1,1,62,0,0.0904843,"\int \frac{\csc ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcCsc[a*x^5]/x,x]","\frac{1}{10} i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(a x^5\right)}\right)+\frac{1}{10} i \csc ^{-1}\left(a x^5\right)^2-\frac{1}{5} \csc ^{-1}\left(a x^5\right) \log \left(1-e^{2 i \csc ^{-1}\left(a x^5\right)}\right)","\frac{1}{10} i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(a x^5\right)}\right)+\frac{1}{10} i \csc ^{-1}\left(a x^5\right)^2-\frac{1}{5} \csc ^{-1}\left(a x^5\right) \log \left(1-e^{2 i \csc ^{-1}\left(a x^5\right)}\right)",1,"(I/10)*ArcCsc[a*x^5]^2 - (ArcCsc[a*x^5]*Log[1 - E^((2*I)*ArcCsc[a*x^5])])/5 + (I/10)*PolyLog[2, E^((2*I)*ArcCsc[a*x^5])]","A",7,6,10,0.6000,1,"{5219, 4625, 3717, 2190, 2279, 2391}"
2,1,58,0,0.019742,"\int x^3 \csc ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^3*ArcCsc[Sqrt[x]],x]","\frac{1}{4} x^4 \csc ^{-1}\left(\sqrt{x}\right)+\frac{1}{28} (x-1)^{7/2}+\frac{3}{20} (x-1)^{5/2}+\frac{1}{4} (x-1)^{3/2}+\frac{\sqrt{x-1}}{4}","\frac{1}{4} x^4 \csc ^{-1}\left(\sqrt{x}\right)+\frac{1}{28} (x-1)^{7/2}+\frac{3}{20} (x-1)^{5/2}+\frac{1}{4} (x-1)^{3/2}+\frac{\sqrt{x-1}}{4}",1,"Sqrt[-1 + x]/4 + (-1 + x)^(3/2)/4 + (3*(-1 + x)^(5/2))/20 + (-1 + x)^(7/2)/28 + (x^4*ArcCsc[Sqrt[x]])/4","A",4,3,10,0.3000,1,"{5271, 12, 43}"
3,1,47,0,0.0186938,"\int x^2 \csc ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcCsc[Sqrt[x]],x]","\frac{1}{3} x^3 \csc ^{-1}\left(\sqrt{x}\right)+\frac{1}{15} (x-1)^{5/2}+\frac{2}{9} (x-1)^{3/2}+\frac{\sqrt{x-1}}{3}","\frac{1}{3} x^3 \csc ^{-1}\left(\sqrt{x}\right)+\frac{1}{15} (x-1)^{5/2}+\frac{2}{9} (x-1)^{3/2}+\frac{\sqrt{x-1}}{3}",1,"Sqrt[-1 + x]/3 + (2*(-1 + x)^(3/2))/9 + (-1 + x)^(5/2)/15 + (x^3*ArcCsc[Sqrt[x]])/3","A",4,3,10,0.3000,1,"{5271, 12, 43}"
4,1,36,0,0.0119593,"\int x \csc ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcCsc[Sqrt[x]],x]","\frac{1}{2} x^2 \csc ^{-1}\left(\sqrt{x}\right)+\frac{1}{6} (x-1)^{3/2}+\frac{\sqrt{x-1}}{2}","\frac{1}{2} x^2 \csc ^{-1}\left(\sqrt{x}\right)+\frac{1}{6} (x-1)^{3/2}+\frac{\sqrt{x-1}}{2}",1,"Sqrt[-1 + x]/2 + (-1 + x)^(3/2)/6 + (x^2*ArcCsc[Sqrt[x]])/2","A",4,3,8,0.3750,1,"{5271, 12, 43}"
5,1,16,0,0.0039246,"\int \csc ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcCsc[Sqrt[x]],x]","\sqrt{x-1}+x \csc ^{-1}\left(\sqrt{x}\right)","\sqrt{x-1}+x \csc ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[-1 + x] + x*ArcCsc[Sqrt[x]]","A",3,3,6,0.5000,1,"{5269, 12, 32}"
6,1,56,0,0.0826394,"\int \frac{\csc ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcCsc[Sqrt[x]]/x,x]","i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(\sqrt{x}\right)}\right)+i \csc ^{-1}\left(\sqrt{x}\right)^2-2 \csc ^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 i \csc ^{-1}\left(\sqrt{x}\right)}\right)","i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(\sqrt{x}\right)}\right)+i \csc ^{-1}\left(\sqrt{x}\right)^2-2 \csc ^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 i \csc ^{-1}\left(\sqrt{x}\right)}\right)",1,"I*ArcCsc[Sqrt[x]]^2 - 2*ArcCsc[Sqrt[x]]*Log[1 - E^((2*I)*ArcCsc[Sqrt[x]])] + I*PolyLog[2, E^((2*I)*ArcCsc[Sqrt[x]])]","A",7,6,10,0.6000,1,"{5219, 4625, 3717, 2190, 2279, 2391}"
7,1,38,0,0.0154438,"\int \frac{\csc ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcCsc[Sqrt[x]]/x^2,x]","-\frac{\sqrt{x-1}}{2 x}-\frac{1}{2} \tan ^{-1}\left(\sqrt{x-1}\right)-\frac{\csc ^{-1}\left(\sqrt{x}\right)}{x}","-\frac{\sqrt{x-1}}{2 x}-\frac{1}{2} \tan ^{-1}\left(\sqrt{x-1}\right)-\frac{\csc ^{-1}\left(\sqrt{x}\right)}{x}",1,"-Sqrt[-1 + x]/(2*x) - ArcCsc[Sqrt[x]]/x - ArcTan[Sqrt[-1 + x]]/2","A",5,5,10,0.5000,1,"{5271, 12, 51, 63, 203}"
8,1,54,0,0.0201348,"\int \frac{\csc ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcCsc[Sqrt[x]]/x^3,x]","-\frac{\sqrt{x-1}}{8 x^2}-\frac{\csc ^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{3 \sqrt{x-1}}{16 x}-\frac{3}{16} \tan ^{-1}\left(\sqrt{x-1}\right)","-\frac{\sqrt{x-1}}{8 x^2}-\frac{\csc ^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{3 \sqrt{x-1}}{16 x}-\frac{3}{16} \tan ^{-1}\left(\sqrt{x-1}\right)",1,"-Sqrt[-1 + x]/(8*x^2) - (3*Sqrt[-1 + x])/(16*x) - ArcCsc[Sqrt[x]]/(2*x^2) - (3*ArcTan[Sqrt[-1 + x]])/16","A",6,5,10,0.5000,1,"{5271, 12, 51, 63, 203}"
9,1,56,0,0.0445915,"\int x^2 \csc ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x^2*ArcCsc[a/x],x]","-\frac{1}{9} a^3 \left(1-\frac{x^2}{a^2}\right)^{3/2}+\frac{1}{3} a^3 \sqrt{1-\frac{x^2}{a^2}}+\frac{1}{3} x^3 \sin ^{-1}\left(\frac{x}{a}\right)","-\frac{1}{9} a^3 \left(1-\frac{x^2}{a^2}\right)^{3/2}+\frac{1}{3} a^3 \sqrt{1-\frac{x^2}{a^2}}+\frac{1}{3} x^3 \sin ^{-1}\left(\frac{x}{a}\right)",1,"(a^3*Sqrt[1 - x^2/a^2])/3 - (a^3*(1 - x^2/a^2)^(3/2))/9 + (x^3*ArcSin[x/a])/3","A",5,4,10,0.4000,1,"{5265, 4627, 266, 43}"
10,1,47,0,0.020382,"\int x \csc ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x*ArcCsc[a/x],x]","\frac{1}{4} a x \sqrt{1-\frac{x^2}{a^2}}-\frac{1}{4} a^2 \sin ^{-1}\left(\frac{x}{a}\right)+\frac{1}{2} x^2 \sin ^{-1}\left(\frac{x}{a}\right)","\frac{1}{4} a x \sqrt{1-\frac{x^2}{a^2}}-\frac{1}{4} a^2 \sin ^{-1}\left(\frac{x}{a}\right)+\frac{1}{2} x^2 \sin ^{-1}\left(\frac{x}{a}\right)",1,"(a*x*Sqrt[1 - x^2/a^2])/4 - (a^2*ArcSin[x/a])/4 + (x^2*ArcSin[x/a])/2","A",4,4,8,0.5000,1,"{5265, 4627, 321, 216}"
11,1,25,0,0.0097707,"\int \csc ^{-1}\left(\frac{a}{x}\right) \, dx","Int[ArcCsc[a/x],x]","a \sqrt{1-\frac{x^2}{a^2}}+x \sin ^{-1}\left(\frac{x}{a}\right)","a \sqrt{1-\frac{x^2}{a^2}}+x \sin ^{-1}\left(\frac{x}{a}\right)",1,"a*Sqrt[1 - x^2/a^2] + x*ArcSin[x/a]","A",3,3,6,0.5000,1,"{5265, 4619, 261}"
