1,1,51,75,0.0748636,"\int x^4 \sin ^{-1}(a x) \, dx","Integrate[x^4*ArcSin[a*x],x]","\frac{\sqrt{1-a^2 x^2} \left(3 a^4 x^4+4 a^2 x^2+8\right)}{75 a^5}+\frac{1}{5} x^5 \sin ^{-1}(a x)","\frac{\left(1-a^2 x^2\right)^{5/2}}{25 a^5}-\frac{2 \left(1-a^2 x^2\right)^{3/2}}{15 a^5}+\frac{\sqrt{1-a^2 x^2}}{5 a^5}+\frac{1}{5} x^5 \sin ^{-1}(a x)",1,"(Sqrt[1 - a^2*x^2]*(8 + 4*a^2*x^2 + 3*a^4*x^4))/(75*a^5) + (x^5*ArcSin[a*x])/5","A",1
2,1,50,69,0.0304099,"\int x^3 \sin ^{-1}(a x) \, dx","Integrate[x^3*ArcSin[a*x],x]","\frac{\left(8 a^4 x^4-3\right) \sin ^{-1}(a x)+a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+3\right)}{32 a^4}","-\frac{3 \sin ^{-1}(a x)}{32 a^4}+\frac{x^3 \sqrt{1-a^2 x^2}}{16 a}+\frac{3 x \sqrt{1-a^2 x^2}}{32 a^3}+\frac{1}{4} x^4 \sin ^{-1}(a x)",1,"(a*x*Sqrt[1 - a^2*x^2]*(3 + 2*a^2*x^2) + (-3 + 8*a^4*x^4)*ArcSin[a*x])/(32*a^4)","A",1
3,1,41,54,0.0245177,"\int x^2 \sin ^{-1}(a x) \, dx","Integrate[x^2*ArcSin[a*x],x]","\frac{1}{9} \left(\frac{\sqrt{1-a^2 x^2} \left(a^2 x^2+2\right)}{a^3}+3 x^3 \sin ^{-1}(a x)\right)","-\frac{\left(1-a^2 x^2\right)^{3/2}}{9 a^3}+\frac{\sqrt{1-a^2 x^2}}{3 a^3}+\frac{1}{3} x^3 \sin ^{-1}(a x)",1,"((Sqrt[1 - a^2*x^2]*(2 + a^2*x^2))/a^3 + 3*x^3*ArcSin[a*x])/9","A",1
4,1,40,45,0.0148667,"\int x \sin ^{-1}(a x) \, dx","Integrate[x*ArcSin[a*x],x]","\frac{a x \sqrt{1-a^2 x^2}+\left(2 a^2 x^2-1\right) \sin ^{-1}(a x)}{4 a^2}","\frac{x \sqrt{1-a^2 x^2}}{4 a}-\frac{\sin ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \sin ^{-1}(a x)",1,"(a*x*Sqrt[1 - a^2*x^2] + (-1 + 2*a^2*x^2)*ArcSin[a*x])/(4*a^2)","A",1
5,1,25,25,0.0085514,"\int \sin ^{-1}(a x) \, dx","Integrate[ArcSin[a*x],x]","\frac{\sqrt{1-a^2 x^2}}{a}+x \sin ^{-1}(a x)","\frac{\sqrt{1-a^2 x^2}}{a}+x \sin ^{-1}(a x)",1,"Sqrt[1 - a^2*x^2]/a + x*ArcSin[a*x]","A",1
6,1,46,51,0.0878669,"\int \frac{\sin ^{-1}(a x)}{x} \, dx","Integrate[ArcSin[a*x]/x,x]","\sin ^{-1}(a x) \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)-\frac{1}{2} i \left(\sin ^{-1}(a x)^2+\text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)\right)","-\frac{1}{2} i \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{1}{2} i \sin ^{-1}(a x)^2+\sin ^{-1}(a x) \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)",1,"ArcSin[a*x]*Log[1 - E^((2*I)*ArcSin[a*x])] - (I/2)*(ArcSin[a*x]^2 + PolyLog[2, E^((2*I)*ArcSin[a*x])])","A",1
7,1,28,28,0.0024618,"\int \frac{\sin ^{-1}(a x)}{x^2} \, dx","Integrate[ArcSin[a*x]/x^2,x]","-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sin ^{-1}(a x)}{x}","-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sin ^{-1}(a x)}{x}",1,"-(ArcSin[a*x]/x) - a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",1
8,1,29,34,0.0075761,"\int \frac{\sin ^{-1}(a x)}{x^3} \, dx","Integrate[ArcSin[a*x]/x^3,x]","-\frac{a x \sqrt{1-a^2 x^2}+\sin ^{-1}(a x)}{2 x^2}","-\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\sin ^{-1}(a x)}{2 x^2}",1,"-1/2*(a*x*Sqrt[1 - a^2*x^2] + ArcSin[a*x])/x^2","A",1
9,1,53,56,0.0176991,"\int \frac{\sin ^{-1}(a x)}{x^4} \, dx","Integrate[ArcSin[a*x]/x^4,x]","-\frac{a x \sqrt{1-a^2 x^2}+a^3 x^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 \sin ^{-1}(a x)}{6 x^3}","-\frac{a \sqrt{1-a^2 x^2}}{6 x^2}-\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sin ^{-1}(a x)}{3 x^3}",1,"-1/6*(a*x*Sqrt[1 - a^2*x^2] + 2*ArcSin[a*x] + a^3*x^3*ArcTanh[Sqrt[1 - a^2*x^2]])/x^3","A",1
10,1,41,58,0.0201113,"\int \frac{\sin ^{-1}(a x)}{x^5} \, dx","Integrate[ArcSin[a*x]/x^5,x]","-\frac{a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+1\right)+3 \sin ^{-1}(a x)}{12 x^4}","-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}-\frac{a^3 \sqrt{1-a^2 x^2}}{6 x}-\frac{\sin ^{-1}(a x)}{4 x^4}",1,"-1/12*(a*x*Sqrt[1 - a^2*x^2]*(1 + 2*a^2*x^2) + 3*ArcSin[a*x])/x^4","A",1
11,1,51,80,0.0137726,"\int \frac{\sin ^{-1}(a x)}{x^6} \, dx","Integrate[ArcSin[a*x]/x^6,x]","-\frac{1}{5} a^5 \sqrt{1-a^2 x^2} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-a^2 x^2\right)-\frac{\sin ^{-1}(a x)}{5 x^5}","-\frac{a \sqrt{1-a^2 x^2}}{20 x^4}-\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}-\frac{\sin ^{-1}(a x)}{5 x^5}",1,"-1/5*ArcSin[a*x]/x^5 - (a^5*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, 3, 3/2, 1 - a^2*x^2])/5","C",1
12,1,82,120,0.0334391,"\int x^4 \sin ^{-1}(a x)^2 \, dx","Integrate[x^4*ArcSin[a*x]^2,x]","\frac{225 a^5 x^5 \sin ^{-1}(a x)^2-2 a x \left(9 a^4 x^4+20 a^2 x^2+120\right)+30 \sqrt{1-a^2 x^2} \left(3 a^4 x^4+4 a^2 x^2+8\right) \sin ^{-1}(a x)}{1125 a^5}","-\frac{16 x}{75 a^4}-\frac{8 x^3}{225 a^2}+\frac{2 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{25 a}+\frac{16 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{75 a^5}+\frac{8 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{75 a^3}+\frac{1}{5} x^5 \sin ^{-1}(a x)^2-\frac{2 x^5}{125}",1,"(-2*a*x*(120 + 20*a^2*x^2 + 9*a^4*x^4) + 30*Sqrt[1 - a^2*x^2]*(8 + 4*a^2*x^2 + 3*a^4*x^4)*ArcSin[a*x] + 225*a^5*x^5*ArcSin[a*x]^2)/(1125*a^5)","A",1
13,1,74,98,0.0278415,"\int x^3 \sin ^{-1}(a x)^2 \, dx","Integrate[x^3*ArcSin[a*x]^2,x]","\frac{\left(8 a^4 x^4-3\right) \sin ^{-1}(a x)^2-a^2 x^2 \left(a^2 x^2+3\right)+2 a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+3\right) \sin ^{-1}(a x)}{32 a^4}","-\frac{3 \sin ^{-1}(a x)^2}{32 a^4}-\frac{3 x^2}{32 a^2}+\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{8 a}+\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{16 a^3}+\frac{1}{4} x^4 \sin ^{-1}(a x)^2-\frac{x^4}{32}",1,"(-(a^2*x^2*(3 + a^2*x^2)) + 2*a*x*Sqrt[1 - a^2*x^2]*(3 + 2*a^2*x^2)*ArcSin[a*x] + (-3 + 8*a^4*x^4)*ArcSin[a*x]^2)/(32*a^4)","A",1
14,1,64,82,0.0256475,"\int x^2 \sin ^{-1}(a x)^2 \, dx","Integrate[x^2*ArcSin[a*x]^2,x]","\frac{9 a^3 x^3 \sin ^{-1}(a x)^2-2 a x \left(a^2 x^2+6\right)+6 \sqrt{1-a^2 x^2} \left(a^2 x^2+2\right) \sin ^{-1}(a x)}{27 a^3}","\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a}-\frac{4 x}{9 a^2}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^3}+\frac{1}{3} x^3 \sin ^{-1}(a x)^2-\frac{2 x^3}{27}",1,"(-2*a*x*(6 + a^2*x^2) + 6*Sqrt[1 - a^2*x^2]*(2 + a^2*x^2)*ArcSin[a*x] + 9*a^3*x^3*ArcSin[a*x]^2)/(27*a^3)","A",1
15,1,55,60,0.0157571,"\int x \sin ^{-1}(a x)^2 \, dx","Integrate[x*ArcSin[a*x]^2,x]","\frac{-a^2 x^2+2 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+\left(2 a^2 x^2-1\right) \sin ^{-1}(a x)^2}{4 a^2}","\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{2 a}-\frac{\sin ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \sin ^{-1}(a x)^2-\frac{x^2}{4}",1,"(-(a^2*x^2) + 2*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + (-1 + 2*a^2*x^2)*ArcSin[a*x]^2)/(4*a^2)","A",1
16,1,35,35,0.0109055,"\int \sin ^{-1}(a x)^2 \, dx","Integrate[ArcSin[a*x]^2,x]","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}+x \sin ^{-1}(a x)^2-2 x","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}+x \sin ^{-1}(a x)^2-2 x",1,"-2*x + (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/a + x*ArcSin[a*x]^2","A",1
17,1,71,71,0.0390129,"\int \frac{\sin ^{-1}(a x)^2}{x} \, dx","Integrate[ArcSin[a*x]^2/x,x]","i \sin ^{-1}(a x) \text{Li}_2\left(e^{-2 i \sin ^{-1}(a x)}\right)+\frac{1}{2} \text{Li}_3\left(e^{-2 i \sin ^{-1}(a x)}\right)+\frac{1}{3} i \sin ^{-1}(a x)^3+\sin ^{-1}(a x)^2 \log \left(1-e^{-2 i \sin ^{-1}(a x)}\right)","-i \sin ^{-1}(a x) \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)+\frac{1}{2} \text{Li}_3\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{1}{3} i \sin ^{-1}(a x)^3+\sin ^{-1}(a x)^2 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)",1,"(I/3)*ArcSin[a*x]^3 + ArcSin[a*x]^2*Log[1 - E^((-2*I)*ArcSin[a*x])] + I*ArcSin[a*x]*PolyLog[2, E^((-2*I)*ArcSin[a*x])] + PolyLog[3, E^((-2*I)*ArcSin[a*x])]/2","A",0
18,1,87,66,0.166159,"\int \frac{\sin ^{-1}(a x)^2}{x^2} \, dx","Integrate[ArcSin[a*x]^2/x^2,x]","a \left(2 i \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-2 i \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-\sin ^{-1}(a x) \left(\frac{\sin ^{-1}(a x)}{a x}-2 \log \left(1-e^{i \sin ^{-1}(a x)}\right)+2 \log \left(1+e^{i \sin ^{-1}(a x)}\right)\right)\right)","2 i a \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-2 i a \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^2}{x}-4 a \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)",1,"a*(-(ArcSin[a*x]*(ArcSin[a*x]/(a*x) - 2*Log[1 - E^(I*ArcSin[a*x])] + 2*Log[1 + E^(I*ArcSin[a*x])])) + (2*I)*PolyLog[2, -E^(I*ArcSin[a*x])] - (2*I)*PolyLog[2, E^(I*ArcSin[a*x])])","A",0
