \, x\right) + \frac{1}{48} \, \cos\left(6 \, x\right) + \frac{3}{64} \, \cos\left(4 \, x\right) - \frac{3}{16} \, \cos\left(2 \, x\right)"," ",0,"1/192*cos(12*x) - 3/128*cos(8*x) + 1/48*cos(6*x) + 3/64*cos(4*x) - 3/16*cos(2*x)","A",0
135,1,23,0,0.306649," ","integrate(sin(b*x+a)*sin(b*x+c),x, algorithm=""maxima"")","\frac{1}{2} \, x \cos\left(-a + c\right) - \frac{\sin\left(2 \, b x + a + c\right)}{4 \, b}"," ",0,"1/2*x*cos(-a + c) - 1/4*sin(2*b*x + a + c)/b","A",0
136,1,23,0,0.702866," ","integrate(-sin(b*x-c)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{1}{2} \, x \cos\left(a + c\right) + \frac{\sin\left(2 \, b x + a - c\right)}{4 \, b}"," ",0,"-1/2*x*cos(a + c) + 1/4*sin(2*b*x + a - c)/b","A",0
137,1,23,0,0.564372," ","integrate(cos(b*x+a)*cos(b*x+c),x, algorithm=""maxima"")","\frac{1}{2} \, x \cos\left(-a + c\right) + \frac{\sin\left(2 \, b x + a + c\right)}{4 \, b}"," ",0,"1/2*x*cos(-a + c) + 1/4*sin(2*b*x + a + c)/b","A",0
138,1,23,0,0.332072," ","integrate(cos(b*x-c)*cos(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x \cos\left(a + c\right) + \frac{\sin\left(2 \, b x + a - c\right)}{4 \, b}"," ",0,"1/2*x*cos(a + c) + 1/4*sin(2*b*x + a - c)/b","A",0
139,1,371,0,0.652604," ","integrate(tan(b*x+a)*tan(b*x+c),x, algorithm=""maxima"")","-\frac{{\left(2 \, b \cos\left(2 \, a\right) \cos\left(2 \, c\right) - b \cos\left(2 \, c\right)^{2} + 2 \, b \sin\left(2 \, a\right) \sin\left(2 \, c\right) - b \sin\left(2 \, c\right)^{2} - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} b\right)} x + {\left(\cos\left(2 \, a\right)^{2} - \cos\left(2 \, c\right)^{2} + \sin\left(2 \, a\right)^{2} - \sin\left(2 \, c\right)^{2}\right)} \arctan\left(\sin\left(2 \, b x\right) - \sin\left(2 \, a\right), \cos\left(2 \, b x\right) + \cos\left(2 \, a\right)\right) - {\left(\cos\left(2 \, a\right)^{2} - \cos\left(2 \, c\right)^{2} + \sin\left(2 \, a\right)^{2} - \sin\left(2 \, c\right)^{2}\right)} \arctan\left(\sin\left(2 \, b x\right) - \sin\left(2 \, c\right), \cos\left(2 \, b x\right) + \cos\left(2 \, c\right)\right) - {\left(\cos\left(2 \, c\right) \sin\left(2 \, a\right) - \cos\left(2 \, a\right) \sin\left(2 \, c\right)\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) + {\left(\cos\left(2 \, c\right) \sin\left(2 \, a\right) - \cos\left(2 \, a\right) \sin\left(2 \, c\right)\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right)}{2 \, b \cos\left(2 \, a\right) \cos\left(2 \, c\right) - b \cos\left(2 \, c\right)^{2} + 2 \, b \sin\left(2 \, a\right) \sin\left(2 \, c\right) - b \sin\left(2 \, c\right)^{2} - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} b}"," ",0,"-((2*b*cos(2*a)*cos(2*c) - b*cos(2*c)^2 + 2*b*sin(2*a)*sin(2*c) - b*sin(2*c)^2 - (cos(2*a)^2 + sin(2*a)^2)*b)*x + (cos(2*a)^2 - cos(2*c)^2 + sin(2*a)^2 - sin(2*c)^2)*arctan2(sin(2*b*x) - sin(2*a), cos(2*b*x) + cos(2*a)) - (cos(2*a)^2 - cos(2*c)^2 + sin(2*a)^2 - sin(2*c)^2)*arctan2(sin(2*b*x) - sin(2*c), cos(2*b*x) + cos(2*c)) - (cos(2*c)*sin(2*a) - cos(2*a)*sin(2*c))*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) + (cos(2*c)*sin(2*a) - cos(2*a)*sin(2*c))*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*c) + cos(2*c)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*c) + sin(2*c)^2))/(2*b*cos(2*a)*cos(2*c) - b*cos(2*c)^2 + 2*b*sin(2*a)*sin(2*c) - b*sin(2*c)^2 - (cos(2*a)^2 + sin(2*a)^2)*b)","B",0
140,1,290,0,0.345517," ","integrate(-tan(b*x-c)*tan(b*x+a),x, algorithm=""maxima"")","\frac{{\left(b \cos\left(2 \, a + 2 \, c\right)^{2} + b \sin\left(2 \, a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, a + 2 \, c\right) + b\right)} x - {\left(\cos\left(2 \, a + 2 \, c\right)^{2} + \sin\left(2 \, a + 2 \, c\right)^{2} - 1\right)} \arctan\left(\sin\left(2 \, b x\right) - \sin\left(2 \, a\right), \cos\left(2 \, b x\right) + \cos\left(2 \, a\right)\right) + {\left(\cos\left(2 \, a + 2 \, c\right)^{2} + \sin\left(2 \, a + 2 \, c\right)^{2} - 1\right)} \arctan\left(\sin\left(2 \, b x\right) + \sin\left(2 \, c\right), \cos\left(2 \, b x\right) + \cos\left(2 \, c\right)\right) + \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) \sin\left(2 \, a + 2 \, c\right) - \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, b x\right)^{2} + 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right) \sin\left(2 \, a + 2 \, c\right)}{b \cos\left(2 \, a + 2 \, c\right)^{2} + b \sin\left(2 \, a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, a + 2 \, c\right) + b}"," ",0,"((b*cos(2*a + 2*c)^2 + b*sin(2*a + 2*c)^2 - 2*b*cos(2*a + 2*c) + b)*x - (cos(2*a + 2*c)^2 + sin(2*a + 2*c)^2 - 1)*arctan2(sin(2*b*x) - sin(2*a), cos(2*b*x) + cos(2*a)) + (cos(2*a + 2*c)^2 + sin(2*a + 2*c)^2 - 1)*arctan2(sin(2*b*x) + sin(2*c), cos(2*b*x) + cos(2*c)) + log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2)*sin(2*a + 2*c) - log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*c) + cos(2*c)^2 + sin(2*b*x)^2 + 2*sin(2*b*x)*sin(2*c) + sin(2*c)^2)*sin(2*a + 2*c))/(b*cos(2*a + 2*c)^2 + b*sin(2*a + 2*c)^2 - 2*b*cos(2*a + 2*c) + b)","B",0
141,1,549,0,0.928143," ","integrate(cot(b*x+a)*cot(b*x+c),x, algorithm=""maxima"")","-\frac{{\left(2 \, b \cos\left(2 \, a\right) \cos\left(2 \, c\right) - b \cos\left(2 \, c\right)^{2} + 2 \, b \sin\left(2 \, a\right) \sin\left(2 \, c\right) - b \sin\left(2 \, c\right)^{2} - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} b\right)} x + {\left(\cos\left(2 \, a\right)^{2} - \cos\left(2 \, c\right)^{2} + \sin\left(2 \, a\right)^{2} - \sin\left(2 \, c\right)^{2}\right)} \arctan\left(\sin\left(b x\right) + \sin\left(a\right), \cos\left(b x\right) - \cos\left(a\right)\right) + {\left(\cos\left(2 \, a\right)^{2} - \cos\left(2 \, c\right)^{2} + \sin\left(2 \, a\right)^{2} - \sin\left(2 \, c\right)^{2}\right)} \arctan\left(\sin\left(b x\right) - \sin\left(a\right), \cos\left(b x\right) + \cos\left(a\right)\right) - {\left(\cos\left(2 \, a\right)^{2} - \cos\left(2 \, c\right)^{2} + \sin\left(2 \, a\right)^{2} - \sin\left(2 \, c\right)^{2}\right)} \arctan\left(\sin\left(b x\right) + \sin\left(c\right), \cos\left(b x\right) - \cos\left(c\right)\right) - {\left(\cos\left(2 \, a\right)^{2} - \cos\left(2 \, c\right)^{2} + \sin\left(2 \, a\right)^{2} - \sin\left(2 \, c\right)^{2}\right)} \arctan\left(\sin\left(b x\right) - \sin\left(c\right), \cos\left(b x\right) + \cos\left(c\right)\right) - {\left(\cos\left(2 \, c\right) \sin\left(2 \, a\right) - \cos\left(2 \, a\right) \sin\left(2 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - {\left(\cos\left(2 \, c\right) \sin\left(2 \, a\right) - \cos\left(2 \, a\right) \sin\left(2 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + {\left(\cos\left(2 \, c\right) \sin\left(2 \, a\right) - \cos\left(2 \, a\right) \sin\left(2 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(\cos\left(2 \, c\right) \sin\left(2 \, a\right) - \cos\left(2 \, a\right) \sin\left(2 \, c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{2 \, b \cos\left(2 \, a\right) \cos\left(2 \, c\right) - b \cos\left(2 \, c\right)^{2} + 2 \, b \sin\left(2 \, a\right) \sin\left(2 \, c\right) - b \sin\left(2 \, c\right)^{2} - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} b}"," ",0,"-((2*b*cos(2*a)*cos(2*c) - b*cos(2*c)^2 + 2*b*sin(2*a)*sin(2*c) - b*sin(2*c)^2 - (cos(2*a)^2 + sin(2*a)^2)*b)*x + (cos(2*a)^2 - cos(2*c)^2 + sin(2*a)^2 - sin(2*c)^2)*arctan2(sin(b*x) + sin(a), cos(b*x) - cos(a)) + (cos(2*a)^2 - cos(2*c)^2 + sin(2*a)^2 - sin(2*c)^2)*arctan2(sin(b*x) - sin(a), cos(b*x) + cos(a)) - (cos(2*a)^2 - cos(2*c)^2 + sin(2*a)^2 - sin(2*c)^2)*arctan2(sin(b*x) + sin(c), cos(b*x) - cos(c)) - (cos(2*a)^2 - cos(2*c)^2 + sin(2*a)^2 - sin(2*c)^2)*arctan2(sin(b*x) - sin(c), cos(b*x) + cos(c)) - (cos(2*c)*sin(2*a) - cos(2*a)*sin(2*c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - (cos(2*c)*sin(2*a) - cos(2*a)*sin(2*c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + (cos(2*c)*sin(2*a) - cos(2*a)*sin(2*c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + (cos(2*c)*sin(2*a) - cos(2*a)*sin(2*c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2))/(2*b*cos(2*a)*cos(2*c) - b*cos(2*c)^2 + 2*b*sin(2*a)*sin(2*c) - b*sin(2*c)^2 - (cos(2*a)^2 + sin(2*a)^2)*b)","B",0
142,1,432,0,0.438802," ","integrate(-cot(b*x-c)*cot(b*x+a),x, algorithm=""maxima"")","\frac{{\left(b \cos\left(2 \, a + 2 \, c\right)^{2} + b \sin\left(2 \, a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, a + 2 \, c\right) + b\right)} x - {\left(\cos\left(2 \, a + 2 \, c\right)^{2} + \sin\left(2 \, a + 2 \, c\right)^{2} - 1\right)} \arctan\left(\sin\left(b x\right) + \sin\left(a\right), \cos\left(b x\right) - \cos\left(a\right)\right) - {\left(\cos\left(2 \, a + 2 \, c\right)^{2} + \sin\left(2 \, a + 2 \, c\right)^{2} - 1\right)} \arctan\left(\sin\left(b x\right) - \sin\left(a\right), \cos\left(b x\right) + \cos\left(a\right)\right) + {\left(\cos\left(2 \, a + 2 \, c\right)^{2} + \sin\left(2 \, a + 2 \, c\right)^{2} - 1\right)} \arctan\left(\sin\left(b x\right) + \sin\left(c\right), \cos\left(b x\right) + \cos\left(c\right)\right) + {\left(\cos\left(2 \, a + 2 \, c\right)^{2} + \sin\left(2 \, a + 2 \, c\right)^{2} - 1\right)} \arctan\left(\sin\left(b x\right) - \sin\left(c\right), \cos\left(b x\right) - \cos\left(c\right)\right) + \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) \sin\left(2 \, a + 2 \, c\right) + \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) \sin\left(2 \, a + 2 \, c\right) - \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) \sin\left(2 \, a + 2 \, c\right) - \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) \sin\left(2 \, a + 2 \, c\right)}{b \cos\left(2 \, a + 2 \, c\right)^{2} + b \sin\left(2 \, a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, a + 2 \, c\right) + b}"," ",0,"((b*cos(2*a + 2*c)^2 + b*sin(2*a + 2*c)^2 - 2*b*cos(2*a + 2*c) + b)*x - (cos(2*a + 2*c)^2 + sin(2*a + 2*c)^2 - 1)*arctan2(sin(b*x) + sin(a), cos(b*x) - cos(a)) - (cos(2*a + 2*c)^2 + sin(2*a + 2*c)^2 - 1)*arctan2(sin(b*x) - sin(a), cos(b*x) + cos(a)) + (cos(2*a + 2*c)^2 + sin(2*a + 2*c)^2 - 1)*arctan2(sin(b*x) + sin(c), cos(b*x) + cos(c)) + (cos(2*a + 2*c)^2 + sin(2*a + 2*c)^2 - 1)*arctan2(sin(b*x) - sin(c), cos(b*x) - cos(c)) + log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2)*sin(2*a + 2*c) + log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2)*sin(2*a + 2*c) - log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2)*sin(2*a + 2*c) - log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2)*sin(2*a + 2*c))/(b*cos(2*a + 2*c)^2 + b*sin(2*a + 2*c)^2 - 2*b*cos(2*a + 2*c) + b)","B",0
143,1,349,0,0.341641," ","integrate(sec(b*x+a)*sec(b*x+c),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \arctan\left(\sin\left(2 \, b x\right) - \sin\left(2 \, a\right), \cos\left(2 \, b x\right) + \cos\left(2 \, a\right)\right) - 2 \, {\left({\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \arctan\left(\sin\left(2 \, b x\right) - \sin\left(2 \, c\right), \cos\left(2 \, b x\right) + \cos\left(2 \, c\right)\right) - {\left({\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) + {\left({\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right)}{2 \, b \cos\left(2 \, a\right) \cos\left(2 \, c\right) - b \cos\left(2 \, c\right)^{2} + 2 \, b \sin\left(2 \, a\right) \sin\left(2 \, c\right) - b \sin\left(2 \, c\right)^{2} - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} b}"," ",0,"-(2*((cos(2*a) - cos(2*c))*cos(a + c) + (sin(2*a) - sin(2*c))*sin(a + c))*arctan2(sin(2*b*x) - sin(2*a), cos(2*b*x) + cos(2*a)) - 2*((cos(2*a) - cos(2*c))*cos(a + c) + (sin(2*a) - sin(2*c))*sin(a + c))*arctan2(sin(2*b*x) - sin(2*c), cos(2*b*x) + cos(2*c)) - ((sin(2*a) - sin(2*c))*cos(a + c) - (cos(2*a) - cos(2*c))*sin(a + c))*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) + ((sin(2*a) - sin(2*c))*cos(a + c) - (cos(2*a) - cos(2*c))*sin(a + c))*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*c) + cos(2*c)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*c) + sin(2*c)^2))/(2*b*cos(2*a)*cos(2*c) - b*cos(2*c)^2 + 2*b*sin(2*a)*sin(2*c) - b*sin(2*c)^2 - (cos(2*a)^2 + sin(2*a)^2)*b)","B",0
144,1,322,0,0.356741," ","integrate(sec(b*x-c)*sec(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(2 \, a + 2 \, c\right) \cos\left(a + c\right) + \sin\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) - \cos\left(a + c\right)\right)} \arctan\left(\sin\left(2 \, b x\right) - \sin\left(2 \, a\right), \cos\left(2 \, b x\right) + \cos\left(2 \, a\right)\right) - 2 \, {\left(\cos\left(2 \, a + 2 \, c\right) \cos\left(a + c\right) + \sin\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) - \cos\left(a + c\right)\right)} \arctan\left(\sin\left(2 \, b x\right) + \sin\left(2 \, c\right), \cos\left(2 \, b x\right) + \cos\left(2 \, c\right)\right) - {\left(\cos\left(a + c\right) \sin\left(2 \, a + 2 \, c\right) - \cos\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) + \sin\left(a + c\right)\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right) + {\left(\cos\left(a + c\right) \sin\left(2 \, a + 2 \, c\right) - \cos\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) + \sin\left(a + c\right)\right)} \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, c\right) + \cos\left(2 \, c\right)^{2} + \sin\left(2 \, b x\right)^{2} + 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, c\right) + \sin\left(2 \, c\right)^{2}\right)}{b \cos\left(2 \, a + 2 \, c\right)^{2} + b \sin\left(2 \, a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, a + 2 \, c\right) + b}"," ",0,"(2*(cos(2*a + 2*c)*cos(a + c) + sin(2*a + 2*c)*sin(a + c) - cos(a + c))*arctan2(sin(2*b*x) - sin(2*a), cos(2*b*x) + cos(2*a)) - 2*(cos(2*a + 2*c)*cos(a + c) + sin(2*a + 2*c)*sin(a + c) - cos(a + c))*arctan2(sin(2*b*x) + sin(2*c), cos(2*b*x) + cos(2*c)) - (cos(a + c)*sin(2*a + 2*c) - cos(2*a + 2*c)*sin(a + c) + sin(a + c))*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2) + (cos(a + c)*sin(2*a + 2*c) - cos(2*a + 2*c)*sin(a + c) + sin(a + c))*log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*c) + cos(2*c)^2 + sin(2*b*x)^2 + 2*sin(2*b*x)*sin(2*c) + sin(2*c)^2))/(b*cos(2*a + 2*c)^2 + b*sin(2*a + 2*c)^2 - 2*b*cos(2*a + 2*c) + b)","B",0
145,1,564,0,0.354031," ","integrate(csc(b*x+a)*csc(b*x+c),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) + \sin\left(a\right), \cos\left(b x\right) - \cos\left(a\right)\right) + 2 \, {\left({\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) - \sin\left(a\right), \cos\left(b x\right) + \cos\left(a\right)\right) - 2 \, {\left({\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) + \sin\left(c\right), \cos\left(b x\right) - \cos\left(c\right)\right) - 2 \, {\left({\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \cos\left(a + c\right) + {\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) - \sin\left(c\right), \cos\left(b x\right) + \cos\left(c\right)\right) - {\left({\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - {\left({\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + {\left({\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left({\left(\sin\left(2 \, a\right) - \sin\left(2 \, c\right)\right)} \cos\left(a + c\right) - {\left(\cos\left(2 \, a\right) - \cos\left(2 \, c\right)\right)} \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{2 \, b \cos\left(2 \, a\right) \cos\left(2 \, c\right) - b \cos\left(2 \, c\right)^{2} + 2 \, b \sin\left(2 \, a\right) \sin\left(2 \, c\right) - b \sin\left(2 \, c\right)^{2} - {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} b}"," ",0,"-(2*((cos(2*a) - cos(2*c))*cos(a + c) + (sin(2*a) - sin(2*c))*sin(a + c))*arctan2(sin(b*x) + sin(a), cos(b*x) - cos(a)) + 2*((cos(2*a) - cos(2*c))*cos(a + c) + (sin(2*a) - sin(2*c))*sin(a + c))*arctan2(sin(b*x) - sin(a), cos(b*x) + cos(a)) - 2*((cos(2*a) - cos(2*c))*cos(a + c) + (sin(2*a) - sin(2*c))*sin(a + c))*arctan2(sin(b*x) + sin(c), cos(b*x) - cos(c)) - 2*((cos(2*a) - cos(2*c))*cos(a + c) + (sin(2*a) - sin(2*c))*sin(a + c))*arctan2(sin(b*x) - sin(c), cos(b*x) + cos(c)) - ((sin(2*a) - sin(2*c))*cos(a + c) - (cos(2*a) - cos(2*c))*sin(a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - ((sin(2*a) - sin(2*c))*cos(a + c) - (cos(2*a) - cos(2*c))*sin(a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + ((sin(2*a) - sin(2*c))*cos(a + c) - (cos(2*a) - cos(2*c))*sin(a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2) + ((sin(2*a) - sin(2*c))*cos(a + c) - (cos(2*a) - cos(2*c))*sin(a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2))/(2*b*cos(2*a)*cos(2*c) - b*cos(2*c)^2 + 2*b*sin(2*a)*sin(2*c) - b*sin(2*c)^2 - (cos(2*a)^2 + sin(2*a)^2)*b)","B",0
146,1,536,0,0.502185," ","integrate(-csc(b*x-c)*csc(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(2 \, a + 2 \, c\right) \cos\left(a + c\right) + \sin\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) - \cos\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) + \sin\left(a\right), \cos\left(b x\right) - \cos\left(a\right)\right) + 2 \, {\left(\cos\left(2 \, a + 2 \, c\right) \cos\left(a + c\right) + \sin\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) - \cos\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) - \sin\left(a\right), \cos\left(b x\right) + \cos\left(a\right)\right) - 2 \, {\left(\cos\left(2 \, a + 2 \, c\right) \cos\left(a + c\right) + \sin\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) - \cos\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) + \sin\left(c\right), \cos\left(b x\right) + \cos\left(c\right)\right) - 2 \, {\left(\cos\left(2 \, a + 2 \, c\right) \cos\left(a + c\right) + \sin\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) - \cos\left(a + c\right)\right)} \arctan\left(\sin\left(b x\right) - \sin\left(c\right), \cos\left(b x\right) - \cos\left(c\right)\right) - {\left(\cos\left(a + c\right) \sin\left(2 \, a + 2 \, c\right) - \cos\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) + \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) - {\left(\cos\left(a + c\right) \sin\left(2 \, a + 2 \, c\right) - \cos\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) + \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + {\left(\cos\left(a + c\right) \sin\left(2 \, a + 2 \, c\right) - \cos\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) + \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) + {\left(\cos\left(a + c\right) \sin\left(2 \, a + 2 \, c\right) - \cos\left(2 \, a + 2 \, c\right) \sin\left(a + c\right) + \sin\left(a + c\right)\right)} \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(c\right) + \cos\left(c\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{b \cos\left(2 \, a + 2 \, c\right)^{2} + b \sin\left(2 \, a + 2 \, c\right)^{2} - 2 \, b \cos\left(2 \, a + 2 \, c\right) + b}"," ",0,"-(2*(cos(2*a + 2*c)*cos(a + c) + sin(2*a + 2*c)*sin(a + c) - cos(a + c))*arctan2(sin(b*x) + sin(a), cos(b*x) - cos(a)) + 2*(cos(2*a + 2*c)*cos(a + c) + sin(2*a + 2*c)*sin(a + c) - cos(a + c))*arctan2(sin(b*x) - sin(a), cos(b*x) + cos(a)) - 2*(cos(2*a + 2*c)*cos(a + c) + sin(2*a + 2*c)*sin(a + c) - cos(a + c))*arctan2(sin(b*x) + sin(c), cos(b*x) + cos(c)) - 2*(cos(2*a + 2*c)*cos(a + c) + sin(2*a + 2*c)*sin(a + c) - cos(a + c))*arctan2(sin(b*x) - sin(c), cos(b*x) - cos(c)) - (cos(a + c)*sin(2*a + 2*c) - cos(2*a + 2*c)*sin(a + c) + sin(a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) - (cos(a + c)*sin(2*a + 2*c) - cos(2*a + 2*c)*sin(a + c) + sin(a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2) + (cos(a + c)*sin(2*a + 2*c) - cos(2*a + 2*c)*sin(a + c) + sin(a + c))*log(cos(b*x)^2 + 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(c) + sin(c)^2) + (cos(a + c)*sin(2*a + 2*c) - cos(2*a + 2*c)*sin(a + c) + sin(a + c))*log(cos(b*x)^2 - 2*cos(b*x)*cos(c) + cos(c)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(c) + sin(c)^2))/(b*cos(2*a + 2*c)^2 + b*sin(2*a + 2*c)^2 - 2*b*cos(2*a + 2*c) + b)","B",0
147,1,57,0,0.492285," ","integrate((sin(x)*tan(x))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)}}{\sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} \sqrt{-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} \sqrt{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1}}"," ",0,"2*(sin(x)^2/(cos(x) + 1)^2 - 1)/(sqrt(sin(x)/(cos(x) + 1) + 1)*sqrt(-sin(x)/(cos(x) + 1) + 1)*sqrt(sin(x)^2/(cos(x) + 1)^2 + 1))","B",0
148,1,57,0,0.473941," ","integrate((sin(x)*tan(x))^(3/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(\frac{\sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - 1\right)}}{3 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"-8/3*(sin(x)^6/(cos(x) + 1)^6 - 1)/((sin(x)/(cos(x) + 1) + 1)^(3/2)*(-sin(x)/(cos(x) + 1) + 1)^(3/2)*(sin(x)^2/(cos(x) + 1)^2 + 1)^(3/2))","B",0
149,1,82,0,0.443795," ","integrate((sin(x)*tan(x))^(5/2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\frac{5 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{2 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} - 2\right)}}{15 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"-32/15*(5*sin(x)^4/(cos(x) + 1)^4 - 5*sin(x)^6/(cos(x) + 1)^6 + 2*sin(x)^10/(cos(x) + 1)^10 - 2)/((sin(x)/(cos(x) + 1) + 1)^(5/2)*(-sin(x)/(cos(x) + 1) + 1)^(5/2)*(sin(x)^2/(cos(x) + 1)^2 + 1)^(5/2))","B",0
150,1,188,0,0.623698," ","integrate((cos(x)*cot(x))^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)}{{\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}"," ",0,"(((cos(3/2*x) - cos(1/2*x) + sin(3/2*x) + sin(1/2*x))*cos(1/2*arctan2(sin(x), cos(x) - 1)) - (cos(3/2*x) - cos(1/2*x) - sin(3/2*x) - sin(1/2*x))*sin(1/2*arctan2(sin(x), cos(x) - 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) - ((cos(3/2*x) - cos(1/2*x) - sin(3/2*x) - sin(1/2*x))*cos(1/2*arctan2(sin(x), cos(x) - 1)) + (cos(3/2*x) - cos(1/2*x) + sin(3/2*x) + sin(1/2*x))*sin(1/2*arctan2(sin(x), cos(x) - 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))/((cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4))","B",0
151,1,314,0,0.542130," ","integrate((cos(x)*cot(x))^(3/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{9}{2} \, x\right) + 15 \, \sin\left(\frac{5}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{9}{2} \, x\right) - 15 \, \sin\left(\frac{5}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left({\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{9}{2} \, x\right) - 15 \, \sin\left(\frac{5}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{9}{2} \, x\right) + 15 \, \sin\left(\frac{5}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)}}{6 \, {\left(\cos\left(x\right)^{4} + \sin\left(x\right)^{4} + 2 \, {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)^{2} - 2 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"1/6*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)*(((cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) - sin(9/2*x) + 15*sin(5/2*x) - sin(3/2*x) - 15*sin(1/2*x))*cos(3/2*arctan2(sin(x), cos(x) - 1)) + (cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) + sin(9/2*x) - 15*sin(5/2*x) + sin(3/2*x) + 15*sin(1/2*x))*sin(3/2*arctan2(sin(x), cos(x) - 1)))*cos(3/2*arctan2(sin(x), cos(x) + 1)) + ((cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) + sin(9/2*x) - 15*sin(5/2*x) + sin(3/2*x) + 15*sin(1/2*x))*cos(3/2*arctan2(sin(x), cos(x) - 1)) - (cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) - sin(9/2*x) + 15*sin(5/2*x) - sin(3/2*x) - 15*sin(1/2*x))*sin(3/2*arctan2(sin(x), cos(x) - 1)))*sin(3/2*arctan2(sin(x), cos(x) + 1)))/(cos(x)^4 + sin(x)^4 + 2*(cos(x)^2 + 1)*sin(x)^2 - 2*cos(x)^2 + 1)","B",0
152,1,427,0,0.626691," ","integrate((cos(x)*cot(x))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) + 3 \, \sin\left(\frac{15}{2} \, x\right) + 105 \, \sin\left(\frac{11}{2} \, x\right) - 410 \, \sin\left(\frac{7}{2} \, x\right) + 3 \, \sin\left(\frac{5}{2} \, x\right) + 410 \, \sin\left(\frac{3}{2} \, x\right) + 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) - 3 \, \sin\left(\frac{15}{2} \, x\right) - 105 \, \sin\left(\frac{11}{2} \, x\right) + 410 \, \sin\left(\frac{7}{2} \, x\right) - 3 \, \sin\left(\frac{5}{2} \, x\right) - 410 \, \sin\left(\frac{3}{2} \, x\right) - 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) - 3 \, \sin\left(\frac{15}{2} \, x\right) - 105 \, \sin\left(\frac{11}{2} \, x\right) + 410 \, \sin\left(\frac{7}{2} \, x\right) - 3 \, \sin\left(\frac{5}{2} \, x\right) - 410 \, \sin\left(\frac{3}{2} \, x\right) - 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) + 3 \, \sin\left(\frac{15}{2} \, x\right) + 105 \, \sin\left(\frac{11}{2} \, x\right) - 410 \, \sin\left(\frac{7}{2} \, x\right) + 3 \, \sin\left(\frac{5}{2} \, x\right) + 410 \, \sin\left(\frac{3}{2} \, x\right) + 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)}{60 \, {\left(\cos\left(x\right)^{4} + \sin\left(x\right)^{4} + 2 \, {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)^{2} - 2 \, \cos\left(x\right)^{2} + 1\right)} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}"," ",0,"-1/60*(((3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) + 3*sin(15/2*x) + 105*sin(11/2*x) - 410*sin(7/2*x) + 3*sin(5/2*x) + 410*sin(3/2*x) + 105*sin(1/2*x))*cos(5/2*arctan2(sin(x), cos(x) - 1)) - (3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) - 3*sin(15/2*x) - 105*sin(11/2*x) + 410*sin(7/2*x) - 3*sin(5/2*x) - 410*sin(3/2*x) - 105*sin(1/2*x))*sin(5/2*arctan2(sin(x), cos(x) - 1)))*cos(5/2*arctan2(sin(x), cos(x) + 1)) - ((3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) - 3*sin(15/2*x) - 105*sin(11/2*x) + 410*sin(7/2*x) - 3*sin(5/2*x) - 410*sin(3/2*x) - 105*sin(1/2*x))*cos(5/2*arctan2(sin(x), cos(x) - 1)) + (3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) + 3*sin(15/2*x) + 105*sin(11/2*x) - 410*sin(7/2*x) + 3*sin(5/2*x) + 410*sin(3/2*x) + 105*sin(1/2*x))*sin(5/2*arctan2(sin(x), cos(x) - 1)))*sin(5/2*arctan2(sin(x), cos(x) + 1)))/((cos(x)^4 + sin(x)^4 + 2*(cos(x)^2 + 1)*sin(x)^2 - 2*cos(x)^2 + 1)*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4))","B",0
153,-2,0,0,0.000000," ","integrate(x*cos(x)/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
154,-2,0,0,0.000000," ","integrate(x*cos(x)/(a+b*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
155,-2,0,0,0.000000," ","integrate(x*sin(x)/(a+b*cos(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
156,-2,0,0,0.000000," ","integrate(x*sin(x)/(a+b*cos(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
157,1,250,0,0.354980," ","integrate(x*sec(x)^2/(a+b*tan(x))^2,x, algorithm=""maxima"")","-\frac{8 \, a b x \cos\left(2 \, x\right) - 4 \, {\left(a^{2} - b^{2}\right)} x \sin\left(2 \, x\right) - {\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, a b \sin\left(2 \, x\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, x\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, x\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, a b \sin\left(2 \, x\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, x\right)^{2} + a^{2} + b^{2} + 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, x\right)}{a^{2} + b^{2}}\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, x\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(a^{4} - b^{4}\right)} \cos\left(2 \, x\right) + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, x\right)\right)}}"," ",0,"-1/2*(8*a*b*x*cos(2*x) - 4*(a^2 - b^2)*x*sin(2*x) - ((a^2 + b^2)*cos(2*x)^2 + 4*a*b*sin(2*x) + (a^2 + b^2)*sin(2*x)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*x))*log(((a^2 + b^2)*cos(2*x)^2 + 4*a*b*sin(2*x) + (a^2 + b^2)*sin(2*x)^2 + a^2 + b^2 + 2*(a^2 - b^2)*cos(2*x))/(a^2 + b^2)))/(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*x)^2 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*x)^2 + 2*(a^4 - b^4)*cos(2*x) + 4*(a^3*b + a*b^3)*sin(2*x))","B",0
158,1,250,0,0.329141," ","integrate(x*csc(x)^2/(a+b*cot(x))^2,x, algorithm=""maxima"")","-\frac{8 \, a b x \cos\left(2 \, x\right) + 4 \, {\left(a^{2} - b^{2}\right)} x \sin\left(2 \, x\right) - {\left({\left(a^{2} + b^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, a b \sin\left(2 \, x\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, x\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, x\right)\right)} \log\left(\frac{{\left(a^{2} + b^{2}\right)} \cos\left(2 \, x\right)^{2} + 4 \, a b \sin\left(2 \, x\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, x\right)^{2} + a^{2} + b^{2} - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(2 \, x\right)}{a^{2} + b^{2}}\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, x\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, x\right)^{2} - 2 \, {\left(a^{4} - b^{4}\right)} \cos\left(2 \, x\right) + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, x\right)\right)}}"," ",0,"-1/2*(8*a*b*x*cos(2*x) + 4*(a^2 - b^2)*x*sin(2*x) - ((a^2 + b^2)*cos(2*x)^2 + 4*a*b*sin(2*x) + (a^2 + b^2)*sin(2*x)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*x))*log(((a^2 + b^2)*cos(2*x)^2 + 4*a*b*sin(2*x) + (a^2 + b^2)*sin(2*x)^2 + a^2 + b^2 - 2*(a^2 - b^2)*cos(2*x))/(a^2 + b^2)))/(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*x)^2 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*x)^2 - 2*(a^4 - b^4)*cos(2*x) + 4*(a^3*b + a*b^3)*sin(2*x))","B",0
159,1,23,0,0.431756," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} d}"," ",0,"arctan(b*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*d)","A",0
160,0,0,0,0.000000," ","integrate(x*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\int \frac{x \sec\left(d x + c\right)^{2}}{b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x*sec(d*x + c)^2/(b*tan(d*x + c)^2 + a), x)","F",0
161,0,0,0,0.000000," ","integrate(x^2*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\int \frac{x^{2} \sec\left(d x + c\right)^{2}}{b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x^2*sec(d*x + c)^2/(b*tan(d*x + c)^2 + a), x)","F",0
162,1,43,0,1.069035," ","integrate(sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{{\left(b + c\right)} \tan\left(d x + c\right)}{\sqrt{a b + {\left(a + b\right)} c + c^{2}}}\right)}{\sqrt{a b + {\left(a + b\right)} c + c^{2}} d}"," ",0,"arctan((b + c)*tan(d*x + c)/sqrt(a*b + (a + b)*c + c^2))/(sqrt(a*b + (a + b)*c + c^2)*d)","A",0
163,0,0,0,0.000000," ","integrate(x*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\int \frac{x \sec\left(d x + c\right)^{2}}{c \sec\left(d x + c\right)^{2} + b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x*sec(d*x + c)^2/(c*sec(d*x + c)^2 + b*tan(d*x + c)^2 + a), x)","F",0
164,0,0,0,0.000000," ","integrate(x^2*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""maxima"")","\int \frac{x^{2} \sec\left(d x + c\right)^{2}}{c \sec\left(d x + c\right)^{2} + b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x^2*sec(d*x + c)^2/(c*sec(d*x + c)^2 + b*tan(d*x + c)^2 + a), x)","F",0
165,0,0,0,0.000000," ","integrate(x^3*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c} x^{3}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)*x^3, x)","F",0
166,0,0,0,0.000000," ","integrate(x^2*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c} x^{2}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)*x^2, x)","F",0
167,0,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c} x\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)*x, x)","F",0
168,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c}}{x}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)/x, x)","F",0
169,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)/x^2, x)","F",0
170,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} \sqrt{c \sin\left(f x + e\right) + c}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*sqrt(c*sin(f*x + e) + c)/x^3, x)","F",0
171,0,0,0,0.000000," ","integrate(x^3*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} x^{3}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^(3/2)*x^3, x)","F",0
172,0,0,0,0.000000," ","integrate(x^2*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^(3/2)*x^2, x)","F",0
173,0,0,0,0.000000," ","integrate(x*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^(3/2)*x, x)","F",0
174,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^(3/2)/x, x)","F",0
175,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^(3/2)/x^2, x)","F",0
176,0,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^(3/2)/x^3, x)","F",0
177,0,0,0,0.000000," ","integrate((h*x+g)^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(h x + g\right)}^{3} \sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((h*x + g)^3*sqrt(-a*sin(f*x + e) + a)/sqrt(c*sin(f*x + e) + c), x)","F",0
178,0,0,0,0.000000," ","integrate((h*x+g)^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(h x + g\right)}^{2} \sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((h*x + g)^2*sqrt(-a*sin(f*x + e) + a)/sqrt(c*sin(f*x + e) + c), x)","F",0
179,0,0,0,0.000000," ","integrate((h*x+g)*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(h x + g\right)} \sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((h*x + g)*sqrt(-a*sin(f*x + e) + a)/sqrt(c*sin(f*x + e) + c), x)","F",0
180,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)/(h*x+g)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a}}{{\left(h x + g\right)} \sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)/((h*x + g)*sqrt(c*sin(f*x + e) + c)), x)","F",0
181,0,0,0,0.000000," ","integrate(x^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} x^{3}}{{\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*x^3/(c*sin(f*x + e) + c)^(3/2), x)","F",0
182,0,0,0,0.000000," ","integrate(x^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} x^{2}}{{\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*x^2/(c*sin(f*x + e) + c)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} x}{{\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*x/(c*sin(f*x + e) + c)^(3/2), x)","F",0
184,1,56,0,0.494111," ","integrate(z^2*(1+cos(z))^(1/2)/(1-cos(z))^(1/2),z, algorithm=""maxima"")","\frac{1}{3} i \, z^{3} + 2 i \, z^{2} \arctan\left(\sin\left(z\right), -\cos\left(z\right) + 1\right) - z^{2} \log\left(\cos\left(z\right)^{2} + \sin\left(z\right)^{2} - 2 \, \cos\left(z\right) + 1\right) + 4 i \, z {\rm Li}_2\left(e^{\left(i \, z\right)}\right) - 4 \, {\rm Li}_{3}(e^{\left(i \, z\right)})"," ",0,"1/3*I*z^3 + 2*I*z^2*arctan2(sin(z), -cos(z) + 1) - z^2*log(cos(z)^2 + sin(z)^2 - 2*cos(z) + 1) + 4*I*z*dilog(e^(I*z)) - 4*polylog(3, e^(I*z))","A",0
185,1,23,0,0.307462," ","integrate((a+a*cos(x))*(A+B*sec(x)),x, algorithm=""maxima"")","A a x + B a x + B a \log\left(\sec\left(x\right) + \tan\left(x\right)\right) + A a \sin\left(x\right)"," ",0,"A*a*x + B*a*x + B*a*log(sec(x) + tan(x)) + A*a*sin(x)","A",0
186,1,54,0,0.319240," ","integrate((a+a*cos(x))^2*(A+B*sec(x)),x, algorithm=""maxima"")","\frac{1}{4} \, A a^{2} {\left(2 \, x + \sin\left(2 \, x\right)\right)} + A a^{2} x + 2 \, B a^{2} x + B a^{2} \log\left(\sec\left(x\right) + \tan\left(x\right)\right) + 2 \, A a^{2} \sin\left(x\right) + B a^{2} \sin\left(x\right)"," ",0,"1/4*A*a^2*(2*x + sin(2*x)) + A*a^2*x + 2*B*a^2*x + B*a^2*log(sec(x) + tan(x)) + 2*A*a^2*sin(x) + B*a^2*sin(x)","A",0
187,1,84,0,0.314159," ","integrate((a+a*cos(x))^3*(A+B*sec(x)),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\sin\left(x\right)^{3} - 3 \, \sin\left(x\right)\right)} A a^{3} + \frac{3}{4} \, A a^{3} {\left(2 \, x + \sin\left(2 \, x\right)\right)} + \frac{1}{4} \, B a^{3} {\left(2 \, x + \sin\left(2 \, x\right)\right)} + A a^{3} x + 3 \, B a^{3} x + B a^{3} \log\left(\sec\left(x\right) + \tan\left(x\right)\right) + 3 \, A a^{3} \sin\left(x\right) + 3 \, B a^{3} \sin\left(x\right)"," ",0,"-1/3*(sin(x)^3 - 3*sin(x))*A*a^3 + 3/4*A*a^3*(2*x + sin(2*x)) + 1/4*B*a^3*(2*x + sin(2*x)) + A*a^3*x + 3*B*a^3*x + B*a^3*log(sec(x) + tan(x)) + 3*A*a^3*sin(x) + 3*B*a^3*sin(x)","A",0
188,1,118,0,0.310410," ","integrate((a+a*cos(x))^4*(A+B*sec(x)),x, algorithm=""maxima"")","-\frac{4}{3} \, {\left(\sin\left(x\right)^{3} - 3 \, \sin\left(x\right)\right)} A a^{4} - \frac{1}{3} \, {\left(\sin\left(x\right)^{3} - 3 \, \sin\left(x\right)\right)} B a^{4} + \frac{1}{32} \, A a^{4} {\left(12 \, x + \sin\left(4 \, x\right) + 8 \, \sin\left(2 \, x\right)\right)} + \frac{3}{2} \, A a^{4} {\left(2 \, x + \sin\left(2 \, x\right)\right)} + B a^{4} {\left(2 \, x + \sin\left(2 \, x\right)\right)} + A a^{4} x + 4 \, B a^{4} x + B a^{4} \log\left(\sec\left(x\right) + \tan\left(x\right)\right) + 4 \, A a^{4} \sin\left(x\right) + 6 \, B a^{4} \sin\left(x\right)"," ",0,"-4/3*(sin(x)^3 - 3*sin(x))*A*a^4 - 1/3*(sin(x)^3 - 3*sin(x))*B*a^4 + 1/32*A*a^4*(12*x + sin(4*x) + 8*sin(2*x)) + 3/2*A*a^4*(2*x + sin(2*x)) + B*a^4*(2*x + sin(2*x)) + A*a^4*x + 4*B*a^4*x + B*a^4*log(sec(x) + tan(x)) + 4*A*a^4*sin(x) + 6*B*a^4*sin(x)","A",0
189,1,63,0,0.423312," ","integrate((A+B*sec(x))/(a+a*cos(x)),x, algorithm=""maxima"")","B {\left(\frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{a} - \frac{\sin\left(x\right)}{a {\left(\cos\left(x\right) + 1\right)}}\right)} + \frac{A \sin\left(x\right)}{a {\left(\cos\left(x\right) + 1\right)}}"," ",0,"B*(log(sin(x)/(cos(x) + 1) + 1)/a - log(sin(x)/(cos(x) + 1) - 1)/a - sin(x)/(a*(cos(x) + 1))) + A*sin(x)/(a*(cos(x) + 1))","B",0
190,1,93,0,0.462883," ","integrate((A+B*sec(x))/(a+a*cos(x))^2,x, algorithm=""maxima"")","-\frac{1}{6} \, B {\left(\frac{\frac{9 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{2}} - \frac{6 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{a^{2}} + \frac{6 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{a^{2}}\right)} + \frac{A {\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{6 \, a^{2}}"," ",0,"-1/6*B*((9*sin(x)/(cos(x) + 1) + sin(x)^3/(cos(x) + 1)^3)/a^2 - 6*log(sin(x)/(cos(x) + 1) + 1)/a^2 + 6*log(sin(x)/(cos(x) + 1) - 1)/a^2) + 1/6*A*(3*sin(x)/(cos(x) + 1) + sin(x)^3/(cos(x) + 1)^3)/a^2","B",0
191,1,119,0,0.638623," ","integrate((A+B*sec(x))/(a+a*cos(x))^3,x, algorithm=""maxima"")","-\frac{1}{60} \, B {\left(\frac{\frac{105 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{20 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{a^{3}} + \frac{60 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{a^{3}}\right)} + \frac{A {\left(\frac{15 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{10 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}\right)}}{60 \, a^{3}}"," ",0,"-1/60*B*((105*sin(x)/(cos(x) + 1) + 20*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^5/(cos(x) + 1)^5)/a^3 - 60*log(sin(x)/(cos(x) + 1) + 1)/a^3 + 60*log(sin(x)/(cos(x) + 1) - 1)/a^3) + 1/60*A*(15*sin(x)/(cos(x) + 1) + 10*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^5/(cos(x) + 1)^5)/a^3","A",0
192,1,143,0,0.770931," ","integrate((A+B*sec(x))/(a+a*cos(x))^4,x, algorithm=""maxima"")","-\frac{1}{168} \, B {\left(\frac{\frac{315 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{77 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}}{a^{4}} - \frac{168 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{a^{4}} + \frac{168 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{a^{4}}\right)} + \frac{A {\left(\frac{35 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{35 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}}{280 \, a^{4}}"," ",0,"-1/168*B*((315*sin(x)/(cos(x) + 1) + 77*sin(x)^3/(cos(x) + 1)^3 + 21*sin(x)^5/(cos(x) + 1)^5 + 3*sin(x)^7/(cos(x) + 1)^7)/a^4 - 168*log(sin(x)/(cos(x) + 1) + 1)/a^4 + 168*log(sin(x)/(cos(x) + 1) - 1)/a^4) + 1/280*A*(35*sin(x)/(cos(x) + 1) + 35*sin(x)^3/(cos(x) + 1)^3 + 21*sin(x)^5/(cos(x) + 1)^5 + 5*sin(x)^7/(cos(x) + 1)^7)/a^4","A",0
193,1,43,0,1.119036," ","integrate((a+a*cos(x))^(5/2)*(A+B*sec(x)),x, algorithm=""maxima"")","\frac{1}{30} \, {\left(3 \, \sqrt{2} a^{2} \sin\left(\frac{5}{2} \, x\right) + 25 \, \sqrt{2} a^{2} \sin\left(\frac{3}{2} \, x\right) + 150 \, \sqrt{2} a^{2} \sin\left(\frac{1}{2} \, x\right)\right)} A \sqrt{a}"," ",0,"1/30*(3*sqrt(2)*a^2*sin(5/2*x) + 25*sqrt(2)*a^2*sin(3/2*x) + 150*sqrt(2)*a^2*sin(1/2*x))*A*sqrt(a)","A",0
194,1,26,0,1.105303," ","integrate((a+a*cos(x))^(3/2)*(A+B*sec(x)),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\sqrt{2} a \sin\left(\frac{3}{2} \, x\right) + 9 \, \sqrt{2} a \sin\left(\frac{1}{2} \, x\right)\right)} A \sqrt{a}"," ",0,"1/3*(sqrt(2)*a*sin(3/2*x) + 9*sqrt(2)*a*sin(1/2*x))*A*sqrt(a)","A",0
195,1,13,0,0.469975," ","integrate((a+a*cos(x))^(1/2)*(A+B*sec(x)),x, algorithm=""maxima"")","2 \, \sqrt{2} A \sqrt{a} \sin\left(\frac{1}{2} \, x\right)"," ",0,"2*sqrt(2)*A*sqrt(a)*sin(1/2*x)","A",0
196,1,58,0,1.053172," ","integrate((A+B*sec(x))/(a+a*cos(x))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, x\right)^{2} + \sin\left(\frac{1}{2} \, x\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, x\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, x\right)^{2} + \sin\left(\frac{1}{2} \, x\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, x\right) + 1\right)\right)} A}{2 \, \sqrt{a}}"," ",0,"1/2*(sqrt(2)*log(cos(1/2*x)^2 + sin(1/2*x)^2 + 2*sin(1/2*x) + 1) - sqrt(2)*log(cos(1/2*x)^2 + sin(1/2*x)^2 - 2*sin(1/2*x) + 1))*A/sqrt(a)","A",0
197,-1,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate((A+B*sec(x))/(a+a*cos(x))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-2,0,0,0.000000," ","integrate(x*(b+a*sin(x))/(a+b*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
200,-2,0,0,0.000000," ","integrate(x*(b+a*cos(x))/(a+b*cos(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
201,1,8,0,0.439303," ","integrate((1+sin(x)^2)/(1-sin(x)^2),x, algorithm=""maxima"")","-x + 2 \, \tan\left(x\right)"," ",0,"-x + 2*tan(x)","A",0
202,1,15,0,0.551489," ","integrate((1-sin(x)^2)/(1+sin(x)^2),x, algorithm=""maxima"")","\sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) - x"," ",0,"sqrt(2)*arctan(sqrt(2)*tan(x)) - x","A",0
203,1,10,0,0.773206," ","integrate((1+cos(x)^2)/(1-cos(x)^2),x, algorithm=""maxima"")","-x - \frac{2}{\tan\left(x\right)}"," ",0,"-x - 2/tan(x)","A",0
204,1,16,0,0.423393," ","integrate((1-cos(x)^2)/(1+cos(x)^2),x, algorithm=""maxima"")","\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - x"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - x","A",0
205,-2,0,0,0.000000," ","integrate((-1+c^2/d^2+sin(x)^2)/(c+d*cos(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
206,-2,0,0,0.000000," ","integrate((a+b*sin(x)^2)/(c+d*cos(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
207,1,29,0,0.423484," ","integrate((a+b*sin(x)^2)/(c+c*cos(x)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(a + 2 \, b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right)}{2 \, c} - \frac{b x}{c}"," ",0,"1/2*sqrt(2)*(a + 2*b)*arctan(1/2*sqrt(2)*tan(x))/c - b*x/c","A",0
208,1,17,0,0.420155," ","integrate((a+b*sin(x)^2)/(c-c*cos(x)^2),x, algorithm=""maxima"")","\frac{b x}{c} - \frac{a}{c \tan\left(x\right)}"," ",0,"b*x/c - a/(c*tan(x))","A",0
209,1,40,0,1.339525," ","integrate((a+b*sin(x)^2)/(c+d*cos(x)^2),x, algorithm=""maxima"")","-\frac{b x}{d} + \frac{{\left(b c + {\left(a + b\right)} d\right)} \arctan\left(\frac{c \tan\left(x\right)}{\sqrt{{\left(c + d\right)} c}}\right)}{\sqrt{{\left(c + d\right)} c} d}"," ",0,"-b*x/d + (b*c + (a + b)*d)*arctan(c*tan(x)/sqrt((c + d)*c))/(sqrt((c + d)*c)*d)","A",0
210,-2,0,0,0.000000," ","integrate((-1+c^2/d^2+cos(x)^2)/(c+d*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
211,-2,0,0,0.000000," ","integrate((a+b*cos(x)^2)/(c+d*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
212,1,28,0,0.432728," ","integrate((a+b*cos(x)^2)/(c+c*sin(x)^2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(a + 2 \, b\right)} \arctan\left(\sqrt{2} \tan\left(x\right)\right)}{2 \, c} - \frac{b x}{c}"," ",0,"1/2*sqrt(2)*(a + 2*b)*arctan(sqrt(2)*tan(x))/c - b*x/c","A",0
213,1,14,0,0.429490," ","integrate((a+b*cos(x)^2)/(c-c*sin(x)^2),x, algorithm=""maxima"")","\frac{b x}{c} + \frac{a \tan\left(x\right)}{c}"," ",0,"b*x/c + a*tan(x)/c","A",0
214,1,42,0,0.428967," ","integrate((a+b*cos(x)^2)/(c+d*sin(x)^2),x, algorithm=""maxima"")","-\frac{b x}{d} + \frac{{\left(b c + {\left(a + b\right)} d\right)} \arctan\left(\frac{{\left(c + d\right)} \tan\left(x\right)}{\sqrt{{\left(c + d\right)} c}}\right)}{\sqrt{{\left(c + d\right)} c} d}"," ",0,"-b*x/d + (b*c + (a + b)*d)*arctan((c + d)*tan(x)/sqrt((c + d)*c))/(sqrt((c + d)*c)*d)","A",0
215,-2,0,0,0.000000," ","integrate((a+b*sec(x)^2)/(c+d*cos(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
216,-2,0,0,0.000000," ","integrate((a+b*csc(x)^2)/(c+d*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
217,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{n}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^n, x)","F",0
218,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^n,x, algorithm=""maxima"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{n}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^n, x)","F",0
219,1,257,0,0.329872," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^7,x, algorithm=""maxima"")","-\frac{35 \, a^{6} b \cos\left(d x + c\right)^{7} - 35 \, a b^{6} \sin\left(d x + c\right)^{7} + {\left(5 \, \sin\left(d x + c\right)^{7} - 21 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3} - 35 \, \sin\left(d x + c\right)\right)} a^{7} - 7 \, {\left(15 \, \sin\left(d x + c\right)^{7} - 42 \, \sin\left(d x + c\right)^{5} + 35 \, \sin\left(d x + c\right)^{3}\right)} a^{5} b^{2} - 35 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{4} b^{3} + 35 \, {\left(5 \, \sin\left(d x + c\right)^{7} - 7 \, \sin\left(d x + c\right)^{5}\right)} a^{3} b^{4} + 7 \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} a^{2} b^{5} - {\left(5 \, \cos\left(d x + c\right)^{7} - 21 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)\right)} b^{7}}{35 \, d}"," ",0,"-1/35*(35*a^6*b*cos(d*x + c)^7 - 35*a*b^6*sin(d*x + c)^7 + (5*sin(d*x + c)^7 - 21*sin(d*x + c)^5 + 35*sin(d*x + c)^3 - 35*sin(d*x + c))*a^7 - 7*(15*sin(d*x + c)^7 - 42*sin(d*x + c)^5 + 35*sin(d*x + c)^3)*a^5*b^2 - 35*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^4*b^3 + 35*(5*sin(d*x + c)^7 - 7*sin(d*x + c)^5)*a^3*b^4 + 7*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^2*b^5 - (5*cos(d*x + c)^7 - 21*cos(d*x + c)^5 + 35*cos(d*x + c)^3 - 35*cos(d*x + c))*b^7)/d","B",0
220,1,238,0,0.329809," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^6,x, algorithm=""maxima"")","-\frac{192 \, a^{5} b \cos\left(d x + c\right)^{6} - 192 \, a b^{5} \sin\left(d x + c\right)^{6} + {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{6} - 15 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} b^{2} + 320 \, {\left(2 \, \sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4}\right)} a^{3} b^{3} + 15 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b^{4} - {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{6}}{192 \, d}"," ",0,"-1/192*(192*a^5*b*cos(d*x + c)^6 - 192*a*b^5*sin(d*x + c)^6 + (4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^6 - 15*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^4*b^2 + 320*(2*sin(d*x + c)^6 - 3*sin(d*x + c)^4)*a^3*b^3 + 15*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^2*b^4 - (4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*b^6)/d","A",0
221,1,172,0,0.747514," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{a^{4} b \cos\left(d x + c\right)^{5}}{d} + \frac{a b^{4} \sin\left(d x + c\right)^{5}}{d} + \frac{{\left(3 \, \sin\left(d x + c\right)^{5} - 10 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)\right)} a^{5}}{15 \, d} - \frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{5} - 5 \, \sin\left(d x + c\right)^{3}\right)} a^{3} b^{2}}{3 \, d} + \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} b^{3}}{3 \, d} - \frac{{\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} b^{5}}{15 \, d}"," ",0,"-a^4*b*cos(d*x + c)^5/d + a*b^4*sin(d*x + c)^5/d + 1/15*(3*sin(d*x + c)^5 - 10*sin(d*x + c)^3 + 15*sin(d*x + c))*a^5/d - 2/3*(3*sin(d*x + c)^5 - 5*sin(d*x + c)^3)*a^3*b^2/d + 2/3*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2*b^3/d - 1/15*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*b^5/d","A",0
222,1,136,0,0.323067," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{a^{3} b \cos\left(d x + c\right)^{4}}{d} + \frac{a b^{3} \sin\left(d x + c\right)^{4}}{d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{32 \, d} + \frac{3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b^{2}}{16 \, d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{4}}{32 \, d}"," ",0,"-a^3*b*cos(d*x + c)^4/d + a*b^3*sin(d*x + c)^4/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4/d + 3/16*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2*b^2/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*b^4/d","A",0
223,1,84,0,0.309583," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{2} b \cos\left(d x + c\right)^{3}}{d} + \frac{a b^{2} \sin\left(d x + c\right)^{3}}{d} - \frac{{\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3}}{3 \, d} + \frac{{\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} b^{3}}{3 \, d}"," ",0,"-a^2*b*cos(d*x + c)^3/d + a*b^2*sin(d*x + c)^3/d - 1/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3/d + 1/3*(cos(d*x + c)^3 - 3*cos(d*x + c))*b^3/d","A",0
224,1,68,0,0.474006," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b \cos\left(d x + c\right)^{2}}{d} + \frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d} + \frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2}}{4 \, d}"," ",0,"-a*b*cos(d*x + c)^2/d + 1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2/d + 1/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*b^2/d","A",0
225,1,24,0,0.401259," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x, algorithm=""maxima"")","-\frac{b \cos\left(d x + c\right)}{d} + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"-b*cos(d*x + c)/d + a*sin(d*x + c)/d","A",0
226,1,80,0,0.682055," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} d}"," ",0,"-log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*d)","A",0
227,1,21,0,0.523029," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(b^{2} \tan\left(d x + c\right) + a b\right)} d}"," ",0,"-1/((b^2*tan(d*x + c) + a*b)*d)","A",0