12,1,59,0,0.0636623,"\int \frac{\csc ^{-1}\left(\frac{a}{x}\right)}{x} \, dx","Int[ArcCsc[a/x]/x,x]","-\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{x}{a}\right)}\right)-\frac{1}{2} i \sin ^{-1}\left(\frac{x}{a}\right)^2+\sin ^{-1}\left(\frac{x}{a}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\frac{x}{a}\right)}\right)","-\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{x}{a}\right)}\right)-\frac{1}{2} i \sin ^{-1}\left(\frac{x}{a}\right)^2+\sin ^{-1}\left(\frac{x}{a}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\frac{x}{a}\right)}\right)",1,"(-I/2)*ArcSin[x/a]^2 + ArcSin[x/a]*Log[1 - E^((2*I)*ArcSin[x/a])] - (I/2)*PolyLog[2, E^((2*I)*ArcSin[x/a])]","A",6,6,10,0.6000,1,"{5265, 4625, 3717, 2190, 2279, 2391}"
13,1,32,0,0.030622,"\int \frac{\csc ^{-1}\left(\frac{a}{x}\right)}{x^2} \, dx","Int[ArcCsc[a/x]/x^2,x]","-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{a}-\frac{\sin ^{-1}\left(\frac{x}{a}\right)}{x}","-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{a}-\frac{\sin ^{-1}\left(\frac{x}{a}\right)}{x}",1,"-(ArcSin[x/a]/x) - ArcTanh[Sqrt[1 - x^2/a^2]]/a","A",5,5,10,0.5000,1,"{5265, 4627, 266, 63, 208}"
14,1,38,0,0.0221313,"\int \frac{\csc ^{-1}\left(\frac{a}{x}\right)}{x^3} \, dx","Int[ArcCsc[a/x]/x^3,x]","-\frac{\sqrt{1-\frac{x^2}{a^2}}}{2 a x}-\frac{\sin ^{-1}\left(\frac{x}{a}\right)}{2 x^2}","-\frac{\sqrt{1-\frac{x^2}{a^2}}}{2 a x}-\frac{\sin ^{-1}\left(\frac{x}{a}\right)}{2 x^2}",1,"-Sqrt[1 - x^2/a^2]/(2*a*x) - ArcSin[x/a]/(2*x^2)","A",3,3,10,0.3000,1,"{5265, 4627, 264}"
15,1,60,0,0.0418601,"\int \frac{\csc ^{-1}\left(\frac{a}{x}\right)}{x^4} \, dx","Int[ArcCsc[a/x]/x^4,x]","-\frac{\sqrt{1-\frac{x^2}{a^2}}}{6 a x^2}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{6 a^3}-\frac{\sin ^{-1}\left(\frac{x}{a}\right)}{3 x^3}","-\frac{\sqrt{1-\frac{x^2}{a^2}}}{6 a x^2}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{6 a^3}-\frac{\sin ^{-1}\left(\frac{x}{a}\right)}{3 x^3}",1,"-Sqrt[1 - x^2/a^2]/(6*a*x^2) - ArcSin[x/a]/(3*x^3) - ArcTanh[Sqrt[1 - x^2/a^2]]/(6*a^3)","A",6,6,10,0.6000,1,"{5265, 4627, 266, 51, 63, 208}"
16,1,69,0,0.0936497,"\int \frac{\csc ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcCsc[a*x^n]/x,x]","\frac{i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{i \csc ^{-1}\left(a x^n\right)^2}{2 n}-\frac{\csc ^{-1}\left(a x^n\right) \log \left(1-e^{2 i \csc ^{-1}\left(a x^n\right)}\right)}{n}","\frac{i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{i \csc ^{-1}\left(a x^n\right)^2}{2 n}-\frac{\csc ^{-1}\left(a x^n\right) \log \left(1-e^{2 i \csc ^{-1}\left(a x^n\right)}\right)}{n}",1,"((I/2)*ArcCsc[a*x^n]^2)/n - (ArcCsc[a*x^n]*Log[1 - E^((2*I)*ArcCsc[a*x^n])])/n + ((I/2)*PolyLog[2, E^((2*I)*ArcCsc[a*x^n])])/n","A",7,6,10,0.6000,1,"{5219, 4625, 3717, 2190, 2279, 2391}"
17,1,197,0,0.2320276,"\int x^4 \csc ^{-1}(a+b x) \, dx","Int[x^4*ArcCsc[a + b*x],x]","-\frac{\left(53 a^2+20\right) a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{30 b^5}+\frac{\left(58 a^2+9\right) (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{120 b^5}+\frac{a^5 \csc ^{-1}(a+b x)}{5 b^5}+\frac{\left(40 a^4+40 a^2+3\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{40 b^5}-\frac{11 a x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{60 b^3}+\frac{x^3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{20 b^2}+\frac{1}{5} x^5 \csc ^{-1}(a+b x)","-\frac{\left(53 a^2+20\right) a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{30 b^5}+\frac{\left(58 a^2+9\right) (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{120 b^5}+\frac{a^5 \csc ^{-1}(a+b x)}{5 b^5}+\frac{\left(40 a^4+40 a^2+3\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{40 b^5}-\frac{11 a x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{60 b^3}+\frac{x^3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{20 b^2}+\frac{1}{5} x^5 \csc ^{-1}(a+b x)",1,"-(a*(20 + 53*a^2)*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(30*b^5) - (11*a*x^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(60*b^3) + (x^3*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(20*b^2) + ((9 + 58*a^2)*(a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)])/(120*b^5) + (a^5*ArcCsc[a + b*x])/(5*b^5) + (x^5*ArcCsc[a + b*x])/5 + ((3 + 40*a^2 + 40*a^4)*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/(40*b^5)","A",9,8,10,0.8000,1,"{5259, 4427, 3782, 4056, 4048, 3770, 3767, 8}"
18,1,155,0,0.1372908,"\int x^3 \csc ^{-1}(a+b x) \, dx","Int[x^3*ArcCsc[a + b*x],x]","\frac{\left(17 a^2+2\right) (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^4}-\frac{a^4 \csc ^{-1}(a+b x)}{4 b^4}-\frac{\left(2 a^2+1\right) a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{2 b^4}+\frac{x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^2}-\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{3 b^4}+\frac{1}{4} x^4 \csc ^{-1}(a+b x)","\frac{\left(17 a^2+2\right) (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^4}-\frac{a^4 \csc ^{-1}(a+b x)}{4 b^4}-\frac{\left(2 a^2+1\right) a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{2 b^4}+\frac{x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^2}-\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{3 b^4}+\frac{1}{4} x^4 \csc ^{-1}(a+b x)",1,"((2 + 17*a^2)*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(12*b^4) + (x^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(12*b^2) - (a*(a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)])/(3*b^4) - (a^4*ArcCsc[a + b*x])/(4*b^4) + (x^4*ArcCsc[a + b*x])/4 - (a*(1 + 2*a^2)*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/(2*b^4)","A",8,7,10,0.7000,1,"{5259, 4427, 3782, 4048, 3770, 3767, 8}"
19,1,116,0,0.0886351,"\int x^2 \csc ^{-1}(a+b x) \, dx","Int[x^2*ArcCsc[a + b*x],x]","\frac{a^3 \csc ^{-1}(a+b x)}{3 b^3}+\frac{\left(6 a^2+1\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{6 b^3}-\frac{5 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^3}+\frac{x (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^2}+\frac{1}{3} x^3 \csc ^{-1}(a+b x)","\frac{a^3 \csc ^{-1}(a+b x)}{3 b^3}+\frac{\left(6 a^2+1\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{6 b^3}-\frac{5 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^3}+\frac{x (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^2}+\frac{1}{3} x^3 \csc ^{-1}(a+b x)",1,"(-5*a*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*b^3) + (x*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*b^2) + (a^3*ArcCsc[a + b*x])/(3*b^3) + (x^3*ArcCsc[a + b*x])/3 + ((1 + 6*a^2)*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/(6*b^3)","A",7,6,10,0.6000,1,"{5259, 4427, 3782, 3770, 3767, 8}"
