1,1,30,0,0.672239," ","integrate(csc(b*x+a),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)}{2 \, b}"," ",0,"-1/2*(log(1/2*cos(b*x + a) + 1/2) - log(-1/2*cos(b*x + a) + 1/2))/b","B",0
2,1,19,0,0.444499," ","integrate(csc(b*x+a)^2,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)}{b \sin\left(b x + a\right)}"," ",0,"-cos(b*x + a)/(b*sin(b*x + a))","A",0
3,1,72,0,0.781375," ","integrate(csc(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 2 \, \cos\left(b x + a\right)}{4 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/4*((cos(b*x + a)^2 - 1)*log(1/2*cos(b*x + a) + 1/2) - (cos(b*x + a)^2 - 1)*log(-1/2*cos(b*x + a) + 1/2) - 2*cos(b*x + a))/(b*cos(b*x + a)^2 - b)","B",0
4,1,45,0,0.688143," ","integrate(csc(b*x+a)^4,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/3*(2*cos(b*x + a)^3 - 3*cos(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
5,1,112,0,0.493720," ","integrate(csc(b*x+a)^5,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{3} - 3 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 10 \, \cos\left(b x + a\right)}{16 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)}}"," ",0,"1/16*(6*cos(b*x + a)^3 - 3*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(1/2*cos(b*x + a) + 1/2) + 3*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*log(-1/2*cos(b*x + a) + 1/2) - 10*cos(b*x + a))/(b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)","B",0
6,1,64,0,0.530174," ","integrate(csc(b*x+a)^6,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{5} - 20 \, \cos\left(b x + a\right)^{3} + 15 \, \cos\left(b x + a\right)}{15 \, {\left(b \cos\left(b x + a\right)^{4} - 2 \, b \cos\left(b x + a\right)^{2} + b\right)} \sin\left(b x + a\right)}"," ",0,"-1/15*(8*cos(b*x + a)^5 - 20*cos(b*x + a)^3 + 15*cos(b*x + a))/((b*cos(b*x + a)^4 - 2*b*cos(b*x + a)^2 + b)*sin(b*x + a))","A",0
7,1,155,0,0.756846," ","integrate(csc(b*x+a)^7,x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x + a\right)^{5} - 80 \, \cos\left(b x + a\right)^{3} - 15 \, {\left(\cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 66 \, \cos\left(b x + a\right)}{96 \, {\left(b \cos\left(b x + a\right)^{6} - 3 \, b \cos\left(b x + a\right)^{4} + 3 \, b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/96*(30*cos(b*x + a)^5 - 80*cos(b*x + a)^3 - 15*(cos(b*x + a)^6 - 3*cos(b*x + a)^4 + 3*cos(b*x + a)^2 - 1)*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^6 - 3*cos(b*x + a)^4 + 3*cos(b*x + a)^2 - 1)*log(-1/2*cos(b*x + a) + 1/2) + 66*cos(b*x + a))/(b*cos(b*x + a)^6 - 3*b*cos(b*x + a)^4 + 3*b*cos(b*x + a)^2 - b)","B",0
8,1,87,0,0.629132," ","integrate(csc(b*x+a)^8,x, algorithm=""fricas"")","-\frac{16 \, \cos\left(b x + a\right)^{7} - 56 \, \cos\left(b x + a\right)^{5} + 70 \, \cos\left(b x + a\right)^{3} - 35 \, \cos\left(b x + a\right)}{35 \, {\left(b \cos\left(b x + a\right)^{6} - 3 \, b \cos\left(b x + a\right)^{4} + 3 \, b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/35*(16*cos(b*x + a)^7 - 56*cos(b*x + a)^5 + 70*cos(b*x + a)^3 - 35*cos(b*x + a))/((b*cos(b*x + a)^6 - 3*b*cos(b*x + a)^4 + 3*b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
9,0,0,0,0.609555," ","integrate(csc(b*x+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{\frac{7}{2}}, x\right)"," ",0,"integral(csc(b*x + a)^(7/2), x)","F",0
10,0,0,0,1.157027," ","integrate(csc(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{\frac{5}{2}}, x\right)"," ",0,"integral(csc(b*x + a)^(5/2), x)","F",0