19,1,44,44,0.0229879,"\int \frac{\sin ^{-1}(a x)^2}{x^3} \, dx","Integrate[ArcSin[a*x]^2/x^3,x]","-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{x}+a^2 \log (x)-\frac{\sin ^{-1}(a x)^2}{2 x^2}","-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{x}+a^2 \log (x)-\frac{\sin ^{-1}(a x)^2}{2 x^2}",1,"-((a*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/x) - ArcSin[a*x]^2/(2*x^2) + a^2*Log[x]","A",1
20,1,139,116,0.5996221,"\int \frac{\sin ^{-1}(a x)^2}{x^4} \, dx","Integrate[ArcSin[a*x]^2/x^4,x]","-\frac{-i a^3 x^3 \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)+i a^3 x^3 \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-a^3 x^3 \sin ^{-1}(a x) \log \left(1-e^{i \sin ^{-1}(a x)}\right)+a^3 x^3 \sin ^{-1}(a x) \log \left(1+e^{i \sin ^{-1}(a x)}\right)+a^2 x^2+a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+\sin ^{-1}(a x)^2}{3 x^3}","\frac{1}{3} i a^3 \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-\frac{1}{3} i a^3 \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-\frac{2}{3} a^3 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 x^2}-\frac{a^2}{3 x}-\frac{\sin ^{-1}(a x)^2}{3 x^3}",1,"-1/3*(a^2*x^2 + a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + ArcSin[a*x]^2 - a^3*x^3*ArcSin[a*x]*Log[1 - E^(I*ArcSin[a*x])] + a^3*x^3*ArcSin[a*x]*Log[1 + E^(I*ArcSin[a*x])] - I*a^3*x^3*PolyLog[2, -E^(I*ArcSin[a*x])] + I*a^3*x^3*PolyLog[2, E^(I*ArcSin[a*x])])/x^3","A",0
21,1,69,87,0.0351691,"\int \frac{\sin ^{-1}(a x)^2}{x^5} \, dx","Integrate[ArcSin[a*x]^2/x^5,x]","\frac{1}{3} a^4 \log (x)-\frac{a^2}{12 x^2}-\frac{a \sqrt{1-a^2 x^2} \left(2 a^2 x^2+1\right) \sin ^{-1}(a x)}{6 x^3}-\frac{\sin ^{-1}(a x)^2}{4 x^4}","\frac{1}{3} a^4 \log (x)-\frac{a^2}{12 x^2}-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{6 x^3}-\frac{a^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 x}-\frac{\sin ^{-1}(a x)^2}{4 x^4}",1,"-1/12*a^2/x^2 - (a*Sqrt[1 - a^2*x^2]*(1 + 2*a^2*x^2)*ArcSin[a*x])/(6*x^3) - ArcSin[a*x]^2/(4*x^4) + (a^4*Log[x])/3","A",1
22,1,122,201,0.0685876,"\int x^4 \sin ^{-1}(a x)^3 \, dx","Integrate[x^4*ArcSin[a*x]^3,x]","\frac{1125 a^5 x^5 \sin ^{-1}(a x)^3-2 \sqrt{1-a^2 x^2} \left(27 a^4 x^4+136 a^2 x^2+2072\right)-30 a x \left(9 a^4 x^4+20 a^2 x^2+120\right) \sin ^{-1}(a x)+225 \sqrt{1-a^2 x^2} \left(3 a^4 x^4+4 a^2 x^2+8\right) \sin ^{-1}(a x)^2}{5625 a^5}","-\frac{16 x \sin ^{-1}(a x)}{25 a^4}-\frac{8 x^3 \sin ^{-1}(a x)}{75 a^2}+\frac{3 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a}-\frac{6 \left(1-a^2 x^2\right)^{5/2}}{625 a^5}+\frac{76 \left(1-a^2 x^2\right)^{3/2}}{1125 a^5}-\frac{298 \sqrt{1-a^2 x^2}}{375 a^5}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a^5}+\frac{4 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a^3}+\frac{1}{5} x^5 \sin ^{-1}(a x)^3-\frac{6}{125} x^5 \sin ^{-1}(a x)",1,"(-2*Sqrt[1 - a^2*x^2]*(2072 + 136*a^2*x^2 + 27*a^4*x^4) - 30*a*x*(120 + 20*a^2*x^2 + 9*a^4*x^4)*ArcSin[a*x] + 225*Sqrt[1 - a^2*x^2]*(8 + 4*a^2*x^2 + 3*a^4*x^4)*ArcSin[a*x]^2 + 1125*a^5*x^5*ArcSin[a*x]^3)/(5625*a^5)","A",1
23,1,112,167,0.0453688,"\int x^3 \sin ^{-1}(a x)^3 \, dx","Integrate[x^3*ArcSin[a*x]^3,x]","\frac{8 \left(8 a^4 x^4-3\right) \sin ^{-1}(a x)^3-3 a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+15\right)+24 a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+3\right) \sin ^{-1}(a x)^2-3 \left(8 a^4 x^4+24 a^2 x^2-15\right) \sin ^{-1}(a x)}{256 a^4}","-\frac{3 \sin ^{-1}(a x)^3}{32 a^4}+\frac{45 \sin ^{-1}(a x)}{256 a^4}-\frac{9 x^2 \sin ^{-1}(a x)}{32 a^2}-\frac{3 x^3 \sqrt{1-a^2 x^2}}{128 a}+\frac{3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{16 a}-\frac{45 x \sqrt{1-a^2 x^2}}{256 a^3}+\frac{9 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{32 a^3}+\frac{1}{4} x^4 \sin ^{-1}(a x)^3-\frac{3}{32} x^4 \sin ^{-1}(a x)",1,"(-3*a*x*Sqrt[1 - a^2*x^2]*(15 + 2*a^2*x^2) - 3*(-15 + 24*a^2*x^2 + 8*a^4*x^4)*ArcSin[a*x] + 24*a*x*Sqrt[1 - a^2*x^2]*(3 + 2*a^2*x^2)*ArcSin[a*x]^2 + 8*(-3 + 8*a^4*x^4)*ArcSin[a*x]^3)/(256*a^4)","A",1
24,1,95,136,0.0411914,"\int x^2 \sin ^{-1}(a x)^3 \, dx","Integrate[x^2*ArcSin[a*x]^3,x]","\frac{9 a^3 x^3 \sin ^{-1}(a x)^3-2 \sqrt{1-a^2 x^2} \left(a^2 x^2+20\right)+9 \sqrt{1-a^2 x^2} \left(a^2 x^2+2\right) \sin ^{-1}(a x)^2-6 a x \left(a^2 x^2+6\right) \sin ^{-1}(a x)}{27 a^3}","\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a}-\frac{4 x \sin ^{-1}(a x)}{3 a^2}+\frac{2 \left(1-a^2 x^2\right)^{3/2}}{27 a^3}-\frac{14 \sqrt{1-a^2 x^2}}{9 a^3}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^3}+\frac{1}{3} x^3 \sin ^{-1}(a x)^3-\frac{2}{9} x^3 \sin ^{-1}(a x)",1,"(-2*Sqrt[1 - a^2*x^2]*(20 + a^2*x^2) - 6*a*x*(6 + a^2*x^2)*ArcSin[a*x] + 9*Sqrt[1 - a^2*x^2]*(2 + a^2*x^2)*ArcSin[a*x]^2 + 9*a^3*x^3*ArcSin[a*x]^3)/(27*a^3)","A",1
25,1,82,99,0.0294483,"\int x \sin ^{-1}(a x)^3 \, dx","Integrate[x*ArcSin[a*x]^3,x]","\frac{-3 a x \sqrt{1-a^2 x^2}+\left(4 a^2 x^2-2\right) \sin ^{-1}(a x)^3+6 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2+\left(3-6 a^2 x^2\right) \sin ^{-1}(a x)}{8 a^2}","-\frac{3 x \sqrt{1-a^2 x^2}}{8 a}+\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{4 a}-\frac{\sin ^{-1}(a x)^3}{4 a^2}+\frac{3 \sin ^{-1}(a x)}{8 a^2}+\frac{1}{2} x^2 \sin ^{-1}(a x)^3-\frac{3}{4} x^2 \sin ^{-1}(a x)",1,"(-3*a*x*Sqrt[1 - a^2*x^2] + (3 - 6*a^2*x^2)*ArcSin[a*x] + 6*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2 + (-2 + 4*a^2*x^2)*ArcSin[a*x]^3)/(8*a^2)","A",1
26,1,60,60,0.0112749,"\int \sin ^{-1}(a x)^3 \, dx","Integrate[ArcSin[a*x]^3,x]","-\frac{6 \sqrt{1-a^2 x^2}}{a}+\frac{3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a}+x \sin ^{-1}(a x)^3-6 x \sin ^{-1}(a x)","-\frac{6 \sqrt{1-a^2 x^2}}{a}+\frac{3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a}+x \sin ^{-1}(a x)^3-6 x \sin ^{-1}(a x)",1,"(-6*Sqrt[1 - a^2*x^2])/a - 6*x*ArcSin[a*x] + (3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/a + x*ArcSin[a*x]^3","A",1
27,1,97,97,0.0554923,"\int \frac{\sin ^{-1}(a x)^3}{x} \, dx","Integrate[ArcSin[a*x]^3/x,x]","-\frac{1}{64} i \left(-96 \sin ^{-1}(a x)^2 \text{Li}_2\left(e^{-2 i \sin ^{-1}(a x)}\right)+96 i \sin ^{-1}(a x) \text{Li}_3\left(e^{-2 i \sin ^{-1}(a x)}\right)+48 \text{Li}_4\left(e^{-2 i \sin ^{-1}(a x)}\right)-16 \sin ^{-1}(a x)^4+64 i \sin ^{-1}(a x)^3 \log \left(1-e^{-2 i \sin ^{-1}(a x)}\right)+\pi ^4\right)","-\frac{3}{2} i \sin ^{-1}(a x)^2 \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{2} \sin ^{-1}(a x) \text{Li}_3\left(e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{4} i \text{Li}_4\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{1}{4} i \sin ^{-1}(a x)^4+\sin ^{-1}(a x)^3 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)",1,"(-1/64*I)*(Pi^4 - 16*ArcSin[a*x]^4 + (64*I)*ArcSin[a*x]^3*Log[1 - E^((-2*I)*ArcSin[a*x])] - 96*ArcSin[a*x]^2*PolyLog[2, E^((-2*I)*ArcSin[a*x])] + (96*I)*ArcSin[a*x]*PolyLog[3, E^((-2*I)*ArcSin[a*x])] + 48*PolyLog[4, E^((-2*I)*ArcSin[a*x])])","A",0
28,1,133,108,0.1199868,"\int \frac{\sin ^{-1}(a x)^3}{x^2} \, dx","Integrate[ArcSin[a*x]^3/x^2,x]","a \left(6 i \sin ^{-1}(a x) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-6 i \sin ^{-1}(a x) \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-6 \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+6 \text{Li}_3\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^3}{a x}+3 \sin ^{-1}(a x)^2 \log \left(1-e^{i \sin ^{-1}(a x)}\right)-3 \sin ^{-1}(a x)^2 \log \left(1+e^{i \sin ^{-1}(a x)}\right)\right)","6 i a \sin ^{-1}(a x) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-6 i a \sin ^{-1}(a x) \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-6 a \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+6 a \text{Li}_3\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^3}{x}-6 a \sin ^{-1}(a x)^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)",1,"a*(-(ArcSin[a*x]^3/(a*x)) + 3*ArcSin[a*x]^2*Log[1 - E^(I*ArcSin[a*x])] - 3*ArcSin[a*x]^2*Log[1 + E^(I*ArcSin[a*x])] + (6*I)*ArcSin[a*x]*PolyLog[2, -E^(I*ArcSin[a*x])] - (6*I)*ArcSin[a*x]*PolyLog[2, E^(I*ArcSin[a*x])] - 6*PolyLog[3, -E^(I*ArcSin[a*x])] + 6*PolyLog[3, E^(I*ArcSin[a*x])])","A",0
29,1,92,102,0.2595341,"\int \frac{\sin ^{-1}(a x)^3}{x^3} \, dx","Integrate[ArcSin[a*x]^3/x^3,x]","-\frac{3}{2} i a^2 \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x) \left(3 a x \left(\sqrt{1-a^2 x^2}+i a x\right) \sin ^{-1}(a x)-6 a^2 x^2 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)+\sin ^{-1}(a x)^2\right)}{2 x^2}","-\frac{3}{2} i a^2 \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{3 a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x}-\frac{3}{2} i a^2 \sin ^{-1}(a x)^2+3 a^2 \sin ^{-1}(a x) \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^3}{2 x^2}",1,"-1/2*(ArcSin[a*x]*(3*a*x*(I*a*x + Sqrt[1 - a^2*x^2])*ArcSin[a*x] + ArcSin[a*x]^2 - 6*a^2*x^2*Log[1 - E^((2*I)*ArcSin[a*x])]))/x^2 - ((3*I)/2)*a^2*PolyLog[2, E^((2*I)*ArcSin[a*x])]","A",1