20,1,79,0,0.0526526,"\int x \csc ^{-1}(a+b x) \, dx","Int[x*ArcCsc[a + b*x],x]","-\frac{a^2 \csc ^{-1}(a+b x)}{2 b^2}+\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 b^2}-\frac{a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^2}+\frac{1}{2} x^2 \csc ^{-1}(a+b x)","-\frac{a^2 \csc ^{-1}(a+b x)}{2 b^2}+\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 b^2}-\frac{a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^2}+\frac{1}{2} x^2 \csc ^{-1}(a+b x)",1,"((a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(2*b^2) - (a^2*ArcCsc[a + b*x])/(2*b^2) + (x^2*ArcCsc[a + b*x])/2 - (a*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/b^2","A",6,6,8,0.7500,1,"{5259, 4427, 3773, 3770, 3767, 8}"
21,1,36,0,0.023543,"\int \csc ^{-1}(a+b x) \, dx","Int[ArcCsc[a + b*x],x]","\frac{(a+b x) \csc ^{-1}(a+b x)}{b}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b}","\frac{(a+b x) \csc ^{-1}(a+b x)}{b}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b}",1,"((a + b*x)*ArcCsc[a + b*x])/b + ArcTanh[Sqrt[1 - (a + b*x)^(-2)]]/b","A",5,5,6,0.8333,1,"{5251, 372, 266, 63, 206}"
22,1,210,0,0.3002295,"\int \frac{\csc ^{-1}(a+b x)}{x} \, dx","Int[ArcCsc[a + b*x]/x,x]","-i \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-i \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)+\csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)","-i \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-i \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{1}{2} i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)+\csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)",1,"ArcCsc[a + b*x]*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] + ArcCsc[a + b*x]*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] - ArcCsc[a + b*x]*Log[1 - E^((2*I)*ArcCsc[a + b*x])] - I*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] - I*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] + (I/2)*PolyLog[2, E^((2*I)*ArcCsc[a + b*x])]","A",14,8,10,0.8000,1,"{5259, 4552, 4529, 3717, 2190, 2279, 2391, 4519}"
23,1,69,0,0.096016,"\int \frac{\csc ^{-1}(a+b x)}{x^2} \, dx","Int[ArcCsc[a + b*x]/x^2,x]","-\frac{2 b \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{b \csc ^{-1}(a+b x)}{a}-\frac{\csc ^{-1}(a+b x)}{x}","-\frac{2 b \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}-\frac{b \csc ^{-1}(a+b x)}{a}-\frac{\csc ^{-1}(a+b x)}{x}",1,"-((b*ArcCsc[a + b*x])/a) - ArcCsc[a + b*x]/x - (2*b*ArcTan[(a - Tan[ArcCsc[a + b*x]/2])/Sqrt[1 - a^2]])/(a*Sqrt[1 - a^2])","A",6,6,10,0.6000,1,"{5259, 4427, 3783, 2660, 618, 204}"
24,1,123,0,0.1941735,"\int \frac{\csc ^{-1}(a+b x)}{x^3} \, dx","Int[ArcCsc[a + b*x]/x^3,x]","\frac{b^2 \csc ^{-1}(a+b x)}{2 a^2}+\frac{\left(1-2 a^2\right) b^2 \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 a \left(1-a^2\right) x}-\frac{\csc ^{-1}(a+b x)}{2 x^2}","\frac{b^2 \csc ^{-1}(a+b x)}{2 a^2}+\frac{\left(1-2 a^2\right) b^2 \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{a^2 \left(1-a^2\right)^{3/2}}-\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 a \left(1-a^2\right) x}-\frac{\csc ^{-1}(a+b x)}{2 x^2}",1,"-(b*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(2*a*(1 - a^2)*x) + (b^2*ArcCsc[a + b*x])/(2*a^2) - ArcCsc[a + b*x]/(2*x^2) + ((1 - 2*a^2)*b^2*ArcTan[(a - Tan[ArcCsc[a + b*x]/2])/Sqrt[1 - a^2]])/(a^2*(1 - a^2)^(3/2))","A",8,8,10,0.8000,1,"{5259, 4427, 3785, 3919, 3831, 2660, 618, 204}"
25,1,180,0,0.2970214,"\int \frac{\csc ^{-1}(a+b x)}{x^4} \, dx","Int[ArcCsc[a + b*x]/x^4,x]","\frac{\left(2-5 a^2\right) b^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a^2 \left(1-a^2\right)^2 x}-\frac{b^3 \csc ^{-1}(a+b x)}{3 a^3}-\frac{\left(6 a^4-5 a^2+2\right) b^3 \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{3 a^3 \left(1-a^2\right)^{5/2}}-\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a \left(1-a^2\right) x^2}-\frac{\csc ^{-1}(a+b x)}{3 x^3}","\frac{\left(2-5 a^2\right) b^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a^2 \left(1-a^2\right)^2 x}-\frac{b^3 \csc ^{-1}(a+b x)}{3 a^3}-\frac{\left(6 a^4-5 a^2+2\right) b^3 \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{3 a^3 \left(1-a^2\right)^{5/2}}-\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a \left(1-a^2\right) x^2}-\frac{\csc ^{-1}(a+b x)}{3 x^3}",1,"-(b*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*a*(1 - a^2)*x^2) + ((2 - 5*a^2)*b^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*a^2*(1 - a^2)^2*x) - (b^3*ArcCsc[a + b*x])/(3*a^3) - ArcCsc[a + b*x]/(3*x^3) - ((2 - 5*a^2 + 6*a^4)*b^3*ArcTan[(a - Tan[ArcCsc[a + b*x]/2])/Sqrt[1 - a^2]])/(3*a^3*(1 - a^2)^(5/2))","A",9,9,10,0.9000,1,"{5259, 4427, 3785, 4060, 3919, 3831, 2660, 618, 204}"