11,0,0,0,0.563781," ","integrate(csc(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(csc(b*x + a)^(3/2), x)","F",0
12,0,0,0,0.837552," ","integrate(csc(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\csc\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(csc(b*x + a)), x)","F",0
13,0,0,0,0.614805," ","integrate(1/csc(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\csc\left(b x + a\right)}}, x\right)"," ",0,"integral(1/sqrt(csc(b*x + a)), x)","F",0
14,0,0,0,0.687364," ","integrate(1/csc(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\csc\left(b x + a\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(csc(b*x + a)^(-3/2), x)","F",0
15,0,0,0,0.681493," ","integrate(1/csc(b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\csc\left(b x + a\right)^{\frac{5}{2}}}, x\right)"," ",0,"integral(csc(b*x + a)^(-5/2), x)","F",0
16,0,0,0,0.517702," ","integrate(1/csc(b*x+a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\csc\left(b x + a\right)^{\frac{7}{2}}}, x\right)"," ",0,"integral(csc(b*x + a)^(-7/2), x)","F",0
17,0,0,0,0.665412," ","integrate((c*csc(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \csc\left(b x + a\right)} c^{3} \csc\left(b x + a\right)^{3}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))*c^3*csc(b*x + a)^3, x)","F",0
18,0,0,0,0.566889," ","integrate((c*csc(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \csc\left(b x + a\right)} c^{2} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))*c^2*csc(b*x + a)^2, x)","F",0
19,0,0,0,0.461778," ","integrate((c*csc(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \csc\left(b x + a\right)} c \csc\left(b x + a\right), x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))*c*csc(b*x + a), x)","F",0
20,0,0,0,0.613008," ","integrate((c*csc(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c \csc\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a)), x)","F",0
21,0,0,0,0.808598," ","integrate(1/(c*csc(b*x+a))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \csc\left(b x + a\right)}}{c \csc\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))/(c*csc(b*x + a)), x)","F",0
22,0,0,0,0.637224," ","integrate(1/(c*csc(b*x+a))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \csc\left(b x + a\right)}}{c^{2} \csc\left(b x + a\right)^{2}}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))/(c^2*csc(b*x + a)^2), x)","F",0
23,0,0,0,0.605516," ","integrate(1/(c*csc(b*x+a))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \csc\left(b x + a\right)}}{c^{3} \csc\left(b x + a\right)^{3}}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))/(c^3*csc(b*x + a)^3), x)","F",0
24,0,0,0,0.671031," ","integrate(1/(c*csc(b*x+a))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c \csc\left(b x + a\right)}}{c^{4} \csc\left(b x + a\right)^{4}}, x\right)"," ",0,"integral(sqrt(c*csc(b*x + a))/(c^4*csc(b*x + a)^4), x)","F",0
25,0,0,0,0.858702," ","integrate(csc(b*x+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{\frac{4}{3}}, x\right)"," ",0,"integral(csc(b*x + a)^(4/3), x)","F",0
26,0,0,0,1.258640," ","integrate(csc(b*x+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{\frac{2}{3}}, x\right)"," ",0,"integral(csc(b*x + a)^(2/3), x)","F",0
27,0,0,0,0.490134," ","integrate(csc(b*x+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{\frac{1}{3}}, x\right)"," ",0,"integral(csc(b*x + a)^(1/3), x)","F",0
28,0,0,0,0.584434," ","integrate(1/csc(b*x+a)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\csc\left(b x + a\right)^{\frac{1}{3}}}, x\right)"," ",0,"integral(csc(b*x + a)^(-1/3), x)","F",0