228,1,326,0,0.463013," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} b - \frac{{\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{6} + a^{4} b^{2} + \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, {\left(a^{6} - a^{4} b^{2} - 2 \, a^{2} b^{4}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{5} b + a^{3} b^{3}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(a^{6} + a^{4} b^{2}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}}}{2 \, d}"," ",0,"-1/2*(2*(a^2*b - (a^3 - 2*a*b^2)*sin(d*x + c)/(cos(d*x + c) + 1) - (a^2*b - 2*b^3)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (a^3 + 2*a*b^2)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/(a^6 + a^4*b^2 + 4*(a^5*b + a^3*b^3)*sin(d*x + c)/(cos(d*x + c) + 1) - 2*(a^6 - a^4*b^2 - 2*a^2*b^4)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*(a^5*b + a^3*b^3)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (a^6 + a^4*b^2)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2))/d","B",0
229,1,85,0,0.338490," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, b^{2} \tan\left(d x + c\right)^{2} + 3 \, a b \tan\left(d x + c\right) + a^{2} + b^{2}}{3 \, {\left(b^{6} \tan\left(d x + c\right)^{3} + 3 \, a b^{5} \tan\left(d x + c\right)^{2} + 3 \, a^{2} b^{4} \tan\left(d x + c\right) + a^{3} b^{3}\right)} d}"," ",0,"-1/3*(3*b^2*tan(d*x + c)^2 + 3*a*b*tan(d*x + c) + a^2 + b^2)/((b^6*tan(d*x + c)^3 + 3*a*b^5*tan(d*x + c)^2 + 3*a^2*b^4*tan(d*x + c) + a^3*b^3)*d)","A",0
230,1,822,0,1.037570," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(5 \, a^{6} b + 2 \, a^{4} b^{3} - \frac{{\left(5 \, a^{7} - 24 \, a^{5} b^{2} - 8 \, a^{3} b^{4}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{{\left(23 \, a^{6} b - 64 \, a^{4} b^{3} - 24 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{{\left(3 \, a^{7} + 84 \, a^{5} b^{2} - 56 \, a^{3} b^{4} - 32 \, a b^{6}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{{\left(15 \, a^{6} b - 114 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 16 \, b^{7}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{{\left(3 \, a^{7} - 36 \, a^{5} b^{2} + 56 \, a^{3} b^{4} + 32 \, a b^{6}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, {\left(a^{6} b + 16 \, a^{4} b^{3} + 8 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{{\left(5 \, a^{7} + 16 \, a^{5} b^{2} + 8 \, a^{3} b^{4}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}\right)}}{a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4} + \frac{8 \, {\left(a^{11} b + 2 \, a^{9} b^{3} + a^{7} b^{5}\right)} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{4 \, {\left(a^{12} - 4 \, a^{10} b^{2} - 11 \, a^{8} b^{4} - 6 \, a^{6} b^{6}\right)} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, {\left(3 \, a^{11} b + 2 \, a^{9} b^{3} - 5 \, a^{7} b^{5} - 4 \, a^{5} b^{7}\right)} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, {\left(3 \, a^{12} - 18 \, a^{10} b^{2} - 37 \, a^{8} b^{4} - 8 \, a^{6} b^{6} + 8 \, a^{4} b^{8}\right)} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{8 \, {\left(3 \, a^{11} b + 2 \, a^{9} b^{3} - 5 \, a^{7} b^{5} - 4 \, a^{5} b^{7}\right)} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{4 \, {\left(a^{12} - 4 \, a^{10} b^{2} - 11 \, a^{8} b^{4} - 6 \, a^{6} b^{6}\right)} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{8 \, {\left(a^{11} b + 2 \, a^{9} b^{3} + a^{7} b^{5}\right)} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{{\left(a^{12} + 2 \, a^{10} b^{2} + a^{8} b^{4}\right)} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{3 \, \log\left(\frac{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \sqrt{a^{2} + b^{2}}}{b - \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}}}{8 \, d}"," ",0,"-1/8*(2*(5*a^6*b + 2*a^4*b^3 - (5*a^7 - 24*a^5*b^2 - 8*a^3*b^4)*sin(d*x + c)/(cos(d*x + c) + 1) - (23*a^6*b - 64*a^4*b^3 - 24*a^2*b^5)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - (3*a^7 + 84*a^5*b^2 - 56*a^3*b^4 - 32*a*b^6)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + (15*a^6*b - 114*a^4*b^3 - 8*a^2*b^5 + 16*b^7)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - (3*a^7 - 36*a^5*b^2 + 56*a^3*b^4 + 32*a*b^6)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*(a^6*b + 16*a^4*b^3 + 8*a^2*b^5)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - (5*a^7 + 16*a^5*b^2 + 8*a^3*b^4)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^12 + 2*a^10*b^2 + a^8*b^4 + 8*(a^11*b + 2*a^9*b^3 + a^7*b^5)*sin(d*x + c)/(cos(d*x + c) + 1) - 4*(a^12 - 4*a^10*b^2 - 11*a^8*b^4 - 6*a^6*b^6)*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*(3*a^11*b + 2*a^9*b^3 - 5*a^7*b^5 - 4*a^5*b^7)*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*(3*a^12 - 18*a^10*b^2 - 37*a^8*b^4 - 8*a^6*b^6 + 8*a^4*b^8)*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 8*(3*a^11*b + 2*a^9*b^3 - 5*a^7*b^5 - 4*a^5*b^7)*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 4*(a^12 - 4*a^10*b^2 - 11*a^8*b^4 - 6*a^6*b^6)*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 8*(a^11*b + 2*a^9*b^3 + a^7*b^5)*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + (a^12 + 2*a^10*b^2 + a^8*b^4)*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 3*log((b - a*sin(d*x + c)/(cos(d*x + c) + 1) + sqrt(a^2 + b^2))/(b - a*sin(d*x + c)/(cos(d*x + c) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)))/d","B",0
231,1,174,0,0.790281," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^6,x, algorithm=""maxima"")","-\frac{15 \, b^{4} \tan\left(d x + c\right)^{4} + 30 \, a b^{3} \tan\left(d x + c\right)^{3} + 3 \, a^{4} + a^{2} b^{2} + 3 \, b^{4} + 10 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{2} + 5 \, {\left(3 \, a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)}{15 \, {\left(b^{10} \tan\left(d x + c\right)^{5} + 5 \, a b^{9} \tan\left(d x + c\right)^{4} + 10 \, a^{2} b^{8} \tan\left(d x + c\right)^{3} + 10 \, a^{3} b^{7} \tan\left(d x + c\right)^{2} + 5 \, a^{4} b^{6} \tan\left(d x + c\right) + a^{5} b^{5}\right)} d}"," ",0,"-1/15*(15*b^4*tan(d*x + c)^4 + 30*a*b^3*tan(d*x + c)^3 + 3*a^4 + a^2*b^2 + 3*b^4 + 10*(3*a^2*b^2 + b^4)*tan(d*x + c)^2 + 5*(3*a^3*b + a*b^3)*tan(d*x + c))/((b^10*tan(d*x + c)^5 + 5*a*b^9*tan(d*x + c)^4 + 10*a^2*b^8*tan(d*x + c)^3 + 10*a^3*b^7*tan(d*x + c)^2 + 5*a^4*b^6*tan(d*x + c) + a^5*b^5)*d)","A",0
232,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(7/2), x)","F",0
233,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(5/2), x)","F",0
234,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(3/2), x)","F",0
235,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(-3/2), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(-5/2), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(-7/2), x)","F",0
240,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(7/2), x)","F",0
241,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(5/2), x)","F",0
242,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(3/2), x)","F",0
243,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(-3/2), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(-5/2), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(-7/2), x)","F",0
248,1,59,0,0.424157," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n,x, algorithm=""maxima"")","-\frac{i \, a^{n} e^{\left(-n \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right) + n \log\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)\right)}}{d n}"," ",0,"-I*a^n*e^(-n*log(sin(d*x + c)/(cos(d*x + c) + 1) + I) + n*log(-sin(d*x + c)/(cos(d*x + c) + 1) + I))/(d*n)","B",0
249,1,132,0,0.461187," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{i \, a^{4} \cos\left(d x + c\right)^{4}}{d} - \frac{i \, a^{4} \sin\left(d x + c\right)^{4}}{d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{32 \, d} + \frac{{\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{32 \, d} - \frac{3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4}}{16 \, d}"," ",0,"-I*a^4*cos(d*x + c)^4/d - I*a^4*sin(d*x + c)^4/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4/d + 1/32*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a^4/d - 3/16*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^4/d","B",0
250,1,83,0,0.310828," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{i \, a^{3} \cos\left(d x + c\right)^{3}}{d} - \frac{a^{3} \sin\left(d x + c\right)^{3}}{d} - \frac{i \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{3}}{3 \, d} - \frac{{\left(\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)\right)} a^{3}}{3 \, d}"," ",0,"-I*a^3*cos(d*x + c)^3/d - a^3*sin(d*x + c)^3/d - 1/3*I*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^3/d - 1/3*(sin(d*x + c)^3 - 3*sin(d*x + c))*a^3/d","B",0
251,1,69,0,0.543525," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{i \, a^{2} \cos\left(d x + c\right)^{2}}{d} + \frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d} - \frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{4 \, d}"," ",0,"-I*a^2*cos(d*x + c)^2/d + 1/4*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2/d - 1/4*(2*d*x + 2*c - sin(2*d*x + 2*c))*a^2/d","B",0
252,1,24,0,1.119629," ","integrate(a*cos(d*x+c)+I*a*sin(d*x+c),x, algorithm=""maxima"")","-\frac{i \, a \cos\left(d x + c\right)}{d} + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"-I*a*cos(d*x + c)/d + a*sin(d*x + c)/d","A",0
253,1,29,0,0.322979," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2}{{\left(-i \, a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)} d}"," ",0,"2/((-I*a + a*sin(d*x + c)/(cos(d*x + c) + 1))*d)","A",0
254,1,22,0,0.328413," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{{\left(a^{2} \tan\left(d x + c\right) - i \, a^{2}\right)} d}"," ",0,"1/((a^2*tan(d*x + c) - I*a^2)*d)","A",0
255,1,29,0,0.628386," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{i \, \cos\left(3 \, d x + 3 \, c\right) + \sin\left(3 \, d x + 3 \, c\right)}{3 \, a^{3} d}"," ",0,"1/3*(I*cos(3*d*x + 3*c) + sin(3*d*x + 3*c))/(a^3*d)","A",0
256,1,29,0,0.565736," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{i \, \cos\left(4 \, d x + 4 \, c\right) + \sin\left(4 \, d x + 4 \, c\right)}{4 \, a^{4} d}"," ",0,"1/4*(I*cos(4*d*x + 4*c) + sin(4*d*x + 4*c))/(a^4*d)","A",0
257,1,51,0,0.693155," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, a^{\frac{5}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{5}{2}}}{5 \, d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{5}{2}}}"," ",0,"-2/5*I*a^(5/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + I)^(5/2)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + I)^(5/2))","B",0
258,1,51,0,0.902642," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, a^{\frac{3}{2}} {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{3}{2}}}{3 \, d {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{3}{2}}}"," ",0,"-2/3*I*a^(3/2)*(-sin(d*x + c)/(cos(d*x + c) + 1) + I)^(3/2)/(d*(sin(d*x + c)/(cos(d*x + c) + 1) + I)^(3/2))","B",0
259,1,51,0,0.844533," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, \sqrt{a} \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i}}{d \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i}}"," ",0,"-2*I*sqrt(a)*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + I)/(d*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + I))","B",0
260,1,51,0,0.429439," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i}}{\sqrt{a} d \sqrt{-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i}}"," ",0,"2*I*sqrt(sin(d*x + c)/(cos(d*x + c) + 1) + I)/(sqrt(a)*d*sqrt(-sin(d*x + c)/(cos(d*x + c) + 1) + I))","B",0
261,1,51,0,1.064380," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{3}{2}}}{3 \, a^{\frac{3}{2}} d {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{3}{2}}}"," ",0,"2/3*I*(sin(d*x + c)/(cos(d*x + c) + 1) + I)^(3/2)/(a^(3/2)*d*(-sin(d*x + c)/(cos(d*x + c) + 1) + I)^(3/2))","B",0
262,1,51,0,0.661533," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{5}{2}}}{5 \, a^{\frac{5}{2}} d {\left(-\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + i\right)}^{\frac{5}{2}}}"," ",0,"2/5*I*(sin(d*x + c)/(cos(d*x + c) + 1) + I)^(5/2)/(a^(5/2)*d*(-sin(d*x + c)/(cos(d*x + c) + 1) + I)^(5/2))","B",0
263,1,204,0,0.318314," ","integrate((a*sec(x)+b*tan(x))^5,x, algorithm=""maxima"")","\frac{5}{2} \, a^{2} b^{3} \tan\left(x\right)^{4} + \frac{5}{16} \, a b^{4} {\left(\frac{2 \, {\left(5 \, \sin\left(x\right)^{3} - 3 \, \sin\left(x\right)\right)}}{\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1} + 3 \, \log\left(\sin\left(x\right) + 1\right) - 3 \, \log\left(\sin\left(x\right) - 1\right)\right)} - \frac{1}{16} \, a^{5} {\left(\frac{2 \, {\left(3 \, \sin\left(x\right)^{3} - 5 \, \sin\left(x\right)\right)}}{\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1} - 3 \, \log\left(\sin\left(x\right) + 1\right) + 3 \, \log\left(\sin\left(x\right) - 1\right)\right)} + \frac{5}{8} \, a^{3} b^{2} {\left(\frac{2 \, {\left(\sin\left(x\right)^{3} + \sin\left(x\right)\right)}}{\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1} - \log\left(\sin\left(x\right) + 1\right) + \log\left(\sin\left(x\right) - 1\right)\right)} + \frac{1}{4} \, b^{5} {\left(\frac{4 \, \sin\left(x\right)^{2} - 3}{\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1} - 2 \, \log\left(\sin\left(x\right)^{2} - 1\right)\right)} + \frac{5 \, a^{4} b}{4 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2}}"," ",0,"5/2*a^2*b^3*tan(x)^4 + 5/16*a*b^4*(2*(5*sin(x)^3 - 3*sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) + 3*log(sin(x) + 1) - 3*log(sin(x) - 1)) - 1/16*a^5*(2*(3*sin(x)^3 - 5*sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) - 3*log(sin(x) + 1) + 3*log(sin(x) - 1)) + 5/8*a^3*b^2*(2*(sin(x)^3 + sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) - log(sin(x) + 1) + log(sin(x) - 1)) + 1/4*b^5*((4*sin(x)^2 - 3)/(sin(x)^4 - 2*sin(x)^2 + 1) - 2*log(sin(x)^2 - 1)) + 5/4*a^4*b/(sin(x)^2 - 1)^2","A",0
264,1,72,0,1.049013," ","integrate((a*sec(x)+b*tan(x))^4,x, algorithm=""maxima"")","2 \, a^{2} b^{2} \tan\left(x\right)^{3} + \frac{1}{3} \, {\left(\tan\left(x\right)^{3} + 3 \, \tan\left(x\right)\right)} a^{4} + \frac{1}{3} \, {\left(\tan\left(x\right)^{3} + 3 \, x - 3 \, \tan\left(x\right)\right)} b^{4} - \frac{4 \, {\left(3 \, \cos\left(x\right)^{2} - 1\right)} a b^{3}}{3 \, \cos\left(x\right)^{3}} + \frac{4 \, a^{3} b}{3 \, \cos\left(x\right)^{3}}"," ",0,"2*a^2*b^2*tan(x)^3 + 1/3*(tan(x)^3 + 3*tan(x))*a^4 + 1/3*(tan(x)^3 + 3*x - 3*tan(x))*b^4 - 4/3*(3*cos(x)^2 - 1)*a*b^3/cos(x)^3 + 4/3*a^3*b/cos(x)^3","A",0
265,1,95,0,0.352593," ","integrate((a*sec(x)+b*tan(x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, a^{2} b \tan\left(x\right)^{2} - \frac{3}{4} \, a b^{2} {\left(\frac{2 \, \sin\left(x\right)}{\sin\left(x\right)^{2} - 1} + \log\left(\sin\left(x\right) + 1\right) - \log\left(\sin\left(x\right) - 1\right)\right)} - \frac{1}{4} \, a^{3} {\left(\frac{2 \, \sin\left(x\right)}{\sin\left(x\right)^{2} - 1} - \log\left(\sin\left(x\right) + 1\right) + \log\left(\sin\left(x\right) - 1\right)\right)} - \frac{1}{2} \, b^{3} {\left(\frac{1}{\sin\left(x\right)^{2} - 1} - \log\left(\sin\left(x\right)^{2} - 1\right)\right)}"," ",0,"3/2*a^2*b*tan(x)^2 - 3/4*a*b^2*(2*sin(x)/(sin(x)^2 - 1) + log(sin(x) + 1) - log(sin(x) - 1)) - 1/4*a^3*(2*sin(x)/(sin(x)^2 - 1) - log(sin(x) + 1) + log(sin(x) - 1)) - 1/2*b^3*(1/(sin(x)^2 - 1) - log(sin(x)^2 - 1))","A",0
266,1,26,0,0.409669," ","integrate((a*sec(x)+b*tan(x))^2,x, algorithm=""maxima"")","-b^{2} {\left(x - \tan\left(x\right)\right)} + a^{2} \tan\left(x\right) + \frac{2 \, a b}{\cos\left(x\right)}"," ",0,"-b^2*(x - tan(x)) + a^2*tan(x) + 2*a*b/cos(x)","A",0
267,1,14,0,0.303126," ","integrate(a*sec(x)+b*tan(x),x, algorithm=""maxima"")","a \log\left(\sec\left(x\right) + \tan\left(x\right)\right) + b \log\left(\sec\left(x\right)\right)"," ",0,"a*log(sec(x) + tan(x)) + b*log(sec(x))","A",0
268,1,50,0,0.503914," ","integrate(1/(a*sec(x)+b*tan(x)),x, algorithm=""maxima"")","\frac{\log\left(a + \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b} - \frac{\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b}"," ",0,"log(a + 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/b - log(sin(x)^2/(cos(x) + 1)^2 + 1)/b","B",0
269,-2,0,0,0.000000," ","integrate(1/(a*sec(x)+b*tan(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
270,1,201,0,0.512515," ","integrate(1/(a*sec(x)+b*tan(x))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{{\left(a^{3} + a b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{{\left(3 \, a^{2} b + b^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(a^{3} + a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{a^{4} b^{2} + \frac{4 \, a^{3} b^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{4 \, a^{3} b^{3} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a^{4} b^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{2 \, {\left(a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}} - \frac{\log\left(a + \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{3}} + \frac{\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{3}}"," ",0,"2*((a^3 + a*b^2)*sin(x)/(cos(x) + 1) + (3*a^2*b + b^3)*sin(x)^2/(cos(x) + 1)^2 + (a^3 + a*b^2)*sin(x)^3/(cos(x) + 1)^3)/(a^4*b^2 + 4*a^3*b^3*sin(x)/(cos(x) + 1) + 4*a^3*b^3*sin(x)^3/(cos(x) + 1)^3 + a^4*b^2*sin(x)^4/(cos(x) + 1)^4 + 2*(a^4*b^2 + 2*a^2*b^4)*sin(x)^2/(cos(x) + 1)^2) - log(a + 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/b^3 + log(sin(x)^2/(cos(x) + 1)^2 + 1)/b^3","B",0
271,-2,0,0,0.000000," ","integrate(1/(a*sec(x)+b*tan(x))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
272,1,483,0,0.507438," ","integrate(1/(a*sec(x)+b*tan(x))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{3 \, {\left(a^{7} - a^{3} b^{4}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, {\left(7 \, a^{6} b - 3 \, a^{2} b^{5}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(9 \, a^{7} + 52 \, a^{5} b^{2} - a^{3} b^{4} - 12 \, a b^{6}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{2 \, {\left(21 \, a^{6} b + 25 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 3 \, b^{7}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{{\left(9 \, a^{7} + 52 \, a^{5} b^{2} - a^{3} b^{4} - 12 \, a b^{6}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{3 \, {\left(7 \, a^{6} b - 3 \, a^{2} b^{5}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{3 \, {\left(a^{7} - a^{3} b^{4}\right)} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}}{3 \, {\left(a^{8} b^{4} + \frac{8 \, a^{7} b^{5} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{8 \, a^{7} b^{5} \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{a^{8} b^{4} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{4 \, {\left(a^{8} b^{4} + 6 \, a^{6} b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{8 \, {\left(3 \, a^{7} b^{5} + 4 \, a^{5} b^{7}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{2 \, {\left(3 \, a^{8} b^{4} + 24 \, a^{6} b^{6} + 8 \, a^{4} b^{8}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{8 \, {\left(3 \, a^{7} b^{5} + 4 \, a^{5} b^{7}\right)} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{4 \, {\left(a^{8} b^{4} + 6 \, a^{6} b^{6}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}} + \frac{\log\left(a + \frac{2 \, b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{5}} - \frac{\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{5}}"," ",0,"-2/3*(3*(a^7 - a^3*b^4)*sin(x)/(cos(x) + 1) + 3*(7*a^6*b - 3*a^2*b^5)*sin(x)^2/(cos(x) + 1)^2 + (9*a^7 + 52*a^5*b^2 - a^3*b^4 - 12*a*b^6)*sin(x)^3/(cos(x) + 1)^3 + 2*(21*a^6*b + 25*a^4*b^3 - 7*a^2*b^5 - 3*b^7)*sin(x)^4/(cos(x) + 1)^4 + (9*a^7 + 52*a^5*b^2 - a^3*b^4 - 12*a*b^6)*sin(x)^5/(cos(x) + 1)^5 + 3*(7*a^6*b - 3*a^2*b^5)*sin(x)^6/(cos(x) + 1)^6 + 3*(a^7 - a^3*b^4)*sin(x)^7/(cos(x) + 1)^7)/(a^8*b^4 + 8*a^7*b^5*sin(x)/(cos(x) + 1) + 8*a^7*b^5*sin(x)^7/(cos(x) + 1)^7 + a^8*b^4*sin(x)^8/(cos(x) + 1)^8 + 4*(a^8*b^4 + 6*a^6*b^6)*sin(x)^2/(cos(x) + 1)^2 + 8*(3*a^7*b^5 + 4*a^5*b^7)*sin(x)^3/(cos(x) + 1)^3 + 2*(3*a^8*b^4 + 24*a^6*b^6 + 8*a^4*b^8)*sin(x)^4/(cos(x) + 1)^4 + 8*(3*a^7*b^5 + 4*a^5*b^7)*sin(x)^5/(cos(x) + 1)^5 + 4*(a^8*b^4 + 6*a^6*b^6)*sin(x)^6/(cos(x) + 1)^6) + log(a + 2*b*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2)/b^5 - log(sin(x)^2/(cos(x) + 1)^2 + 1)/b^5","B",0
273,1,141,0,0.344093," ","integrate((sec(x)+tan(x))^5,x, algorithm=""maxima"")","\frac{5}{2} \, \tan\left(x\right)^{4} + \frac{5 \, {\left(5 \, \sin\left(x\right)^{3} - 3 \, \sin\left(x\right)\right)}}{8 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} - \frac{3 \, \sin\left(x\right)^{3} - 5 \, \sin\left(x\right)}{8 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} + \frac{5 \, {\left(\sin\left(x\right)^{3} + \sin\left(x\right)\right)}}{4 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} + \frac{4 \, \sin\left(x\right)^{2} - 3}{4 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} + \frac{5}{4 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2}} - \frac{1}{2} \, \log\left(\sin\left(x\right)^{2} - 1\right) + \frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\sin\left(x\right) - 1\right)"," ",0,"5/2*tan(x)^4 + 5/8*(5*sin(x)^3 - 3*sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) - 1/8*(3*sin(x)^3 - 5*sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) + 5/4*(sin(x)^3 + sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) + 1/4*(4*sin(x)^2 - 3)/(sin(x)^4 - 2*sin(x)^2 + 1) + 5/4/(sin(x)^2 - 1)^2 - 1/2*log(sin(x)^2 - 1) + 1/2*log(sin(x) + 1) - 1/2*log(sin(x) - 1)","B",0
274,1,28,0,0.440254," ","integrate((sec(x)+tan(x))^4,x, algorithm=""maxima"")","\frac{8}{3} \, \tan\left(x\right)^{3} + x - \frac{4 \, {\left(3 \, \cos\left(x\right)^{2} - 1\right)}}{3 \, \cos\left(x\right)^{3}} + \frac{4}{3 \, \cos\left(x\right)^{3}}"," ",0,"8/3*tan(x)^3 + x - 4/3*(3*cos(x)^2 - 1)/cos(x)^3 + 4/3/cos(x)^3","A",0
275,1,52,0,0.329133," ","integrate((sec(x)+tan(x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, \tan\left(x\right)^{2} - \frac{2 \, \sin\left(x\right)}{\sin\left(x\right)^{2} - 1} - \frac{1}{2 \, {\left(\sin\left(x\right)^{2} - 1\right)}} + \frac{1}{2} \, \log\left(\sin\left(x\right)^{2} - 1\right) - \frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\sin\left(x\right) - 1\right)"," ",0,"3/2*tan(x)^2 - 2*sin(x)/(sin(x)^2 - 1) - 1/2/(sin(x)^2 - 1) + 1/2*log(sin(x)^2 - 1) - 1/2*log(sin(x) + 1) + 1/2*log(sin(x) - 1)","B",0
276,1,14,0,0.451177," ","integrate((sec(x)+tan(x))^2,x, algorithm=""maxima"")","-x + \frac{2}{\cos\left(x\right)} + 2 \, \tan\left(x\right)"," ",0,"-x + 2/cos(x) + 2*tan(x)","A",0
277,1,10,0,0.310035," ","integrate(sec(x)+tan(x),x, algorithm=""maxima"")","\log\left(\sec\left(x\right) + \tan\left(x\right)\right) + \log\left(\sec\left(x\right)\right)"," ",0,"log(sec(x) + tan(x)) + log(sec(x))","A",0
278,1,31,0,0.316228," ","integrate(1/(sec(x)+tan(x)),x, algorithm=""maxima"")","2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"2*log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
279,1,28,0,0.413116," ","integrate(1/(sec(x)+tan(x))^2,x, algorithm=""maxima"")","-\frac{4}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-4/(sin(x)/(cos(x) + 1) + 1) - 2*arctan(sin(x)/(cos(x) + 1))","A",0
280,1,64,0,0.442065," ","integrate(1/(sec(x)+tan(x))^3,x, algorithm=""maxima"")","\frac{4 \, \sin\left(x\right)}{{\left(\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}} - 2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) + \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"4*sin(x)/((2*sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 + 1)*(cos(x) + 1)) - 2*log(sin(x)/(cos(x) + 1) + 1) + log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
281,1,64,0,0.437906," ","integrate(1/(sec(x)+tan(x))^4,x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}}{3 \, {\left(\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + 1\right)}} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"8/3*(3*sin(x)/(cos(x) + 1) + 1)/(3*sin(x)/(cos(x) + 1) + 3*sin(x)^2/(cos(x) + 1)^2 + sin(x)^3/(cos(x) + 1)^3 + 1) + 2*arctan(sin(x)/(cos(x) + 1))","B",0
282,1,92,0,0.661496," ","integrate(1/(sec(x)+tan(x))^5,x, algorithm=""maxima"")","-\frac{8 \, \sin\left(x\right)^{2}}{{\left(\frac{4 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{4 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{\sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 1\right)} {\left(\cos\left(x\right) + 1\right)}^{2}} + 2 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"-8*sin(x)^2/((4*sin(x)/(cos(x) + 1) + 6*sin(x)^2/(cos(x) + 1)^2 + 4*sin(x)^3/(cos(x) + 1)^3 + sin(x)^4/(cos(x) + 1)^4 + 1)*(cos(x) + 1)^2) + 2*log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
283,1,188,0,0.308705," ","integrate((a*cot(x)+b*csc(x))^5,x, algorithm=""maxima"")","-\frac{5}{2} \, a^{3} b^{2} \cot\left(x\right)^{4} - \frac{5}{16} \, a^{4} b {\left(\frac{2 \, {\left(5 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)\right)}}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1} + 3 \, \log\left(\cos\left(x\right) + 1\right) - 3 \, \log\left(\cos\left(x\right) - 1\right)\right)} + \frac{1}{16} \, b^{5} {\left(\frac{2 \, {\left(3 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)\right)}}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1} - 3 \, \log\left(\cos\left(x\right) + 1\right) + 3 \, \log\left(\cos\left(x\right) - 1\right)\right)} - \frac{5}{8} \, a^{2} b^{3} {\left(\frac{2 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)\right)}}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1} - \log\left(\cos\left(x\right) + 1\right) + \log\left(\cos\left(x\right) - 1\right)\right)} + \frac{1}{4} \, a^{5} {\left(\frac{4 \, \sin\left(x\right)^{2} - 1}{\sin\left(x\right)^{4}} + 2 \, \log\left(\sin\left(x\right)^{2}\right)\right)} - \frac{5 \, a b^{4}}{4 \, \sin\left(x\right)^{4}}"," ",0,"-5/2*a^3*b^2*cot(x)^4 - 5/16*a^4*b*(2*(5*cos(x)^3 - 3*cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) + 3*log(cos(x) + 1) - 3*log(cos(x) - 1)) + 1/16*b^5*(2*(3*cos(x)^3 - 5*cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) - 3*log(cos(x) + 1) + 3*log(cos(x) - 1)) - 5/8*a^2*b^3*(2*(cos(x)^3 + cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) - log(cos(x) + 1) + log(cos(x) - 1)) + 1/4*a^5*((4*sin(x)^2 - 1)/sin(x)^4 + 2*log(sin(x)^2)) - 5/4*a*b^4/sin(x)^4","A",0
284,1,80,0,0.414192," ","integrate((a*cot(x)+b*csc(x))^4,x, algorithm=""maxima"")","-2 \, a^{2} b^{2} \cot\left(x\right)^{3} + \frac{1}{3} \, a^{4} {\left(3 \, x + \frac{3 \, \tan\left(x\right)^{2} - 1}{\tan\left(x\right)^{3}}\right)} + \frac{4 \, {\left(3 \, \sin\left(x\right)^{2} - 1\right)} a^{3} b}{3 \, \sin\left(x\right)^{3}} - \frac{{\left(3 \, \tan\left(x\right)^{2} + 1\right)} b^{4}}{3 \, \tan\left(x\right)^{3}} - \frac{4 \, a b^{3}}{3 \, \sin\left(x\right)^{3}}"," ",0,"-2*a^2*b^2*cot(x)^3 + 1/3*a^4*(3*x + (3*tan(x)^2 - 1)/tan(x)^3) + 4/3*(3*sin(x)^2 - 1)*a^3*b/sin(x)^3 - 1/3*(3*tan(x)^2 + 1)*b^4/tan(x)^3 - 4/3*a*b^3/sin(x)^3","A",0
285,1,87,0,0.312791," ","integrate((a*cot(x)+b*csc(x))^3,x, algorithm=""maxima"")","-\frac{3}{2} \, a b^{2} \cot\left(x\right)^{2} + \frac{3}{4} \, a^{2} b {\left(\frac{2 \, \cos\left(x\right)}{\cos\left(x\right)^{2} - 1} + \log\left(\cos\left(x\right) + 1\right) - \log\left(\cos\left(x\right) - 1\right)\right)} + \frac{1}{4} \, b^{3} {\left(\frac{2 \, \cos\left(x\right)}{\cos\left(x\right)^{2} - 1} - \log\left(\cos\left(x\right) + 1\right) + \log\left(\cos\left(x\right) - 1\right)\right)} - \frac{1}{2} \, a^{3} {\left(\frac{1}{\sin\left(x\right)^{2}} + \log\left(\sin\left(x\right)^{2}\right)\right)}"," ",0,"-3/2*a*b^2*cot(x)^2 + 3/4*a^2*b*(2*cos(x)/(cos(x)^2 - 1) + log(cos(x) + 1) - log(cos(x) - 1)) + 1/4*b^3*(2*cos(x)/(cos(x)^2 - 1) - log(cos(x) + 1) + log(cos(x) - 1)) - 1/2*a^3*(1/sin(x)^2 + log(sin(x)^2))","A",0
286,1,29,0,0.424823," ","integrate((a*cot(x)+b*csc(x))^2,x, algorithm=""maxima"")","-a^{2} {\left(x + \frac{1}{\tan\left(x\right)}\right)} - \frac{2 \, a b}{\sin\left(x\right)} - \frac{b^{2}}{\tan\left(x\right)}"," ",0,"-a^2*(x + 1/tan(x)) - 2*a*b/sin(x) - b^2/tan(x)","A",0
287,1,15,0,0.313703," ","integrate(a*cot(x)+b*csc(x),x, algorithm=""maxima"")","-b \log\left(\cot\left(x\right) + \csc\left(x\right)\right) + a \log\left(\sin\left(x\right)\right)"," ",0,"-b*log(cot(x) + csc(x)) + a*log(sin(x))","A",0
288,1,45,0,0.404378," ","integrate(1/(a*cot(x)+b*csc(x)),x, algorithm=""maxima"")","-\frac{\log\left(a + b - \frac{{\left(a - b\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a} + \frac{\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a}"," ",0,"-log(a + b - (a - b)*sin(x)^2/(cos(x) + 1)^2)/a + log(sin(x)^2/(cos(x) + 1)^2 + 1)/a","B",0
289,-2,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
290,1,177,0,0.428164," ","integrate(1/(a*cot(x)+b*csc(x))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a b + b^{2} + \frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}}{a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} - \frac{2 \, {\left(a^{5} - a^{4} b - a^{3} b^{2} + a^{2} b^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} + \frac{\log\left(a + b - \frac{{\left(a - b\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{3}} - \frac{\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{3}}"," ",0,"2*(a*b + b^2 + (a^2 - 2*a*b + b^2)*sin(x)^2/(cos(x) + 1)^2)/(a^5 + a^4*b - a^3*b^2 - a^2*b^3 - 2*(a^5 - a^4*b - a^3*b^2 + a^2*b^3)*sin(x)^2/(cos(x) + 1)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*sin(x)^4/(cos(x) + 1)^4) + log(a + b - (a - b)*sin(x)^2/(cos(x) + 1)^2)/a^3 - log(sin(x)^2/(cos(x) + 1)^2 + 1)/a^3","B",0
291,-2,0,0,0.000000," ","integrate(1/(a*cot(x)+b*csc(x))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
292,1,497,0,0.480340," ","integrate(1/(a*cot(x)+b*csc(x))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, a^{4} b + 10 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 6 \, a b^{4} - 3 \, b^{5} + \frac{{\left(3 \, a^{5} - 17 \, a^{4} b - 6 \, a^{3} b^{2} + 26 \, a^{2} b^{3} + 3 \, a b^{4} - 9 \, b^{5}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{3 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 12 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 8 \, a b^{4} + 3 \, b^{5}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{3 \, {\left(a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}}{3 \, {\left(a^{10} + 2 \, a^{9} b - a^{8} b^{2} - 4 \, a^{7} b^{3} - a^{6} b^{4} + 2 \, a^{5} b^{5} + a^{4} b^{6} - \frac{4 \, {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{6 \, {\left(a^{10} - 2 \, a^{9} b - a^{8} b^{2} + 4 \, a^{7} b^{3} - a^{6} b^{4} - 2 \, a^{5} b^{5} + a^{4} b^{6}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{4 \, {\left(a^{10} - 4 \, a^{9} b + 5 \, a^{8} b^{2} - 5 \, a^{6} b^{4} + 4 \, a^{5} b^{5} - a^{4} b^{6}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{{\left(a^{10} - 6 \, a^{9} b + 15 \, a^{8} b^{2} - 20 \, a^{7} b^{3} + 15 \, a^{6} b^{4} - 6 \, a^{5} b^{5} + a^{4} b^{6}\right)} \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}} - \frac{\log\left(a + b - \frac{{\left(a - b\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{a^{5}} + \frac{\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{a^{5}}"," ",0,"-2/3*(5*a^4*b + 10*a^3*b^2 + 2*a^2*b^3 - 6*a*b^4 - 3*b^5 + (3*a^5 - 17*a^4*b - 6*a^3*b^2 + 26*a^2*b^3 + 3*a*b^4 - 9*b^5)*sin(x)^2/(cos(x) + 1)^2 - 3*(4*a^5 - 13*a^4*b + 12*a^3*b^2 + 2*a^2*b^3 - 8*a*b^4 + 3*b^5)*sin(x)^4/(cos(x) + 1)^4 + 3*(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5)*sin(x)^6/(cos(x) + 1)^6)/(a^10 + 2*a^9*b - a^8*b^2 - 4*a^7*b^3 - a^6*b^4 + 2*a^5*b^5 + a^4*b^6 - 4*(a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*sin(x)^2/(cos(x) + 1)^2 + 6*(a^10 - 2*a^9*b - a^8*b^2 + 4*a^7*b^3 - a^6*b^4 - 2*a^5*b^5 + a^4*b^6)*sin(x)^4/(cos(x) + 1)^4 - 4*(a^10 - 4*a^9*b + 5*a^8*b^2 - 5*a^6*b^4 + 4*a^5*b^5 - a^4*b^6)*sin(x)^6/(cos(x) + 1)^6 + (a^10 - 6*a^9*b + 15*a^8*b^2 - 20*a^7*b^3 + 15*a^6*b^4 - 6*a^5*b^5 + a^4*b^6)*sin(x)^8/(cos(x) + 1)^8) - log(a + b - (a - b)*sin(x)^2/(cos(x) + 1)^2)/a^5 + log(sin(x)^2/(cos(x) + 1)^2 + 1)/a^5","B",0
293,1,125,0,0.314763," ","integrate((cot(x)+csc(x))^5,x, algorithm=""maxima"")","-\frac{5}{2} \, \cot\left(x\right)^{4} - \frac{5 \, {\left(5 \, \cos\left(x\right)^{3} - 3 \, \cos\left(x\right)\right)}}{8 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}} + \frac{3 \, \cos\left(x\right)^{3} - 5 \, \cos\left(x\right)}{8 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}} - \frac{5 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)\right)}}{4 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}} + \frac{4 \, \sin\left(x\right)^{2} - 1}{4 \, \sin\left(x\right)^{4}} - \frac{5}{4 \, \sin\left(x\right)^{4}} + \frac{1}{2} \, \log\left(\sin\left(x\right)^{2}\right) - \frac{1}{2} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"-5/2*cot(x)^4 - 5/8*(5*cos(x)^3 - 3*cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) + 1/8*(3*cos(x)^3 - 5*cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) - 5/4*(cos(x)^3 + cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1) + 1/4*(4*sin(x)^2 - 1)/sin(x)^4 - 5/4/sin(x)^4 + 1/2*log(sin(x)^2) - 1/2*log(cos(x) + 1) + 1/2*log(cos(x) - 1)","B",0
294,1,56,0,0.417607," ","integrate((cot(x)+csc(x))^4,x, algorithm=""maxima"")","-2 \, \cot\left(x\right)^{3} + x + \frac{4 \, {\left(3 \, \sin\left(x\right)^{2} - 1\right)}}{3 \, \sin\left(x\right)^{3}} - \frac{3 \, \tan\left(x\right)^{2} + 1}{3 \, \tan\left(x\right)^{3}} + \frac{3 \, \tan\left(x\right)^{2} - 1}{3 \, \tan\left(x\right)^{3}} - \frac{4}{3 \, \sin\left(x\right)^{3}}"," ",0,"-2*cot(x)^3 + x + 4/3*(3*sin(x)^2 - 1)/sin(x)^3 - 1/3*(3*tan(x)^2 + 1)/tan(x)^3 + 1/3*(3*tan(x)^2 - 1)/tan(x)^3 - 4/3/sin(x)^3","B",0
295,1,46,0,0.309025," ","integrate((cot(x)+csc(x))^3,x, algorithm=""maxima"")","-\frac{3}{2} \, \cot\left(x\right)^{2} + \frac{2 \, \cos\left(x\right)}{\cos\left(x\right)^{2} - 1} - \frac{1}{2 \, \sin\left(x\right)^{2}} - \frac{1}{2} \, \log\left(\sin\left(x\right)^{2}\right) + \frac{1}{2} \, \log\left(\cos\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"-3/2*cot(x)^2 + 2*cos(x)/(cos(x)^2 - 1) - 1/2/sin(x)^2 - 1/2*log(sin(x)^2) + 1/2*log(cos(x) + 1) - 1/2*log(cos(x) - 1)","B",0
296,1,16,0,0.406434," ","integrate((cot(x)+csc(x))^2,x, algorithm=""maxima"")","-x - \frac{2}{\sin\left(x\right)} - \frac{2}{\tan\left(x\right)}"," ",0,"-x - 2/sin(x) - 2/tan(x)","A",0
297,1,12,0,0.303798," ","integrate(cot(x)+csc(x),x, algorithm=""maxima"")","-\log\left(\cot\left(x\right) + \csc\left(x\right)\right) + \log\left(\sin\left(x\right)\right)"," ",0,"-log(cot(x) + csc(x)) + log(sin(x))","A",0
298,1,14,0,0.406311," ","integrate(1/(cot(x)+csc(x)),x, algorithm=""maxima"")","\log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"log(sin(x)^2/(cos(x) + 1)^2 + 1)","A",0
299,1,23,0,0.406444," ","integrate(1/(cot(x)+csc(x))^2,x, algorithm=""maxima"")","\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"2*sin(x)/(cos(x) + 1) - 2*arctan(sin(x)/(cos(x) + 1))","A",0
300,1,28,0,0.410333," ","integrate(1/(cot(x)+csc(x))^3,x, algorithm=""maxima"")","\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"sin(x)^2/(cos(x) + 1)^2 - log(sin(x)^2/(cos(x) + 1)^2 + 1)","A",0
301,1,35,0,0.407155," ","integrate(1/(cot(x)+csc(x))^4,x, algorithm=""maxima"")","-\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, \sin\left(x\right)^{3}}{3 \, {\left(\cos\left(x\right) + 1\right)}^{3}} + 2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-2*sin(x)/(cos(x) + 1) + 2/3*sin(x)^3/(cos(x) + 1)^3 + 2*arctan(sin(x)/(cos(x) + 1))","A",0
302,1,39,0,0.413004," ","integrate(1/(cot(x)+csc(x))^5,x, algorithm=""maxima"")","-\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{4}}{2 \, {\left(\cos\left(x\right) + 1\right)}^{4}} + \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"-sin(x)^2/(cos(x) + 1)^2 + 1/2*sin(x)^4/(cos(x) + 1)^4 + log(sin(x)^2/(cos(x) + 1)^2 + 1)","A",0
303,1,36,0,0.313648," ","integrate((csc(x)-sin(x))^4,x, algorithm=""maxima"")","\frac{35}{8} \, x + \frac{4}{\tan\left(x\right)} - \frac{3 \, \tan\left(x\right)^{2} + 1}{3 \, \tan\left(x\right)^{3}} + \frac{1}{32} \, \sin\left(4 \, x\right) + \frac{3}{4} \, \sin\left(2 \, x\right)"," ",0,"35/8*x + 4/tan(x) - 1/3*(3*tan(x)^2 + 1)/tan(x)^3 + 1/32*sin(4*x) + 3/4*sin(2*x)","A",0
304,1,37,0,0.310806," ","integrate((csc(x)-sin(x))^3,x, algorithm=""maxima"")","-\frac{1}{3} \, \cos\left(x\right)^{3} + \frac{\cos\left(x\right)}{2 \, {\left(\cos\left(x\right)^{2} - 1\right)}} - 2 \, \cos\left(x\right) + \frac{5}{4} \, \log\left(\cos\left(x\right) + 1\right) - \frac{5}{4} \, \log\left(\cos\left(x\right) - 1\right)"," ",0,"-1/3*cos(x)^3 + 1/2*cos(x)/(cos(x)^2 - 1) - 2*cos(x) + 5/4*log(cos(x) + 1) - 5/4*log(cos(x) - 1)","A",0
305,1,16,0,0.312392," ","integrate((csc(x)-sin(x))^2,x, algorithm=""maxima"")","-\frac{3}{2} \, x - \frac{1}{\tan\left(x\right)} - \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-3/2*x - 1/tan(x) - 1/4*sin(2*x)","A",0
306,1,11,0,0.318048," ","integrate(csc(x)-sin(x),x, algorithm=""maxima"")","\cos\left(x\right) - \log\left(\cot\left(x\right) + \csc\left(x\right)\right)"," ",0,"cos(x) - log(cot(x) + csc(x))","A",0
307,1,17,0,0.307887," ","integrate(1/(csc(x)-sin(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1}"," ",0,"-2/(sin(x)^2/(cos(x) + 1)^2 - 1)","B",0
308,1,6,0,0.326165," ","integrate(1/(csc(x)-sin(x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, \tan\left(x\right)^{3}"," ",0,"1/3*tan(x)^3","A",0
309,1,103,0,0.311132," ","integrate(1/(csc(x)-sin(x))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{5 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{15 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - 1\right)}}{15 \, {\left(\frac{5 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{10 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{5 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{\sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} - 1\right)}}"," ",0,"-4/15*(5*sin(x)^2/(cos(x) + 1)^2 + 5*sin(x)^4/(cos(x) + 1)^4 + 15*sin(x)^6/(cos(x) + 1)^6 - 1)/(5*sin(x)^2/(cos(x) + 1)^2 - 10*sin(x)^4/(cos(x) + 1)^4 + 10*sin(x)^6/(cos(x) + 1)^6 - 5*sin(x)^8/(cos(x) + 1)^8 + sin(x)^10/(cos(x) + 1)^10 - 1)","B",0
310,1,13,0,0.311463," ","integrate(1/(csc(x)-sin(x))^4,x, algorithm=""maxima"")","\frac{1}{7} \, \tan\left(x\right)^{7} + \frac{1}{5} \, \tan\left(x\right)^{5}"," ",0,"1/7*tan(x)^7 + 1/5*tan(x)^5","A",0
311,1,187,0,0.358150," ","integrate(1/(csc(x)-sin(x))^5,x, algorithm=""maxima"")","\frac{16 \, {\left(\frac{9 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{36 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{126 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{441 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} - \frac{315 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} - \frac{210 \, \sin\left(x\right)^{12}}{{\left(\cos\left(x\right) + 1\right)}^{12}} - 1\right)}}{315 \, {\left(\frac{9 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{36 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{84 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{126 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{126 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} - \frac{84 \, \sin\left(x\right)^{12}}{{\left(\cos\left(x\right) + 1\right)}^{12}} + \frac{36 \, \sin\left(x\right)^{14}}{{\left(\cos\left(x\right) + 1\right)}^{14}} - \frac{9 \, \sin\left(x\right)^{16}}{{\left(\cos\left(x\right) + 1\right)}^{16}} + \frac{\sin\left(x\right)^{18}}{{\left(\cos\left(x\right) + 1\right)}^{18}} - 1\right)}}"," ",0,"16/315*(9*sin(x)^2/(cos(x) + 1)^2 - 36*sin(x)^4/(cos(x) + 1)^4 - 126*sin(x)^6/(cos(x) + 1)^6 - 441*sin(x)^8/(cos(x) + 1)^8 - 315*sin(x)^10/(cos(x) + 1)^10 - 210*sin(x)^12/(cos(x) + 1)^12 - 1)/(9*sin(x)^2/(cos(x) + 1)^2 - 36*sin(x)^4/(cos(x) + 1)^4 + 84*sin(x)^6/(cos(x) + 1)^6 - 126*sin(x)^8/(cos(x) + 1)^8 + 126*sin(x)^10/(cos(x) + 1)^10 - 84*sin(x)^12/(cos(x) + 1)^12 + 36*sin(x)^14/(cos(x) + 1)^14 - 9*sin(x)^16/(cos(x) + 1)^16 + sin(x)^18/(cos(x) + 1)^18 - 1)","B",0
312,1,19,0,0.346285," ","integrate(1/(csc(x)-sin(x))^6,x, algorithm=""maxima"")","\frac{1}{11} \, \tan\left(x\right)^{11} + \frac{2}{9} \, \tan\left(x\right)^{9} + \frac{1}{7} \, \tan\left(x\right)^{7}"," ",0,"1/11*tan(x)^11 + 2/9*tan(x)^9 + 1/7*tan(x)^7","A",0
313,1,271,0,0.342930," ","integrate(1/(csc(x)-sin(x))^7,x, algorithm=""maxima"")","-\frac{32 \, {\left(\frac{13 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{78 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{286 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{2288 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{10296 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} + \frac{16302 \, \sin\left(x\right)^{12}}{{\left(\cos\left(x\right) + 1\right)}^{12}} + \frac{18018 \, \sin\left(x\right)^{14}}{{\left(\cos\left(x\right) + 1\right)}^{14}} + \frac{9009 \, \sin\left(x\right)^{16}}{{\left(\cos\left(x\right) + 1\right)}^{16}} + \frac{3003 \, \sin\left(x\right)^{18}}{{\left(\cos\left(x\right) + 1\right)}^{18}} - 1\right)}}{3003 \, {\left(\frac{13 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{78 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{286 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{715 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{1287 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} - \frac{1716 \, \sin\left(x\right)^{12}}{{\left(\cos\left(x\right) + 1\right)}^{12}} + \frac{1716 \, \sin\left(x\right)^{14}}{{\left(\cos\left(x\right) + 1\right)}^{14}} - \frac{1287 \, \sin\left(x\right)^{16}}{{\left(\cos\left(x\right) + 1\right)}^{16}} + \frac{715 \, \sin\left(x\right)^{18}}{{\left(\cos\left(x\right) + 1\right)}^{18}} - \frac{286 \, \sin\left(x\right)^{20}}{{\left(\cos\left(x\right) + 1\right)}^{20}} + \frac{78 \, \sin\left(x\right)^{22}}{{\left(\cos\left(x\right) + 1\right)}^{22}} - \frac{13 \, \sin\left(x\right)^{24}}{{\left(\cos\left(x\right) + 1\right)}^{24}} + \frac{\sin\left(x\right)^{26}}{{\left(\cos\left(x\right) + 1\right)}^{26}} - 1\right)}}"," ",0,"-32/3003*(13*sin(x)^2/(cos(x) + 1)^2 - 78*sin(x)^4/(cos(x) + 1)^4 + 286*sin(x)^6/(cos(x) + 1)^6 + 2288*sin(x)^8/(cos(x) + 1)^8 + 10296*sin(x)^10/(cos(x) + 1)^10 + 16302*sin(x)^12/(cos(x) + 1)^12 + 18018*sin(x)^14/(cos(x) + 1)^14 + 9009*sin(x)^16/(cos(x) + 1)^16 + 3003*sin(x)^18/(cos(x) + 1)^18 - 1)/(13*sin(x)^2/(cos(x) + 1)^2 - 78*sin(x)^4/(cos(x) + 1)^4 + 286*sin(x)^6/(cos(x) + 1)^6 - 715*sin(x)^8/(cos(x) + 1)^8 + 1287*sin(x)^10/(cos(x) + 1)^10 - 1716*sin(x)^12/(cos(x) + 1)^12 + 1716*sin(x)^14/(cos(x) + 1)^14 - 1287*sin(x)^16/(cos(x) + 1)^16 + 715*sin(x)^18/(cos(x) + 1)^18 - 286*sin(x)^20/(cos(x) + 1)^20 + 78*sin(x)^22/(cos(x) + 1)^22 - 13*sin(x)^24/(cos(x) + 1)^24 + sin(x)^26/(cos(x) + 1)^26 - 1)","B",0
314,1,578,0,0.571960," ","integrate((csc(x)-sin(x))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(5 \, \cos\left(\frac{21}{2} \, x\right) + 105 \, \cos\left(\frac{17}{2} \, x\right) - 2275 \, \cos\left(\frac{13}{2} \, x\right) + 5817 \, \cos\left(\frac{9}{2} \, x\right) - 5 \, \cos\left(\frac{7}{2} \, x\right) - 5817 \, \cos\left(\frac{5}{2} \, x\right) - 105 \, \cos\left(\frac{3}{2} \, x\right) + 2275 \, \cos\left(\frac{1}{2} \, x\right) - 5 \, \sin\left(\frac{21}{2} \, x\right) - 105 \, \sin\left(\frac{17}{2} \, x\right) + 2275 \, \sin\left(\frac{13}{2} \, x\right) - 5817 \, \sin\left(\frac{9}{2} \, x\right) - 5 \, \sin\left(\frac{7}{2} \, x\right) + 5817 \, \sin\left(\frac{5}{2} \, x\right) - 105 \, \sin\left(\frac{3}{2} \, x\right) - 2275 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(5 \, \cos\left(\frac{21}{2} \, x\right) + 105 \, \cos\left(\frac{17}{2} \, x\right) - 2275 \, \cos\left(\frac{13}{2} \, x\right) + 5817 \, \cos\left(\frac{9}{2} \, x\right) - 5 \, \cos\left(\frac{7}{2} \, x\right) - 5817 \, \cos\left(\frac{5}{2} \, x\right) - 105 \, \cos\left(\frac{3}{2} \, x\right) + 2275 \, \cos\left(\frac{1}{2} \, x\right) + 5 \, \sin\left(\frac{21}{2} \, x\right) + 105 \, \sin\left(\frac{17}{2} \, x\right) - 2275 \, \sin\left(\frac{13}{2} \, x\right) + 5817 \, \sin\left(\frac{9}{2} \, x\right) + 5 \, \sin\left(\frac{7}{2} \, x\right) - 5817 \, \sin\left(\frac{5}{2} \, x\right) + 105 \, \sin\left(\frac{3}{2} \, x\right) + 2275 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left({\left(5 \, \cos\left(\frac{21}{2} \, x\right) + 105 \, \cos\left(\frac{17}{2} \, x\right) - 2275 \, \cos\left(\frac{13}{2} \, x\right) + 5817 \, \cos\left(\frac{9}{2} \, x\right) - 5 \, \cos\left(\frac{7}{2} \, x\right) - 5817 \, \cos\left(\frac{5}{2} \, x\right) - 105 \, \cos\left(\frac{3}{2} \, x\right) + 2275 \, \cos\left(\frac{1}{2} \, x\right) + 5 \, \sin\left(\frac{21}{2} \, x\right) + 105 \, \sin\left(\frac{17}{2} \, x\right) - 2275 \, \sin\left(\frac{13}{2} \, x\right) + 5817 \, \sin\left(\frac{9}{2} \, x\right) + 5 \, \sin\left(\frac{7}{2} \, x\right) - 5817 \, \sin\left(\frac{5}{2} \, x\right) + 105 \, \sin\left(\frac{3}{2} \, x\right) + 2275 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(5 \, \cos\left(\frac{21}{2} \, x\right) + 105 \, \cos\left(\frac{17}{2} \, x\right) - 2275 \, \cos\left(\frac{13}{2} \, x\right) + 5817 \, \cos\left(\frac{9}{2} \, x\right) - 5 \, \cos\left(\frac{7}{2} \, x\right) - 5817 \, \cos\left(\frac{5}{2} \, x\right) - 105 \, \cos\left(\frac{3}{2} \, x\right) + 2275 \, \cos\left(\frac{1}{2} \, x\right) - 5 \, \sin\left(\frac{21}{2} \, x\right) - 105 \, \sin\left(\frac{17}{2} \, x\right) + 2275 \, \sin\left(\frac{13}{2} \, x\right) - 5817 \, \sin\left(\frac{9}{2} \, x\right) - 5 \, \sin\left(\frac{7}{2} \, x\right) + 5817 \, \sin\left(\frac{5}{2} \, x\right) - 105 \, \sin\left(\frac{3}{2} \, x\right) - 2275 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)}}{280 \, {\left(\cos\left(x\right)^{8} + \sin\left(x\right)^{8} + 4 \, {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)^{6} - 4 \, \cos\left(x\right)^{6} + 2 \, {\left(3 \, \cos\left(x\right)^{4} + 2 \, \cos\left(x\right)^{2} + 3\right)} \sin\left(x\right)^{4} + 6 \, \cos\left(x\right)^{4} + 4 \, {\left(\cos\left(x\right)^{6} - \cos\left(x\right)^{4} - \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)^{2} - 4 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"-1/280*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)*(((5*cos(21/2*x) + 105*cos(17/2*x) - 2275*cos(13/2*x) + 5817*cos(9/2*x) - 5*cos(7/2*x) - 5817*cos(5/2*x) - 105*cos(3/2*x) + 2275*cos(1/2*x) - 5*sin(21/2*x) - 105*sin(17/2*x) + 2275*sin(13/2*x) - 5817*sin(9/2*x) - 5*sin(7/2*x) + 5817*sin(5/2*x) - 105*sin(3/2*x) - 2275*sin(1/2*x))*cos(7/2*arctan2(sin(x), cos(x) - 1)) + (5*cos(21/2*x) + 105*cos(17/2*x) - 2275*cos(13/2*x) + 5817*cos(9/2*x) - 5*cos(7/2*x) - 5817*cos(5/2*x) - 105*cos(3/2*x) + 2275*cos(1/2*x) + 5*sin(21/2*x) + 105*sin(17/2*x) - 2275*sin(13/2*x) + 5817*sin(9/2*x) + 5*sin(7/2*x) - 5817*sin(5/2*x) + 105*sin(3/2*x) + 2275*sin(1/2*x))*sin(7/2*arctan2(sin(x), cos(x) - 1)))*cos(7/2*arctan2(sin(x), cos(x) + 1)) + ((5*cos(21/2*x) + 105*cos(17/2*x) - 2275*cos(13/2*x) + 5817*cos(9/2*x) - 5*cos(7/2*x) - 5817*cos(5/2*x) - 105*cos(3/2*x) + 2275*cos(1/2*x) + 5*sin(21/2*x) + 105*sin(17/2*x) - 2275*sin(13/2*x) + 5817*sin(9/2*x) + 5*sin(7/2*x) - 5817*sin(5/2*x) + 105*sin(3/2*x) + 2275*sin(1/2*x))*cos(7/2*arctan2(sin(x), cos(x) - 1)) - (5*cos(21/2*x) + 105*cos(17/2*x) - 2275*cos(13/2*x) + 5817*cos(9/2*x) - 5*cos(7/2*x) - 5817*cos(5/2*x) - 105*cos(3/2*x) + 2275*cos(1/2*x) - 5*sin(21/2*x) - 105*sin(17/2*x) + 2275*sin(13/2*x) - 5817*sin(9/2*x) - 5*sin(7/2*x) + 5817*sin(5/2*x) - 105*sin(3/2*x) - 2275*sin(1/2*x))*sin(7/2*arctan2(sin(x), cos(x) - 1)))*sin(7/2*arctan2(sin(x), cos(x) + 1)))/(cos(x)^8 + sin(x)^8 + 4*(cos(x)^2 + 1)*sin(x)^6 - 4*cos(x)^6 + 2*(3*cos(x)^4 + 2*cos(x)^2 + 3)*sin(x)^4 + 6*cos(x)^4 + 4*(cos(x)^6 - cos(x)^4 - cos(x)^2 + 1)*sin(x)^2 - 4*cos(x)^2 + 1)","B",0
315,1,427,0,0.556169," ","integrate((csc(x)-sin(x))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) + 3 \, \sin\left(\frac{15}{2} \, x\right) + 105 \, \sin\left(\frac{11}{2} \, x\right) - 410 \, \sin\left(\frac{7}{2} \, x\right) + 3 \, \sin\left(\frac{5}{2} \, x\right) + 410 \, \sin\left(\frac{3}{2} \, x\right) + 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) - 3 \, \sin\left(\frac{15}{2} \, x\right) - 105 \, \sin\left(\frac{11}{2} \, x\right) + 410 \, \sin\left(\frac{7}{2} \, x\right) - 3 \, \sin\left(\frac{5}{2} \, x\right) - 410 \, \sin\left(\frac{3}{2} \, x\right) - 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) - 3 \, \sin\left(\frac{15}{2} \, x\right) - 105 \, \sin\left(\frac{11}{2} \, x\right) + 410 \, \sin\left(\frac{7}{2} \, x\right) - 3 \, \sin\left(\frac{5}{2} \, x\right) - 410 \, \sin\left(\frac{3}{2} \, x\right) - 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(3 \, \cos\left(\frac{15}{2} \, x\right) + 105 \, \cos\left(\frac{11}{2} \, x\right) - 410 \, \cos\left(\frac{7}{2} \, x\right) - 3 \, \cos\left(\frac{5}{2} \, x\right) + 410 \, \cos\left(\frac{3}{2} \, x\right) - 105 \, \cos\left(\frac{1}{2} \, x\right) + 3 \, \sin\left(\frac{15}{2} \, x\right) + 105 \, \sin\left(\frac{11}{2} \, x\right) - 410 \, \sin\left(\frac{7}{2} \, x\right) + 3 \, \sin\left(\frac{5}{2} \, x\right) + 410 \, \sin\left(\frac{3}{2} \, x\right) + 105 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)}{60 \, {\left(\cos\left(x\right)^{4} + \sin\left(x\right)^{4} + 2 \, {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)^{2} - 2 \, \cos\left(x\right)^{2} + 1\right)} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}"," ",0,"-1/60*(((3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) + 3*sin(15/2*x) + 105*sin(11/2*x) - 410*sin(7/2*x) + 3*sin(5/2*x) + 410*sin(3/2*x) + 105*sin(1/2*x))*cos(5/2*arctan2(sin(x), cos(x) - 1)) - (3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) - 3*sin(15/2*x) - 105*sin(11/2*x) + 410*sin(7/2*x) - 3*sin(5/2*x) - 410*sin(3/2*x) - 105*sin(1/2*x))*sin(5/2*arctan2(sin(x), cos(x) - 1)))*cos(5/2*arctan2(sin(x), cos(x) + 1)) - ((3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) - 3*sin(15/2*x) - 105*sin(11/2*x) + 410*sin(7/2*x) - 3*sin(5/2*x) - 410*sin(3/2*x) - 105*sin(1/2*x))*cos(5/2*arctan2(sin(x), cos(x) - 1)) + (3*cos(15/2*x) + 105*cos(11/2*x) - 410*cos(7/2*x) - 3*cos(5/2*x) + 410*cos(3/2*x) - 105*cos(1/2*x) + 3*sin(15/2*x) + 105*sin(11/2*x) - 410*sin(7/2*x) + 3*sin(5/2*x) + 410*sin(3/2*x) + 105*sin(1/2*x))*sin(5/2*arctan2(sin(x), cos(x) - 1)))*sin(5/2*arctan2(sin(x), cos(x) + 1)))/((cos(x)^4 + sin(x)^4 + 2*(cos(x)^2 + 1)*sin(x)^2 - 2*cos(x)^2 + 1)*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4))","B",0
