1,1,19,0,0.319852," ","integrate(csc(b*x+a),x, algorithm=""maxima"")","-\frac{\log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right)}{b}"," ",0,"-log(cot(b*x + a) + csc(b*x + a))/b","A",0
2,1,13,0,0.328389," ","integrate(csc(b*x+a)^2,x, algorithm=""maxima"")","-\frac{1}{b \tan\left(b x + a\right)}"," ",0,"-1/(b*tan(b*x + a))","A",0
3,1,46,0,0.319749," ","integrate(csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)}{4 \, b}"," ",0,"1/4*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b","A",0
4,1,25,0,0.319108," ","integrate(csc(b*x+a)^4,x, algorithm=""maxima"")","-\frac{3 \, \tan\left(b x + a\right)^{2} + 1}{3 \, b \tan\left(b x + a\right)^{3}}"," ",0,"-1/3*(3*tan(b*x + a)^2 + 1)/(b*tan(b*x + a)^3)","A",0
5,1,71,0,0.328320," ","integrate(csc(b*x+a)^5,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{3} - 5 \, \cos\left(b x + a\right)\right)}}{\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)}{16 \, b}"," ",0,"1/16*(2*(3*cos(b*x + a)^3 - 5*cos(b*x + a))/(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1))/b","A",0
6,1,35,0,0.354738," ","integrate(csc(b*x+a)^6,x, algorithm=""maxima"")","-\frac{15 \, \tan\left(b x + a\right)^{4} + 10 \, \tan\left(b x + a\right)^{2} + 3}{15 \, b \tan\left(b x + a\right)^{5}}"," ",0,"-1/15*(15*tan(b*x + a)^4 + 10*tan(b*x + a)^2 + 3)/(b*tan(b*x + a)^5)","A",0
7,1,91,0,0.335893," ","integrate(csc(b*x+a)^7,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \cos\left(b x + a\right)^{5} - 40 \, \cos\left(b x + a\right)^{3} + 33 \, \cos\left(b x + a\right)\right)}}{\cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2} - 1} - 15 \, \log\left(\cos\left(b x + a\right) + 1\right) + 15 \, \log\left(\cos\left(b x + a\right) - 1\right)}{96 \, b}"," ",0,"1/96*(2*(15*cos(b*x + a)^5 - 40*cos(b*x + a)^3 + 33*cos(b*x + a))/(cos(b*x + a)^6 - 3*cos(b*x + a)^4 + 3*cos(b*x + a)^2 - 1) - 15*log(cos(b*x + a) + 1) + 15*log(cos(b*x + a) - 1))/b","A",0
8,1,45,0,0.403365," ","integrate(csc(b*x+a)^8,x, algorithm=""maxima"")","-\frac{35 \, \tan\left(b x + a\right)^{6} + 35 \, \tan\left(b x + a\right)^{4} + 21 \, \tan\left(b x + a\right)^{2} + 5}{35 \, b \tan\left(b x + a\right)^{7}}"," ",0,"-1/35*(35*tan(b*x + a)^6 + 35*tan(b*x + a)^4 + 21*tan(b*x + a)^2 + 5)/(b*tan(b*x + a)^7)","A",0
9,0,0,0,0.000000," ","integrate(csc(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(7/2), x)","F",0
10,0,0,0,0.000000," ","integrate(csc(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(5/2), x)","F",0
11,0,0,0,0.000000," ","integrate(csc(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\csc\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(csc(b*x + a)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(csc(b*x + a)), x)","F",0
14,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\csc\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(-3/2), x)","F",0
15,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\csc\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(-5/2), x)","F",0
16,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\csc\left(b x + a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(-7/2), x)","F",0
17,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(7/2),x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(7/2), x)","F",0
18,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(5/2), x)","F",0
19,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(3/2), x)","F",0
20,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c \csc\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(c*csc(b*x + a)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c \csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(c*csc(b*x + a)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \csc\left(b x + a\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(-3/2), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \csc\left(b x + a\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(-5/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\left(c \csc\left(b x + a\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(-7/2), x)","F",0
25,0,0,0,0.000000," ","integrate(csc(b*x+a)^(4/3),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(4/3), x)","F",0
26,0,0,0,0.000000," ","integrate(csc(b*x+a)^(2/3),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(2/3), x)","F",0
27,0,0,0,0.000000," ","integrate(csc(b*x+a)^(1/3),x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(1/3), x)","F",0
28,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\csc\left(b x + a\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(-1/3), x)","F",0
29,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\csc\left(b x + a\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(-2/3), x)","F",0
30,0,0,0,0.000000," ","integrate(1/csc(b*x+a)^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\csc\left(b x + a\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^(-4/3), x)","F",0
31,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(4/3),x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(4/3), x)","F",0
32,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(2/3),x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(2/3), x)","F",0
33,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^(1/3),x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(1/3), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \csc\left(b x + a\right)\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(-1/3), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \csc\left(b x + a\right)\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(-2/3), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(c*csc(b*x+a))^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\left(c \csc\left(b x + a\right)\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^(-4/3), x)","F",0
37,0,0,0,0.000000," ","integrate(csc(b*x+a)^n,x, algorithm=""maxima"")","\int \csc\left(b x + a\right)^{n}\,{d x}"," ",0,"integrate(csc(b*x + a)^n, x)","F",0
38,0,0,0,0.000000," ","integrate((c*csc(b*x+a))^n,x, algorithm=""maxima"")","\int \left(c \csc\left(b x + a\right)\right)^{n}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^n, x)","F",0