30,1,284,179,2.7338598,"\int \frac{\sin ^{-1}(a x)^3}{x^4} \, dx","Integrate[ArcSin[a*x]^3/x^4,x]","\frac{1}{48} a^3 \left(-\frac{16 \sin ^{-1}(a x)^3 \sin ^4\left(\frac{1}{2} \sin ^{-1}(a x)\right)}{a^3 x^3}+48 i \sin ^{-1}(a x) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-48 i \sin ^{-1}(a x) \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-48 \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+48 \text{Li}_3\left(e^{i \sin ^{-1}(a x)}\right)+24 \sin ^{-1}(a x)^2 \log \left(1-e^{i \sin ^{-1}(a x)}\right)-24 \sin ^{-1}(a x)^2 \log \left(1+e^{i \sin ^{-1}(a x)}\right)-4 \sin ^{-1}(a x)^3 \tan \left(\frac{1}{2} \sin ^{-1}(a x)\right)-24 \sin ^{-1}(a x) \tan \left(\frac{1}{2} \sin ^{-1}(a x)\right)-4 \sin ^{-1}(a x)^3 \cot \left(\frac{1}{2} \sin ^{-1}(a x)\right)-24 \sin ^{-1}(a x) \cot \left(\frac{1}{2} \sin ^{-1}(a x)\right)-a x \sin ^{-1}(a x)^3 \csc ^4\left(\frac{1}{2} \sin ^{-1}(a x)\right)-6 \sin ^{-1}(a x)^2 \csc ^2\left(\frac{1}{2} \sin ^{-1}(a x)\right)+6 \sin ^{-1}(a x)^2 \sec ^2\left(\frac{1}{2} \sin ^{-1}(a x)\right)+48 \log \left(\tan \left(\frac{1}{2} \sin ^{-1}(a x)\right)\right)\right)","i a^3 \sin ^{-1}(a x) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-i a^3 \sin ^{-1}(a x) \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-a^3 \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+a^3 \text{Li}_3\left(e^{i \sin ^{-1}(a x)}\right)+a^3 \left(-\sin ^{-1}(a x)^2\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x^2}-\frac{a^2 \sin ^{-1}(a x)}{x}-a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sin ^{-1}(a x)^3}{3 x^3}",1,"(a^3*(-24*ArcSin[a*x]*Cot[ArcSin[a*x]/2] - 4*ArcSin[a*x]^3*Cot[ArcSin[a*x]/2] - 6*ArcSin[a*x]^2*Csc[ArcSin[a*x]/2]^2 - a*x*ArcSin[a*x]^3*Csc[ArcSin[a*x]/2]^4 + 24*ArcSin[a*x]^2*Log[1 - E^(I*ArcSin[a*x])] - 24*ArcSin[a*x]^2*Log[1 + E^(I*ArcSin[a*x])] + 48*Log[Tan[ArcSin[a*x]/2]] + (48*I)*ArcSin[a*x]*PolyLog[2, -E^(I*ArcSin[a*x])] - (48*I)*ArcSin[a*x]*PolyLog[2, E^(I*ArcSin[a*x])] - 48*PolyLog[3, -E^(I*ArcSin[a*x])] + 48*PolyLog[3, E^(I*ArcSin[a*x])] + 6*ArcSin[a*x]^2*Sec[ArcSin[a*x]/2]^2 - (16*ArcSin[a*x]^3*Sin[ArcSin[a*x]/2]^4)/(a^3*x^3) - 24*ArcSin[a*x]*Tan[ArcSin[a*x]/2] - 4*ArcSin[a*x]^3*Tan[ArcSin[a*x]/2]))/48","A",0
31,1,116,169,0.6325662,"\int \frac{\sin ^{-1}(a x)^3}{x^5} \, dx","Integrate[ArcSin[a*x]^3/x^5,x]","\frac{1}{4} \left(-\frac{\sin ^{-1}(a x)^3}{x^4}+a^4 \left(-\frac{\sqrt{1-a^2 x^2} \left(\left(\frac{1}{a^2 x^2}+2\right) \sin ^{-1}(a x)^2+1\right)}{a x}-\sin ^{-1}(a x) \left(\frac{1}{a^2 x^2}+2 i \sin ^{-1}(a x)-4 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)\right)-2 i \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)\right)\right)","-\frac{1}{2} i a^4 \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{1}{2} i a^4 \sin ^{-1}(a x)^2+a^4 \sin ^{-1}(a x) \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)-\frac{a^2 \sin ^{-1}(a x)}{4 x^2}-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{4 x^3}-\frac{a^3 \sqrt{1-a^2 x^2}}{4 x}-\frac{a^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x}-\frac{\sin ^{-1}(a x)^3}{4 x^4}",1,"(-(ArcSin[a*x]^3/x^4) + a^4*(-((Sqrt[1 - a^2*x^2]*(1 + (2 + 1/(a^2*x^2))*ArcSin[a*x]^2))/(a*x)) - ArcSin[a*x]*(1/(a^2*x^2) + (2*I)*ArcSin[a*x] - 4*Log[1 - E^((2*I)*ArcSin[a*x])]) - (2*I)*PolyLog[2, E^((2*I)*ArcSin[a*x])]))/4","A",1
32,1,167,282,0.0817211,"\int x^5 \sin ^{-1}(a x)^4 \, dx","Integrate[x^5*ArcSin[a*x]^4,x]","\frac{108 \left(16 a^6 x^6-5\right) \sin ^{-1}(a x)^4+a^2 x^2 \left(32 a^4 x^4+195 a^2 x^2+2205\right)+144 a x \sqrt{1-a^2 x^2} \left(8 a^4 x^4+10 a^2 x^2+15\right) \sin ^{-1}(a x)^3-6 a x \sqrt{1-a^2 x^2} \left(32 a^4 x^4+130 a^2 x^2+735\right) \sin ^{-1}(a x)-9 \left(64 a^6 x^6+120 a^4 x^4+360 a^2 x^2-245\right) \sin ^{-1}(a x)^2}{10368 a^6}","-\frac{5 \sin ^{-1}(a x)^4}{96 a^6}+\frac{245 \sin ^{-1}(a x)^2}{1152 a^6}+\frac{245 x^2}{1152 a^4}-\frac{5 x^2 \sin ^{-1}(a x)^2}{16 a^4}+\frac{65 x^4}{3456 a^2}-\frac{5 x^4 \sin ^{-1}(a x)^2}{48 a^2}+\frac{x^5 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a}-\frac{x^5 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{54 a}+\frac{5 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{24 a^5}-\frac{245 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{576 a^5}+\frac{5 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{36 a^3}-\frac{65 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{864 a^3}+\frac{1}{6} x^6 \sin ^{-1}(a x)^4-\frac{1}{18} x^6 \sin ^{-1}(a x)^2+\frac{x^6}{324}",1,"(a^2*x^2*(2205 + 195*a^2*x^2 + 32*a^4*x^4) - 6*a*x*Sqrt[1 - a^2*x^2]*(735 + 130*a^2*x^2 + 32*a^4*x^4)*ArcSin[a*x] - 9*(-245 + 360*a^2*x^2 + 120*a^4*x^4 + 64*a^6*x^6)*ArcSin[a*x]^2 + 144*a*x*Sqrt[1 - a^2*x^2]*(15 + 10*a^2*x^2 + 8*a^4*x^4)*ArcSin[a*x]^3 + 108*(-5 + 16*a^6*x^6)*ArcSin[a*x]^4)/(10368*a^6)","A",1
33,1,150,250,0.0724673,"\int x^4 \sin ^{-1}(a x)^4 \, dx","Integrate[x^4*ArcSin[a*x]^4,x]","\frac{16875 a^5 x^5 \sin ^{-1}(a x)^4+8 a x \left(81 a^4 x^4+680 a^2 x^2+31080\right)-900 a x \left(9 a^4 x^4+20 a^2 x^2+120\right) \sin ^{-1}(a x)^2+4500 \sqrt{1-a^2 x^2} \left(3 a^4 x^4+4 a^2 x^2+8\right) \sin ^{-1}(a x)^3-120 \sqrt{1-a^2 x^2} \left(27 a^4 x^4+136 a^2 x^2+2072\right) \sin ^{-1}(a x)}{84375 a^5}","\frac{16576 x}{5625 a^4}-\frac{32 x \sin ^{-1}(a x)^2}{25 a^4}+\frac{1088 x^3}{16875 a^2}-\frac{16 x^3 \sin ^{-1}(a x)^2}{75 a^2}+\frac{4 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{25 a}-\frac{24 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{625 a}+\frac{32 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{75 a^5}-\frac{16576 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{5625 a^5}+\frac{16 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{75 a^3}-\frac{1088 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{5625 a^3}+\frac{1}{5} x^5 \sin ^{-1}(a x)^4-\frac{12}{125} x^5 \sin ^{-1}(a x)^2+\frac{24 x^5}{3125}",1,"(8*a*x*(31080 + 680*a^2*x^2 + 81*a^4*x^4) - 120*Sqrt[1 - a^2*x^2]*(2072 + 136*a^2*x^2 + 27*a^4*x^4)*ArcSin[a*x] - 900*a*x*(120 + 20*a^2*x^2 + 9*a^4*x^4)*ArcSin[a*x]^2 + 4500*Sqrt[1 - a^2*x^2]*(8 + 4*a^2*x^2 + 3*a^4*x^4)*ArcSin[a*x]^3 + 16875*a^5*x^5*ArcSin[a*x]^4)/(84375*a^5)","A",1
34,1,135,198,0.0580905,"\int x^3 \sin ^{-1}(a x)^4 \, dx","Integrate[x^3*ArcSin[a*x]^4,x]","\frac{4 \left(8 a^4 x^4-3\right) \sin ^{-1}(a x)^4+3 a^2 x^2 \left(a^2 x^2+15\right)+16 a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+3\right) \sin ^{-1}(a x)^3-6 a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2+15\right) \sin ^{-1}(a x)-3 \left(8 a^4 x^4+24 a^2 x^2-15\right) \sin ^{-1}(a x)^2}{128 a^4}","-\frac{3 \sin ^{-1}(a x)^4}{32 a^4}+\frac{45 \sin ^{-1}(a x)^2}{128 a^4}+\frac{45 x^2}{128 a^2}-\frac{9 x^2 \sin ^{-1}(a x)^2}{16 a^2}+\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{4 a}-\frac{3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{32 a}+\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{8 a^3}-\frac{45 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{64 a^3}+\frac{1}{4} x^4 \sin ^{-1}(a x)^4-\frac{3}{16} x^4 \sin ^{-1}(a x)^2+\frac{3 x^4}{128}",1,"(3*a^2*x^2*(15 + a^2*x^2) - 6*a*x*Sqrt[1 - a^2*x^2]*(15 + 2*a^2*x^2)*ArcSin[a*x] - 3*(-15 + 24*a^2*x^2 + 8*a^4*x^4)*ArcSin[a*x]^2 + 16*a*x*Sqrt[1 - a^2*x^2]*(3 + 2*a^2*x^2)*ArcSin[a*x]^3 + 4*(-3 + 8*a^4*x^4)*ArcSin[a*x]^4)/(128*a^4)","A",1
35,1,114,166,0.0477041,"\int x^2 \sin ^{-1}(a x)^4 \, dx","Integrate[x^2*ArcSin[a*x]^4,x]","\frac{27 a^3 x^3 \sin ^{-1}(a x)^4+8 a x \left(a^2 x^2+60\right)+36 \sqrt{1-a^2 x^2} \left(a^2 x^2+2\right) \sin ^{-1}(a x)^3-36 a x \left(a^2 x^2+6\right) \sin ^{-1}(a x)^2-24 \sqrt{1-a^2 x^2} \left(a^2 x^2+20\right) \sin ^{-1}(a x)}{81 a^3}","\frac{4 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a}-\frac{8 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a}+\frac{160 x}{27 a^2}-\frac{8 x \sin ^{-1}(a x)^2}{3 a^2}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a^3}-\frac{160 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a^3}+\frac{1}{3} x^3 \sin ^{-1}(a x)^4-\frac{4}{9} x^3 \sin ^{-1}(a x)^2+\frac{8 x^3}{81}",1,"(8*a*x*(60 + a^2*x^2) - 24*Sqrt[1 - a^2*x^2]*(20 + a^2*x^2)*ArcSin[a*x] - 36*a*x*(6 + a^2*x^2)*ArcSin[a*x]^2 + 36*Sqrt[1 - a^2*x^2]*(2 + a^2*x^2)*ArcSin[a*x]^3 + 27*a^3*x^3*ArcSin[a*x]^4)/(81*a^3)","A",1