316,1,314,0,0.523935," ","integrate((csc(x)-sin(x))^(3/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left({\left({\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{9}{2} \, x\right) + 15 \, \sin\left(\frac{5}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{9}{2} \, x\right) - 15 \, \sin\left(\frac{5}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) + {\left({\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{9}{2} \, x\right) - 15 \, \sin\left(\frac{5}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(\cos\left(\frac{9}{2} \, x\right) - 15 \, \cos\left(\frac{5}{2} \, x\right) - \cos\left(\frac{3}{2} \, x\right) + 15 \, \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{9}{2} \, x\right) + 15 \, \sin\left(\frac{5}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - 15 \, \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)\right)}}{6 \, {\left(\cos\left(x\right)^{4} + \sin\left(x\right)^{4} + 2 \, {\left(\cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)^{2} - 2 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"1/6*(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4)*(((cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) - sin(9/2*x) + 15*sin(5/2*x) - sin(3/2*x) - 15*sin(1/2*x))*cos(3/2*arctan2(sin(x), cos(x) - 1)) + (cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) + sin(9/2*x) - 15*sin(5/2*x) + sin(3/2*x) + 15*sin(1/2*x))*sin(3/2*arctan2(sin(x), cos(x) - 1)))*cos(3/2*arctan2(sin(x), cos(x) + 1)) + ((cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) + sin(9/2*x) - 15*sin(5/2*x) + sin(3/2*x) + 15*sin(1/2*x))*cos(3/2*arctan2(sin(x), cos(x) - 1)) - (cos(9/2*x) - 15*cos(5/2*x) - cos(3/2*x) + 15*cos(1/2*x) - sin(9/2*x) + 15*sin(5/2*x) - sin(3/2*x) - 15*sin(1/2*x))*sin(3/2*arctan2(sin(x), cos(x) - 1)))*sin(3/2*arctan2(sin(x), cos(x) + 1)))/(cos(x)^4 + sin(x)^4 + 2*(cos(x)^2 + 1)*sin(x)^2 - 2*cos(x)^2 + 1)","B",0
317,1,188,0,0.507549," ","integrate((csc(x)-sin(x))^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) - {\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right) - {\left({\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) - \sin\left(\frac{3}{2} \, x\right) - \sin\left(\frac{1}{2} \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right) + {\left(\cos\left(\frac{3}{2} \, x\right) - \cos\left(\frac{1}{2} \, x\right) + \sin\left(\frac{3}{2} \, x\right) + \sin\left(\frac{1}{2} \, x\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)\right)}{{\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)}^{\frac{1}{4}}}"," ",0,"(((cos(3/2*x) - cos(1/2*x) + sin(3/2*x) + sin(1/2*x))*cos(1/2*arctan2(sin(x), cos(x) - 1)) - (cos(3/2*x) - cos(1/2*x) - sin(3/2*x) - sin(1/2*x))*sin(1/2*arctan2(sin(x), cos(x) - 1)))*cos(1/2*arctan2(sin(x), cos(x) + 1)) - ((cos(3/2*x) - cos(1/2*x) - sin(3/2*x) - sin(1/2*x))*cos(1/2*arctan2(sin(x), cos(x) - 1)) + (cos(3/2*x) - cos(1/2*x) + sin(3/2*x) + sin(1/2*x))*sin(1/2*arctan2(sin(x), cos(x) - 1)))*sin(1/2*arctan2(sin(x), cos(x) + 1)))/((cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^(1/4)*(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^(1/4))","B",0
318,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\csc\left(x\right) - \sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/sqrt(csc(x) - sin(x)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(-3/2), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(-5/2), x)","F",0
321,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(-7/2), x)","F",0
322,1,26,0,0.321636," ","integrate((-cos(x)+sec(x))^4,x, algorithm=""maxima"")","\frac{1}{3} \, \tan\left(x\right)^{3} + \frac{35}{8} \, x + \frac{1}{32} \, \sin\left(4 \, x\right) - \frac{3}{4} \, \sin\left(2 \, x\right) - 3 \, \tan\left(x\right)"," ",0,"1/3*tan(x)^3 + 35/8*x + 1/32*sin(4*x) - 3/4*sin(2*x) - 3*tan(x)","A",0
323,1,37,0,0.319378," ","integrate((-cos(x)+sec(x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, \sin\left(x\right)^{3} - \frac{\sin\left(x\right)}{2 \, {\left(\sin\left(x\right)^{2} - 1\right)}} - \frac{5}{4} \, \log\left(\sin\left(x\right) + 1\right) + \frac{5}{4} \, \log\left(\sin\left(x\right) - 1\right) + 2 \, \sin\left(x\right)"," ",0,"1/3*sin(x)^3 - 1/2*sin(x)/(sin(x)^2 - 1) - 5/4*log(sin(x) + 1) + 5/4*log(sin(x) - 1) + 2*sin(x)","A",0
324,1,12,0,0.306646," ","integrate((-cos(x)+sec(x))^2,x, algorithm=""maxima"")","-\frac{3}{2} \, x + \frac{1}{4} \, \sin\left(2 \, x\right) + \tan\left(x\right)"," ",0,"-3/2*x + 1/4*sin(2*x) + tan(x)","A",0
325,1,11,0,0.315447," ","integrate(-cos(x)+sec(x),x, algorithm=""maxima"")","\log\left(\sec\left(x\right) + \tan\left(x\right)\right) - \sin\left(x\right)"," ",0,"log(sec(x) + tan(x)) - sin(x)","A",0
326,1,21,0,0.321831," ","integrate(1/(-cos(x)+sec(x)),x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{2 \, \sin\left(x\right)} - \frac{\sin\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/2*(cos(x) + 1)/sin(x) - 1/2*sin(x)/(cos(x) + 1)","B",0
327,1,6,0,0.320544," ","integrate(1/(-cos(x)+sec(x))^2,x, algorithm=""maxima"")","-\frac{1}{3 \, \tan\left(x\right)^{3}}"," ",0,"-1/3/tan(x)^3","A",0
328,1,73,0,0.318926," ","integrate(1/(-cos(x)+sec(x))^3,x, algorithm=""maxima"")","\frac{{\left(\frac{5 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(x\right) + 1\right)}^{5}}{480 \, \sin\left(x\right)^{5}} + \frac{\sin\left(x\right)}{16 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{\sin\left(x\right)^{3}}{96 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{\sin\left(x\right)^{5}}{160 \, {\left(\cos\left(x\right) + 1\right)}^{5}}"," ",0,"1/480*(5*sin(x)^2/(cos(x) + 1)^2 + 30*sin(x)^4/(cos(x) + 1)^4 - 3)*(cos(x) + 1)^5/sin(x)^5 + 1/16*sin(x)/(cos(x) + 1) + 1/96*sin(x)^3/(cos(x) + 1)^3 - 1/160*sin(x)^5/(cos(x) + 1)^5","B",0
329,1,14,0,0.321446," ","integrate(1/(-cos(x)+sec(x))^4,x, algorithm=""maxima"")","-\frac{7 \, \tan\left(x\right)^{2} + 5}{35 \, \tan\left(x\right)^{7}}"," ",0,"-1/35*(7*tan(x)^2 + 5)/tan(x)^7","A",0
330,1,121,0,0.334932," ","integrate(1/(-cos(x)+sec(x))^5,x, algorithm=""maxima"")","\frac{{\left(\frac{45 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{252 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{420 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{1890 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} - 35\right)} {\left(\cos\left(x\right) + 1\right)}^{9}}{161280 \, \sin\left(x\right)^{9}} - \frac{3 \, \sin\left(x\right)}{256 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{\sin\left(x\right)^{3}}{384 \, {\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{\sin\left(x\right)^{5}}{640 \, {\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{\sin\left(x\right)^{7}}{3584 \, {\left(\cos\left(x\right) + 1\right)}^{7}} - \frac{\sin\left(x\right)^{9}}{4608 \, {\left(\cos\left(x\right) + 1\right)}^{9}}"," ",0,"1/161280*(45*sin(x)^2/(cos(x) + 1)^2 + 252*sin(x)^4/(cos(x) + 1)^4 - 420*sin(x)^6/(cos(x) + 1)^6 - 1890*sin(x)^8/(cos(x) + 1)^8 - 35)*(cos(x) + 1)^9/sin(x)^9 - 3/256*sin(x)/(cos(x) + 1) - 1/384*sin(x)^3/(cos(x) + 1)^3 + 1/640*sin(x)^5/(cos(x) + 1)^5 + 1/3584*sin(x)^7/(cos(x) + 1)^7 - 1/4608*sin(x)^9/(cos(x) + 1)^9","B",0
331,1,20,0,0.319225," ","integrate(1/(-cos(x)+sec(x))^6,x, algorithm=""maxima"")","-\frac{99 \, \tan\left(x\right)^{4} + 154 \, \tan\left(x\right)^{2} + 63}{693 \, \tan\left(x\right)^{11}}"," ",0,"-1/693*(99*tan(x)^4 + 154*tan(x)^2 + 63)/tan(x)^11","A",0
332,1,169,0,0.333936," ","integrate(1/(-cos(x)+sec(x))^7,x, algorithm=""maxima"")","\frac{{\left(\frac{273 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2002 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2574 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{9009 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{15015 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} + \frac{60060 \, \sin\left(x\right)^{12}}{{\left(\cos\left(x\right) + 1\right)}^{12}} - 231\right)} {\left(\cos\left(x\right) + 1\right)}^{13}}{24600576 \, \sin\left(x\right)^{13}} + \frac{5 \, \sin\left(x\right)}{2048 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{5 \, \sin\left(x\right)^{3}}{8192 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(x\right)^{5}}{8192 \, {\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(x\right)^{7}}{28672 \, {\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{\sin\left(x\right)^{9}}{12288 \, {\left(\cos\left(x\right) + 1\right)}^{9}} + \frac{\sin\left(x\right)^{11}}{90112 \, {\left(\cos\left(x\right) + 1\right)}^{11}} - \frac{\sin\left(x\right)^{13}}{106496 \, {\left(\cos\left(x\right) + 1\right)}^{13}}"," ",0,"1/24600576*(273*sin(x)^2/(cos(x) + 1)^2 + 2002*sin(x)^4/(cos(x) + 1)^4 - 2574*sin(x)^6/(cos(x) + 1)^6 - 9009*sin(x)^8/(cos(x) + 1)^8 + 15015*sin(x)^10/(cos(x) + 1)^10 + 60060*sin(x)^12/(cos(x) + 1)^12 - 231)*(cos(x) + 1)^13/sin(x)^13 + 5/2048*sin(x)/(cos(x) + 1) + 5/8192*sin(x)^3/(cos(x) + 1)^3 - 3/8192*sin(x)^5/(cos(x) + 1)^5 - 3/28672*sin(x)^7/(cos(x) + 1)^7 + 1/12288*sin(x)^9/(cos(x) + 1)^9 + 1/90112*sin(x)^11/(cos(x) + 1)^11 - 1/106496*sin(x)^13/(cos(x) + 1)^13","B",0
333,1,82,0,0.440674," ","integrate((-cos(x)+sec(x))^(7/2),x, algorithm=""maxima"")","\frac{128 \, {\left(\frac{7 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{7 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} + \frac{2 \, \sin\left(x\right)^{14}}{{\left(\cos\left(x\right) + 1\right)}^{14}} - 2\right)}}{35 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{7}{2}} {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}"," ",0,"128/35*(7*sin(x)^4/(cos(x) + 1)^4 - 7*sin(x)^10/(cos(x) + 1)^10 + 2*sin(x)^14/(cos(x) + 1)^14 - 2)/((sin(x)/(cos(x) + 1) + 1)^(7/2)*(-sin(x)/(cos(x) + 1) + 1)^(7/2)*(sin(x)^2/(cos(x) + 1)^2 + 1)^(7/2))","A",0
334,1,82,0,0.428164," ","integrate((-cos(x)+sec(x))^(5/2),x, algorithm=""maxima"")","-\frac{32 \, {\left(\frac{5 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{2 \, \sin\left(x\right)^{10}}{{\left(\cos\left(x\right) + 1\right)}^{10}} - 2\right)}}{15 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{5}{2}} {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"-32/15*(5*sin(x)^4/(cos(x) + 1)^4 - 5*sin(x)^6/(cos(x) + 1)^6 + 2*sin(x)^10/(cos(x) + 1)^10 - 2)/((sin(x)/(cos(x) + 1) + 1)^(5/2)*(-sin(x)/(cos(x) + 1) + 1)^(5/2)*(sin(x)^2/(cos(x) + 1)^2 + 1)^(5/2))","B",0
335,1,57,0,0.428379," ","integrate((-cos(x)+sec(x))^(3/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(\frac{\sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - 1\right)}}{3 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"-8/3*(sin(x)^6/(cos(x) + 1)^6 - 1)/((sin(x)/(cos(x) + 1) + 1)^(3/2)*(-sin(x)/(cos(x) + 1) + 1)^(3/2)*(sin(x)^2/(cos(x) + 1)^2 + 1)^(3/2))","B",0
336,1,57,0,0.434474," ","integrate((-cos(x)+sec(x))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)}}{\sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} \sqrt{-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1} \sqrt{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1}}"," ",0,"2*(sin(x)^2/(cos(x) + 1)^2 - 1)/(sqrt(sin(x)/(cos(x) + 1) + 1)*sqrt(-sin(x)/(cos(x) + 1) + 1)*sqrt(sin(x)^2/(cos(x) + 1)^2 + 1))","B",0
337,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-\cos\left(x\right) + \sec\left(x\right)}}\,{d x}"," ",0,"integrate(1/sqrt(-cos(x) + sec(x)), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-\cos\left(x\right) + \sec\left(x\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-cos(x) + sec(x))^(-3/2), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-\cos\left(x\right) + \sec\left(x\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-cos(x) + sec(x))^(-5/2), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-\cos\left(x\right) + \sec\left(x\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((-cos(x) + sec(x))^(-7/2), x)","F",0
341,1,68,0,0.421802," ","integrate((sin(x)+tan(x))^4,x, algorithm=""maxima"")","-\frac{4}{3} \, \sin\left(x\right)^{3} + \frac{1}{3} \, \tan\left(x\right)^{3} - \frac{61}{8} \, x - \frac{2 \, \sin\left(x\right)}{\sin\left(x\right)^{2} - 1} + \frac{3 \, \tan\left(x\right)}{\tan\left(x\right)^{2} + 1} - \log\left(\sin\left(x\right) + 1\right) + \log\left(\sin\left(x\right) - 1\right) + \frac{1}{32} \, \sin\left(4 \, x\right) - \frac{1}{4} \, \sin\left(2 \, x\right) + 5 \, \tan\left(x\right)"," ",0,"-4/3*sin(x)^3 + 1/3*tan(x)^3 - 61/8*x - 2*sin(x)/(sin(x)^2 - 1) + 3*tan(x)/(tan(x)^2 + 1) - log(sin(x) + 1) + log(sin(x) - 1) + 1/32*sin(4*x) - 1/4*sin(2*x) + 5*tan(x)","A",0
342,1,42,0,0.316585," ","integrate((sin(x)+tan(x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, \cos\left(x\right)^{3} - \frac{3}{2} \, \sin\left(x\right)^{2} - \frac{1}{2 \, {\left(\sin\left(x\right)^{2} - 1\right)}} + \frac{3}{\cos\left(x\right)} + 2 \, \cos\left(x\right) - \log\left(\sin\left(x\right)^{2} - 1\right)"," ",0,"1/3*cos(x)^3 - 3/2*sin(x)^2 - 1/2/(sin(x)^2 - 1) + 3/cos(x) + 2*cos(x) - log(sin(x)^2 - 1)","A",0
343,1,28,0,0.409080," ","integrate((sin(x)+tan(x))^2,x, algorithm=""maxima"")","-\frac{1}{2} \, x + \log\left(\sin\left(x\right) + 1\right) - \log\left(\sin\left(x\right) - 1\right) - \frac{1}{4} \, \sin\left(2 \, x\right) - 2 \, \sin\left(x\right) + \tan\left(x\right)"," ",0,"-1/2*x + log(sin(x) + 1) - log(sin(x) - 1) - 1/4*sin(2*x) - 2*sin(x) + tan(x)","A",0
344,1,8,0,0.309063," ","integrate(sin(x)+tan(x),x, algorithm=""maxima"")","-\cos\left(x\right) + \log\left(\sec\left(x\right)\right)"," ",0,"-cos(x) + log(sec(x))","A",0
345,1,25,0,0.308365," ","integrate(1/(sin(x)+tan(x)),x, algorithm=""maxima"")","-\frac{\sin\left(x\right)^{2}}{4 \, {\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{1}{2} \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/4*sin(x)^2/(cos(x) + 1)^2 + 1/2*log(sin(x)/(cos(x) + 1))","A",0
346,1,45,0,0.310140," ","integrate(1/(sin(x)+tan(x))^2,x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{8 \, \sin\left(x\right)} - \frac{\sin\left(x\right)}{8 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{\sin\left(x\right)^{3}}{24 \, {\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{\sin\left(x\right)^{5}}{40 \, {\left(\cos\left(x\right) + 1\right)}^{5}}"," ",0,"-1/8*(cos(x) + 1)/sin(x) - 1/8*sin(x)/(cos(x) + 1) - 1/24*sin(x)^3/(cos(x) + 1)^3 + 1/40*sin(x)^5/(cos(x) + 1)^5","A",0
347,1,73,0,0.314461," ","integrate(1/(sin(x)+tan(x))^3,x, algorithm=""maxima"")","-\frac{{\left(\cos\left(x\right) + 1\right)}^{2}}{64 \, \sin\left(x\right)^{2}} - \frac{\sin\left(x\right)^{2}}{32 \, {\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{4}}{64 \, {\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{\sin\left(x\right)^{6}}{192 \, {\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{\sin\left(x\right)^{8}}{256 \, {\left(\cos\left(x\right) + 1\right)}^{8}} - \frac{1}{32} \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/64*(cos(x) + 1)^2/sin(x)^2 - 1/32*sin(x)^2/(cos(x) + 1)^2 + 1/64*sin(x)^4/(cos(x) + 1)^4 + 1/192*sin(x)^6/(cos(x) + 1)^6 - 1/256*sin(x)^8/(cos(x) + 1)^8 - 1/32*log(sin(x)/(cos(x) + 1))","A",0
348,1,97,0,0.324232," ","integrate(1/(sin(x)+tan(x))^4,x, algorithm=""maxima"")","\frac{{\left(\frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{384 \, \sin\left(x\right)^{3}} - \frac{3 \, \sin\left(x\right)}{128 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{\sin\left(x\right)^{3}}{128 \, {\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{5}}{640 \, {\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(x\right)^{7}}{896 \, {\left(\cos\left(x\right) + 1\right)}^{7}} - \frac{\sin\left(x\right)^{9}}{1152 \, {\left(\cos\left(x\right) + 1\right)}^{9}} + \frac{\sin\left(x\right)^{11}}{1408 \, {\left(\cos\left(x\right) + 1\right)}^{11}}"," ",0,"1/384*(3*sin(x)^2/(cos(x) + 1)^2 - 1)*(cos(x) + 1)^3/sin(x)^3 - 3/128*sin(x)/(cos(x) + 1) + 1/128*sin(x)^3/(cos(x) + 1)^3 + 3/640*sin(x)^5/(cos(x) + 1)^5 - 3/896*sin(x)^7/(cos(x) + 1)^7 - 1/1152*sin(x)^9/(cos(x) + 1)^9 + 1/1408*sin(x)^11/(cos(x) + 1)^11","A",0
349,1,153,0,0.423101," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","C {\left(\frac{2 \, c \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2} + c^{2}} - \frac{b \log\left(-b - \frac{2 \, c \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{2} + c^{2}} + \frac{b \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{2} + c^{2}}\right)} - \frac{A \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{\sqrt{b^{2} + c^{2}}}"," ",0,"C*(2*c*arctan(sin(x)/(cos(x) + 1))/(b^2 + c^2) - b*log(-b - 2*c*sin(x)/(cos(x) + 1) + b*sin(x)^2/(cos(x) + 1)^2)/(b^2 + c^2) + b*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(b^2 + c^2)) - A*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/sqrt(b^2 + c^2)","B",0
350,1,146,0,0.421339," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","-C {\left(\frac{c \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b + \frac{c \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{b^{3} + b c^{2} + \frac{2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{3} + b c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}\right)} - \frac{A}{c^{2} \tan\left(x\right) + b c}"," ",0,"-C*(c*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(b + c*sin(x)/(cos(x) + 1))/(b^3 + b*c^2 + 2*(b^2*c + c^3)*sin(x)/(cos(x) + 1) - (b^3 + b*c^2)*sin(x)^2/(cos(x) + 1)^2)) - A/(c^2*tan(x) + b*c)","A",0
351,1,338,0,0.435817," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","-\frac{1}{2} \, A {\left(\frac{2 \, {\left(b^{2} c - \frac{{\left(b^{3} - 2 \, b c^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{2} c - 2 \, c^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(b^{3} + 2 \, b c^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{b^{6} + b^{4} c^{2} + \frac{4 \, {\left(b^{5} c + b^{3} c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(b^{6} - b^{4} c^{2} - 2 \, b^{2} c^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, {\left(b^{5} c + b^{3} c^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(b^{6} + b^{4} c^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} + \frac{\log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}}\right)} + \frac{2 \, C \sin\left(x\right)^{2}}{{\left(b^{3} + \frac{4 \, b^{2} c \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, b^{2} c \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{b^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(b^{3} - 2 \, b c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}"," ",0,"-1/2*A*(2*(b^2*c - (b^3 - 2*b*c^2)*sin(x)/(cos(x) + 1) - (b^2*c - 2*c^3)*sin(x)^2/(cos(x) + 1)^2 - (b^3 + 2*b*c^2)*sin(x)^3/(cos(x) + 1)^3)/(b^6 + b^4*c^2 + 4*(b^5*c + b^3*c^3)*sin(x)/(cos(x) + 1) - 2*(b^6 - b^4*c^2 - 2*b^2*c^4)*sin(x)^2/(cos(x) + 1)^2 - 4*(b^5*c + b^3*c^3)*sin(x)^3/(cos(x) + 1)^3 + (b^6 + b^4*c^2)*sin(x)^4/(cos(x) + 1)^4) + log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2)) + 2*C*sin(x)^2/((b^3 + 4*b^2*c*sin(x)/(cos(x) + 1) - 4*b^2*c*sin(x)^3/(cos(x) + 1)^3 + b^3*sin(x)^4/(cos(x) + 1)^4 - 2*(b^3 - 2*b*c^2)*sin(x)^2/(cos(x) + 1)^2)*(cos(x) + 1)^2)","B",0
352,1,153,0,0.423399," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","B {\left(\frac{2 \, b \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2} + c^{2}} + \frac{c \log\left(-b - \frac{2 \, c \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{2} + c^{2}} - \frac{c \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{2} + c^{2}}\right)} - \frac{A \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{\sqrt{b^{2} + c^{2}}}"," ",0,"B*(2*b*arctan(sin(x)/(cos(x) + 1))/(b^2 + c^2) + c*log(-b - 2*c*sin(x)/(cos(x) + 1) + b*sin(x)^2/(cos(x) + 1)^2)/(b^2 + c^2) - c*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(b^2 + c^2)) - A*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/sqrt(b^2 + c^2)","B",0
353,1,156,0,0.424884," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","-B {\left(\frac{b \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(b c + \frac{c^{2} \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{b^{4} + b^{2} c^{2} + \frac{2 \, {\left(b^{3} c + b c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{4} + b^{2} c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}\right)} - \frac{A}{c^{2} \tan\left(x\right) + b c}"," ",0,"-B*(b*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) + 2*(b*c + c^2*sin(x)/(cos(x) + 1))/(b^4 + b^2*c^2 + 2*(b^3*c + b*c^3)*sin(x)/(cos(x) + 1) - (b^4 + b^2*c^2)*sin(x)^2/(cos(x) + 1)^2)) - A/(c^2*tan(x) + b*c)","B",0
354,1,366,0,0.443194," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","-\frac{1}{2} \, A {\left(\frac{2 \, {\left(b^{2} c - \frac{{\left(b^{3} - 2 \, b c^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{2} c - 2 \, c^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(b^{3} + 2 \, b c^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{b^{6} + b^{4} c^{2} + \frac{4 \, {\left(b^{5} c + b^{3} c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(b^{6} - b^{4} c^{2} - 2 \, b^{2} c^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, {\left(b^{5} c + b^{3} c^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(b^{6} + b^{4} c^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} + \frac{\log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}}\right)} + \frac{2 \, B {\left(\frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{c \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{b^{4} + \frac{4 \, b^{3} c \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, b^{3} c \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{b^{4} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(b^{4} - 2 \, b^{2} c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}"," ",0,"-1/2*A*(2*(b^2*c - (b^3 - 2*b*c^2)*sin(x)/(cos(x) + 1) - (b^2*c - 2*c^3)*sin(x)^2/(cos(x) + 1)^2 - (b^3 + 2*b*c^2)*sin(x)^3/(cos(x) + 1)^3)/(b^6 + b^4*c^2 + 4*(b^5*c + b^3*c^3)*sin(x)/(cos(x) + 1) - 2*(b^6 - b^4*c^2 - 2*b^2*c^4)*sin(x)^2/(cos(x) + 1)^2 - 4*(b^5*c + b^3*c^3)*sin(x)^3/(cos(x) + 1)^3 + (b^6 + b^4*c^2)*sin(x)^4/(cos(x) + 1)^4) + log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2)) + 2*B*(b*sin(x)/(cos(x) + 1) + c*sin(x)^2/(cos(x) + 1)^2 - b*sin(x)^3/(cos(x) + 1)^3)/(b^4 + 4*b^3*c*sin(x)/(cos(x) + 1) - 4*b^3*c*sin(x)^3/(cos(x) + 1)^3 + b^4*sin(x)^4/(cos(x) + 1)^4 - 2*(b^4 - 2*b^2*c^2)*sin(x)^2/(cos(x) + 1)^2)","B",0
355,1,354,0,0.328108," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x, algorithm=""maxima"")","-\frac{b^{3} c \cos\left(e x + d\right)^{4}}{e} + \frac{b c^{3} \sin\left(e x + d\right)^{4}}{e} + \frac{{\left(12 \, e x + 12 \, d + \sin\left(4 \, e x + 4 \, d\right) + 8 \, \sin\left(2 \, e x + 2 \, d\right)\right)} b^{4}}{32 \, e} + \frac{3 \, {\left(4 \, e x + 4 \, d - \sin\left(4 \, e x + 4 \, d\right)\right)} b^{2} c^{2}}{16 \, e} + \frac{{\left(12 \, e x + 12 \, d + \sin\left(4 \, e x + 4 \, d\right) - 8 \, \sin\left(2 \, e x + 2 \, d\right)\right)} c^{4}}{32 \, e} + {\left(b^{2} + c^{2}\right)}^{2} x - 4 \, {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}} {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)} - \frac{3}{2} \, {\left(\frac{4 \, b c \cos\left(e x + d\right)^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e}\right)} {\left(b^{2} + c^{2}\right)} - \frac{4}{3} \, {\left(\frac{3 \, b^{2} c \cos\left(e x + d\right)^{3}}{e} - \frac{3 \, b c^{2} \sin\left(e x + d\right)^{3}}{e} + \frac{{\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} b^{3}}{e} - \frac{{\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} c^{3}}{e}\right)} \sqrt{b^{2} + c^{2}}"," ",0,"-b^3*c*cos(e*x + d)^4/e + b*c^3*sin(e*x + d)^4/e + 1/32*(12*e*x + 12*d + sin(4*e*x + 4*d) + 8*sin(2*e*x + 2*d))*b^4/e + 3/16*(4*e*x + 4*d - sin(4*e*x + 4*d))*b^2*c^2/e + 1/32*(12*e*x + 12*d + sin(4*e*x + 4*d) - 8*sin(2*e*x + 2*d))*c^4/e + (b^2 + c^2)^2*x - 4*(b^2 + c^2)^(3/2)*(c*cos(e*x + d)/e - b*sin(e*x + d)/e) - 3/2*(4*b*c*cos(e*x + d)^2/e - (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e - (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e)*(b^2 + c^2) - 4/3*(3*b^2*c*cos(e*x + d)^3/e - 3*b*c^2*sin(e*x + d)^3/e + (sin(e*x + d)^3 - 3*sin(e*x + d))*b^3/e - (cos(e*x + d)^3 - 3*cos(e*x + d))*c^3/e)*sqrt(b^2 + c^2)","A",0
356,1,207,0,0.322317," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x, algorithm=""maxima"")","-\frac{b^{2} c \cos\left(e x + d\right)^{3}}{e} + \frac{b c^{2} \sin\left(e x + d\right)^{3}}{e} - \frac{{\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} b^{3}}{3 \, e} + \frac{{\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} c^{3}}{3 \, e} + {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}} x - 3 \, {\left(b^{2} + c^{2}\right)} {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)} - \frac{3}{4} \, {\left(\frac{4 \, b c \cos\left(e x + d\right)^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e}\right)} \sqrt{b^{2} + c^{2}}"," ",0,"-b^2*c*cos(e*x + d)^3/e + b*c^2*sin(e*x + d)^3/e - 1/3*(sin(e*x + d)^3 - 3*sin(e*x + d))*b^3/e + 1/3*(cos(e*x + d)^3 - 3*cos(e*x + d))*c^3/e + (b^2 + c^2)^(3/2)*x - 3*(b^2 + c^2)*(c*cos(e*x + d)/e - b*sin(e*x + d)/e) - 3/4*(4*b*c*cos(e*x + d)^2/e - (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e - (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e)*sqrt(b^2 + c^2)","A",0
357,1,113,0,0.307085," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x, algorithm=""maxima"")","b^{2} x + c^{2} x - \frac{b c \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{4 \, e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{4 \, e} - 2 \, \sqrt{b^{2} + c^{2}} {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)}"," ",0,"b^2*x + c^2*x - b*c*cos(e*x + d)^2/e + 1/4*(2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e + 1/4*(2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e - 2*sqrt(b^2 + c^2)*(c*cos(e*x + d)/e - b*sin(e*x + d)/e)","A",0
358,1,35,0,0.305861," ","integrate(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2),x, algorithm=""maxima"")","\sqrt{b^{2} + c^{2}} x - \frac{c \cos\left(e x + d\right)}{e} + \frac{b \sin\left(e x + d\right)}{e}"," ",0,"sqrt(b^2 + c^2)*x - c*cos(e*x + d)/e + b*sin(e*x + d)/e","A",0
359,1,40,0,0.307050," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2)),x, algorithm=""maxima"")","-\frac{2}{{\left(c - \frac{{\left(b - \sqrt{b^{2} + c^{2}}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)} e}"," ",0,"-2/((c - (b - sqrt(b^2 + c^2))*sin(e*x + d)/(cos(e*x + d) + 1))*e)","A",0
360,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
361,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
362,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
363,1,191,0,0.321055," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""maxima"")","-\frac{8 \, a^{2} c \cos\left(e x + d\right)^{3}}{e} + \frac{8 \, a c^{2} \sin\left(e x + d\right)^{3}}{e} + 8 \, a^{3} x - \frac{8 \, {\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} a^{3}}{3 \, e} + \frac{8 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} c^{3}}{3 \, e} - 24 \, a^{2} {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{a \sin\left(e x + d\right)}{e}\right)} - 6 \, {\left(\frac{4 \, a c \cos\left(e x + d\right)^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e}\right)} a"," ",0,"-8*a^2*c*cos(e*x + d)^3/e + 8*a*c^2*sin(e*x + d)^3/e + 8*a^3*x - 8/3*(sin(e*x + d)^3 - 3*sin(e*x + d))*a^3/e + 8/3*(cos(e*x + d)^3 - 3*cos(e*x + d))*c^3/e - 24*a^2*(c*cos(e*x + d)/e - a*sin(e*x + d)/e) - 6*(4*a*c*cos(e*x + d)^2/e - (2*e*x + 2*d + sin(2*e*x + 2*d))*a^2/e - (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e)*a","A",0
364,1,99,0,0.304965," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""maxima"")","4 \, a^{2} x - \frac{4 \, a c \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e} - 8 \, a {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{a \sin\left(e x + d\right)}{e}\right)}"," ",0,"4*a^2*x - 4*a*c*cos(e*x + d)^2/e + (2*e*x + 2*d + sin(2*e*x + 2*d))*a^2/e + (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e - 8*a*(c*cos(e*x + d)/e - a*sin(e*x + d)/e)","A",0
365,1,29,0,0.303154," ","integrate(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d),x, algorithm=""maxima"")","2 \, a x - \frac{2 \, c \cos\left(e x + d\right)}{e} + \frac{2 \, a \sin\left(e x + d\right)}{e}"," ",0,"2*a*x - 2*c*cos(e*x + d)/e + 2*a*sin(e*x + d)/e","A",0
366,1,29,0,0.313471," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d)),x, algorithm=""maxima"")","\frac{\log\left(a + \frac{c \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{2 \, c e}"," ",0,"1/2*log(a + c*sin(e*x + d)/(cos(e*x + d) + 1))/(c*e)","A",0
367,1,90,0,0.322050," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""maxima"")","-\frac{\frac{a^{2} + c^{2}}{a c^{3} + \frac{c^{4} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}} + \frac{2 \, a \log\left(a + \frac{c \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{3}} - \frac{\sin\left(e x + d\right)}{c^{2} {\left(\cos\left(e x + d\right) + 1\right)}}}{8 \, e}"," ",0,"-1/8*((a^2 + c^2)/(a*c^3 + c^4*sin(e*x + d)/(cos(e*x + d) + 1)) + 2*a*log(a + c*sin(e*x + d)/(cos(e*x + d) + 1))/c^3 - sin(e*x + d)/(c^2*(cos(e*x + d) + 1)))/e","A",0
368,1,190,0,0.336084," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""maxima"")","\frac{\frac{7 \, a^{4} + 6 \, a^{2} c^{2} - c^{4} + \frac{8 \, {\left(a^{3} c + a c^{3}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}}{a^{2} c^{5} + \frac{2 \, a c^{6} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{c^{7} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}} - \frac{\frac{6 \, a \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - \frac{c \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}}{c^{4}} + \frac{4 \, {\left(3 \, a^{2} + c^{2}\right)} \log\left(a + \frac{c \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{5}}}{64 \, e}"," ",0,"1/64*((7*a^4 + 6*a^2*c^2 - c^4 + 8*(a^3*c + a*c^3)*sin(e*x + d)/(cos(e*x + d) + 1))/(a^2*c^5 + 2*a*c^6*sin(e*x + d)/(cos(e*x + d) + 1) + c^7*sin(e*x + d)^2/(cos(e*x + d) + 1)^2) - (6*a*sin(e*x + d)/(cos(e*x + d) + 1) - c*sin(e*x + d)^2/(cos(e*x + d) + 1)^2)/c^4 + 4*(3*a^2 + c^2)*log(a + c*sin(e*x + d)/(cos(e*x + d) + 1))/c^5)/e","A",0
369,1,307,0,0.357648," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x, algorithm=""maxima"")","-\frac{\frac{37 \, a^{6} + 39 \, a^{4} c^{2} + 3 \, a^{2} c^{4} + c^{6} + \frac{9 \, {\left(9 \, a^{5} c + 10 \, a^{3} c^{3} + a c^{5}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{9 \, {\left(5 \, a^{4} c^{2} + 6 \, a^{2} c^{4} + c^{6}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}}{a^{3} c^{7} + \frac{3 \, a^{2} c^{8} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{3 \, a c^{9} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{c^{10} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}} + \frac{\frac{6 \, a c \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} - \frac{3 \, {\left(10 \, a^{2} + 3 \, c^{2}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}}{c^{6}} + \frac{12 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} \log\left(a + \frac{c \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{7}}}{384 \, e}"," ",0,"-1/384*((37*a^6 + 39*a^4*c^2 + 3*a^2*c^4 + c^6 + 9*(9*a^5*c + 10*a^3*c^3 + a*c^5)*sin(e*x + d)/(cos(e*x + d) + 1) + 9*(5*a^4*c^2 + 6*a^2*c^4 + c^6)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2)/(a^3*c^7 + 3*a^2*c^8*sin(e*x + d)/(cos(e*x + d) + 1) + 3*a*c^9*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + c^10*sin(e*x + d)^3/(cos(e*x + d) + 1)^3) + (6*a*c*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - c^2*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 - 3*(10*a^2 + 3*c^2)*sin(e*x + d)/(cos(e*x + d) + 1))/c^6 + 12*(5*a^3 + 3*a*c^2)*log(a + c*sin(e*x + d)/(cos(e*x + d) + 1))/c^7)/e","A",0
370,1,28,0,0.309021," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d)),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{2 \, a e}"," ",0,"1/2*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/(a*e)","A",0
371,1,80,0,0.324270," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""maxima"")","-\frac{\frac{2}{a^{2} + \frac{a^{2} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}} + \frac{2 \, \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{a^{2}} - \frac{\sin\left(e x + d\right)}{a^{2} {\left(\cos\left(e x + d\right) + 1\right)}}}{8 \, e}"," ",0,"-1/8*(2/(a^2 + a^2*sin(e*x + d)/(cos(e*x + d) + 1)) + 2*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/a^2 - sin(e*x + d)/(a^2*(cos(e*x + d) + 1)))/e","A",0
372,1,146,0,0.340097," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\frac{4 \, \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 3\right)}}{a^{3} + \frac{2 \, a^{3} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{a^{3} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}} - \frac{\frac{6 \, \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - \frac{\sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}}{a^{3}} + \frac{16 \, \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{a^{3}}}{64 \, e}"," ",0,"1/64*(4*(4*sin(e*x + d)/(cos(e*x + d) + 1) + 3)/(a^3 + 2*a^3*sin(e*x + d)/(cos(e*x + d) + 1) + a^3*sin(e*x + d)^2/(cos(e*x + d) + 1)^2) - (6*sin(e*x + d)/(cos(e*x + d) + 1) - sin(e*x + d)^2/(cos(e*x + d) + 1)^2)/a^3 + 16*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/a^3)/e","A",0
373,1,208,0,0.345969," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^4,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(\frac{45 \, \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{27 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + 20\right)}}{a^{4} + \frac{3 \, a^{4} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{3 \, a^{4} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{a^{4} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}} - \frac{\frac{39 \, \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - \frac{6 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{\sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}}{a^{4}} + \frac{96 \, \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{a^{4}}}{384 \, e}"," ",0,"-1/384*(4*(45*sin(e*x + d)/(cos(e*x + d) + 1) + 27*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 20)/(a^4 + 3*a^4*sin(e*x + d)/(cos(e*x + d) + 1) + 3*a^4*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + a^4*sin(e*x + d)^3/(cos(e*x + d) + 1)^3) - (39*sin(e*x + d)/(cos(e*x + d) + 1) - 6*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + sin(e*x + d)^3/(cos(e*x + d) + 1)^3)/a^4 + 96*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/a^4)/e","A",0
374,1,188,0,0.328504," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""maxima"")","-\frac{8 \, a^{2} c \cos\left(e x + d\right)^{3}}{e} - \frac{8 \, a c^{2} \sin\left(e x + d\right)^{3}}{e} + 8 \, a^{3} x + \frac{8 \, {\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} a^{3}}{3 \, e} + \frac{8 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} c^{3}}{3 \, e} - 24 \, a^{2} {\left(\frac{c \cos\left(e x + d\right)}{e} + \frac{a \sin\left(e x + d\right)}{e}\right)} + 6 \, {\left(\frac{4 \, a c \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e}\right)} a"," ",0,"-8*a^2*c*cos(e*x + d)^3/e - 8*a*c^2*sin(e*x + d)^3/e + 8*a^3*x + 8/3*(sin(e*x + d)^3 - 3*sin(e*x + d))*a^3/e + 8/3*(cos(e*x + d)^3 - 3*cos(e*x + d))*c^3/e - 24*a^2*(c*cos(e*x + d)/e + a*sin(e*x + d)/e) + 6*(4*a*c*cos(e*x + d)^2/e + (2*e*x + 2*d + sin(2*e*x + 2*d))*a^2/e + (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e)*a","A",0
375,1,98,0,0.322880," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""maxima"")","4 \, a^{2} x + \frac{4 \, a c \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e} - 8 \, a {\left(\frac{c \cos\left(e x + d\right)}{e} + \frac{a \sin\left(e x + d\right)}{e}\right)}"," ",0,"4*a^2*x + 4*a*c*cos(e*x + d)^2/e + (2*e*x + 2*d + sin(2*e*x + 2*d))*a^2/e + (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e - 8*a*(c*cos(e*x + d)/e + a*sin(e*x + d)/e)","A",0
376,1,29,0,0.310521," ","integrate(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d),x, algorithm=""maxima"")","2 \, a x - \frac{2 \, c \cos\left(e x + d\right)}{e} - \frac{2 \, a \sin\left(e x + d\right)}{e}"," ",0,"2*a*x - 2*c*cos(e*x + d)/e - 2*a*sin(e*x + d)/e","A",0
377,1,54,0,0.315485," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(c + \frac{a \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c} - \frac{\log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c}}{2 \, e}"," ",0,"-1/2*(log(c + a*sin(e*x + d)/(cos(e*x + d) + 1))/c - log(sin(e*x + d)/(cos(e*x + d) + 1))/c)/e","B",0
378,1,137,0,0.332448," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""maxima"")","-\frac{\frac{a c + \frac{{\left(2 \, a^{2} + c^{2}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}}{\frac{a c^{3} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{a^{2} c^{2} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}} - \frac{2 \, a \log\left(c + \frac{a \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{3}} + \frac{2 \, a \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{3}}}{8 \, e}"," ",0,"-1/8*((a*c + (2*a^2 + c^2)*sin(e*x + d)/(cos(e*x + d) + 1))/(a*c^3*sin(e*x + d)/(cos(e*x + d) + 1) + a^2*c^2*sin(e*x + d)^2/(cos(e*x + d) + 1)^2) - 2*a*log(c + a*sin(e*x + d)/(cos(e*x + d) + 1))/c^3 + 2*a*log(sin(e*x + d)/(cos(e*x + d) + 1))/c^3)/e","A",0
379,1,265,0,0.349002," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""maxima"")","-\frac{\frac{a^{2} c^{3} - \frac{4 \, a^{3} c^{2} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - \frac{{\left(18 \, a^{4} c + 6 \, a^{2} c^{3} - c^{5}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{2 \, {\left(6 \, a^{5} + 2 \, a^{3} c^{2} - a c^{4}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}}{\frac{a^{2} c^{6} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{2 \, a^{3} c^{5} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{a^{4} c^{4} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}}} + \frac{4 \, {\left(3 \, a^{2} + c^{2}\right)} \log\left(c + \frac{a \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{5}} - \frac{4 \, {\left(3 \, a^{2} + c^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{5}}}{64 \, e}"," ",0,"-1/64*((a^2*c^3 - 4*a^3*c^2*sin(e*x + d)/(cos(e*x + d) + 1) - (18*a^4*c + 6*a^2*c^3 - c^5)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - 2*(6*a^5 + 2*a^3*c^2 - a*c^4)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3)/(a^2*c^6*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 2*a^3*c^5*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + a^4*c^4*sin(e*x + d)^4/(cos(e*x + d) + 1)^4) + 4*(3*a^2 + c^2)*log(c + a*sin(e*x + d)/(cos(e*x + d) + 1))/c^5 - 4*(3*a^2 + c^2)*log(sin(e*x + d)/(cos(e*x + d) + 1))/c^5)/e","B",0
380,1,382,0,0.377899," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x, algorithm=""maxima"")","-\frac{\frac{a^{3} c^{5} - \frac{3 \, a^{4} c^{4} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{3 \, {\left(5 \, a^{5} c^{3} + 3 \, a^{3} c^{5}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{{\left(110 \, a^{6} c^{2} + 66 \, a^{4} c^{4} + 3 \, a^{2} c^{6} + c^{8}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, {\left(50 \, a^{7} c + 30 \, a^{5} c^{3} + a c^{7}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{3 \, {\left(20 \, a^{8} + 12 \, a^{6} c^{2} + a^{2} c^{6}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}}}{\frac{a^{3} c^{9} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, a^{4} c^{8} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{3 \, a^{5} c^{7} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}} + \frac{a^{6} c^{6} \sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}}} - \frac{12 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} \log\left(c + \frac{a \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{7}} + \frac{12 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{c^{7}}}{384 \, e}"," ",0,"-1/384*((a^3*c^5 - 3*a^4*c^4*sin(e*x + d)/(cos(e*x + d) + 1) + 3*(5*a^5*c^3 + 3*a^3*c^5)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + (110*a^6*c^2 + 66*a^4*c^4 + 3*a^2*c^6 + c^8)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*(50*a^7*c + 30*a^5*c^3 + a*c^7)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + 3*(20*a^8 + 12*a^6*c^2 + a^2*c^6)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5)/(a^3*c^9*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*a^4*c^8*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + 3*a^5*c^7*sin(e*x + d)^5/(cos(e*x + d) + 1)^5 + a^6*c^6*sin(e*x + d)^6/(cos(e*x + d) + 1)^6) - 12*(5*a^3 + 3*a*c^2)*log(c + a*sin(e*x + d)/(cos(e*x + d) + 1))/c^7 + 12*(5*a^3 + 3*a*c^2)*log(sin(e*x + d)/(cos(e*x + d) + 1))/c^7)/e","A",0
381,1,191,0,0.329164," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""maxima"")","-\frac{8 \, a b^{2} \cos\left(e x + d\right)^{3}}{e} + \frac{8 \, a^{2} b \sin\left(e x + d\right)^{3}}{e} + 8 \, a^{3} x + \frac{8 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} a^{3}}{3 \, e} - \frac{8 \, {\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} b^{3}}{3 \, e} - 24 \, a^{2} {\left(\frac{a \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)} - 6 \, {\left(\frac{4 \, a b \cos\left(e x + d\right)^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e}\right)} a"," ",0,"-8*a*b^2*cos(e*x + d)^3/e + 8*a^2*b*sin(e*x + d)^3/e + 8*a^3*x + 8/3*(cos(e*x + d)^3 - 3*cos(e*x + d))*a^3/e - 8/3*(sin(e*x + d)^3 - 3*sin(e*x + d))*b^3/e - 24*a^2*(a*cos(e*x + d)/e - b*sin(e*x + d)/e) - 6*(4*a*b*cos(e*x + d)^2/e - (2*e*x + 2*d - sin(2*e*x + 2*d))*a^2/e - (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e)*a","A",0
382,1,99,0,0.318946," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""maxima"")","4 \, a^{2} x - \frac{4 \, a b \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e} - 8 \, a {\left(\frac{a \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)}"," ",0,"4*a^2*x - 4*a*b*cos(e*x + d)^2/e + (2*e*x + 2*d - sin(2*e*x + 2*d))*a^2/e + (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e - 8*a*(a*cos(e*x + d)/e - b*sin(e*x + d)/e)","A",0
383,1,29,0,0.314850," ","integrate(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d),x, algorithm=""maxima"")","2 \, a x - \frac{2 \, a \cos\left(e x + d\right)}{e} + \frac{2 \, b \sin\left(e x + d\right)}{e}"," ",0,"2*a*x - 2*a*cos(e*x + d)/e + 2*b*sin(e*x + d)/e","A",0
384,1,66,0,0.320531," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(-a - b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b} - \frac{\log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{b}}{2 \, e}"," ",0,"-1/2*(log(-a - b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b - log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/b)/e","B",0
385,1,185,0,0.336789," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{2} + \frac{{\left(a^{2} - a b + b^{2}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}}{a^{2} b^{2} - b^{4} + \frac{2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{{\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}} - \frac{a \log\left(-a - b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b^{3}} + \frac{a \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{b^{3}}}{4 \, e}"," ",0,"-1/4*(2*(a^2 + (a^2 - a*b + b^2)*sin(e*x + d)/(cos(e*x + d) + 1))/(a^2*b^2 - b^4 + 2*(a^2*b^2 - a*b^3)*sin(e*x + d)/(cos(e*x + d) + 1) + (a^2*b^2 - 2*a*b^3 + b^4)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2) - a*log(-a - b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b^3 + a*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/b^3)/e","B",0
386,1,493,0,0.347841," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} - a b^{4} + \frac{{\left(9 \, a^{5} - 9 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{{\left(9 \, a^{5} - 18 \, a^{4} b + 12 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{{\left(3 \, a^{5} - 9 \, a^{4} b + 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}\right)}}{a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8} + \frac{4 \, {\left(a^{4} b^{4} - a^{3} b^{5} - a^{2} b^{6} + a b^{7}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{2 \, {\left(3 \, a^{4} b^{4} - 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 2 \, a b^{7} - b^{8}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{4 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{{\left(a^{4} b^{4} - 4 \, a^{3} b^{5} + 6 \, a^{2} b^{6} - 4 \, a b^{7} + b^{8}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}}} - \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(-a - b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b^{5}} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{b^{5}}}{16 \, e}"," ",0,"1/16*(2*(3*a^5 - 4*a^3*b^2 - a*b^4 + (9*a^5 - 9*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 5*a*b^4 + b^5)*sin(e*x + d)/(cos(e*x + d) + 1) + (9*a^5 - 18*a^4*b + 12*a^3*b^2 - 6*a^2*b^3 + a*b^4)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + (3*a^5 - 9*a^4*b + 10*a^3*b^2 - 6*a^2*b^3 + a*b^4 + b^5)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3)/(a^4*b^4 - 2*a^2*b^6 + b^8 + 4*(a^4*b^4 - a^3*b^5 - a^2*b^6 + a*b^7)*sin(e*x + d)/(cos(e*x + d) + 1) + 2*(3*a^4*b^4 - 6*a^3*b^5 + 2*a^2*b^6 + 2*a*b^7 - b^8)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 4*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + (a^4*b^4 - 4*a^3*b^5 + 6*a^2*b^6 - 4*a*b^7 + b^8)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4) - (3*a^2 + b^2)*log(-a - b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b^5 + (3*a^2 + b^2)*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/b^5)/e","B",0
387,1,963,0,0.392536," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^4,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, a^{8} - 31 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + 15 \, a^{2} b^{6} + \frac{3 \, {\left(25 \, a^{8} - 25 \, a^{7} b - 25 \, a^{6} b^{2} + 25 \, a^{5} b^{3} - 13 \, a^{4} b^{4} + 13 \, a^{3} b^{5} + 11 \, a^{2} b^{6} - 5 \, a b^{7} + 2 \, b^{8}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{6 \, {\left(25 \, a^{8} - 50 \, a^{7} b + 20 \, a^{6} b^{2} + 10 \, a^{5} b^{3} - 17 \, a^{4} b^{4} + 24 \, a^{3} b^{5} - 10 \, a^{2} b^{6} + 2 \, a b^{7}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{2 \, {\left(75 \, a^{8} - 225 \, a^{7} b + 250 \, a^{6} b^{2} - 150 \, a^{5} b^{3} + 63 \, a^{4} b^{4} + 11 \, a^{3} b^{5} - 24 \, a^{2} b^{6} + 6 \, a b^{7} - 2 \, b^{8}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, {\left(25 \, a^{8} - 100 \, a^{7} b + 165 \, a^{6} b^{2} - 160 \, a^{5} b^{3} + 115 \, a^{4} b^{4} - 60 \, a^{3} b^{5} + 19 \, a^{2} b^{6} - 4 \, a b^{7}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{3 \, {\left(5 \, a^{8} - 25 \, a^{7} b + 53 \, a^{6} b^{2} - 65 \, a^{5} b^{3} + 55 \, a^{4} b^{4} - 35 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 7 \, a b^{7} + 2 \, b^{8}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}}\right)}}{a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12} + \frac{6 \, {\left(a^{6} b^{6} - a^{5} b^{7} - 2 \, a^{4} b^{8} + 2 \, a^{3} b^{9} + a^{2} b^{10} - a b^{11}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{3 \, {\left(5 \, a^{6} b^{6} - 10 \, a^{5} b^{7} - a^{4} b^{8} + 12 \, a^{3} b^{9} - 5 \, a^{2} b^{10} - 2 \, a b^{11} + b^{12}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{4 \, {\left(5 \, a^{6} b^{6} - 15 \, a^{5} b^{7} + 12 \, a^{4} b^{8} + 4 \, a^{3} b^{9} - 9 \, a^{2} b^{10} + 3 \, a b^{11}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, {\left(5 \, a^{6} b^{6} - 20 \, a^{5} b^{7} + 29 \, a^{4} b^{8} - 16 \, a^{3} b^{9} - a^{2} b^{10} + 4 \, a b^{11} - b^{12}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{6 \, {\left(a^{6} b^{6} - 5 \, a^{5} b^{7} + 10 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + 5 \, a^{2} b^{10} - a b^{11}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}} + \frac{{\left(a^{6} b^{6} - 6 \, a^{5} b^{7} + 15 \, a^{4} b^{8} - 20 \, a^{3} b^{9} + 15 \, a^{2} b^{10} - 6 \, a b^{11} + b^{12}\right)} \sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}}} - \frac{3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(-a - b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b^{7}} + \frac{3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right)}{b^{7}}}{96 \, e}"," ",0,"-1/96*(2*(15*a^8 - 31*a^6*b^2 + 9*a^4*b^4 + 15*a^2*b^6 + 3*(25*a^8 - 25*a^7*b - 25*a^6*b^2 + 25*a^5*b^3 - 13*a^4*b^4 + 13*a^3*b^5 + 11*a^2*b^6 - 5*a*b^7 + 2*b^8)*sin(e*x + d)/(cos(e*x + d) + 1) + 6*(25*a^8 - 50*a^7*b + 20*a^6*b^2 + 10*a^5*b^3 - 17*a^4*b^4 + 24*a^3*b^5 - 10*a^2*b^6 + 2*a*b^7)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 2*(75*a^8 - 225*a^7*b + 250*a^6*b^2 - 150*a^5*b^3 + 63*a^4*b^4 + 11*a^3*b^5 - 24*a^2*b^6 + 6*a*b^7 - 2*b^8)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*(25*a^8 - 100*a^7*b + 165*a^6*b^2 - 160*a^5*b^3 + 115*a^4*b^4 - 60*a^3*b^5 + 19*a^2*b^6 - 4*a*b^7)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + 3*(5*a^8 - 25*a^7*b + 53*a^6*b^2 - 65*a^5*b^3 + 55*a^4*b^4 - 35*a^3*b^5 + 17*a^2*b^6 - 7*a*b^7 + 2*b^8)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5)/(a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12 + 6*(a^6*b^6 - a^5*b^7 - 2*a^4*b^8 + 2*a^3*b^9 + a^2*b^10 - a*b^11)*sin(e*x + d)/(cos(e*x + d) + 1) + 3*(5*a^6*b^6 - 10*a^5*b^7 - a^4*b^8 + 12*a^3*b^9 - 5*a^2*b^10 - 2*a*b^11 + b^12)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 4*(5*a^6*b^6 - 15*a^5*b^7 + 12*a^4*b^8 + 4*a^3*b^9 - 9*a^2*b^10 + 3*a*b^11)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*(5*a^6*b^6 - 20*a^5*b^7 + 29*a^4*b^8 - 16*a^3*b^9 - a^2*b^10 + 4*a*b^11 - b^12)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + 6*(a^6*b^6 - 5*a^5*b^7 + 10*a^4*b^8 - 10*a^3*b^9 + 5*a^2*b^10 - a*b^11)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5 + (a^6*b^6 - 6*a^5*b^7 + 15*a^4*b^8 - 20*a^3*b^9 + 15*a^2*b^10 - 6*a*b^11 + b^12)*sin(e*x + d)^6/(cos(e*x + d) + 1)^6) - 3*(5*a^3 + 3*a*b^2)*log(-a - b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b^7 + 3*(5*a^3 + 3*a*b^2)*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1)/b^7)/e","B",0