39,1,1669,0,0.760378," ","integrate((csc(x)^2)^(7/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(15 \, \cos\left(11 \, x\right) - 85 \, \cos\left(9 \, x\right) + 198 \, \cos\left(7 \, x\right) + 198 \, \cos\left(5 \, x\right) - 85 \, \cos\left(3 \, x\right) + 15 \, \cos\left(x\right)\right)} \cos\left(12 \, x\right) - 60 \, {\left(6 \, \cos\left(10 \, x\right) - 15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(11 \, x\right) + 24 \, {\left(85 \, \cos\left(9 \, x\right) - 198 \, \cos\left(7 \, x\right) - 198 \, \cos\left(5 \, x\right) + 85 \, \cos\left(3 \, x\right) - 15 \, \cos\left(x\right)\right)} \cos\left(10 \, x\right) - 340 \, {\left(15 \, \cos\left(8 \, x\right) - 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(9 \, x\right) + 60 \, {\left(198 \, \cos\left(7 \, x\right) + 198 \, \cos\left(5 \, x\right) - 85 \, \cos\left(3 \, x\right) + 15 \, \cos\left(x\right)\right)} \cos\left(8 \, x\right) - 792 \, {\left(20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(7 \, x\right) - 80 \, {\left(198 \, \cos\left(5 \, x\right) - 85 \, \cos\left(3 \, x\right) + 15 \, \cos\left(x\right)\right)} \cos\left(6 \, x\right) + 792 \, {\left(15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(5 \, x\right) - 300 \, {\left(17 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \cos\left(4 \, x\right) + 340 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 360 \, \cos\left(2 \, x\right) \cos\left(x\right) + 15 \, {\left(2 \, {\left(6 \, \cos\left(10 \, x\right) - 15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(12 \, x\right) - \cos\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, x\right) - 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(10 \, x\right) - 36 \, \cos\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - 225 \, \cos\left(8 \, x\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 400 \, \cos\left(6 \, x\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 225 \, \cos\left(4 \, x\right)^{2} - 36 \, \cos\left(2 \, x\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, x\right) - 15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) - \sin\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, x\right) - 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) - 36 \, \sin\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 225 \, \sin\left(8 \, x\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 400 \, \sin\left(6 \, x\right)^{2} - 225 \, \sin\left(4 \, x\right)^{2} + 180 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \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) - 15 \, {\left(2 \, {\left(6 \, \cos\left(10 \, x\right) - 15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(12 \, x\right) - \cos\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, x\right) - 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(10 \, x\right) - 36 \, \cos\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - 225 \, \cos\left(8 \, x\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 400 \, \cos\left(6 \, x\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 225 \, \cos\left(4 \, x\right)^{2} - 36 \, \cos\left(2 \, x\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, x\right) - 15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) - \sin\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, x\right) - 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) - 36 \, \sin\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 225 \, \sin\left(8 \, x\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 400 \, \sin\left(6 \, x\right)^{2} - 225 \, \sin\left(4 \, x\right)^{2} + 180 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \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 \, {\left(15 \, \sin\left(11 \, x\right) - 85 \, \sin\left(9 \, x\right) + 198 \, \sin\left(7 \, x\right) + 198 \, \sin\left(5 \, x\right) - 85 \, \sin\left(3 \, x\right) + 15 \, \sin\left(x\right)\right)} \sin\left(12 \, x\right) - 60 \, {\left(6 \, \sin\left(10 \, x\right) - 15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(11 \, x\right) + 24 \, {\left(85 \, \sin\left(9 \, x\right) - 198 \, \sin\left(7 \, x\right) - 198 \, \sin\left(5 \, x\right) + 85 \, \sin\left(3 \, x\right) - 15 \, \sin\left(x\right)\right)} \sin\left(10 \, x\right) - 340 \, {\left(15 \, \sin\left(8 \, x\right) - 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right)\right)} \sin\left(9 \, x\right) + 60 \, {\left(198 \, \sin\left(7 \, x\right) + 198 \, \sin\left(5 \, x\right) - 85 \, \sin\left(3 \, x\right) + 15 \, \sin\left(x\right)\right)} \sin\left(8 \, x\right) - 792 \, {\left(20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(7 \, x\right) - 80 \, {\left(198 \, \sin\left(5 \, x\right) - 85 \, \sin\left(3 \, x\right) + 15 \, \sin\left(x\right)\right)} \sin\left(6 \, x\right) + 2376 \, {\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(5 \, x\right) - 300 \, {\left(17 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 2040 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 360 \, \sin\left(2 \, x\right) \sin\left(x\right) + 60 \, \cos\left(x\right)}{96 \, {\left(2 \, {\left(6 \, \cos\left(10 \, x\right) - 15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(12 \, x\right) - \cos\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, x\right) - 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(10 \, x\right) - 36 \, \cos\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - 225 \, \cos\left(8 \, x\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 400 \, \cos\left(6 \, x\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 225 \, \cos\left(4 \, x\right)^{2} - 36 \, \cos\left(2 \, x\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, x\right) - 15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) - \sin\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, x\right) - 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) - 36 \, \sin\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 225 \, \sin\left(8 \, x\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 400 \, \sin\left(6 \, x\right)^{2} - 225 \, \sin\left(4 \, x\right)^{2} + 180 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"-1/96*(4*(15*cos(11*x) - 85*cos(9*x) + 198*cos(7*x) + 198*cos(5*x) - 85*cos(3*x) + 15*cos(x))*cos(12*x) - 60*(6*cos(10*x) - 15*cos(8*x) + 20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(11*x) + 24*(85*cos(9*x) - 198*cos(7*x) - 198*cos(5*x) + 85*cos(3*x) - 15*cos(x))*cos(10*x) - 340*(15*cos(8*x) - 