36,1,96,111,0.0262687,"\int x \sin ^{-1}(a x)^4 \, dx","Integrate[x*ArcSin[a*x]^4,x]","\frac{3 a^2 x^2+\left(2 a^2 x^2-1\right) \sin ^{-1}(a x)^4+4 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3+\left(3-6 a^2 x^2\right) \sin ^{-1}(a x)^2-6 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{4 a^2}","\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{2 a}-\frac{\sin ^{-1}(a x)^4}{4 a^2}+\frac{3 \sin ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \sin ^{-1}(a x)^4-\frac{3}{2} x^2 \sin ^{-1}(a x)^2+\frac{3 x^2}{4}",1,"(3*a^2*x^2 - 6*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + (3 - 6*a^2*x^2)*ArcSin[a*x]^2 + 4*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3 + (-1 + 2*a^2*x^2)*ArcSin[a*x]^4)/(4*a^2)","A",1
37,1,69,69,0.0214141,"\int \sin ^{-1}(a x)^4 \, dx","Integrate[ArcSin[a*x]^4,x]","\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a}-\frac{24 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}+x \sin ^{-1}(a x)^4-12 x \sin ^{-1}(a x)^2+24 x","\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a}-\frac{24 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}+x \sin ^{-1}(a x)^4-12 x \sin ^{-1}(a x)^2+24 x",1,"24*x - (24*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/a - 12*x*ArcSin[a*x]^2 + (4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/a + x*ArcSin[a*x]^4","A",1
38,1,113,113,0.0456548,"\int \frac{\sin ^{-1}(a x)^4}{x} \, dx","Integrate[ArcSin[a*x]^4/x,x]","2 i \sin ^{-1}(a x)^3 \text{Li}_2\left(e^{-2 i \sin ^{-1}(a x)}\right)+3 \sin ^{-1}(a x)^2 \text{Li}_3\left(e^{-2 i \sin ^{-1}(a x)}\right)-3 i \sin ^{-1}(a x) \text{Li}_4\left(e^{-2 i \sin ^{-1}(a x)}\right)-\frac{3}{2} \text{Li}_5\left(e^{-2 i \sin ^{-1}(a x)}\right)+\frac{1}{5} i \sin ^{-1}(a x)^5+\sin ^{-1}(a x)^4 \log \left(1-e^{-2 i \sin ^{-1}(a x)}\right)","-2 i \sin ^{-1}(a x)^3 \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)+3 \sin ^{-1}(a x)^2 \text{Li}_3\left(e^{2 i \sin ^{-1}(a x)}\right)+3 i \sin ^{-1}(a x) \text{Li}_4\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{3}{2} \text{Li}_5\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{1}{5} i \sin ^{-1}(a x)^5+\sin ^{-1}(a x)^4 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)",1,"(I/5)*ArcSin[a*x]^5 + ArcSin[a*x]^4*Log[1 - E^((-2*I)*ArcSin[a*x])] + (2*I)*ArcSin[a*x]^3*PolyLog[2, E^((-2*I)*ArcSin[a*x])] + 3*ArcSin[a*x]^2*PolyLog[3, E^((-2*I)*ArcSin[a*x])] - (3*I)*ArcSin[a*x]*PolyLog[4, E^((-2*I)*ArcSin[a*x])] - (3*PolyLog[5, E^((-2*I)*ArcSin[a*x])])/2","A",0
39,1,198,156,0.2600646,"\int \frac{\sin ^{-1}(a x)^4}{x^2} \, dx","Integrate[ArcSin[a*x]^4/x^2,x]","a \left(12 i \sin ^{-1}(a x)^2 \text{Li}_2\left(e^{-i \sin ^{-1}(a x)}\right)+12 i \sin ^{-1}(a x)^2 \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)+24 \sin ^{-1}(a x) \text{Li}_3\left(e^{-i \sin ^{-1}(a x)}\right)-24 \sin ^{-1}(a x) \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)-24 i \text{Li}_4\left(e^{-i \sin ^{-1}(a x)}\right)-24 i \text{Li}_4\left(-e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^4}{a x}+i \sin ^{-1}(a x)^4+4 \sin ^{-1}(a x)^3 \log \left(1-e^{-i \sin ^{-1}(a x)}\right)-4 \sin ^{-1}(a x)^3 \log \left(1+e^{i \sin ^{-1}(a x)}\right)-\frac{i \pi ^4}{2}\right)","12 i a \sin ^{-1}(a x)^2 \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-12 i a \sin ^{-1}(a x)^2 \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-24 a \sin ^{-1}(a x) \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+24 a \sin ^{-1}(a x) \text{Li}_3\left(e^{i \sin ^{-1}(a x)}\right)-24 i a \text{Li}_4\left(-e^{i \sin ^{-1}(a x)}\right)+24 i a \text{Li}_4\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^4}{x}-8 a \sin ^{-1}(a x)^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)",1,"a*((-1/2*I)*Pi^4 + I*ArcSin[a*x]^4 - ArcSin[a*x]^4/(a*x) + 4*ArcSin[a*x]^3*Log[1 - E^((-I)*ArcSin[a*x])] - 4*ArcSin[a*x]^3*Log[1 + E^(I*ArcSin[a*x])] + (12*I)*ArcSin[a*x]^2*PolyLog[2, E^((-I)*ArcSin[a*x])] + (12*I)*ArcSin[a*x]^2*PolyLog[2, -E^(I*ArcSin[a*x])] + 24*ArcSin[a*x]*PolyLog[3, E^((-I)*ArcSin[a*x])] - 24*ArcSin[a*x]*PolyLog[3, -E^(I*ArcSin[a*x])] - (24*I)*PolyLog[4, E^((-I)*ArcSin[a*x])] - (24*I)*PolyLog[4, -E^(I*ArcSin[a*x])])","A",0
40,1,124,119,0.2645715,"\int \frac{\sin ^{-1}(a x)^4}{x^3} \, dx","Integrate[ArcSin[a*x]^4/x^3,x]","-\frac{\sin ^{-1}(a x)^4}{2 x^2}+\frac{1}{4} a^2 \left(-\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a x}+24 i \sin ^{-1}(a x) \text{Li}_2\left(e^{-2 i \sin ^{-1}(a x)}\right)+12 \text{Li}_3\left(e^{-2 i \sin ^{-1}(a x)}\right)+8 i \sin ^{-1}(a x)^3+24 \sin ^{-1}(a x)^2 \log \left(1-e^{-2 i \sin ^{-1}(a x)}\right)-i \pi ^3\right)","-6 i a^2 \sin ^{-1}(a x) \text{Li}_2\left(e^{2 i \sin ^{-1}(a x)}\right)+3 a^2 \text{Li}_3\left(e^{2 i \sin ^{-1}(a x)}\right)-\frac{2 a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{x}-2 i a^2 \sin ^{-1}(a x)^3+6 a^2 \sin ^{-1}(a x)^2 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^4}{2 x^2}",1,"-1/2*ArcSin[a*x]^4/x^2 + (a^2*((-I)*Pi^3 + (8*I)*ArcSin[a*x]^3 - (8*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(a*x) + 24*ArcSin[a*x]^2*Log[1 - E^((-2*I)*ArcSin[a*x])] + (24*I)*ArcSin[a*x]*PolyLog[2, E^((-2*I)*ArcSin[a*x])] + 12*PolyLog[3, E^((-2*I)*ArcSin[a*x])]))/4","A",0
41,1,399,276,3.9744157,"\int \frac{\sin ^{-1}(a x)^4}{x^4} \, dx","Integrate[ArcSin[a*x]^4/x^4,x]","\frac{1}{24} a^3 \left(-\frac{8 \sin ^4\left(\frac{1}{2} \sin ^{-1}(a x)\right) \sin ^{-1}(a x)^4}{a^3 x^3}+48 i \sin ^{-1}(a x)^2 \text{Li}_2\left(e^{-i \sin ^{-1}(a x)}\right)+96 \sin ^{-1}(a x) \text{Li}_3\left(e^{-i \sin ^{-1}(a x)}\right)-96 \sin ^{-1}(a x) \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+48 i \left(\sin ^{-1}(a x)^2+2\right) \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-96 i \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-96 i \text{Li}_4\left(e^{-i \sin ^{-1}(a x)}\right)-96 i \text{Li}_4\left(-e^{i \sin ^{-1}(a x)}\right)+4 i \sin ^{-1}(a x)^4+16 \sin ^{-1}(a x)^3 \log \left(1-e^{-i \sin ^{-1}(a x)}\right)-16 \sin ^{-1}(a x)^3 \log \left(1+e^{i \sin ^{-1}(a x)}\right)+96 \sin ^{-1}(a x) \log \left(1-e^{i \sin ^{-1}(a x)}\right)-96 \sin ^{-1}(a x) \log \left(1+e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x)^4 \tan \left(\frac{1}{2} \sin ^{-1}(a x)\right)-24 \sin ^{-1}(a x)^2 \tan \left(\frac{1}{2} \sin ^{-1}(a x)\right)-2 \sin ^{-1}(a x)^4 \cot \left(\frac{1}{2} \sin ^{-1}(a x)\right)-24 \sin ^{-1}(a x)^2 \cot \left(\frac{1}{2} \sin ^{-1}(a x)\right)-\frac{1}{2} a x \sin ^{-1}(a x)^4 \csc ^4\left(\frac{1}{2} \sin ^{-1}(a x)\right)-4 \sin ^{-1}(a x)^3 \csc ^2\left(\frac{1}{2} \sin ^{-1}(a x)\right)+4 \sin ^{-1}(a x)^3 \sec ^2\left(\frac{1}{2} \sin ^{-1}(a x)\right)-2 i \pi ^4\right)","2 i a^3 \sin ^{-1}(a x)^2 \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-2 i a^3 \sin ^{-1}(a x)^2 \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-4 a^3 \sin ^{-1}(a x) \text{Li}_3\left(-e^{i \sin ^{-1}(a x)}\right)+4 a^3 \sin ^{-1}(a x) \text{Li}_3\left(e^{i \sin ^{-1}(a x)}\right)+4 i a^3 \text{Li}_2\left(-e^{i \sin ^{-1}(a x)}\right)-4 i a^3 \text{Li}_2\left(e^{i \sin ^{-1}(a x)}\right)-4 i a^3 \text{Li}_4\left(-e^{i \sin ^{-1}(a x)}\right)+4 i a^3 \text{Li}_4\left(e^{i \sin ^{-1}(a x)}\right)-\frac{4}{3} a^3 \sin ^{-1}(a x)^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-8 a^3 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{2 a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 x^2}-\frac{2 a^2 \sin ^{-1}(a x)^2}{x}-\frac{\sin ^{-1}(a x)^4}{3 x^3}",1,"(a^3*((-2*I)*Pi^4 + (4*I)*ArcSin[a*x]^4 - 24*ArcSin[a*x]^2*Cot[ArcSin[a*x]/2] - 2*ArcSin[a*x]^4*Cot[ArcSin[a*x]/2] - 4*ArcSin[a*x]^3*Csc[ArcSin[a*x]/2]^2 - (a*x*ArcSin[a*x]^4*Csc[ArcSin[a*x]/2]^4)/2 + 16*ArcSin[a*x]^3*Log[1 - E^((-I)*ArcSin[a*x])] + 96*ArcSin[a*x]*Log[1 - E^(I*ArcSin[a*x])] - 96*ArcSin[a*x]*Log[1 + E^(I*ArcSin[a*x])] - 16*ArcSin[a*x]^3*Log[1 + E^(I*ArcSin[a*x])] + (48*I)*ArcSin[a*x]^2*PolyLog[2, E^((-I)*ArcSin[a*x])] + (48*I)*(2 + ArcSin[a*x]^2)*PolyLog[2, -E^(I*ArcSin[a*x])] - (96*I)*PolyLog[2, E^(I*ArcSin[a*x])] + 96*ArcSin[a*x]*PolyLog[3, E^((-I)*ArcSin[a*x])] - 96*ArcSin[a*x]*PolyLog[3, -E^(I*ArcSin[a*x])] - (96*I)*PolyLog[4, E^((-I)*ArcSin[a*x])] - (96*I)*PolyLog[4, -E^(I*ArcSin[a*x])] + 4*ArcSin[a*x]^3*Sec[ArcSin[a*x]/2]^2 - (8*ArcSin[a*x]^4*Sin[ArcSin[a*x]/2]^4)/(a^3*x^3) - 24*ArcSin[a*x]^2*Tan[ArcSin[a*x]/2] - 2*ArcSin[a*x]^4*Tan[ArcSin[a*x]/2]))/24","A",0