29,0,0,0,0.586299," ","integrate(1/csc(b*x+a)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\csc\left(b x + a\right)^{\frac{2}{3}}}, x\right)"," ",0,"integral(csc(b*x + a)^(-2/3), x)","F",0
30,0,0,0,0.604838," ","integrate(1/csc(b*x+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\csc\left(b x + a\right)^{\frac{4}{3}}}, x\right)"," ",0,"integral(csc(b*x + a)^(-4/3), x)","F",0
31,0,0,0,0.665360," ","integrate((c*csc(b*x+a))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(c \csc\left(b x + a\right)\right)^{\frac{1}{3}} c \csc\left(b x + a\right), x\right)"," ",0,"integral((c*csc(b*x + a))^(1/3)*c*csc(b*x + a), x)","F",0
32,0,0,0,0.682970," ","integrate((c*csc(b*x+a))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(c \csc\left(b x + a\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((c*csc(b*x + a))^(2/3), x)","F",0
33,0,0,0,0.672763," ","integrate((c*csc(b*x+a))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(c \csc\left(b x + a\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((c*csc(b*x + a))^(1/3), x)","F",0
34,0,0,0,0.849720," ","integrate(1/(c*csc(b*x+a))^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c \csc\left(b x + a\right)\right)^{\frac{2}{3}}}{c \csc\left(b x + a\right)}, x\right)"," ",0,"integral((c*csc(b*x + a))^(2/3)/(c*csc(b*x + a)), x)","F",0
35,0,0,0,0.534704," ","integrate(1/(c*csc(b*x+a))^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c \csc\left(b x + a\right)\right)^{\frac{1}{3}}}{c \csc\left(b x + a\right)}, x\right)"," ",0,"integral((c*csc(b*x + a))^(1/3)/(c*csc(b*x + a)), x)","F",0
36,0,0,0,0.613600," ","integrate(1/(c*csc(b*x+a))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(c \csc\left(b x + a\right)\right)^{\frac{2}{3}}}{c^{2} \csc\left(b x + a\right)^{2}}, x\right)"," ",0,"integral((c*csc(b*x + a))^(2/3)/(c^2*csc(b*x + a)^2), x)","F",0
37,0,0,0,0.664492," ","integrate(csc(b*x+a)^n,x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{n}, x\right)"," ",0,"integral(csc(b*x + a)^n, x)","F",0
38,0,0,0,0.621255," ","integrate((c*csc(b*x+a))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(c \csc\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral((c*csc(b*x + a))^n, x)","F",0
39,1,93,0,0.605024," ","integrate((csc(x)^2)^(7/2),x, algorithm=""fricas"")","\frac{30 \, \cos\left(x\right)^{5} - 80 \, \cos\left(x\right)^{3} - 15 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 66 \, \cos\left(x\right)}{96 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)}}"," ",0,"1/96*(30*cos(x)^5 - 80*cos(x)^3 - 15*(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*log(1/2*cos(x) + 1/2) + 15*(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*log(-1/2*cos(x) + 1/2) + 66*cos(x))/(cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)","B",0
40,1,69,0,0.662871," ","integrate((csc(x)^2)^(5/2),x, algorithm=""fricas"")","\frac{6 \, \cos\left(x\right)^{3} - 3 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 10 \, \cos\left(x\right)}{16 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)}}"," ",0,"1/16*(6*cos(x)^3 - 3*(cos(x)^4 - 2*cos(x)^2 + 1)*log(1/2*cos(x) + 1/2) + 3*(cos(x)^4 - 2*cos(x)^2 + 1)*log(-1/2*cos(x) + 1/2) - 10*cos(x))/(cos(x)^4 - 2*cos(x)^2 + 1)","B",0
41,1,44,0,0.503205," ","integrate((csc(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 2 \, \cos\left(x\right)}{4 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/4*((cos(x)^2 - 1)*log(1/2*cos(x) + 1/2) - (cos(x)^2 - 1)*log(-1/2*cos(x) + 1/2) - 2*cos(x))/(cos(x)^2 - 1)","B",0