20*cos(6*x) + 15*cos(4*x) - 6*cos(2*x) + 1)*cos(9*x) + 60*(198*cos(7*x) + 198*cos(5*x) - 85*cos(3*x) + 15*cos(x))*cos(8*x) - 792*(20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(7*x) - 80*(198*cos(5*x) - 85*cos(3*x) + 15*cos(x))*cos(6*x) + 792*(15*cos(4*x) - 6*cos(2*x) + 1)*cos(5*x) - 300*(17*cos(3*x) - 3*cos(x))*cos(4*x) + 340*(6*cos(2*x) - 1)*cos(3*x) - 360*cos(2*x)*cos(x) + 15*(2*(6*cos(10*x) - 15*cos(8*x) + 20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(12*x) - cos(12*x)^2 + 12*(15*cos(8*x) - 20*cos(6*x) + 15*cos(4*x) - 6*cos(2*x) + 1)*cos(10*x) - 36*cos(10*x)^2 + 30*(20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(8*x) - 225*cos(8*x)^2 + 40*(15*cos(4*x) - 6*cos(2*x) + 1)*cos(6*x) - 400*cos(6*x)^2 + 30*(6*cos(2*x) - 1)*cos(4*x) - 225*cos(4*x)^2 - 36*cos(2*x)^2 + 2*(6*sin(10*x) - 15*sin(8*x) + 20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(12*x) - sin(12*x)^2 + 12*(15*sin(8*x) - 20*sin(6*x) + 15*sin(4*x) - 6*sin(2*x))*sin(10*x) - 36*sin(10*x)^2 + 30*(20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(8*x) - 225*sin(8*x)^2 + 120*(5*sin(4*x) - 2*sin(2*x))*sin(6*x) - 400*sin(6*x)^2 - 225*sin(4*x)^2 + 180*sin(4*x)*sin(2*x) - 36*sin(2*x)^2 + 12*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - 15*(2*(6*cos(10*x) - 15*cos(8*x) + 20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(12*x) - cos(12*x)^2 + 12*(15*cos(8*x) - 20*cos(6*x) + 15*cos(4*x) - 6*cos(2*x) + 1)*cos(10*x) - 36*cos(10*x)^2 + 30*(20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(8*x) - 225*cos(8*x)^2 + 40*(15*cos(4*x) - 6*cos(2*x) + 1)*cos(6*x) - 400*cos(6*x)^2 + 30*(6*cos(2*x) - 1)*cos(4*x) - 225*cos(4*x)^2 - 36*cos(2*x)^2 + 2*(6*sin(10*x) - 15*sin(8*x) + 20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(12*x) - sin(12*x)^2 + 12*(15*sin(8*x) - 20*sin(6*x) + 15*sin(4*x) - 6*sin(2*x))*sin(10*x) - 36*sin(10*x)^2 + 30*(20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(8*x) - 225*sin(8*x)^2 + 120*(5*sin(4*x) - 2*sin(2*x))*sin(6*x) - 400*sin(6*x)^2 - 225*sin(4*x)^2 + 180*sin(4*x)*sin(2*x) - 36*sin(2*x)^2 + 12*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*(15*sin(11*x) - 85*sin(9*x) + 198*sin(7*x) + 198*sin(5*x) - 85*sin(3*x) + 15*sin(x))*sin(12*x) - 60*(6*sin(10*x) - 15*sin(8*x) + 20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(11*x) + 24*(85*sin(9*x) - 198*sin(7*x) - 198*sin(5*x) + 85*sin(3*x) - 15*sin(x))*sin(10*x) - 340*(15*sin(8*x) - 20*sin(6*x) + 15*sin(4*x) - 6*sin(2*x))*sin(9*x) + 60*(198*sin(7*x) + 198*sin(5*x) - 85*sin(3*x) + 15*sin(x))*sin(8*x) - 792*(20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(7*x) - 80*(198*sin(5*x) - 85*sin(3*x) + 15*sin(x))*sin(6*x) + 2376*(5*sin(4*x) - 2*sin(2*x))*sin(5*x) - 300*(17*sin(3*x) - 3*sin(x))*sin(4*x) + 2040*sin(3*x)*sin(2*x) - 360*sin(2*x)*sin(x) + 60*cos(x))/(2*(6*cos(10*x) - 15*cos(8*x) + 20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(12*x) - cos(12*x)^2 + 12*(15*cos(8*x) - 20*cos(6*x) + 15*cos(4*x) - 6*cos(2*x) + 1)*cos(10*x) - 36*cos(10*x)^2 + 30*(20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(8*x) - 225*cos(8*x)^2 + 40*(15*cos(4*x) - 6*cos(2*x) + 1)*cos(6*x) - 400*cos(6*x)^2 + 30*(6*cos(2*x) - 1)*cos(4*x) - 225*cos(4*x)^2 - 36*cos(2*x)^2 + 2*(6*sin(10*x) - 15*sin(8*x) + 20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(12*x) - sin(12*x)^2 + 12*(15*sin(8*x) - 20*sin(6*x) + 15*sin(4*x) - 6*sin(2*x))*sin(10*x) - 36*sin(10*x)^2 + 30*(20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(8*x) - 225*sin(8*x)^2 + 120*(5*sin(4*x) - 2*sin(2*x))*sin(6*x) - 400*sin(6*x)^2 - 225*sin(4*x)^2 + 180*sin(4*x)*sin(2*x) - 36*sin(2*x)^2 + 12*cos(2*x) - 1)","B",0
40,1,869,0,0.600682," ","integrate((csc(x)^2)^(5/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(3 \, \cos\left(7 \, x\right) - 11 \, \cos\left(5 \, x\right) - 11 \, \cos\left(3 \, x\right) + 3 \, \cos\left(x\right)\right)} \cos\left(8 \, x\right) - 12 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(7 \, x\right) + 16 \, {\left(11 \, \cos\left(5 \, x\right) + 11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \cos\left(6 \, x\right) - 44 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(5 \, x\right) - 24 \, {\left(11 \, \cos\left(3 \, x\right) - 3 \, \cos\left(x\right)\right)} \cos\left(4 \, x\right) + 44 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 48 \, \cos\left(2 \, x\right) \cos\left(x\right) + 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 36 \, \cos\left(4 \, x\right)^{2} - 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 16 \, \sin\left(6 \, x\right)^{2} - 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \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) - 3 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 36 \, \cos\left(4 \, x\right)^{2} - 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 16 \, \sin\left(6 \, x\right)^{2} - 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \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 \, {\left(3 \, \sin\left(7 \, x\right) - 11 \, \sin\left(5 \, x\right) - 11 \, \sin\left(3 \, x\right) + 3 \, \sin\left(x\right)\right)} \sin\left(8 \, x\right) - 24 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(7 \, x\right) + 16 \, {\left(11 \, \sin\left(5 \, x\right) + 11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \sin\left(6 \, x\right) - 88 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(5 \, x\right) - 24 \, {\left(11 \, \sin\left(3 \, x\right) - 3 \, \sin\left(x\right)\right)} \sin\left(4 \, x\right) + 176 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 48 \, \sin\left(2 \, x\right) \sin\left(x\right) + 12 \, \cos\left(x\right)}{16 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 36 \, \cos\left(4 \, x\right)^{2} - 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 16 \, \sin\left(6 \, x\right)^{2} - 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"-1/16*(4*(3*cos(7*x) - 11*cos(5*x) - 11*cos(3*x) + 3*cos(x))*cos(8*x) - 12*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(7*x) + 16*(11*cos(5*x) + 11*cos(3*x) - 3*cos(x))*cos(6*x) - 44*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(5*x) - 24*(11*cos(3*x) - 3*cos(x))*cos(4*x) + 44*(4*cos(2*x) - 1)*cos(3*x) - 48*cos(2*x)*cos(x) + 3*(2*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 12*(4*cos(2*x) - 1)*cos(4*x) - 36*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(3*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - 3*(2*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 12*(4*cos(2*x) - 1)*cos(4*x) - 36*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(3*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*(3*sin(7*x) - 11*sin(5*x) - 11*sin(3*x) + 3*sin(x))*sin(8*x) - 24*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(7*x) + 16*(11*sin(5*x) + 11*sin(3*x) - 3*sin(x))*sin(6*x) - 88*(3*sin(4*x) - 2*sin(2*x))*sin(5*x) - 24*(11*sin(3*x) - 3*sin(x))*sin(4*x) + 176*sin(3*x)*sin(2*x) - 48*sin(2*x)*sin(x) + 12*cos(x))/(2*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 12*(4*cos(2*x) - 1)*cos(4*x) - 36*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(3*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1)","B",0