42,1,40,55,0.0147554,"\int \frac{x^6}{\sin ^{-1}(a x)} \, dx","Integrate[x^6/ArcSin[a*x],x]","-\frac{-5 \text{Ci}\left(\sin ^{-1}(a x)\right)+9 \text{Ci}\left(3 \sin ^{-1}(a x)\right)-5 \text{Ci}\left(5 \sin ^{-1}(a x)\right)+\text{Ci}\left(7 \sin ^{-1}(a x)\right)}{64 a^7}","\frac{5 \text{Ci}\left(\sin ^{-1}(a x)\right)}{64 a^7}-\frac{9 \text{Ci}\left(3 \sin ^{-1}(a x)\right)}{64 a^7}+\frac{5 \text{Ci}\left(5 \sin ^{-1}(a x)\right)}{64 a^7}-\frac{\text{Ci}\left(7 \sin ^{-1}(a x)\right)}{64 a^7}",1,"-1/64*(-5*CosIntegral[ArcSin[a*x]] + 9*CosIntegral[3*ArcSin[a*x]] - 5*CosIntegral[5*ArcSin[a*x]] + CosIntegral[7*ArcSin[a*x]])/a^7","A",1
43,1,33,43,0.1204114,"\int \frac{x^5}{\sin ^{-1}(a x)} \, dx","Integrate[x^5/ArcSin[a*x],x]","\frac{5 \text{Si}\left(2 \sin ^{-1}(a x)\right)-4 \text{Si}\left(4 \sin ^{-1}(a x)\right)+\text{Si}\left(6 \sin ^{-1}(a x)\right)}{32 a^6}","\frac{5 \text{Si}\left(2 \sin ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Si}\left(4 \sin ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Si}\left(6 \sin ^{-1}(a x)\right)}{32 a^6}",1,"(5*SinIntegral[2*ArcSin[a*x]] - 4*SinIntegral[4*ArcSin[a*x]] + SinIntegral[6*ArcSin[a*x]])/(32*a^6)","A",1
44,1,31,41,0.0081235,"\int \frac{x^4}{\sin ^{-1}(a x)} \, dx","Integrate[x^4/ArcSin[a*x],x]","\frac{2 \text{Ci}\left(\sin ^{-1}(a x)\right)-3 \text{Ci}\left(3 \sin ^{-1}(a x)\right)+\text{Ci}\left(5 \sin ^{-1}(a x)\right)}{16 a^5}","\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{Ci}\left(3 \sin ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Ci}\left(5 \sin ^{-1}(a x)\right)}{16 a^5}",1,"(2*CosIntegral[ArcSin[a*x]] - 3*CosIntegral[3*ArcSin[a*x]] + CosIntegral[5*ArcSin[a*x]])/(16*a^5)","A",1
45,1,24,29,0.0764267,"\int \frac{x^3}{\sin ^{-1}(a x)} \, dx","Integrate[x^3/ArcSin[a*x],x]","-\frac{\text{Si}\left(4 \sin ^{-1}(a x)\right)-2 \text{Si}\left(2 \sin ^{-1}(a x)\right)}{8 a^4}","\frac{\text{Si}\left(2 \sin ^{-1}(a x)\right)}{4 a^4}-\frac{\text{Si}\left(4 \sin ^{-1}(a x)\right)}{8 a^4}",1,"-1/8*(-2*SinIntegral[2*ArcSin[a*x]] + SinIntegral[4*ArcSin[a*x]])/a^4","A",1
46,1,22,27,0.0067499,"\int \frac{x^2}{\sin ^{-1}(a x)} \, dx","Integrate[x^2/ArcSin[a*x],x]","\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)-\text{Ci}\left(3 \sin ^{-1}(a x)\right)}{4 a^3}","\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{4 a^3}-\frac{\text{Ci}\left(3 \sin ^{-1}(a x)\right)}{4 a^3}",1,"(CosIntegral[ArcSin[a*x]] - CosIntegral[3*ArcSin[a*x]])/(4*a^3)","A",1
47,1,14,14,0.0195783,"\int \frac{x}{\sin ^{-1}(a x)} \, dx","Integrate[x/ArcSin[a*x],x]","\frac{\text{Si}\left(2 \sin ^{-1}(a x)\right)}{2 a^2}","\frac{\text{Si}\left(2 \sin ^{-1}(a x)\right)}{2 a^2}",1,"SinIntegral[2*ArcSin[a*x]]/(2*a^2)","A",1
48,1,9,9,0.0088005,"\int \frac{1}{\sin ^{-1}(a x)} \, dx","Integrate[ArcSin[a*x]^(-1),x]","\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{a}","\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{a}",1,"CosIntegral[ArcSin[a*x]]/a","A",1
49,0,0,13,0.1958052,"\int \frac{1}{x \sin ^{-1}(a x)} \, dx","Integrate[1/(x*ArcSin[a*x]),x]","\int \frac{1}{x \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)},x\right)",0,"Integrate[1/(x*ArcSin[a*x]), x]","A",-1
50,0,0,13,1.0250074,"\int \frac{1}{x^2 \sin ^{-1}(a x)} \, dx","Integrate[1/(x^2*ArcSin[a*x]),x]","\int \frac{1}{x^2 \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \sin ^{-1}(a x)},x\right)",0,"Integrate[1/(x^2*ArcSin[a*x]), x]","A",-1
51,1,86,83,0.2483244,"\int \frac{x^6}{\sin ^{-1}(a x)^2} \, dx","Integrate[x^6/ArcSin[a*x]^2,x]","-\frac{64 a^6 x^6 \sqrt{1-a^2 x^2}+5 \sin ^{-1}(a x) \text{Si}\left(\sin ^{-1}(a x)\right)-27 \sin ^{-1}(a x) \text{Si}\left(3 \sin ^{-1}(a x)\right)+25 \sin ^{-1}(a x) \text{Si}\left(5 \sin ^{-1}(a x)\right)-7 \sin ^{-1}(a x) \text{Si}\left(7 \sin ^{-1}(a x)\right)}{64 a^7 \sin ^{-1}(a x)}","-\frac{5 \text{Si}\left(\sin ^{-1}(a x)\right)}{64 a^7}+\frac{27 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{64 a^7}-\frac{25 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{64 a^7}+\frac{7 \text{Si}\left(7 \sin ^{-1}(a x)\right)}{64 a^7}-\frac{x^6 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"-1/64*(64*a^6*x^6*Sqrt[1 - a^2*x^2] + 5*ArcSin[a*x]*SinIntegral[ArcSin[a*x]] - 27*ArcSin[a*x]*SinIntegral[3*ArcSin[a*x]] + 25*ArcSin[a*x]*SinIntegral[5*ArcSin[a*x]] - 7*ArcSin[a*x]*SinIntegral[7*ArcSin[a*x]])/(a^7*ArcSin[a*x])","A",1
52,1,78,71,0.042834,"\int \frac{x^5}{\sin ^{-1}(a x)^2} \, dx","Integrate[x^5/ArcSin[a*x]^2,x]","-\frac{-10 \sin ^{-1}(a x) \text{Ci}\left(2 \sin ^{-1}(a x)\right)+16 \sin ^{-1}(a x) \text{Ci}\left(4 \sin ^{-1}(a x)\right)-6 \sin ^{-1}(a x) \text{Ci}\left(6 \sin ^{-1}(a x)\right)+5 \sin \left(2 \sin ^{-1}(a x)\right)-4 \sin \left(4 \sin ^{-1}(a x)\right)+\sin \left(6 \sin ^{-1}(a x)\right)}{32 a^6 \sin ^{-1}(a x)}","\frac{5 \text{Ci}\left(2 \sin ^{-1}(a x)\right)}{16 a^6}-\frac{\text{Ci}\left(4 \sin ^{-1}(a x)\right)}{2 a^6}+\frac{3 \text{Ci}\left(6 \sin ^{-1}(a x)\right)}{16 a^6}-\frac{x^5 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"-1/32*(-10*ArcSin[a*x]*CosIntegral[2*ArcSin[a*x]] + 16*ArcSin[a*x]*CosIntegral[4*ArcSin[a*x]] - 6*ArcSin[a*x]*CosIntegral[6*ArcSin[a*x]] + 5*Sin[2*ArcSin[a*x]] - 4*Sin[4*ArcSin[a*x]] + Sin[6*ArcSin[a*x]])/(a^6*ArcSin[a*x])","A",1
53,1,61,69,0.1843361,"\int \frac{x^4}{\sin ^{-1}(a x)^2} \, dx","Integrate[x^4/ArcSin[a*x]^2,x]","-\frac{\frac{16 a^4 x^4 \sqrt{1-a^2 x^2}}{\sin ^{-1}(a x)}+2 \text{Si}\left(\sin ^{-1}(a x)\right)-9 \text{Si}\left(3 \sin ^{-1}(a x)\right)+5 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{16 a^5}","-\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{8 a^5}+\frac{9 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{16 a^5}-\frac{5 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{16 a^5}-\frac{x^4 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"-1/16*((16*a^4*x^4*Sqrt[1 - a^2*x^2])/ArcSin[a*x] + 2*SinIntegral[ArcSin[a*x]] - 9*SinIntegral[3*ArcSin[a*x]] + 5*SinIntegral[5*ArcSin[a*x]])/a^5","A",1
54,1,56,57,0.0155439,"\int \frac{x^3}{\sin ^{-1}(a x)^2} \, dx","Integrate[x^3/ArcSin[a*x]^2,x]","\frac{4 \sin ^{-1}(a x) \text{Ci}\left(2 \sin ^{-1}(a x)\right)-4 \sin ^{-1}(a x) \text{Ci}\left(4 \sin ^{-1}(a x)\right)-2 \sin \left(2 \sin ^{-1}(a x)\right)+\sin \left(4 \sin ^{-1}(a x)\right)}{8 a^4 \sin ^{-1}(a x)}","\frac{\text{Ci}\left(2 \sin ^{-1}(a x)\right)}{2 a^4}-\frac{\text{Ci}\left(4 \sin ^{-1}(a x)\right)}{2 a^4}-\frac{x^3 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"(4*ArcSin[a*x]*CosIntegral[2*ArcSin[a*x]] - 4*ArcSin[a*x]*CosIntegral[4*ArcSin[a*x]] - 2*Sin[2*ArcSin[a*x]] + Sin[4*ArcSin[a*x]])/(8*a^4*ArcSin[a*x])","A",1
55,1,50,55,0.1588802,"\int \frac{x^2}{\sin ^{-1}(a x)^2} \, dx","Integrate[x^2/ArcSin[a*x]^2,x]","-\frac{\frac{4 a^2 x^2 \sqrt{1-a^2 x^2}}{\sin ^{-1}(a x)}+\text{Si}\left(\sin ^{-1}(a x)\right)-3 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{4 a^3}","-\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{4 a^3}+\frac{3 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{4 a^3}-\frac{x^2 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"-1/4*((4*a^2*x^2*Sqrt[1 - a^2*x^2])/ArcSin[a*x] + SinIntegral[ArcSin[a*x]] - 3*SinIntegral[3*ArcSin[a*x]])/a^3","A",1
56,1,32,38,0.0030853,"\int \frac{x}{\sin ^{-1}(a x)^2} \, dx","Integrate[x/ArcSin[a*x]^2,x]","\frac{\text{Ci}\left(2 \sin ^{-1}(a x)\right)}{a^2}-\frac{\sin \left(2 \sin ^{-1}(a x)\right)}{2 a^2 \sin ^{-1}(a x)}","\frac{\text{Ci}\left(2 \sin ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"CosIntegral[2*ArcSin[a*x]]/a^2 - Sin[2*ArcSin[a*x]]/(2*a^2*ArcSin[a*x])","A",1
57,1,32,36,0.0656712,"\int \frac{1}{\sin ^{-1}(a x)^2} \, dx","Integrate[ArcSin[a*x]^(-2),x]","-\frac{\frac{\sqrt{1-a^2 x^2}}{\sin ^{-1}(a x)}+\text{Si}\left(\sin ^{-1}(a x)\right)}{a}","-\frac{\sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}-\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{a}",1,"-((Sqrt[1 - a^2*x^2]/ArcSin[a*x] + SinIntegral[ArcSin[a*x]])/a)","A",1
58,0,0,13,0.860781,"\int \frac{1}{x \sin ^{-1}(a x)^2} \, dx","Integrate[1/(x*ArcSin[a*x]^2),x]","\int \frac{1}{x \sin ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)^2},x\right)",0,"Integrate[1/(x*ArcSin[a*x]^2), x]","A",-1
59,0,0,13,9.0090384,"\int \frac{1}{x^2 \sin ^{-1}(a x)^2} \, dx","Integrate[1/(x^2*ArcSin[a*x]^2),x]","\int \frac{1}{x^2 \sin ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \sin ^{-1}(a x)^2},x\right)",0,"Integrate[1/(x^2*ArcSin[a*x]^2), x]","A",-1