388,1,188,0,0.320073," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x, algorithm=""maxima"")","\frac{8 \, a b^{2} \cos\left(e x + d\right)^{3}}{e} + \frac{8 \, a^{2} b \sin\left(e x + d\right)^{3}}{e} + 8 \, a^{3} x - \frac{8 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} a^{3}}{3 \, e} - \frac{8 \, {\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} b^{3}}{3 \, e} + 24 \, a^{2} {\left(\frac{a \cos\left(e x + d\right)}{e} + \frac{b \sin\left(e x + d\right)}{e}\right)} + 6 \, {\left(\frac{4 \, a b \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e}\right)} a"," ",0,"8*a*b^2*cos(e*x + d)^3/e + 8*a^2*b*sin(e*x + d)^3/e + 8*a^3*x - 8/3*(cos(e*x + d)^3 - 3*cos(e*x + d))*a^3/e - 8/3*(sin(e*x + d)^3 - 3*sin(e*x + d))*b^3/e + 24*a^2*(a*cos(e*x + d)/e + b*sin(e*x + d)/e) + 6*(4*a*b*cos(e*x + d)^2/e + (2*e*x + 2*d - sin(2*e*x + 2*d))*a^2/e + (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e)*a","A",0
389,1,98,0,0.323790," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x, algorithm=""maxima"")","4 \, a^{2} x + \frac{4 \, a b \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e} + 8 \, a {\left(\frac{a \cos\left(e x + d\right)}{e} + \frac{b \sin\left(e x + d\right)}{e}\right)}"," ",0,"4*a^2*x + 4*a*b*cos(e*x + d)^2/e + (2*e*x + 2*d - sin(2*e*x + 2*d))*a^2/e + (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e + 8*a*(a*cos(e*x + d)/e + b*sin(e*x + d)/e)","A",0
390,1,29,0,0.327561," ","integrate(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d),x, algorithm=""maxima"")","2 \, a x + \frac{2 \, a \cos\left(e x + d\right)}{e} + \frac{2 \, b \sin\left(e x + d\right)}{e}"," ",0,"2*a*x + 2*a*cos(e*x + d)/e + 2*b*sin(e*x + d)/e","A",0
391,1,62,0,0.328966," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d)),x, algorithm=""maxima"")","\frac{\frac{\log\left(a + b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b} - \frac{\log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right)}{b}}{2 \, e}"," ",0,"1/2*(log(a + b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b - log(sin(e*x + d)/(cos(e*x + d) + 1) - 1)/b)/e","B",0
392,1,182,0,0.337716," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{2} - \frac{{\left(a^{2} - a b + b^{2}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}}{a^{2} b^{2} - b^{4} - \frac{2 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{{\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}} - \frac{a \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b^{3}} + \frac{a \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right)}{b^{3}}}{4 \, e}"," ",0,"1/4*(2*(a^2 - (a^2 - a*b + b^2)*sin(e*x + d)/(cos(e*x + d) + 1))/(a^2*b^2 - b^4 - 2*(a^2*b^2 - a*b^3)*sin(e*x + d)/(cos(e*x + d) + 1) + (a^2*b^2 - 2*a*b^3 + b^4)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2) - a*log(a + b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b^3 + a*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1)/b^3)/e","B",0
393,1,491,0,0.358714," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} - a b^{4} - \frac{{\left(9 \, a^{5} - 9 \, a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{{\left(9 \, a^{5} - 18 \, a^{4} b + 12 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{{\left(3 \, a^{5} - 9 \, a^{4} b + 10 \, a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}\right)}}{a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8} - \frac{4 \, {\left(a^{4} b^{4} - a^{3} b^{5} - a^{2} b^{6} + a b^{7}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{2 \, {\left(3 \, a^{4} b^{4} - 6 \, a^{3} b^{5} + 2 \, a^{2} b^{6} + 2 \, a b^{7} - b^{8}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{4 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{{\left(a^{4} b^{4} - 4 \, a^{3} b^{5} + 6 \, a^{2} b^{6} - 4 \, a b^{7} + b^{8}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}}} - \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b^{5}} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right)}{b^{5}}}{16 \, e}"," ",0,"-1/16*(2*(3*a^5 - 4*a^3*b^2 - a*b^4 - (9*a^5 - 9*a^4*b - 2*a^3*b^2 + 2*a^2*b^3 - 5*a*b^4 + b^5)*sin(e*x + d)/(cos(e*x + d) + 1) + (9*a^5 - 18*a^4*b + 12*a^3*b^2 - 6*a^2*b^3 + a*b^4)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - (3*a^5 - 9*a^4*b + 10*a^3*b^2 - 6*a^2*b^3 + a*b^4 + b^5)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3)/(a^4*b^4 - 2*a^2*b^6 + b^8 - 4*(a^4*b^4 - a^3*b^5 - a^2*b^6 + a*b^7)*sin(e*x + d)/(cos(e*x + d) + 1) + 2*(3*a^4*b^4 - 6*a^3*b^5 + 2*a^2*b^6 + 2*a*b^7 - b^8)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - 4*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + (a^4*b^4 - 4*a^3*b^5 + 6*a^2*b^6 - 4*a*b^7 + b^8)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4) - (3*a^2 + b^2)*log(a + b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b^5 + (3*a^2 + b^2)*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1)/b^5)/e","B",0
394,1,959,0,0.391792," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^4,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, a^{8} - 31 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + 15 \, a^{2} b^{6} - \frac{3 \, {\left(25 \, a^{8} - 25 \, a^{7} b - 25 \, a^{6} b^{2} + 25 \, a^{5} b^{3} - 13 \, a^{4} b^{4} + 13 \, a^{3} b^{5} + 11 \, a^{2} b^{6} - 5 \, a b^{7} + 2 \, b^{8}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{6 \, {\left(25 \, a^{8} - 50 \, a^{7} b + 20 \, a^{6} b^{2} + 10 \, a^{5} b^{3} - 17 \, a^{4} b^{4} + 24 \, a^{3} b^{5} - 10 \, a^{2} b^{6} + 2 \, a b^{7}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{2 \, {\left(75 \, a^{8} - 225 \, a^{7} b + 250 \, a^{6} b^{2} - 150 \, a^{5} b^{3} + 63 \, a^{4} b^{4} + 11 \, a^{3} b^{5} - 24 \, a^{2} b^{6} + 6 \, a b^{7} - 2 \, b^{8}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, {\left(25 \, a^{8} - 100 \, a^{7} b + 165 \, a^{6} b^{2} - 160 \, a^{5} b^{3} + 115 \, a^{4} b^{4} - 60 \, a^{3} b^{5} + 19 \, a^{2} b^{6} - 4 \, a b^{7}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} - \frac{3 \, {\left(5 \, a^{8} - 25 \, a^{7} b + 53 \, a^{6} b^{2} - 65 \, a^{5} b^{3} + 55 \, a^{4} b^{4} - 35 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 7 \, a b^{7} + 2 \, b^{8}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}}\right)}}{a^{6} b^{6} - 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} - b^{12} - \frac{6 \, {\left(a^{6} b^{6} - a^{5} b^{7} - 2 \, a^{4} b^{8} + 2 \, a^{3} b^{9} + a^{2} b^{10} - a b^{11}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{3 \, {\left(5 \, a^{6} b^{6} - 10 \, a^{5} b^{7} - a^{4} b^{8} + 12 \, a^{3} b^{9} - 5 \, a^{2} b^{10} - 2 \, a b^{11} + b^{12}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{4 \, {\left(5 \, a^{6} b^{6} - 15 \, a^{5} b^{7} + 12 \, a^{4} b^{8} + 4 \, a^{3} b^{9} - 9 \, a^{2} b^{10} + 3 \, a b^{11}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, {\left(5 \, a^{6} b^{6} - 20 \, a^{5} b^{7} + 29 \, a^{4} b^{8} - 16 \, a^{3} b^{9} - a^{2} b^{10} + 4 \, a b^{11} - b^{12}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} - \frac{6 \, {\left(a^{6} b^{6} - 5 \, a^{5} b^{7} + 10 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + 5 \, a^{2} b^{10} - a b^{11}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}} + \frac{{\left(a^{6} b^{6} - 6 \, a^{5} b^{7} + 15 \, a^{4} b^{8} - 20 \, a^{3} b^{9} + 15 \, a^{2} b^{10} - 6 \, a b^{11} + b^{12}\right)} \sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}}} - \frac{3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(a + b - \frac{{\left(a - b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right)}{b^{7}} + \frac{3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right)}{b^{7}}}{96 \, e}"," ",0,"1/96*(2*(15*a^8 - 31*a^6*b^2 + 9*a^4*b^4 + 15*a^2*b^6 - 3*(25*a^8 - 25*a^7*b - 25*a^6*b^2 + 25*a^5*b^3 - 13*a^4*b^4 + 13*a^3*b^5 + 11*a^2*b^6 - 5*a*b^7 + 2*b^8)*sin(e*x + d)/(cos(e*x + d) + 1) + 6*(25*a^8 - 50*a^7*b + 20*a^6*b^2 + 10*a^5*b^3 - 17*a^4*b^4 + 24*a^3*b^5 - 10*a^2*b^6 + 2*a*b^7)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - 2*(75*a^8 - 225*a^7*b + 250*a^6*b^2 - 150*a^5*b^3 + 63*a^4*b^4 + 11*a^3*b^5 - 24*a^2*b^6 + 6*a*b^7 - 2*b^8)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*(25*a^8 - 100*a^7*b + 165*a^6*b^2 - 160*a^5*b^3 + 115*a^4*b^4 - 60*a^3*b^5 + 19*a^2*b^6 - 4*a*b^7)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 - 3*(5*a^8 - 25*a^7*b + 53*a^6*b^2 - 65*a^5*b^3 + 55*a^4*b^4 - 35*a^3*b^5 + 17*a^2*b^6 - 7*a*b^7 + 2*b^8)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5)/(a^6*b^6 - 3*a^4*b^8 + 3*a^2*b^10 - b^12 - 6*(a^6*b^6 - a^5*b^7 - 2*a^4*b^8 + 2*a^3*b^9 + a^2*b^10 - a*b^11)*sin(e*x + d)/(cos(e*x + d) + 1) + 3*(5*a^6*b^6 - 10*a^5*b^7 - a^4*b^8 + 12*a^3*b^9 - 5*a^2*b^10 - 2*a*b^11 + b^12)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - 4*(5*a^6*b^6 - 15*a^5*b^7 + 12*a^4*b^8 + 4*a^3*b^9 - 9*a^2*b^10 + 3*a*b^11)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*(5*a^6*b^6 - 20*a^5*b^7 + 29*a^4*b^8 - 16*a^3*b^9 - a^2*b^10 + 4*a*b^11 - b^12)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 - 6*(a^6*b^6 - 5*a^5*b^7 + 10*a^4*b^8 - 10*a^3*b^9 + 5*a^2*b^10 - a*b^11)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5 + (a^6*b^6 - 6*a^5*b^7 + 15*a^4*b^8 - 20*a^3*b^9 + 15*a^2*b^10 - 6*a*b^11 + b^12)*sin(e*x + d)^6/(cos(e*x + d) + 1)^6) - 3*(5*a^3 + 3*a*b^2)*log(a + b - (a - b)*sin(e*x + d)/(cos(e*x + d) + 1))/b^7 + 3*(5*a^3 + 3*a*b^2)*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1)/b^7)/e","B",0
395,1,330,0,0.332815," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^4,x, algorithm=""maxima"")","-\frac{b^{3} c \cos\left(e x + d\right)^{4}}{e} + \frac{b c^{3} \sin\left(e x + d\right)^{4}}{e} + a^{4} x + \frac{{\left(12 \, e x + 12 \, d + \sin\left(4 \, e x + 4 \, d\right) + 8 \, \sin\left(2 \, e x + 2 \, d\right)\right)} b^{4}}{32 \, e} + \frac{3 \, {\left(4 \, e x + 4 \, d - \sin\left(4 \, e x + 4 \, d\right)\right)} b^{2} c^{2}}{16 \, e} + \frac{{\left(12 \, e x + 12 \, d + \sin\left(4 \, e x + 4 \, d\right) - 8 \, \sin\left(2 \, e x + 2 \, d\right)\right)} c^{4}}{32 \, e} - 4 \, a^{3} {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)} - \frac{3}{2} \, {\left(\frac{4 \, b c \cos\left(e x + d\right)^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e}\right)} a^{2} - \frac{4}{3} \, {\left(\frac{3 \, b^{2} c \cos\left(e x + d\right)^{3}}{e} - \frac{3 \, b c^{2} \sin\left(e x + d\right)^{3}}{e} + \frac{{\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} b^{3}}{e} - \frac{{\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} c^{3}}{e}\right)} a"," ",0,"-b^3*c*cos(e*x + d)^4/e + b*c^3*sin(e*x + d)^4/e + a^4*x + 1/32*(12*e*x + 12*d + sin(4*e*x + 4*d) + 8*sin(2*e*x + 2*d))*b^4/e + 3/16*(4*e*x + 4*d - sin(4*e*x + 4*d))*b^2*c^2/e + 1/32*(12*e*x + 12*d + sin(4*e*x + 4*d) - 8*sin(2*e*x + 2*d))*c^4/e - 4*a^3*(c*cos(e*x + d)/e - b*sin(e*x + d)/e) - 3/2*(4*b*c*cos(e*x + d)^2/e - (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e - (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e)*a^2 - 4/3*(3*b^2*c*cos(e*x + d)^3/e - 3*b*c^2*sin(e*x + d)^3/e + (sin(e*x + d)^3 - 3*sin(e*x + d))*b^3/e - (cos(e*x + d)^3 - 3*cos(e*x + d))*c^3/e)*a","A",0
396,1,189,0,0.330573," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^3,x, algorithm=""maxima"")","-\frac{b^{2} c \cos\left(e x + d\right)^{3}}{e} + \frac{b c^{2} \sin\left(e x + d\right)^{3}}{e} + a^{3} x - \frac{{\left(\sin\left(e x + d\right)^{3} - 3 \, \sin\left(e x + d\right)\right)} b^{3}}{3 \, e} + \frac{{\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} c^{3}}{3 \, e} - 3 \, a^{2} {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)} - \frac{3}{4} \, {\left(\frac{4 \, b c \cos\left(e x + d\right)^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{e} - \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{e}\right)} a"," ",0,"-b^2*c*cos(e*x + d)^3/e + b*c^2*sin(e*x + d)^3/e + a^3*x - 1/3*(sin(e*x + d)^3 - 3*sin(e*x + d))*b^3/e + 1/3*(cos(e*x + d)^3 - 3*cos(e*x + d))*c^3/e - 3*a^2*(c*cos(e*x + d)/e - b*sin(e*x + d)/e) - 3/4*(4*b*c*cos(e*x + d)^2/e - (2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e - (2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e)*a","A",0
397,1,100,0,0.310864," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^2,x, algorithm=""maxima"")","a^{2} x - \frac{b c \cos\left(e x + d\right)^{2}}{e} + \frac{{\left(2 \, e x + 2 \, d + \sin\left(2 \, e x + 2 \, d\right)\right)} b^{2}}{4 \, e} + \frac{{\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} c^{2}}{4 \, e} - 2 \, a {\left(\frac{c \cos\left(e x + d\right)}{e} - \frac{b \sin\left(e x + d\right)}{e}\right)}"," ",0,"a^2*x - b*c*cos(e*x + d)^2/e + 1/4*(2*e*x + 2*d + sin(2*e*x + 2*d))*b^2/e + 1/4*(2*e*x + 2*d - sin(2*e*x + 2*d))*c^2/e - 2*a*(c*cos(e*x + d)/e - b*sin(e*x + d)/e)","A",0
398,1,27,0,0.310777," ","integrate(a+b*cos(e*x+d)+c*sin(e*x+d),x, algorithm=""maxima"")","a x - \frac{c \cos\left(e x + d\right)}{e} + \frac{b \sin\left(e x + d\right)}{e}"," ",0,"a*x - c*cos(e*x + d)/e + b*sin(e*x + d)/e","A",0
399,-2,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
400,-2,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
401,-2,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
402,-2,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
403,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int {\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(5/2), x)","F",0
404,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int {\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(3/2), x)","F",0
405,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}\,{d x}"," ",0,"integrate(sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
406,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
407,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(-3/2), x)","F",0
408,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(-5/2), x)","F",0
409,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(-7/2), x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(5/2), x)","F",0
411,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(3/2), x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(-3/2), x)","F",0
415,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(-5/2), x)","F",0
416,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(-7/2), x)","F",0
417,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) + 5)^(5/2), x)","F",0
418,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) + 5)^(3/2), x)","F",0
419,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}\,{d x}"," ",0,"integrate(sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5), x)","F",0
420,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}}\,{d x}"," ",0,"integrate(1/sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5), x)","F",0
421,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) + 5)^(-3/2), x)","F",0
422,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) + 5)^(-5/2), x)","F",0
423,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(7/2),x, algorithm=""maxima"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(7/2), x)","F",0
424,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(5/2), x)","F",0
425,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}\,{d x}"," ",0,"integrate(sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5), x)","F",0
427,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}\,{d x}"," ",0,"integrate(1/sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5), x)","F",0
428,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(-3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(-5/2), x)","F",0
430,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
431,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
432,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
433,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
434,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
435,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
436,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
437,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
438,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
439,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
440,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
441,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
442,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
443,-2,0,0,0.000000," ","integrate(sin(x)/(a+b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
444,1,41,0,0.408996," ","integrate(sin(x)/(1+cos(x)+sin(x)),x, algorithm=""maxima"")","\arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) + \frac{1}{2} \, \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"arctan(sin(x)/(cos(x) + 1)) - log(sin(x)/(cos(x) + 1) + 1) + 1/2*log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
445,-2,0,0,0.000000," ","integrate(1/(a+c*sec(x)+b*tan(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2-b^2-a^2>0)', see `assume?` for more details)Is c^2-b^2-a^2 positive or negative?","F(-2)",0
446,-2,0,0,0.000000," ","integrate(sec(x)/(a+c*sec(x)+b*tan(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2-b^2-a^2>0)', see `assume?` for more details)Is c^2-b^2-a^2 positive or negative?","F(-2)",0
447,-2,0,0,0.000000," ","integrate(sec(x)^2/(a+c*sec(x)+b*tan(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2-b^2-a^2>0)', see `assume?` for more details)Is c^2-b^2-a^2 positive or negative?","F(-2)",0
448,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2)/sec(e*x+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}}}{\sec\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)/sec(e*x + d)^(3/2), x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2)/sec(e*x+d)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a}}{\sqrt{\sec\left(e x + d\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)/sqrt(sec(e*x + d)), x)","F",0
450,0,0,0,0.000000," ","integrate(sec(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\sec\left(e x + d\right)}}{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a}}\,{d x}"," ",0,"integrate(sqrt(sec(e*x + d))/sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a), x)","F",0
451,0,0,0,0.000000," ","integrate(sec(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(e x + d\right)^{\frac{3}{2}}}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(e*x + d)^(3/2)/(b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2), x)","F",0
452,0,0,0,0.000000," ","integrate(sec(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{\sec\left(e x + d\right)^{\frac{5}{2}}}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(e*x + d)^(5/2)/(b*sec(e*x + d) + c*tan(e*x + d) + a)^(5/2), x)","F",0
453,0,0,0,0.000000," ","integrate(cos(e*x+d)^(3/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}} \cos\left(e x + d\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)*cos(e*x + d)^(3/2), x)","F",0
454,0,0,0,0.000000," ","integrate(cos(e*x+d)^(1/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d)), x)","F",0
455,0,0,0,0.000000," ","integrate(1/cos(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d))), x)","F",0
456,0,0,0,0.000000," ","integrate(1/cos(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}} \cos\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)*cos(e*x + d)^(3/2)), x)","F",0
457,0,0,0,0.000000," ","integrate(1/cos(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{5}{2}} \cos\left(e x + d\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(e*x + d) + c*tan(e*x + d) + a)^(5/2)*cos(e*x + d)^(5/2)), x)","F",0
458,-2,0,0,0.000000," ","integrate(1/(a+b*cot(x)+c*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2-b^2-a^2>0)', see `assume?` for more details)Is c^2-b^2-a^2 positive or negative?","F(-2)",0
459,-2,0,0,0.000000," ","integrate(csc(x)/(a+b*cot(x)+c*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2-b^2-a^2>0)', see `assume?` for more details)Is c^2-b^2-a^2 positive or negative?","F(-2)",0
460,-2,0,0,0.000000," ","integrate(csc(x)^2/(a+b*cot(x)+c*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2-b^2-a^2>0)', see `assume?` for more details)Is c^2-b^2-a^2 positive or negative?","F(-2)",0
461,1,14,0,0.409411," ","integrate(csc(x)/(2+2*cot(x)+3*csc(x)),x, algorithm=""maxima"")","2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 2\right)"," ",0,"2*arctan(sin(x)/(cos(x) + 1) + 2)","A",0
462,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/csc(e*x+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}}}{\csc\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)/csc(e*x + d)^(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/csc(e*x+d)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a}}{\sqrt{\csc\left(e x + d\right)}}\,{d x}"," ",0,"integrate(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)/sqrt(csc(e*x + d)), x)","F",0
464,0,0,0,0.000000," ","integrate(csc(e*x+d)^(1/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\csc\left(e x + d\right)}}{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a}}\,{d x}"," ",0,"integrate(sqrt(csc(e*x + d))/sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a), x)","F",0
465,0,0,0,0.000000," ","integrate(csc(e*x+d)^(3/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2),x, algorithm=""maxima"")","\int \frac{\csc\left(e x + d\right)^{\frac{3}{2}}}{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(e*x + d)^(3/2)/(c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2), x)","F",0
466,0,0,0,0.000000," ","integrate(csc(e*x+d)^(5/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2),x, algorithm=""maxima"")","\int \frac{\csc\left(e x + d\right)^{\frac{5}{2}}}{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(e*x + d)^(5/2)/(c*cot(e*x + d) + b*csc(e*x + d) + a)^(5/2), x)","F",0
467,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)*sin(e*x+d)^(3/2),x, algorithm=""maxima"")","\int {\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}} \sin\left(e x + d\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)*sin(e*x + d)^(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)*sin(e*x+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}\,{d x}"," ",0,"integrate(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d)), x)","F",0
469,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/sin(e*x+d)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d))), x)","F",0
470,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/sin(e*x+d)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}} \sin\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)*sin(e*x + d)^(3/2)), x)","F",0
471,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2)/sin(e*x+d)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{5}{2}} \sin\left(e x + d\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((c*cot(e*x + d) + b*csc(e*x + d) + a)^(5/2)*sin(e*x + d)^(5/2)), x)","F",0
472,1,1,0,0.405100," ","integrate(1/(cos(x)^2+sin(x)^2),x, algorithm=""maxima"")","x"," ",0,"x","A",0
473,1,1,0,0.410878," ","integrate(1/(cos(x)^2+sin(x)^2)^2,x, algorithm=""maxima"")","x"," ",0,"x","A",0
474,1,1,0,0.411411," ","integrate(1/(cos(x)^2+sin(x)^2)^3,x, algorithm=""maxima"")","x"," ",0,"x","A",0
475,1,15,0,0.320515," ","integrate(1/(cos(x)^2-sin(x)^2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\tan\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\tan\left(x\right) - 1\right)"," ",0,"1/2*log(tan(x) + 1) - 1/2*log(tan(x) - 1)","A",0
476,1,12,0,0.304367," ","integrate(1/(cos(x)^2-sin(x)^2)^2,x, algorithm=""maxima"")","-\frac{\tan\left(x\right)}{\tan\left(x\right)^{2} - 1}"," ",0,"-tan(x)/(tan(x)^2 - 1)","A",0
477,1,38,0,0.311271," ","integrate(1/(cos(x)^2-sin(x)^2)^3,x, algorithm=""maxima"")","\frac{\tan\left(x\right)^{3} + \tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{4} - 2 \, \tan\left(x\right)^{2} + 1\right)}} + \frac{1}{4} \, \log\left(\tan\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(\tan\left(x\right) - 1\right)"," ",0,"1/2*(tan(x)^3 + tan(x))/(tan(x)^4 - 2*tan(x)^2 + 1) + 1/4*log(tan(x) + 1) - 1/4*log(tan(x) - 1)","A",0
478,1,9,0,0.404629," ","integrate(1/(cos(x)^2+a^2*sin(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(a \tan\left(x\right)\right)}{a}"," ",0,"arctan(a*tan(x))/a","A",0
479,1,11,0,0.410768," ","integrate(1/(b^2*cos(x)^2+sin(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{\tan\left(x\right)}{b}\right)}{b}"," ",0,"arctan(tan(x)/b)/b","A",0
480,1,15,0,0.404068," ","integrate(1/(b^2*cos(x)^2+a^2*sin(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{a \tan\left(x\right)}{b}\right)}{a b}"," ",0,"arctan(a*tan(x)/b)/(a*b)","A",0
481,1,17,0,0.410209," ","integrate(1/(4*cos(1+2*x)^2+3*sin(1+2*x)^2),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{2} \, \sqrt{3} \tan\left(2 \, x + 1\right)\right)"," ",0,"1/12*sqrt(3)*arctan(1/2*sqrt(3)*tan(2*x + 1))","A",0
482,1,35,0,0.405134," ","integrate(sin(x)^2/(a*cos(x)^2+b*sin(x)^2),x, algorithm=""maxima"")","\frac{a \arctan\left(\frac{b \tan\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} - \frac{x}{a - b}"," ",0,"a*arctan(b*tan(x)/sqrt(a*b))/(sqrt(a*b)*(a - b)) - x/(a - b)","A",0
483,1,35,0,0.405347," ","integrate(cos(x)^2/(a*cos(x)^2+b*sin(x)^2),x, algorithm=""maxima"")","-\frac{b \arctan\left(\frac{b \tan\left(x\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} + \frac{x}{a - b}"," ",0,"-b*arctan(b*tan(x)/sqrt(a*b))/(sqrt(a*b)*(a - b)) + x/(a - b)","A",0
484,1,15,0,0.407420," ","integrate(1/(sec(x)^2+tan(x)^2),x, algorithm=""maxima"")","\sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) - x"," ",0,"sqrt(2)*arctan(sqrt(2)*tan(x)) - x","A",0
485,1,27,0,0.404985," ","integrate(1/(sec(x)^2+tan(x)^2)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) + x + \frac{\tan\left(x\right)}{2 \, \tan\left(x\right)^{2} + 1}"," ",0,"-1/2*sqrt(2)*arctan(sqrt(2)*tan(x)) + x + tan(x)/(2*tan(x)^2 + 1)","A",0
486,1,45,0,0.415318," ","integrate(1/(sec(x)^2+tan(x)^2)^3,x, algorithm=""maxima"")","\frac{7}{8} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) - x - \frac{2 \, \tan\left(x\right)^{3} - \tan\left(x\right)}{4 \, {\left(4 \, \tan\left(x\right)^{4} + 4 \, \tan\left(x\right)^{2} + 1\right)}}"," ",0,"7/8*sqrt(2)*arctan(sqrt(2)*tan(x)) - x - 1/4*(2*tan(x)^3 - tan(x))/(4*tan(x)^4 + 4*tan(x)^2 + 1)","A",0
487,1,1,0,0.427791," ","integrate(1/(sec(x)^2-tan(x)^2),x, algorithm=""maxima"")","x"," ",0,"x","A",0
488,1,1,0,0.408151," ","integrate(1/(sec(x)^2-tan(x)^2)^2,x, algorithm=""maxima"")","x"," ",0,"x","A",0
489,1,1,0,0.405827," ","integrate(1/(sec(x)^2-tan(x)^2)^3,x, algorithm=""maxima"")","x"," ",0,"x","A",0
490,1,16,0,0.409739," ","integrate(1/(cot(x)^2+csc(x)^2),x, algorithm=""maxima"")","\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - x"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - x","A",0
491,1,27,0,0.403801," ","integrate(1/(cot(x)^2+csc(x)^2)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) + x - \frac{\tan\left(x\right)}{\tan\left(x\right)^{2} + 2}"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) + x - tan(x)/(tan(x)^2 + 2)","A",0
492,1,42,0,0.424059," ","integrate(1/(cot(x)^2+csc(x)^2)^3,x, algorithm=""maxima"")","\frac{7}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(x\right)\right) - x - \frac{\tan\left(x\right)^{3} - 2 \, \tan\left(x\right)}{4 \, {\left(\tan\left(x\right)^{4} + 4 \, \tan\left(x\right)^{2} + 4\right)}}"," ",0,"7/8*sqrt(2)*arctan(1/2*sqrt(2)*tan(x)) - x - 1/4*(tan(x)^3 - 2*tan(x))/(tan(x)^4 + 4*tan(x)^2 + 4)","A",0
493,1,3,0,0.422569," ","integrate(1/(cot(x)^2-csc(x)^2),x, algorithm=""maxima"")","-x"," ",0,"-x","A",0
494,1,1,0,0.415800," ","integrate(1/(cot(x)^2-csc(x)^2)^2,x, algorithm=""maxima"")","x"," ",0,"x","A",0
495,1,3,0,0.410573," ","integrate(1/(cot(x)^2-csc(x)^2)^3,x, algorithm=""maxima"")","-x"," ",0,"-x","A",0
496,1,26,0,0.430945," ","integrate(1/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""maxima"")","\frac{\arctan\left(\frac{{\left(a + c\right)} \tan\left(x\right)}{\sqrt{{\left(a + b\right)} {\left(a + c\right)}}}\right)}{\sqrt{{\left(a + b\right)} {\left(a + c\right)}}}"," ",0,"arctan((a + c)*tan(x)/sqrt((a + b)*(a + c)))/sqrt((a + b)*(a + c))","A",0
497,0,0,0,0.000000," ","integrate(x/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""maxima"")","\int \frac{x}{b \cos\left(x\right)^{2} + c \sin\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(x/(b*cos(x)^2 + c*sin(x)^2 + a), x)","F",0
498,0,0,0,0.000000," ","integrate(x^2/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""maxima"")","\int \frac{x^{2}}{b \cos\left(x\right)^{2} + c \sin\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(x^2/(b*cos(x)^2 + c*sin(x)^2 + a), x)","F",0
499,1,246,0,0.323037," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x, algorithm=""maxima"")","\frac{15 \, {\left(12 \, e x + 12 \, d + \sin\left(4 \, e x + 4 \, d\right) - 8 \, \sin\left(2 \, e x + 2 \, d\right)\right)} a^{5} - 32 \, {\left(3 \, \cos\left(e x + d\right)^{5} - 10 \, \cos\left(e x + d\right)^{3} + 15 \, \cos\left(e x + d\right)\right)} a^{4} b + 640 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} a^{4} b + 60 \, {\left(12 \, e x + 12 \, d + \sin\left(4 \, e x + 4 \, d\right) - 8 \, \sin\left(2 \, e x + 2 \, d\right)\right)} a^{3} b^{2} + 720 \, {\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a^{3} b^{2} + 960 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} a^{2} b^{3} + 480 \, {\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a b^{4} + 480 \, {\left(e x + d\right)} a b^{4} - 1920 \, a^{2} b^{3} \cos\left(e x + d\right) - 480 \, b^{5} \cos\left(e x + d\right)}{480 \, e}"," ",0,"1/480*(15*(12*e*x + 12*d + sin(4*e*x + 4*d) - 8*sin(2*e*x + 2*d))*a^5 - 32*(3*cos(e*x + d)^5 - 10*cos(e*x + d)^3 + 15*cos(e*x + d))*a^4*b + 640*(cos(e*x + d)^3 - 3*cos(e*x + d))*a^4*b + 60*(12*e*x + 12*d + sin(4*e*x + 4*d) - 8*sin(2*e*x + 2*d))*a^3*b^2 + 720*(2*e*x + 2*d - sin(2*e*x + 2*d))*a^3*b^2 + 960*(cos(e*x + d)^3 - 3*cos(e*x + d))*a^2*b^3 + 480*(2*e*x + 2*d - sin(2*e*x + 2*d))*a*b^4 + 480*(e*x + d)*a*b^4 - 1920*a^2*b^3*cos(e*x + d) - 480*b^5*cos(e*x + d))/e","A",0
500,1,112,0,0.319659," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a^{3} + 4 \, {\left(\cos\left(e x + d\right)^{3} - 3 \, \cos\left(e x + d\right)\right)} a^{2} b + 6 \, {\left(2 \, e x + 2 \, d - \sin\left(2 \, e x + 2 \, d\right)\right)} a b^{2} + 12 \, {\left(e x + d\right)} a b^{2} - 24 \, a^{2} b \cos\left(e x + d\right) - 12 \, b^{3} \cos\left(e x + d\right)}{12 \, e}"," ",0,"1/12*(3*(2*e*x + 2*d - sin(2*e*x + 2*d))*a^3 + 4*(cos(e*x + d)^3 - 3*cos(e*x + d))*a^2*b + 6*(2*e*x + 2*d - sin(2*e*x + 2*d))*a*b^2 + 12*(e*x + d)*a*b^2 - 24*a^2*b*cos(e*x + d) - 12*b^3*cos(e*x + d))/e","A",0
501,-2,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
502,-2,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
503,0,0,0,0.000000," ","integrate((d+e*sin(x))/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""maxima"")","\int \frac{e \sin\left(x\right) + d}{c \sin\left(x\right)^{2} + b \sin\left(x\right) + a}\,{d x}"," ",0,"integrate((e*sin(x) + d)/(c*sin(x)^2 + b*sin(x) + a), x)","F",0
504,1,556,0,0.453187," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \arctan\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right) - \frac{4 \, a^{3} + 18 \, a b^{2} + \frac{9 \, a^{2} b \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{18 \, a b^{2} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} - \frac{9 \, a^{2} b \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}} + \frac{12 \, {\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}}}{\frac{3 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{\sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}} + 1}\right)} a + 3 \, {\left(3 \, {\left(a^{3} + 4 \, a b^{2}\right)} \arctan\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right) - \frac{16 \, a^{2} b + 8 \, b^{3} + \frac{8 \, b^{3} \sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}} + \frac{3 \, {\left(a^{3} + 4 \, a b^{2}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{8 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{{\left(11 \, a^{3} + 12 \, a b^{2}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{24 \, {\left(2 \, a^{2} b + b^{3}\right)} \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} - \frac{{\left(11 \, a^{3} + 12 \, a b^{2}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}} - \frac{3 \, {\left(a^{3} + 4 \, a b^{2}\right)} \sin\left(e x + d\right)^{7}}{{\left(\cos\left(e x + d\right) + 1\right)}^{7}}}{\frac{4 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{6 \, \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}} + \frac{\sin\left(e x + d\right)^{8}}{{\left(\cos\left(e x + d\right) + 1\right)}^{8}} + 1}\right)} b}{12 \, e}"," ",0,"1/12*(4*(3*(3*a^2*b + 2*b^3)*arctan(sin(e*x + d)/(cos(e*x + d) + 1)) - (4*a^3 + 18*a*b^2 + 9*a^2*b*sin(e*x + d)/(cos(e*x + d) + 1) + 18*a*b^2*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 - 9*a^2*b*sin(e*x + d)^5/(cos(e*x + d) + 1)^5 + 12*(a^3 + 3*a*b^2)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2)/(3*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 3*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + sin(e*x + d)^6/(cos(e*x + d) + 1)^6 + 1))*a + 3*(3*(a^3 + 4*a*b^2)*arctan(sin(e*x + d)/(cos(e*x + d) + 1)) - (16*a^2*b + 8*b^3 + 8*b^3*sin(e*x + d)^6/(cos(e*x + d) + 1)^6 + 3*(a^3 + 4*a*b^2)*sin(e*x + d)/(cos(e*x + d) + 1) + 8*(8*a^2*b + 3*b^3)*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + (11*a^3 + 12*a*b^2)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 24*(2*a^2*b + b^3)*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 - (11*a^3 + 12*a*b^2)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5 - 3*(a^3 + 4*a*b^2)*sin(e*x + d)^7/(cos(e*x + d) + 1)^7)/(4*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 6*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + 4*sin(e*x + d)^6/(cos(e*x + d) + 1)^6 + sin(e*x + d)^8/(cos(e*x + d) + 1)^8 + 1))*b)/e","A",0
505,1,187,0,0.429966," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(b \arctan\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right) - \frac{a}{\frac{\sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + 1}\right)} a + {\left(a \arctan\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right) - \frac{2 \, b + \frac{a \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{2 \, b \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{a \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}}{\frac{2 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} + \frac{\sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + 1}\right)} b}{e}"," ",0,"(2*(b*arctan(sin(e*x + d)/(cos(e*x + d) + 1)) - a/(sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + 1))*a + (a*arctan(sin(e*x + d)/(cos(e*x + d) + 1)) - (2*b + a*sin(e*x + d)/(cos(e*x + d) + 1) + 2*b*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - a*sin(e*x + d)^3/(cos(e*x + d) + 1)^3)/(2*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 + sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + 1))*b)/e","A",0
506,-2,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
507,-2,0,0,0.000000," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
508,-2,0,0,0.000000," ","integrate((a+b*cos(x))/(b^2+2*a*b*cos(x)+a^2*cos(x)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
509,0,0,0,0.000000," ","integrate((d+e*cos(x))/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""maxima"")","\int \frac{e \cos\left(x\right) + d}{c \cos\left(x\right)^{2} + b \cos\left(x\right) + a}\,{d x}"," ",0,"integrate((e*cos(x) + d)/(c*cos(x)^2 + b*cos(x) + a), x)","F",0
510,1,150,0,0.404831," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x, algorithm=""maxima"")","\frac{3 \, a^{4} b \tan\left(e x + d\right)^{4} + 4 \, {\left(a^{5} + 4 \, a^{3} b^{2}\right)} \tan\left(e x + d\right)^{3} + 18 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \tan\left(e x + d\right)^{2} + 12 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} {\left(e x + d\right)} - 6 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right) - 12 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \tan\left(e x + d\right)}{12 \, e}"," ",0,"1/12*(3*a^4*b*tan(e*x + d)^4 + 4*(a^5 + 4*a^3*b^2)*tan(e*x + d)^3 + 18*(a^4*b + 2*a^2*b^3)*tan(e*x + d)^2 + 12*(a^5 - 2*a^3*b^2 - 3*a*b^4)*(e*x + d) - 6*(3*a^4*b + 2*a^2*b^3 - b^5)*log(tan(e*x + d)^2 + 1) - 12*(a^5 - 2*a^3*b^2 - 4*a*b^4)*tan(e*x + d))/e","A",0
511,1,74,0,0.409327," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x, algorithm=""maxima"")","\frac{a^{2} b \tan\left(e x + d\right)^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} {\left(e x + d\right)} + {\left(a^{2} b + b^{3}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right) + 2 \, {\left(a^{3} + 2 \, a b^{2}\right)} \tan\left(e x + d\right)}{2 \, e}"," ",0,"1/2*(a^2*b*tan(e*x + d)^2 - 2*(a^3 + a*b^2)*(e*x + d) + (a^2*b + b^3)*log(tan(e*x + d)^2 + 1) + 2*(a^3 + 2*a*b^2)*tan(e*x + d))/e","A",0
512,1,161,0,0.411993," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(e x + d\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(a \tan\left(e x + d\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(a^{2} - b^{2}\right)}}{a^{2} b + b^{3} + {\left(a^{3} + a b^{2}\right)} \tan\left(e x + d\right)}}{2 \, e}"," ",0,"-1/2*(2*(a^3 - 3*a*b^2)*(e*x + d)/(a^4 + 2*a^2*b^2 + b^4) - 2*(3*a^2*b - b^3)*log(a*tan(e*x + d) + b)/(a^4 + 2*a^2*b^2 + b^4) + (3*a^2*b - b^3)*log(tan(e*x + d)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(a^2 - b^2)/(a^2*b + b^3 + (a^3 + a*b^2)*tan(e*x + d)))/e","A",0
513,1,419,0,0.431935," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} {\left(e x + d\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \log\left(a \tan\left(e x + d\right) + b\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{3 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{2 \, a^{6} + 5 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 11 \, b^{6} - 6 \, {\left(a^{6} - 6 \, a^{4} b^{2} + a^{2} b^{4}\right)} \tan\left(e x + d\right)^{2} - 3 \, {\left(a^{5} b - 26 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \tan\left(e x + d\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9} + {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} \tan\left(e x + d\right)^{3} + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} \tan\left(e x + d\right)^{2} + 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(e x + d\right)}}{6 \, e}"," ",0,"1/6*(6*(a^5 - 10*a^3*b^2 + 5*a*b^4)*(e*x + d)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(5*a^4*b - 10*a^2*b^3 + b^5)*log(a*tan(e*x + d) + b)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(5*a^4*b - 10*a^2*b^3 + b^5)*log(tan(e*x + d)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - (2*a^6 + 5*a^4*b^2 + 40*a^2*b^4 - 11*b^6 - 6*(a^6 - 6*a^4*b^2 + a^2*b^4)*tan(e*x + d)^2 - 3*(a^5*b - 26*a^3*b^3 + 5*a*b^5)*tan(e*x + d))/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9 + (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*tan(e*x + d)^3 + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*tan(e*x + d)^2 + 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*tan(e*x + d)))/e","B",0
514,1,166,0,0.426222," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(3/2),x, algorithm=""maxima"")","\frac{3 \, {\left(a^{3} \tan\left(e x + d\right)^{2} + 6 \, a^{2} b \tan\left(e x + d\right) - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(e x + d\right)} - {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right)\right)} a + {\left(2 \, a^{3} \tan\left(e x + d\right)^{3} + 9 \, a^{2} b \tan\left(e x + d\right)^{2} + 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(e x + d\right)} - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right) - 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(e x + d\right)\right)} b}{6 \, e}"," ",0,"1/6*(3*(a^3*tan(e*x + d)^2 + 6*a^2*b*tan(e*x + d) - 2*(3*a^2*b - b^3)*(e*x + d) - (a^3 - 3*a*b^2)*log(tan(e*x + d)^2 + 1))*a + (2*a^3*tan(e*x + d)^3 + 9*a^2*b*tan(e*x + d)^2 + 6*(a^3 - 3*a*b^2)*(e*x + d) - 3*(3*a^2*b - b^3)*log(tan(e*x + d)^2 + 1) - 6*(a^3 - 3*a*b^2)*tan(e*x + d))*b)/e","A",0
515,1,65,0,0.420624," ","integrate((b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(1/2)*(a+b*tan(e*x+d)),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(e x + d\right)} b + a \log\left(\tan\left(e x + d\right)^{2} + 1\right)\right)} a - {\left(2 \, {\left(e x + d\right)} a - b \log\left(\tan\left(e x + d\right)^{2} + 1\right) - 2 \, a \tan\left(e x + d\right)\right)} b}{2 \, e}"," ",0,"1/2*((2*(e*x + d)*b + a*log(tan(e*x + d)^2 + 1))*a - (2*(e*x + d)*a - b*log(tan(e*x + d)^2 + 1) - 2*a*tan(e*x + d))*b)/e","A",0
516,1,137,0,0.424362," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(1/2),x, algorithm=""maxima"")","\frac{a {\left(\frac{2 \, {\left(e x + d\right)} b}{a^{2} + b^{2}} + \frac{2 \, a \log\left(a \tan\left(e x + d\right) + b\right)}{a^{2} + b^{2}} - \frac{a \log\left(\tan\left(e x + d\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} + {\left(\frac{2 \, {\left(e x + d\right)} a}{a^{2} + b^{2}} - \frac{2 \, b \log\left(a \tan\left(e x + d\right) + b\right)}{a^{2} + b^{2}} + \frac{b \log\left(\tan\left(e x + d\right)^{2} + 1\right)}{a^{2} + b^{2}}\right)} b}{2 \, e}"," ",0,"1/2*(a*(2*(e*x + d)*b/(a^2 + b^2) + 2*a*log(a*tan(e*x + d) + b)/(a^2 + b^2) - a*log(tan(e*x + d)^2 + 1)/(a^2 + b^2)) + (2*(e*x + d)*a/(a^2 + b^2) - 2*b*log(a*tan(e*x + d) + b)/(a^2 + b^2) + b*log(tan(e*x + d)^2 + 1)/(a^2 + b^2))*b)/e","A",0
517,1,498,0,0.440155," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(e x + d\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(a \tan\left(e x + d\right) + b\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{4 \, a^{2} b \tan\left(e x + d\right) + a^{3} + 5 \, a b^{2}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \tan\left(e x + d\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(e x + d\right)}\right)} a + {\left(\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(e x + d\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(a \tan\left(e x + d\right) + b\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(e x + d\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{a^{2} b - 3 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \tan\left(e x + d\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \tan\left(e x + d\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(e x + d\right)}\right)} b}{2 \, e}"," ",0,"-1/2*((2*(3*a^2*b - b^3)*(e*x + d)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(a^3 - 3*a*b^2)*log(a*tan(e*x + d) + b)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (a^3 - 3*a*b^2)*log(tan(e*x + d)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (4*a^2*b*tan(e*x + d) + a^3 + 5*a*b^2)/(a^4*b^2 + 2*a^2*b^4 + b^6 + (a^6 + 2*a^4*b^2 + a^2*b^4)*tan(e*x + d)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(e*x + d)))*a + (2*(a^3 - 3*a*b^2)*(e*x + d)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(3*a^2*b - b^3)*log(a*tan(e*x + d) + b)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*a^2*b - b^3)*log(tan(e*x + d)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^2*b - 3*b^3 + 2*(a^3 - a*b^2)*tan(e*x + d))/(a^4*b^2 + 2*a^2*b^4 + b^6 + (a^6 + 2*a^4*b^2 + a^2*b^4)*tan(e*x + d)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(e*x + d)))*b)/e","A",0
518,1,299,0,0.336779," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x, algorithm=""maxima"")","\frac{16 \, {\left(\tan\left(e x + d\right)^{3} + 3 \, \tan\left(e x + d\right)\right)} a^{5} + 64 \, {\left(\tan\left(e x + d\right)^{3} + 3 \, \tan\left(e x + d\right)\right)} a^{3} b^{2} + 48 \, {\left(e x + d\right)} a b^{4} - 3 \, a^{4} b {\left(\frac{2 \, {\left(3 \, \sin\left(e x + d\right)^{3} - 5 \, \sin\left(e x + d\right)\right)}}{\sin\left(e x + d\right)^{4} - 2 \, \sin\left(e x + d\right)^{2} + 1} - 3 \, \log\left(\sin\left(e x + d\right) + 1\right) + 3 \, \log\left(\sin\left(e x + d\right) - 1\right)\right)} - 48 \, a^{4} b {\left(\frac{2 \, \sin\left(e x + d\right)}{\sin\left(e x + d\right)^{2} - 1} - \log\left(\sin\left(e x + d\right) + 1\right) + \log\left(\sin\left(e x + d\right) - 1\right)\right)} - 72 \, a^{2} b^{3} {\left(\frac{2 \, \sin\left(e x + d\right)}{\sin\left(e x + d\right)^{2} - 1} - \log\left(\sin\left(e x + d\right) + 1\right) + \log\left(\sin\left(e x + d\right) - 1\right)\right)} + 192 \, a^{2} b^{3} \log\left(\sec\left(e x + d\right) + \tan\left(e x + d\right)\right) + 48 \, b^{5} \log\left(\sec\left(e x + d\right) + \tan\left(e x + d\right)\right) + 288 \, a^{3} b^{2} \tan\left(e x + d\right) + 192 \, a b^{4} \tan\left(e x + d\right)}{48 \, e}"," ",0,"1/48*(16*(tan(e*x + d)^3 + 3*tan(e*x + d))*a^5 + 64*(tan(e*x + d)^3 + 3*tan(e*x + d))*a^3*b^2 + 48*(e*x + d)*a*b^4 - 3*a^4*b*(2*(3*sin(e*x + d)^3 - 5*sin(e*x + d))/(sin(e*x + d)^4 - 2*sin(e*x + d)^2 + 1) - 3*log(sin(e*x + d) + 1) + 3*log(sin(e*x + d) - 1)) - 48*a^4*b*(2*sin(e*x + d)/(sin(e*x + d)^2 - 1) - log(sin(e*x + d) + 1) + log(sin(e*x + d) - 1)) - 72*a^2*b^3*(2*sin(e*x + d)/(sin(e*x + d)^2 - 1) - log(sin(e*x + d) + 1) + log(sin(e*x + d) - 1)) + 192*a^2*b^3*log(sec(e*x + d) + tan(e*x + d)) + 48*b^5*log(sec(e*x + d) + tan(e*x + d)) + 288*a^3*b^2*tan(e*x + d) + 192*a*b^4*tan(e*x + d))/e","A",0
519,1,126,0,0.337390," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x, algorithm=""maxima"")","\frac{4 \, {\left(e x + d\right)} a b^{2} - a^{2} b {\left(\frac{2 \, \sin\left(e x + d\right)}{\sin\left(e x + d\right)^{2} - 1} - \log\left(\sin\left(e x + d\right) + 1\right) + \log\left(\sin\left(e x + d\right) - 1\right)\right)} + 8 \, a^{2} b \log\left(\sec\left(e x + d\right) + \tan\left(e x + d\right)\right) + 4 \, b^{3} \log\left(\sec\left(e x + d\right) + \tan\left(e x + d\right)\right) + 4 \, a^{3} \tan\left(e x + d\right) + 8 \, a b^{2} \tan\left(e x + d\right)}{4 \, e}"," ",0,"1/4*(4*(e*x + d)*a*b^2 - a^2*b*(2*sin(e*x + d)/(sin(e*x + d)^2 - 1) - log(sin(e*x + d) + 1) + log(sin(e*x + d) - 1)) + 8*a^2*b*log(sec(e*x + d) + tan(e*x + d)) + 4*b^3*log(sec(e*x + d) + tan(e*x + d)) + 4*a^3*tan(e*x + d) + 8*a*b^2*tan(e*x + d))/e","A",0
520,-2,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
521,-2,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
522,1,440,0,0.452218," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(3/2),x, algorithm=""maxima"")","\frac{3 \, {\left(4 \, b^{3} \arctan\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right) + {\left(a^{3} + 6 \, a b^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right) - {\left(a^{3} + 6 \, a b^{2}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right) - \frac{2 \, {\left(\frac{{\left(a^{3} + 6 \, a^{2} b\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + \frac{{\left(a^{3} - 6 \, a^{2} b\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}}\right)}}{\frac{2 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{\sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} - 1}\right)} a + {\left(3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right) - 3 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right) - \frac{2 \, {\left(\frac{3 \, {\left(2 \, a^{3} + 3 \, a^{2} b + 6 \, a b^{2}\right)} \sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - \frac{4 \, {\left(a^{3} + 9 \, a b^{2}\right)} \sin\left(e x + d\right)^{3}}{{\left(\cos\left(e x + d\right) + 1\right)}^{3}} + \frac{3 \, {\left(2 \, a^{3} - 3 \, a^{2} b + 6 \, a b^{2}\right)} \sin\left(e x + d\right)^{5}}{{\left(\cos\left(e x + d\right) + 1\right)}^{5}}\right)}}{\frac{3 \, \sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - \frac{3 \, \sin\left(e x + d\right)^{4}}{{\left(\cos\left(e x + d\right) + 1\right)}^{4}} + \frac{\sin\left(e x + d\right)^{6}}{{\left(\cos\left(e x + d\right) + 1\right)}^{6}} - 1}\right)} b}{6 \, e}"," ",0,"1/6*(3*(4*b^3*arctan(sin(e*x + d)/(cos(e*x + d) + 1)) + (a^3 + 6*a*b^2)*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1) - (a^3 + 6*a*b^2)*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1) - 2*((a^3 + 6*a^2*b)*sin(e*x + d)/(cos(e*x + d) + 1) + (a^3 - 6*a^2*b)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3)/(2*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - sin(e*x + d)^4/(cos(e*x + d) + 1)^4 - 1))*a + (3*(3*a^2*b + 2*b^3)*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1) - 3*(3*a^2*b + 2*b^3)*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1) - 2*(3*(2*a^3 + 3*a^2*b + 6*a*b^2)*sin(e*x + d)/(cos(e*x + d) + 1) - 4*(a^3 + 9*a*b^2)*sin(e*x + d)^3/(cos(e*x + d) + 1)^3 + 3*(2*a^3 - 3*a^2*b + 6*a*b^2)*sin(e*x + d)^5/(cos(e*x + d) + 1)^5)/(3*sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - 3*sin(e*x + d)^4/(cos(e*x + d) + 1)^4 + sin(e*x + d)^6/(cos(e*x + d) + 1)^6 - 1))*b)/e","A",0