26,1,239,0,0.4565793,"\int \frac{\csc ^{-1}(a+b x)}{x^5} \, dx","Int[ArcCsc[a + b*x]/x^5,x]","\frac{\left(3-8 a^2\right) b^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{24 a^2 \left(1-a^2\right)^2 x^2}-\frac{\left(26 a^4-17 a^2+6\right) b^3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{24 a^3 \left(1-a^2\right)^3 x}+\frac{b^4 \csc ^{-1}(a+b x)}{4 a^4}+\frac{\left(-8 a^6+8 a^4-7 a^2+2\right) b^4 \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{4 a^4 \left(1-a^2\right)^{7/2}}-\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 a \left(1-a^2\right) x^3}-\frac{\csc ^{-1}(a+b x)}{4 x^4}","\frac{\left(3-8 a^2\right) b^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{24 a^2 \left(1-a^2\right)^2 x^2}-\frac{\left(26 a^4-17 a^2+6\right) b^3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{24 a^3 \left(1-a^2\right)^3 x}+\frac{b^4 \csc ^{-1}(a+b x)}{4 a^4}+\frac{\left(-8 a^6+8 a^4-7 a^2+2\right) b^4 \tan ^{-1}\left(\frac{a-\tan \left(\frac{1}{2} \csc ^{-1}(a+b x)\right)}{\sqrt{1-a^2}}\right)}{4 a^4 \left(1-a^2\right)^{7/2}}-\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 a \left(1-a^2\right) x^3}-\frac{\csc ^{-1}(a+b x)}{4 x^4}",1,"-(b*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(12*a*(1 - a^2)*x^3) + ((3 - 8*a^2)*b^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(24*a^2*(1 - a^2)^2*x^2) - ((6 - 17*a^2 + 26*a^4)*b^3*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(24*a^3*(1 - a^2)^3*x) + (b^4*ArcCsc[a + b*x])/(4*a^4) - ArcCsc[a + b*x]/(4*x^4) + ((2 - 7*a^2 + 8*a^4 - 8*a^6)*b^4*ArcTan[(a - Tan[ArcCsc[a + b*x]/2])/Sqrt[1 - a^2]])/(4*a^4*(1 - a^2)^(7/2))","A",10,9,10,0.9000,1,"{5259, 4427, 3785, 4060, 3919, 3831, 2660, 618, 204}"
27,1,366,0,0.3052886,"\int x^3 \csc ^{-1}(a+b x)^2 \, dx","Int[x^3*ArcCsc[a + b*x]^2,x]","\frac{2 i a^3 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^4}-\frac{2 i a^3 \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^4}+\frac{i a \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^4}-\frac{i a \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^4}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{a^4 \csc ^{-1}(a+b x)^2}{4 b^4}+\frac{3 a^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^4}-\frac{4 a^3 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log (a+b x)}{3 b^4}-\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^4}+\frac{(a+b x)^3 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{6 b^4}+\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{3 b^4}-\frac{2 a \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^4}+\frac{1}{4} x^4 \csc ^{-1}(a+b x)^2","\frac{2 i a^3 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^4}-\frac{2 i a^3 \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^4}+\frac{i a \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^4}-\frac{i a \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^4}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{a^4 \csc ^{-1}(a+b x)^2}{4 b^4}+\frac{3 a^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^4}-\frac{4 a^3 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log (a+b x)}{3 b^4}-\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^4}+\frac{(a+b x)^3 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{6 b^4}+\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{3 b^4}-\frac{2 a \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^4}+\frac{1}{4} x^4 \csc ^{-1}(a+b x)^2",1,"-((a*x)/b^3) + (a + b*x)^2/(12*b^4) + ((a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/(3*b^4) + (3*a^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/b^4 - (a*(a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/b^4 + ((a + b*x)^3*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/(6*b^4) - (a^4*ArcCsc[a + b*x]^2)/(4*b^4) + (x^4*ArcCsc[a + b*x]^2)/4 - (2*a*ArcCsc[a + b*x]*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^4 - (4*a^3*ArcCsc[a + b*x]*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^4 + Log[a + b*x]/(3*b^4) + (3*a^2*Log[a + b*x])/b^4 + (I*a*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^4 + ((2*I)*a^3*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^4 - (I*a*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^4 - ((2*I)*a^3*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^4","A",20,9,12,0.7500,1,"{5259, 4427, 4190, 4183, 2279, 2391, 4184, 3475, 4185}"
28,1,272,0,0.2308167,"\int x^2 \csc ^{-1}(a+b x)^2 \, dx","Int[x^2*ArcCsc[a + b*x]^2,x]","-\frac{2 i a^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{2 i a^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{i \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{3 b^3}+\frac{i \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{3 b^3}+\frac{a^3 \csc ^{-1}(a+b x)^2}{3 b^3}+\frac{4 a^2 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{2 a \log (a+b x)}{b^3}-\frac{2 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^3}+\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{3 b^3}+\frac{2 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{3 b^3}+\frac{1}{3} x^3 \csc ^{-1}(a+b x)^2+\frac{x}{3 b^2}","-\frac{2 i a^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{2 i a^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{i \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{3 b^3}+\frac{i \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{3 b^3}+\frac{a^3 \csc ^{-1}(a+b x)^2}{3 b^3}+\frac{4 a^2 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{2 a \log (a+b x)}{b^3}-\frac{2 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^3}+\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{3 b^3}+\frac{2 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{3 b^3}+\frac{1}{3} x^3 \csc ^{-1}(a+b x)^2+\frac{x}{3 b^2}",1,"x/(3*b^2) - (2*a*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/b^3 + ((a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/(3*b^3) + (a^3*ArcCsc[a + b*x]^2)/(3*b^3) + (x^3*ArcCsc[a + b*x]^2)/3 + (2*ArcCsc[a + b*x]*ArcTanh[E^(I*ArcCsc[a + b*x])])/(3*b^3) + (4*a^2*ArcCsc[a + b*x]*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^3 - (2*a*Log[a + b*x])/b^3 - ((I/3)*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^3 - ((2*I)*a^2*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^3 + ((I/3)*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^3 + ((2*I)*a^2*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^3","A",17,9,12,0.7500,1,"{5259, 4427, 4190, 4183, 2279, 2391, 4184, 3475, 4185}"