42,1,19,0,0.536314," ","integrate((csc(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)"," ",0,"-1/2*log(1/2*cos(x) + 1/2) + 1/2*log(-1/2*cos(x) + 1/2)","B",0
43,1,4,0,0.646287," ","integrate(1/(csc(x)^2)^(1/2),x, algorithm=""fricas"")","-\cos\left(x\right)"," ",0,"-cos(x)","A",0
44,1,11,0,0.566344," ","integrate(1/(csc(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{3} \, \cos\left(x\right)^{3} - \cos\left(x\right)"," ",0,"1/3*cos(x)^3 - cos(x)","A",0
45,1,17,0,0.578729," ","integrate(1/(csc(x)^2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{5} \, \cos\left(x\right)^{5} + \frac{2}{3} \, \cos\left(x\right)^{3} - \cos\left(x\right)"," ",0,"-1/5*cos(x)^5 + 2/3*cos(x)^3 - cos(x)","A",0
46,1,21,0,0.667298," ","integrate(1/(csc(x)^2)^(7/2),x, algorithm=""fricas"")","\frac{1}{7} \, \cos\left(x\right)^{7} - \frac{3}{5} \, \cos\left(x\right)^{5} + \cos\left(x\right)^{3} - \cos\left(x\right)"," ",0,"1/7*cos(x)^7 - 3/5*cos(x)^5 + cos(x)^3 - cos(x)","A",0
47,1,106,0,0.614580," ","integrate((a*csc(x)^2)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(30 \, a^{3} \cos\left(x\right)^{5} - 80 \, a^{3} \cos\left(x\right)^{3} + 66 \, a^{3} \cos\left(x\right) + 15 \, {\left(a^{3} \cos\left(x\right)^{6} - 3 \, a^{3} \cos\left(x\right)^{4} + 3 \, a^{3} \cos\left(x\right)^{2} - a^{3}\right)} \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)\right)} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}}}{96 \, {\left(\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right)}"," ",0,"-1/96*(30*a^3*cos(x)^5 - 80*a^3*cos(x)^3 + 66*a^3*cos(x) + 15*(a^3*cos(x)^6 - 3*a^3*cos(x)^4 + 3*a^3*cos(x)^2 - a^3)*log(-(cos(x) - 1)/(cos(x) + 1)))*sqrt(-a/(cos(x)^2 - 1))/((cos(x)^4 - 2*cos(x)^2 + 1)*sin(x))","A",0
48,1,80,0,0.658285," ","integrate((a*csc(x)^2)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{2} \cos\left(x\right)^{3} - 10 \, a^{2} \cos\left(x\right) + 3 \, {\left(a^{2} \cos\left(x\right)^{4} - 2 \, a^{2} \cos\left(x\right)^{2} + a^{2}\right)} \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)\right)} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}}}{16 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"-1/16*(6*a^2*cos(x)^3 - 10*a^2*cos(x) + 3*(a^2*cos(x)^4 - 2*a^2*cos(x)^2 + a^2)*log(-(cos(x) - 1)/(cos(x) + 1)))*sqrt(-a/(cos(x)^2 - 1))/((cos(x)^2 - 1)*sin(x))","A",0
49,1,49,0,0.586132," ","integrate((a*csc(x)^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, a \cos\left(x\right) + {\left(a \cos\left(x\right)^{2} - a\right)} \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)\right)} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}}}{4 \, \sin\left(x\right)}"," ",0,"-1/4*(2*a*cos(x) + (a*cos(x)^2 - a)*log(-(cos(x) - 1)/(cos(x) + 1)))*sqrt(-a/(cos(x)^2 - 1))/sin(x)","A",0
50,1,64,0,0.547435," ","integrate((a*csc(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}} \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right) \sin\left(x\right), \sqrt{-a} \arctan\left(\frac{\sqrt{-a} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}} \cos\left(x\right) \sin\left(x\right)}{a}\right)\right]"," ",0,"[1/2*sqrt(-a/(cos(x)^2 - 1))*log(-(cos(x) - 1)/(cos(x) + 1))*sin(x), sqrt(-a)*arctan(sqrt(-a)*sqrt(-a/(cos(x)^2 - 1))*cos(x)*sin(x)/a)]","A",0
51,1,22,0,0.834798," ","integrate(1/(a*csc(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}} \cos\left(x\right) \sin\left(x\right)}{a}"," ",0,"-sqrt(-a/(cos(x)^2 - 1))*cos(x)*sin(x)/a","A",0