523,1,164,0,0.438730," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, b \arctan\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1}\right) + a \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right) - a \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right)\right)} a + {\left(b \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} + 1\right) - b \log\left(\frac{\sin\left(e x + d\right)}{\cos\left(e x + d\right) + 1} - 1\right) - \frac{2 \, a \sin\left(e x + d\right)}{{\left(\frac{\sin\left(e x + d\right)^{2}}{{\left(\cos\left(e x + d\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(e x + d\right) + 1\right)}}\right)} b}{e}"," ",0,"((2*b*arctan(sin(e*x + d)/(cos(e*x + d) + 1)) + a*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1) - a*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1))*a + (b*log(sin(e*x + d)/(cos(e*x + d) + 1) + 1) - b*log(sin(e*x + d)/(cos(e*x + d) + 1) - 1) - 2*a*sin(e*x + d)/((sin(e*x + d)^2/(cos(e*x + d) + 1)^2 - 1)*(cos(e*x + d) + 1)))*b)/e","A",0
524,-2,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
525,-2,0,0,0.000000," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
526,-2,0,0,0.000000," ","integrate((cos(x)-I*sin(x))/(cos(x)+I*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
527,-2,0,0,0.000000," ","integrate((cos(x)+I*sin(x))/(cos(x)-I*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
528,1,6,0,0.309411," ","integrate((cos(x)-sin(x))/(cos(x)+sin(x)),x, algorithm=""maxima"")","\log\left(\cos\left(x\right) + \sin\left(x\right)\right)"," ",0,"log(cos(x) + sin(x))","A",0
529,1,181,0,0.422038," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","B {\left(\frac{2 \, b \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2} + c^{2}} + \frac{c \log\left(-b - \frac{2 \, c \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{2} + c^{2}} - \frac{c \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{2} + c^{2}}\right)} + C {\left(\frac{2 \, c \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2} + c^{2}} - \frac{b \log\left(-b - \frac{2 \, c \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{2} + c^{2}} + \frac{b \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{2} + c^{2}}\right)}"," ",0,"B*(2*b*arctan(sin(x)/(cos(x) + 1))/(b^2 + c^2) + c*log(-b - 2*c*sin(x)/(cos(x) + 1) + b*sin(x)^2/(cos(x) + 1)^2)/(b^2 + c^2) - c*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(b^2 + c^2)) + C*(2*c*arctan(sin(x)/(cos(x) + 1))/(b^2 + c^2) - b*log(-b - 2*c*sin(x)/(cos(x) + 1) + b*sin(x)^2/(cos(x) + 1)^2)/(b^2 + c^2) + b*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(b^2 + c^2))","B",0
530,1,271,0,0.426298," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","-B {\left(\frac{b \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(b c + \frac{c^{2} \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{b^{4} + b^{2} c^{2} + \frac{2 \, {\left(b^{3} c + b c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{4} + b^{2} c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}\right)} - C {\left(\frac{c \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b + \frac{c \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{b^{3} + b c^{2} + \frac{2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{3} + b c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}\right)}"," ",0,"-B*(b*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) + 2*(b*c + c^2*sin(x)/(cos(x) + 1))/(b^4 + b^2*c^2 + 2*(b^3*c + b*c^3)*sin(x)/(cos(x) + 1) - (b^4 + b^2*c^2)*sin(x)^2/(cos(x) + 1)^2)) - C*(c*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(b + c*sin(x)/(cos(x) + 1))/(b^3 + b*c^2 + 2*(b^2*c + c^3)*sin(x)/(cos(x) + 1) - (b^3 + b*c^2)*sin(x)^2/(cos(x) + 1)^2))","B",0
531,1,199,0,0.339763," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","\frac{2 \, B {\left(\frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{c \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{b^{4} + \frac{4 \, b^{3} c \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, b^{3} c \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{b^{4} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(b^{4} - 2 \, b^{2} c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}} + \frac{2 \, C \sin\left(x\right)^{2}}{{\left(b^{3} + \frac{4 \, b^{2} c \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, b^{2} c \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{b^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(b^{3} - 2 \, b c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}"," ",0,"2*B*(b*sin(x)/(cos(x) + 1) + c*sin(x)^2/(cos(x) + 1)^2 - b*sin(x)^3/(cos(x) + 1)^3)/(b^4 + 4*b^3*c*sin(x)/(cos(x) + 1) - 4*b^3*c*sin(x)^3/(cos(x) + 1)^3 + b^4*sin(x)^4/(cos(x) + 1)^4 - 2*(b^4 - 2*b^2*c^2)*sin(x)^2/(cos(x) + 1)^2) + 2*C*sin(x)^2/((b^3 + 4*b^2*c*sin(x)/(cos(x) + 1) - 4*b^2*c*sin(x)^3/(cos(x) + 1)^3 + b^3*sin(x)^4/(cos(x) + 1)^4 - 2*(b^3 - 2*b*c^2)*sin(x)^2/(cos(x) + 1)^2)*(cos(x) + 1)^2)","B",0
532,1,243,0,0.415860," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","B {\left(\frac{2 \, b \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2} + c^{2}} + \frac{c \log\left(-b - \frac{2 \, c \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{2} + c^{2}} - \frac{c \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{2} + c^{2}}\right)} + C {\left(\frac{2 \, c \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2} + c^{2}} - \frac{b \log\left(-b - \frac{2 \, c \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}{b^{2} + c^{2}} + \frac{b \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}{b^{2} + c^{2}}\right)} - \frac{A \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{\sqrt{b^{2} + c^{2}}}"," ",0,"B*(2*b*arctan(sin(x)/(cos(x) + 1))/(b^2 + c^2) + c*log(-b - 2*c*sin(x)/(cos(x) + 1) + b*sin(x)^2/(cos(x) + 1)^2)/(b^2 + c^2) - c*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(b^2 + c^2)) + C*(2*c*arctan(sin(x)/(cos(x) + 1))/(b^2 + c^2) - b*log(-b - 2*c*sin(x)/(cos(x) + 1) + b*sin(x)^2/(cos(x) + 1)^2)/(b^2 + c^2) + b*log(sin(x)^2/(cos(x) + 1)^2 + 1)/(b^2 + c^2)) - A*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/sqrt(b^2 + c^2)","B",0
533,1,286,0,0.424383," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","-B {\left(\frac{b \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(b c + \frac{c^{2} \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{b^{4} + b^{2} c^{2} + \frac{2 \, {\left(b^{3} c + b c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{4} + b^{2} c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}\right)} - C {\left(\frac{c \log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b + \frac{c \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{b^{3} + b c^{2} + \frac{2 \, {\left(b^{2} c + c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{3} + b c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}\right)} - \frac{A}{c^{2} \tan\left(x\right) + b c}"," ",0,"-B*(b*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) + 2*(b*c + c^2*sin(x)/(cos(x) + 1))/(b^4 + b^2*c^2 + 2*(b^3*c + b*c^3)*sin(x)/(cos(x) + 1) - (b^4 + b^2*c^2)*sin(x)^2/(cos(x) + 1)^2)) - C*(c*log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(b + c*sin(x)/(cos(x) + 1))/(b^3 + b*c^2 + 2*(b^2*c + c^3)*sin(x)/(cos(x) + 1) - (b^3 + b*c^2)*sin(x)^2/(cos(x) + 1)^2)) - A/(c^2*tan(x) + b*c)","B",0
534,1,451,0,0.452562," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","-\frac{1}{2} \, A {\left(\frac{2 \, {\left(b^{2} c - \frac{{\left(b^{3} - 2 \, b c^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{{\left(b^{2} c - 2 \, c^{3}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(b^{3} + 2 \, b c^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{b^{6} + b^{4} c^{2} + \frac{4 \, {\left(b^{5} c + b^{3} c^{3}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, {\left(b^{6} - b^{4} c^{2} - 2 \, b^{2} c^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{4 \, {\left(b^{5} c + b^{3} c^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(b^{6} + b^{4} c^{2}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} + \frac{\log\left(\frac{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{b^{2} + c^{2}}}{c - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{b^{2} + c^{2}}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}}\right)} + \frac{2 \, B {\left(\frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{c \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{b \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}}{b^{4} + \frac{4 \, b^{3} c \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, b^{3} c \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{b^{4} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(b^{4} - 2 \, b^{2} c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}} + \frac{2 \, C \sin\left(x\right)^{2}}{{\left(b^{3} + \frac{4 \, b^{2} c \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{4 \, b^{2} c \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{b^{3} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{2 \, {\left(b^{3} - 2 \, b c^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}"," ",0,"-1/2*A*(2*(b^2*c - (b^3 - 2*b*c^2)*sin(x)/(cos(x) + 1) - (b^2*c - 2*c^3)*sin(x)^2/(cos(x) + 1)^2 - (b^3 + 2*b*c^2)*sin(x)^3/(cos(x) + 1)^3)/(b^6 + b^4*c^2 + 4*(b^5*c + b^3*c^3)*sin(x)/(cos(x) + 1) - 2*(b^6 - b^4*c^2 - 2*b^2*c^4)*sin(x)^2/(cos(x) + 1)^2 - 4*(b^5*c + b^3*c^3)*sin(x)^3/(cos(x) + 1)^3 + (b^6 + b^4*c^2)*sin(x)^4/(cos(x) + 1)^4) + log((c - b*sin(x)/(cos(x) + 1) + sqrt(b^2 + c^2))/(c - b*sin(x)/(cos(x) + 1) - sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2)) + 2*B*(b*sin(x)/(cos(x) + 1) + c*sin(x)^2/(cos(x) + 1)^2 - b*sin(x)^3/(cos(x) + 1)^3)/(b^4 + 4*b^3*c*sin(x)/(cos(x) + 1) - 4*b^3*c*sin(x)^3/(cos(x) + 1)^3 + b^4*sin(x)^4/(cos(x) + 1)^4 - 2*(b^4 - 2*b^2*c^2)*sin(x)^2/(cos(x) + 1)^2) + 2*C*sin(x)^2/((b^3 + 4*b^2*c*sin(x)/(cos(x) + 1) - 4*b^2*c*sin(x)^3/(cos(x) + 1)^3 + b^3*sin(x)^4/(cos(x) + 1)^4 - 2*(b^3 - 2*b*c^2)*sin(x)^2/(cos(x) + 1)^2)*(cos(x) + 1)^2)","B",0
535,-2,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
536,-2,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
537,-2,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
538,-2,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
539,-2,0,0,0.000000," ","integrate((A+B*cos(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
540,-2,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
541,-2,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
542,-2,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
543,-2,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
544,-2,0,0,0.000000," ","integrate((A+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
545,-2,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
546,-2,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
547,-2,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
548,-2,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
549,-2,0,0,0.000000," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
550,-2,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
551,-2,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
552,-2,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
553,-2,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
554,-2,0,0,0.000000," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
555,-2,0,0,0.000000," ","integrate((b^2+c^2+a*b*cos(x)+a*c*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c^2+b^2-a^2>0)', see `assume?` for more details)Is c^2+b^2-a^2 positive or negative?","F(-2)",0
556,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))^(5/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""maxima"")","\int {\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} {\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)*(b*cos(x) + c*sin(x) + a)^(5/2), x)","F",0
557,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))^(3/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""maxima"")","\int {\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} {\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)*(b*cos(x) + c*sin(x) + a)^(3/2), x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))^(1/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""maxima"")","\int {\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)*sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
559,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(1/2),x, algorithm=""maxima"")","\int \frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{\sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)/sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
560,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(3/2),x, algorithm=""maxima"")","\int \frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{{\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)/(b*cos(x) + c*sin(x) + a)^(3/2), x)","F",0
561,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(5/2),x, algorithm=""maxima"")","\int \frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{{\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)/(b*cos(x) + c*sin(x) + a)^(5/2), x)","F",0
562,-2,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*a^2>0)', see `assume?` for more details)Is 4*c^2-4*a^2 positive or negative?","F(-2)",0
563,-2,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*a^2>0)', see `assume?` for more details)Is 4*c^2-4*a^2 positive or negative?","F(-2)",0
564,-2,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*a^2>0)', see `assume?` for more details)Is 4*c^2-4*a^2 positive or negative?","F(-2)",0
565,-2,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*c^2-4*a^2>0)', see `assume?` for more details)Is 4*c^2-4*a^2 positive or negative?","F(-2)",0
566,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^m, x)","F",0
567,1,80,0,0.383341," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x - \frac{3 \, a^{2} b \cos\left(d x + c\right)^{2}}{2 \, d} + \frac{3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2}}{32 \, d} - \frac{{\left(2 \, \sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4}\right)} b^{3}}{12 \, d}"," ",0,"a^3*x - 3/2*a^2*b*cos(d*x + c)^2/d + 3/32*(4*d*x + 4*c - sin(4*d*x + 4*c))*a*b^2/d - 1/12*(2*sin(d*x + c)^6 - 3*sin(d*x + c)^4)*b^3/d","A",0
568,1,48,0,0.334547," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x - \frac{a b \cos\left(d x + c\right)^{2}}{d} + \frac{{\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{32 \, d}"," ",0,"a^2*x - a*b*cos(d*x + c)^2/d + 1/32*(4*d*x + 4*c - sin(4*d*x + 4*c))*b^2/d","A",0
569,1,18,0,0.482671," ","integrate(a+b*cos(d*x+c)*sin(d*x+c),x, algorithm=""maxima"")","a x - \frac{b \cos\left(d x + c\right)^{2}}{2 \, d}"," ",0,"a*x - 1/2*b*cos(d*x + c)^2/d","A",0
570,-2,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b^2-4*a^2>0)', see `assume?` for more details)Is b^2-4*a^2 positive or negative?","F(-2)",0
571,-2,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b^2-4*a^2>0)', see `assume?` for more details)Is b^2-4*a^2 positive or negative?","F(-2)",0
572,-2,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b^2-4*a^2>0)', see `assume?` for more details)Is b^2-4*a^2 positive or negative?","F(-2)",0
573,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^(5/2), x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^(3/2), x)","F",0
575,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
576,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
577,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^(-3/2), x)","F",0
578,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^(-5/2), x)","F",0
579,0,0,0,0.000000," ","integrate(x^3/(a+b*cos(x)*sin(x)),x, algorithm=""maxima"")","\int \frac{x^{3}}{b \cos\left(x\right) \sin\left(x\right) + a}\,{d x}"," ",0,"integrate(x^3/(b*cos(x)*sin(x) + a), x)","F",0
580,0,0,0,0.000000," ","integrate(x^2/(a+b*cos(x)*sin(x)),x, algorithm=""maxima"")","\int \frac{x^{2}}{b \cos\left(x\right) \sin\left(x\right) + a}\,{d x}"," ",0,"integrate(x^2/(b*cos(x)*sin(x) + a), x)","F",0
581,0,0,0,0.000000," ","integrate(x/(a+b*cos(x)*sin(x)),x, algorithm=""maxima"")","\int \frac{x}{b \cos\left(x\right) \sin\left(x\right) + a}\,{d x}"," ",0,"integrate(x/(b*cos(x)*sin(x) + a), x)","F",0
582,0,0,0,0.000000," ","integrate(1/x/(a+b*cos(x)*sin(x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(x\right) \sin\left(x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*cos(x)*sin(x) + a)*x), x)","F",0
583,0,0,0,0.000000," ","integrate((b*x)^(2-n)*sin(a*x)^n/(a*c*x*cos(a*x)-c*sin(a*x))^2,x, algorithm=""maxima"")","\int \frac{\left(b x\right)^{-n + 2} \sin\left(a x\right)^{n}}{{\left(a c x \cos\left(a x\right) - c \sin\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate((b*x)^(-n + 2)*sin(a*x)^n/(a*c*x*cos(a*x) - c*sin(a*x))^2, x)","F",0
584,0,0,0,0.000000," ","integrate((b*x)^(2-n)*cos(a*x)^n/(c*cos(a*x)+a*c*x*sin(a*x))^2,x, algorithm=""maxima"")","\int \frac{\left(b x\right)^{-n + 2} \cos\left(a x\right)^{n}}{{\left(a c x \sin\left(a x\right) + c \cos\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate((b*x)^(-n + 2)*cos(a*x)^n/(a*c*x*sin(a*x) + c*cos(a*x))^2, x)","F",0
585,-2,0,0,0.000000," ","integrate(sin(a*x)^6/x^4/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
586,-2,0,0,0.000000," ","integrate(sin(a*x)^5/x^3/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
587,-2,0,0,0.000000," ","integrate(sin(a*x)^4/x^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
588,-2,0,0,0.000000," ","integrate(sin(a*x)^3/x/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
589,1,114,0,0.316741," ","integrate(sin(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\frac{a x \cos\left(2 \, a x\right)^{2} + a x \sin\left(2 \, a x\right)^{2} + 2 \, a x \cos\left(2 \, a x\right) + a x - 2 \, \sin\left(2 \, a x\right)}{{\left(a^{2} x^{2} + {\left(a^{2} x^{2} + 1\right)} \cos\left(2 \, a x\right)^{2} - 4 \, a x \sin\left(2 \, a x\right) + {\left(a^{2} x^{2} + 1\right)} \sin\left(2 \, a x\right)^{2} + 2 \, {\left(a^{2} x^{2} - 1\right)} \cos\left(2 \, a x\right) + 1\right)} a}"," ",0,"(a*x*cos(2*a*x)^2 + a*x*sin(2*a*x)^2 + 2*a*x*cos(2*a*x) + a*x - 2*sin(2*a*x))/((a^2*x^2 + (a^2*x^2 + 1)*cos(2*a*x)^2 - 4*a*x*sin(2*a*x) + (a^2*x^2 + 1)*sin(2*a*x)^2 + 2*(a^2*x^2 - 1)*cos(2*a*x) + 1)*a)","B",0
590,1,20,0,0.311272," ","integrate(x*sin(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\frac{1}{{\left(a x \cos\left(a x\right) - \sin\left(a x\right)\right)} a^{2}}"," ",0,"1/((a*x*cos(a*x) - sin(a*x))*a^2)","A",0
591,1,100,0,0.312068," ","integrate(x^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, a x \cos\left(2 \, a x\right) + {\left(a^{2} x^{2} - 1\right)} \sin\left(2 \, a x\right)\right)}}{{\left(a^{2} x^{2} + {\left(a^{2} x^{2} + 1\right)} \cos\left(2 \, a x\right)^{2} - 4 \, a x \sin\left(2 \, a x\right) + {\left(a^{2} x^{2} + 1\right)} \sin\left(2 \, a x\right)^{2} + 2 \, {\left(a^{2} x^{2} - 1\right)} \cos\left(2 \, a x\right) + 1\right)} a^{3}}"," ",0,"2*(2*a*x*cos(2*a*x) + (a^2*x^2 - 1)*sin(2*a*x))/((a^2*x^2 + (a^2*x^2 + 1)*cos(2*a*x)^2 - 4*a*x*sin(2*a*x) + (a^2*x^2 + 1)*sin(2*a*x)^2 + 2*(a^2*x^2 - 1)*cos(2*a*x) + 1)*a^3)","B",0
592,-2,0,0,0.000000," ","integrate(x^3*csc(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
593,1,608,0,0.378490," ","integrate(x^4*csc(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""maxima"")","-\frac{2 \, a x + {\left(4 \, a^{2} x^{2} + 8 i \, a x \cos\left(2 \, a x\right) - 8 \, a x \sin\left(2 \, a x\right) - 4 i \, a x - {\left(4 \, a^{2} x^{2} + 4 i \, a x\right)} \cos\left(4 \, a x\right) + 4 \, {\left(-i \, a^{2} x^{2} + a x\right)} \sin\left(4 \, a x\right)\right)} \arctan\left(\sin\left(a x\right), \cos\left(a x\right) + 1\right) - {\left(4 \, a^{2} x^{2} + 8 i \, a x \cos\left(2 \, a x\right) - 8 \, a x \sin\left(2 \, a x\right) - 4 i \, a x - {\left(4 \, a^{2} x^{2} + 4 i \, a x\right)} \cos\left(4 \, a x\right) - 4 \, {\left(i \, a^{2} x^{2} - a x\right)} \sin\left(4 \, a x\right)\right)} \arctan\left(\sin\left(a x\right), -\cos\left(a x\right) + 1\right) + 4 \, {\left(a^{3} x^{3} + i \, a^{2} x^{2}\right)} \cos\left(4 \, a x\right) - {\left(4 i \, a^{2} x^{2} + 2 \, a x - 2 i\right)} \cos\left(2 \, a x\right) - {\left(4 \, a x - {\left(4 \, a x + 4 i\right)} \cos\left(4 \, a x\right) - 4 \, {\left(i \, a x - 1\right)} \sin\left(4 \, a x\right) + 8 i \, \cos\left(2 \, a x\right) - 8 \, \sin\left(2 \, a x\right) - 4 i\right)} {\rm Li}_2\left(-e^{\left(i \, a x\right)}\right) - {\left(4 \, a x - {\left(4 \, a x + 4 i\right)} \cos\left(4 \, a x\right) - 4 \, {\left(i \, a x - 1\right)} \sin\left(4 \, a x\right) + 8 i \, \cos\left(2 \, a x\right) - 8 \, \sin\left(2 \, a x\right) - 4 i\right)} {\rm Li}_2\left(e^{\left(i \, a x\right)}\right) - {\left(2 i \, a^{2} x^{2} - 4 \, a x \cos\left(2 \, a x\right) - 4 i \, a x \sin\left(2 \, a x\right) + 2 \, a x - 2 \, {\left(i \, a^{2} x^{2} - a x\right)} \cos\left(4 \, a x\right) + {\left(2 \, a^{2} x^{2} + 2 i \, a x\right)} \sin\left(4 \, a x\right)\right)} \log\left(\cos\left(a x\right)^{2} + \sin\left(a x\right)^{2} + 2 \, \cos\left(a x\right) + 1\right) - {\left(2 i \, a^{2} x^{2} - 4 \, a x \cos\left(2 \, a x\right) - 4 i \, a x \sin\left(2 \, a x\right) + 2 \, a x - 2 \, {\left(i \, a^{2} x^{2} - a x\right)} \cos\left(4 \, a x\right) + {\left(2 \, a^{2} x^{2} + 2 i \, a x\right)} \sin\left(4 \, a x\right)\right)} \log\left(\cos\left(a x\right)^{2} + \sin\left(a x\right)^{2} - 2 \, \cos\left(a x\right) + 1\right) - {\left(-4 i \, a^{3} x^{3} + 4 \, a^{2} x^{2}\right)} \sin\left(4 \, a x\right) + {\left(4 \, a^{2} x^{2} - 2 i \, a x - 2\right)} \sin\left(2 \, a x\right) - 2 i}{{\left(i \, a x + {\left(-i \, a x + 1\right)} \cos\left(4 \, a x\right) + {\left(a x + i\right)} \sin\left(4 \, a x\right) - 2 \, \cos\left(2 \, a x\right) - 2 i \, \sin\left(2 \, a x\right) + 1\right)} a^{5}}"," ",0,"-(2*a*x + (4*a^2*x^2 + 8*I*a*x*cos(2*a*x) - 8*a*x*sin(2*a*x) - 4*I*a*x - (4*a^2*x^2 + 4*I*a*x)*cos(4*a*x) + 4*(-I*a^2*x^2 + a*x)*sin(4*a*x))*arctan2(sin(a*x), cos(a*x) + 1) - (4*a^2*x^2 + 8*I*a*x*cos(2*a*x) - 8*a*x*sin(2*a*x) - 4*I*a*x - (4*a^2*x^2 + 4*I*a*x)*cos(4*a*x) - 4*(I*a^2*x^2 - a*x)*sin(4*a*x))*arctan2(sin(a*x), -cos(a*x) + 1) + 4*(a^3*x^3 + I*a^2*x^2)*cos(4*a*x) - (4*I*a^2*x^2 + 2*a*x - 2*I)*cos(2*a*x) - (4*a*x - (4*a*x + 4*I)*cos(4*a*x) - 4*(I*a*x - 1)*sin(4*a*x) + 8*I*cos(2*a*x) - 8*sin(2*a*x) - 4*I)*dilog(-e^(I*a*x)) - (4*a*x - (4*a*x + 4*I)*cos(4*a*x) - 4*(I*a*x - 1)*sin(4*a*x) + 8*I*cos(2*a*x) - 8*sin(2*a*x) - 4*I)*dilog(e^(I*a*x)) - (2*I*a^2*x^2 - 4*a*x*cos(2*a*x) - 4*I*a*x*sin(2*a*x) + 2*a*x - 2*(I*a^2*x^2 - a*x)*cos(4*a*x) + (2*a^2*x^2 + 2*I*a*x)*sin(4*a*x))*log(cos(a*x)^2 + sin(a*x)^2 + 2*cos(a*x) + 1) - (2*I*a^2*x^2 - 4*a*x*cos(2*a*x) - 4*I*a*x*sin(2*a*x) + 2*a*x - 2*(I*a^2*x^2 - a*x)*cos(4*a*x) + (2*a^2*x^2 + 2*I*a*x)*sin(4*a*x))*log(cos(a*x)^2 + sin(a*x)^2 - 2*cos(a*x) + 1) - (-4*I*a^3*x^3 + 4*a^2*x^2)*sin(4*a*x) + (4*a^2*x^2 - 2*I*a*x - 2)*sin(2*a*x) - 2*I)/((I*a*x + (-I*a*x + 1)*cos(4*a*x) + (a*x + I)*sin(4*a*x) - 2*cos(2*a*x) - 2*I*sin(2*a*x) + 1)*a^5)","B",0
594,-2,0,0,0.000000," ","integrate(cos(a*x)^6/x^4/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
595,-2,0,0,0.000000," ","integrate(cos(a*x)^5/x^3/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
596,-2,0,0,0.000000," ","integrate(cos(a*x)^4/x^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
597,-2,0,0,0.000000," ","integrate(cos(a*x)^3/x/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
598,1,114,0,0.327710," ","integrate(cos(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","\frac{a x \cos\left(2 \, a x\right)^{2} + a x \sin\left(2 \, a x\right)^{2} - 2 \, a x \cos\left(2 \, a x\right) + a x + 2 \, \sin\left(2 \, a x\right)}{{\left(a^{2} x^{2} + {\left(a^{2} x^{2} + 1\right)} \cos\left(2 \, a x\right)^{2} + 4 \, a x \sin\left(2 \, a x\right) + {\left(a^{2} x^{2} + 1\right)} \sin\left(2 \, a x\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \cos\left(2 \, a x\right) + 1\right)} a}"," ",0,"(a*x*cos(2*a*x)^2 + a*x*sin(2*a*x)^2 - 2*a*x*cos(2*a*x) + a*x + 2*sin(2*a*x))/((a^2*x^2 + (a^2*x^2 + 1)*cos(2*a*x)^2 + 4*a*x*sin(2*a*x) + (a^2*x^2 + 1)*sin(2*a*x)^2 - 2*(a^2*x^2 - 1)*cos(2*a*x) + 1)*a)","B",0
599,1,19,0,0.305421," ","integrate(x*cos(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(a x \sin\left(a x\right) + \cos\left(a x\right)\right)} a^{2}}"," ",0,"-1/((a*x*sin(a*x) + cos(a*x))*a^2)","A",0
600,1,100,0,0.313237," ","integrate(x^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, a x \cos\left(2 \, a x\right) + {\left(a^{2} x^{2} - 1\right)} \sin\left(2 \, a x\right)\right)}}{{\left(a^{2} x^{2} + {\left(a^{2} x^{2} + 1\right)} \cos\left(2 \, a x\right)^{2} + 4 \, a x \sin\left(2 \, a x\right) + {\left(a^{2} x^{2} + 1\right)} \sin\left(2 \, a x\right)^{2} - 2 \, {\left(a^{2} x^{2} - 1\right)} \cos\left(2 \, a x\right) + 1\right)} a^{3}}"," ",0,"-2*(2*a*x*cos(2*a*x) + (a^2*x^2 - 1)*sin(2*a*x))/((a^2*x^2 + (a^2*x^2 + 1)*cos(2*a*x)^2 + 4*a*x*sin(2*a*x) + (a^2*x^2 + 1)*sin(2*a*x)^2 - 2*(a^2*x^2 - 1)*cos(2*a*x) + 1)*a^3)","B",0
601,-2,0,0,0.000000," ","integrate(x^3*sec(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
602,1,381,0,0.462718," ","integrate(x^4*sec(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""maxima"")","-\frac{2 \, a x + {\left(4 \, a^{2} x^{2} - 8 i \, a x \cos\left(2 \, a x\right) + 8 \, a x \sin\left(2 \, a x\right) - 4 i \, a x - {\left(4 \, a^{2} x^{2} + 4 i \, a x\right)} \cos\left(4 \, a x\right) + 4 \, {\left(-i \, a^{2} x^{2} + a x\right)} \sin\left(4 \, a x\right)\right)} \arctan\left(\sin\left(2 \, a x\right), \cos\left(2 \, a x\right) + 1\right) + 4 \, {\left(a^{3} x^{3} + i \, a^{2} x^{2}\right)} \cos\left(4 \, a x\right) - {\left(-4 i \, a^{2} x^{2} - 2 \, a x + 2 i\right)} \cos\left(2 \, a x\right) - {\left(2 \, a x - {\left(2 \, a x + 2 i\right)} \cos\left(4 \, a x\right) - 2 \, {\left(i \, a x - 1\right)} \sin\left(4 \, a x\right) - 4 i \, \cos\left(2 \, a x\right) + 4 \, \sin\left(2 \, a x\right) - 2 i\right)} {\rm Li}_2\left(-e^{\left(2 i \, a x\right)}\right) - {\left(2 i \, a^{2} x^{2} + 4 \, a x \cos\left(2 \, a x\right) + 4 i \, a x \sin\left(2 \, a x\right) + 2 \, a x - 2 \, {\left(i \, a^{2} x^{2} - a x\right)} \cos\left(4 \, a x\right) + {\left(2 \, a^{2} x^{2} + 2 i \, a x\right)} \sin\left(4 \, a x\right)\right)} \log\left(\cos\left(2 \, a x\right)^{2} + \sin\left(2 \, a x\right)^{2} + 2 \, \cos\left(2 \, a x\right) + 1\right) - {\left(-4 i \, a^{3} x^{3} + 4 \, a^{2} x^{2}\right)} \sin\left(4 \, a x\right) - {\left(4 \, a^{2} x^{2} - 2 i \, a x - 2\right)} \sin\left(2 \, a x\right) - 2 i}{{\left(i \, a x + {\left(-i \, a x + 1\right)} \cos\left(4 \, a x\right) + {\left(a x + i\right)} \sin\left(4 \, a x\right) + 2 \, \cos\left(2 \, a x\right) + 2 i \, \sin\left(2 \, a x\right) + 1\right)} a^{5}}"," ",0,"-(2*a*x + (4*a^2*x^2 - 8*I*a*x*cos(2*a*x) + 8*a*x*sin(2*a*x) - 4*I*a*x - (4*a^2*x^2 + 4*I*a*x)*cos(4*a*x) + 4*(-I*a^2*x^2 + a*x)*sin(4*a*x))*arctan2(sin(2*a*x), cos(2*a*x) + 1) + 4*(a^3*x^3 + I*a^2*x^2)*cos(4*a*x) - (-4*I*a^2*x^2 - 2*a*x + 2*I)*cos(2*a*x) - (2*a*x - (2*a*x + 2*I)*cos(4*a*x) - 2*(I*a*x - 1)*sin(4*a*x) - 4*I*cos(2*a*x) + 4*sin(2*a*x) - 2*I)*dilog(-e^(2*I*a*x)) - (2*I*a^2*x^2 + 4*a*x*cos(2*a*x) + 4*I*a*x*sin(2*a*x) + 2*a*x - 2*(I*a^2*x^2 - a*x)*cos(4*a*x) + (2*a^2*x^2 + 2*I*a*x)*sin(4*a*x))*log(cos(2*a*x)^2 + sin(2*a*x)^2 + 2*cos(2*a*x) + 1) - (-4*I*a^3*x^3 + 4*a^2*x^2)*sin(4*a*x) - (4*a^2*x^2 - 2*I*a*x - 2)*sin(2*a*x) - 2*I)/((I*a*x + (-I*a*x + 1)*cos(4*a*x) + (a*x + I)*sin(4*a*x) + 2*cos(2*a*x) + 2*I*sin(2*a*x) + 1)*a^5)","B",0
603,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(-\frac{1}{2} \, {\left(12 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{3}{4}} b \int \frac{{\left({\left(\cos\left(12 \, b x + 12 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(12 \, b x + 12 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) + {\left(\cos\left(4 \, b x + 4 \, a\right) \sin\left(12 \, b x + 12 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) \sin\left(8 \, b x + 8 \, a\right) - \cos\left(12 \, b x + 12 \, a\right) \sin\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right) - {\left({\left(\cos\left(4 \, b x + 4 \, a\right) \sin\left(12 \, b x + 12 \, a\right) + 2 \, \cos\left(4 \, b x + 4 \, a\right) \sin\left(8 \, b x + 8 \, a\right) - \cos\left(12 \, b x + 12 \, a\right) \sin\left(4 \, b x + 4 \, a\right) - 2 \, \cos\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) - {\left(\cos\left(12 \, b x + 12 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + 2 \, \cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(12 \, b x + 12 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + 2 \, \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)}{2 \, {\left({\left(2 \, {\left(2 \, \cos\left(8 \, b x + 8 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + \cos\left(12 \, b x + 12 \, a\right)^{2} + 4 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, \cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(8 \, b x + 8 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + \sin\left(12 \, b x + 12 \, a\right)^{2} + 4 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2} + {\left(2 \, {\left(2 \, \cos\left(8 \, b x + 8 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)\right)} \cos\left(12 \, b x + 12 \, a\right) + \cos\left(12 \, b x + 12 \, a\right)^{2} + 4 \, \cos\left(8 \, b x + 8 \, a\right)^{2} + 4 \, \cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 2 \, {\left(2 \, \sin\left(8 \, b x + 8 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)\right)} \sin\left(12 \, b x + 12 \, a\right) + \sin\left(12 \, b x + 12 \, a\right)^{2} + 4 \, \sin\left(8 \, b x + 8 \, a\right)^{2} + 4 \, \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}}}\,{d x} + \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)\right)} \sqrt{c} + \sqrt{c} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)}}{3 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{3}{4}} b}"," ",0,"-2/3*(6*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(3/4)*b*sqrt(c)*integrate(-(((cos(12*b*x + 12*a)*cos(4*b*x + 4*a) + 2*cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + sin(12*b*x + 12*a)*sin(4*b*x + 4*a) + 2*sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + (cos(4*b*x + 4*a)*sin(12*b*x + 12*a) + 2*cos(4*b*x + 4*a)*sin(8*b*x + 8*a) - cos(12*b*x + 12*a)*sin(4*b*x + 4*a) - 2*cos(8*b*x + 8*a)*sin(4*b*x + 4*a))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*cos(3/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))) + ((cos(4*b*x + 4*a)*sin(12*b*x + 12*a) + 2*cos(4*b*x + 4*a)*sin(8*b*x + 8*a) - cos(12*b*x + 12*a)*sin(4*b*x + 4*a) - 2*cos(8*b*x + 8*a)*sin(4*b*x + 4*a))*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) - (cos(12*b*x + 12*a)*cos(4*b*x + 4*a) + 2*cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + sin(12*b*x + 12*a)*sin(4*b*x + 4*a) + 2*sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*sin(3/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))))/(((2*(2*cos(8*b*x + 8*a) + cos(4*b*x + 4*a))*cos(12*b*x + 12*a) + cos(12*b*x + 12*a)^2 + 4*cos(8*b*x + 8*a)^2 + 4*cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 2*(2*sin(8*b*x + 8*a) + sin(4*b*x + 4*a))*sin(12*b*x + 12*a) + sin(12*b*x + 12*a)^2 + 4*sin(8*b*x + 8*a)^2 + 4*sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + (2*(2*cos(8*b*x + 8*a) + cos(4*b*x + 4*a))*cos(12*b*x + 12*a) + cos(12*b*x + 12*a)^2 + 4*cos(8*b*x + 8*a)^2 + 4*cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 2*(2*sin(8*b*x + 8*a) + sin(4*b*x + 4*a))*sin(12*b*x + 12*a) + sin(12*b*x + 12*a)^2 + 4*sin(8*b*x + 8*a)^2 + 4*sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)), x) + sqrt(c)*sin(3/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(3/4)*b)","F",0
606,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\frac{-\frac{1}{2} \, {\left(4 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} b \int \frac{{\left({\left(\cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) + {\left(\cos\left(4 \, b x + 4 \, a\right) \sin\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right) - {\left({\left(\cos\left(4 \, b x + 4 \, a\right) \sin\left(8 \, b x + 8 \, a\right) - \cos\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) - {\left(\cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)}{2 \, {\left({\left(\cos\left(8 \, b x + 8 \, a\right)^{2} + 2 \, \cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(8 \, b x + 8 \, a\right)^{2} + 2 \, \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2} + {\left(\cos\left(8 \, b x + 8 \, a\right)^{2} + 2 \, \cos\left(8 \, b x + 8 \, a\right) \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(8 \, b x + 8 \, a\right)^{2} + 2 \, \sin\left(8 \, b x + 8 \, a\right) \sin\left(4 \, b x + 4 \, a\right) + \sin\left(4 \, b x + 4 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2}\right)} {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}}}\,{d x} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)\right)} \sqrt{c} - \sqrt{c} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)}{{\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} b}"," ",0,"(2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*b*sqrt(c)*integrate(-(((cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + (cos(4*b*x + 4*a)*sin(8*b*x + 8*a) - cos(8*b*x + 8*a)*sin(4*b*x + 4*a))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))) + ((cos(4*b*x + 4*a)*sin(8*b*x + 8*a) - cos(8*b*x + 8*a)*sin(4*b*x + 4*a))*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) - (cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))))/(((cos(8*b*x + 8*a)^2 + 2*cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + sin(8*b*x + 8*a)^2 + 2*sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + (cos(8*b*x + 8*a)^2 + 2*cos(8*b*x + 8*a)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + sin(8*b*x + 8*a)^2 + 2*sin(8*b*x + 8*a)*sin(4*b*x + 4*a) + sin(4*b*x + 4*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)), x) - sqrt(c)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*b)","F",0
607,1,430,0,0.496256," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{c} {\left(\log\left(4 \, \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2} + 4 \, \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2} + 8 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right) + 4\right) - \log\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)^{2}\right)} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(2 \, b x + 2 \, a\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right) + \sin\left(2 \, b x + 2 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right) + 1\right)\right)\right)}\right)\right)}}{4 \, b}"," ",0,"1/4*sqrt(c)*(log(4*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1))^2 + 4*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1))^2 + 8*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1)) + 4) - log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*(cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1))^2) + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(2*b*x + 2*a)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1)) + sin(2*b*x + 2*a)*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a) + 1)))))/b","B",0
608,1,1049,0,0.609719," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(\cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} \sqrt{c} - \sqrt{c} {\left(\log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) - \log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) + \log\left({\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} + 1\right) - \log\left({\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} + 1\right)\right)}}{16 \, b}"," ",0,"1/16*(4*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(2*b*x + 2*a) + (cos(2*b*x + 2*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*sqrt(c) - sqrt(c)*(log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) - log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) + log(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(2*b*x + 2*a) + cos(2*b*x + 2*a)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))) + 1) - log(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(2*b*x + 2*a) + cos(2*b*x + 2*a)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))) + 1)))/b","B",0
609,1,1421,0,0.720665," ","integrate(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(4 \, b x + 4 \, a\right) - {\left(\cos\left(4 \, b x + 4 \, a\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) - \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(4 \, b x + 4 \, a\right) - {\left(\cos\left(4 \, b x + 4 \, a\right) - 2\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) - {\left({\left(\cos\left(4 \, b x + 4 \, a\right) - 2\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + \sin\left(4 \, b x + 4 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} \sqrt{c} - 3 \, \sqrt{c} {\left(\log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) - \log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) + \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} + 1\right) - \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} + 1\right)\right)}}{64 \, b}"," ",0,"-1/64*(4*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*((cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(4*b*x + 4*a) - (cos(4*b*x + 4*a) - 2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))) - cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(4*b*x + 4*a) - (cos(4*b*x + 4*a) - 2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) - ((cos(4*b*x + 4*a) - 2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + sin(4*b*x + 4*a)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))))*sqrt(c) - 3*sqrt(c)*(log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) - log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) + log(((cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2 + (cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))) + 1) - log(((cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2 + (cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))) + 1)))/b","B",0
610,1,2333,0,1.131094," ","integrate(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1\right)}^{\frac{3}{4}} {\left(\cos\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right) \sin\left(6 \, b x + 6 \, a\right) + {\left(\cos\left(6 \, b x + 6 \, a\right) + 1\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)\right)} \sqrt{c} + 12 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left({\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 5 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right) + {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 3 \, \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 4\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)\right)} \sqrt{c} + 15 \, \sqrt{c} {\left(\log\left(\sqrt{\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2} + \sqrt{\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2} + 2 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right) + 1\right) - \log\left(\sqrt{\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2} + \sqrt{\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2} - 2 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right) + 1\right) + \log\left({\left({\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2}\right)} \sqrt{\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1} + 2 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)\right)} + 1\right) - \log\left({\left({\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2} + {\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)^{2}\right)} \sqrt{\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1} - 2 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right)^{2} + 2 \, \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right) \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) + \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right), -\cos\left(\frac{2}{3} \, \arctan\left(\sin\left(6 \, b x + 6 \, a\right), \cos\left(6 \, b x + 6 \, a\right)\right)\right) - 1\right)\right)\right)} + 1\right)\right)}}{384 \, b}"," ",0,"-1/384*(8*(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)^(3/4)*(cos(3/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))*sin(6*b*x + 6*a) + (cos(6*b*x + 6*a) + 1)*sin(3/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1)))*sqrt(c) + 12*(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)^(1/4)*((sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 5*sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))))*cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1)) + (cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 3*cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1)))*sqrt(c) + 15*sqrt(c)*(log(sqrt(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)*cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2 + sqrt(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2 + 2*(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1)) + 1) - log(sqrt(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)*cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2 + sqrt(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2 - 2*(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)^(1/4)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1)) + 1) + log(((cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2)*cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2 + (cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2)*sqrt(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1) + 2*(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))*sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))) + 1) - log(((cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2)*cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2 + (cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2)*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))^2)*sqrt(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1) - 2*(cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))^2 + 2*cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + 1)^(1/4)*(cos(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))*sin(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) + cos(1/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a)))*sin(1/2*arctan2(sin(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))), -cos(2/3*arctan2(sin(6*b*x + 6*a), cos(6*b*x + 6*a))) - 1))) + 1)))/b","B",0
611,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,1,1317,0,0.893779," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(c \log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) - c \log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) + c \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} + 1\right) - c \log\left({\left({\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2} + {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right)\right)} + 1\right)\right)} \sqrt{c} + 8 \, {\left(c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), \cos\left(4 \, b x + 4 \, a\right)\right)\right) + c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} \sqrt{c}}{8 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} b}"," ",0,"-1/8*((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(c*log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) - c*log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) + c*log(((cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2 + (cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))) + 1) - c*log(((cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2 + (cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))) + 1))*sqrt(c) + 8*(c*cos(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a)))*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + c*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(1/2*arctan2(sin(4*b*x + 4*a), cos(4*b*x + 4*a))) + c*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*sqrt(c))/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*b)","B",0
616,1,1058,0,1.148488," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(c \cos\left(2 \, b x + 2 \, a\right) + c\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sqrt{c} - 3 \, {\left(c \log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) - c \log\left(\sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) + 1\right) + c \log\left({\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} + 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} + 1\right) - c \log\left({\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2} + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)^{2}\right)} \sqrt{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1} - 2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right) \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, b x + 4 \, a\right), -\cos\left(4 \, b x + 4 \, a\right) - 1\right)\right)\right)} + 1\right)\right)} \sqrt{c}}{16 \, b}"," ",0,"-1/16*(4*(c*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(2*b*x + 2*a) + (c*cos(2*b*x + 2*a) + c)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)))*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sqrt(c) - 3*(c*log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) - c*log(sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1)) + 1) + c*log(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) + 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(2*b*x + 2*a) + cos(2*b*x + 2*a)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))) + 1) - c*log(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))^2)*sqrt(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1) - 2*(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1)^(1/4)*(cos(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))*sin(2*b*x + 2*a) + cos(2*b*x + 2*a)*sin(1/2*arctan2(sin(4*b*x + 4*a), -cos(4*b*x + 4*a) - 1))) + 1))*sqrt(c))/b","B",0
617,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)^{4}}{\sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)^4/sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a)), x)","F",0
620,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)^{3}}{\sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)^3/sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a)), x)","F",0
621,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)^{2}}{\sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)^2/sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a)), x)","F",0
622,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)}{\sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)/sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a)), x)","F",0
623,-2,0,0,0.000000," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
624,0,0,0,0.000000," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(2 \, b x + 2 \, a\right)}{\sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)}}\,{d x}"," ",0,"integrate(cos(2*b*x + 2*a)/sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a)), x)","F",0
625,0,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(2 \, b x + 2 \, a\right)^{2}}{\sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)}}\,{d x}"," ",0,"integrate(cos(2*b*x + 2*a)^2/sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a)), x)","F",0
626,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)^{4}}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)^4/(c*tan(2*b*x + 2*a)*tan(b*x + a))^(3/2), x)","F",0
627,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)^{3}}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)^3/(c*tan(2*b*x + 2*a)*tan(b*x + a))^(3/2), x)","F",0
628,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)^{2}}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)^2/(c*tan(2*b*x + 2*a)*tan(b*x + a))^(3/2), x)","F",0
629,0,0,0,0.000000," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{\sec\left(2 \, b x + 2 \, a\right)}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(2*b*x + 2*a)/(c*tan(2*b*x + 2*a)*tan(b*x + a))^(3/2), x)","F",0
630,0,0,0,0.000000," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*tan(2*b*x + 2*a)*tan(b*x + a))^(-3/2), x)","F",0
631,0,0,0,0.000000," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(2 \, b x + 2 \, a\right)}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(2*b*x + 2*a)/(c*tan(2*b*x + 2*a)*tan(b*x + a))^(3/2), x)","F",0
632,0,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(2 \, b x + 2 \, a\right)^{2}}{\left(c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(2*b*x + 2*a)^2/(c*tan(2*b*x + 2*a)*tan(b*x + a))^(3/2), x)","F",0
633,0,0,0,0.000000," ","integrate(cot(x)*csc(x)/sin(2*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right) \csc\left(x\right)}{\sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(cot(x)*csc(x)/sqrt(sin(2*x)), x)","F",0
634,0,0,0,0.000000," ","integrate(csc(x)^2*sec(x)/sin(2*x)^(1/2)/(-2+tan(x)),x, algorithm=""maxima"")","\int \frac{\csc\left(x\right)^{2} \sec\left(x\right)}{{\left(\tan\left(x\right) - 2\right)} \sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(csc(x)^2*sec(x)/((tan(x) - 2)*sqrt(sin(2*x))), x)","F",0
635,-1,0,0,0.000000," ","integrate(cos(x)^2*sin(x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(cos(x)^3*cos(2*x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,1,30,0,0.305483," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))^n*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}^{n + 1}}{d {\left(n + 1\right)}}"," ",0,"(b*sec(d*x + c) + a*sin(d*x + c))^(n + 1)/(d*(n + 1))","A",0
638,1,24,0,0.307910," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))^3*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}^{4}}{4 \, d}"," ",0,"1/4*(b*sec(d*x + c) + a*sin(d*x + c))^4/d","A",0
639,1,24,0,0.309951," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))^2*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}^{3}}{3 \, d}"," ",0,"1/3*(b*sec(d*x + c) + a*sin(d*x + c))^3/d","A",0