41,1,300,0,0.574037," ","integrate((csc(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) \cos\left(x\right) + {\left(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\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(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\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + 4 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 8 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 8 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \cos\left(x\right)}{4 \, {\left(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\right)}}"," ",0,"-1/4*(4*(cos(3*x) + cos(x))*cos(4*x) - 4*(2*cos(2*x) - 1)*cos(3*x) - 8*cos(2*x)*cos(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)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (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)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*(sin(3*x) + sin(x))*sin(4*x) - 8*sin(3*x)*sin(2*x) - 8*sin(2*x)*sin(x) + 4*cos(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
42,1,35,0,0.578871," ","integrate((csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
43,1,10,0,0.571019," ","integrate(1/(csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{\tan\left(x\right)^{2} + 1}}"," ",0,"-1/sqrt(tan(x)^2 + 1)","A",0
44,1,11,0,0.515152," ","integrate(1/(csc(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{12} \, \cos\left(3 \, x\right) - \frac{3}{4} \, \cos\left(x\right)"," ",0,"1/12*cos(3*x) - 3/4*cos(x)","A",0
45,1,17,0,0.679572," ","integrate(1/(csc(x)^2)^(5/2),x, algorithm=""maxima"")","-\frac{1}{80} \, \cos\left(5 \, x\right) + \frac{5}{48} \, \cos\left(3 \, x\right) - \frac{5}{8} \, \cos\left(x\right)"," ",0,"-1/80*cos(5*x) + 5/48*cos(3*x) - 5/8*cos(x)","A",0
46,1,23,0,0.524672," ","integrate(1/(csc(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{1}{448} \, \cos\left(7 \, x\right) - \frac{7}{320} \, \cos\left(5 \, x\right) + \frac{7}{64} \, \cos\left(3 \, x\right) - \frac{35}{64} \, \cos\left(x\right)"," ",0,"1/448*cos(7*x) - 7/320*cos(5*x) + 7/64*cos(3*x) - 35/64*cos(x)","A",0
47,1,2183,0,4.136900," ","integrate((a*csc(x)^2)^(7/2),x, algorithm=""maxima"")","\frac{{\left(1020 \, a^{3} \cos\left(3 \, x\right) \sin\left(2 \, x\right) - 180 \, a^{3} \cos\left(x\right) \sin\left(2 \, x\right) + 180 \, a^{3} \cos\left(2 \, x\right) \sin\left(x\right) - 30 \, a^{3} \sin\left(x\right) + 15 \, {\left(a^{3} \cos\left(12 \, x\right)^{2} + 36 \, a^{3} \cos\left(10 \, x\right)^{2} + 225 \, a^{3} \cos\left(8 \, x\right)^{2} + 400 \, a^{3} \cos\left(6 \, x\right)^{2} + 225 \, a^{3} \cos\left(4 \, x\right)^{2} + 36 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(12 \, x\right)^{2} + 36 \, a^{3} \sin\left(10 \, x\right)^{2} + 225 \, a^{3} \sin\left(8 \, x\right)^{2} + 400 \, a^{3} \sin\left(6 \, x\right)^{2} + 225 \, a^{3} \sin\left(4 \, x\right)^{2} - 180 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, a^{3} \sin\left(2 \, x\right)^{2} - 12 \, a^{3} \cos\left(2 \, x\right) + a^{3} - 2 \, {\left(6 \, a^{3} \cos\left(10 \, x\right) - 15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) - 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(12 \, x\right) - 12 \, {\left(15 \, a^{3} \cos\left(8 \, x\right) - 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) - 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(10 \, x\right) - 30 \, {\left(20 \, a^{3} \cos\left(6 \, x\right) - 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(8 \, x\right) - 40 \, {\left(15 \, a^{3} \cos\left(4 \, x\right) - 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(6 \, x\right) - 30 \, {\left(6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(4 \, x\right) - 2 \, {\left(6 \, a^{3} \sin\left(10 \, x\right) - 15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) - 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) - 12 \, {\left(15 \, a^{3} \sin\left(8 \, x\right) - 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) - 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) - 30 \, {\left(20 \, a^{3} \sin\left(6 \, x\right) - 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 120 \, {\left(5 \, a^{3} \sin\left(4 \, x\right) - 2 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 15 \, {\left(a^{3} \cos\left(12 \, x\right)^{2} + 36 \, a^{3} \cos\left(10 \, x\right)^{2} + 225 \, a^{3} \cos\left(8 \, x\right)^{2} + 400 \, a^{3} \cos\left(6 \, x\right)^{2} + 225 \, a^{3} \cos\left(4 \, x\right)^{2} + 36 \, a^{3} \cos\left(2 \, x\right)^{2} + a^{3} \sin\left(12 \, x\right)^{2} + 36 \, a^{3} \sin\left(10 \, x\right)^{2} + 225 \, a^{3} \sin\left(8 \, x\right)^{2} + 400 \, a^{3} \sin\left(6 \, x\right)^{2} + 225 \, a^{3} \sin\left(4 \, x\right)^{2} - 180 \, a^{3} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 36 \, a^{3} \sin\left(2 \, x\right)^{2} - 12 \, a^{3} \cos\left(2 \, x\right) + a^{3} - 2 \, {\left(6 \, a^{3} \cos\left(10 \, x\right) - 15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) - 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(12 \, x\right) - 12 \, {\left(15 \, a^{3} \cos\left(8 \, x\right) - 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) - 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(10 \, x\right) - 30 \, {\left(20 \, a^{3} \cos\left(6 \, x\right) - 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(8 \, x\right) - 40 \, {\left(15 \, a^{3} \cos\left(4 \, x\right) - 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \cos\left(6 \, x\right) - 30 \, {\left(6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \cos\left(4 \, x\right) - 2 \, {\left(6 \, a^{3} \sin\left(10 \, x\right) - 15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) - 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) - 12 \, {\left(15 \, a^{3} \sin\left(8 \, x\right) - 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) - 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) - 30 \, {\left(20 \, a^{3} \sin\left(6 \, x\right) - 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 120 \, {\left(5 \, a^{3} \sin\left(4 \, x\right) - 2 \, a^{3} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) - 2 \, {\left(15 \, a^{3} \sin\left(11 \, x\right) - 85 \, a^{3} \sin\left(9 \, x\right) + 198 \, a^{3} \sin\left(7 \, x\right) + 198 \, a^{3} \sin\left(5 \, x\right) - 85 \, a^{3} \sin\left(3 \, x\right) + 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(12 \, x\right) - 30 \, {\left(6 \, a^{3} \sin\left(10 \, x\right) - 15 \, a^{3} \sin\left(8 \, x\right) + 20 \, a^{3} \sin\left(6 \, x\right) - 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(11 \, x\right) - 12 \, {\left(85 \, a^{3} \sin\left(9 \, x\right) - 198 \, a^{3} \sin\left(7 \, x\right) - 198 \, a^{3} \sin\left(5 \, x\right) + 85 \, a^{3} \sin\left(3 \, x\right) - 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(10 \, x\right) - 170 \, {\left(15 \, a^{3} \sin\left(8 \, x\right) - 20 \, a^{3} \sin\left(6 \, x\right) + 15 \, a^{3} \sin\left(4 \, x\right) - 6 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(9 \, x\right) - 30 \, {\left(198 \, a^{3} \sin\left(7 \, x\right) + 198 \, a^{3} \sin\left(5 \, x\right) - 85 \, a^{3} \sin\left(3 \, x\right) + 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 396 \, {\left(20 \, a^{3} \sin\left(6 \, x\right) - 15 \, a^{3} \sin\left(4 \, x\right) + 6 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) + 40 \, {\left(198 \, a^{3} \sin\left(5 \, x\right) - 85 \, a^{3} \sin\left(3 \, x\right) + 15 \, a^{3} \sin\left(x\right)\right)} \cos\left(6 \, x\right) + 1188 \, {\left(5 \, a^{3} \sin\left(4 \, x\right) - 2 \, a^{3} \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) + 150 \, {\left(17 \, a^{3} \sin\left(3 \, x\right) - 3 \, a^{3} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 2 \, {\left(15 \, a^{3} \cos\left(11 \, x\right) - 85 \, a^{3} \cos\left(9 \, x\right) + 198 \, a^{3} \cos\left(7 \, x\right) + 198 \, a^{3} \cos\left(5 \, x\right) - 85 \, a^{3} \cos\left(3 \, x\right) + 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(12 \, x\right) + 30 \, {\left(6 \, a^{3} \cos\left(10 \, x\right) - 15 \, a^{3} \cos\left(8 \, x\right) + 20 \, a^{3} \cos\left(6 \, x\right) - 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \sin\left(11 \, x\right) + 12 \, {\left(85 \, a^{3} \cos\left(9 \, x\right) - 198 \, a^{3} \cos\left(7 \, x\right) - 198 \, a^{3} \cos\left(5 \, x\right) + 85 \, a^{3} \cos\left(3 \, x\right) - 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(10 \, x\right) + 170 \, {\left(15 \, a^{3} \cos\left(8 \, x\right) - 20 \, a^{3} \cos\left(6 \, x\right) + 15 \, a^{3} \cos\left(4 \, x\right) - 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(9 \, x\right) + 30 \, {\left(198 \, a^{3} \cos\left(7 \, x\right) + 198 \, a^{3} \cos\left(5 \, x\right) - 85 \, a^{3} \cos\left(3 \, x\right) + 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 396 \, {\left(20 \, a^{3} \cos\left(6 \, x\right) - 15 \, a^{3} \cos\left(4 \, x\right) + 6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \sin\left(7 \, x\right) - 40 \, {\left(198 \, a^{3} \cos\left(5 \, x\right) - 85 \, a^{3} \cos\left(3 \, x\right) + 15 \, a^{3} \cos\left(x\right)\right)} \sin\left(6 \, x\right) - 396 \, {\left(15 \, a^{3} \cos\left(4 \, x\right) - 6 \, a^{3} \cos\left(2 \, x\right) + a^{3}\right)} \sin\left(5 \, x\right) - 150 \, {\left(17 \, a^{3} \cos\left(3 \, x\right) - 3 \, a^{3} \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 170 \, {\left(6 \, a^{3} \cos\left(2 \, x\right) - a^{3}\right)} \sin\left(3 \, x\right)\right)} \sqrt{-a}}{48 \, {\left(2 \, {\left(6 \, \cos\left(10 \, x\right) - 15 \, \cos\left(8 \, x\right) + 20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(12 \, x\right) - \cos\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \cos\left(8 \, x\right) - 20 \, \cos\left(6 \, x\right) + 15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(10 \, x\right) - 36 \, \cos\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \cos\left(6 \, x\right) - 15 \, \cos\left(4 \, x\right) + 6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - 225 \, \cos\left(8 \, x\right)^{2} + 40 \, {\left(15 \, \cos\left(4 \, x\right) - 6 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 400 \, \cos\left(6 \, x\right)^{2} + 30 \, {\left(6 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 225 \, \cos\left(4 \, x\right)^{2} - 36 \, \cos\left(2 \, x\right)^{2} + 2 \, {\left(6 \, \sin\left(10 \, x\right) - 15 \, \sin\left(8 \, x\right) + 20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(12 \, x\right) - \sin\left(12 \, x\right)^{2} + 12 \, {\left(15 \, \sin\left(8 \, x\right) - 20 \, \sin\left(6 \, x\right) + 15 \, \sin\left(4 \, x\right) - 6 \, \sin\left(2 \, x\right)\right)} \sin\left(10 \, x\right) - 36 \, \sin\left(10 \, x\right)^{2} + 30 \, {\left(20 \, \sin\left(6 \, x\right) - 15 \, \sin\left(4 \, x\right) + 6 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 225 \, \sin\left(8 \, x\right)^{2} + 120 \, {\left(5 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 400 \, \sin\left(6 \, x\right)^{2} - 225 \, \sin\left(4 \, x\right)^{2} + 180 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 36 \, \sin\left(2 \, x\right)^{2} + 12 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"1/48*(1020*a^3*cos(3*x)*sin(2*x) - 180*a^3*cos(x)*sin(2*x) + 180*a^3*cos(2*x)*sin(x) - 30*a^3*sin(x) + 15*(a^3*cos(12*x)^2 + 36*a^3*cos(10*x)^2 + 225*a^3*cos(8*x)^2 + 400*a^3*cos(6*x)^2 + 225*a^3*cos(4*x)^2 + 36*a^3*cos(2*x)^2 + a^3*sin(12*x)^2 + 36*a^3*sin(10*x)^2 + 225*a^3*sin(8*x)^2 + 400*a^3*sin(6*x)^2 + 225*a^3*sin(4*x)^2 - 180*a^3*sin(4*x)*sin(2*x) + 36*a^3*sin(2*x)^2 - 12*a^3*cos(2*x) + a^3 - 2*(6*a^3*cos(10*x) - 15*a^3*cos(8*x) + 20*a^3*cos(6*x) - 15*a^3*cos(4*x) + 6*a^3*cos(2*x) - a^3)*cos(12*x) - 12*(15*a^3*cos(8*x) - 20*a^3*cos(6*x) + 15*a^3*cos(4*x) - 6*a^3*cos(2*x) + a^3)*cos(10*x) - 