1,1,15,0,0.166574," ","integrate(csc(b*x+a),x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \right|}\right)}{b}"," ",0,"log(abs(tan(1/2*b*x + 1/2*a)))/b","A",0
2,1,13,0,0.213313," ","integrate(csc(b*x+a)^2,x, algorithm=""giac"")","-\frac{1}{b \tan\left(b x + a\right)}"," ",0,"-1/(b*tan(b*x + a))","A",0
3,1,92,0,0.468889," ","integrate(csc(b*x+a)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{2 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}}{\cos\left(b x + a\right) - 1} + \frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 2 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{8 \, b}"," ",0,"-1/8*((2*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)*(cos(b*x + a) + 1)/(cos(b*x + a) - 1) + (cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 2*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
4,1,25,0,0.151444," ","integrate(csc(b*x+a)^4,x, algorithm=""giac"")","-\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
5,1,138,0,0.186313," ","integrate(csc(b*x+a)^5,x, algorithm=""giac"")","\frac{\frac{{\left(\frac{8 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{18 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}^{2}}{{\left(\cos\left(b x + a\right) - 1\right)}^{2}} - \frac{8 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 12 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{64 \, b}"," ",0,"1/64*((8*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 18*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 - 1)*(cos(b*x + a) + 1)^2/(cos(b*x + a) - 1)^2 - 8*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + (cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 12*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
6,1,35,0,0.189282," ","integrate(csc(b*x+a)^6,x, algorithm=""giac"")","-\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
7,1,182,0,0.206220," ","integrate(csc(b*x+a)^7,x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{9 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{45 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{110 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}^{3}}{{\left(\cos\left(b x + a\right) - 1\right)}^{3}} + \frac{45 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{9 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} - 60 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{384 \, b}"," ",0,"-1/384*((9*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 45*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 110*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 - 1)*(cos(b*x + a) + 1)^3/(cos(b*x + a) - 1)^3 + 45*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 9*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + (cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 - 60*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
8,1,45,0,0.349963," ","integrate(csc(b*x+a)^8,x, algorithm=""giac"")","-\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\int \left(c \csc\left(b x + a\right)\right)^{n}\,{d x}"," ",0,"integrate((c*csc(b*x + a))^n, x)","F",0
39,1,129,0,0.267282," ","integrate((csc(x)^2)^(7/2),x, algorithm=""giac"")","-\frac{\frac{45 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - \frac{9 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(\cos\left(x\right) - 1\right)}^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{384 \, \mathrm{sgn}\left(\sin\left(x\right)\right)} - \frac{{\left(\frac{9 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - \frac{45 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{110 \, {\left(\cos\left(x\right) - 1\right)}^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{384 \, {\left(\cos\left(x\right) - 1\right)}^{3} \mathrm{sgn}\left(\sin\left(x\right)\right)} + \frac{5 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)}{32 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"-1/384*(45*(cos(x) - 1)/(cos(x) + 1) - 9*(cos(x) - 1)^2/(cos(x) + 1)^2 + (cos(x) - 1)^3/(cos(x) + 1)^3)/sgn(sin(x)) - 1/384*(9*(cos(x) - 1)/(cos(x) + 1) - 45*(cos(x) - 1)^2/(cos(x) + 1)^2 + 110*(cos(x) - 1)^3/(cos(x) + 1)^3 - 1)*(cos(x) + 1)^3/((cos(x) - 1)^3*sgn(sin(x))) + 5/32*log(-(cos(x) - 1)/(cos(x) + 1))/sgn(sin(x))","B",0