640,1,24,0,0.549485," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}^{2}}{2 \, d}"," ",0,"1/2*(b*sec(d*x + c) + a*sin(d*x + c))^2/d","A",0
641,1,22,0,0.318495," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}{d}"," ",0,"log(b*sec(d*x + c) + a*sin(d*x + c))/d","A",0
642,1,24,0,0.425678," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)} d}"," ",0,"-1/((b*sec(d*x + c) + a*sin(d*x + c))*d)","A",0
643,1,24,0,0.308020," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}^{2} d}"," ",0,"-1/2/((b*sec(d*x + c) + a*sin(d*x + c))^2*d)","A",0
644,0,0,0,0.000000," ","integrate(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x, algorithm=""maxima"")","\int F\left(c, d, \cos\left(b x + a\right), r, s\right) \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(F(c, d, cos(b*x + a), r, s)*sin(b*x + a), x)","F",0
645,0,0,0,0.000000," ","integrate(cos(b*x+a)*F(c,d,sin(b*x+a),r,s),x, algorithm=""maxima"")","\int F\left(c, d, \sin\left(b x + a\right), r, s\right) \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(F(c, d, sin(b*x + a), r, s)*cos(b*x + a), x)","F",0
646,0,0,0,0.000000," ","integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x, algorithm=""maxima"")","\int F\left(c, d, \tan\left(b x + a\right), r, s\right) \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(F(c, d, tan(b*x + a), r, s)*sec(b*x + a)^2, x)","F",0
647,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*F(c,d,cot(b*x+a),r,s),x, algorithm=""maxima"")","\int F\left(c, d, \cot\left(b x + a\right), r, s\right) \csc\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(F(c, d, cot(b*x + a), r, s)*csc(b*x + a)^2, x)","F",0
648,1,12,0,0.310178," ","integrate(sin(x)/(a+b*cos(x)),x, algorithm=""maxima"")","-\frac{\log\left(b \cos\left(x\right) + a\right)}{b}"," ",0,"-log(b*cos(x) + a)/b","A",0
649,1,20,0,0.379565," ","integrate((a+b*cos(x))^n*sin(x),x, algorithm=""maxima"")","-\frac{{\left(b \cos\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"-(b*cos(x) + a)^(n + 1)/(b*(n + 1))","A",0
650,1,5,0,1.414051," ","integrate(sin(x)/(1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","-\operatorname{arsinh}\left(\cos\left(x\right)\right)"," ",0,"-arcsinh(cos(x))","A",0
651,1,5,0,0.545399," ","integrate(cos(cos(x))*sin(x),x, algorithm=""maxima"")","-\sin\left(\cos\left(x\right)\right)"," ",0,"-sin(cos(x))","A",0
652,1,17,0,0.585646," ","integrate(cos(x)*cos(cos(x))*sin(x)*sin(cos(x)),x, algorithm=""maxima"")","\frac{1}{4} \, \cos\left(x\right) \cos\left(2 \, \cos\left(x\right)\right) - \frac{1}{8} \, \sin\left(2 \, \cos\left(x\right)\right)"," ",0,"1/4*cos(x)*cos(2*cos(x)) - 1/8*sin(2*cos(x))","A",0
653,1,20,0,0.326292," ","integrate(cos(cos(x))*sin(x)*sin(6*cos(x))^2,x, algorithm=""maxima"")","\frac{1}{52} \, \sin\left(13 \, \cos\left(x\right)\right) + \frac{1}{44} \, \sin\left(11 \, \cos\left(x\right)\right) - \frac{1}{2} \, \sin\left(\cos\left(x\right)\right)"," ",0,"1/52*sin(13*cos(x)) + 1/44*sin(11*cos(x)) - 1/2*sin(cos(x))","A",0
654,1,103,0,0.392177," ","integrate(cos(x)^3*(a+b*cos(x)^2)^3*sin(x),x, algorithm=""maxima"")","\frac{1}{10} \, b^{3} \sin\left(x\right)^{10} - \frac{1}{8} \, {\left(3 \, a b^{2} + 4 \, b^{3}\right)} \sin\left(x\right)^{8} + \frac{1}{2} \, {\left(a^{2} b + 3 \, a b^{2} + 2 \, b^{3}\right)} \sin\left(x\right)^{6} - \frac{1}{4} \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3}\right)} \sin\left(x\right)^{4} + \frac{1}{2} \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sin\left(x\right)^{2}"," ",0,"1/10*b^3*sin(x)^10 - 1/8*(3*a*b^2 + 4*b^3)*sin(x)^8 + 1/2*(a^2*b + 3*a*b^2 + 2*b^3)*sin(x)^6 - 1/4*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3)*sin(x)^4 + 1/2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sin(x)^2","B",0
655,1,7,0,0.317887," ","integrate(sin(3*x)*sin(cos(3*x)),x, algorithm=""maxima"")","\frac{1}{3} \, \cos\left(\cos\left(3 \, x\right)\right)"," ",0,"1/3*cos(cos(3*x))","A",0
656,1,17,0,0.317277," ","integrate(exp(cos(1+3*x))*cos(1+3*x)*sin(1+3*x),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\cos\left(3 \, x + 1\right) - 1\right)} e^{\left(\cos\left(3 \, x + 1\right)\right)}"," ",0,"-1/3*(cos(3*x + 1) - 1)*e^(cos(3*x + 1))","A",0
657,1,18,0,0.600472," ","integrate(cos(x)^2*sin(x)/(1-cos(x)^6)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \arctan\left(\frac{\sqrt{-\cos\left(x\right)^{6} + 1}}{\cos\left(x\right)^{3}}\right)"," ",0,"1/3*arctan(sqrt(-cos(x)^6 + 1)/cos(x)^3)","B",0
658,1,51,0,0.318465," ","integrate(sin(x)^5/(1-5*cos(x))^(1/2),x, algorithm=""maxima"")","\frac{2}{28125} \, {\left(-5 \, \cos\left(x\right) + 1\right)}^{\frac{9}{2}} - \frac{8}{21875} \, {\left(-5 \, \cos\left(x\right) + 1\right)}^{\frac{7}{2}} - \frac{88}{15625} \, {\left(-5 \, \cos\left(x\right) + 1\right)}^{\frac{5}{2}} + \frac{64}{3125} \, {\left(-5 \, \cos\left(x\right) + 1\right)}^{\frac{3}{2}} + \frac{1152}{3125} \, \sqrt{-5 \, \cos\left(x\right) + 1}"," ",0,"2/28125*(-5*cos(x) + 1)^(9/2) - 8/21875*(-5*cos(x) + 1)^(7/2) - 88/15625*(-5*cos(x) + 1)^(5/2) + 64/3125*(-5*cos(x) + 1)^(3/2) + 1152/3125*sqrt(-5*cos(x) + 1)","A",0
659,1,17,0,0.310297," ","integrate(exp(n*cos(b*x+a))*sin(b*x+a),x, algorithm=""maxima"")","-\frac{e^{\left(n \cos\left(b x + a\right)\right)}}{b n}"," ",0,"-e^(n*cos(b*x + a))/(b*n)","A",0
660,1,23,0,0.371206," ","integrate(exp(n*cos(b*c*x+a*c))*sin(c*(b*x+a)),x, algorithm=""maxima"")","-\frac{e^{\left(n \cos\left(b c x + a c\right)\right)}}{b c n}"," ",0,"-e^(n*cos(b*c*x + a*c))/(b*c*n)","A",0
661,1,23,0,0.321232," ","integrate(exp(n*cos(c*(b*x+a)))*sin(b*c*x+a*c),x, algorithm=""maxima"")","-\frac{e^{\left(n \cos\left(b c x + a c\right)\right)}}{b c n}"," ",0,"-e^(n*cos(b*c*x + a*c))/(b*c*n)","A",0
662,1,14,0,0.373527," ","integrate(exp(n*cos(b*x+a))*tan(b*x+a),x, algorithm=""maxima"")","-\frac{{\rm Ei}\left(n \cos\left(b x + a\right)\right)}{b}"," ",0,"-Ei(n*cos(b*x + a))/b","A",0
663,1,20,0,0.384658," ","integrate(exp(n*cos(b*c*x+a*c))*tan(c*(b*x+a)),x, algorithm=""maxima"")","-\frac{{\rm Ei}\left(n \cos\left(b c x + a c\right)\right)}{b c}"," ",0,"-Ei(n*cos(b*c*x + a*c))/(b*c)","A",0
664,1,20,0,0.435057," ","integrate(exp(n*cos(c*(b*x+a)))*tan(b*c*x+a*c),x, algorithm=""maxima"")","-\frac{{\rm Ei}\left(n \cos\left(b c x + a c\right)\right)}{b c}"," ",0,"-Ei(n*cos(b*c*x + a*c))/(b*c)","A",0
665,1,11,0,0.321048," ","integrate(cos(x)/(a+b*sin(x)),x, algorithm=""maxima"")","\frac{\log\left(b \sin\left(x\right) + a\right)}{b}"," ",0,"log(b*sin(x) + a)/b","A",0
666,1,19,0,0.320764," ","integrate(cos(x)*(a+b*sin(x))^n,x, algorithm=""maxima"")","\frac{{\left(b \sin\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"(b*sin(x) + a)^(n + 1)/(b*(n + 1))","A",0
667,1,3,0,0.414431," ","integrate(cos(x)/(1+sin(x)^2)^(1/2),x, algorithm=""maxima"")","\operatorname{arsinh}\left(\sin\left(x\right)\right)"," ",0,"arcsinh(sin(x))","A",0
668,1,5,0,0.417553," ","integrate(cos(x)/(4-sin(x)^2)^(1/2),x, algorithm=""maxima"")","\arcsin\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"arcsin(1/2*sin(x))","A",0
669,1,9,0,0.416813," ","integrate(cos(3*x)/(4-sin(3*x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, \arcsin\left(\frac{1}{2} \, \sin\left(3 \, x\right)\right)"," ",0,"1/3*arcsin(1/2*sin(3*x))","A",0
670,1,38,0,0.328004," ","integrate(cos(x)*(1+csc(x))^(1/2),x, algorithm=""maxima"")","\sqrt{\frac{1}{\sin\left(x\right)} + 1} \sin\left(x\right) + \frac{1}{2} \, \log\left(\sqrt{\frac{1}{\sin\left(x\right)} + 1} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{1}{\sin\left(x\right)} + 1} - 1\right)"," ",0,"sqrt(1/sin(x) + 1)*sin(x) + 1/2*log(sqrt(1/sin(x) + 1) + 1) - 1/2*log(sqrt(1/sin(x) + 1) - 1)","B",0
671,1,22,0,0.462759," ","integrate(cos(x)*(4-sin(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-\sin\left(x\right)^{2} + 4} \sin\left(x\right) + 2 \, \arcsin\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"1/2*sqrt(-sin(x)^2 + 4)*sin(x) + 2*arcsin(1/2*sin(x))","A",0
672,1,10,0,0.367201," ","integrate(cos(x)*sin(x)*(1+sin(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\sin\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/3*(sin(x)^2 + 1)^(3/2)","A",0
673,1,20,0,0.311947," ","integrate(cos(x)/(2*sin(x)+sin(x)^2)^(1/2),x, algorithm=""maxima"")","\log\left(2 \, \sqrt{\sin\left(x\right)^{2} + 2 \, \sin\left(x\right)} + 2 \, \sin\left(x\right) + 2\right)"," ",0,"log(2*sqrt(sin(x)^2 + 2*sin(x)) + 2*sin(x) + 2)","A",0
674,1,3,0,0.318759," ","integrate(cos(x)*cos(sin(x)),x, algorithm=""maxima"")","\sin\left(\sin\left(x\right)\right)"," ",0,"sin(sin(x))","A",0
675,1,4,0,0.317972," ","integrate(cos(x)*cos(sin(x))*cos(sin(sin(x))),x, algorithm=""maxima"")","\sin\left(\sin\left(\sin\left(x\right)\right)\right)"," ",0,"sin(sin(sin(x)))","A",0
676,1,8,0,0.330419," ","integrate(cos(x)*sec(sin(x)),x, algorithm=""maxima"")","\log\left(\sec\left(\sin\left(x\right)\right) + \tan\left(\sin\left(x\right)\right)\right)"," ",0,"log(sec(sin(x)) + tan(sin(x)))","A",0
677,1,39,0,0.333622," ","integrate(cos(x)*sin(x)^3*(a+b*sin(x)^2)^3,x, algorithm=""maxima"")","\frac{1}{10} \, b^{3} \sin\left(x\right)^{10} + \frac{3}{8} \, a b^{2} \sin\left(x\right)^{8} + \frac{1}{2} \, a^{2} b \sin\left(x\right)^{6} + \frac{1}{4} \, a^{3} \sin\left(x\right)^{4}"," ",0,"1/10*b^3*sin(x)^10 + 3/8*a*b^2*sin(x)^8 + 1/2*a^2*b*sin(x)^6 + 1/4*a^3*sin(x)^4","A",0
678,1,8,0,0.330396," ","integrate(exp(sin(x))*cos(x)*sin(x),x, algorithm=""maxima"")","{\left(\sin\left(x\right) - 1\right)} e^{\sin\left(x\right)}"," ",0,"(sin(x) - 1)*e^sin(x)","A",0
679,1,19,0,0.321784," ","integrate(cos(x)^3/(sin(x)^3)^(1/2),x, algorithm=""maxima"")","-\frac{2}{3} \, \sqrt{\sin\left(x\right)^{3}} - \frac{2 \, \sin\left(x\right)}{\sqrt{\sin\left(x\right)^{3}}}"," ",0,"-2/3*sqrt(sin(x)^3) - 2*sin(x)/sqrt(sin(x)^3)","A",0
680,1,7,0,0.319198," ","integrate(exp(sin(x)^(1/2))*cos(x)/sin(x)^(1/2),x, algorithm=""maxima"")","2 \, e^{\sqrt{\sin\left(x\right)}}"," ",0,"2*e^sqrt(sin(x))","A",0
681,1,5,0,0.315065," ","integrate(exp(4+sin(x))*cos(x),x, algorithm=""maxima"")","e^{\left(\sin\left(x\right) + 4\right)}"," ",0,"e^(sin(x) + 4)","A",0
682,1,7,0,0.950359," ","integrate(exp(cos(x)*sin(x))*cos(2*x),x, algorithm=""maxima"")","e^{\left(\frac{1}{2} \, \sin\left(2 \, x\right)\right)}"," ",0,"e^(1/2*sin(2*x))","A",0
683,1,7,0,0.328045," ","integrate(exp(cos(1/2*x)*sin(1/2*x))*cos(x),x, algorithm=""maxima"")","2 \, e^{\left(\frac{1}{2} \, \sin\left(x\right)\right)}"," ",0,"2*e^(1/2*sin(x))","A",0
684,1,16,0,0.310448," ","integrate(exp(n*sin(b*x+a))*cos(b*x+a),x, algorithm=""maxima"")","\frac{e^{\left(n \sin\left(b x + a\right)\right)}}{b n}"," ",0,"e^(n*sin(b*x + a))/(b*n)","A",0
685,1,22,0,0.316572," ","integrate(exp(n*sin(b*c*x+a*c))*cos(c*(b*x+a)),x, algorithm=""maxima"")","\frac{e^{\left(n \sin\left(b c x + a c\right)\right)}}{b c n}"," ",0,"e^(n*sin(b*c*x + a*c))/(b*c*n)","A",0
686,1,22,0,0.310875," ","integrate(exp(n*sin(c*(b*x+a)))*cos(b*c*x+a*c),x, algorithm=""maxima"")","\frac{e^{\left(n \sin\left(b c x + a c\right)\right)}}{b c n}"," ",0,"e^(n*sin(b*c*x + a*c))/(b*c*n)","A",0
687,1,13,0,0.371507," ","integrate(exp(n*sin(b*x+a))*cot(b*x+a),x, algorithm=""maxima"")","\frac{{\rm Ei}\left(n \sin\left(b x + a\right)\right)}{b}"," ",0,"Ei(n*sin(b*x + a))/b","A",0
688,1,19,0,0.380404," ","integrate(exp(n*sin(b*c*x+a*c))*cot(c*(b*x+a)),x, algorithm=""maxima"")","\frac{{\rm Ei}\left(n \sin\left(b c x + a c\right)\right)}{b c}"," ",0,"Ei(n*sin(b*c*x + a*c))/(b*c)","A",0
689,1,19,0,0.410402," ","integrate(exp(n*sin(c*(b*x+a)))*cot(b*c*x+a*c),x, algorithm=""maxima"")","\frac{{\rm Ei}\left(n \sin\left(b c x + a c\right)\right)}{b c}"," ",0,"Ei(n*sin(b*c*x + a*c))/(b*c)","A",0
690,1,11,0,0.311246," ","integrate(sec(x)^2/(a+b*tan(x)),x, algorithm=""maxima"")","\frac{\log\left(b \tan\left(x\right) + a\right)}{b}"," ",0,"log(b*tan(x) + a)/b","A",0
691,1,15,0,0.313106," ","integrate(sec(x)^2/(1-tan(x)^2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\tan\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\tan\left(x\right) - 1\right)"," ",0,"1/2*log(tan(x) + 1) - 1/2*log(tan(x) - 1)","A",0
692,1,7,0,0.408649," ","integrate(sec(x)^2/(9+tan(x)^2),x, algorithm=""maxima"")","\frac{1}{3} \, \arctan\left(\frac{1}{3} \, \tan\left(x\right)\right)"," ",0,"1/3*arctan(1/3*tan(x))","A",0
693,1,19,0,0.314403," ","integrate(sec(x)^2*(a+b*tan(x))^n,x, algorithm=""maxima"")","\frac{{\left(b \tan\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"(b*tan(x) + a)^(n + 1)/(b*(n + 1))","A",0
694,1,4,0,0.413202," ","integrate(sec(x)^2*(1+1/(1+tan(x)^2)),x, algorithm=""maxima"")","x + \tan\left(x\right)"," ",0,"x + tan(x)","A",0
695,1,4,0,0.499297," ","integrate(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^2),x, algorithm=""maxima"")","x + \tan\left(x\right)"," ",0,"x + tan(x)","A",0
696,1,5,0,0.410506," ","integrate(sec(x)^2/(2+2*tan(x)+tan(x)^2),x, algorithm=""maxima"")","\arctan\left(\tan\left(x\right) + 1\right)"," ",0,"arctan(tan(x) + 1)","A",0
697,1,17,0,0.311620," ","integrate(sec(x)^2/(tan(x)^2+tan(x)^3),x, algorithm=""maxima"")","-\frac{1}{\tan\left(x\right)} + \log\left(\tan\left(x\right) + 1\right) - \log\left(\tan\left(x\right)\right)"," ",0,"-1/tan(x) + log(tan(x) + 1) - log(tan(x))","A",0
698,1,15,0,0.311423," ","integrate(sec(x)^2/(-tan(x)^2+tan(x)^3),x, algorithm=""maxima"")","\frac{1}{\tan\left(x\right)} + \log\left(\tan\left(x\right) - 1\right) - \log\left(\tan\left(x\right)\right)"," ",0,"1/tan(x) + log(tan(x) - 1) - log(tan(x))","A",0
699,1,89,0,0.434960," ","integrate(sec(x)^2/(3-4*tan(x)^3),x, algorithm=""maxima"")","\frac{1}{36} \cdot 4^{\frac{2}{3}} 3^{\frac{5}{6}} \arctan\left(\frac{1}{12} \cdot 4^{\frac{2}{3}} 3^{\frac{1}{6}} {\left(2 \cdot 4^{\frac{2}{3}} \tan\left(x\right) + 4^{\frac{1}{3}} 3^{\frac{1}{3}}\right)}\right) + \frac{1}{72} \cdot 4^{\frac{2}{3}} 3^{\frac{1}{3}} \log\left(4^{\frac{2}{3}} \tan\left(x\right)^{2} + 4^{\frac{1}{3}} 3^{\frac{1}{3}} \tan\left(x\right) + 3^{\frac{2}{3}}\right) - \frac{1}{36} \cdot 4^{\frac{2}{3}} 3^{\frac{1}{3}} \log\left(\frac{1}{4} \cdot 4^{\frac{2}{3}} {\left(4^{\frac{1}{3}} \tan\left(x\right) - 3^{\frac{1}{3}}\right)}\right)"," ",0,"1/36*4^(2/3)*3^(5/6)*arctan(1/12*4^(2/3)*3^(1/6)*(2*4^(2/3)*tan(x) + 4^(1/3)*3^(1/3))) + 1/72*4^(2/3)*3^(1/3)*log(4^(2/3)*tan(x)^2 + 4^(1/3)*3^(1/3)*tan(x) + 3^(2/3)) - 1/36*4^(2/3)*3^(1/3)*log(1/4*4^(2/3)*(4^(1/3)*tan(x) - 3^(1/3)))","A",0
700,1,17,0,0.448037," ","integrate(sec(x)^2/(11-5*tan(x)+5*tan(x)^2),x, algorithm=""maxima"")","\frac{2}{195} \, \sqrt{195} \arctan\left(\frac{1}{39} \, \sqrt{195} {\left(2 \, \tan\left(x\right) - 1\right)}\right)"," ",0,"2/195*sqrt(195)*arctan(1/39*sqrt(195)*(2*tan(x) - 1))","A",0
701,1,28,0,0.317599," ","integrate(sec(x)^2*(a+b*tan(x))/(c+d*tan(x)),x, algorithm=""maxima"")","\frac{b \tan\left(x\right)}{d} - \frac{{\left(b c - a d\right)} \log\left(d \tan\left(x\right) + c\right)}{d^{2}}"," ",0,"b*tan(x)/d - (b*c - a*d)*log(d*tan(x) + c)/d^2","A",0
702,1,63,0,0.352898," ","integrate(sec(x)^2*(a+b*tan(x))^2/(c+d*tan(x)),x, algorithm=""maxima"")","\frac{b^{2} d \tan\left(x\right)^{2} - 2 \, {\left(b^{2} c - 2 \, a b d\right)} \tan\left(x\right)}{2 \, d^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d \tan\left(x\right) + c\right)}{d^{3}}"," ",0,"1/2*(b^2*d*tan(x)^2 - 2*(b^2*c - 2*a*b*d)*tan(x))/d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*tan(x) + c)/d^3","A",0
703,1,118,0,0.524325," ","integrate(sec(x)^2*(a+b*tan(x))^3/(c+d*tan(x)),x, algorithm=""maxima"")","\frac{2 \, b^{3} d^{2} \tan\left(x\right)^{3} - 3 \, {\left(b^{3} c d - 3 \, a b^{2} d^{2}\right)} \tan\left(x\right)^{2} + 6 \, {\left(b^{3} c^{2} - 3 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} \tan\left(x\right)}{6 \, d^{3}} - \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(d \tan\left(x\right) + c\right)}{d^{4}}"," ",0,"1/6*(2*b^3*d^2*tan(x)^3 - 3*(b^3*c*d - 3*a*b^2*d^2)*tan(x)^2 + 6*(b^3*c^2 - 3*a*b^2*c*d + 3*a^2*b*d^2)*tan(x))/d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(d*tan(x) + c)/d^4","A",0
704,1,10,0,0.317783," ","integrate(sec(x)^2*tan(x)^2/(2+tan(x)^3)^2,x, algorithm=""maxima"")","-\frac{1}{3 \, {\left(\tan\left(x\right)^{3} + 2\right)}}"," ",0,"-1/3/(tan(x)^3 + 2)","A",0
705,1,25,0,0.394041," ","integrate(sec(x)^2*tan(x)^6*(1+tan(x)^2)^3,x, algorithm=""maxima"")","\frac{1}{13} \, \tan\left(x\right)^{13} + \frac{3}{11} \, \tan\left(x\right)^{11} + \frac{1}{3} \, \tan\left(x\right)^{9} + \frac{1}{7} \, \tan\left(x\right)^{7}"," ",0,"1/13*tan(x)^13 + 3/11*tan(x)^11 + 1/3*tan(x)^9 + 1/7*tan(x)^7","A",0
706,1,23,0,0.410069," ","integrate(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^3),x, algorithm=""maxima"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(x\right) - 1\right)}\right) + \log\left(\tan\left(x\right) + 1\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(x) - 1)) + log(tan(x) + 1)","A",0
707,1,4,0,0.459087," ","integrate((1+cos(x)^2)*sec(x)^2,x, algorithm=""maxima"")","x + \tan\left(x\right)"," ",0,"x + tan(x)","A",0
708,1,13,0,0.317763," ","integrate(sec(x)^2/(1+sec(x)^2-3*tan(x)),x, algorithm=""maxima"")","-\log\left(\tan\left(x\right) - 1\right) + \log\left(\tan\left(x\right) - 2\right)"," ",0,"-log(tan(x) - 1) + log(tan(x) - 2)","A",0
709,1,8,0,0.425499," ","integrate(sec(x)^2/(4-sec(x)^2)^(1/2),x, algorithm=""maxima"")","\arcsin\left(\frac{1}{3} \, \sqrt{3} \tan\left(x\right)\right)"," ",0,"arcsin(1/3*sqrt(3)*tan(x))","A",0
710,1,7,0,0.422520," ","integrate(sec(x)^2/(1-4*tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \arcsin\left(2 \, \tan\left(x\right)\right)"," ",0,"1/2*arcsin(2*tan(x))","A",0
711,1,16,0,0.313930," ","integrate(sec(x)^2/(-4+tan(x)^2)^(1/2),x, algorithm=""maxima"")","\log\left(2 \, \sqrt{\tan\left(x\right)^{2} - 4} + 2 \, \tan\left(x\right)\right)"," ",0,"log(2*sqrt(tan(x)^2 - 4) + 2*tan(x))","A",0
712,1,30,0,0.414613," ","integrate(sec(x)^2*(1-cot(x)^2)^(1/2),x, algorithm=""maxima"")","\sqrt{-\frac{1}{\tan\left(x\right)^{2}} + 1} \tan\left(x\right) - \arctan\left(\sqrt{-\frac{1}{\tan\left(x\right)^{2}} + 1} \tan\left(x\right)\right)"," ",0,"sqrt(-1/tan(x)^2 + 1)*tan(x) - arctan(sqrt(-1/tan(x)^2 + 1)*tan(x))","A",0
713,1,20,0,0.407592," ","integrate(sec(x)^2*(1-tan(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{-\tan\left(x\right)^{2} + 1} \tan\left(x\right) + \frac{1}{2} \, \arcsin\left(\tan\left(x\right)\right)"," ",0,"1/2*sqrt(-tan(x)^2 + 1)*tan(x) + 1/2*arcsin(tan(x))","A",0
714,1,3,0,0.316935," ","integrate(exp(tan(x))*sec(x)^2,x, algorithm=""maxima"")","e^{\tan\left(x\right)}"," ",0,"e^tan(x)","A",0
715,1,42,0,0.311795," ","integrate(sec(x)^4*(-1+sec(x)^2)^2*tan(x),x, algorithm=""maxima"")","\frac{6 \, \sin\left(x\right)^{4} - 4 \, \sin\left(x\right)^{2} + 1}{24 \, {\left(\sin\left(x\right)^{8} - 4 \, \sin\left(x\right)^{6} + 6 \, \sin\left(x\right)^{4} - 4 \, \sin\left(x\right)^{2} + 1\right)}}"," ",0,"1/24*(6*sin(x)^4 - 4*sin(x)^2 + 1)/(sin(x)^8 - 4*sin(x)^6 + 6*sin(x)^4 - 4*sin(x)^2 + 1)","B",0
716,1,12,0,0.332181," ","integrate(csc(x)^2/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{\log\left(b \cot\left(x\right) + a\right)}{b}"," ",0,"-log(b*cot(x) + a)/b","A",0
717,1,20,0,0.316915," ","integrate((a+b*cot(x))^n*csc(x)^2,x, algorithm=""maxima"")","-\frac{{\left(b \cot\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"-(b*cot(x) + a)^(n + 1)/(b*(n + 1))","A",0
718,1,8,0,0.409002," ","integrate(csc(x)^2*(1+sin(x)^2),x, algorithm=""maxima"")","x - \frac{1}{\tan\left(x\right)}"," ",0,"x - 1/tan(x)","A",0
719,1,8,0,0.409232," ","integrate((1+1/(1+cot(x)^2))*csc(x)^2,x, algorithm=""maxima"")","x - \frac{1}{\tan\left(x\right)}"," ",0,"x - 1/tan(x)","A",0
720,1,46,0,0.318922," ","integrate((a+b*cot(x))*csc(x)^2/(c+d*cot(x)),x, algorithm=""maxima"")","\frac{{\left(b c - a d\right)} \log\left(c \tan\left(x\right) + d\right)}{d^{2}} - \frac{{\left(b c - a d\right)} \log\left(\tan\left(x\right)\right)}{d^{2}} - \frac{b}{d \tan\left(x\right)}"," ",0,"(b*c - a*d)*log(c*tan(x) + d)/d^2 - (b*c - a*d)*log(tan(x))/d^2 - b/(d*tan(x))","A",0
721,1,92,0,0.318774," ","integrate((a+b*cot(x))^2*csc(x)^2/(c+d*cot(x)),x, algorithm=""maxima"")","-\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(c \tan\left(x\right) + d\right)}{d^{3}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\tan\left(x\right)\right)}{d^{3}} - \frac{b^{2} d - 2 \, {\left(b^{2} c - 2 \, a b d\right)} \tan\left(x\right)}{2 \, d^{2} \tan\left(x\right)^{2}}"," ",0,"-(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(c*tan(x) + d)/d^3 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(tan(x))/d^3 - 1/2*(b^2*d - 2*(b^2*c - 2*a*b*d)*tan(x))/(d^2*tan(x)^2)","A",0
722,1,161,0,0.316601," ","integrate((a+b*cot(x))^3*csc(x)^2/(c+d*cot(x)),x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(c \tan\left(x\right) + d\right)}{d^{4}} - \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\tan\left(x\right)\right)}{d^{4}} - \frac{2 \, b^{3} d^{2} + 6 \, {\left(b^{3} c^{2} - 3 \, a b^{2} c d + 3 \, a^{2} b d^{2}\right)} \tan\left(x\right)^{2} - 3 \, {\left(b^{3} c d - 3 \, a b^{2} d^{2}\right)} \tan\left(x\right)}{6 \, d^{3} \tan\left(x\right)^{3}}"," ",0,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(c*tan(x) + d)/d^4 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(tan(x))/d^4 - 1/6*(2*b^3*d^2 + 6*(b^3*c^2 - 3*a*b^2*c*d + 3*a^2*b*d^2)*tan(x)^2 - 3*(b^3*c*d - 3*a*b^2*d^2)*tan(x))/(d^3*tan(x)^3)","B",0
723,1,5,0,0.315763," ","integrate(csc(x)^2/exp(cot(x)),x, algorithm=""maxima"")","e^{\left(-\cot\left(x\right)\right)}"," ",0,"e^(-cot(x))","A",0
724,1,11,0,0.308514," ","integrate(sec(x)*tan(x)/(a+b*sec(x)),x, algorithm=""maxima"")","\frac{\log\left(b \sec\left(x\right) + a\right)}{b}"," ",0,"log(b*sec(x) + a)/b","A",0
725,1,5,0,0.415143," ","integrate(sec(x)*tan(x)/(1+sec(x)^2),x, algorithm=""maxima"")","-\arctan\left(\cos\left(x\right)\right)"," ",0,"-arctan(cos(x))","A",0
726,1,7,0,0.438056," ","integrate(sec(x)*tan(x)/(9+4*sec(x)^2),x, algorithm=""maxima"")","-\frac{1}{6} \, \arctan\left(\frac{3}{2} \, \cos\left(x\right)\right)"," ",0,"-1/6*arctan(3/2*cos(x))","A",0
727,1,7,0,0.309617," ","integrate(sec(x)*tan(x)/(sec(x)+sec(x)^2),x, algorithm=""maxima"")","-\log\left(\cos\left(x\right) + 1\right)"," ",0,"-log(cos(x) + 1)","A",0
728,1,33,0,0.312720," ","integrate(sec(x)*tan(x)/(4+sec(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\sqrt{\frac{1}{\cos\left(x\right)^{2}} + 4} \cos\left(x\right) + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{1}{\cos\left(x\right)^{2}} + 4} \cos\left(x\right) - 1\right)"," ",0,"1/2*log(sqrt(1/cos(x)^2 + 4)*cos(x) + 1) - 1/2*log(sqrt(1/cos(x)^2 + 4)*cos(x) - 1)","B",0
729,1,13,0,0.420366," ","integrate(sec(x)*tan(x)/(1+cos(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(x\right)^{2} + 1}}{\cos\left(x\right)}"," ",0,"sqrt(cos(x)^2 + 1)/cos(x)","A",0
730,1,3,0,0.330974," ","integrate(exp(sec(x))*sec(x)*tan(x),x, algorithm=""maxima"")","e^{\sec\left(x\right)}"," ",0,"e^sec(x)","A",0
731,1,9,0,0.313499," ","integrate(2^sec(x)*sec(x)*tan(x),x, algorithm=""maxima"")","\frac{2^{\sec\left(x\right)}}{\log\left(2\right)}"," ",0,"2^sec(x)/log(2)","A",0
732,1,10,0,0.315693," ","integrate(sec(2*x)*tan(2*x)/(1+sec(2*x))^(3/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{\sec\left(2 \, x\right) + 1}}"," ",0,"-1/sqrt(sec(2*x) + 1)","A",0
733,1,35,0,0.425788," ","integrate(sec(3*x)*(1+5*cos(3*x)^2)^(1/2)*tan(3*x),x, algorithm=""maxima"")","-\frac{1}{3} \, \sqrt{5} \operatorname{arsinh}\left(\sqrt{5} \cos\left(3 \, x\right)\right) + \frac{\sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1}}{3 \, \cos\left(3 \, x\right)}"," ",0,"-1/3*sqrt(5)*arcsinh(sqrt(5)*cos(3*x)) + 1/3*sqrt(5*cos(3*x)^2 + 1)/cos(3*x)","A",0
734,1,20,0,0.422149," ","integrate(sec(3*x)*tan(3*x)/(1+5*cos(3*x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1}}{3 \, \cos\left(3 \, x\right)}"," ",0,"1/3*sqrt(5*cos(3*x)^2 + 1)/cos(3*x)","A",0
735,1,12,0,0.309892," ","integrate(cot(x)*csc(x)/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{\log\left(b \csc\left(x\right) + a\right)}{b}"," ",0,"-log(b*csc(x) + a)/b","A",0
736,1,12,0,0.302033," ","integrate(5^csc(3*x)*cot(3*x)*csc(3*x),x, algorithm=""maxima"")","-\frac{5^{\csc\left(3 \, x\right)}}{3 \, \log\left(5\right)}"," ",0,"-1/3*5^csc(3*x)/log(5)","A",0
737,1,3,0,0.401647," ","integrate(cot(x)*csc(x)/(1+csc(x)^2),x, algorithm=""maxima"")","\arctan\left(\sin\left(x\right)\right)"," ",0,"arctan(sin(x))","A",0
738,1,49,0,0.402377," ","integrate(cot(6*x)*csc(6*x)/(5-11*csc(6*x)^2)^2,x, algorithm=""maxima"")","\frac{1}{6600} \, \sqrt{55} \log\left(-\frac{\sqrt{55} - 5 \, \sin\left(6 \, x\right)}{\sqrt{55} + 5 \, \sin\left(6 \, x\right)}\right) - \frac{\sin\left(6 \, x\right)}{60 \, {\left(5 \, \sin\left(6 \, x\right)^{2} - 11\right)}}"," ",0,"1/6600*sqrt(55)*log(-(sqrt(55) - 5*sin(6*x))/(sqrt(55) + 5*sin(6*x))) - 1/60*sin(6*x)/(5*sin(6*x)^2 - 11)","A",0
739,1,14,0,0.400225," ","integrate(cot(x)*csc(x)/(1+sin(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{\sin\left(x\right)^{2} + 1}}{\sin\left(x\right)}"," ",0,"-sqrt(sin(x)^2 + 1)/sin(x)","A",0
740,1,37,0,0.401154," ","integrate(cot(5*x)*csc(5*x)^3/(1+sin(5*x)^2)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{\sin\left(5 \, x\right)^{2} + 1}}{15 \, \sin\left(5 \, x\right)} - \frac{\sqrt{\sin\left(5 \, x\right)^{2} + 1}}{15 \, \sin\left(5 \, x\right)^{3}}"," ",0,"2/15*sqrt(sin(5*x)^2 + 1)/sin(5*x) - 1/15*sqrt(sin(5*x)^2 + 1)/sin(5*x)^3","A",0
741,1,37,0,0.338921," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{2 \, {\left(n e^{\left(n \sin\left(b x + a\right)\right)} \sin\left(b x + a\right) - e^{\left(n \sin\left(b x + a\right)\right)}\right)}}{b n^{2}}"," ",0,"2*(n*e^(n*sin(b*x + a))*sin(b*x + a) - e^(n*sin(b*x + a)))/(b*n^2)","A",0
742,1,37,0,0.352322," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x, algorithm=""maxima"")","\frac{2 \, {\left(n e^{\left(n \sin\left(b x + a\right)\right)} \sin\left(b x + a\right) - e^{\left(n \sin\left(b x + a\right)\right)}\right)}}{b n^{2}}"," ",0,"2*(n*e^(n*sin(b*x + a))*sin(b*x + a) - e^(n*sin(b*x + a)))/(b*n^2)","A",0
743,0,0,0,0.000000," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""maxima"")","\int e^{\left(n \sin\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(e^(n*sin(1/2*b*x + 1/2*a))*sin(b*x + a), x)","F",0
744,0,0,0,0.000000," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""maxima"")","\int e^{\left(n \sin\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(e^(n*sin(1/2*b*x + 1/2*a))*sin(b*x + a), x)","F",0
745,1,37,0,0.339364," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{2 \, {\left(n \cos\left(b x + a\right) e^{\left(n \cos\left(b x + a\right)\right)} - e^{\left(n \cos\left(b x + a\right)\right)}\right)}}{b n^{2}}"," ",0,"-2*(n*cos(b*x + a)*e^(n*cos(b*x + a)) - e^(n*cos(b*x + a)))/(b*n^2)","A",0
746,1,37,0,0.341236," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x, algorithm=""maxima"")","-\frac{2 \, {\left(n \cos\left(b x + a\right) e^{\left(n \cos\left(b x + a\right)\right)} - e^{\left(n \cos\left(b x + a\right)\right)}\right)}}{b n^{2}}"," ",0,"-2*(n*cos(b*x + a)*e^(n*cos(b*x + a)) - e^(n*cos(b*x + a)))/(b*n^2)","A",0
747,0,0,0,0.000000," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""maxima"")","\int e^{\left(n \cos\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(e^(n*cos(1/2*b*x + 1/2*a))*sin(b*x + a), x)","F",0
748,0,0,0,0.000000," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""maxima"")","\int e^{\left(n \cos\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(e^(n*cos(1/2*b*x + 1/2*a))*sin(b*x + a), x)","F",0
749,1,7,0,0.320951," ","integrate(csc(x)*log(tan(x))*sec(x),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\tan\left(x\right)\right)^{2}"," ",0,"1/2*log(tan(x))^2","A",0
750,1,265,0,0.456180," ","integrate(csc(2*x)*log(tan(x)),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(\pi - 2 \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 2 \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)} \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) + \frac{1}{4} \, \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right)^{2} - \frac{1}{4} \, {\left(\pi - 2 \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + \frac{1}{4} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right)^{2} - \frac{1}{4} \, \pi \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) + \frac{1}{4} \, \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)^{2} + \frac{1}{8} \, {\left(\log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) - \frac{1}{16} \, \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)^{2} - \frac{1}{16} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right)^{2} - \frac{1}{8} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - \frac{1}{16} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)^{2} - \frac{1}{2} \, \log\left(\cot\left(2 \, x\right) + \csc\left(2 \, x\right)\right) \log\left(\tan\left(x\right)\right)"," ",0,"1/4*(pi - 2*arctan2(sin(x), cos(x) + 1) - 2*arctan2(sin(x), cos(x) - 1))*arctan2(sin(2*x), cos(2*x) + 1) + 1/4*arctan2(sin(2*x), cos(2*x) + 1)^2 - 1/4*(pi - 2*arctan2(sin(x), cos(x) - 1))*arctan2(sin(x), cos(x) + 1) + 1/4*arctan2(sin(x), cos(x) + 1)^2 - 1/4*pi*arctan2(sin(x), cos(x) - 1) + 1/4*arctan2(sin(x), cos(x) - 1)^2 + 1/8*(log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1))*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) - 1/16*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)^2 - 1/16*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)^2 - 1/8*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 1/16*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)^2 - 1/2*log(cot(2*x) + csc(2*x))*log(tan(x))","B",0
751,1,4,0,0.425827," ","integrate(exp(cos(x)^2+sin(x)^2),x, algorithm=""maxima"")","x e"," ",0,"x*e","C",0
752,1,74,0,0.422997," ","integrate(x*sec(x)^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) + 4 \, x \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/2*((cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) + 4*x*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
753,1,22,0,0.318285," ","integrate(x*cos(x^2)^4,x, algorithm=""maxima"")","\frac{3}{16} \, x^{2} + \frac{1}{64} \, \sin\left(4 \, x^{2}\right) + \frac{1}{8} \, \sin\left(2 \, x^{2}\right)"," ",0,"3/16*x^2 + 1/64*sin(4*x^2) + 1/8*sin(2*x^2)","A",0
754,1,6,0,0.317862," ","integrate(sin(x)*cos(x)^(1/2),x, algorithm=""maxima"")","-\frac{2}{3} \, \cos\left(x\right)^{\frac{3}{2}}"," ",0,"-2/3*cos(x)^(3/2)","A",0
755,1,8,0,0.314070," ","integrate(tan(exp(-2*x))/exp(2*x),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\sec\left(e^{\left(-2 \, x\right)}\right)\right)"," ",0,"-1/2*log(sec(e^(-2*x)))","A",0
756,1,7,0,0.316406," ","integrate(sec(x)*sin(2*x)/(1+cos(x)),x, algorithm=""maxima"")","-2 \, \log\left(\cos\left(x\right) + 1\right)"," ",0,"-2*log(cos(x) + 1)","A",0
757,1,74,0,0.414153," ","integrate(x*sec(3*x)^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(6 \, x\right)^{2} + \sin\left(6 \, x\right)^{2} + 2 \, \cos\left(6 \, x\right) + 1\right)} \log\left(\cos\left(6 \, x\right)^{2} + \sin\left(6 \, x\right)^{2} + 2 \, \cos\left(6 \, x\right) + 1\right) + 12 \, x \sin\left(6 \, x\right)}{18 \, {\left(\cos\left(6 \, x\right)^{2} + \sin\left(6 \, x\right)^{2} + 2 \, \cos\left(6 \, x\right) + 1\right)}}"," ",0,"1/18*((cos(6*x)^2 + sin(6*x)^2 + 2*cos(6*x) + 1)*log(cos(6*x)^2 + sin(6*x)^2 + 2*cos(6*x) + 1) + 12*x*sin(6*x))/(cos(6*x)^2 + sin(6*x)^2 + 2*cos(6*x) + 1)","B",0
758,1,26,0,0.316982," ","integrate(cos(2*pi*x)/exp(2*pi*x),x, algorithm=""maxima"")","-\frac{{\left(\pi \cos\left(2 \, \pi x\right) - \pi \sin\left(2 \, \pi x\right)\right)} e^{\left(-2 \, \pi x\right)}}{4 \, \pi^{2}}"," ",0,"-1/4*(pi*cos(2*pi*x) - pi*sin(2*pi*x))*e^(-2*pi*x)/pi^2","A",0
759,1,8,0,0.337321," ","integrate(cos(x)^12*sin(x)^10-cos(x)^10*sin(x)^12,x, algorithm=""maxima"")","\frac{1}{22528} \, \sin\left(2 \, x\right)^{11}"," ",0,"1/22528*sin(2*x)^11","A",0
760,1,7,0,0.322895," ","integrate(x*cot(x^2),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\sin\left(x^{2}\right)\right)"," ",0,"1/2*log(sin(x^2))","A",0
761,1,35,0,0.323823," ","integrate(x*sec(x^2)^2,x, algorithm=""maxima"")","\frac{\sin\left(2 \, x^{2}\right)}{\cos\left(2 \, x^{2}\right)^{2} + \sin\left(2 \, x^{2}\right)^{2} + 2 \, \cos\left(2 \, x^{2}\right) + 1}"," ",0,"sin(2*x^2)/(cos(2*x^2)^2 + sin(2*x^2)^2 + 2*cos(2*x^2) + 1)","B",0
762,0,0,0,0.000000," ","integrate(sin(8*x)/(9+sin(4*x)^4),x, algorithm=""maxima"")","\int \frac{\sin\left(8 \, x\right)}{\sin\left(4 \, x\right)^{4} + 9}\,{d x}"," ",0,"integrate(sin(8*x)/(sin(4*x)^4 + 9), x)","F",0
763,1,15,0,0.428567," ","integrate(cos(2*x)/(8+sin(2*x)^2),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} \sin\left(2 \, x\right)\right)"," ",0,"1/8*sqrt(2)*arctan(1/4*sqrt(2)*sin(2*x))","A",0
764,1,29,0,0.327826," ","integrate(x*(cos(x^2)^3-sin(x^2)^3),x, algorithm=""maxima"")","-\frac{1}{24} \, \cos\left(3 \, x^{2}\right) + \frac{3}{8} \, \cos\left(x^{2}\right) + \frac{1}{24} \, \sin\left(3 \, x^{2}\right) + \frac{3}{8} \, \sin\left(x^{2}\right)"," ",0,"-1/24*cos(3*x^2) + 3/8*cos(x^2) + 1/24*sin(3*x^2) + 3/8*sin(x^2)","A",0
765,1,8,0,0.321415," ","integrate(cos(x)*sin(x)/(1-cos(x)),x, algorithm=""maxima"")","\cos\left(x\right) + \log\left(\cos\left(x\right) - 1\right)"," ",0,"cos(x) + log(cos(x) - 1)","A",0
766,1,6,0,0.315394," ","integrate(x*cos(x^2),x, algorithm=""maxima"")","\frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"1/2*sin(x^2)","A",0
767,1,8,0,0.317375," ","integrate(x^2*cos(4*x^3),x, algorithm=""maxima"")","\frac{1}{12} \, \sin\left(4 \, x^{3}\right)"," ",0,"1/12*sin(4*x^3)","A",0
768,1,6,0,0.313774," ","integrate(x^3*cos(x^4),x, algorithm=""maxima"")","\frac{1}{4} \, \sin\left(x^{4}\right)"," ",0,"1/4*sin(x^4)","A",0
769,1,8,0,0.325701," ","integrate(x*sin(1/2*x^2),x, algorithm=""maxima"")","-\cos\left(\frac{1}{2} \, x^{2}\right)"," ",0,"-cos(1/2*x^2)","A",0
770,1,56,0,0.328829," ","integrate(x*sec(x^2)*tan(x^2),x, algorithm=""maxima"")","\frac{\cos\left(2 \, x^{2}\right) \cos\left(x^{2}\right) + \sin\left(2 \, x^{2}\right) \sin\left(x^{2}\right) + \cos\left(x^{2}\right)}{\cos\left(2 \, x^{2}\right)^{2} + \sin\left(2 \, x^{2}\right)^{2} + 2 \, \cos\left(2 \, x^{2}\right) + 1}"," ",0,"(cos(2*x^2)*cos(x^2) + sin(2*x^2)*sin(x^2) + cos(x^2))/(cos(2*x^2)^2 + sin(2*x^2)^2 + 2*cos(2*x^2) + 1)","B",0
771,1,67,0,0.330385," ","integrate(tan(1/x)^2/x^2,x, algorithm=""maxima"")","\frac{\cos\left(\frac{2}{x}\right)^{2} - 2 \, x \sin\left(\frac{2}{x}\right) + \sin\left(\frac{2}{x}\right)^{2} + 2 \, \cos\left(\frac{2}{x}\right) + 1}{{\left(\cos\left(\frac{2}{x}\right)^{2} + \sin\left(\frac{2}{x}\right)^{2} + 2 \, \cos\left(\frac{2}{x}\right) + 1\right)} x}"," ",0,"(cos(2/x)^2 - 2*x*sin(2/x) + sin(2/x)^2 + 2*cos(2/x) + 1)/((cos(2/x)^2 + sin(2/x)^2 + 2*cos(2/x) + 1)*x)","B",0
772,1,9,0,0.327398," ","integrate(x*tan(x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\sec\left(x^{2} + 1\right)\right)"," ",0,"1/2*log(sec(x^2 + 1))","A",0
773,1,10,0,0.322057," ","integrate(sin(pi*(1+2*x)),x, algorithm=""maxima"")","\frac{\cos\left(2 \, \pi x\right)}{2 \, \pi}"," ",0,"1/2*cos(2*pi*x)/pi","A",0
774,1,18,0,0.325573," ","integrate((cot(x)+csc(x)^2)/(1-cos(x)^2),x, algorithm=""maxima"")","-\frac{6 \, \tan\left(x\right)^{2} + 3 \, \tan\left(x\right) + 2}{6 \, \tan\left(x\right)^{3}}"," ",0,"-1/6*(6*tan(x)^2 + 3*tan(x) + 2)/tan(x)^3","A",0
775,1,15,0,0.331469," ","integrate(x^2*cos(4*x^3)*cos(5*x^3),x, algorithm=""maxima"")","\frac{1}{54} \, \sin\left(9 \, x^{3}\right) + \frac{1}{6} \, \sin\left(x^{3}\right)"," ",0,"1/54*sin(9*x^3) + 1/6*sin(x^3)","A",0
776,1,32,0,0.327401," ","integrate(x^14*sin(x^3),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(x^{12} - 12 \, x^{6} + 24\right)} \cos\left(x^{3}\right) + \frac{4}{3} \, {\left(x^{9} - 6 \, x^{3}\right)} \sin\left(x^{3}\right)"," ",0,"-1/3*(x^12 - 12*x^6 + 24)*cos(x^3) + 4/3*(x^9 - 6*x^3)*sin(x^3)","A",0
777,1,25,0,0.333925," ","integrate(x^2*sin(2*x^3)/exp(3*x^3),x, algorithm=""maxima"")","-\frac{1}{39} \, {\left(2 \, \cos\left(2 \, x^{3}\right) + 3 \, \sin\left(2 \, x^{3}\right)\right)} e^{\left(-3 \, x^{3}\right)}"," ",0,"-1/39*(2*cos(2*x^3) + 3*sin(2*x^3))*e^(-3*x^3)","A",0
778,1,4,0,0.325010," ","integrate(2*x*cos(x^2),x, algorithm=""maxima"")","\sin\left(x^{2}\right)"," ",0,"sin(x^2)","A",0
779,1,6,0,0.321675," ","integrate(3*x^2*cos(x^3+7),x, algorithm=""maxima"")","\sin\left(x^{3} + 7\right)"," ",0,"sin(x^3 + 7)","A",0
780,1,7,0,0.426821," ","integrate(1/(x^2+1)+sin(x),x, algorithm=""maxima"")","\arctan\left(x\right) - \cos\left(x\right)"," ",0,"arctan(x) - cos(x)","A",0
781,1,8,0,0.324160," ","integrate(x*sin(x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, \cos\left(x^{2} + 1\right)"," ",0,"-1/2*cos(x^2 + 1)","A",0
782,1,8,0,0.316003," ","integrate(x*cos(x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, \sin\left(x^{2} + 1\right)"," ",0,"1/2*sin(x^2 + 1)","A",0
783,1,8,0,0.324661," ","integrate(1+x^2*cos(x^3),x, algorithm=""maxima"")","x + \frac{1}{3} \, \sin\left(x^{3}\right)"," ",0,"x + 1/3*sin(x^3)","A",0
784,1,8,0,0.323554," ","integrate(x^2*sin(x^3+1),x, algorithm=""maxima"")","-\frac{1}{3} \, \cos\left(x^{3} + 1\right)"," ",0,"-1/3*cos(x^3 + 1)","A",0
785,1,6,0,0.322611," ","integrate(12*x^2*cos(x^3),x, algorithm=""maxima"")","4 \, \sin\left(x^{3}\right)"," ",0,"4*sin(x^3)","A",0
786,1,14,0,0.323995," ","integrate((1+x)*sin(1+x),x, algorithm=""maxima"")","-{\left(x + 1\right)} \cos\left(x + 1\right) + \sin\left(x + 1\right)"," ",0,"-(x + 1)*cos(x + 1) + sin(x + 1)","A",0
787,1,16,0,0.326653," ","integrate(x^5*cos(x^3),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \sin\left(x^{3}\right) + \frac{1}{3} \, \cos\left(x^{3}\right)"," ",0,"1/3*x^3*sin(x^3) + 1/3*cos(x^3)","A",0
788,1,15,0,0.327354," ","integrate(cos(x)/exp(3*x),x, algorithm=""maxima"")","-\frac{1}{10} \, {\left(3 \, \cos\left(x\right) - \sin\left(x\right)\right)} e^{\left(-3 \, x\right)}"," ",0,"-1/10*(3*cos(x) - sin(x))*e^(-3*x)","A",0
789,1,16,0,0.327405," ","integrate(x^3*sin(x^2),x, algorithm=""maxima"")","-\frac{1}{2} \, x^{2} \cos\left(x^{2}\right) + \frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"-1/2*x^2*cos(x^2) + 1/2*sin(x^2)","A",0
790,1,16,0,0.327318," ","integrate(x^3*cos(x^2),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \sin\left(x^{2}\right) + \frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"1/2*x^2*sin(x^2) + 1/2*cos(x^2)","A",0
791,1,7,0,0.328338," ","integrate(cos(x)*cos(2*sin(x)),x, algorithm=""maxima"")","\frac{1}{2} \, \sin\left(2 \, \sin\left(x\right)\right)"," ",0,"1/2*sin(2*sin(x))","A",0
792,1,9,0,0.325227," ","integrate(cos(x)*sin(x)/(1+cos(x)^2),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + 1\right)"," ",0,"-1/2*log(cos(x)^2 + 1)","A",0
793,1,8,0,0.326092," ","integrate((1+cos(x))*(x+sin(x))^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(x + \sin\left(x\right)\right)}^{4}"," ",0,"1/4*(x + sin(x))^4","A",0
794,1,13,0,0.329887," ","integrate((1+cos(x))*csc(x)^2,x, algorithm=""maxima"")","-\frac{1}{\sin\left(x\right)} - \frac{1}{\tan\left(x\right)}"," ",0,"-1/sin(x) - 1/tan(x)","A",0
795,1,7,0,0.313660," ","integrate(sin(x)*tan(x)^2,x, algorithm=""maxima"")","\frac{1}{\cos\left(x\right)} + \cos\left(x\right)"," ",0,"1/cos(x) + cos(x)","A",0
796,1,88,0,0.770749," ","integrate(exp(sin(x))*sec(x)^2*(x*cos(x)^3-sin(x)),x, algorithm=""maxima"")","\frac{x \cos\left(2 \, x\right)^{2} e^{\sin\left(x\right)} + x e^{\sin\left(x\right)} \sin\left(2 \, x\right)^{2} - 2 \, e^{\sin\left(x\right)} \sin\left(2 \, x\right) \sin\left(x\right) + 2 \, {\left(x e^{\sin\left(x\right)} - \cos\left(x\right) e^{\sin\left(x\right)}\right)} \cos\left(2 \, x\right) + x e^{\sin\left(x\right)} - 2 \, \cos\left(x\right) e^{\sin\left(x\right)}}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}"," ",0,"(x*cos(2*x)^2*e^sin(x) + x*e^sin(x)*sin(2*x)^2 - 2*e^sin(x)*sin(2*x)*sin(x) + 2*(x*e^sin(x) - cos(x)*e^sin(x))*cos(2*x) + x*e^sin(x) - 2*cos(x)*e^sin(x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
797,1,104,0,0.317584," ","integrate(x*csc(x)^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 4 \, x \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/2*((cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 4*x*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 - 2*cos(2*x) + 1)","B",0
798,1,14,0,0.306198," ","integrate(cos(x)*sin(1/6*pi+x),x, algorithm=""maxima"")","\frac{1}{4} \, x - \frac{1}{4} \, \cos\left(\frac{1}{6} \, \pi + 2 \, x\right)"," ",0,"1/4*x - 1/4*cos(1/6*pi + 2*x)","A",0
799,1,15,0,0.315444," ","integrate(x*sin(x^2)^3,x, algorithm=""maxima"")","\frac{1}{24} \, \cos\left(3 \, x^{2}\right) - \frac{3}{8} \, \cos\left(x^{2}\right)"," ",0,"1/24*cos(3*x^2) - 3/8*cos(x^2)","A",0
800,1,16,0,0.304718," ","integrate(sin(x)^2*tan(x),x, algorithm=""maxima"")","-\frac{1}{2} \, \sin\left(x\right)^{2} - \frac{1}{2} \, \log\left(\sin\left(x\right)^{2} - 1\right)"," ",0,"-1/2*sin(x)^2 - 1/2*log(sin(x)^2 - 1)","A",0
801,1,20,0,0.317519," ","integrate(cos(x)^2*cot(x)^3,x, algorithm=""maxima"")","\frac{1}{2} \, \sin\left(x\right)^{2} - \frac{1}{2 \, \sin\left(x\right)^{2}} - \log\left(\sin\left(x\right)^{2}\right)"," ",0,"1/2*sin(x)^2 - 1/2/sin(x)^2 - log(sin(x)^2)","A",0
802,1,5,0,0.314448," ","integrate(sec(x)*(1-sin(x)),x, algorithm=""maxima"")","\log\left(\sin\left(x\right) + 1\right)"," ",0,"log(sin(x) + 1)","A",0
803,1,5,0,0.313914," ","integrate((1+cos(x))*csc(x),x, algorithm=""maxima"")","\log\left(\cos\left(x\right) - 1\right)"," ",0,"log(cos(x) - 1)","A",0
804,1,11,0,0.308944," ","integrate(cos(x)^2*(1-tan(x)^2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)}{\tan\left(x\right)^{2} + 1}"," ",0,"tan(x)/(tan(x)^2 + 1)","B",0
805,1,69,0,0.421586," ","integrate(csc(2*x)*(cos(x)+sin(x)),x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)"," ",0,"-1/4*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/4*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 1/4*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - 1/4*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1)","B",0
806,1,11,0,0.307482," ","integrate(cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)^2),x, algorithm=""maxima"")","\log\left(\sin\left(x\right)^{2} - 3 \, \sin\left(x\right) + 2\right)"," ",0,"log(sin(x)^2 - 3*sin(x) + 2)","A",0
807,1,17,0,0.427775," ","integrate(cos(x)^2*sin(x)/(5+cos(x)^2),x, algorithm=""maxima"")","\sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} \cos\left(x\right)\right) - \cos\left(x\right)"," ",0,"sqrt(5)*arctan(1/5*sqrt(5)*cos(x)) - cos(x)","A",0
808,1,11,0,0.312527," ","integrate(cos(x)/(sin(x)+sin(x)^2),x, algorithm=""maxima"")","-\log\left(\sin\left(x\right) + 1\right) + \log\left(\sin\left(x\right)\right)"," ",0,"-log(sin(x) + 1) + log(sin(x))","A",0
809,1,34,0,0.424756," ","integrate(cos(x)/(sin(x)+sin(x)^(2^(1/2))),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(\sin\left(x\right)\right)}{\sqrt{2} - 1} - \frac{\log\left(\sin\left(x\right)^{\left(\sqrt{2}\right)} + \sin\left(x\right)\right)}{\sqrt{2} - 1}"," ",0,"sqrt(2)*log(sin(x))/(sqrt(2) - 1) - log(sin(x)^sqrt(2) + sin(x))/(sqrt(2) - 1)","A",0
810,1,220,0,0.329464," ","integrate(1/(2*sin(x)+sin(2*x)),x, algorithm=""maxima"")","\frac{4 \, \cos\left(2 \, x\right) \cos\left(x\right) + 8 \, \cos\left(x\right)^{2} - {\left(2 \, {\left(2 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(2 \, {\left(2 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + 8 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right)}{8 \, {\left(2 \, {\left(2 \, \cos\left(x\right) + 1\right)} \cos\left(2 \, x\right) + \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(x\right)^{2} + \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \sin\left(x\right)^{2} + 4 \, \cos\left(x\right) + 1\right)}}"," ",0,"1/8*(4*cos(2*x)*cos(x) + 8*cos(x)^2 - (2*(2*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 4*cos(x)^2 + sin(2*x)^2 + 4*sin(2*x)*sin(x) + 4*sin(x)^2 + 4*cos(x) + 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (2*(2*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 4*cos(x)^2 + sin(2*x)^2 + 4*sin(2*x)*sin(x) + 4*sin(x)^2 + 4*cos(x) + 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*sin(2*x)*sin(x) + 8*sin(x)^2 + 4*cos(x))/(2*(2*cos(x) + 1)*cos(2*x) + cos(2*x)^2 + 4*cos(x)^2 + sin(2*x)^2 + 4*sin(2*x)*sin(x) + 4*sin(x)^2 + 4*cos(x) + 1)","B",0
811,1,38,0,0.330441," ","integrate((x^2+4*x-3)*sin(2*x),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - 2 \, x \cos\left(2 \, x\right) + \frac{1}{2} \, x \sin\left(2 \, x\right) + \frac{3}{2} \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right)"," ",0,"-1/4*(2*x^2 - 1)*cos(2*x) - 2*x*cos(2*x) + 1/2*x*sin(2*x) + 3/2*cos(2*x) + sin(2*x)","A",0
812,1,19,0,0.325754," ","integrate(cos(4*x)/exp(3*x),x, algorithm=""maxima"")","-\frac{1}{25} \, {\left(3 \, \cos\left(4 \, x\right) - 4 \, \sin\left(4 \, x\right)\right)} e^{\left(-3 \, x\right)}"," ",0,"-1/25*(3*cos(4*x) - 4*sin(4*x))*e^(-3*x)","A",0
813,1,17,0,0.322690," ","integrate(cos(x)*sin(x)/(1+sin(x))^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, {\left(\sin\left(x\right) + 1\right)}^{\frac{3}{2}} - 2 \, \sqrt{\sin\left(x\right) + 1}"," ",0,"2/3*(sin(x) + 1)^(3/2) - 2*sqrt(sin(x) + 1)","A",0
814,1,24,0,0.327167," ","integrate(x+60*cos(x)^5*sin(x)^4,x, algorithm=""maxima"")","\frac{20}{3} \, \sin\left(x\right)^{9} - \frac{120}{7} \, \sin\left(x\right)^{7} + 12 \, \sin\left(x\right)^{5} + \frac{1}{2} \, x^{2}"," ",0,"20/3*sin(x)^9 - 120/7*sin(x)^7 + 12*sin(x)^5 + 1/2*x^2","A",0
815,1,6,0,0.330618," ","integrate(cos(x)*(sec(x)+tan(x)),x, algorithm=""maxima"")","x - \cos\left(x\right)"," ",0,"x - cos(x)","A",0
816,1,7,0,0.327739," ","integrate(cos(x)*(sec(x)^3+tan(x)),x, algorithm=""maxima"")","-\cos\left(x\right) + \tan\left(x\right)"," ",0,"-cos(x) + tan(x)","A",0
817,1,13,0,0.320593," ","integrate(-1/2*cot(x)*csc(x)+1/2*csc(x)^2,x, algorithm=""maxima"")","\frac{1}{2 \, \sin\left(x\right)} - \frac{1}{2 \, \tan\left(x\right)}"," ",0,"1/2/sin(x) - 1/2/tan(x)","A",0
818,1,11,0,0.326186," ","integrate(-csc(x)^2+sin(2*x),x, algorithm=""maxima"")","\frac{1}{\tan\left(x\right)} - \frac{1}{2} \, \cos\left(2 \, x\right)"," ",0,"1/tan(x) - 1/2*cos(2*x)","A",0
819,1,10,0,0.320130," ","integrate(2*cot(2*x)-3*sin(3*x),x, algorithm=""maxima"")","\cos\left(3 \, x\right) + \log\left(\sin\left(2 \, x\right)\right)"," ",0,"cos(3*x) + log(sin(2*x))","A",0
820,1,8,0,0.321492," ","integrate(x*sin(2*x^2),x, algorithm=""maxima"")","-\frac{1}{4} \, \cos\left(2 \, x^{2}\right)"," ",0,"-1/4*cos(2*x^2)","A",0
821,1,12,0,0.326833," ","integrate(cos(-1+x)*sin(-1+x)*(1+sin(-1+x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\sin\left(x - 1\right)^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/3*(sin(x - 1)^2 + 1)^(3/2)","A",0
822,1,8,0,0.326056," ","integrate(cos(1/x)*sin(1/x)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, \cos\left(\frac{1}{x}\right)^{2}"," ",0,"1/2*cos(1/x)^2","A",0
823,1,10,0,0.327666," ","integrate(cos(1/2+3/2*x)*sin(1/2+3/2*x)^3,x, algorithm=""maxima"")","\frac{1}{6} \, \sin\left(\frac{3}{2} \, x + \frac{1}{2}\right)^{4}"," ",0,"1/6*sin(3/2*x + 1/2)^4","A",0
824,1,7,0,0.326170," ","integrate(4*x*tan(x^2),x, algorithm=""maxima"")","2 \, \log\left(\sec\left(x^{2}\right)\right)"," ",0,"2*log(sec(x^2))","A",0
825,1,16,0,0.324254," ","integrate(x*sec(x^2-5),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\sec\left(x^{2} - 5\right) + \tan\left(x^{2} - 5\right)\right)"," ",0,"1/2*log(sec(x^2 - 5) + tan(x^2 - 5))","A",0
826,1,10,0,0.326313," ","integrate(csc(1/x)/x^2,x, algorithm=""maxima"")","\log\left(\cot\left(\frac{1}{x}\right) + \csc\left(\frac{1}{x}\right)\right)"," ",0,"log(cot(1/x) + csc(1/x))","A",0
827,1,15,0,0.327172," ","integrate((csc(x)-sec(x))*(cos(x)+sin(x)),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(-\sin\left(x\right)^{2} + 1\right) + \log\left(\sin\left(x\right)\right)"," ",0,"1/2*log(-sin(x)^2 + 1) + log(sin(x))","B",0
828,1,4,0,0.324805," ","integrate(-cos(3*x)*sin(2*x)+cos(2*x)*sin(3*x),x, algorithm=""maxima"")","-\cos\left(x\right)"," ",0,"-cos(x)","A",0
829,1,74,0,0.436236," ","integrate(4*x*sec(2*x)^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)} \log\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right) + 8 \, x \sin\left(4 \, x\right)}{2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}}"," ",0,"1/2*((cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*log(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1) + 8*x*sin(4*x))/(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)","B",0
830,1,20,0,0.430867," ","integrate(4*sin(x)^2*tan(x)^2,x, algorithm=""maxima"")","-6 \, x + \frac{2 \, \tan\left(x\right)}{\tan\left(x\right)^{2} + 1} + 4 \, \tan\left(x\right)"," ",0,"-6*x + 2*tan(x)/(tan(x)^2 + 1) + 4*tan(x)","A",0
831,1,35,0,0.428304," ","integrate(cos(x)^4*cot(x)^2,x, algorithm=""maxima"")","-\frac{15}{8} \, x - \frac{15 \, \tan\left(x\right)^{4} + 25 \, \tan\left(x\right)^{2} + 8}{8 \, {\left(\tan\left(x\right)^{5} + 2 \, \tan\left(x\right)^{3} + \tan\left(x\right)\right)}}"," ",0,"-15/8*x - 1/8*(15*tan(x)^4 + 25*tan(x)^2 + 8)/(tan(x)^5 + 2*tan(x)^3 + tan(x))","A",0
832,1,10,0,0.330158," ","integrate(16*cos(x)^2*sin(x)^2,x, algorithm=""maxima"")","2 \, x - \frac{1}{2} \, \sin\left(4 \, x\right)"," ",0,"2*x - 1/2*sin(4*x)","A",0
833,1,18,0,0.325645," ","integrate(8*cos(x)^2*sin(x)^4,x, algorithm=""maxima"")","-\frac{1}{6} \, \sin\left(2 \, x\right)^{3} + \frac{1}{2} \, x - \frac{1}{8} \, \sin\left(4 \, x\right)"," ",0,"-1/6*sin(2*x)^3 + 1/2*x - 1/8*sin(4*x)","A",0
834,1,13,0,0.323500," ","integrate(35*cos(x)^3*sin(x)^4,x, algorithm=""maxima"")","-5 \, \sin\left(x\right)^{7} + 7 \, \sin\left(x\right)^{5}"," ",0,"-5*sin(x)^7 + 7*sin(x)^5","A",0