30*(20*a^3*cos(6*x) - 15*a^3*cos(4*x) + 6*a^3*cos(2*x) - a^3)*cos(8*x) - 40*(15*a^3*cos(4*x) - 6*a^3*cos(2*x) + a^3)*cos(6*x) - 30*(6*a^3*cos(2*x) - a^3)*cos(4*x) - 2*(6*a^3*sin(10*x) - 15*a^3*sin(8*x) + 20*a^3*sin(6*x) - 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(12*x) - 12*(15*a^3*sin(8*x) - 20*a^3*sin(6*x) + 15*a^3*sin(4*x) - 6*a^3*sin(2*x))*sin(10*x) - 30*(20*a^3*sin(6*x) - 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(8*x) - 120*(5*a^3*sin(4*x) - 2*a^3*sin(2*x))*sin(6*x))*arctan2(sin(x), cos(x) + 1) - 15*(a^3*cos(12*x)^2 + 36*a^3*cos(10*x)^2 + 225*a^3*cos(8*x)^2 + 400*a^3*cos(6*x)^2 + 225*a^3*cos(4*x)^2 + 36*a^3*cos(2*x)^2 + a^3*sin(12*x)^2 + 36*a^3*sin(10*x)^2 + 225*a^3*sin(8*x)^2 + 400*a^3*sin(6*x)^2 + 225*a^3*sin(4*x)^2 - 180*a^3*sin(4*x)*sin(2*x) + 36*a^3*sin(2*x)^2 - 12*a^3*cos(2*x) + a^3 - 2*(6*a^3*cos(10*x) - 15*a^3*cos(8*x) + 20*a^3*cos(6*x) - 15*a^3*cos(4*x) + 6*a^3*cos(2*x) - a^3)*cos(12*x) - 12*(15*a^3*cos(8*x) - 20*a^3*cos(6*x) + 15*a^3*cos(4*x) - 6*a^3*cos(2*x) + a^3)*cos(10*x) - 30*(20*a^3*cos(6*x) - 15*a^3*cos(4*x) + 6*a^3*cos(2*x) - a^3)*cos(8*x) - 40*(15*a^3*cos(4*x) - 6*a^3*cos(2*x) + a^3)*cos(6*x) - 30*(6*a^3*cos(2*x) - a^3)*cos(4*x) - 2*(6*a^3*sin(10*x) - 15*a^3*sin(8*x) + 20*a^3*sin(6*x) - 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(12*x) - 12*(15*a^3*sin(8*x) - 20*a^3*sin(6*x) + 15*a^3*sin(4*x) - 6*a^3*sin(2*x))*sin(10*x) - 30*(20*a^3*sin(6*x) - 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*sin(8*x) - 120*(5*a^3*sin(4*x) - 2*a^3*sin(2*x))*sin(6*x))*arctan2(sin(x), cos(x) - 1) - 2*(15*a^3*sin(11*x) - 85*a^3*sin(9*x) + 198*a^3*sin(7*x) + 198*a^3*sin(5*x) - 85*a^3*sin(3*x) + 15*a^3*sin(x))*cos(12*x) - 30*(6*a^3*sin(10*x) - 15*a^3*sin(8*x) + 20*a^3*sin(6*x) - 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*cos(11*x) - 12*(85*a^3*sin(9*x) - 198*a^3*sin(7*x) - 198*a^3*sin(5*x) + 85*a^3*sin(3*x) - 15*a^3*sin(x))*cos(10*x) - 170*(15*a^3*sin(8*x) - 20*a^3*sin(6*x) + 15*a^3*sin(4*x) - 6*a^3*sin(2*x))*cos(9*x) - 30*(198*a^3*sin(7*x) + 198*a^3*sin(5*x) - 85*a^3*sin(3*x) + 15*a^3*sin(x))*cos(8*x) - 396*(20*a^3*sin(6*x) - 15*a^3*sin(4*x) + 6*a^3*sin(2*x))*cos(7*x) + 40*(198*a^3*sin(5*x) - 85*a^3*sin(3*x) + 15*a^3*sin(x))*cos(6*x) + 1188*(5*a^3*sin(4*x) - 2*a^3*sin(2*x))*cos(5*x) + 150*(17*a^3*sin(3*x) - 3*a^3*sin(x))*cos(4*x) + 2*(15*a^3*cos(11*x) - 85*a^3*cos(9*x) + 198*a^3*cos(7*x) + 198*a^3*cos(5*x) - 85*a^3*cos(3*x) + 15*a^3*cos(x))*sin(12*x) + 30*(6*a^3*cos(10*x) - 15*a^3*cos(8*x) + 20*a^3*cos(6*x) - 15*a^3*cos(4*x) + 6*a^3*cos(2*x) - a^3)*sin(11*x) + 12*(85*a^3*cos(9*x) - 198*a^3*cos(7*x) - 198*a^3*cos(5*x) + 85*a^3*cos(3*x) - 15*a^3*cos(x))*sin(10*x) + 170*(15*a^3*cos(8*x) - 20*a^3*cos(6*x) + 15*a^3*cos(4*x) - 6*a^3*cos(2*x) + a^3)*sin(9*x) + 30*(198*a^3*cos(7*x) + 198*a^3*cos(5*x) - 85*a^3*cos(3*x) + 15*a^3*cos(x))*sin(8*x) + 396*(20*a^3*cos(6*x) - 15*a^3*cos(4*x) + 6*a^3*cos(2*x) - a^3)*sin(7*x) - 40*(198*a^3*cos(5*x) - 85*a^3*cos(3*x) + 15*a^3*cos(x))*sin(6*x) - 396*(15*a^3*cos(4*x) - 6*a^3*cos(2*x) + a^3)*sin(5*x) - 150*(17*a^3*cos(3*x) - 3*a^3*cos(x))*sin(4*x) - 170*(6*a^3*cos(2*x) - a^3)*sin(3*x))*sqrt(-a)/(2*(6*cos(10*x) - 15*cos(8*x) + 20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(12*x) - cos(12*x)^2 + 12*(15*cos(8*x) - 20*cos(6*x) + 15*cos(4*x) - 6*cos(2*x) + 1)*cos(10*x) - 36*cos(10*x)^2 + 30*(20*cos(6*x) - 15*cos(4*x) + 6*cos(2*x) - 1)*cos(8*x) - 225*cos(8*x)^2 + 40*(15*cos(4*x) - 6*cos(2*x) + 1)*cos(6*x) - 400*cos(6*x)^2 + 30*(6*cos(2*x) - 1)*cos(4*x) - 225*cos(4*x)^2 - 36*cos(2*x)^2 + 2*(6*sin(10*x) - 15*sin(8*x) + 20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(12*x) - sin(12*x)^2 + 12*(15*sin(8*x) - 20*sin(6*x) + 15*sin(4*x) - 6*sin(2*x))*sin(10*x) - 36*sin(10*x)^2 + 30*(20*sin(6*x) - 15*sin(4*x) + 6*sin(2*x))*sin(8*x) - 225*sin(8*x)^2 + 120*(5*sin(4*x) - 2*sin(2*x))*sin(6*x) - 400*sin(6*x)^2 - 225*sin(4*x)^2 + 180*sin(4*x)*sin(2*x) - 36*sin(2*x)^2 + 12*cos(2*x) - 1)","B",0
48,1,1113,0,0.868207," ","integrate((a*csc(x)^2)^(5/2),x, algorithm=""maxima"")","\frac{{\left(88 \, a^{2} \cos\left(3 \, x\right) \sin\left(2 \, x\right) - 24 \, a^{2} \cos\left(x\right) \sin\left(2 \, x\right) + 24 \, a^{2} \cos\left(2 \, x\right) \sin\left(x\right) - 6 \, a^{2} \sin\left(x\right) + 3 \, {\left(a^{2} \cos\left(8 \, x\right)^{2} + 16 \, a^{2} \cos\left(6 \, x\right)^{2} + 36 \, a^{2} \cos\left(4 \, x\right)^{2} + 16 \, a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(8 \, x\right)^{2} + 16 \, a^{2} \sin\left(6 \, x\right)^{2} + 36 \, a^{2} \sin\left(4 \, x\right)^{2} - 48 \, a^{2} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a^{2} \sin\left(2 \, x\right)^{2} - 8 \, a^{2} \cos\left(2 \, x\right) + a^{2} - 2 \, {\left(4 \, a^{2} \cos\left(6 \, x\right) - 6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \cos\left(8 \, x\right) - 8 \, {\left(6 \, a^{2} \cos\left(4 \, x\right) - 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(6 \, x\right) - 12 \, {\left(4 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, a^{2} \sin\left(6 \, x\right) - 3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 16 \, {\left(3 \, a^{2} \sin\left(4 \, x\right) - 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - 3 \, {\left(a^{2} \cos\left(8 \, x\right)^{2} + 16 \, a^{2} \cos\left(6 \, x\right)^{2} + 36 \, a^{2} \cos\left(4 \, x\right)^{2} + 16 \, a^{2} \cos\left(2 \, x\right)^{2} + a^{2} \sin\left(8 \, x\right)^{2} + 16 \, a^{2} \sin\left(6 \, x\right)^{2} + 36 \, a^{2} \sin\left(4 \, x\right)^{2} - 48 \, a^{2} \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 16 \, a^{2} \sin\left(2 \, x\right)^{2} - 8 \, a^{2} \cos\left(2 \, x\right) + a^{2} - 2 \, {\left(4 \, a^{2} \cos\left(6 \, x\right) - 6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \cos\left(8 \, x\right) - 8 \, {\left(6 \, a^{2} \cos\left(4 \, x\right) - 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \cos\left(6 \, x\right) - 12 \, {\left(4 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, a^{2} \sin\left(6 \, x\right) - 3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - 16 \, {\left(3 \, a^{2} \sin\left(4 \, x\right) - 2 \, a^{2} \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) - 2 \, {\left(3 \, a^{2} \sin\left(7 \, x\right) - 11 \, a^{2} \sin\left(5 \, x\right) - 11 \, a^{2} \sin\left(3 \, x\right) + 3 \, a^{2} \sin\left(x\right)\right)} \cos\left(8 \, x\right) - 12 \, {\left(2 \, a^{2} \sin\left(6 \, x\right) - 3 \, a^{2} \sin\left(4 \, x\right) + 2 \, a^{2} \sin\left(2 \, x\right)\right)} \cos\left(7 \, x\right) - 8 \, {\left(11 \, a^{2} \sin\left(5 \, x\right) + 11 \, a^{2} \sin\left(3 \, x\right) - 3 \, a^{2} \sin\left(x\right)\right)} \cos\left(6 \, x\right) - 44 \, {\left(3 \, a^{2} \sin\left(4 \, x\right) - 2 \, a^{2} \sin\left(2 \, x\right)\right)} \cos\left(5 \, x\right) + 12 \, {\left(11 \, a^{2} \sin\left(3 \, x\right) - 3 \, a^{2} \sin\left(x\right)\right)} \cos\left(4 \, x\right) + 2 \, {\left(3 \, a^{2} \cos\left(7 \, x\right) - 11 \, a^{2} \cos\left(5 \, x\right) - 11 \, a^{2} \cos\left(3 \, x\right) + 3 \, a^{2} \cos\left(x\right)\right)} \sin\left(8 \, x\right) + 6 \, {\left(4 \, a^{2} \cos\left(6 \, x\right) - 6 \, a^{2} \cos\left(4 \, x\right) + 4 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \sin\left(7 \, x\right) + 8 \, {\left(11 \, a^{2} \cos\left(5 \, x\right) + 11 \, a^{2} \cos\left(3 \, x\right) - 3 \, a^{2} \cos\left(x\right)\right)} \sin\left(6 \, x\right) + 22 \, {\left(6 \, a^{2} \cos\left(4 \, x\right) - 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)} \sin\left(5 \, x\right) - 12 \, {\left(11 \, a^{2} \cos\left(3 \, x\right) - 3 \, a^{2} \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 22 \, {\left(4 \, a^{2} \cos\left(2 \, x\right) - a^{2}\right)} \sin\left(3 \, x\right)\right)} \sqrt{-a}}{8 \, {\left(2 \, {\left(4 \, \cos\left(6 \, x\right) - 6 \, \cos\left(4 \, x\right) + 4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(8 \, x\right) - \cos\left(8 \, x\right)^{2} + 8 \, {\left(6 \, \cos\left(4 \, x\right) - 4 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(6 \, x\right) - 16 \, \cos\left(6 \, x\right)^{2} + 12 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - 36 \, \cos\left(4 \, x\right)^{2} - 16 \, \cos\left(2 \, x\right)^{2} + 4 \, {\left(2 \, \sin\left(6 \, x\right) - 3 \, \sin\left(4 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sin\left(8 \, x\right) - \sin\left(8 \, x\right)^{2} + 16 \, {\left(3 \, \sin\left(4 \, x\right) - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(6 \, x\right) - 16 \, \sin\left(6 \, x\right)^{2} - 36 \, \sin\left(4 \, x\right)^{2} + 48 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 16 \, \sin\left(2 \, x\right)^{2} + 8 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"1/8*(88*a^2*cos(3*x)*sin(2*x) - 24*a^2*cos(x)*sin(2*x) + 24*a^2*cos(2*x)*sin(x) - 6*a^2*sin(x) + 3*(a^2*cos(8*x)^2 + 16*a^2*cos(6*x)^2 + 36*a^2*cos(4*x)^2 + 16*a^2*cos(2*x)^2 + a^2*sin(8*x)^2 + 16*a^2*sin(6*x)^2 + 36*a^2*sin(4*x)^2 - 48*a^2*sin(4*x)*sin(2*x) + 16*a^2*sin(2*x)^2 - 8*a^2*cos(2*x) + a^2 - 2*(4*a^2*cos(6*x) - 6*a^2*cos(4*x) + 4*a^2*cos(2*x) - a^2)*cos(8*x) - 8*(6*a^2*cos(4*x) - 4*a^2*cos(2*x) + a^2)*cos(6*x) - 12*(4*a^2*cos(2*x) - a^2)*cos(4*x) - 4*(2*a^2*sin(6*x) - 3*a^2*sin(4*x) + 2*a^2*sin(2*x))*sin(8*x) - 16*(3*a^2*sin(4*x) - 2*a^2*sin(2*x))*sin(6*x))*arctan2(sin(x), cos(x) + 1) - 3*(a^2*cos(8*x)^2 + 16*a^2*cos(6*x)^2 + 36*a^2*cos(4*x)^2 + 16*a^2*cos(2*x)^2 + a^2*sin(8*x)^2 + 16*a^2*sin(6*x)^2 + 36*a^2*sin(4*x)^2 - 48*a^2*sin(4*x)*sin(2*x) + 16*a^2*sin(2*x)^2 - 8*a^2*cos(2*x) + a^2 - 2*(4*a^2*cos(6*x) - 6*a^2*cos(4*x) + 4*a^2*cos(2*x) - a^2)*cos(8*x) - 8*(6*a^2*cos(4*x) - 4*a^2*cos(2*x) + a^2)*cos(6*x) - 12*(4*a^2*cos(2*x) - a^2)*cos(4*x) - 4*(2*a^2*sin(6*x) - 3*a^2*sin(4*x) + 2*a^2*sin(2*x))*sin(8*x) - 16*(3*a^2*sin(4*x) - 2*a^2*sin(2*x))*sin(6*x))*arctan2(sin(x), cos(x) - 1) - 2*(3*a^2*sin(7*x) - 11*a^2*sin(5*x) - 11*a^2*sin(3*x) + 3*a^2*sin(x))*cos(8*x) - 12*(2*a^2*sin(6*x) - 3*a^2*sin(4*x) + 2*a^2*sin(2*x))*cos(7*x) - 8*(11*a^2*sin(5*x) + 11*a^2*sin(3*x) - 3*a^2*sin(x))*cos(6*x) - 44*(3*a^2*sin(4*x) - 2*a^2*sin(2*x))*cos(5*x) + 12*(11*a^2*sin(3*x) - 3*a^2*sin(x))*cos(4*x) + 2*(3*a^2*cos(7*x) - 11*a^2*cos(5*x) - 11*a^2*cos(3*x) + 3*a^2*cos(x))*sin(8*x) + 6*(4*a^2*cos(6*x) - 6*a^2*cos(4*x) + 4*a^2*cos(2*x) - a^2)*sin(7*x) + 8*(11*a^2*cos(5*x) + 11*a^2*cos(3*x) - 3*a^2*cos(x))*sin(6*x) + 22*(6*a^2*cos(4*x) - 4*a^2*cos(2*x) + a^2)*sin(5*x) - 12*(11*a^2*cos(3*x) - 3*a^2*cos(x))*sin(4*x) - 22*(4*a^2*cos(2*x) - a^2)*sin(3*x))*sqrt(-a)/(2*(4*cos(6*x) - 6*cos(4*x) + 4*cos(2*x) - 1)*cos(8*x) - cos(8*x)^2 + 8*(6*cos(4*x) - 4*cos(2*x) + 1)*cos(6*x) - 16*cos(6*x)^2 + 12*(4*cos(2*x) - 1)*cos(4*x) - 36*cos(4*x)^2 - 16*cos(2*x)^2 + 4*(2*sin(6*x) - 3*sin(4*x) + 2*sin(2*x))*sin(8*x) - sin(8*x)^2 + 16*(3*sin(4*x) - 2*sin(2*x))*sin(6*x) - 16*sin(6*x)^2 - 36*sin(4*x)^2 + 48*sin(4*x)*sin(2*x) - 16*sin(2*x)^2 + 8*cos(2*x) - 1)","B",0
49,1,318,0,0.538804," ","integrate((a*csc(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, a \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 4 \, a \cos\left(x\right) \sin\left(2 \, x\right) - 4 \, a \cos\left(2 \, x\right) \sin\left(x\right) - {\left(a \cos\left(4 \, x\right)^{2} + 4 \, a \cos\left(2 \, x\right)^{2} + a \sin\left(4 \, x\right)^{2} - 4 \, a \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a \sin\left(2 \, x\right)^{2} - 2 \, {\left(2 \, a \cos\left(2 \, x\right) - a\right)} \cos\left(4 \, x\right) - 4 \, a \cos\left(2 \, x\right) + a\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + {\left(a \cos\left(4 \, x\right)^{2} + 4 \, a \cos\left(2 \, x\right)^{2} + a \sin\left(4 \, x\right)^{2} - 4 \, a \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, a \sin\left(2 \, x\right)^{2} - 2 \, {\left(2 \, a \cos\left(2 \, x\right) - a\right)} \cos\left(4 \, x\right) - 4 \, a \cos\left(2 \, x\right) + a\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) + 2 \, {\left(a \sin\left(3 \, x\right) + a \sin\left(x\right)\right)} \cos\left(4 \, x\right) - 2 \, {\left(a \cos\left(3 \, x\right) + a \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 2 \, {\left(2 \, a \cos\left(2 \, x\right) - a\right)} \sin\left(3 \, x\right) + 2 \, a \sin\left(x\right)\right)} \sqrt{-a}}{2 \, {\left(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\right)}}"," ",0,"-1/2*(4*a*cos(3*x)*sin(2*x) + 4*a*cos(x)*sin(2*x) - 4*a*cos(2*x)*sin(x) - (a*cos(4*x)^2 + 4*a*cos(2*x)^2 + a*sin(4*x)^2 - 4*a*sin(4*x)*sin(2*x) + 4*a*sin(2*x)^2 - 2*(2*a*cos(2*x) - a)*cos(4*x) - 4*a*cos(2*x) + a)*arctan2(sin(x), cos(x) + 1) + (a*cos(4*x)^2 + 4*a*cos(2*x)^2 + a*sin(4*x)^2 - 4*a*sin(4*x)*sin(2*x) + 4*a*sin(2*x)^2 - 2*(2*a*cos(2*x) - a)*cos(4*x) - 4*a*cos(2*x) + a)*arctan2(sin(x), cos(x) - 1) + 2*(a*sin(3*x) + a*sin(x))*cos(4*x) - 2*(a*cos(3*x) + a*cos(x))*sin(4*x) - 2*(2*a*cos(2*x) - a)*sin(3*x) + 2*a*sin(x))*sqrt(-a)/(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