52,1,29,0,0.534297," ","integrate(1/(a*csc(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(\cos\left(x\right)^{3} - 3 \, \cos\left(x\right)\right)} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}} \sin\left(x\right)}{3 \, a^{2}}"," ",0,"1/3*(cos(x)^3 - 3*cos(x))*sqrt(-a/(cos(x)^2 - 1))*sin(x)/a^2","A",0
53,1,37,0,0.597554," ","integrate(1/(a*csc(x)^2)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \cos\left(x\right)^{5} - 10 \, \cos\left(x\right)^{3} + 15 \, \cos\left(x\right)\right)} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}} \sin\left(x\right)}{15 \, a^{3}}"," ",0,"-1/15*(3*cos(x)^5 - 10*cos(x)^3 + 15*cos(x))*sqrt(-a/(cos(x)^2 - 1))*sin(x)/a^3","A",0
54,1,43,0,0.814634," ","integrate(1/(a*csc(x)^2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(5 \, \cos\left(x\right)^{7} - 21 \, \cos\left(x\right)^{5} + 35 \, \cos\left(x\right)^{3} - 35 \, \cos\left(x\right)\right)} \sqrt{-\frac{a}{\cos\left(x\right)^{2} - 1}} \sin\left(x\right)}{35 \, a^{4}}"," ",0,"1/35*(5*cos(x)^7 - 21*cos(x)^5 + 35*cos(x)^3 - 35*cos(x))*sqrt(-a/(cos(x)^2 - 1))*sin(x)/a^4","A",0
55,0,0,0,0.636858," ","integrate((a*csc(x)^3)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \csc\left(x\right)^{3}} a^{2} \csc\left(x\right)^{6}, x\right)"," ",0,"integral(sqrt(a*csc(x)^3)*a^2*csc(x)^6, x)","F",0
56,0,0,0,0.813513," ","integrate((a*csc(x)^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \csc\left(x\right)^{3}} a \csc\left(x\right)^{3}, x\right)"," ",0,"integral(sqrt(a*csc(x)^3)*a*csc(x)^3, x)","F",0
57,0,0,0,0.594475," ","integrate((a*csc(x)^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \csc\left(x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a*csc(x)^3), x)","F",0
58,0,0,0,0.562823," ","integrate(1/(a*csc(x)^3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \csc\left(x\right)^{3}}}{a \csc\left(x\right)^{3}}, x\right)"," ",0,"integral(sqrt(a*csc(x)^3)/(a*csc(x)^3), x)","F",0
59,0,0,0,0.509517," ","integrate(1/(a*csc(x)^3)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \csc\left(x\right)^{3}}}{a^{2} \csc\left(x\right)^{6}}, x\right)"," ",0,"integral(sqrt(a*csc(x)^3)/(a^2*csc(x)^6), x)","F",0
60,0,0,0,0.736223," ","integrate(1/(a*csc(x)^3)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \csc\left(x\right)^{3}}}{a^{3} \csc\left(x\right)^{9}}, x\right)"," ",0,"integral(sqrt(a*csc(x)^3)/(a^3*csc(x)^9), x)","F",0
61,1,118,0,0.579291," ","integrate((a*csc(x)^4)^(7/2),x, algorithm=""fricas"")","\frac{{\left(1024 \, a^{3} \cos\left(x\right)^{13} - 6656 \, a^{3} \cos\left(x\right)^{11} + 18304 \, a^{3} \cos\left(x\right)^{9} - 27456 \, a^{3} \cos\left(x\right)^{7} + 24024 \, a^{3} \cos\left(x\right)^{5} - 12012 \, a^{3} \cos\left(x\right)^{3} + 3003 \, a^{3} \cos\left(x\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}}}{3003 \, {\left(\cos\left(x\right)^{10} - 5 \, \cos\left(x\right)^{8} + 10 \, \cos\left(x\right)^{6} - 10 \, \cos\left(x\right)^{4} + 5 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/3003*(1024*a^3*cos(x)^13 - 6656*a^3*cos(x)^11 + 18304*a^3*cos(x)^9 - 27456*a^3*cos(x)^7 + 24024*a^3*cos(x)^5 - 12012*a^3*cos(x)^3 + 3003*a^3*cos(x))*sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))/((cos(x)^10 - 5*cos(x)^8 + 10*cos(x)^6 - 10*cos(x)^4 + 5*cos(x)^2 - 1)*sin(x))","A",0