835,1,16,0,0.325732," ","integrate(4*cos(x)^4*sin(x)^4,x, algorithm=""maxima"")","\frac{3}{32} \, x + \frac{1}{256} \, \sin\left(8 \, x\right) - \frac{1}{32} \, \sin\left(4 \, x\right)"," ",0,"3/32*x + 1/256*sin(8*x) - 1/32*sin(4*x)","A",0
836,1,20,0,0.322539," ","integrate(cos(x)/(-sin(x)+sin(x)^3),x, algorithm=""maxima"")","\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\sin\left(x\right) - 1\right) - \log\left(\sin\left(x\right)\right)"," ",0,"1/2*log(sin(x) + 1) + 1/2*log(sin(x) - 1) - log(sin(x))","B",0
837,1,13,0,0.324317," ","integrate(-1+2*cos(x)^2+cos(x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2} \, \sin\left(2 \, x\right)"," ",0,"-1/2*cos(x)^2 + 1/2*sin(2*x)","A",0
838,1,1,0,0.332159," ","integrate(cos(x)^2+sin(x)^2,x, algorithm=""maxima"")","x"," ",0,"x","A",0
839,1,6,0,0.322523," ","integrate(-cos(x)^2+sin(x)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, \sin\left(2 \, x\right)"," ",0,"-1/2*sin(2*x)","A",0
840,1,9,0,0.310475," ","integrate(2^sin(x)*cos(x),x, algorithm=""maxima"")","\frac{2^{\sin\left(x\right)}}{\log\left(2\right)}"," ",0,"2^sin(x)/log(2)","A",0
841,1,35,0,0.316449," ","integrate(tan(x)^3+tan(x)^5,x, algorithm=""maxima"")","\frac{4 \, \sin\left(x\right)^{2} - 3}{4 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} - \frac{1}{2 \, {\left(\sin\left(x\right)^{2} - 1\right)}}"," ",0,"1/4*(4*sin(x)^2 - 3)/(sin(x)^4 - 2*sin(x)^2 + 1) - 1/2/(sin(x)^2 - 1)","B",0
842,1,51,0,0.482986," ","integrate(x*sec(x)*(2+x*tan(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(x^{2} \cos\left(2 \, x\right) \cos\left(x\right) + x^{2} \sin\left(2 \, x\right) \sin\left(x\right) + x^{2} \cos\left(x\right)\right)}}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}"," ",0,"2*(x^2*cos(2*x)*cos(x) + x^2*sin(2*x)*sin(x) + x^2*cos(x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
843,1,8,0,0.313832," ","integrate(cot(x^(1/2))*csc(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","-\frac{2}{\sin\left(\sqrt{x}\right)}"," ",0,"-2/sin(sqrt(x))","A",0
844,1,8,0,0.308642," ","integrate(cos(x^(1/2))*sin(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","-\cos\left(\sqrt{x}\right)^{2}"," ",0,"-cos(sqrt(x))^2","A",0
845,1,8,0,0.310503," ","integrate(sec(x^(1/2))*tan(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","\frac{2}{\cos\left(\sqrt{x}\right)}"," ",0,"2/cos(sqrt(x))","A",0
846,-2,0,0,0.000000," ","integrate(sin(x)^2/(a+b*sin(2*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
847,-2,0,0,0.000000," ","integrate(cos(x)^2/(a+b*sin(2*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
848,-2,0,0,0.000000," ","integrate(sin(x)^2/(a+b*cos(2*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
849,-2,0,0,0.000000," ","integrate(cos(x)^2/(a+b*cos(2*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
850,1,76,0,0.425539," ","integrate(tan(d*x+c)/(a*sin(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","\frac{\frac{\left(-1\right)^{2 \, a \sin\left(d x + c\right)} \log\left(-\frac{a \sin\left(d x + c\right)}{\sin\left(d x + c\right) + 1}\right)}{\sqrt{a}} + \frac{\left(-1\right)^{2 \, a \sin\left(d x + c\right)} \log\left(-\frac{a \sin\left(d x + c\right)}{\sin\left(d x + c\right) - 1}\right)}{\sqrt{a}}}{2 \, d}"," ",0,"1/2*((-1)^(2*a*sin(d*x + c))*log(-a*sin(d*x + c)/(sin(d*x + c) + 1))/sqrt(a) + (-1)^(2*a*sin(d*x + c))*log(-a*sin(d*x + c)/(sin(d*x + c) - 1))/sqrt(a))/d","B",0
851,1,51,0,0.321724," ","integrate(cot(d*x+c)/(a*cos(d*x+c)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{2 \, \sqrt{-a \sin\left(d x + c\right)^{2} + a} \sqrt{a}}{{\left| \sin\left(d x + c\right) \right|}} + \frac{2 \, a}{{\left| \sin\left(d x + c\right) \right|}}\right)}{\sqrt{a} d}"," ",0,"-log(2*sqrt(-a*sin(d*x + c)^2 + a)*sqrt(a)/abs(sin(d*x + c)) + 2*a/abs(sin(d*x + c)))/(sqrt(a)*d)","B",0
852,1,6,0,0.309585," ","integrate(x*cos(x^2)/sin(x^2)^(1/2),x, algorithm=""maxima"")","\sqrt{\sin\left(x^{2}\right)}"," ",0,"sqrt(sin(x^2))","A",0
853,1,41,0,0.424770," ","integrate(cos(x)/(1-cos(2*x))^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{4} \, \sqrt{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"1/4*sqrt(2)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/4*sqrt(2)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
854,1,12,0,0.301656," ","integrate(cos(log(x))^2*sin(log(x))^2/x,x, algorithm=""maxima"")","\frac{1}{8} \, \log\left(x\right) - \frac{1}{32} \, \sin\left(4 \, \log\left(x\right)\right)"," ",0,"1/8*log(x) - 1/32*sin(4*log(x))","A",0
855,1,103,0,0.411367," ","integrate(sin(x)^3/(cos(x)^3+sin(x)^3),x, algorithm=""maxima"")","\arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) + \frac{1}{3} \, \log\left(-\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{\sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 1\right) - \frac{1}{6} \, \log\left(-\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right) - \frac{1}{2} \, \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"arctan(sin(x)/(cos(x) + 1)) + 1/3*log(-2*sin(x)/(cos(x) + 1) + 2*sin(x)^2/(cos(x) + 1)^2 + 2*sin(x)^3/(cos(x) + 1)^3 + sin(x)^4/(cos(x) + 1)^4 + 1) - 1/6*log(-2*sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 - 1) - 1/2*log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
856,1,103,0,0.419603," ","integrate(cos(x)^3/(cos(x)^3+sin(x)^3),x, algorithm=""maxima"")","\arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right) - \frac{1}{3} \, \log\left(-\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{\sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 1\right) + \frac{1}{6} \, \log\left(-\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right) + \frac{1}{2} \, \log\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)"," ",0,"arctan(sin(x)/(cos(x) + 1)) - 1/3*log(-2*sin(x)/(cos(x) + 1) + 2*sin(x)^2/(cos(x) + 1)^2 + 2*sin(x)^3/(cos(x) + 1)^3 + sin(x)^4/(cos(x) + 1)^4 + 1) + 1/6*log(-2*sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 - 1) + 1/2*log(sin(x)^2/(cos(x) + 1)^2 + 1)","B",0
857,1,30,0,0.313854," ","integrate(sec(x)/(-5+cos(x)^2+4*sin(x)),x, algorithm=""maxima"")","-\frac{1}{3 \, {\left(\sin\left(x\right) - 2\right)}} - \frac{1}{18} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\sin\left(x\right) - 1\right) - \frac{4}{9} \, \log\left(\sin\left(x\right) - 2\right)"," ",0,"-1/3/(sin(x) - 2) - 1/18*log(sin(x) + 1) + 1/2*log(sin(x) - 1) - 4/9*log(sin(x) - 2)","A",0
858,1,145,0,0.466592," ","integrate(1/cos(x)^(3/2)/(3*cos(x)+sin(x))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{6 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{2 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 3\right)} {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}^{2}}{\sqrt{\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 3} {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(-\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}^{\frac{3}{2}} {\left(\frac{2 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 1\right)}}"," ",0,"2*(2*sin(x)/(cos(x) + 1) - 6*sin(x)^2/(cos(x) + 1)^2 - 2*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^4/(cos(x) + 1)^4 + 3)*(sin(x)^2/(cos(x) + 1)^2 + 1)^2/(sqrt(2*sin(x)/(cos(x) + 1) - 3*sin(x)^2/(cos(x) + 1)^2 + 3)*(sin(x)/(cos(x) + 1) + 1)^(3/2)*(-sin(x)/(cos(x) + 1) + 1)^(3/2)*(2*sin(x)^2/(cos(x) + 1)^2 + sin(x)^4/(cos(x) + 1)^4 + 1))","B",0
859,1,518,0,0.763954," ","integrate(csc(x)*(cos(x)+sin(x))^(1/2)/cos(x)^(3/2),x, algorithm=""maxima"")","\frac{4 \, {\left({\left(2 \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)^{3} + {\left(2 \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right) \sin\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)^{2} - {\left(\cos\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right) + 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)^{3} - {\left(\cos\left(2 \, x\right) - \sin\left(2 \, x\right) - 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right) - {\left({\left(\cos\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right) + 1\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)^{2} + \cos\left(2 \, x\right) + \sin\left(2 \, x\right) - 1\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)\right)}}{{\left(4 \, {\left(\cos\left(2 \, x\right) - \sin\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 2 \, \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(\cos\left(2 \, x\right) + \sin\left(2 \, x\right) + 1\right)} \sin\left(4 \, x\right) + 2 \, \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right) + 2\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(-\cos\left(4 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) + 1, \cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 1\right)\right)^{2}\right)}}"," ",0,"4*((2*cos(2*x) + sin(2*x))*cos(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))^3 + (2*cos(2*x) + sin(2*x))*cos(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))*sin(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))^2 - (cos(2*x) - 2*sin(2*x) + 1)*sin(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))^3 - (cos(2*x) - sin(2*x) - 1)*cos(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1)) - ((cos(2*x) - 2*sin(2*x) + 1)*cos(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))^2 + cos(2*x) + sin(2*x) - 1)*sin(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1)))/((4*(cos(2*x) - sin(2*x))*cos(4*x) + 2*cos(4*x)^2 + 4*cos(2*x)^2 + 4*(cos(2*x) + sin(2*x) + 1)*sin(4*x) + 2*sin(4*x)^2 + 4*sin(2*x)^2 + 4*cos(2*x) + 4*sin(2*x) + 2)^(1/4)*(cos(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))^2 + sin(1/2*arctan2(-cos(4*x) + sin(4*x) + 2*sin(2*x) + 1, cos(4*x) + 2*cos(2*x) + sin(4*x) + 1))^2))","B",0
860,1,329,0,0.495198," ","integrate((cos(x)+sin(x))/(1+sin(2*x))^(1/2),x, algorithm=""maxima"")","\frac{1}{16} \, \sqrt{2} {\left(2 \, \sqrt{2} \arctan\left(\sin\left(2 \, x\right) + 1, \cos\left(2 \, x\right)\right) + \sqrt{2} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) + 1\right) + 4 \, {\left(\cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} - 4 \, \cos\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2}\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\cos\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right), 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right)\right)\right) \sin\left(2 \, x\right) + \cos\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\cos\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right), 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right)\right)\right)\right)}\right)} + \frac{1}{16} \, \sqrt{2} {\left(2 \, \sqrt{2} \arctan\left(\sin\left(2 \, x\right) + 1, \cos\left(2 \, x\right)\right) - \sqrt{2} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) + 1\right) - 4 \, {\left(\cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) \sin\left(4 \, x\right) + \sin\left(4 \, x\right)^{2} - 4 \, \cos\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2}\right)}^{\frac{1}{4}} {\left(\cos\left(2 \, x\right) \cos\left(\frac{1}{2} \, \arctan\left(\cos\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right), 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right)\right)\right) - \sin\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\cos\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right), 2 \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right)\right)\right)\right)}\right)}"," ",0,"1/16*sqrt(2)*(2*sqrt(2)*arctan2(sin(2*x) + 1, cos(2*x)) + sqrt(2)*log(cos(2*x)^2 + sin(2*x)^2 + 2*sin(2*x) + 1) + 4*(cos(4*x)^2 + 4*cos(2*x)^2 + 4*cos(2*x)*sin(4*x) + sin(4*x)^2 - 4*cos(4*x)*sin(2*x) + 4*sin(2*x)^2)^(1/4)*(cos(1/2*arctan2(cos(4*x) - 2*sin(2*x), 2*cos(2*x) + sin(4*x)))*sin(2*x) + cos(2*x)*sin(1/2*arctan2(cos(4*x) - 2*sin(2*x), 2*cos(2*x) + sin(4*x))))) + 1/16*sqrt(2)*(2*sqrt(2)*arctan2(sin(2*x) + 1, cos(2*x)) - sqrt(2)*log(cos(2*x)^2 + sin(2*x)^2 + 2*sin(2*x) + 1) - 4*(cos(4*x)^2 + 4*cos(2*x)^2 + 4*cos(2*x)*sin(4*x) + sin(4*x)^2 - 4*cos(4*x)*sin(2*x) + 4*sin(2*x)^2)^(1/4)*(cos(2*x)*cos(1/2*arctan2(cos(4*x) - 2*sin(2*x), 2*cos(2*x) + sin(4*x))) - sin(2*x)*sin(1/2*arctan2(cos(4*x) - 2*sin(2*x), 2*cos(2*x) + sin(4*x)))))","B",0
861,0,0,0,0.000000," ","integrate(sec(x)*(sec(x)+tan(x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\sec\left(x\right) + \tan\left(x\right)} \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(sec(x) + tan(x))*sec(x), x)","F",0
862,1,10,0,0.324270," ","integrate(sec(x)*(4+3*sec(x))^(1/2)*tan(x),x, algorithm=""maxima"")","\frac{2}{9} \, {\left(3 \, \sec\left(x\right) + 4\right)}^{\frac{3}{2}}"," ",0,"2/9*(3*sec(x) + 4)^(3/2)","A",0
863,1,21,0,0.333359," ","integrate(sec(x)*(1+sec(x))^(1/2)*tan(x)^3,x, algorithm=""maxima"")","\frac{2}{7} \, {\left(\frac{1}{\cos\left(x\right)} + 1\right)}^{\frac{7}{2}} - \frac{4}{5} \, {\left(\frac{1}{\cos\left(x\right)} + 1\right)}^{\frac{5}{2}}"," ",0,"2/7*(1/cos(x) + 1)^(7/2) - 4/5*(1/cos(x) + 1)^(5/2)","A",0
864,1,21,0,0.320963," ","integrate(cot(x)^3*csc(x)*(1+csc(x))^(1/2),x, algorithm=""maxima"")","-\frac{2}{7} \, {\left(\frac{1}{\sin\left(x\right)} + 1\right)}^{\frac{7}{2}} + \frac{4}{5} \, {\left(\frac{1}{\sin\left(x\right)} + 1\right)}^{\frac{5}{2}}"," ",0,"-2/7*(1/sin(x) + 1)^(7/2) + 4/5*(1/sin(x) + 1)^(5/2)","A",0
865,0,0,0,0.000000," ","integrate(csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)),x, algorithm=""maxima"")","\int {\left(x \cos\left(x\right) - 4 \, \sec\left(x\right) \tan\left(x\right)\right)} \sqrt{\csc\left(x\right)}\,{d x}"," ",0,"integrate((x*cos(x) - 4*sec(x)*tan(x))*sqrt(csc(x)), x)","F",0
866,1,136,0,0.712590," ","integrate(cot(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{3}{2} \, \sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1} \sin\left(x\right)^{2} - \sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1} + \frac{3 \, {\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{\frac{5}{2}} + 8 \, {\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{\frac{3}{2}} - 3 \, \sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1}}{48 \, {\left({\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{3} + 3 \, {\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{2} + \frac{3}{\sin\left(x\right)^{2}} - 2\right)}} - \frac{3 \, {\left({\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{\frac{3}{2}} - \sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1}\right)}}{8 \, {\left({\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{2} + \frac{2}{\sin\left(x\right)^{2}} - 1\right)}} + \frac{35}{16} \, \arctan\left(\sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1}\right)"," ",0,"-3/2*sqrt(1/sin(x)^2 - 1)*sin(x)^2 - sqrt(1/sin(x)^2 - 1) + 1/48*(3*(1/sin(x)^2 - 1)^(5/2) + 8*(1/sin(x)^2 - 1)^(3/2) - 3*sqrt(1/sin(x)^2 - 1))/((1/sin(x)^2 - 1)^3 + 3*(1/sin(x)^2 - 1)^2 + 3/sin(x)^2 - 2) - 3/8*((1/sin(x)^2 - 1)^(3/2) - sqrt(1/sin(x)^2 - 1))/((1/sin(x)^2 - 1)^2 + 2/sin(x)^2 - 1) + 35/16*arctan(sqrt(1/sin(x)^2 - 1))","B",0
867,1,86,0,0.929667," ","integrate(cos(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{7} \, {\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{\frac{7}{2}} \sin\left(x\right)^{7} + \frac{1}{5} \, {\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{\frac{5}{2}} \sin\left(x\right)^{5} + \frac{1}{3} \, {\left(\frac{1}{\sin\left(x\right)^{2}} - 1\right)}^{\frac{3}{2}} \sin\left(x\right)^{3} + \sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1} \sin\left(x\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1} \sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\sqrt{\frac{1}{\sin\left(x\right)^{2}} - 1} \sin\left(x\right) - 1\right)"," ",0,"1/7*(1/sin(x)^2 - 1)^(7/2)*sin(x)^7 + 1/5*(1/sin(x)^2 - 1)^(5/2)*sin(x)^5 + 1/3*(1/sin(x)^2 - 1)^(3/2)*sin(x)^3 + sqrt(1/sin(x)^2 - 1)*sin(x) - 1/2*log(sqrt(1/sin(x)^2 - 1)*sin(x) + 1) + 1/2*log(sqrt(1/sin(x)^2 - 1)*sin(x) - 1)","A",0
868,1,79,0,0.846657," ","integrate(x*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, x \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + 2 i \, x \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + x \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - x \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 2 i \, {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) + 2 i \, {\rm Li}_2\left(e^{\left(i \, x\right)}\right)}{2 \, \sqrt{a}}"," ",0,"-1/2*(2*I*x*arctan2(sin(x), cos(x) + 1) + 2*I*x*arctan2(sin(x), -cos(x) + 1) + x*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - x*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 2*I*dilog(-e^(I*x)) + 2*I*dilog(e^(I*x)))/sqrt(a)","A",0
869,1,107,0,0.677305," ","integrate(x^2*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, x^{2} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + 2 i \, x^{2} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + x^{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - x^{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 4 i \, x {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) + 4 i \, x {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + 4 \, {\rm Li}_{3}(-e^{\left(i \, x\right)}) - 4 \, {\rm Li}_{3}(e^{\left(i \, x\right)})}{2 \, \sqrt{a}}"," ",0,"-1/2*(2*I*x^2*arctan2(sin(x), cos(x) + 1) + 2*I*x^2*arctan2(sin(x), -cos(x) + 1) + x^2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - x^2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 4*I*x*dilog(-e^(I*x)) + 4*I*x*dilog(e^(I*x)) + 4*polylog(3, -e^(I*x)) - 4*polylog(3, e^(I*x)))/sqrt(a)","A",0
870,1,131,0,0.822325," ","integrate(x^3*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, x^{3} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + 2 i \, x^{3} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + x^{3} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - x^{3} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 6 i \, x^{2} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) + 6 i \, x^{2} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + 12 \, x {\rm Li}_{3}(-e^{\left(i \, x\right)}) - 12 \, x {\rm Li}_{3}(e^{\left(i \, x\right)}) + 12 i \, {\rm Li}_{4}(-e^{\left(i \, x\right)}) - 12 i \, {\rm Li}_{4}(e^{\left(i \, x\right)})}{2 \, \sqrt{a}}"," ",0,"-1/2*(2*I*x^3*arctan2(sin(x), cos(x) + 1) + 2*I*x^3*arctan2(sin(x), -cos(x) + 1) + x^3*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - x^3*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 6*I*x^2*dilog(-e^(I*x)) + 6*I*x^2*dilog(e^(I*x)) + 12*x*polylog(3, -e^(I*x)) - 12*x*polylog(3, e^(I*x)) + 12*I*polylog(4, -e^(I*x)) - 12*I*polylog(4, e^(I*x)))/sqrt(a)","A",0
871,1,83,0,1.921680," ","integrate(x*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{-i \, x^{2} + 2 i \, x \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 2 i \, x \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + x \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + x \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 2 i \, {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - 2 i \, {\rm Li}_2\left(e^{\left(i \, x\right)}\right)}{2 \, \sqrt{a}}"," ",0,"1/2*(-I*x^2 + 2*I*x*arctan2(sin(x), cos(x) + 1) - 2*I*x*arctan2(sin(x), -cos(x) + 1) + x*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + x*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 2*I*dilog(-e^(I*x)) - 2*I*dilog(e^(I*x)))/sqrt(a)","A",0
872,1,113,0,1.097669," ","integrate(x^2*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{-2 i \, x^{3} + 6 i \, x^{2} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 6 i \, x^{2} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + 3 \, x^{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + 3 \, x^{2} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 12 i \, x {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - 12 i \, x {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + 12 \, {\rm Li}_{3}(-e^{\left(i \, x\right)}) + 12 \, {\rm Li}_{3}(e^{\left(i \, x\right)})}{6 \, \sqrt{a}}"," ",0,"1/6*(-2*I*x^3 + 6*I*x^2*arctan2(sin(x), cos(x) + 1) - 6*I*x^2*arctan2(sin(x), -cos(x) + 1) + 3*x^2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 3*x^2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 12*I*x*dilog(-e^(I*x)) - 12*I*x*dilog(e^(I*x)) + 12*polylog(3, -e^(I*x)) + 12*polylog(3, e^(I*x)))/sqrt(a)","A",0
873,1,137,0,0.553782," ","integrate(x^3*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{-i \, x^{4} + 4 i \, x^{3} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 4 i \, x^{3} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + 2 \, x^{3} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + 2 \, x^{3} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 12 i \, x^{2} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - 12 i \, x^{2} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + 24 \, x {\rm Li}_{3}(-e^{\left(i \, x\right)}) + 24 \, x {\rm Li}_{3}(e^{\left(i \, x\right)}) + 24 i \, {\rm Li}_{4}(-e^{\left(i \, x\right)}) + 24 i \, {\rm Li}_{4}(e^{\left(i \, x\right)})}{4 \, \sqrt{a}}"," ",0,"1/4*(-I*x^4 + 4*I*x^3*arctan2(sin(x), cos(x) + 1) - 4*I*x^3*arctan2(sin(x), -cos(x) + 1) + 2*x^3*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 2*x^3*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - 12*I*x^2*dilog(-e^(I*x)) - 12*I*x^2*dilog(e^(I*x)) + 24*x*polylog(3, -e^(I*x)) + 24*x*polylog(3, e^(I*x)) + 24*I*polylog(4, -e^(I*x)) + 24*I*polylog(4, e^(I*x)))/sqrt(a)","A",0
874,1,299,0,0.703628," ","integrate(x*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(2 \, \cos\left(2 \, x\right) + 2 i \, \sin\left(2 \, x\right) + 2\right)} \arctan\left(\cos\left(x\right), \sin\left(x\right) + 1\right) + {\left(2 \, \cos\left(2 \, x\right) + 2 i \, \sin\left(2 \, x\right) + 2\right)} \arctan\left(\cos\left(x\right), -\sin\left(x\right) + 1\right) - 2 \, {\left(x \cos\left(2 \, x\right) + i \, x \sin\left(2 \, x\right) + x\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 2 \, {\left(x \cos\left(2 \, x\right) + i \, x \sin\left(2 \, x\right) + x\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - 4 i \, x \cos\left(x\right) + {\left(2 \, \cos\left(2 \, x\right) + 2 i \, \sin\left(2 \, x\right) + 2\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - {\left(2 \, \cos\left(2 \, x\right) + 2 i \, \sin\left(2 \, x\right) + 2\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) - {\left(-i \, x \cos\left(2 \, x\right) + x \sin\left(2 \, x\right) - i \, x\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(i \, x \cos\left(2 \, x\right) - x \sin\left(2 \, x\right) + i \, x\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - {\left(-i \, \cos\left(2 \, x\right) + \sin\left(2 \, x\right) - i\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) - {\left(i \, \cos\left(2 \, x\right) - \sin\left(2 \, x\right) + i\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 4 \, x \sin\left(x\right)\right)} \sqrt{a}}{-2 i \, \cos\left(2 \, x\right) + 2 \, \sin\left(2 \, x\right) - 2 i}"," ",0,"((2*cos(2*x) + 2*I*sin(2*x) + 2)*arctan2(cos(x), sin(x) + 1) + (2*cos(2*x) + 2*I*sin(2*x) + 2)*arctan2(cos(x), -sin(x) + 1) - 2*(x*cos(2*x) + I*x*sin(2*x) + x)*arctan2(sin(x), cos(x) + 1) - 2*(x*cos(2*x) + I*x*sin(2*x) + x)*arctan2(sin(x), -cos(x) + 1) - 4*I*x*cos(x) + (2*cos(2*x) + 2*I*sin(2*x) + 2)*dilog(-e^(I*x)) - (2*cos(2*x) + 2*I*sin(2*x) + 2)*dilog(e^(I*x)) - (-I*x*cos(2*x) + x*sin(2*x) - I*x)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (I*x*cos(2*x) - x*sin(2*x) + I*x)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - (-I*cos(2*x) + sin(2*x) - I)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) - (I*cos(2*x) - sin(2*x) + I)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + 4*x*sin(x))*sqrt(a)/(-2*I*cos(2*x) + 2*sin(2*x) - 2*I)","B",0
875,0,0,0,0.000000," ","integrate(x^2*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{-\frac{1}{8} \, {\left(-32 i \, x^{2} \cos\left(x\right) + 32 \, x^{2} \sin\left(x\right) - {\left(4 \, x \cos\left(x\right) - \frac{2 \, {\left(x \cos\left(2 \, x\right) + x + \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right)^{3} + 8 \, x \cos\left(x\right)^{3} + 2 \, {\left(x \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right)^{3} + 8 \, x \cos\left(x\right) \sin\left(x\right)^{2} + 4 \, {\left(3 \, x \cos\left(2 \, x\right) \cos\left(x\right) + 3 \, x \cos\left(x\right) + {\left(2 \, x \sin\left(x\right) + \cos\left(x\right)\right)} \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right)^{2} + 2 \, {\left(x \cos\left(x\right) - \sin\left(x\right)\right)} \cos\left(2 \, x\right)^{2} + 2 \, {\left(6 \, x \sin\left(2 \, x\right) \sin\left(x\right) + {\left(x \cos\left(2 \, x\right) + x + \sin\left(2 \, x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(2 \, x \cos\left(x\right) - \sin\left(x\right)\right)} \cos\left(2 \, x\right) + 4 \, x \cos\left(x\right) - 2 \, \sin\left(x\right)\right)} \sin\left(3 \, x\right)^{2} + 2 \, {\left(x \cos\left(x\right) - \sin\left(x\right)\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(x \cos\left(2 \, x\right)^{2} + 9 \, x \cos\left(x\right)^{2} + x \sin\left(2 \, x\right)^{2} + x \sin\left(x\right)^{2} + {\left(9 \, x \cos\left(x\right)^{2} + x \sin\left(x\right)^{2} + 2 \, x\right)} \cos\left(2 \, x\right) + {\left(8 \, x \cos\left(x\right) \sin\left(x\right) + \cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \sin\left(2 \, x\right) + x\right)} \cos\left(3 \, x\right) + 4 \, {\left(2 \, x \cos\left(x\right)^{3} + 2 \, x \cos\left(x\right) \sin\left(x\right)^{2} + x \cos\left(x\right) - \sin\left(x\right)\right)} \cos\left(2 \, x\right) + 2 \, x \cos\left(x\right) - {\left({\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(3 \, x\right)^{2} + {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \cos\left(2 \, x\right)^{2} + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right)^{2} + {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right)^{2} \cos\left(x\right) + \cos\left(x\right) \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \cos\left(2 \, x\right) + \cos\left(x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right)^{2} \sin\left(x\right) + \sin\left(2 \, x\right)^{2} \sin\left(x\right) + 2 \, \cos\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(x\right)^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left({\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(3 \, x\right)^{2} + {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \cos\left(2 \, x\right)^{2} + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right)^{2} + {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right)^{2} \cos\left(x\right) + \cos\left(x\right) \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \cos\left(2 \, x\right) + \cos\left(x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right)^{2} \sin\left(x\right) + \sin\left(2 \, x\right)^{2} \sin\left(x\right) + 2 \, \cos\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(x\right)^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + 2 \, {\left({\left(x \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right)^{2} + 8 \, x \cos\left(x\right) \sin\left(x\right) + 2 \, {\left({\left(x \sin\left(x\right) - \cos\left(x\right)\right)} \cos\left(2 \, x\right) + {\left(x \cos\left(x\right) + \sin\left(x\right)\right)} \sin\left(2 \, x\right) + x \sin\left(x\right) - \cos\left(x\right)\right)} \cos\left(3 \, x\right) + {\left(8 \, x \cos\left(x\right) \sin\left(x\right) - \cos\left(x\right)^{2} - \sin\left(x\right)^{2} - 2\right)} \cos\left(2 \, x\right) - \cos\left(2 \, x\right)^{2} - \cos\left(x\right)^{2} + {\left(x \cos\left(x\right)^{2} + 9 \, x \sin\left(x\right)^{2}\right)} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)^{2} - \sin\left(x\right)^{2} - 1\right)} \sin\left(3 \, x\right) + 8 \, {\left(x \cos\left(x\right)^{2} \sin\left(x\right) + x \sin\left(x\right)^{3}\right)} \sin\left(2 \, x\right) - 2 \, \sin\left(x\right)}{{\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(3 \, x\right)^{2} + {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \cos\left(2 \, x\right)^{2} + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \sin\left(3 \, x\right)^{2} + {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \sin\left(2 \, x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right)^{2} \cos\left(x\right) + \cos\left(x\right) \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) \cos\left(x\right) + \cos\left(x\right)\right)} \cos\left(3 \, x\right) + 2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \cos\left(2 \, x\right) + \cos\left(x\right)^{2} + 2 \, {\left(\cos\left(2 \, x\right)^{2} \sin\left(x\right) + \sin\left(2 \, x\right)^{2} \sin\left(x\right) + 2 \, \cos\left(2 \, x\right) \sin\left(x\right) + \sin\left(x\right)\right)} \sin\left(3 \, x\right) + \sin\left(x\right)^{2}} + \frac{4 \, x \cos\left(2 \, x\right) \cos\left(x\right) + 4 \, x \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, x \cos\left(x\right) - {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right)}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1} - 4 \, \sin\left(x\right)\right)} {\left(8 \, \cos\left(2 \, x\right) + 8 i \, \sin\left(2 \, x\right) + 8\right)} - 16 \, {\left(x^{2} \cos\left(2 \, x\right) + i \, x^{2} \sin\left(2 \, x\right) + x^{2}\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 16 \, {\left(x^{2} \cos\left(2 \, x\right) + i \, x^{2} \sin\left(2 \, x\right) + x^{2}\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) + 32 \, {\left(x \cos\left(2 \, x\right) + i \, x \sin\left(2 \, x\right) + x\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - 32 \, {\left(x \cos\left(2 \, x\right) + i \, x \sin\left(2 \, x\right) + x\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) - 8 \, {\left(-8 i \, \cos\left(2 \, x\right) + 8 \, \sin\left(2 \, x\right) - 8 i\right)} \int \frac{{\left(\cos\left(2 \, x\right) \cos\left(x\right) + \sin\left(2 \, x\right) \sin\left(x\right) + \cos\left(x\right)\right)} x}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x} - 8 \, {\left(-i \, x^{2} \cos\left(2 \, x\right) + x^{2} \sin\left(2 \, x\right) - i \, x^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - 8 \, {\left(i \, x^{2} \cos\left(2 \, x\right) - x^{2} \sin\left(2 \, x\right) + i \, x^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - 8 \, {\left(-4 i \, \cos\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right) - 4 i\right)} {\rm Li}_{3}(-e^{\left(i \, x\right)}) - 8 \, {\left(4 i \, \cos\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right) + 4 i\right)} {\rm Li}_{3}(e^{\left(i \, x\right)})\right)} \sqrt{a}}{-2 i \, \cos\left(2 \, x\right) + 2 \, \sin\left(2 \, x\right) - 2 i}"," ",0,"-(4*I*x^2*cos(x) - 4*x^2*sin(x) + 2*(x^2*cos(2*x) + I*x^2*sin(2*x) + x^2)*arctan2(sin(x), cos(x) + 1) + 2*(x^2*cos(2*x) + I*x^2*sin(2*x) + x^2)*arctan2(sin(x), -cos(x) + 1) - 4*(x*cos(2*x) + I*x*sin(2*x) + x)*dilog(-e^(I*x)) + 4*(x*cos(2*x) + I*x*sin(2*x) + x)*dilog(e^(I*x)) + (-8*I*cos(2*x) + 8*sin(2*x) - 8*I)*integrate((x*cos(2*x)*cos(x) + x*sin(2*x)*sin(x) + x*cos(x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1), x) - (8*cos(2*x) + 8*I*sin(2*x) + 8)*integrate((x*cos(x)*sin(2*x) - x*cos(2*x)*sin(x) - x*sin(x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1), x) + (-I*x^2*cos(2*x) + x^2*sin(2*x) - I*x^2)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (I*x^2*cos(2*x) - x^2*sin(2*x) + I*x^2)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + (-4*I*cos(2*x) + 4*sin(2*x) - 4*I)*polylog(3, -e^(I*x)) + (4*I*cos(2*x) - 4*sin(2*x) + 4*I)*polylog(3, e^(I*x)))*sqrt(a)/(-2*I*cos(2*x) + 2*sin(2*x) - 2*I)","F",0
876,1,568,0,0.475784," ","integrate(x^3*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(4 i \, x^{3} \cos\left(x\right) - 4 \, x^{3} \sin\left(x\right) - 6 \, {\left(x^{2} \cos\left(2 \, x\right) + i \, x^{2} \sin\left(2 \, x\right) + x^{2}\right)} \arctan\left(\cos\left(x\right), \sin\left(x\right) + 1\right) - 6 \, {\left(x^{2} \cos\left(2 \, x\right) + i \, x^{2} \sin\left(2 \, x\right) + x^{2}\right)} \arctan\left(\cos\left(x\right), -\sin\left(x\right) + 1\right) + 2 \, {\left(x^{3} \cos\left(2 \, x\right) + i \, x^{3} \sin\left(2 \, x\right) + x^{3}\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + 2 \, {\left(x^{3} \cos\left(2 \, x\right) + i \, x^{3} \sin\left(2 \, x\right) + x^{3}\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - 12 \, {\left(x \cos\left(2 \, x\right) + i \, x \sin\left(2 \, x\right) + x\right)} {\rm Li}_2\left(i \, e^{\left(i \, x\right)}\right) + 12 \, {\left(x \cos\left(2 \, x\right) + i \, x \sin\left(2 \, x\right) + x\right)} {\rm Li}_2\left(-i \, e^{\left(i \, x\right)}\right) - 6 \, {\left(x^{2} \cos\left(2 \, x\right) + i \, x^{2} \sin\left(2 \, x\right) + x^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) + 6 \, {\left(x^{2} \cos\left(2 \, x\right) + i \, x^{2} \sin\left(2 \, x\right) + x^{2}\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + {\left(-i \, x^{3} \cos\left(2 \, x\right) + x^{3} \sin\left(2 \, x\right) - i \, x^{3}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(i \, x^{3} \cos\left(2 \, x\right) - x^{3} \sin\left(2 \, x\right) + i \, x^{3}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + {\left(-3 i \, x^{2} \cos\left(2 \, x\right) + 3 \, x^{2} \sin\left(2 \, x\right) - 3 i \, x^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \sin\left(x\right) + 1\right) + {\left(3 i \, x^{2} \cos\left(2 \, x\right) - 3 \, x^{2} \sin\left(2 \, x\right) + 3 i \, x^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) + {\left(12 \, \cos\left(2 \, x\right) + 12 i \, \sin\left(2 \, x\right) + 12\right)} {\rm Li}_{4}(-e^{\left(i \, x\right)}) - {\left(12 \, \cos\left(2 \, x\right) + 12 i \, \sin\left(2 \, x\right) + 12\right)} {\rm Li}_{4}(e^{\left(i \, x\right)}) + {\left(-12 i \, \cos\left(2 \, x\right) + 12 \, \sin\left(2 \, x\right) - 12 i\right)} {\rm Li}_{3}(i \, e^{\left(i \, x\right)}) + {\left(12 i \, \cos\left(2 \, x\right) - 12 \, \sin\left(2 \, x\right) + 12 i\right)} {\rm Li}_{3}(-i \, e^{\left(i \, x\right)}) + {\left(-12 i \, x \cos\left(2 \, x\right) + 12 \, x \sin\left(2 \, x\right) - 12 i \, x\right)} {\rm Li}_{3}(-e^{\left(i \, x\right)}) + {\left(12 i \, x \cos\left(2 \, x\right) - 12 \, x \sin\left(2 \, x\right) + 12 i \, x\right)} {\rm Li}_{3}(e^{\left(i \, x\right)})\right)} \sqrt{a}}{-2 i \, \cos\left(2 \, x\right) + 2 \, \sin\left(2 \, x\right) - 2 i}"," ",0,"-(4*I*x^3*cos(x) - 4*x^3*sin(x) - 6*(x^2*cos(2*x) + I*x^2*sin(2*x) + x^2)*arctan2(cos(x), sin(x) + 1) - 6*(x^2*cos(2*x) + I*x^2*sin(2*x) + x^2)*arctan2(cos(x), -sin(x) + 1) + 2*(x^3*cos(2*x) + I*x^3*sin(2*x) + x^3)*arctan2(sin(x), cos(x) + 1) + 2*(x^3*cos(2*x) + I*x^3*sin(2*x) + x^3)*arctan2(sin(x), -cos(x) + 1) - 12*(x*cos(2*x) + I*x*sin(2*x) + x)*dilog(I*e^(I*x)) + 12*(x*cos(2*x) + I*x*sin(2*x) + x)*dilog(-I*e^(I*x)) - 6*(x^2*cos(2*x) + I*x^2*sin(2*x) + x^2)*dilog(-e^(I*x)) + 6*(x^2*cos(2*x) + I*x^2*sin(2*x) + x^2)*dilog(e^(I*x)) + (-I*x^3*cos(2*x) + x^3*sin(2*x) - I*x^3)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (I*x^3*cos(2*x) - x^3*sin(2*x) + I*x^3)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + (-3*I*x^2*cos(2*x) + 3*x^2*sin(2*x) - 3*I*x^2)*log(cos(x)^2 + sin(x)^2 + 2*sin(x) + 1) + (3*I*x^2*cos(2*x) - 3*x^2*sin(2*x) + 3*I*x^2)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) + (12*cos(2*x) + 12*I*sin(2*x) + 12)*polylog(4, -e^(I*x)) - (12*cos(2*x) + 12*I*sin(2*x) + 12)*polylog(4, e^(I*x)) + (-12*I*cos(2*x) + 12*sin(2*x) - 12*I)*polylog(3, I*e^(I*x)) + (12*I*cos(2*x) - 12*sin(2*x) + 12*I)*polylog(3, -I*e^(I*x)) + (-12*I*x*cos(2*x) + 12*x*sin(2*x) - 12*I*x)*polylog(3, -e^(I*x)) + (12*I*x*cos(2*x) - 12*x*sin(2*x) + 12*I*x)*polylog(3, e^(I*x)))*sqrt(a)/(-2*I*cos(2*x) + 2*sin(2*x) - 2*I)","B",0
877,1,432,0,0.503872," ","integrate(x*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(2 \, x \cos\left(4 \, x\right) + 4 \, x \cos\left(2 \, x\right) + 2 i \, x \sin\left(4 \, x\right) + 4 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) - {\left(2 \, x \cos\left(4 \, x\right) + 4 \, x \cos\left(2 \, x\right) + 2 i \, x \sin\left(4 \, x\right) + 4 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + {\left(2 \, x \cos\left(4 \, x\right) + 4 \, x \cos\left(2 \, x\right) + 2 i \, x \sin\left(4 \, x\right) + 4 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - 2 \, {\left(-2 i \, x - 1\right)} \cos\left(2 \, x\right) - {\left(\cos\left(4 \, x\right) + 2 \, \cos\left(2 \, x\right) + i \, \sin\left(4 \, x\right) + 2 i \, \sin\left(2 \, x\right) + 1\right)} {\rm Li}_2\left(-e^{\left(2 i \, x\right)}\right) + {\left(2 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 2 i \, \sin\left(4 \, x\right) + 4 i \, \sin\left(2 \, x\right) + 2\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) + {\left(2 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) + 2 i \, \sin\left(4 \, x\right) + 4 i \, \sin\left(2 \, x\right) + 2\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + {\left(-i \, x \cos\left(4 \, x\right) - 2 i \, x \cos\left(2 \, x\right) + x \sin\left(4 \, x\right) + 2 \, x \sin\left(2 \, x\right) - i \, x\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) + {\left(i \, x \cos\left(4 \, x\right) + 2 i \, x \cos\left(2 \, x\right) - x \sin\left(4 \, x\right) - 2 \, x \sin\left(2 \, x\right) + i \, x\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(i \, x \cos\left(4 \, x\right) + 2 i \, x \cos\left(2 \, x\right) - x \sin\left(4 \, x\right) - 2 \, x \sin\left(2 \, x\right) + i \, x\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - {\left(4 \, x - 2 i\right)} \sin\left(2 \, x\right) + 2\right)} \sqrt{a}}{-2 i \, \cos\left(4 \, x\right) - 4 i \, \cos\left(2 \, x\right) + 2 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right) - 2 i}"," ",0,"-((2*x*cos(4*x) + 4*x*cos(2*x) + 2*I*x*sin(4*x) + 4*I*x*sin(2*x) + 2*x)*arctan2(sin(2*x), cos(2*x) + 1) - (2*x*cos(4*x) + 4*x*cos(2*x) + 2*I*x*sin(4*x) + 4*I*x*sin(2*x) + 2*x)*arctan2(sin(x), cos(x) + 1) + (2*x*cos(4*x) + 4*x*cos(2*x) + 2*I*x*sin(4*x) + 4*I*x*sin(2*x) + 2*x)*arctan2(sin(x), -cos(x) + 1) - 2*(-2*I*x - 1)*cos(2*x) - (cos(4*x) + 2*cos(2*x) + I*sin(4*x) + 2*I*sin(2*x) + 1)*dilog(-e^(2*I*x)) + (2*cos(4*x) + 4*cos(2*x) + 2*I*sin(4*x) + 4*I*sin(2*x) + 2)*dilog(-e^(I*x)) + (2*cos(4*x) + 4*cos(2*x) + 2*I*sin(4*x) + 4*I*sin(2*x) + 2)*dilog(e^(I*x)) + (-I*x*cos(4*x) - 2*I*x*cos(2*x) + x*sin(4*x) + 2*x*sin(2*x) - I*x)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) + (I*x*cos(4*x) + 2*I*x*cos(2*x) - x*sin(4*x) - 2*x*sin(2*x) + I*x)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (I*x*cos(4*x) + 2*I*x*cos(2*x) - x*sin(4*x) - 2*x*sin(2*x) + I*x)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - (4*x - 2*I)*sin(2*x) + 2)*sqrt(a)/(-2*I*cos(4*x) - 4*I*cos(2*x) + 2*sin(4*x) + 4*sin(2*x) - 2*I)","B",0
878,1,653,0,0.521128," ","integrate(x^2*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(2 \, x^{2} + 2 \, {\left(x^{2} + 1\right)} \cos\left(4 \, x\right) + 4 \, {\left(x^{2} + 1\right)} \cos\left(2 \, x\right) + {\left(2 i \, x^{2} + 2 i\right)} \sin\left(4 \, x\right) + {\left(4 i \, x^{2} + 4 i\right)} \sin\left(2 \, x\right) + 2\right)} \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) - {\left(2 \, x^{2} \cos\left(4 \, x\right) + 4 \, x^{2} \cos\left(2 \, x\right) + 2 i \, x^{2} \sin\left(4 \, x\right) + 4 i \, x^{2} \sin\left(2 \, x\right) + 2 \, x^{2}\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + {\left(2 \, x^{2} \cos\left(4 \, x\right) + 4 \, x^{2} \cos\left(2 \, x\right) + 2 i \, x^{2} \sin\left(4 \, x\right) + 4 i \, x^{2} \sin\left(2 \, x\right) + 2 \, x^{2}\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - 4 \, x \cos\left(4 \, x\right) + {\left(4 i \, x^{2} - 4 \, x\right)} \cos\left(2 \, x\right) - {\left(2 \, x \cos\left(4 \, x\right) + 4 \, x \cos\left(2 \, x\right) + 2 i \, x \sin\left(4 \, x\right) + 4 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} {\rm Li}_2\left(-e^{\left(2 i \, x\right)}\right) + {\left(4 \, x \cos\left(4 \, x\right) + 8 \, x \cos\left(2 \, x\right) + 4 i \, x \sin\left(4 \, x\right) + 8 i \, x \sin\left(2 \, x\right) + 4 \, x\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) + {\left(4 \, x \cos\left(4 \, x\right) + 8 \, x \cos\left(2 \, x\right) + 4 i \, x \sin\left(4 \, x\right) + 8 i \, x \sin\left(2 \, x\right) + 4 \, x\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) + {\left(-i \, x^{2} + {\left(-i \, x^{2} - i\right)} \cos\left(4 \, x\right) + {\left(-2 i \, x^{2} - 2 i\right)} \cos\left(2 \, x\right) + {\left(x^{2} + 1\right)} \sin\left(4 \, x\right) + 2 \, {\left(x^{2} + 1\right)} \sin\left(2 \, x\right) - i\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) + {\left(i \, x^{2} \cos\left(4 \, x\right) + 2 i \, x^{2} \cos\left(2 \, x\right) - x^{2} \sin\left(4 \, x\right) - 2 \, x^{2} \sin\left(2 \, x\right) + i \, x^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + {\left(i \, x^{2} \cos\left(4 \, x\right) + 2 i \, x^{2} \cos\left(2 \, x\right) - x^{2} \sin\left(4 \, x\right) - 2 \, x^{2} \sin\left(2 \, x\right) + i \, x^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + {\left(-i \, \cos\left(4 \, x\right) - 2 i \, \cos\left(2 \, x\right) + \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right) - i\right)} {\rm Li}_{3}(-e^{\left(2 i \, x\right)}) + {\left(4 i \, \cos\left(4 \, x\right) + 8 i \, \cos\left(2 \, x\right) - 4 \, \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right) + 4 i\right)} {\rm Li}_{3}(-e^{\left(i \, x\right)}) + {\left(4 i \, \cos\left(4 \, x\right) + 8 i \, \cos\left(2 \, x\right) - 4 \, \sin\left(4 \, x\right) - 8 \, \sin\left(2 \, x\right) + 4 i\right)} {\rm Li}_{3}(e^{\left(i \, x\right)}) - 4 i \, x \sin\left(4 \, x\right) - 4 \, {\left(x^{2} + i \, x\right)} \sin\left(2 \, x\right)\right)} \sqrt{a}}{-2 i \, \cos\left(4 \, x\right) - 4 i \, \cos\left(2 \, x\right) + 2 \, \sin\left(4 \, x\right) + 4 \, \sin\left(2 \, x\right) - 2 i}"," ",0,"-((2*x^2 + 2*(x^2 + 1)*cos(4*x) + 4*(x^2 + 1)*cos(2*x) + (2*I*x^2 + 2*I)*sin(4*x) + (4*I*x^2 + 4*I)*sin(2*x) + 2)*arctan2(sin(2*x), cos(2*x) + 1) - (2*x^2*cos(4*x) + 4*x^2*cos(2*x) + 2*I*x^2*sin(4*x) + 4*I*x^2*sin(2*x) + 2*x^2)*arctan2(sin(x), cos(x) + 1) + (2*x^2*cos(4*x) + 4*x^2*cos(2*x) + 2*I*x^2*sin(4*x) + 4*I*x^2*sin(2*x) + 2*x^2)*arctan2(sin(x), -cos(x) + 1) - 4*x*cos(4*x) + (4*I*x^2 - 4*x)*cos(2*x) - (2*x*cos(4*x) + 4*x*cos(2*x) + 2*I*x*sin(4*x) + 4*I*x*sin(2*x) + 2*x)*dilog(-e^(2*I*x)) + (4*x*cos(4*x) + 8*x*cos(2*x) + 4*I*x*sin(4*x) + 8*I*x*sin(2*x) + 4*x)*dilog(-e^(I*x)) + (4*x*cos(4*x) + 8*x*cos(2*x) + 4*I*x*sin(4*x) + 8*I*x*sin(2*x) + 4*x)*dilog(e^(I*x)) + (-I*x^2 + (-I*x^2 - I)*cos(4*x) + (-2*I*x^2 - 2*I)*cos(2*x) + (x^2 + 1)*sin(4*x) + 2*(x^2 + 1)*sin(2*x) - I)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) + (I*x^2*cos(4*x) + 2*I*x^2*cos(2*x) - x^2*sin(4*x) - 2*x^2*sin(2*x) + I*x^2)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + (I*x^2*cos(4*x) + 2*I*x^2*cos(2*x) - x^2*sin(4*x) - 2*x^2*sin(2*x) + I*x^2)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + (-I*cos(4*x) - 2*I*cos(2*x) + sin(4*x) + 2*sin(2*x) - I)*polylog(3, -e^(2*I*x)) + (4*I*cos(4*x) + 8*I*cos(2*x) - 4*sin(4*x) - 8*sin(2*x) + 4*I)*polylog(3, -e^(I*x)) + (4*I*cos(4*x) + 8*I*cos(2*x) - 4*sin(4*x) - 8*sin(2*x) + 4*I)*polylog(3, e^(I*x)) - 4*I*x*sin(4*x) - 4*(x^2 + I*x)*sin(2*x))*sqrt(a)/(-2*I*cos(4*x) - 4*I*cos(2*x) + 2*sin(4*x) + 4*sin(2*x) - 2*I)","B",0
879,1,870,0,1.396894," ","integrate(x^3*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{{\left(18 \, x^{2} \cos\left(4 \, x\right) + 18 i \, x^{2} \sin\left(4 \, x\right) - {\left(8 \, x^{3} + 2 \, {\left(4 \, x^{3} + 9 \, x\right)} \cos\left(4 \, x\right) + 4 \, {\left(4 \, x^{3} + 9 \, x\right)} \cos\left(2 \, x\right) + {\left(8 i \, x^{3} + 18 i \, x\right)} \sin\left(4 \, x\right) + {\left(16 i \, x^{3} + 36 i \, x\right)} \sin\left(2 \, x\right) + 18 \, x\right)} \arctan\left(\sin\left(2 \, x\right), \cos\left(2 \, x\right) + 1\right) + {\left(6 \, x^{3} \cos\left(4 \, x\right) + 12 \, x^{3} \cos\left(2 \, x\right) + 6 i \, x^{3} \sin\left(4 \, x\right) + 12 i \, x^{3} \sin\left(2 \, x\right) + 6 \, x^{3}\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left(6 \, x^{3} \cos\left(4 \, x\right) + 12 \, x^{3} \cos\left(2 \, x\right) + 6 i \, x^{3} \sin\left(4 \, x\right) + 12 i \, x^{3} \sin\left(2 \, x\right) + 6 \, x^{3}\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - {\left(12 i \, x^{3} - 18 \, x^{2}\right)} \cos\left(2 \, x\right) + {\left(12 \, x^{2} + 3 \, {\left(4 \, x^{2} + 3\right)} \cos\left(4 \, x\right) + 6 \, {\left(4 \, x^{2} + 3\right)} \cos\left(2 \, x\right) - {\left(-12 i \, x^{2} - 9 i\right)} \sin\left(4 \, x\right) - {\left(-24 i \, x^{2} - 18 i\right)} \sin\left(2 \, x\right) + 9\right)} {\rm Li}_2\left(-e^{\left(2 i \, x\right)}\right) - {\left(18 \, x^{2} \cos\left(4 \, x\right) + 36 \, x^{2} \cos\left(2 \, x\right) + 18 i \, x^{2} \sin\left(4 \, x\right) + 36 i \, x^{2} \sin\left(2 \, x\right) + 18 \, x^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - {\left(18 \, x^{2} \cos\left(4 \, x\right) + 36 \, x^{2} \cos\left(2 \, x\right) + 18 i \, x^{2} \sin\left(4 \, x\right) + 36 i \, x^{2} \sin\left(2 \, x\right) + 18 \, x^{2}\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) - {\left(-4 i \, x^{3} + {\left(-4 i \, x^{3} - 9 i \, x\right)} \cos\left(4 \, x\right) + {\left(-8 i \, x^{3} - 18 i \, x\right)} \cos\left(2 \, x\right) + {\left(4 \, x^{3} + 9 \, x\right)} \sin\left(4 \, x\right) + 2 \, {\left(4 \, x^{3} + 9 \, x\right)} \sin\left(2 \, x\right) - 9 i \, x\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) - {\left(3 i \, x^{3} \cos\left(4 \, x\right) + 6 i \, x^{3} \cos\left(2 \, x\right) - 3 \, x^{3} \sin\left(4 \, x\right) - 6 \, x^{3} \sin\left(2 \, x\right) + 3 i \, x^{3}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(3 i \, x^{3} \cos\left(4 \, x\right) + 6 i \, x^{3} \cos\left(2 \, x\right) - 3 \, x^{3} \sin\left(4 \, x\right) - 6 \, x^{3} \sin\left(2 \, x\right) + 3 i \, x^{3}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - {\left(6 \, \cos\left(4 \, x\right) + 12 \, \cos\left(2 \, x\right) + 6 i \, \sin\left(4 \, x\right) + 12 i \, \sin\left(2 \, x\right) + 6\right)} {\rm Li}_{4}(-e^{\left(2 i \, x\right)}) + {\left(36 \, \cos\left(4 \, x\right) + 72 \, \cos\left(2 \, x\right) + 36 i \, \sin\left(4 \, x\right) + 72 i \, \sin\left(2 \, x\right) + 36\right)} {\rm Li}_{4}(-e^{\left(i \, x\right)}) + {\left(36 \, \cos\left(4 \, x\right) + 72 \, \cos\left(2 \, x\right) + 36 i \, \sin\left(4 \, x\right) + 72 i \, \sin\left(2 \, x\right) + 36\right)} {\rm Li}_{4}(e^{\left(i \, x\right)}) - {\left(-12 i \, x \cos\left(4 \, x\right) - 24 i \, x \cos\left(2 \, x\right) + 12 \, x \sin\left(4 \, x\right) + 24 \, x \sin\left(2 \, x\right) - 12 i \, x\right)} {\rm Li}_{3}(-e^{\left(2 i \, x\right)}) - {\left(36 i \, x \cos\left(4 \, x\right) + 72 i \, x \cos\left(2 \, x\right) - 36 \, x \sin\left(4 \, x\right) - 72 \, x \sin\left(2 \, x\right) + 36 i \, x\right)} {\rm Li}_{3}(-e^{\left(i \, x\right)}) - {\left(36 i \, x \cos\left(4 \, x\right) + 72 i \, x \cos\left(2 \, x\right) - 36 \, x \sin\left(4 \, x\right) - 72 \, x \sin\left(2 \, x\right) + 36 i \, x\right)} {\rm Li}_{3}(e^{\left(i \, x\right)}) + 6 \, {\left(2 \, x^{3} + 3 i \, x^{2}\right)} \sin\left(2 \, x\right)\right)} \sqrt{a}}{-6 i \, \cos\left(4 \, x\right) - 12 i \, \cos\left(2 \, x\right) + 6 \, \sin\left(4 \, x\right) + 12 \, \sin\left(2 \, x\right) - 6 i}"," ",0,"(18*x^2*cos(4*x) + 18*I*x^2*sin(4*x) - (8*x^3 + 2*(4*x^3 + 9*x)*cos(4*x) + 4*(4*x^3 + 9*x)*cos(2*x) + (8*I*x^3 + 18*I*x)*sin(4*x) + (16*I*x^3 + 36*I*x)*sin(2*x) + 18*x)*arctan2(sin(2*x), cos(2*x) + 1) + (6*x^3*cos(4*x) + 12*x^3*cos(2*x) + 6*I*x^3*sin(4*x) + 12*I*x^3*sin(2*x) + 6*x^3)*arctan2(sin(x), cos(x) + 1) - (6*x^3*cos(4*x) + 12*x^3*cos(2*x) + 6*I*x^3*sin(4*x) + 12*I*x^3*sin(2*x) + 6*x^3)*arctan2(sin(x), -cos(x) + 1) - (12*I*x^3 - 18*x^2)*cos(2*x) + (12*x^2 + 3*(4*x^2 + 3)*cos(4*x) + 6*(4*x^2 + 3)*cos(2*x) - (-12*I*x^2 - 9*I)*sin(4*x) - (-24*I*x^2 - 18*I)*sin(2*x) + 9)*dilog(-e^(2*I*x)) - (18*x^2*cos(4*x) + 36*x^2*cos(2*x) + 18*I*x^2*sin(4*x) + 36*I*x^2*sin(2*x) + 18*x^2)*dilog(-e^(I*x)) - (18*x^2*cos(4*x) + 36*x^2*cos(2*x) + 18*I*x^2*sin(4*x) + 36*I*x^2*sin(2*x) + 18*x^2)*dilog(e^(I*x)) - (-4*I*x^3 + (-4*I*x^3 - 9*I*x)*cos(4*x) + (-8*I*x^3 - 18*I*x)*cos(2*x) + (4*x^3 + 9*x)*sin(4*x) + 2*(4*x^3 + 9*x)*sin(2*x) - 9*I*x)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) - (3*I*x^3*cos(4*x) + 6*I*x^3*cos(2*x) - 3*x^3*sin(4*x) - 6*x^3*sin(2*x) + 3*I*x^3)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (3*I*x^3*cos(4*x) + 6*I*x^3*cos(2*x) - 3*x^3*sin(4*x) - 6*x^3*sin(2*x) + 3*I*x^3)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - (6*cos(4*x) + 12*cos(2*x) + 6*I*sin(4*x) + 12*I*sin(2*x) + 6)*polylog(4, -e^(2*I*x)) + (36*cos(4*x) + 72*cos(2*x) + 36*I*sin(4*x) + 72*I*sin(2*x) + 36)*polylog(4, -e^(I*x)) + (36*cos(4*x) + 72*cos(2*x) + 36*I*sin(4*x) + 72*I*sin(2*x) + 36)*polylog(4, e^(I*x)) - (-12*I*x*cos(4*x) - 24*I*x*cos(2*x) + 12*x*sin(4*x) + 24*x*sin(2*x) - 12*I*x)*polylog(3, -e^(2*I*x)) - (36*I*x*cos(4*x) + 72*I*x*cos(2*x) - 36*x*sin(4*x) - 72*x*sin(2*x) + 36*I*x)*polylog(3, -e^(I*x)) - (36*I*x*cos(4*x) + 72*I*x*cos(2*x) - 36*x*sin(4*x) - 72*x*sin(2*x) + 36*I*x)*polylog(3, e^(I*x)) + 6*(2*x^3 + 3*I*x^2)*sin(2*x))*sqrt(a)/(-6*I*cos(4*x) - 12*I*cos(2*x) + 6*sin(4*x) + 12*sin(2*x) - 6*I)","B",0
880,1,19,0,0.319378," ","integrate(sin(x)*sin(2*x)*sin(3*x),x, algorithm=""maxima"")","\frac{1}{24} \, \cos\left(6 \, x\right) - \frac{1}{16} \, \cos\left(4 \, x\right) - \frac{1}{8} \, \cos\left(2 \, x\right)"," ",0,"1/24*cos(6*x) - 1/16*cos(4*x) - 1/8*cos(2*x)","A",0