40,1,100,0,0.505411," ","integrate((csc(x)^2)^(5/2),x, algorithm=""giac"")","-\frac{{\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{8 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{{\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{64 \, {\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{{\left(\frac{8 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - \frac{18 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}{64 \, {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)} + \frac{3 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)}{16 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"-1/8*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) + 1/64*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2 + 1/64*(8*(cos(x) - 1)/(cos(x) + 1) - 18*(cos(x) - 1)^2/(cos(x) + 1)^2 - 1)*(cos(x) + 1)^2/((cos(x) - 1)^2*sgn(sin(x))) + 3/16*log(-(cos(x) - 1)/(cos(x) + 1))/sgn(sin(x))","B",0
41,1,69,0,0.491933," ","integrate((csc(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{{\left(\frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 1\right)} {\left(\cos\left(x\right) + 1\right)}}{8 \, {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)} + \frac{\log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)}{4 \, \mathrm{sgn}\left(\sin\left(x\right)\right)} - \frac{\cos\left(x\right) - 1}{8 \, {\left(\cos\left(x\right) + 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"-1/8*(2*(cos(x) - 1)/(cos(x) + 1) - 1)*(cos(x) + 1)/((cos(x) - 1)*sgn(sin(x))) + 1/4*log(-(cos(x) - 1)/(cos(x) + 1))/sgn(sin(x)) - 1/8*(cos(x) - 1)/((cos(x) + 1)*sgn(sin(x)))","B",0
42,1,12,0,0.296571," ","integrate((csc(x)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{\mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"log(abs(tan(1/2*x)))/sgn(sin(x))","B",0
43,1,11,0,0.288863," ","integrate(1/(csc(x)^2)^(1/2),x, algorithm=""giac"")","-\cos\left(x\right) \mathrm{sgn}\left(\sin\left(x\right)\right) + \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-cos(x)*sgn(sin(x)) + sgn(sin(x))","A",0
44,1,44,0,0.423813," ","integrate(1/(csc(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{3 \, {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} - \mathrm{sgn}\left(\sin\left(x\right)\right)\right)}}{3 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 1\right)}^{3}} + \frac{4}{3} \, \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-4/3*(3*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) - sgn(sin(x)))/((cos(x) - 1)/(cos(x) + 1) - 1)^3 + 4/3*sgn(sin(x))","B",0
45,1,61,0,0.332672," ","integrate(1/(csc(x)^2)^(5/2),x, algorithm=""giac"")","-\frac{16 \, {\left(\frac{5 \, {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} - \frac{10 \, {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \mathrm{sgn}\left(\sin\left(x\right)\right)\right)}}{15 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 1\right)}^{5}} + \frac{16}{15} \, \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-16/15*(5*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) - 10*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2 - sgn(sin(x)))/((cos(x) - 1)/(cos(x) + 1) - 1)^5 + 16/15*sgn(sin(x))","A",0
46,1,78,0,0.547360," ","integrate(1/(csc(x)^2)^(7/2),x, algorithm=""giac"")","-\frac{32 \, {\left(\frac{7 \, {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} - \frac{21 \, {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{35 \, {\left(\cos\left(x\right) - 1\right)}^{3} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \mathrm{sgn}\left(\sin\left(x\right)\right)\right)}}{35 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 1\right)}^{7}} + \frac{32}{35} \, \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-32/35*(7*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) - 21*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2 + 35*(cos(x) - 1)^3*sgn(sin(x))/(cos(x) + 1)^3 - sgn(sin(x)))/((cos(x) - 1)/(cos(x) + 1) - 1)^7 + 32/35*sgn(sin(x))","A",0