60,1,103,98,0.1617951,"\int \frac{x^4}{\sin ^{-1}(a x)^3} \, dx","Integrate[x^4/ArcSin[a*x]^3,x]","-\frac{-80 a^5 x^5 \sin ^{-1}(a x)+64 a^3 x^3 \sin ^{-1}(a x)+16 a^4 x^4 \sqrt{1-a^2 x^2}+2 \sin ^{-1}(a x)^2 \text{Ci}\left(\sin ^{-1}(a x)\right)-27 \sin ^{-1}(a x)^2 \text{Ci}\left(3 \sin ^{-1}(a x)\right)+25 \sin ^{-1}(a x)^2 \text{Ci}\left(5 \sin ^{-1}(a x)\right)}{32 a^5 \sin ^{-1}(a x)^2}","-\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{Ci}\left(3 \sin ^{-1}(a x)\right)}{32 a^5}-\frac{25 \text{Ci}\left(5 \sin ^{-1}(a x)\right)}{32 a^5}-\frac{2 x^3}{a^2 \sin ^{-1}(a x)}-\frac{x^4 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}+\frac{5 x^5}{2 \sin ^{-1}(a x)}",1,"-1/32*(16*a^4*x^4*Sqrt[1 - a^2*x^2] + 64*a^3*x^3*ArcSin[a*x] - 80*a^5*x^5*ArcSin[a*x] + 2*ArcSin[a*x]^2*CosIntegral[ArcSin[a*x]] - 27*ArcSin[a*x]^2*CosIntegral[3*ArcSin[a*x]] + 25*ArcSin[a*x]^2*CosIntegral[5*ArcSin[a*x]])/(a^5*ArcSin[a*x]^2)","A",1
61,1,73,83,0.1857661,"\int \frac{x^3}{\sin ^{-1}(a x)^3} \, dx","Integrate[x^3/ArcSin[a*x]^3,x]","\frac{\frac{a^2 x^2 \left(\left(4 a^2 x^2-3\right) \sin ^{-1}(a x)-a x \sqrt{1-a^2 x^2}\right)}{\sin ^{-1}(a x)^2}-\text{Si}\left(2 \sin ^{-1}(a x)\right)+2 \text{Si}\left(4 \sin ^{-1}(a x)\right)}{2 a^4}","-\frac{\text{Si}\left(2 \sin ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Si}\left(4 \sin ^{-1}(a x)\right)}{a^4}-\frac{3 x^2}{2 a^2 \sin ^{-1}(a x)}-\frac{x^3 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}+\frac{2 x^4}{\sin ^{-1}(a x)}",1,"((a^2*x^2*(-(a*x*Sqrt[1 - a^2*x^2]) + (-3 + 4*a^2*x^2)*ArcSin[a*x]))/ArcSin[a*x]^2 - SinIntegral[2*ArcSin[a*x]] + 2*SinIntegral[4*ArcSin[a*x]])/(2*a^4)","A",1
62,1,68,82,0.1119597,"\int \frac{x^2}{\sin ^{-1}(a x)^3} \, dx","Integrate[x^2/ArcSin[a*x]^3,x]","\frac{\frac{4 a x \left(\left(3 a^2 x^2-2\right) \sin ^{-1}(a x)-a x \sqrt{1-a^2 x^2}\right)}{\sin ^{-1}(a x)^2}-\text{Ci}\left(\sin ^{-1}(a x)\right)+9 \text{Ci}\left(3 \sin ^{-1}(a x)\right)}{8 a^3}","-\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Ci}\left(3 \sin ^{-1}(a x)\right)}{8 a^3}-\frac{x^2 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{x}{a^2 \sin ^{-1}(a x)}+\frac{3 x^3}{2 \sin ^{-1}(a x)}",1,"((4*a*x*(-(a*x*Sqrt[1 - a^2*x^2]) + (-2 + 3*a^2*x^2)*ArcSin[a*x]))/ArcSin[a*x]^2 - CosIntegral[ArcSin[a*x]] + 9*CosIntegral[3*ArcSin[a*x]])/(8*a^3)","A",1
63,1,61,64,0.0679502,"\int \frac{x}{\sin ^{-1}(a x)^3} \, dx","Integrate[x/ArcSin[a*x]^3,x]","-\frac{a x \sqrt{1-a^2 x^2}+\left(1-2 a^2 x^2\right) \sin ^{-1}(a x)+2 \sin ^{-1}(a x)^2 \text{Si}\left(2 \sin ^{-1}(a x)\right)}{2 a^2 \sin ^{-1}(a x)^2}","-\frac{\text{Si}\left(2 \sin ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{1}{2 a^2 \sin ^{-1}(a x)}+\frac{x^2}{\sin ^{-1}(a x)}",1,"-1/2*(a*x*Sqrt[1 - a^2*x^2] + (1 - 2*a^2*x^2)*ArcSin[a*x] + 2*ArcSin[a*x]^2*SinIntegral[2*ArcSin[a*x]])/(a^2*ArcSin[a*x]^2)","A",1
64,1,48,51,0.0216434,"\int \frac{1}{\sin ^{-1}(a x)^3} \, dx","Integrate[ArcSin[a*x]^(-3),x]","-\frac{\sqrt{1-a^2 x^2}+\sin ^{-1}(a x)^2 \text{Ci}\left(\sin ^{-1}(a x)\right)-a x \sin ^{-1}(a x)}{2 a \sin ^{-1}(a x)^2}","-\frac{\sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{\text{Ci}\left(\sin ^{-1}(a x)\right)}{2 a}+\frac{x}{2 \sin ^{-1}(a x)}",1,"-1/2*(Sqrt[1 - a^2*x^2] - a*x*ArcSin[a*x] + ArcSin[a*x]^2*CosIntegral[ArcSin[a*x]])/(a*ArcSin[a*x]^2)","A",1
65,0,0,13,0.5016402,"\int \frac{1}{x \sin ^{-1}(a x)^3} \, dx","Integrate[1/(x*ArcSin[a*x]^3),x]","\int \frac{1}{x \sin ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)^3},x\right)",0,"Integrate[1/(x*ArcSin[a*x]^3), x]","A",-1
66,0,0,13,6.3696544,"\int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx","Integrate[1/(x^2*ArcSin[a*x]^3),x]","\int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x^2 \sin ^{-1}(a x)^3},x\right)",0,"Integrate[1/(x^2*ArcSin[a*x]^3), x]","A",-1
67,1,159,158,0.2931851,"\int \frac{x^4}{\sin ^{-1}(a x)^4} \, dx","Integrate[x^4/ArcSin[a*x]^4,x]","\frac{80 a^5 x^5 \sin ^{-1}(a x)-64 a^3 x^3 \sin ^{-1}(a x)-192 a^2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2-32 a^4 x^4 \sqrt{1-a^2 x^2}+400 a^4 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2+2 \sin ^{-1}(a x)^3 \text{Si}\left(\sin ^{-1}(a x)\right)-81 \sin ^{-1}(a x)^3 \text{Si}\left(3 \sin ^{-1}(a x)\right)+125 \sin ^{-1}(a x)^3 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{96 a^5 \sin ^{-1}(a x)^3}","\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{48 a^5}-\frac{27 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{96 a^5}-\frac{2 x^3}{3 a^2 \sin ^{-1}(a x)^2}+\frac{25 x^4 \sqrt{1-a^2 x^2}}{6 a \sin ^{-1}(a x)}-\frac{x^4 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^3}-\frac{2 x^2 \sqrt{1-a^2 x^2}}{a^3 \sin ^{-1}(a x)}+\frac{5 x^5}{6 \sin ^{-1}(a x)^2}",1,"(-32*a^4*x^4*Sqrt[1 - a^2*x^2] - 64*a^3*x^3*ArcSin[a*x] + 80*a^5*x^5*ArcSin[a*x] - 192*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2 + 400*a^4*x^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2 + 2*ArcSin[a*x]^3*SinIntegral[ArcSin[a*x]] - 81*ArcSin[a*x]^3*SinIntegral[3*ArcSin[a*x]] + 125*ArcSin[a*x]^3*SinIntegral[5*ArcSin[a*x]])/(96*a^5*ArcSin[a*x]^3)","A",1
68,1,107,144,0.3547005,"\int \frac{x^3}{\sin ^{-1}(a x)^4} \, dx","Integrate[x^3/ArcSin[a*x]^4,x]","\frac{\frac{a x \left(-2 a^2 x^2 \sqrt{1-a^2 x^2}+a x \left(4 a^2 x^2-3\right) \sin ^{-1}(a x)+2 \sqrt{1-a^2 x^2} \left(8 a^2 x^2-3\right) \sin ^{-1}(a x)^2\right)}{\sin ^{-1}(a x)^3}-2 \text{Ci}\left(2 \sin ^{-1}(a x)\right)+8 \text{Ci}\left(4 \sin ^{-1}(a x)\right)}{6 a^4}","-\frac{\text{Ci}\left(2 \sin ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{Ci}\left(4 \sin ^{-1}(a x)\right)}{3 a^4}-\frac{x^2}{2 a^2 \sin ^{-1}(a x)^2}+\frac{8 x^3 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)}-\frac{x^3 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^3}-\frac{x \sqrt{1-a^2 x^2}}{a^3 \sin ^{-1}(a x)}+\frac{2 x^4}{3 \sin ^{-1}(a x)^2}",1,"((a*x*(-2*a^2*x^2*Sqrt[1 - a^2*x^2] + a*x*(-3 + 4*a^2*x^2)*ArcSin[a*x] + 2*Sqrt[1 - a^2*x^2]*(-3 + 8*a^2*x^2)*ArcSin[a*x]^2))/ArcSin[a*x]^3 - 2*CosIntegral[2*ArcSin[a*x]] + 8*CosIntegral[4*ArcSin[a*x]])/(6*a^4)","A",1
69,1,102,141,0.2268441,"\int \frac{x^2}{\sin ^{-1}(a x)^4} \, dx","Integrate[x^2/ArcSin[a*x]^4,x]","\frac{-\frac{8 a^2 x^2 \sqrt{1-a^2 x^2}}{\sin ^{-1}(a x)^3}+\frac{4 a x \left(3 a^2 x^2-2\right)}{\sin ^{-1}(a x)^2}+\frac{4 \sqrt{1-a^2 x^2} \left(9 a^2 x^2-2\right)}{\sin ^{-1}(a x)}+\text{Si}\left(\sin ^{-1}(a x)\right)-27 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{24 a^3}","\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{24 a^3}-\frac{9 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{8 a^3}+\frac{3 x^2 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^3}-\frac{x}{3 a^2 \sin ^{-1}(a x)^2}-\frac{\sqrt{1-a^2 x^2}}{3 a^3 \sin ^{-1}(a x)}+\frac{x^3}{2 \sin ^{-1}(a x)^2}",1,"((-8*a^2*x^2*Sqrt[1 - a^2*x^2])/ArcSin[a*x]^3 + (4*a*x*(-2 + 3*a^2*x^2))/ArcSin[a*x]^2 + (4*Sqrt[1 - a^2*x^2]*(-2 + 9*a^2*x^2))/ArcSin[a*x] + SinIntegral[ArcSin[a*x]] - 27*SinIntegral[3*ArcSin[a*x]])/(24*a^3)","A",1
70,1,86,97,0.118166,"\int \frac{x}{\sin ^{-1}(a x)^4} \, dx","Integrate[x/ArcSin[a*x]^4,x]","\frac{-2 a x \sqrt{1-a^2 x^2}+4 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2+\left(2 a^2 x^2-1\right) \sin ^{-1}(a x)-4 \sin ^{-1}(a x)^3 \text{Ci}\left(2 \sin ^{-1}(a x)\right)}{6 a^2 \sin ^{-1}(a x)^3}","-\frac{2 \text{Ci}\left(2 \sin ^{-1}(a x)\right)}{3 a^2}+\frac{2 x \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)}-\frac{x \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^3}-\frac{1}{6 a^2 \sin ^{-1}(a x)^2}+\frac{x^2}{3 \sin ^{-1}(a x)^2}",1,"(-2*a*x*Sqrt[1 - a^2*x^2] + (-1 + 2*a^2*x^2)*ArcSin[a*x] + 4*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2 - 4*ArcSin[a*x]^3*CosIntegral[2*ArcSin[a*x]])/(6*a^2*ArcSin[a*x]^3)","A",1
71,1,70,78,0.0552486,"\int \frac{1}{\sin ^{-1}(a x)^4} \, dx","Integrate[ArcSin[a*x]^(-4),x]","\frac{-2 \sqrt{1-a^2 x^2}+\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2+\sin ^{-1}(a x)^3 \text{Si}\left(\sin ^{-1}(a x)\right)+a x \sin ^{-1}(a x)}{6 a \sin ^{-1}(a x)^3}","\frac{\sqrt{1-a^2 x^2}}{6 a \sin ^{-1}(a x)}-\frac{\sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^3}+\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{6 a}+\frac{x}{6 \sin ^{-1}(a x)^2}",1,"(-2*Sqrt[1 - a^2*x^2] + a*x*ArcSin[a*x] + Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2 + ArcSin[a*x]^3*SinIntegral[ArcSin[a*x]])/(6*a*ArcSin[a*x]^3)","A",1