62,1,88,0,0.975061," ","integrate((a*csc(x)^4)^(5/2),x, algorithm=""fricas"")","\frac{{\left(128 \, a^{2} \cos\left(x\right)^{9} - 576 \, a^{2} \cos\left(x\right)^{7} + 1008 \, a^{2} \cos\left(x\right)^{5} - 840 \, a^{2} \cos\left(x\right)^{3} + 315 \, a^{2} \cos\left(x\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}}}{315 \, {\left(\cos\left(x\right)^{6} - 3 \, \cos\left(x\right)^{4} + 3 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/315*(128*a^2*cos(x)^9 - 576*a^2*cos(x)^7 + 1008*a^2*cos(x)^5 - 840*a^2*cos(x)^3 + 315*a^2*cos(x))*sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))/((cos(x)^6 - 3*cos(x)^4 + 3*cos(x)^2 - 1)*sin(x))","A",0
63,1,52,0,0.565751," ","integrate((a*csc(x)^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left(8 \, a \cos\left(x\right)^{5} - 20 \, a \cos\left(x\right)^{3} + 15 \, a \cos\left(x\right)\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}}}{15 \, {\left(\cos\left(x\right)^{2} - 1\right)} \sin\left(x\right)}"," ",0,"1/15*(8*a*cos(x)^5 - 20*a*cos(x)^3 + 15*a*cos(x))*sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))/((cos(x)^2 - 1)*sin(x))","A",0
64,1,24,0,0.415743," ","integrate((a*csc(x)^4)^(1/2),x, algorithm=""fricas"")","-\sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}} \cos\left(x\right) \sin\left(x\right)"," ",0,"-sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))*cos(x)*sin(x)","A",0
65,1,46,0,0.546441," ","integrate(1/(a*csc(x)^4)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(x \cos\left(x\right)^{2} - {\left(\cos\left(x\right)^{3} - \cos\left(x\right)\right)} \sin\left(x\right) - x\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}}}{2 \, a}"," ",0,"-1/2*(x*cos(x)^2 - (cos(x)^3 - cos(x))*sin(x) - x)*sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))/a","A",0
66,1,61,0,0.665247," ","integrate(1/(a*csc(x)^4)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, x \cos\left(x\right)^{2} - {\left(8 \, \cos\left(x\right)^{7} - 34 \, \cos\left(x\right)^{5} + 59 \, \cos\left(x\right)^{3} - 33 \, \cos\left(x\right)\right)} \sin\left(x\right) - 15 \, x\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}}}{48 \, a^{2}}"," ",0,"-1/48*(15*x*cos(x)^2 - (8*cos(x)^7 - 34*cos(x)^5 + 59*cos(x)^3 - 33*cos(x))*sin(x) - 15*x)*sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))/a^2","A",0
67,1,73,0,0.469526," ","integrate(1/(a*csc(x)^4)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(315 \, x \cos\left(x\right)^{2} - {\left(128 \, \cos\left(x\right)^{11} - 784 \, \cos\left(x\right)^{9} + 2024 \, \cos\left(x\right)^{7} - 2858 \, \cos\left(x\right)^{5} + 2455 \, \cos\left(x\right)^{3} - 965 \, \cos\left(x\right)\right)} \sin\left(x\right) - 315 \, x\right)} \sqrt{\frac{a}{\cos\left(x\right)^{4} - 2 \, \cos\left(x\right)^{2} + 1}}}{1280 \, a^{3}}"," ",0,"-1/1280*(315*x*cos(x)^2 - (128*cos(x)^11 - 784*cos(x)^9 + 2024*cos(x)^7 - 2858*cos(x)^5 + 2455*cos(x)^3 - 965*cos(x))*sin(x) - 315*x)*sqrt(a/(cos(x)^4 - 2*cos(x)^2 + 1))/a^3","A",0
68,0,0,0,0.620940," ","integrate(((b*csc(d*x+c))^p)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(\left(b \csc\left(d x + c\right)\right)^{p}\right)}^{n}, x\right)"," ",0,"integral(((b*csc(d*x + c))^p)^n, x)","F",0
69,0,0,0,0.671384," ","integrate((a*(b*csc(d*x+c))^p)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\left(b \csc\left(d x + c\right)\right)^{p} a\right)^{n}, x\right)"," ",0,"integral(((b*csc(d*x + c))^p*a)^n, x)","F",0
70,0,0,0,0.667039," ","integrate((a*csc(f*x+e))^m*(b*csc(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(a \csc\left(f x + e\right)\right)^{m} \left(b \csc\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*csc(f*x + e))^m*(b*csc(f*x + e))^n, x)","F",0