47,1,164,0,0.361639," ","integrate((a*csc(x)^2)^(7/2),x, algorithm=""giac"")","\frac{1}{384} \, {\left(60 \, a^{3} \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right) \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{45 \, a^{3} {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} + \frac{9 \, a^{3} {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{a^{3} {\left(\cos\left(x\right) - 1\right)}^{3} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{{\left(a^{3} \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{9 \, a^{3} {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} + \frac{45 \, a^{3} {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{110 \, a^{3} {\left(\cos\left(x\right) - 1\right)}^{3} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{{\left(\cos\left(x\right) - 1\right)}^{3}}\right)} \sqrt{a}"," ",0,"1/384*(60*a^3*log(-(cos(x) - 1)/(cos(x) + 1))*sgn(sin(x)) - 45*a^3*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) + 9*a^3*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2 - a^3*(cos(x) - 1)^3*sgn(sin(x))/(cos(x) + 1)^3 + (a^3*sgn(sin(x)) - 9*a^3*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) + 45*a^3*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2 - 110*a^3*(cos(x) - 1)^3*sgn(sin(x))/(cos(x) + 1)^3)*(cos(x) + 1)^3/(cos(x) - 1)^3)*sqrt(a)","B",0
48,1,124,0,0.290399," ","integrate((a*csc(x)^2)^(5/2),x, algorithm=""giac"")","\frac{1}{64} \, {\left(12 \, a^{2} \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right) \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{8 \, a^{2} {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} + \frac{a^{2} {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(a^{2} \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{8 \, a^{2} {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} + \frac{18 \, a^{2} {\left(\cos\left(x\right) - 1\right)}^{2} \mathrm{sgn}\left(\sin\left(x\right)\right)}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}{{\left(\cos\left(x\right) - 1\right)}^{2}}\right)} \sqrt{a}"," ",0,"1/64*(12*a^2*log(-(cos(x) - 1)/(cos(x) + 1))*sgn(sin(x)) - 8*a^2*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) + a^2*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2 - (a^2*sgn(sin(x)) - 8*a^2*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) + 18*a^2*(cos(x) - 1)^2*sgn(sin(x))/(cos(x) + 1)^2)*(cos(x) + 1)^2/(cos(x) - 1)^2)*sqrt(a)","B",0
49,1,72,0,0.282624," ","integrate((a*csc(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right) \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{{\left(\frac{2 \, {\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1} - \mathrm{sgn}\left(\sin\left(x\right)\right)\right)} {\left(\cos\left(x\right) + 1\right)}}{\cos\left(x\right) - 1} - \frac{{\left(\cos\left(x\right) - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{\cos\left(x\right) + 1}\right)} a^{\frac{3}{2}}"," ",0,"1/8*(2*log(-(cos(x) - 1)/(cos(x) + 1))*sgn(sin(x)) - (2*(cos(x) - 1)*sgn(sin(x))/(cos(x) + 1) - sgn(sin(x)))*(cos(x) + 1)/(cos(x) - 1) - (cos(x) - 1)*sgn(sin(x))/(cos(x) + 1))*a^(3/2)","B",0
50,1,13,0,0.560992," ","integrate((a*csc(x)^2)^(1/2),x, algorithm=""giac"")","\sqrt{a} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right) \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"sqrt(a)*log(abs(tan(1/2*x)))*sgn(sin(x))","A",0
51,1,34,0,0.355837," ","integrate(1/(a*csc(x)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}{\sqrt{a}} + \frac{2}{\sqrt{a} {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 1\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"2*sgn(sin(x))/sqrt(a) + 2/(sqrt(a)*((cos(x) - 1)/(cos(x) + 1) - 1)*sgn(sin(x)))","B",0
52,1,43,0,0.429992," ","integrate(1/(a*csc(x)^2)^(3/2),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{3 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}} - \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{3 \, a^{\frac{3}{2}}}"," ",0,"-4/3*((3*sgn(tan(1/2*x))*tan(1/2*x)^2 + sgn(tan(1/2*x)))/(tan(1/2*x)^2 + 1)^3 - sgn(tan(1/2*x)))/a^(3/2)","A",0