72,0,0,13,2.3303856,"\int \frac{1}{x \sin ^{-1}(a x)^4} \, dx","Integrate[1/(x*ArcSin[a*x]^4),x]","\int \frac{1}{x \sin ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)^4},x\right)",0,"Integrate[1/(x*ArcSin[a*x]^4), x]","A",-1
73,0,0,13,17.4031619,"\int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx","Integrate[1/(x^2*ArcSin[a*x]^4),x]","\int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x^2 \sin ^{-1}(a x)^4},x\right)",0,"Integrate[1/(x^2*ArcSin[a*x]^4), x]","A",-1
74,1,204,121,0.099962,"\int x^4 \sqrt{\sin ^{-1}(a x)} \, dx","Integrate[x^4*Sqrt[ArcSin[a*x]],x]","\frac{i \sqrt{\sin ^{-1}(a x)} \left(-150 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-i \sin ^{-1}(a x)\right)+150 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},i \sin ^{-1}(a x)\right)+25 \sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-3 i \sin ^{-1}(a x)\right)-25 \sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},3 i \sin ^{-1}(a x)\right)-3 \sqrt{5} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-5 i \sin ^{-1}(a x)\right)+3 \sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},5 i \sin ^{-1}(a x)\right)\right)}{2400 a^5 \sqrt{\sin ^{-1}(a x)^2}}","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}+\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{80 a^5}+\frac{1}{5} x^5 \sqrt{\sin ^{-1}(a x)}",1,"((I/2400)*Sqrt[ArcSin[a*x]]*(-150*Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (-I)*ArcSin[a*x]] + 150*Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, I*ArcSin[a*x]] + 25*Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (-3*I)*ArcSin[a*x]] - 25*Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (3*I)*ArcSin[a*x]] - 3*Sqrt[5]*Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (-5*I)*ArcSin[a*x]] + 3*Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (5*I)*ArcSin[a*x]]))/(a^5*Sqrt[ArcSin[a*x]^2])","C",0
75,1,138,95,0.0591888,"\int x^3 \sqrt{\sin ^{-1}(a x)} \, dx","Integrate[x^3*Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\sin ^{-1}(a x)} \left(-4 \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-2 i \sin ^{-1}(a x)\right)-4 \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},2 i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-4 i \sin ^{-1}(a x)\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},4 i \sin ^{-1}(a x)\right)\right)}{128 a^4 \sqrt{\sin ^{-1}(a x)^2}}","-\frac{\sqrt{\frac{\pi }{2}} C\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{64 a^4}+\frac{\sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{16 a^4}-\frac{3 \sqrt{\sin ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\sin ^{-1}(a x)}",1,"(Sqrt[ArcSin[a*x]]*(-4*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (-2*I)*ArcSin[a*x]] - 4*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (2*I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (-4*I)*ArcSin[a*x]] + Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (4*I)*ArcSin[a*x]]))/(128*a^4*Sqrt[ArcSin[a*x]^2])","C",0
76,1,126,86,0.0450281,"\int x^2 \sqrt{\sin ^{-1}(a x)} \, dx","Integrate[x^2*Sqrt[ArcSin[a*x]],x]","\frac{9 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-i \sin ^{-1}(a x)\right)+9 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},i \sin ^{-1}(a x)\right)-\sqrt{3} \left(\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-3 i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},3 i \sin ^{-1}(a x)\right)\right)}{72 a^3 \sqrt{\sin ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{12 a^3}+\frac{1}{3} x^3 \sqrt{\sin ^{-1}(a x)}",1,"(9*Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (-I)*ArcSin[a*x]] + 9*Sqrt[I*ArcSin[a*x]]*Gamma[3/2, I*ArcSin[a*x]] - Sqrt[3]*(Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (-3*I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (3*I)*ArcSin[a*x]]))/(72*a^3*Sqrt[ArcSin[a*x]])","C",0
77,1,81,59,0.0192743,"\int x \sqrt{\sin ^{-1}(a x)} \, dx","Integrate[x*Sqrt[ArcSin[a*x]],x]","-\frac{\sqrt{\sin ^{-1}(a x)} \left(\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-2 i \sin ^{-1}(a x)\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},2 i \sin ^{-1}(a x)\right)\right)}{8 \sqrt{2} a^2 \sqrt{\sin ^{-1}(a x)^2}}","\frac{\sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a^2}-\frac{\sqrt{\sin ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\sin ^{-1}(a x)}",1,"-1/8*(Sqrt[ArcSin[a*x]]*(Sqrt[I*ArcSin[a*x]]*Gamma[3/2, (-2*I)*ArcSin[a*x]] + Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (2*I)*ArcSin[a*x]]))/(Sqrt[2]*a^2*Sqrt[ArcSin[a*x]^2])","C",0
78,1,66,44,0.0255509,"\int \sqrt{\sin ^{-1}(a x)} \, dx","Integrate[Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},-i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{3}{2},i \sin ^{-1}(a x)\right)}{2 a \sqrt{\sin ^{-1}(a x)}}","x \sqrt{\sin ^{-1}(a x)}-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a}",1,"(Sqrt[(-I)*ArcSin[a*x]]*Gamma[3/2, (-I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[3/2, I*ArcSin[a*x]])/(2*a*Sqrt[ArcSin[a*x]])","C",0
79,0,0,15,0.4623168,"\int \frac{\sqrt{\sin ^{-1}(a x)}}{x} \, dx","Integrate[Sqrt[ArcSin[a*x]]/x,x]","\int \frac{\sqrt{\sin ^{-1}(a x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{\sin ^{-1}(a x)}}{x},x\right)",0,"Integrate[Sqrt[ArcSin[a*x]]/x, x]","A",-1
80,1,202,214,0.0652373,"\int x^4 \sin ^{-1}(a x)^{3/2} \, dx","Integrate[x^4*ArcSin[a*x]^(3/2),x]","\frac{\sqrt{\sin ^{-1}(a x)} \left(2250 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-i \sin ^{-1}(a x)\right)+2250 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},i \sin ^{-1}(a x)\right)-125 \sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-3 i \sin ^{-1}(a x)\right)-125 \sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},3 i \sin ^{-1}(a x)\right)+9 \sqrt{5} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-5 i \sin ^{-1}(a x)\right)+9 \sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},5 i \sin ^{-1}(a x)\right)\right)}{36000 a^5 \sqrt{\sin ^{-1}(a x)^2}}","-\frac{3 \sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{\frac{\pi }{6}} C\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{32 a^5}-\frac{3 \sqrt{\frac{\pi }{10}} C\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{800 a^5}+\frac{3 x^4 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{50 a}+\frac{4 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{25 a^5}+\frac{2 x^2 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{25 a^3}+\frac{1}{5} x^5 \sin ^{-1}(a x)^{3/2}",1,"(Sqrt[ArcSin[a*x]]*(2250*Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (-I)*ArcSin[a*x]] + 2250*Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, I*ArcSin[a*x]] - 125*Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (-3*I)*ArcSin[a*x]] - 125*Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, (3*I)*ArcSin[a*x]] + 9*Sqrt[5]*Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (-5*I)*ArcSin[a*x]] + 9*Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, (5*I)*ArcSin[a*x]]))/(36000*a^5*Sqrt[ArcSin[a*x]^2])","C",0
81,1,130,157,0.0333352,"\int x^3 \sin ^{-1}(a x)^{3/2} \, dx","Integrate[x^3*ArcSin[a*x]^(3/2),x]","\frac{8 \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-2 i \sin ^{-1}(a x)\right)+8 \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},2 i \sin ^{-1}(a x)\right)-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-4 i \sin ^{-1}(a x)\right)-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},4 i \sin ^{-1}(a x)\right)}{512 a^4 \sqrt{\sin ^{-1}(a x)}}","\frac{3 \sqrt{\frac{\pi }{2}} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{512 a^4}-\frac{3 \sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{64 a^4}-\frac{3 \sin ^{-1}(a x)^{3/2}}{32 a^4}+\frac{3 x^3 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{32 a}+\frac{9 x \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{64 a^3}+\frac{1}{4} x^4 \sin ^{-1}(a x)^{3/2}",1,"(8*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, (-2*I)*ArcSin[a*x]] + 8*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (2*I)*ArcSin[a*x]] - Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, (-4*I)*ArcSin[a*x]] - Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (4*I)*ArcSin[a*x]])/(512*a^4*Sqrt[ArcSin[a*x]])","C",0