881,1,22,0,0.308344," ","integrate(cos(x)*cos(2*x)*cos(3*x),x, algorithm=""maxima"")","\frac{1}{4} \, x + \frac{1}{24} \, \sin\left(6 \, x\right) + \frac{1}{16} \, \sin\left(4 \, x\right) + \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/4*x + 1/24*sin(6*x) + 1/16*sin(4*x) + 1/8*sin(2*x)","A",0
882,1,22,0,0.316044," ","integrate(cos(x)*sin(2*x)*sin(3*x),x, algorithm=""maxima"")","\frac{1}{4} \, x - \frac{1}{24} \, \sin\left(6 \, x\right) - \frac{1}{16} \, \sin\left(4 \, x\right) + \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/4*x - 1/24*sin(6*x) - 1/16*sin(4*x) + 1/8*sin(2*x)","A",0
883,1,19,0,0.312481," ","integrate(cos(2*x)*cos(3*x)*sin(x),x, algorithm=""maxima"")","-\frac{1}{24} \, \cos\left(6 \, x\right) + \frac{1}{16} \, \cos\left(4 \, x\right) - \frac{1}{8} \, \cos\left(2 \, x\right)"," ",0,"-1/24*cos(6*x) + 1/16*cos(4*x) - 1/8*cos(2*x)","A",0
884,1,6,0,0.313061," ","integrate(x*sin(x^2),x, algorithm=""maxima"")","-\frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"-1/2*cos(x^2)","A",0
885,1,9,0,0.326983," ","integrate((-cos(x)+sin(x))*(cos(x)+sin(x))^5,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\cos\left(x\right) + \sin\left(x\right)\right)}^{6}"," ",0,"-1/6*(cos(x) + sin(x))^6","A",0
886,1,133,0,0.319893," ","integrate(2*x*sec(x)^2*tan(x),x, algorithm=""maxima"")","\frac{2 \, {\left(4 \, x \cos\left(2 \, x\right)^{2} + 4 \, x \sin\left(2 \, x\right)^{2} + {\left(2 \, x \cos\left(2 \, x\right) + \sin\left(2 \, x\right)\right)} \cos\left(4 \, x\right) + 2 \, x \cos\left(2 \, x\right) + {\left(2 \, x \sin\left(2 \, x\right) - \cos\left(2 \, x\right) - 1\right)} \sin\left(4 \, x\right) - \sin\left(2 \, x\right)\right)}}{2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1}"," ",0,"2*(4*x*cos(2*x)^2 + 4*x*sin(2*x)^2 + (2*x*cos(2*x) + sin(2*x))*cos(4*x) + 2*x*cos(2*x) + (2*x*sin(2*x) - cos(2*x) - 1)*sin(4*x) - sin(2*x))/(2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)","B",0
887,1,18,0,0.313853," ","integrate((1+cos(x)^2)/(1+cos(2*x)),x, algorithm=""maxima"")","\frac{1}{2} \, x + \frac{\sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/2*x + 1/2*sin(2*x)/(cos(2*x) + 1)","B",0
888,1,26,0,0.306437," ","integrate(sin(x)/(cos(x)^3-cos(x)^5),x, algorithm=""maxima"")","\frac{1}{2 \, \cos\left(x\right)^{2}} + \frac{1}{2} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right) - 1\right) - \log\left(\cos\left(x\right)\right)"," ",0,"1/2/cos(x)^2 + 1/2*log(cos(x) + 1) + 1/2*log(cos(x) - 1) - log(cos(x))","B",0
889,1,20,0,0.307022," ","integrate(sec(x)*(5-11*sec(x)^5)^2*tan(x),x, algorithm=""maxima"")","\frac{75 \, \cos\left(x\right)^{10} - 55 \, \cos\left(x\right)^{5} + 33}{3 \, \cos\left(x\right)^{11}}"," ",0,"1/3*(75*cos(x)^10 - 55*cos(x)^5 + 33)/cos(x)^11","A",0
890,1,49,0,0.310652," ","integrate(sin(5*x)^3*tan(5*x)^3,x, algorithm=""maxima"")","\frac{1}{15} \, \sin\left(5 \, x\right)^{3} - \frac{\sin\left(5 \, x\right)}{10 \, {\left(\sin\left(5 \, x\right)^{2} - 1\right)}} - \frac{1}{4} \, \log\left(\sin\left(5 \, x\right) + 1\right) + \frac{1}{4} \, \log\left(\sin\left(5 \, x\right) - 1\right) + \frac{2}{5} \, \sin\left(5 \, x\right)"," ",0,"1/15*sin(5*x)^3 - 1/10*sin(5*x)/(sin(5*x)^2 - 1) - 1/4*log(sin(5*x) + 1) + 1/4*log(sin(5*x) - 1) + 2/5*sin(5*x)","A",0
891,1,33,0,0.306732," ","integrate(sin(5*x)^3*tan(5*x)^4,x, algorithm=""maxima"")","\frac{1}{15} \, \cos\left(5 \, x\right)^{3} - \frac{9 \, \cos\left(5 \, x\right)^{2} - 1}{15 \, \cos\left(5 \, x\right)^{3}} - \frac{3}{5} \, \cos\left(5 \, x\right)"," ",0,"1/15*cos(5*x)^3 - 1/15*(9*cos(5*x)^2 - 1)/cos(5*x)^3 - 3/5*cos(5*x)","A",0
892,1,57,0,0.308398," ","integrate(sin(6*x)^5*tan(6*x)^3,x, algorithm=""maxima"")","\frac{1}{30} \, \sin\left(6 \, x\right)^{5} + \frac{1}{9} \, \sin\left(6 \, x\right)^{3} - \frac{\sin\left(6 \, x\right)}{12 \, {\left(\sin\left(6 \, x\right)^{2} - 1\right)}} - \frac{7}{24} \, \log\left(\sin\left(6 \, x\right) + 1\right) + \frac{7}{24} \, \log\left(\sin\left(6 \, x\right) - 1\right) + \frac{1}{2} \, \sin\left(6 \, x\right)"," ",0,"1/30*sin(6*x)^5 + 1/9*sin(6*x)^3 - 1/12*sin(6*x)/(sin(6*x)^2 - 1) - 7/24*log(sin(6*x) + 1) + 7/24*log(sin(6*x) - 1) + 1/2*sin(6*x)","A",0
893,1,31,0,0.304801," ","integrate((-1+sec(2*x)^2)^3*sin(2*x),x, algorithm=""maxima"")","\frac{3}{2 \, \cos\left(2 \, x\right)} - \frac{1}{2 \, \cos\left(2 \, x\right)^{3}} + \frac{1}{10 \, \cos\left(2 \, x\right)^{5}} + \frac{1}{2} \, \cos\left(2 \, x\right)"," ",0,"3/2/cos(2*x) - 1/2/cos(2*x)^3 + 1/10/cos(2*x)^5 + 1/2*cos(2*x)","A",0
894,1,46,0,0.310199," ","integrate(sin(x)*tan(x)^5,x, algorithm=""maxima"")","\frac{9 \, \sin\left(x\right)^{3} - 7 \, \sin\left(x\right)}{8 \, {\left(\sin\left(x\right)^{4} - 2 \, \sin\left(x\right)^{2} + 1\right)}} + \frac{15}{16} \, \log\left(\sin\left(x\right) + 1\right) - \frac{15}{16} \, \log\left(\sin\left(x\right) - 1\right) - \sin\left(x\right)"," ",0,"1/8*(9*sin(x)^3 - 7*sin(x))/(sin(x)^4 - 2*sin(x)^2 + 1) + 15/16*log(sin(x) + 1) - 15/16*log(sin(x) - 1) - sin(x)","A",0
895,1,41,0,0.305753," ","integrate(cos(2*x)^5*cot(2*x)^4,x, algorithm=""maxima"")","\frac{1}{10} \, \sin\left(2 \, x\right)^{5} - \frac{2}{3} \, \sin\left(2 \, x\right)^{3} + \frac{12 \, \sin\left(2 \, x\right)^{2} - 1}{6 \, \sin\left(2 \, x\right)^{3}} + 3 \, \sin\left(2 \, x\right)"," ",0,"1/10*sin(2*x)^5 - 2/3*sin(2*x)^3 + 1/6*(12*sin(2*x)^2 - 1)/sin(2*x)^3 + 3*sin(2*x)","A",0
896,1,73,0,0.307755," ","integrate(cos(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^5,x, algorithm=""maxima"")","\frac{1}{33} \, \sin\left(3 \, x\right)^{11} - \frac{8}{27} \, \sin\left(3 \, x\right)^{9} + \frac{4}{3} \, \sin\left(3 \, x\right)^{7} - \frac{56}{15} \, \sin\left(3 \, x\right)^{5} + \frac{70}{9} \, \sin\left(3 \, x\right)^{3} - \frac{420 \, \sin\left(3 \, x\right)^{4} - 40 \, \sin\left(3 \, x\right)^{2} + 3}{45 \, \sin\left(3 \, x\right)^{5}} - \frac{56}{3} \, \sin\left(3 \, x\right)"," ",0,"1/33*sin(3*x)^11 - 8/27*sin(3*x)^9 + 4/3*sin(3*x)^7 - 56/15*sin(3*x)^5 + 70/9*sin(3*x)^3 - 1/45*(420*sin(3*x)^4 - 40*sin(3*x)^2 + 3)/sin(3*x)^5 - 56/3*sin(3*x)","A",0
897,1,44,0,0.304097," ","integrate(cot(2*x)*(-1+csc(2*x)^2)^2*(1-sin(2*x)^2)^2,x, algorithm=""maxima"")","\frac{1}{8} \, \sin\left(2 \, x\right)^{4} - \sin\left(2 \, x\right)^{2} + \frac{8 \, \sin\left(2 \, x\right)^{2} - 1}{8 \, \sin\left(2 \, x\right)^{4}} + \frac{3}{2} \, \log\left(\sin\left(2 \, x\right)^{2}\right)"," ",0,"1/8*sin(2*x)^4 - sin(2*x)^2 + 1/8*(8*sin(2*x)^2 - 1)/sin(2*x)^4 + 3/2*log(sin(2*x)^2)","A",0
898,1,57,0,0.310891," ","integrate(cos(2*x)*(-1+csc(2*x)^2)^4*(1-sin(2*x)^2)^2,x, algorithm=""maxima"")","\frac{1}{10} \, \sin\left(2 \, x\right)^{5} - \sin\left(2 \, x\right)^{3} + \frac{700 \, \sin\left(2 \, x\right)^{6} - 175 \, \sin\left(2 \, x\right)^{4} + 42 \, \sin\left(2 \, x\right)^{2} - 5}{70 \, \sin\left(2 \, x\right)^{7}} + \frac{15}{2} \, \sin\left(2 \, x\right)"," ",0,"1/10*sin(2*x)^5 - sin(2*x)^3 + 1/70*(700*sin(2*x)^6 - 175*sin(2*x)^4 + 42*sin(2*x)^2 - 5)/sin(2*x)^7 + 15/2*sin(2*x)","A",0
899,1,52,0,0.318139," ","integrate(cot(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^2,x, algorithm=""maxima"")","-\frac{1}{12} \, \sin\left(3 \, x\right)^{4} + \frac{5}{6} \, \sin\left(3 \, x\right)^{2} - \frac{60 \, \sin\left(3 \, x\right)^{4} - 15 \, \sin\left(3 \, x\right)^{2} + 2}{36 \, \sin\left(3 \, x\right)^{6}} - \frac{5}{3} \, \log\left(\sin\left(3 \, x\right)^{2}\right)"," ",0,"-1/12*sin(3*x)^4 + 5/6*sin(3*x)^2 - 1/36*(60*sin(3*x)^4 - 15*sin(3*x)^2 + 2)/sin(3*x)^6 - 5/3*log(sin(3*x)^2)","A",0
900,1,41,0,0.325651," ","integrate((1+cot(9*x)^2)^2*(1+tan(9*x)^2)^3,x, algorithm=""maxima"")","\frac{1}{45} \, \tan\left(9 \, x\right)^{5} + \frac{4}{27} \, \tan\left(9 \, x\right)^{3} - \frac{12 \, \tan\left(9 \, x\right)^{2} + 1}{27 \, \tan\left(9 \, x\right)^{3}} + \frac{2}{3} \, \tan\left(9 \, x\right)"," ",0,"1/45*tan(9*x)^5 + 4/27*tan(9*x)^3 - 1/27*(12*tan(9*x)^2 + 1)/tan(9*x)^3 + 2/3*tan(9*x)","A",0
901,1,37,0,0.320636," ","integrate(cos(x)*(9-7*sin(x)^3)^2/(1-sin(x)^2),x, algorithm=""maxima"")","-\frac{49}{5} \, \sin\left(x\right)^{5} - \frac{49}{3} \, \sin\left(x\right)^{3} + 63 \, \sin\left(x\right)^{2} + 128 \, \log\left(\sin\left(x\right) + 1\right) - 2 \, \log\left(\sin\left(x\right) - 1\right) - 49 \, \sin\left(x\right)"," ",0,"-49/5*sin(x)^5 - 49/3*sin(x)^3 + 63*sin(x)^2 + 128*log(sin(x) + 1) - 2*log(sin(x) - 1) - 49*sin(x)","A",0
902,1,44,0,0.335436," ","integrate(cos(2*x)^4*cot(2*x)^5,x, algorithm=""maxima"")","\frac{1}{8} \, \sin\left(2 \, x\right)^{4} - \sin\left(2 \, x\right)^{2} + \frac{8 \, \sin\left(2 \, x\right)^{2} - 1}{8 \, \sin\left(2 \, x\right)^{4}} + \frac{3}{2} \, \log\left(\sin\left(2 \, x\right)^{2}\right)"," ",0,"1/8*sin(2*x)^4 - sin(2*x)^2 + 1/8*(8*sin(2*x)^2 - 1)/sin(2*x)^4 + 3/2*log(sin(2*x)^2)","A",0
903,1,91,0,1.075050," ","integrate(sec(x)*tan(x)^2/(4+3*sec(x)),x, algorithm=""maxima"")","-\frac{1}{9} \, \sqrt{7} \log\left(-\frac{\sqrt{7} - \frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}{\sqrt{7} + \frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right) - \frac{2 \, \sin\left(x\right)}{3 \, {\left(\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}} - \frac{4}{9} \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) + \frac{4}{9} \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"-1/9*sqrt(7)*log(-(sqrt(7) - sin(x)/(cos(x) + 1))/(sqrt(7) + sin(x)/(cos(x) + 1))) - 2/3*sin(x)/((sin(x)^2/(cos(x) + 1)^2 - 1)*(cos(x) + 1)) - 4/9*log(sin(x)/(cos(x) + 1) + 1) + 4/9*log(sin(x)/(cos(x) + 1) - 1)","A",0
904,1,176,0,1.316205," ","integrate(x*sec(1+x)*tan(1+x),x, algorithm=""maxima"")","\frac{4 \, {\left(x + 1\right)} \cos\left(2 \, x + 2\right) \cos\left(x + 1\right) + 4 \, {\left(x + 1\right)} \sin\left(2 \, x + 2\right) \sin\left(x + 1\right) + 4 \, {\left(x + 1\right)} \cos\left(x + 1\right) - {\left(\cos\left(2 \, x + 2\right)^{2} + \sin\left(2 \, x + 2\right)^{2} + 2 \, \cos\left(2 \, x + 2\right) + 1\right)} \log\left(\cos\left(x + 1\right)^{2} + \sin\left(x + 1\right)^{2} + 2 \, \sin\left(x + 1\right) + 1\right) + {\left(\cos\left(2 \, x + 2\right)^{2} + \sin\left(2 \, x + 2\right)^{2} + 2 \, \cos\left(2 \, x + 2\right) + 1\right)} \log\left(\cos\left(x + 1\right)^{2} + \sin\left(x + 1\right)^{2} - 2 \, \sin\left(x + 1\right) + 1\right)}{2 \, {\left(\cos\left(2 \, x + 2\right)^{2} + \sin\left(2 \, x + 2\right)^{2} + 2 \, \cos\left(2 \, x + 2\right) + 1\right)}} - \frac{1}{\cos\left(x + 1\right)}"," ",0,"1/2*(4*(x + 1)*cos(2*x + 2)*cos(x + 1) + 4*(x + 1)*sin(2*x + 2)*sin(x + 1) + 4*(x + 1)*cos(x + 1) - (cos(2*x + 2)^2 + sin(2*x + 2)^2 + 2*cos(2*x + 2) + 1)*log(cos(x + 1)^2 + sin(x + 1)^2 + 2*sin(x + 1) + 1) + (cos(2*x + 2)^2 + sin(2*x + 2)^2 + 2*cos(2*x + 2) + 1)*log(cos(x + 1)^2 + sin(x + 1)^2 - 2*sin(x + 1) + 1))/(cos(2*x + 2)^2 + sin(2*x + 2)^2 + 2*cos(2*x + 2) + 1) - 1/cos(x + 1)","B",0
905,1,12,0,0.330754," ","integrate(sin(2*x)/(9-sin(x)^2)^(1/2),x, algorithm=""maxima"")","-2 \, \sqrt{-\sin\left(x\right)^{2} + 9}"," ",0,"-2*sqrt(-sin(x)^2 + 9)","A",0
906,0,0,0,0.000000," ","integrate(sin(2*x)/(9-cos(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(2 \, x\right)}{\sqrt{-\cos\left(x\right)^{4} + 9}}\,{d x}"," ",0,"integrate(sin(2*x)/sqrt(-cos(x)^4 + 9), x)","F",0
907,1,19,0,0.366943," ","integrate(cos(1/x)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, \Gamma\left(4, \frac{i}{x}\right) + \frac{1}{2} \, \Gamma\left(4, -\frac{i}{x}\right)"," ",0,"1/2*gamma(4, I/x) + 1/2*gamma(4, -I/x)","C",0
908,1,17,0,0.559059," ","integrate(cos(1+x)^3*sin(1+x)^3,x, algorithm=""maxima"")","-\frac{1}{6} \, \sin\left(x + 1\right)^{6} + \frac{1}{4} \, \sin\left(x + 1\right)^{4}"," ",0,"-1/6*sin(x + 1)^6 + 1/4*sin(x + 1)^4","A",0
909,1,51,0,0.397638," ","integrate((1+2*x)^3*sin(1+2*x)^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(2 \, x + 1\right)}^{4} - \frac{3}{32} \, {\left(2 \, {\left(2 \, x + 1\right)}^{2} - 1\right)} \cos\left(4 \, x + 2\right) - \frac{1}{16} \, {\left(2 \, {\left(2 \, x + 1\right)}^{3} - 6 \, x - 3\right)} \sin\left(4 \, x + 2\right)"," ",0,"1/16*(2*x + 1)^4 - 3/32*(2*(2*x + 1)^2 - 1)*cos(4*x + 2) - 1/16*(2*(2*x + 1)^3 - 6*x - 3)*sin(4*x + 2)","A",0
910,1,59,0,0.582784," ","integrate((-1+sec(x))/(1-tan(x)),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1}{\sqrt{2} + \frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1}\right) - \frac{1}{2} \, x - \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \frac{1}{2} \, \log\left(\tan\left(x\right) - 1\right)"," ",0,"-1/2*sqrt(2)*log(-(sqrt(2) - sin(x)/(cos(x) + 1) - 1)/(sqrt(2) + sin(x)/(cos(x) + 1) + 1)) - 1/2*x - 1/4*log(tan(x)^2 + 1) + 1/2*log(tan(x) - 1)","A",0
911,1,41,0,0.325174," ","integrate(x^2*cos(3*x)*cos(5*x),x, algorithm=""maxima"")","\frac{1}{64} \, x \cos\left(8 \, x\right) + \frac{1}{4} \, x \cos\left(2 \, x\right) + \frac{1}{512} \, {\left(32 \, x^{2} - 1\right)} \sin\left(8 \, x\right) + \frac{1}{8} \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)"," ",0,"1/64*x*cos(8*x) + 1/4*x*cos(2*x) + 1/512*(32*x^2 - 1)*sin(8*x) + 1/8*(2*x^2 - 1)*sin(2*x)","A",0
912,0,0,0,0.000000," ","integrate((cos(x)+sin(x))/cos(x)^(1/2)/sin(x)^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(x\right) + \sin\left(x\right)}{\sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate((cos(x) + sin(x))/(sqrt(cos(x))*sqrt(sin(x))), x)","F",0
913,1,7,0,0.321609," ","integrate(sec(x)^2*(1+sin(x)),x, algorithm=""maxima"")","\frac{1}{\cos\left(x\right)} + \tan\left(x\right)"," ",0,"1/cos(x) + tan(x)","A",0
914,1,11,0,0.743789," ","integrate(10*x^9*cos(x^5*log(x))-x^10*(x^4+5*x^4*log(x))*sin(x^5*log(x)),x, algorithm=""maxima"")","x^{10} \cos\left(x^{5} \log\left(x\right)\right)"," ",0,"x^10*cos(x^5*log(x))","A",0
915,1,74,0,0.641584," ","integrate(cos(1/2*x)^2*tan(1/4*pi+1/2*x),x, algorithm=""maxima"")","\frac{2 \, x \cos\left(x\right)^{2} + 2 \, x \sin\left(x\right)^{2} - \cos\left(2 \, x\right) \cos\left(x\right) - 2 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \sin\left(x\right) + 1\right) - \sin\left(2 \, x\right) \sin\left(x\right) - \cos\left(x\right)}{4 \, {\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2}\right)}}"," ",0,"1/4*(2*x*cos(x)^2 + 2*x*sin(x)^2 - cos(2*x)*cos(x) - 2*(cos(x)^2 + sin(x)^2)*log(cos(x)^2 + sin(x)^2 - 2*sin(x) + 1) - sin(2*x)*sin(x) - cos(x))/(cos(x)^2 + sin(x)^2)","B",0
916,1,66,0,0.332324," ","integrate((2+3*x)^2*sin(x)^3,x, algorithm=""maxima"")","\frac{4}{3} \, \cos\left(x\right)^{3} + \frac{1}{12} \, {\left(9 \, x^{2} - 2\right)} \cos\left(3 \, x\right) + x \cos\left(3 \, x\right) - \frac{27}{4} \, {\left(x^{2} - 2\right)} \cos\left(x\right) - 9 \, x \cos\left(x\right) - \frac{1}{2} \, x \sin\left(3 \, x\right) + \frac{27}{2} \, x \sin\left(x\right) - 4 \, \cos\left(x\right) - \frac{1}{3} \, \sin\left(3 \, x\right) + 9 \, \sin\left(x\right)"," ",0,"4/3*cos(x)^3 + 1/12*(9*x^2 - 2)*cos(3*x) + x*cos(3*x) - 27/4*(x^2 - 2)*cos(x) - 9*x*cos(x) - 1/2*x*sin(3*x) + 27/2*x*sin(x) - 4*cos(x) - 1/3*sin(3*x) + 9*sin(x)","A",0
917,1,10,0,0.313475," ","integrate(sec(x)^(1+m)*sin(x),x, algorithm=""maxima"")","\frac{\cos\left(x\right)^{-m}}{m}"," ",0,"cos(x)^(-m)/m","A",0
918,1,125,0,0.444103," ","integrate(cos(b*x+a)^n*sin(b*x+a)^(-2-n),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)} e^{\left(n \log\left(\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + 1\right) - n \log\left(\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1}\right) + n \log\left(-\frac{\sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + 1\right)\right)}}{{\left(2^{n + 2} n + 2^{n + 2}\right)} b \sin\left(b x + a\right)}"," ",0,"2*(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 - 1)*(cos(b*x + a) + 1)*e^(n*log(sin(b*x + a)/(cos(b*x + a) + 1) + 1) - n*log(sin(b*x + a)/(cos(b*x + a) + 1)) + n*log(-sin(b*x + a)/(cos(b*x + a) + 1) + 1))/((2^(n + 2)*n + 2^(n + 2))*b*sin(b*x + a))","B",0
919,1,45,0,0.334164," ","integrate(1/(sec(x)+sin(x)*tan(x)),x, algorithm=""maxima"")","\frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right) + 2 \, \sin\left(x\right), \cos\left(2 \, x\right) + 2 \, \cos\left(x\right) - 1\right) - \frac{1}{2} \, \arctan\left(\sin\left(2 \, x\right) - 2 \, \sin\left(x\right), \cos\left(2 \, x\right) - 2 \, \cos\left(x\right) - 1\right)"," ",0,"1/2*arctan2(sin(2*x) + 2*sin(x), cos(2*x) + 2*cos(x) - 1) - 1/2*arctan2(sin(2*x) - 2*sin(x), cos(2*x) - 2*cos(x) - 1)","B",0
920,1,35,0,0.323014," ","integrate((c*x^2+b*x+a)*sin(x),x, algorithm=""maxima"")","-{\left(x \cos\left(x\right) - \sin\left(x\right)\right)} b - {\left({\left(x^{2} - 2\right)} \cos\left(x\right) - 2 \, x \sin\left(x\right)\right)} c - a \cos\left(x\right)"," ",0,"-(x*cos(x) - sin(x))*b - ((x^2 - 2)*cos(x) - 2*x*sin(x))*c - a*cos(x)","A",0
921,1,17,0,0.360585," ","integrate(sin(x^5)/x,x, algorithm=""maxima"")","-\frac{1}{10} i \, {\rm Ei}\left(i \, x^{5}\right) + \frac{1}{10} i \, {\rm Ei}\left(-i \, x^{5}\right)"," ",0,"-1/10*I*Ei(I*x^5) + 1/10*I*Ei(-I*x^5)","C",0
922,0,0,0,0.000000," ","integrate(sin(2^x)/(1+2^x),x, algorithm=""maxima"")","\int \frac{\sin\left(2^{x}\right)}{2^{x} + 1}\,{d x}"," ",0,"integrate(sin(2^x)/(2^x + 1), x)","F",0
923,1,10,0,0.324711," ","integrate(x*cos(2*x^2)*sin(2*x^2)^(3/4),x, algorithm=""maxima"")","\frac{1}{7} \, \sin\left(2 \, x^{2}\right)^{\frac{7}{4}}"," ",0,"1/7*sin(2*x^2)^(7/4)","A",0
924,1,8,0,0.320910," ","integrate(x*sec(x^2)^2*tan(x^2)^2,x, algorithm=""maxima"")","\frac{1}{6} \, \tan\left(x^{2}\right)^{3}"," ",0,"1/6*tan(x^2)^3","A",0
925,1,15,0,0.343444," ","integrate(x^2*cos(b*x^3+a)^7*sin(b*x^3+a),x, algorithm=""maxima"")","-\frac{\cos\left(b x^{3} + a\right)^{8}}{24 \, b}"," ",0,"-1/24*cos(b*x^3 + a)^8/b","A",0
926,1,126,0,0.339300," ","integrate(x^5*cos(b*x^3+a)^7*sin(b*x^3+a),x, algorithm=""maxima"")","-\frac{24 \, b x^{3} \cos\left(8 \, b x^{3} + 8 \, a\right) + 192 \, b x^{3} \cos\left(6 \, b x^{3} + 6 \, a\right) + 672 \, b x^{3} \cos\left(4 \, b x^{3} + 4 \, a\right) + 1344 \, b x^{3} \cos\left(2 \, b x^{3} + 2 \, a\right) - 3 \, \sin\left(8 \, b x^{3} + 8 \, a\right) - 32 \, \sin\left(6 \, b x^{3} + 6 \, a\right) - 168 \, \sin\left(4 \, b x^{3} + 4 \, a\right) - 672 \, \sin\left(2 \, b x^{3} + 2 \, a\right)}{73728 \, b^{2}}"," ",0,"-1/73728*(24*b*x^3*cos(8*b*x^3 + 8*a) + 192*b*x^3*cos(6*b*x^3 + 6*a) + 672*b*x^3*cos(4*b*x^3 + 4*a) + 1344*b*x^3*cos(2*b*x^3 + 2*a) - 3*sin(8*b*x^3 + 8*a) - 32*sin(6*b*x^3 + 6*a) - 168*sin(4*b*x^3 + 4*a) - 672*sin(2*b*x^3 + 2*a))/b^2","A",0
927,1,3830,0,0.858733," ","integrate(x^5*sec(b*x^3+a)^7*tan(b*x^3+a),x, algorithm=""maxima"")","\frac{4 \, {\left(3072 \, b x^{3} \cos\left(7 \, b x^{3} + 7 \, a\right) - 15 \, \sin\left(13 \, b x^{3} + 13 \, a\right) - 100 \, \sin\left(11 \, b x^{3} + 11 \, a\right) - 283 \, \sin\left(9 \, b x^{3} + 9 \, a\right) + 283 \, \sin\left(5 \, b x^{3} + 5 \, a\right) + 100 \, \sin\left(3 \, b x^{3} + 3 \, a\right) + 15 \, \sin\left(b x^{3} + a\right)\right)} \cos\left(14 \, b x^{3} + 14 \, a\right) + 420 \, {\left(\sin\left(12 \, b x^{3} + 12 \, a\right) + 3 \, \sin\left(10 \, b x^{3} + 10 \, a\right) + 5 \, \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \cos\left(13 \, b x^{3} + 13 \, a\right) + 28 \, {\left(3072 \, b x^{3} \cos\left(7 \, b x^{3} + 7 \, a\right) - 100 \, \sin\left(11 \, b x^{3} + 11 \, a\right) - 283 \, \sin\left(9 \, b x^{3} + 9 \, a\right) + 283 \, \sin\left(5 \, b x^{3} + 5 \, a\right) + 100 \, \sin\left(3 \, b x^{3} + 3 \, a\right) + 15 \, \sin\left(b x^{3} + a\right)\right)} \cos\left(12 \, b x^{3} + 12 \, a\right) + 2800 \, {\left(3 \, \sin\left(10 \, b x^{3} + 10 \, a\right) + 5 \, \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \cos\left(11 \, b x^{3} + 11 \, a\right) + 84 \, {\left(3072 \, b x^{3} \cos\left(7 \, b x^{3} + 7 \, a\right) - 283 \, \sin\left(9 \, b x^{3} + 9 \, a\right) + 283 \, \sin\left(5 \, b x^{3} + 5 \, a\right) + 100 \, \sin\left(3 \, b x^{3} + 3 \, a\right) + 15 \, \sin\left(b x^{3} + a\right)\right)} \cos\left(10 \, b x^{3} + 10 \, a\right) + 7924 \, {\left(5 \, \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \cos\left(9 \, b x^{3} + 9 \, a\right) + 140 \, {\left(3072 \, b x^{3} \cos\left(7 \, b x^{3} + 7 \, a\right) + 283 \, \sin\left(5 \, b x^{3} + 5 \, a\right) + 100 \, \sin\left(3 \, b x^{3} + 3 \, a\right) + 15 \, \sin\left(b x^{3} + a\right)\right)} \cos\left(8 \, b x^{3} + 8 \, a\right) + 12288 \, {\left(35 \, b x^{3} \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, b x^{3} \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, b x^{3} \cos\left(2 \, b x^{3} + 2 \, a\right) + b x^{3}\right)} \cos\left(7 \, b x^{3} + 7 \, a\right) + 140 \, {\left(283 \, \sin\left(5 \, b x^{3} + 5 \, a\right) + 100 \, \sin\left(3 \, b x^{3} + 3 \, a\right) + 15 \, \sin\left(b x^{3} + a\right)\right)} \cos\left(6 \, b x^{3} + 6 \, a\right) - 7924 \, {\left(3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \cos\left(5 \, b x^{3} + 5 \, a\right) + 420 \, {\left(20 \, \sin\left(3 \, b x^{3} + 3 \, a\right) + 3 \, \sin\left(b x^{3} + a\right)\right)} \cos\left(4 \, b x^{3} + 4 \, a\right) + 15 \, {\left(2 \, {\left(7 \, \cos\left(12 \, b x^{3} + 12 \, a\right) + 21 \, \cos\left(10 \, b x^{3} + 10 \, a\right) + 35 \, \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \cos\left(14 \, b x^{3} + 14 \, a\right) + \cos\left(14 \, b x^{3} + 14 \, a\right)^{2} + 14 \, {\left(21 \, \cos\left(10 \, b x^{3} + 10 \, a\right) + 35 \, \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \cos\left(12 \, b x^{3} + 12 \, a\right) + 49 \, \cos\left(12 \, b x^{3} + 12 \, a\right)^{2} + 42 \, {\left(35 \, \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \cos\left(10 \, b x^{3} + 10 \, a\right) + 441 \, \cos\left(10 \, b x^{3} + 10 \, a\right)^{2} + 70 \, {\left(35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \cos\left(8 \, b x^{3} + 8 \, a\right) + 1225 \, \cos\left(8 \, b x^{3} + 8 \, a\right)^{2} + 70 \, {\left(21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \cos\left(6 \, b x^{3} + 6 \, a\right) + 1225 \, \cos\left(6 \, b x^{3} + 6 \, a\right)^{2} + 42 \, {\left(7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \cos\left(4 \, b x^{3} + 4 \, a\right) + 441 \, \cos\left(4 \, b x^{3} + 4 \, a\right)^{2} + 49 \, \cos\left(2 \, b x^{3} + 2 \, a\right)^{2} + 14 \, {\left(\sin\left(12 \, b x^{3} + 12 \, a\right) + 3 \, \sin\left(10 \, b x^{3} + 10 \, a\right) + 5 \, \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(14 \, b x^{3} + 14 \, a\right) + \sin\left(14 \, b x^{3} + 14 \, a\right)^{2} + 98 \, {\left(3 \, \sin\left(10 \, b x^{3} + 10 \, a\right) + 5 \, \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(12 \, b x^{3} + 12 \, a\right) + 49 \, \sin\left(12 \, b x^{3} + 12 \, a\right)^{2} + 294 \, {\left(5 \, \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(10 \, b x^{3} + 10 \, a\right) + 441 \, \sin\left(10 \, b x^{3} + 10 \, a\right)^{2} + 490 \, {\left(5 \, \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(8 \, b x^{3} + 8 \, a\right) + 1225 \, \sin\left(8 \, b x^{3} + 8 \, a\right)^{2} + 490 \, {\left(3 \, \sin\left(4 \, b x^{3} + 4 \, a\right) + \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(6 \, b x^{3} + 6 \, a\right) + 1225 \, \sin\left(6 \, b x^{3} + 6 \, a\right)^{2} + 441 \, \sin\left(4 \, b x^{3} + 4 \, a\right)^{2} + 294 \, \sin\left(4 \, b x^{3} + 4 \, a\right) \sin\left(2 \, b x^{3} + 2 \, a\right) + 49 \, \sin\left(2 \, b x^{3} + 2 \, a\right)^{2} + 14 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \log\left(\frac{\cos\left(b x^{3} + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x^{3} + 2 \, a\right) + \sin\left(b x^{3} + 2 \, a\right)^{2} + 2 \, \cos\left(b x^{3} + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x^{3} + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x^{3} + 2 \, a\right) + \sin\left(b x^{3} + 2 \, a\right)^{2} - 2 \, \cos\left(b x^{3} + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + 4 \, {\left(3072 \, b x^{3} \sin\left(7 \, b x^{3} + 7 \, a\right) + 15 \, \cos\left(13 \, b x^{3} + 13 \, a\right) + 100 \, \cos\left(11 \, b x^{3} + 11 \, a\right) + 283 \, \cos\left(9 \, b x^{3} + 9 \, a\right) - 283 \, \cos\left(5 \, b x^{3} + 5 \, a\right) - 100 \, \cos\left(3 \, b x^{3} + 3 \, a\right) - 15 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(14 \, b x^{3} + 14 \, a\right) - 60 \, {\left(7 \, \cos\left(12 \, b x^{3} + 12 \, a\right) + 21 \, \cos\left(10 \, b x^{3} + 10 \, a\right) + 35 \, \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \sin\left(13 \, b x^{3} + 13 \, a\right) + 28 \, {\left(3072 \, b x^{3} \sin\left(7 \, b x^{3} + 7 \, a\right) + 100 \, \cos\left(11 \, b x^{3} + 11 \, a\right) + 283 \, \cos\left(9 \, b x^{3} + 9 \, a\right) - 283 \, \cos\left(5 \, b x^{3} + 5 \, a\right) - 100 \, \cos\left(3 \, b x^{3} + 3 \, a\right) - 15 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(12 \, b x^{3} + 12 \, a\right) - 400 \, {\left(21 \, \cos\left(10 \, b x^{3} + 10 \, a\right) + 35 \, \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \sin\left(11 \, b x^{3} + 11 \, a\right) + 84 \, {\left(3072 \, b x^{3} \sin\left(7 \, b x^{3} + 7 \, a\right) + 283 \, \cos\left(9 \, b x^{3} + 9 \, a\right) - 283 \, \cos\left(5 \, b x^{3} + 5 \, a\right) - 100 \, \cos\left(3 \, b x^{3} + 3 \, a\right) - 15 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(10 \, b x^{3} + 10 \, a\right) - 1132 \, {\left(35 \, \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \sin\left(9 \, b x^{3} + 9 \, a\right) + 140 \, {\left(3072 \, b x^{3} \sin\left(7 \, b x^{3} + 7 \, a\right) - 283 \, \cos\left(5 \, b x^{3} + 5 \, a\right) - 100 \, \cos\left(3 \, b x^{3} + 3 \, a\right) - 15 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(8 \, b x^{3} + 8 \, a\right) + 86016 \, {\left(5 \, b x^{3} \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, b x^{3} \sin\left(4 \, b x^{3} + 4 \, a\right) + b x^{3} \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(7 \, b x^{3} + 7 \, a\right) - 140 \, {\left(283 \, \cos\left(5 \, b x^{3} + 5 \, a\right) + 100 \, \cos\left(3 \, b x^{3} + 3 \, a\right) + 15 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(6 \, b x^{3} + 6 \, a\right) + 1132 \, {\left(21 \, \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \sin\left(5 \, b x^{3} + 5 \, a\right) - 420 \, {\left(20 \, \cos\left(3 \, b x^{3} + 3 \, a\right) + 3 \, \cos\left(b x^{3} + a\right)\right)} \sin\left(4 \, b x^{3} + 4 \, a\right) + 400 \, {\left(7 \, \cos\left(2 \, b x^{3} + 2 \, a\right) + 1\right)} \sin\left(3 \, b x^{3} + 3 \, a\right) - 2800 \, \cos\left(3 \, b x^{3} + 3 \, a\right) \sin\left(2 \, b x^{3} + 2 \, a\right) - 420 \, \cos\left(b x^{3} + a\right) \sin\left(2 \, b x^{3} + 2 \, a\right) + 420 \, \cos\left(2 \, b x^{3} + 2 \, a\right) \sin\left(b x^{3} + a\right) + 60 \, \sin\left(b x^{3} + a\right)}{2016 \, {\left(b^{2} \cos\left(14 \, b x^{3} + 14 \, a\right)^{2} + 49 \, b^{2} \cos\left(12 \, b x^{3} + 12 \, a\right)^{2} + 441 \, b^{2} \cos\left(10 \, b x^{3} + 10 \, a\right)^{2} + 1225 \, b^{2} \cos\left(8 \, b x^{3} + 8 \, a\right)^{2} + 1225 \, b^{2} \cos\left(6 \, b x^{3} + 6 \, a\right)^{2} + 441 \, b^{2} \cos\left(4 \, b x^{3} + 4 \, a\right)^{2} + 49 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right)^{2} + b^{2} \sin\left(14 \, b x^{3} + 14 \, a\right)^{2} + 49 \, b^{2} \sin\left(12 \, b x^{3} + 12 \, a\right)^{2} + 441 \, b^{2} \sin\left(10 \, b x^{3} + 10 \, a\right)^{2} + 1225 \, b^{2} \sin\left(8 \, b x^{3} + 8 \, a\right)^{2} + 1225 \, b^{2} \sin\left(6 \, b x^{3} + 6 \, a\right)^{2} + 441 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right)^{2} + 294 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right) \sin\left(2 \, b x^{3} + 2 \, a\right) + 49 \, b^{2} \sin\left(2 \, b x^{3} + 2 \, a\right)^{2} + 14 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2} + 2 \, {\left(7 \, b^{2} \cos\left(12 \, b x^{3} + 12 \, a\right) + 21 \, b^{2} \cos\left(10 \, b x^{3} + 10 \, a\right) + 35 \, b^{2} \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, b^{2} \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, b^{2} \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2}\right)} \cos\left(14 \, b x^{3} + 14 \, a\right) + 14 \, {\left(21 \, b^{2} \cos\left(10 \, b x^{3} + 10 \, a\right) + 35 \, b^{2} \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, b^{2} \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, b^{2} \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2}\right)} \cos\left(12 \, b x^{3} + 12 \, a\right) + 42 \, {\left(35 \, b^{2} \cos\left(8 \, b x^{3} + 8 \, a\right) + 35 \, b^{2} \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, b^{2} \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2}\right)} \cos\left(10 \, b x^{3} + 10 \, a\right) + 70 \, {\left(35 \, b^{2} \cos\left(6 \, b x^{3} + 6 \, a\right) + 21 \, b^{2} \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2}\right)} \cos\left(8 \, b x^{3} + 8 \, a\right) + 70 \, {\left(21 \, b^{2} \cos\left(4 \, b x^{3} + 4 \, a\right) + 7 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2}\right)} \cos\left(6 \, b x^{3} + 6 \, a\right) + 42 \, {\left(7 \, b^{2} \cos\left(2 \, b x^{3} + 2 \, a\right) + b^{2}\right)} \cos\left(4 \, b x^{3} + 4 \, a\right) + 14 \, {\left(b^{2} \sin\left(12 \, b x^{3} + 12 \, a\right) + 3 \, b^{2} \sin\left(10 \, b x^{3} + 10 \, a\right) + 5 \, b^{2} \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, b^{2} \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right) + b^{2} \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(14 \, b x^{3} + 14 \, a\right) + 98 \, {\left(3 \, b^{2} \sin\left(10 \, b x^{3} + 10 \, a\right) + 5 \, b^{2} \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, b^{2} \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right) + b^{2} \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(12 \, b x^{3} + 12 \, a\right) + 294 \, {\left(5 \, b^{2} \sin\left(8 \, b x^{3} + 8 \, a\right) + 5 \, b^{2} \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right) + b^{2} \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(10 \, b x^{3} + 10 \, a\right) + 490 \, {\left(5 \, b^{2} \sin\left(6 \, b x^{3} + 6 \, a\right) + 3 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right) + b^{2} \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(8 \, b x^{3} + 8 \, a\right) + 490 \, {\left(3 \, b^{2} \sin\left(4 \, b x^{3} + 4 \, a\right) + b^{2} \sin\left(2 \, b x^{3} + 2 \, a\right)\right)} \sin\left(6 \, b x^{3} + 6 \, a\right)\right)}}"," ",0,"1/2016*(4*(3072*b*x^3*cos(7*b*x^3 + 7*a) - 15*sin(13*b*x^3 + 13*a) - 100*sin(11*b*x^3 + 11*a) - 283*sin(9*b*x^3 + 9*a) + 283*sin(5*b*x^3 + 5*a) + 100*sin(3*b*x^3 + 3*a) + 15*sin(b*x^3 + a))*cos(14*b*x^3 + 14*a) + 420*(sin(12*b*x^3 + 12*a) + 3*sin(10*b*x^3 + 10*a) + 5*sin(8*b*x^3 + 8*a) + 5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*cos(13*b*x^3 + 13*a) + 28*(3072*b*x^3*cos(7*b*x^3 + 7*a) - 100*sin(11*b*x^3 + 11*a) - 283*sin(9*b*x^3 + 9*a) + 283*sin(5*b*x^3 + 5*a) + 100*sin(3*b*x^3 + 3*a) + 15*sin(b*x^3 + a))*cos(12*b*x^3 + 12*a) + 2800*(3*sin(10*b*x^3 + 10*a) + 5*sin(8*b*x^3 + 8*a) + 5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*cos(11*b*x^3 + 11*a) + 84*(3072*b*x^3*cos(7*b*x^3 + 7*a) - 283*sin(9*b*x^3 + 9*a) + 283*sin(5*b*x^3 + 5*a) + 100*sin(3*b*x^3 + 3*a) + 15*sin(b*x^3 + a))*cos(10*b*x^3 + 10*a) + 7924*(5*sin(8*b*x^3 + 8*a) + 5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*cos(9*b*x^3 + 9*a) + 140*(3072*b*x^3*cos(7*b*x^3 + 7*a) + 283*sin(5*b*x^3 + 5*a) + 100*sin(3*b*x^3 + 3*a) + 15*sin(b*x^3 + a))*cos(8*b*x^3 + 8*a) + 12288*(35*b*x^3*cos(6*b*x^3 + 6*a) + 21*b*x^3*cos(4*b*x^3 + 4*a) + 7*b*x^3*cos(2*b*x^3 + 2*a) + b*x^3)*cos(7*b*x^3 + 7*a) + 140*(283*sin(5*b*x^3 + 5*a) + 100*sin(3*b*x^3 + 3*a) + 15*sin(b*x^3 + a))*cos(6*b*x^3 + 6*a) - 7924*(3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*cos(5*b*x^3 + 5*a) + 420*(20*sin(3*b*x^3 + 3*a) + 3*sin(b*x^3 + a))*cos(4*b*x^3 + 4*a) + 15*(2*(7*cos(12*b*x^3 + 12*a) + 21*cos(10*b*x^3 + 10*a) + 35*cos(8*b*x^3 + 8*a) + 35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*cos(14*b*x^3 + 14*a) + cos(14*b*x^3 + 14*a)^2 + 14*(21*cos(10*b*x^3 + 10*a) + 35*cos(8*b*x^3 + 8*a) + 35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*cos(12*b*x^3 + 12*a) + 49*cos(12*b*x^3 + 12*a)^2 + 42*(35*cos(8*b*x^3 + 8*a) + 35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*cos(10*b*x^3 + 10*a) + 441*cos(10*b*x^3 + 10*a)^2 + 70*(35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*cos(8*b*x^3 + 8*a) + 1225*cos(8*b*x^3 + 8*a)^2 + 70*(21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*cos(6*b*x^3 + 6*a) + 1225*cos(6*b*x^3 + 6*a)^2 + 42*(7*cos(2*b*x^3 + 2*a) + 1)*cos(4*b*x^3 + 4*a) + 441*cos(4*b*x^3 + 4*a)^2 + 49*cos(2*b*x^3 + 2*a)^2 + 14*(sin(12*b*x^3 + 12*a) + 3*sin(10*b*x^3 + 10*a) + 5*sin(8*b*x^3 + 8*a) + 5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*sin(14*b*x^3 + 14*a) + sin(14*b*x^3 + 14*a)^2 + 98*(3*sin(10*b*x^3 + 10*a) + 5*sin(8*b*x^3 + 8*a) + 5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*sin(12*b*x^3 + 12*a) + 49*sin(12*b*x^3 + 12*a)^2 + 294*(5*sin(8*b*x^3 + 8*a) + 5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*sin(10*b*x^3 + 10*a) + 441*sin(10*b*x^3 + 10*a)^2 + 490*(5*sin(6*b*x^3 + 6*a) + 3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*sin(8*b*x^3 + 8*a) + 1225*sin(8*b*x^3 + 8*a)^2 + 490*(3*sin(4*b*x^3 + 4*a) + sin(2*b*x^3 + 2*a))*sin(6*b*x^3 + 6*a) + 1225*sin(6*b*x^3 + 6*a)^2 + 441*sin(4*b*x^3 + 4*a)^2 + 294*sin(4*b*x^3 + 4*a)*sin(2*b*x^3 + 2*a) + 49*sin(2*b*x^3 + 2*a)^2 + 14*cos(2*b*x^3 + 2*a) + 1)*log((cos(b*x^3 + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x^3 + 2*a) + sin(b*x^3 + 2*a)^2 + 2*cos(b*x^3 + 2*a)*sin(a) + sin(a)^2)/(cos(b*x^3 + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x^3 + 2*a) + sin(b*x^3 + 2*a)^2 - 2*cos(b*x^3 + 2*a)*sin(a) + sin(a)^2)) + 4*(3072*b*x^3*sin(7*b*x^3 + 7*a) + 15*cos(13*b*x^3 + 13*a) + 100*cos(11*b*x^3 + 11*a) + 283*cos(9*b*x^3 + 9*a) - 283*cos(5*b*x^3 + 5*a) - 100*cos(3*b*x^3 + 3*a) - 15*cos(b*x^3 + a))*sin(14*b*x^3 + 14*a) - 60*(7*cos(12*b*x^3 + 12*a) + 21*cos(10*b*x^3 + 10*a) + 35*cos(8*b*x^3 + 8*a) + 35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*sin(13*b*x^3 + 13*a) + 28*(3072*b*x^3*sin(7*b*x^3 + 7*a) + 100*cos(11*b*x^3 + 11*a) + 283*cos(9*b*x^3 + 9*a) - 283*cos(5*b*x^3 + 5*a) - 100*cos(3*b*x^3 + 3*a) - 15*cos(b*x^3 + a))*sin(12*b*x^3 + 12*a) - 400*(21*cos(10*b*x^3 + 10*a) + 35*cos(8*b*x^3 + 8*a) + 35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*sin(11*b*x^3 + 11*a) + 84*(3072*b*x^3*sin(7*b*x^3 + 7*a) + 283*cos(9*b*x^3 + 9*a) - 283*cos(5*b*x^3 + 5*a) - 100*cos(3*b*x^3 + 3*a) - 15*cos(b*x^3 + a))*sin(10*b*x^3 + 10*a) - 1132*(35*cos(8*b*x^3 + 8*a) + 35*cos(6*b*x^3 + 6*a) + 21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*sin(9*b*x^3 + 9*a) + 140*(3072*b*x^3*sin(7*b*x^3 + 7*a) - 283*cos(5*b*x^3 + 5*a) - 100*cos(3*b*x^3 + 3*a) - 15*cos(b*x^3 + a))*sin(8*b*x^3 + 8*a) + 86016*(5*b*x^3*sin(6*b*x^3 + 6*a) + 3*b*x^3*sin(4*b*x^3 + 4*a) + b*x^3*sin(2*b*x^3 + 2*a))*sin(7*b*x^3 + 7*a) - 140*(283*cos(5*b*x^3 + 5*a) + 100*cos(3*b*x^3 + 3*a) + 15*cos(b*x^3 + a))*sin(6*b*x^3 + 6*a) + 1132*(21*cos(4*b*x^3 + 4*a) + 7*cos(2*b*x^3 + 2*a) + 1)*sin(5*b*x^3 + 5*a) - 420*(20*cos(3*b*x^3 + 3*a) + 3*cos(b*x^3 + a))*sin(4*b*x^3 + 4*a) + 400*(7*cos(2*b*x^3 + 2*a) + 1)*sin(3*b*x^3 + 3*a) - 2800*cos(3*b*x^3 + 3*a)*sin(2*b*x^3 + 2*a) - 420*cos(b*x^3 + a)*sin(2*b*x^3 + 2*a) + 420*cos(2*b*x^3 + 2*a)*sin(b*x^3 + a) + 60*sin(b*x^3 + a))/(b^2*cos(14*b*x^3 + 14*a)^2 + 49*b^2*cos(12*b*x^3 + 12*a)^2 + 441*b^2*cos(10*b*x^3 + 10*a)^2 + 1225*b^2*cos(8*b*x^3 + 8*a)^2 + 1225*b^2*cos(6*b*x^3 + 6*a)^2 + 441*b^2*cos(4*b*x^3 + 4*a)^2 + 49*b^2*cos(2*b*x^3 + 2*a)^2 + b^2*sin(14*b*x^3 + 14*a)^2 + 49*b^2*sin(12*b*x^3 + 12*a)^2 + 441*b^2*sin(10*b*x^3 + 10*a)^2 + 1225*b^2*sin(8*b*x^3 + 8*a)^2 + 1225*b^2*sin(6*b*x^3 + 6*a)^2 + 441*b^2*sin(4*b*x^3 + 4*a)^2 + 294*b^2*sin(4*b*x^3 + 4*a)*sin(2*b*x^3 + 2*a) + 49*b^2*sin(2*b*x^3 + 2*a)^2 + 14*b^2*cos(2*b*x^3 + 2*a) + b^2 + 2*(7*b^2*cos(12*b*x^3 + 12*a) + 21*b^2*cos(10*b*x^3 + 10*a) + 35*b^2*cos(8*b*x^3 + 8*a) + 35*b^2*cos(6*b*x^3 + 6*a) + 21*b^2*cos(4*b*x^3 + 4*a) + 7*b^2*cos(2*b*x^3 + 2*a) + b^2)*cos(14*b*x^3 + 14*a) + 14*(21*b^2*cos(10*b*x^3 + 10*a) + 35*b^2*cos(8*b*x^3 + 8*a) + 35*b^2*cos(6*b*x^3 + 6*a) + 21*b^2*cos(4*b*x^3 + 4*a) + 7*b^2*cos(2*b*x^3 + 2*a) + b^2)*cos(12*b*x^3 + 12*a) + 42*(35*b^2*cos(8*b*x^3 + 8*a) + 35*b^2*cos(6*b*x^3 + 6*a) + 21*b^2*cos(4*b*x^3 + 4*a) + 7*b^2*cos(2*b*x^3 + 2*a) + b^2)*cos(10*b*x^3 + 10*a) + 70*(35*b^2*cos(6*b*x^3 + 6*a) + 21*b^2*cos(4*b*x^3 + 4*a) + 7*b^2*cos(2*b*x^3 + 2*a) + b^2)*cos(8*b*x^3 + 8*a) + 70*(21*b^2*cos(4*b*x^3 + 4*a) + 7*b^2*cos(2*b*x^3 + 2*a) + b^2)*cos(6*b*x^3 + 6*a) + 42*(7*b^2*cos(2*b*x^3 + 2*a) + b^2)*cos(4*b*x^3 + 4*a) + 14*(b^2*sin(12*b*x^3 + 12*a) + 3*b^2*sin(10*b*x^3 + 10*a) + 5*b^2*sin(8*b*x^3 + 8*a) + 5*b^2*sin(6*b*x^3 + 6*a) + 3*b^2*sin(4*b*x^3 + 4*a) + b^2*sin(2*b*x^3 + 2*a))*sin(14*b*x^3 + 14*a) + 98*(3*b^2*sin(10*b*x^3 + 10*a) + 5*b^2*sin(8*b*x^3 + 8*a) + 5*b^2*sin(6*b*x^3 + 6*a) + 3*b^2*sin(4*b*x^3 + 4*a) + b^2*sin(2*b*x^3 + 2*a))*sin(12*b*x^3 + 12*a) + 294*(5*b^2*sin(8*b*x^3 + 8*a) + 5*b^2*sin(6*b*x^3 + 6*a) + 3*b^2*sin(4*b*x^3 + 4*a) + b^2*sin(2*b*x^3 + 2*a))*sin(10*b*x^3 + 10*a) + 490*(5*b^2*sin(6*b*x^3 + 6*a) + 3*b^2*sin(4*b*x^3 + 4*a) + b^2*sin(2*b*x^3 + 2*a))*sin(8*b*x^3 + 8*a) + 490*(3*b^2*sin(4*b*x^3 + 4*a) + b^2*sin(2*b*x^3 + 2*a))*sin(6*b*x^3 + 6*a))","B",0
928,1,36,0,0.381249," ","integrate(sec(1/x)^2/x^2,x, algorithm=""maxima"")","-\frac{2 \, \sin\left(\frac{2}{x}\right)}{\cos\left(\frac{2}{x}\right)^{2} + \sin\left(\frac{2}{x}\right)^{2} + 2 \, \cos\left(\frac{2}{x}\right) + 1}"," ",0,"-2*sin(2/x)/(cos(2/x)^2 + sin(2/x)^2 + 2*cos(2/x) + 1)","B",0
929,1,4,0,0.319219," ","integrate(3*x^2*cos(x^3),x, algorithm=""maxima"")","\sin\left(x^{3}\right)"," ",0,"sin(x^3)","A",0
930,1,98,0,0.451085," ","integrate((1+2*x)*sec(1+2*x)^2,x, algorithm=""maxima"")","\frac{{\left(\cos\left(4 \, x + 2\right)^{2} + \sin\left(4 \, x + 2\right)^{2} + 2 \, \cos\left(4 \, x + 2\right) + 1\right)} \log\left(\cos\left(4 \, x + 2\right)^{2} + \sin\left(4 \, x + 2\right)^{2} + 2 \, \cos\left(4 \, x + 2\right) + 1\right) + 4 \, {\left(2 \, x + 1\right)} \sin\left(4 \, x + 2\right)}{4 \, {\left(\cos\left(4 \, x + 2\right)^{2} + \sin\left(4 \, x + 2\right)^{2} + 2 \, \cos\left(4 \, x + 2\right) + 1\right)}}"," ",0,"1/4*((cos(4*x + 2)^2 + sin(4*x + 2)^2 + 2*cos(4*x + 2) + 1)*log(cos(4*x + 2)^2 + sin(4*x + 2)^2 + 2*cos(4*x + 2) + 1) + 4*(2*x + 1)*sin(4*x + 2))/(cos(4*x + 2)^2 + sin(4*x + 2)^2 + 2*cos(4*x + 2) + 1)","B",0
931,0,0,0,0.000000," ","integrate(x^4/b/(x^3+3*sin(b*x+a))^(1/2)+x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2)+4/3*x*(x^3+3*sin(b*x+a))^(1/2)/b,x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{x^{3} + 3 \, \sin\left(b x + a\right)} b} + \frac{x^{2} \cos\left(b x + a\right)}{\sqrt{x^{3} + 3 \, \sin\left(b x + a\right)}} + \frac{4 \, \sqrt{x^{3} + 3 \, \sin\left(b x + a\right)} x}{3 \, b}\,{d x}"," ",0,"integrate(x^4/(sqrt(x^3 + 3*sin(b*x + a))*b) + x^2*cos(b*x + a)/sqrt(x^3 + 3*sin(b*x + a)) + 4/3*sqrt(x^3 + 3*sin(b*x + a))*x/b, x)","F",0
932,0,0,0,0.000000," ","integrate(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \cos\left(b x + a\right)}{\sqrt{x^{3} + 3 \, \sin\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x^2*cos(b*x + a)/sqrt(x^3 + 3*sin(b*x + a)), x)","F",0
933,1,82,0,0.563317," ","integrate((cos(x)+sin(x))/(exp(-x)+sin(x)),x, algorithm=""maxima"")","x + \frac{1}{2} \, \log\left({\left(\cos\left(2 \, x\right)^{2} e^{\left(2 \, x\right)} + 4 \, \cos\left(x\right) e^{x} \sin\left(2 \, x\right) + e^{\left(2 \, x\right)} \sin\left(2 \, x\right)^{2} - 2 \, {\left(2 \, e^{x} \sin\left(x\right) + e^{\left(2 \, x\right)}\right)} \cos\left(2 \, x\right) + 4 \, \cos\left(x\right)^{2} + 4 \, e^{x} \sin\left(x\right) + 4 \, \sin\left(x\right)^{2} + e^{\left(2 \, x\right)}\right)} e^{\left(-2 \, x\right)}\right)"," ",0,"x + 1/2*log((cos(2*x)^2*e^(2*x) + 4*cos(x)*e^x*sin(2*x) + e^(2*x)*sin(2*x)^2 - 2*(2*e^x*sin(x) + e^(2*x))*cos(2*x) + 4*cos(x)^2 + 4*e^x*sin(x) + 4*sin(x)^2 + e^(2*x))*e^(-2*x))","B",0
934,1,57,0,0.493012," ","integrate(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b}{96 \, d}"," ",0,"1/96*(32*(cos(d*x + c)^3 - 3*cos(d*x + c))*a + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*b)/d","A",0
935,1,131,0,0.325534," ","integrate(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","-\frac{224 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} a^{2} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b - 96 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 21 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)\right)} b^{2}}{3360 \, d}"," ",0,"-1/3360*(224*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*a^2 - 35*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a*b - 96*(5*cos(d*x + c)^7 - 21*cos(d*x + c)^5 + 35*cos(d*x + c)^3 - 35*cos(d*x + c))*b^2)/d","A",0
936,1,79,0,0.460133," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} a + 32 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} b + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} c}{96 \, d}"," ",0,"1/96*(24*(2*d*x + 2*c - sin(2*d*x + 2*c))*a + 32*(cos(d*x + c)^3 - 3*cos(d*x + c))*b + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*c)/d","A",0
937,1,218,0,0.404457," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3)^2,x, algorithm=""maxima"")","\frac{1120 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} a^{2} + 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b - 224 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} b^{2} - 448 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} a c + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b c + 96 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 21 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)\right)} c^{2}}{3360 \, d}"," ",0,"1/3360*(1120*(cos(d*x + c)^3 - 3*cos(d*x + c))*a^2 + 210*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*a*b - 224*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*b^2 - 448*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*a*c + 35*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*b*c + 96*(5*cos(d*x + c)^7 - 21*cos(d*x + c)^5 + 35*cos(d*x + c)^3 - 35*cos(d*x + c))*c^2)/d","A",0
938,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2)),x, algorithm=""maxima"")","\frac{2 \, c d x - 4 \, a \cos\left(d x + c\right) - 2 \, d \int \frac{{\left({\left(b \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - b \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - b \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right)\right) - {\left(b \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - b \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + b \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right)\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right)\right) + {\left({\left(b \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - b \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) + b \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right)\right) + {\left(b \cos\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - b \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b \sin\left(\frac{3}{2} \, d x + \frac{3}{2} \, c\right) - b \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right)\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right)\right)}{{\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right)}^{\frac{1}{4}}}\,{d x} - c \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/4*(2*c*d*x - 4*a*cos(d*x + c) + 2*d*integrate(-(((b*cos(3/2*d*x + 3/2*c) - b*cos(1/2*d*x + 1/2*c) - b*sin(3/2*d*x + 3/2*c) - b*sin(1/2*d*x + 1/2*c))*cos(1/2*arctan2(sin(d*x + c), -cos(d*x + c) + 1)) - (b*cos(3/2*d*x + 3/2*c) - b*cos(1/2*d*x + 1/2*c) + b*sin(3/2*d*x + 3/2*c) + b*sin(1/2*d*x + 1/2*c))*sin(1/2*arctan2(sin(d*x + c), -cos(d*x + c) + 1)))*cos(1/2*arctan2(sin(d*x + c), cos(d*x + c) + 1)) + ((b*cos(3/2*d*x + 3/2*c) - b*cos(1/2*d*x + 1/2*c) + b*sin(3/2*d*x + 3/2*c) + b*sin(1/2*d*x + 1/2*c))*cos(1/2*arctan2(sin(d*x + c), -cos(d*x + c) + 1)) + (b*cos(3/2*d*x + 3/2*c) - b*cos(1/2*d*x + 1/2*c) - b*sin(3/2*d*x + 3/2*c) - b*sin(1/2*d*x + 1/2*c))*sin(1/2*arctan2(sin(d*x + c), -cos(d*x + c) + 1)))*sin(1/2*arctan2(sin(d*x + c), cos(d*x + c) + 1)))/((cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1)^(1/4)*(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1)^(1/4)), x) - c*sin(2*d*x + 2*c))/d","F",0
939,-1,0,0,0.000000," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
940,1,50,0,0.806823," ","integrate(f^(b*x+a)*(cos(d*x+c)+I*sin(d*x+c))^n,x, algorithm=""maxima"")","\frac{-i \, f^{b x} f^{a} \cos\left(d n x + c n\right) + f^{b x} f^{a} \sin\left(d n x + c n\right)}{d n - i \, b \log\left(f\right)}"," ",0,"(-I*f^(b*x)*f^a*cos(d*n*x + c*n) + f^(b*x)*f^a*sin(d*n*x + c*n))/(d*n - I*b*log(f))","A",0
941,1,62,0,0.491668," ","integrate(f^(b*x+a)*(cos(d*x+c)-I*sin(d*x+c))^n,x, algorithm=""maxima"")","\frac{f^{b x} f^{a} \cos\left(d n x\right) - i \, f^{b x} f^{a} \sin\left(d n x\right)}{{\left(-i \, d n + b \log\left(f\right)\right)} \cos\left(c n\right) + {\left(d n + i \, b \log\left(f\right)\right)} \sin\left(c n\right)}"," ",0,"(f^(b*x)*f^a*cos(d*n*x) - I*f^(b*x)*f^a*sin(d*n*x))/((-I*d*n + b*log(f))*cos(c*n) + (d*n + I*b*log(f))*sin(c*n))","A",0
942,0,0,0,0.000000," ","integrate((cos(b*x+a)^5-sin(b*x+a)^5)/(cos(b*x+a)^5+sin(b*x+a)^5),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{5} - \sin\left(b x + a\right)^{5}}{\cos\left(b x + a\right)^{5} + \sin\left(b x + a\right)^{5}}\,{d x}"," ",0,"integrate((cos(b*x + a)^5 - sin(b*x + a)^5)/(cos(b*x + a)^5 + sin(b*x + a)^5), x)","F",0
943,1,58,0,0.456964," ","integrate((cos(b*x+a)^4-sin(b*x+a)^4)/(cos(b*x+a)^4+sin(b*x+a)^4),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(\tan\left(b x + a\right)^{2} + \sqrt{2} \tan\left(b x + a\right) + 1\right) - \sqrt{2} \log\left(\tan\left(b x + a\right)^{2} - \sqrt{2} \tan\left(b x + a\right) + 1\right)}{4 \, b}"," ",0,"1/4*(sqrt(2)*log(tan(b*x + a)^2 + sqrt(2)*tan(b*x + a) + 1) - sqrt(2)*log(tan(b*x + a)^2 - sqrt(2)*tan(b*x + a) + 1))/b","A",0
944,1,154,0,0.433747," ","integrate((cos(b*x+a)^3-sin(b*x+a)^3)/(cos(b*x+a)^3+sin(b*x+a)^3),x, algorithm=""maxima"")","-\frac{2 \, \log\left(-\frac{2 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + \frac{2 \, \sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(b x + a\right)^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{\sin\left(b x + a\right)^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1\right) - \log\left(-\frac{2 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + \frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right) - 3 \, \log\left(\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1\right)}{3 \, b}"," ",0,"-1/3*(2*log(-2*sin(b*x + a)/(cos(b*x + a) + 1) + 2*sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 2*sin(b*x + a)^3/(cos(b*x + a) + 1)^3 + sin(b*x + a)^4/(cos(b*x + a) + 1)^4 + 1) - log(-2*sin(b*x + a)/(cos(b*x + a) + 1) + sin(b*x + a)^2/(cos(b*x + a) + 1)^2 - 1) - 3*log(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1))/b","B",0
945,1,22,0,0.330942," ","integrate((cos(b*x+a)^2-sin(b*x+a)^2)/(cos(b*x+a)^2+sin(b*x+a)^2),x, algorithm=""maxima"")","\frac{\tan\left(b x + a\right)}{{\left(\tan\left(b x + a\right)^{2} + 1\right)} b}"," ",0,"tan(b*x + a)/((tan(b*x + a)^2 + 1)*b)","A",0
946,1,18,0,0.311651," ","integrate((cos(b*x+a)-sin(b*x+a))/(cos(b*x+a)+sin(b*x+a)),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(b x + a\right) + \sin\left(b x + a\right)\right)}{b}"," ",0,"log(cos(b*x + a) + sin(b*x + a))/b","A",0
947,1,70,0,0.413607," ","integrate((-csc(b*x+a)+sec(b*x+a))/(csc(b*x+a)+sec(b*x+a)),x, algorithm=""maxima"")","-\frac{\log\left(-\frac{2 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + \frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right) - \log\left(\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1\right)}{b}"," ",0,"-(log(-2*sin(b*x + a)/(cos(b*x + a) + 1) + sin(b*x + a)^2/(cos(b*x + a) + 1)^2 - 1) - log(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1))/b","B",0
948,1,23,0,0.310800," ","integrate((-csc(b*x+a)^2+sec(b*x+a)^2)/(csc(b*x+a)^2+sec(b*x+a)^2),x, algorithm=""maxima"")","-\frac{\tan\left(b x + a\right)}{{\left(\tan\left(b x + a\right)^{2} + 1\right)} b}"," ",0,"-tan(b*x + a)/((tan(b*x + a)^2 + 1)*b)","A",0
949,1,154,0,0.437842," ","integrate((-csc(b*x+a)^3+sec(b*x+a)^3)/(csc(b*x+a)^3+sec(b*x+a)^3),x, algorithm=""maxima"")","\frac{2 \, \log\left(-\frac{2 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + \frac{2 \, \sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(b x + a\right)^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{\sin\left(b x + a\right)^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1\right) - \log\left(-\frac{2 \, \sin\left(b x + a\right)}{\cos\left(b x + a\right) + 1} + \frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right) - 3 \, \log\left(\frac{\sin\left(b x + a\right)^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1\right)}{3 \, b}"," ",0,"1/3*(2*log(-2*sin(b*x + a)/(cos(b*x + a) + 1) + 2*sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 2*sin(b*x + a)^3/(cos(b*x + a) + 1)^3 + sin(b*x + a)^4/(cos(b*x + a) + 1)^4 + 1) - log(-2*sin(b*x + a)/(cos(b*x + a) + 1) + sin(b*x + a)^2/(cos(b*x + a) + 1)^2 - 1) - 3*log(sin(b*x + a)^2/(cos(b*x + a) + 1)^2 + 1))/b","B",0
950,1,58,0,0.427818," ","integrate((-csc(b*x+a)^4+sec(b*x+a)^4)/(csc(b*x+a)^4+sec(b*x+a)^4),x, algorithm=""maxima"")","-\frac{\sqrt{2} \log\left(\tan\left(b x + a\right)^{2} + \sqrt{2} \tan\left(b x + a\right) + 1\right) - \sqrt{2} \log\left(\tan\left(b x + a\right)^{2} - \sqrt{2} \tan\left(b x + a\right) + 1\right)}{4 \, b}"," ",0,"-1/4*(sqrt(2)*log(tan(b*x + a)^2 + sqrt(2)*tan(b*x + a) + 1) - sqrt(2)*log(tan(b*x + a)^2 - sqrt(2)*tan(b*x + a) + 1))/b","A",0