53,1,56,0,0.496232," ","integrate(1/(a*csc(x)^2)^(5/2),x, algorithm=""giac"")","-\frac{16 \, {\left(\frac{10 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 5 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{5}} - \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{15 \, a^{\frac{5}{2}}}"," ",0,"-16/15*((10*sgn(tan(1/2*x))*tan(1/2*x)^4 + 5*sgn(tan(1/2*x))*tan(1/2*x)^2 + sgn(tan(1/2*x)))/(tan(1/2*x)^2 + 1)^5 - sgn(tan(1/2*x)))/a^(5/2)","A",0
54,1,69,0,0.720600," ","integrate(1/(a*csc(x)^2)^(7/2),x, algorithm=""giac"")","-\frac{32 \, {\left(\frac{35 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{6} + 21 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 7 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{7}} - \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{35 \, a^{\frac{7}{2}}}"," ",0,"-32/35*((35*sgn(tan(1/2*x))*tan(1/2*x)^6 + 21*sgn(tan(1/2*x))*tan(1/2*x)^4 + 7*sgn(tan(1/2*x))*tan(1/2*x)^2 + sgn(tan(1/2*x)))/(tan(1/2*x)^2 + 1)^7 - sgn(tan(1/2*x)))/a^(7/2)","A",0
55,0,0,0,0.000000," ","integrate((a*csc(x)^3)^(5/2),x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
61,1,69,0,0.650725," ","integrate((a*csc(x)^4)^(7/2),x, algorithm=""giac"")","-\frac{{\left(3003 \, a^{3} \tan\left(x\right)^{12} + 6006 \, a^{3} \tan\left(x\right)^{10} + 9009 \, a^{3} \tan\left(x\right)^{8} + 8580 \, a^{3} \tan\left(x\right)^{6} + 5005 \, a^{3} \tan\left(x\right)^{4} + 1638 \, a^{3} \tan\left(x\right)^{2} + 231 \, a^{3}\right)} \sqrt{a}}{3003 \, \tan\left(x\right)^{13}}"," ",0,"-1/3003*(3003*a^3*tan(x)^12 + 6006*a^3*tan(x)^10 + 9009*a^3*tan(x)^8 + 8580*a^3*tan(x)^6 + 5005*a^3*tan(x)^4 + 1638*a^3*tan(x)^2 + 231*a^3)*sqrt(a)/tan(x)^13","A",0
62,1,51,0,0.308246," ","integrate((a*csc(x)^4)^(5/2),x, algorithm=""giac"")","-\frac{{\left(315 \, a^{2} \tan\left(x\right)^{8} + 420 \, a^{2} \tan\left(x\right)^{6} + 378 \, a^{2} \tan\left(x\right)^{4} + 180 \, a^{2} \tan\left(x\right)^{2} + 35 \, a^{2}\right)} \sqrt{a}}{315 \, \tan\left(x\right)^{9}}"," ",0,"-1/315*(315*a^2*tan(x)^8 + 420*a^2*tan(x)^6 + 378*a^2*tan(x)^4 + 180*a^2*tan(x)^2 + 35*a^2)*sqrt(a)/tan(x)^9","A",0
63,1,23,0,0.290914," ","integrate((a*csc(x)^4)^(3/2),x, algorithm=""giac"")","-\frac{{\left(15 \, \tan\left(x\right)^{4} + 10 \, \tan\left(x\right)^{2} + 3\right)} a^{\frac{3}{2}}}{15 \, \tan\left(x\right)^{5}}"," ",0,"-1/15*(15*tan(x)^4 + 10*tan(x)^2 + 3)*a^(3/2)/tan(x)^5","A",0
64,1,9,0,0.249138," ","integrate((a*csc(x)^4)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{a}}{\tan\left(x\right)}"," ",0,"-sqrt(a)/tan(x)","A",0
65,1,22,0,0.414475," ","integrate(1/(a*csc(x)^4)^(1/2),x, algorithm=""giac"")","\frac{x}{2 \, \sqrt{a}} - \frac{\tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)} \sqrt{a}}"," ",0,"1/2*x/sqrt(a) - 1/2*tan(x)/((tan(x)^2 + 1)*sqrt(a))","A",0
66,1,42,0,0.301720," ","integrate(1/(a*csc(x)^4)^(3/2),x, algorithm=""giac"")","\frac{\frac{15 \, x}{\sqrt{a}} - \frac{33 \, \tan\left(x\right)^{5} + 40 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{{\left(\tan\left(x\right)^{2} + 1\right)}^{3} \sqrt{a}}}{48 \, a}"," ",0,"1/48*(15*x/sqrt(a) - (33*tan(x)^5 + 40*tan(x)^3 + 15*tan(x))/((tan(x)^2 + 1)^3*sqrt(a)))/a","A",0
67,1,49,0,0.268707," ","integrate(1/(a*csc(x)^4)^(5/2),x, algorithm=""giac"")","\frac{63 \, x}{256 \, a^{\frac{5}{2}}} - \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(\tan\left(x\right)^{2} + 1\right)}^{5} a^{\frac{5}{2}}}"," ",0,"63/256*x/a^(5/2) - 1/1280*(965*tan(x)^9 + 2370*tan(x)^7 + 2688*tan(x)^5 + 1470*tan(x)^3 + 315*tan(x))/((tan(x)^2 + 1)^5*a^(5/2))","A",0
68,0,0,0,0.000000," ","integrate(((b*csc(d*x+c))^p)^n,x, algorithm=""giac"")","\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=""giac"")","\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=""giac"")","\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