29,1,145,0,0.1339061,"\int x \csc ^{-1}(a+b x)^2 \, dx","Int[x*ArcCsc[a + b*x]^2,x]","\frac{2 i a \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{2 i a \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \csc ^{-1}(a+b x)^2}{2 b^2}+\frac{\log (a+b x)}{b^2}+\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^2}-\frac{4 a \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \csc ^{-1}(a+b x)^2","\frac{2 i a \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{2 i a \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \csc ^{-1}(a+b x)^2}{2 b^2}+\frac{\log (a+b x)}{b^2}+\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)}{b^2}-\frac{4 a \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \csc ^{-1}(a+b x)^2",1,"((a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x])/b^2 - (a^2*ArcCsc[a + b*x]^2)/(2*b^2) + (x^2*ArcCsc[a + b*x]^2)/2 - (4*a*ArcCsc[a + b*x]*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^2 + Log[a + b*x]/b^2 + ((2*I)*a*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^2 - ((2*I)*a*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^2","A",11,8,10,0.8000,1,"{5259, 4427, 4190, 4183, 2279, 2391, 4184, 3475}"
30,1,86,0,0.0635541,"\int \csc ^{-1}(a+b x)^2 \, dx","Int[ArcCsc[a + b*x]^2,x]","-\frac{2 i \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{2 i \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \csc ^{-1}(a+b x)^2}{b}+\frac{4 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b}","-\frac{2 i \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{2 i \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \csc ^{-1}(a+b x)^2}{b}+\frac{4 \csc ^{-1}(a+b x) \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*ArcCsc[a + b*x]^2)/b + (4*ArcCsc[a + b*x]*ArcTanh[E^(I*ArcCsc[a + b*x])])/b - ((2*I)*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b + ((2*I)*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b","A",8,6,8,0.7500,1,"{5253, 5217, 3758, 4183, 2279, 2391}"
31,1,324,0,0.4934711,"\int \frac{\csc ^{-1}(a+b x)^2}{x} \, dx","Int[ArcCsc[a + b*x]^2/x,x]","-2 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+2 \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(a+b x)}\right)+\csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\csc ^{-1}(a+b x)^2 \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)","-2 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+2 \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(a+b x)}\right)+\csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\csc ^{-1}(a+b x)^2 \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)",1,"ArcCsc[a + b*x]^2*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] + ArcCsc[a + b*x]^2*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] - ArcCsc[a + b*x]^2*Log[1 - E^((2*I)*ArcCsc[a + b*x])] - (2*I)*ArcCsc[a + b*x]*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] - (2*I)*ArcCsc[a + b*x]*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] + I*ArcCsc[a + b*x]*PolyLog[2, E^((2*I)*ArcCsc[a + b*x])] + 2*PolyLog[3, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] + 2*PolyLog[3, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] - PolyLog[3, E^((2*I)*ArcCsc[a + b*x])]/2","A",17,9,12,0.7500,1,"{5259, 4552, 4529, 3717, 2190, 2531, 2282, 6589, 4519}"
32,1,254,0,0.4156226,"\int \frac{\csc ^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcCsc[a + b*x]^2/x^2,x]","-\frac{2 b \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 b \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{2 i b \csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 i b \csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \csc ^{-1}(a+b x)^2}{a}-\frac{\csc ^{-1}(a+b x)^2}{x}","-\frac{2 b \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 b \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{2 i b \csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 i b \csc ^{-1}(a+b x) \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \csc ^{-1}(a+b x)^2}{a}-\frac{\csc ^{-1}(a+b x)^2}{x}",1,"-((b*ArcCsc[a + b*x]^2)/a) - ArcCsc[a + b*x]^2/x - ((2*I)*b*ArcCsc[a + b*x]*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + ((2*I)*b*ArcCsc[a + b*x]*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (2*b*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (2*b*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2])","A",12,8,12,0.6667,1,"{5259, 4427, 4191, 3323, 2264, 2190, 2279, 2391}"
33,1,464,0,0.4021942,"\int x^2 \csc ^{-1}(a+b x)^3 \, dx","Int[x^2*ArcCsc[a + b*x]^3,x]","-\frac{6 i a^2 \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{6 i a^2 \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{6 a^2 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{6 a^2 \text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{3 i a \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{\text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{\text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{a^3 \csc ^{-1}(a+b x)^3}{3 b^3}+\frac{6 a^2 \csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)^2}{2 b^3}-\frac{3 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)^2}{b^3}-\frac{3 i a \csc ^{-1}(a+b x)^2}{b^3}+\frac{(a+b x) \csc ^{-1}(a+b x)}{b^3}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^3}+\frac{6 a \csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{\csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{1}{3} x^3 \csc ^{-1}(a+b x)^3","-\frac{6 i a^2 \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{6 i a^2 \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{6 a^2 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{6 a^2 \text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{3 i a \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{\text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b^3}-\frac{\text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{a^3 \csc ^{-1}(a+b x)^3}{3 b^3}+\frac{6 a^2 \csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)^2}{2 b^3}-\frac{3 