50,1,24,0,0.789196," ","integrate((a*csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\sqrt{-a} {\left(\arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)}"," ",0,"-sqrt(-a)*(arctan2(sin(x), cos(x) + 1) - arctan2(sin(x), cos(x) - 1))","A",0
51,1,13,0,0.577621," ","integrate(1/(a*csc(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{\tan\left(x\right)^{2} + 1} \sqrt{a}}"," ",0,"-1/(sqrt(tan(x)^2 + 1)*sqrt(a))","A",0
52,0,0,0,0.000000," ","integrate(1/(a*csc(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \csc\left(x\right)^{2}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*csc(x)^2)^(-3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(1/(a*csc(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \csc\left(x\right)^{2}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*csc(x)^2)^(-5/2), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(a*csc(x)^2)^(7/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \csc\left(x\right)^{2}\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*csc(x)^2)^(-7/2), x)","F",0
55,0,0,0,0.000000," ","integrate((a*csc(x)^3)^(5/2),x, algorithm=""maxima"")","\int \left(a \csc\left(x\right)^{3}\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*csc(x)^3)^(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate((a*csc(x)^3)^(3/2),x, algorithm=""maxima"")","\int \left(a \csc\left(x\right)^{3}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*csc(x)^3)^(3/2), x)","F",0
57,0,0,0,0.000000," ","integrate((a*csc(x)^3)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a*csc(x)^3), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(a*csc(x)^3)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \csc\left(x\right)^{3}}}\,{d x}"," ",0,"integrate(1/sqrt(a*csc(x)^3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(a*csc(x)^3)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \csc\left(x\right)^{3}\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*csc(x)^3)^(-3/2), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(a*csc(x)^3)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\left(a \csc\left(x\right)^{3}\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*csc(x)^3)^(-5/2), x)","F",0
61,1,66,0,0.439042," ","integrate((a*csc(x)^4)^(7/2),x, algorithm=""maxima"")","-\frac{3003 \, a^{\frac{7}{2}} \tan\left(x\right)^{12} + 6006 \, a^{\frac{7}{2}} \tan\left(x\right)^{10} + 9009 \, a^{\frac{7}{2}} \tan\left(x\right)^{8} + 8580 \, a^{\frac{7}{2}} \tan\left(x\right)^{6} + 5005 \, a^{\frac{7}{2}} \tan\left(x\right)^{4} + 1638 \, a^{\frac{7}{2}} \tan\left(x\right)^{2} + 231 \, a^{\frac{7}{2}}}{3003 \, \tan\left(x\right)^{13}}"," ",0,"-1/3003*(3003*a^(7/2)*tan(x)^12 + 6006*a^(7/2)*tan(x)^10 + 9009*a^(7/2)*tan(x)^8 + 8580*a^(7/2)*tan(x)^6 + 5005*a^(7/2)*tan(x)^4 + 1638*a^(7/2)*tan(x)^2 + 231*a^(7/2))/tan(x)^13","A",0
62,1,48,0,0.435680," ","integrate((a*csc(x)^4)^(5/2),x, algorithm=""maxima"")","-\frac{315 \, a^{\frac{5}{2}} \tan\left(x\right)^{8} + 420 \, a^{\frac{5}{2}} \tan\left(x\right)^{6} + 378 \, a^{\frac{5}{2}} \tan\left(x\right)^{4} + 180 \, a^{\frac{5}{2}} \tan\left(x\right)^{2} + 35 \, a^{\frac{5}{2}}}{315 \, \tan\left(x\right)^{9}}"," ",0,"-1/315*(315*a^(5/2)*tan(x)^8 + 420*a^(5/2)*tan(x)^6 + 378*a^(5/2)*tan(x)^4 + 180*a^(5/2)*tan(x)^2 + 35*a^(5/2))/tan(x)^9","A",0
63,1,30,0,0.476509," ","integrate((a*csc(x)^4)^(3/2),x, algorithm=""maxima"")","-\frac{15 \, a^{\frac{3}{2}} \tan\left(x\right)^{4} + 10 \, a^{\frac{3}{2}} \tan\left(x\right)^{2} + 3 \, a^{\frac{3}{2}}}{15 \, \tan\left(x\right)^{5}}"," ",0,"-1/15*(15*a^(3/2)*tan(x)^4 + 10*a^(3/2)*tan(x)^2 + 3*a^(3/2))/tan(x)^5","A",0
64,1,9,0,0.583638," ","integrate((a*csc(x)^4)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a}}{\tan\left(x\right)}"," ",0,"-sqrt(a)/tan(x)","A",0
65,1,25,0,0.468482," ","integrate(1/(a*csc(x)^4)^(1/2),x, algorithm=""maxima"")","\frac{x}{2 \, \sqrt{a}} - \frac{\tan\left(x\right)}{2 \, {\left(\sqrt{a} \tan\left(x\right)^{2} + \sqrt{a}\right)}}"," ",0,"1/2*x/sqrt(a) - 1/2*tan(x)/(sqrt(a)*tan(x)^2 + sqrt(a))","A",0
66,1,58,0,0.453161," ","integrate(1/(a*csc(x)^4)^(3/2),x, algorithm=""maxima"")","-\frac{33 \, \tan\left(x\right)^{5} + 40 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{48 \, {\left(a^{\frac{3}{2}} \tan\left(x\right)^{6} + 3 \, a^{\frac{3}{2}} \tan\left(x\right)^{4} + 3 \, a^{\frac{3}{2}} \tan\left(x\right)^{2} + a^{\frac{3}{2}}\right)}} + \frac{5 \, x}{16 \, a^{\frac{3}{2}}}"," ",0,"-1/48*(33*tan(x)^5 + 40*tan(x)^3 + 15*tan(x))/(a^(3/2)*tan(x)^6 + 3*a^(3/2)*tan(x)^4 + 3*a^(3/2)*tan(x)^2 + a^(3/2)) + 5/16*x/a^(3/2)","A",0
67,1,88,0,0.506354," ","integrate(1/(a*csc(x)^4)^(5/2),x, algorithm=""maxima"")","-\frac{965 \, \tan\left(x\right)^{9} + 2370 \, \tan\left(x\right)^{7} + 2688 \, \tan\left(x\right)^{5} + 1470 \, \tan\left(x\right)^{3} + 315 \, \tan\left(x\right)}{1280 \, {\left(a^{\frac{5}{2}} \tan\left(x\right)^{10} + 5 \, a^{\frac{5}{2}} \tan\left(x\right)^{8} + 10 \, a^{\frac{5}{2}} \tan\left(x\right)^{6} + 10 \, a^{\frac{5}{2}} \tan\left(x\right)^{4} + 5 \, a^{\frac{5}{2}} \tan\left(x\right)^{2} + a^{\frac{5}{2}}\right)}} + \frac{63 \, x}{256 \, a^{\frac{5}{2}}}"," ",0,"-1/1280*(965*tan(x)^9 + 2370*tan(x)^7 + 2688*tan(x)^5 + 1470*tan(x)^3 + 315*tan(x))/(a^(5/2)*tan(x)^10 + 5*a^(5/2)*tan(x)^8 + 10*a^(5/2)*tan(x)^6 + 10*a^(5/2)*tan(x)^4 + 5*a^(5/2)*tan(x)^2 + a^(5/2)) + 63/256*x/a^(5/2)","A",0
68,0,0,0,0.000000," ","integrate(((b*csc(d*x+c))^p)^n,x, algorithm=""maxima"")","\int {\left(\left(b \csc\left(d x + c\right)\right)^{p}\right)}^{n}\,{d x}"," ",0,"integrate(((b*csc(d*x + c))^p)^n, x)","F",0
69,0,0,0,0.000000," ","integrate((a*(b*csc(d*x+c))^p)^n,x, algorithm=""maxima"")","\int \left(\left(b \csc\left(d x + c\right)\right)^{p} a\right)^{n}\,{d x}"," ",0,"integrate(((b*csc(d*x + c))^p*a)^n, x)","F",0
70,0,0,0,0.000000," ","integrate((a*csc(f*x+e))^m*(b*csc(f*x+e))^n,x, algorithm=""maxima"")","\int \left(a \csc\left(f x + e\right)\right)^{m} \left(b \csc\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*csc(f*x + e))^m*(b*csc(f*x + e))^n, x)","F",0