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)^2}{b^3}-\frac{3 i a \csc ^{-1}(a+b x)^2}{b^3}+\frac{(a+b x) \csc ^{-1}(a+b x)}{b^3}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^3}+\frac{6 a \csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{\csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^3}+\frac{1}{3} x^3 \csc ^{-1}(a+b x)^3",1,"((a + b*x)*ArcCsc[a + b*x])/b^3 - ((3*I)*a*ArcCsc[a + b*x]^2)/b^3 - (3*a*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x]^2)/b^3 + ((a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x]^2)/(2*b^3) + (a^3*ArcCsc[a + b*x]^3)/(3*b^3) + (x^3*ArcCsc[a + b*x]^3)/3 + (ArcCsc[a + b*x]^2*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^3 + (6*a^2*ArcCsc[a + b*x]^2*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^3 + ArcTanh[Sqrt[1 - (a + b*x)^(-2)]]/b^3 + (6*a*ArcCsc[a + b*x]*Log[1 - E^((2*I)*ArcCsc[a + b*x])])/b^3 - (I*ArcCsc[a + b*x]*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^3 - ((6*I)*a^2*ArcCsc[a + b*x]*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^3 + (I*ArcCsc[a + b*x]*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^3 + ((6*I)*a^2*ArcCsc[a + b*x]*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^3 - ((3*I)*a*PolyLog[2, E^((2*I)*ArcCsc[a + b*x])])/b^3 + PolyLog[3, -E^(I*ArcCsc[a + b*x])]/b^3 + (6*a^2*PolyLog[3, -E^(I*ArcCsc[a + b*x])])/b^3 - PolyLog[3, E^(I*ArcCsc[a + b*x])]/b^3 - (6*a^2*PolyLog[3, E^(I*ArcCsc[a + b*x])])/b^3","A",25,14,12,1.167,1,"{5259, 4427, 4190, 4183, 2531, 2282, 6589, 4184, 3717, 2190, 2279, 2391, 4186, 3770}"
34,1,264,0,0.2556321,"\int x \csc ^{-1}(a+b x)^3 \, dx","Int[x*ArcCsc[a + b*x]^3,x]","\frac{6 i a \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{3 i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)}{2 b^2}-\frac{6 a \text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{6 a \text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \csc ^{-1}(a+b x)^3}{2 b^2}+\frac{3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)^2}{2 b^2}+\frac{3 i \csc ^{-1}(a+b x)^2}{2 b^2}-\frac{3 \csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{6 a \csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \csc ^{-1}(a+b x)^3","\frac{6 i a \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{3 i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)}{2 b^2}-\frac{6 a \text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{6 a \text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \csc ^{-1}(a+b x)^3}{2 b^2}+\frac{3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \csc ^{-1}(a+b x)^2}{2 b^2}+\frac{3 i \csc ^{-1}(a+b x)^2}{2 b^2}-\frac{3 \csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)}{b^2}-\frac{6 a \csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \csc ^{-1}(a+b x)^3",1,"(((3*I)/2)*ArcCsc[a + b*x]^2)/b^2 + (3*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcCsc[a + b*x]^2)/(2*b^2) - (a^2*ArcCsc[a + b*x]^3)/(2*b^2) + (x^2*ArcCsc[a + b*x]^3)/2 - (6*a*ArcCsc[a + b*x]^2*ArcTanh[E^(I*ArcCsc[a + b*x])])/b^2 - (3*ArcCsc[a + b*x]*Log[1 - E^((2*I)*ArcCsc[a + b*x])])/b^2 + ((6*I)*a*ArcCsc[a + b*x]*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b^2 - ((6*I)*a*ArcCsc[a + b*x]*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b^2 + (((3*I)/2)*PolyLog[2, E^((2*I)*ArcCsc[a + b*x])])/b^2 - (6*a*PolyLog[3, -E^(I*ArcCsc[a + b*x])])/b^2 + (6*a*PolyLog[3, E^(I*ArcCsc[a + b*x])])/b^2","A",16,12,10,1.200,1,"{5259, 4427, 4190, 4183, 2531, 2282, 6589, 4184, 3717, 2190, 2279, 2391}"
35,1,140,0,0.1016287,"\int \csc ^{-1}(a+b x)^3 \, dx","Int[ArcCsc[a + b*x]^3,x]","-\frac{6 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{6 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{6 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b}-\frac{6 \text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \csc ^{-1}(a+b x)^3}{b}+\frac{6 \csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b}","-\frac{6 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{6 i \csc ^{-1}(a+b x) \text{PolyLog}\left(2,e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{6 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(a+b x)}\right)}{b}-\frac{6 \text{PolyLog}\left(3,e^{i \csc ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \csc ^{-1}(a+b x)^3}{b}+\frac{6 \csc ^{-1}(a+b x)^2 \tanh ^{-1}\left(e^{i \csc ^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*ArcCsc[a + b*x]^3)/b + (6*ArcCsc[a + b*x]^2*ArcTanh[E^(I*ArcCsc[a + b*x])])/b - ((6*I)*ArcCsc[a + b*x]*PolyLog[2, -E^(I*ArcCsc[a + b*x])])/b + ((6*I)*ArcCsc[a + b*x]*PolyLog[2, E^(I*ArcCsc[a + b*x])])/b + (6*PolyLog[3, -E^(I*ArcCsc[a + b*x])])/b - (6*PolyLog[3, E^(I*ArcCsc[a + b*x])])/b","A",10,7,8,0.8750,1,"{5253, 5217, 3758, 4183, 2531, 2282, 6589}"
36,1,448,0,0.5421085,"\int \frac{\csc ^{-1}(a+b x)^3}{x} \, dx","Int[ArcCsc[a + b*x]^3/x,x]","-3 i \csc ^{-1}(a+b x)^2 \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-3 i \csc ^{-1}(a+b x)^2 \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \csc ^{-1}(a+b x) \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \csc ^{-1}(a+b x) \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 i \text{PolyLog}\left(4,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 i \text{PolyLog}\left(4,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{3}{2} i \csc ^{-1}(a+b x)^2 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)-\frac{3}{2} \csc ^{-1}(a+b x) \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(a+b x)}\right)-\frac{3}{4} i \text{PolyLog}\left(4,e^{2 i \csc ^{-1}(a+b x)}\right)+\csc ^{-1}(a+b x)^3 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\csc ^{-1}(a+b x)^3 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\csc ^{-1}(a+b x)^3 \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)","-3 i \csc ^{-1}(a+b x)^2 \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-3 i \csc ^{-1}(a+b x)^2 \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \csc ^{-1}(a+b x) \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \csc ^{-1}(a+b x) \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 i \text{PolyLog}\left(4,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 i \text{PolyLog}\left(4,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{3}{2} i \csc ^{-1}(a+b x)^2 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)-\frac{3}{2} \csc ^{-1}(a+b x) \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(a+b x)}\right)-\frac{3}{4} i \text{PolyLog}\left(4,e^{2 i \csc ^{-1}(a+b x)}\right)+\csc ^{-1}(a+b x)^3 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\csc ^{-1}(a+b x)^3 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\csc ^{-1}(a+b x)^3 \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)",1,"ArcCsc[a + b*x]^3*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] + ArcCsc[a + b*x]^3*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] - ArcCsc[a + b*x]^3*Log[1 - E^((2*I)*ArcCsc[a + b*x])] - (3*I)*ArcCsc[a + b*x]^2*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] - (3*I)*ArcCsc[a + b*x]^2*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] + ((3*I)/2)*ArcCsc[a + b*x]^2*PolyLog[2, E^((2*I)*ArcCsc[a + b*x])] + 6*ArcCsc[a + b*x]*PolyLog[3, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] + 6*ArcCsc[a + b*x]*PolyLog[3, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] - (3*ArcCsc[a + b*x]*PolyLog[3, E^((2*I)*ArcCsc[a + b*x])])/2 + (6*I)*PolyLog[4, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])] + (6*I)*PolyLog[4, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])] - ((3*I)/4)*PolyLog[4, E^((2*I)*ArcCsc[a + b*x])]","A",20,10,12,0.8333,1,"{5259, 4552, 4529, 3717, 2190, 2531, 6609, 2282, 6589, 4519}"
37,1,378,0,0.6166079,"\int \frac{\csc ^{-1}(a+b x)^3}{x^2} \, dx","Int[ArcCsc[a + b*x]^3/x^2,x]","-\frac{6 b \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 i b \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 i b \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{3 i b \csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{3 i b \csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \csc ^{-1}(a+b x)^3}{a}-\frac{\csc ^{-1}(a+b x)^3}{x}","-\frac{6 b \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \csc ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 i b \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 i b \text{PolyLog}\left(3,-\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{3 i b \csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{3 i b \csc ^{-1}(a+b x)^2 \log \left(1+\frac{i a e^{i \csc ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \csc ^{-1}(a+b x)^3}{a}-\frac{\csc ^{-1}(a+b x)^3}{x}",1,"-((b*ArcCsc[a + b*x]^3)/a) - ArcCsc[a + b*x]^3/x - ((3*I)*b*ArcCsc[a + b*x]^2*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + ((3*I)*b*ArcCsc[a + b*x]^2*Log[1 + (I*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (6*b*ArcCsc[a + b*x]*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (6*b*ArcCsc[a + b*x]*PolyLog[2, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - ((6*I)*b*PolyLog[3, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + ((6*I)*b*PolyLog[3, ((-I)*a*E^(I*ArcCsc[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2])","A",14,9,12,0.7500,1,"{5259, 4427, 4191, 3323, 2264, 2190, 2531, 2282, 6589}"
38,1,48,0,0.0632184,"\int x^3 \csc ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcCsc[a + b*x^4],x]","\frac{\left(a+b x^4\right) \csc ^{-1}\left(a+b x^4\right)}{4 b}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(a+b x^4\right)^2}}\right)}{4 b}","\frac{\left(a+b x^4\right) \csc ^{-1}\left(a+b x^4\right)}{4 b}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(a+b x^4\right)^2}}\right)}{4 b}",1,"((a + b*x^4)*ArcCsc[a + b*x^4])/(4*b) + ArcTanh[Sqrt[1 - (a + b*x^4)^(-2)]]/(4*b)","A",6,6,12,0.5000,1,"{6715, 5251, 372, 266, 63, 206}"
39,1,48,0,0.0697476,"\int x^{-1+n} \csc ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcCsc[a + b*x^n],x]","\frac{\left(a+b x^n\right) \csc ^{-1}\left(a+b x^n\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(a+b x^n\right)^2}}\right)}{b n}","\frac{\left(a+b x^n\right) \csc ^{-1}\left(a+b x^n\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(a+b x^n\right)^2}}\right)}{b n}",1,"((a + b*x^n)*ArcCsc[a + b*x^n])/(b*n) + ArcTanh[Sqrt[1 - (a + b*x^n)^(-2)]]/(b*n)","A",6,6,14,0.4286,1,"{6715, 5251, 372, 266, 63, 206}"
40,1,85,0,0.0857296,"\int \csc ^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcCsc[c*E^(a + b*x)],x]","\frac{i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{i \csc ^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\csc ^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 i \csc ^{-1}\left(c e^{a+b x}\right)}\right)}{b}","\frac{i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{i \csc ^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\csc ^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 i \csc ^{-1}\left(c e^{a+b x}\right)}\right)}{b}",1,"((I/2)*ArcCsc[c*E^(a + b*x)]^2)/b - (ArcCsc[c*E^(a + b*x)]*Log[1 - E^((2*I)*ArcCsc[c*E^(a + b*x)])])/b + ((I/2)*PolyLog[2, E^((2*I)*ArcCsc[c*E^(a + b*x)])])/b","A",7,7,10,0.7000,1,"{2282, 5219, 4625, 3717, 2190, 2279, 2391}"
41,1,95,0,0.1209344,"\int e^{\csc ^{-1}(a x)} x^2 \, dx","Int[E^ArcCsc[a*x]*x^2,x]","\frac{\left(\frac{4}{5}-\frac{12 i}{5}\right) e^{(1+3 i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},3;\frac{5}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^3}-\frac{\left(\frac{8}{5}-\frac{24 i}{5}\right) e^{(1+3 i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},4;\frac{5}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^3}","\frac{\left(\frac{4}{5}-\frac{12 i}{5}\right) e^{(1+3 i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},3;\frac{5}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^3}-\frac{\left(\frac{8}{5}-\frac{24 i}{5}\right) e^{(1+3 i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},4;\frac{5}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^3}",1,"((4/5 - (12*I)/5)*E^((1 + 3*I)*ArcCsc[a*x])*Hypergeometric2F1[3/2 - I/2, 3, 5/2 - I/2, E^((2*I)*ArcCsc[a*x])])/a^3 - ((8/5 - (24*I)/5)*E^((1 + 3*I)*ArcCsc[a*x])*Hypergeometric2F1[3/2 - I/2, 4, 5/2 - I/2, E^((2*I)*ArcCsc[a*x])])/a^3","A",6,4,10,0.4000,1,"{5267, 12, 4471, 2251}"
42,1,87,0,0.1061694,"\int e^{\csc ^{-1}(a x)} x \, dx","Int[E^ArcCsc[a*x]*x,x]","\frac{\left(\frac{8}{5}+\frac{4 i}{5}\right) e^{(1+2 i) \csc ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^2}-\frac{\left(\frac{16}{5}+\frac{8 i}{5}\right) e^{(1+2 i) \csc ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},3;2-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^2}","\frac{\left(\frac{8}{5}+\frac{4 i}{5}\right) e^{(1+2 i) \csc ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^2}-\frac{\left(\frac{16}{5}+\frac{8 i}{5}\right) e^{(1+2 i) \csc ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},3;2-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a^2}",1,"((8/5 + (4*I)/5)*E^((1 + 2*I)*ArcCsc[a*x])*Hypergeometric2F1[1 - I/2, 2, 2 - I/2, E^((2*I)*ArcCsc[a*x])])/a^2 - ((16/5 + (8*I)/5)*E^((1 + 2*I)*ArcCsc[a*x])*Hypergeometric2F1[1 - I/2, 3, 2 - I/2, E^((2*I)*ArcCsc[a*x])])/a^2","A",6,4,8,0.5000,1,"{5267, 12, 4471, 2251}"
43,1,87,0,0.0941809,"\int e^{\csc ^{-1}(a x)} \, dx","Int[E^ArcCsc[a*x],x]","\frac{(2-2 i) e^{(1+i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a}-\frac{(1-i) e^{(1+i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a}","\frac{(2-2 i) e^{(1+i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a}-\frac{(1-i) e^{(1+i) \csc ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)}{a}",1,"((-1 + I)*E^((1 + I)*ArcCsc[a*x])*Hypergeometric2F1[1/2 - I/2, 1, 3/2 - I/2, E^((2*I)*ArcCsc[a*x])])/a + ((2 - 2*I)*E^((1 + I)*ArcCsc[a*x])*Hypergeometric2F1[1/2 - I/2, 2, 3/2 - I/2, E^((2*I)*ArcCsc[a*x])])/a","A",5,3,6,0.5000,1,"{5267, 4471, 2251}"
44,1,43,0,0.0585483,"\int \frac{e^{\csc ^{-1}(a x)}}{x} \, dx","Int[E^ArcCsc[a*x]/x,x]","2 i e^{\csc ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)-i e^{\csc ^{-1}(a x)}","2 i e^{\csc ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};e^{2 i \csc ^{-1}(a x)}\right)-i e^{\csc ^{-1}(a x)}",1,"(-I)*E^ArcCsc[a*x] + (2*I)*E^ArcCsc[a*x]*Hypergeometric2F1[-I/2, 1, 1 - I/2, E^((2*I)*ArcCsc[a*x])]","A",6,5,10,0.5000,1,"{5267, 12, 4443, 2194, 2251}"
45,1,39,0,0.0302034,"\int \frac{e^{\csc ^{-1}(a x)}}{x^2} \, dx","Int[E^ArcCsc[a*x]/x^2,x]","-\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} e^{\csc ^{-1}(a x)}-\frac{e^{\csc ^{-1}(a x)}}{2 x}","-\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} e^{\csc ^{-1}(a x)}-\frac{e^{\csc ^{-1}(a x)}}{2 x}",1,"-(a*E^ArcCsc[a*x]*Sqrt[1 - 1/(a^2*x^2)])/2 - E^ArcCsc[a*x]/(2*x)","A",3,3,10,0.3000,1,"{5267, 12, 4433}"
46,1,41,0,0.0431414,"\int \frac{e^{\csc ^{-1}(a x)}}{x^3} \, dx","Int[E^ArcCsc[a*x]/x^3,x]","\frac{1}{5} a^2 e^{\csc ^{-1}(a x)} \cos \left(2 \csc ^{-1}(a x)\right)-\frac{1}{10} a^2 e^{\csc ^{-1}(a x)} \sin \left(2 \csc ^{-1}(a x)\right)","\frac{1}{5} a^2 e^{\csc ^{-1}(a x)} \cos \left(2 \csc ^{-1}(a x)\right)-\frac{1}{10} a^2 e^{\csc ^{-1}(a x)} \sin \left(2 \csc ^{-1}(a x)\right)",1,"(a^2*E^ArcCsc[a*x]*Cos[2*ArcCsc[a*x]])/5 - (a^2*E^ArcCsc[a*x]*Sin[2*ArcCsc[a*x]])/10","A",5,4,10,0.4000,1,"{5267, 12, 4469, 4432}"
47,1,84,0,0.0671424,"\int \frac{e^{\csc ^{-1}(a x)}}{x^4} \, dx","Int[E^ArcCsc[a*x]/x^4,x]","-\frac{1}{8} a^3 \sqrt{1-\frac{1}{a^2 x^2}} e^{\csc ^{-1}(a x)}-\frac{a^2 e^{\csc ^{-1}(a x)}}{8 x}+\frac{1}{40} a^3 e^{\csc ^{-1}(a x)} \cos \left(3 \csc ^{-1}(a x)\right)+\frac{3}{40} a^3 e^{\csc ^{-1}(a x)} \sin \left(3 \csc ^{-1}(a x)\right)","-\frac{1}{8} a^3 \sqrt{1-\frac{1}{a^2 x^2}} e^{\csc ^{-1}(a x)}-\frac{a^2 e^{\csc ^{-1}(a x)}}{8 x}+\frac{1}{40} a^3 e^{\csc ^{-1}(a x)} \cos \left(3 \csc ^{-1}(a x)\right)+\frac{3}{40} a^3 e^{\csc ^{-1}(a x)} \sin \left(3 \csc ^{-1}(a x)\right)",1,"-(a^3*E^ArcCsc[a*x]*Sqrt[1 - 1/(a^2*x^2)])/8 - (a^2*E^ArcCsc[a*x])/(8*x) + (a^3*E^ArcCsc[a*x]*Cos[3*ArcCsc[a*x]])/40 + (3*a^3*E^ArcCsc[a*x]*Sin[3*ArcCsc[a*x]])/40","A",6,4,10,0.4000,1,"{5267, 12, 4469, 4433}"
48,1,81,0,0.0679689,"\int \frac{e^{\csc ^{-1}(a x)}}{x^5} \, dx","Int[E^ArcCsc[a*x]/x^5,x]","\frac{1}{10} a^4 e^{\csc ^{-1}(a x)} \cos \left(2 \csc ^{-1}(a x)\right)-\frac{1}{34} a^4 e^{\csc ^{-1}(a x)} \cos \left(4 \csc ^{-1}(a x)\right)-\frac{1}{20} a^4 e^{\csc ^{-1}(a x)} \sin \left(2 \csc ^{-1}(a x)\right)+\frac{1}{136} a^4 e^{\csc ^{-1}(a x)} \sin \left(4 \csc ^{-1}(a x)\right)","\frac{1}{10} a^4 e^{\csc ^{-1}(a x)} \cos \left(2 \csc ^{-1}(a x)\right)-\frac{1}{34} a^4 e^{\csc ^{-1}(a x)} \cos \left(4 \csc ^{-1}(a x)\right)-\frac{1}{20} a^4 e^{\csc ^{-1}(a x)} \sin \left(2 \csc ^{-1}(a x)\right)+\frac{1}{136} a^4 e^{\csc ^{-1}(a x)} \sin \left(4 \csc ^{-1}(a x)\right)",1,"(a^4*E^ArcCsc[a*x]*Cos[2*ArcCsc[a*x]])/10 - (a^4*E^ArcCsc[a*x]*Cos[4*ArcCsc[a*x]])/34 - (a^4*E^ArcCsc[a*x]*Sin[2*ArcCsc[a*x]])/20 + (a^4*E^ArcCsc[a*x]*Sin[4*ArcCsc[a*x]])/136","A",6,4,10,0.4000,1,"{5267, 12, 4469, 4432}"
49,1,69,0,0.0954275,"\int \frac{\csc ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcCsc[a + b*x]/((a*d)/b + d*x),x]","\frac{i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)}{2 d}+\frac{i \csc ^{-1}(a+b x)^2}{2 d}-\frac{\csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)}{d}","\frac{i \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(a+b x)}\right)}{2 d}+\frac{i \csc ^{-1}(a+b x)^2}{2 d}-\frac{\csc ^{-1}(a+b x) \log \left(1-e^{2 i \csc ^{-1}(a+b x)}\right)}{d}",1,"((I/2)*ArcCsc[a + b*x]^2)/d - (ArcCsc[a + b*x]*Log[1 - E^((2*I)*ArcCsc[a + b*x])])/d + ((I/2)*PolyLog[2, E^((2*I)*ArcCsc[a + b*x])])/d","A",8,8,19,0.4211,1,"{5257, 12, 5219, 4625, 3717, 2190, 2279, 2391}"