82,1,136,147,0.0501654,"\int x^2 \sin ^{-1}(a x)^{3/2} \, dx","Integrate[x^2*ArcSin[a*x]^(3/2),x]","\frac{\sqrt{\sin ^{-1}(a x)} \left(27 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-i \sin ^{-1}(a x)\right)+27 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},i \sin ^{-1}(a x)\right)-\sqrt{3} \left(\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-3 i \sin ^{-1}(a x)\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},3 i \sin ^{-1}(a x)\right)\right)\right)}{216 a^3 \sqrt{\sin ^{-1}(a x)^2}}","-\frac{3 \sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{6}} C\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{24 a^3}+\frac{x^2 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{6 a}+\frac{\sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \sin ^{-1}(a x)^{3/2}",1,"(Sqrt[ArcSin[a*x]]*(27*Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (-I)*ArcSin[a*x]] + 27*Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, I*ArcSin[a*x]] - Sqrt[3]*(Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (-3*I)*ArcSin[a*x]] + Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, (3*I)*ArcSin[a*x]])))/(216*a^3*Sqrt[ArcSin[a*x]^2])","C",0
83,1,71,89,0.014092,"\int x \sin ^{-1}(a x)^{3/2} \, dx","Integrate[x*ArcSin[a*x]^(3/2),x]","\frac{\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-2 i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},2 i \sin ^{-1}(a x)\right)}{16 \sqrt{2} a^2 \sqrt{\sin ^{-1}(a x)}}","-\frac{3 \sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a^2}+\frac{3 x \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{8 a}-\frac{\sin ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \sin ^{-1}(a x)^{3/2}",1,"(Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, (-2*I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (2*I)*ArcSin[a*x]])/(16*Sqrt[2]*a^2*Sqrt[ArcSin[a*x]])","C",0
84,1,76,75,0.038053,"\int \sin ^{-1}(a x)^{3/2} \, dx","Integrate[ArcSin[a*x]^(3/2),x]","\frac{\sqrt{\sin ^{-1}(a x)} \left(\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},-i \sin ^{-1}(a x)\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{5}{2},i \sin ^{-1}(a x)\right)\right)}{2 a \sqrt{\sin ^{-1}(a x)^2}}","\frac{3 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{2 a}-\frac{3 \sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a}+x \sin ^{-1}(a x)^{3/2}",1,"(Sqrt[ArcSin[a*x]]*(Sqrt[I*ArcSin[a*x]]*Gamma[5/2, (-I)*ArcSin[a*x]] + Sqrt[(-I)*ArcSin[a*x]]*Gamma[5/2, I*ArcSin[a*x]]))/(2*a*Sqrt[ArcSin[a*x]^2])","C",0
85,0,0,15,0.3726174,"\int \frac{\sin ^{-1}(a x)^{3/2}}{x} \, dx","Integrate[ArcSin[a*x]^(3/2)/x,x]","\int \frac{\sin ^{-1}(a x)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^{3/2}}{x},x\right)",0,"Integrate[ArcSin[a*x]^(3/2)/x, x]","A",-1
86,1,204,263,0.0665376,"\int x^4 \sin ^{-1}(a x)^{5/2} \, dx","Integrate[x^4*ArcSin[a*x]^(5/2),x]","\frac{i \sqrt{\sin ^{-1}(a x)} \left(33750 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-i \sin ^{-1}(a x)\right)-33750 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},i \sin ^{-1}(a x)\right)-625 \sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-3 i \sin ^{-1}(a x)\right)+625 \sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},3 i \sin ^{-1}(a x)\right)+27 \sqrt{5} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-5 i \sin ^{-1}(a x)\right)-27 \sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},5 i \sin ^{-1}(a x)\right)\right)}{540000 a^5 \sqrt{\sin ^{-1}(a x)^2}}","\frac{15 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{32 a^5}-\frac{5 \sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{192 a^5}+\frac{3 \sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{1600 a^5}-\frac{2 x \sqrt{\sin ^{-1}(a x)}}{5 a^4}-\frac{x^3 \sqrt{\sin ^{-1}(a x)}}{15 a^2}+\frac{x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{10 a}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{15 a^5}+\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{15 a^3}+\frac{1}{5} x^5 \sin ^{-1}(a x)^{5/2}-\frac{3}{100} x^5 \sqrt{\sin ^{-1}(a x)}",1,"((I/540000)*Sqrt[ArcSin[a*x]]*(33750*Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (-I)*ArcSin[a*x]] - 33750*Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, I*ArcSin[a*x]] - 625*Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (-3*I)*ArcSin[a*x]] + 625*Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (3*I)*ArcSin[a*x]] + 27*Sqrt[5]*Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (-5*I)*ArcSin[a*x]] - 27*Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (5*I)*ArcSin[a*x]]))/(a^5*Sqrt[ArcSin[a*x]^2])","C",0
87,1,140,205,0.0388963,"\int x^3 \sin ^{-1}(a x)^{5/2} \, dx","Integrate[x^3*ArcSin[a*x]^(5/2),x]","\frac{\sqrt{\sin ^{-1}(a x)} \left(16 \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-2 i \sin ^{-1}(a x)\right)+16 \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},2 i \sin ^{-1}(a x)\right)-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-4 i \sin ^{-1}(a x)\right)-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},4 i \sin ^{-1}(a x)\right)\right)}{2048 a^4 \sqrt{\sin ^{-1}(a x)^2}}","\frac{15 \sqrt{\frac{\pi }{2}} C\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4096 a^4}-\frac{15 \sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{256 a^4}-\frac{3 \sin ^{-1}(a x)^{5/2}}{32 a^4}+\frac{225 \sqrt{\sin ^{-1}(a x)}}{2048 a^4}-\frac{45 x^2 \sqrt{\sin ^{-1}(a x)}}{256 a^2}+\frac{5 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{32 a}+\frac{15 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{64 a^3}+\frac{1}{4} x^4 \sin ^{-1}(a x)^{5/2}-\frac{15}{256} x^4 \sqrt{\sin ^{-1}(a x)}",1,"(Sqrt[ArcSin[a*x]]*(16*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (-2*I)*ArcSin[a*x]] + 16*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (2*I)*ArcSin[a*x]] - Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (-4*I)*ArcSin[a*x]] - Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (4*I)*ArcSin[a*x]]))/(2048*a^4*Sqrt[ArcSin[a*x]^2])","C",0
88,1,125,178,0.0577637,"\int x^2 \sin ^{-1}(a x)^{5/2} \, dx","Integrate[x^2*ArcSin[a*x]^(5/2),x]","\frac{-81 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-i \sin ^{-1}(a x)\right)-81 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},i \sin ^{-1}(a x)\right)+\sqrt{3} \left(\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-3 i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},3 i \sin ^{-1}(a x)\right)\right)}{648 a^3 \sqrt{\sin ^{-1}(a x)}}","\frac{15 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^3}-\frac{5 \sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{144 a^3}+\frac{5 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{18 a}-\frac{5 x \sqrt{\sin ^{-1}(a x)}}{6 a^2}+\frac{5 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{9 a^3}+\frac{1}{3} x^3 \sin ^{-1}(a x)^{5/2}-\frac{5}{36} x^3 \sqrt{\sin ^{-1}(a x)}",1,"(-81*Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (-I)*ArcSin[a*x]] - 81*Sqrt[I*ArcSin[a*x]]*Gamma[7/2, I*ArcSin[a*x]] + Sqrt[3]*(Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (-3*I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (3*I)*ArcSin[a*x]]))/(648*a^3*Sqrt[ArcSin[a*x]])","C",0
89,1,81,119,0.0146519,"\int x \sin ^{-1}(a x)^{5/2} \, dx","Integrate[x*ArcSin[a*x]^(5/2),x]","\frac{\sqrt{\sin ^{-1}(a x)} \left(\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-2 i \sin ^{-1}(a x)\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},2 i \sin ^{-1}(a x)\right)\right)}{32 \sqrt{2} a^2 \sqrt{\sin ^{-1}(a x)^2}}","-\frac{15 \sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a^2}+\frac{5 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{8 a}-\frac{\sin ^{-1}(a x)^{5/2}}{4 a^2}+\frac{15 \sqrt{\sin ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \sin ^{-1}(a x)^{5/2}-\frac{15}{32} x^2 \sqrt{\sin ^{-1}(a x)}",1,"(Sqrt[ArcSin[a*x]]*(Sqrt[I*ArcSin[a*x]]*Gamma[7/2, (-2*I)*ArcSin[a*x]] + Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (2*I)*ArcSin[a*x]]))/(32*Sqrt[2]*a^2*Sqrt[ArcSin[a*x]^2])","C",0
90,1,68,88,0.0358165,"\int \sin ^{-1}(a x)^{5/2} \, dx","Integrate[ArcSin[a*x]^(5/2),x]","\frac{-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},-i \sin ^{-1}(a x)\right)-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{7}{2},i \sin ^{-1}(a x)\right)}{2 a \sqrt{\sin ^{-1}(a x)}}","\frac{5 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{2 a}+\frac{15 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a}+x \sin ^{-1}(a x)^{5/2}-\frac{15}{4} x \sqrt{\sin ^{-1}(a x)}",1,"(-(Sqrt[(-I)*ArcSin[a*x]]*Gamma[7/2, (-I)*ArcSin[a*x]]) - Sqrt[I*ArcSin[a*x]]*Gamma[7/2, I*ArcSin[a*x]])/(2*a*Sqrt[ArcSin[a*x]])","C",0
91,0,0,15,0.3808756,"\int \frac{\sin ^{-1}(a x)^{5/2}}{x} \, dx","Integrate[ArcSin[a*x]^(5/2)/x,x]","\int \frac{\sin ^{-1}(a x)^{5/2}}{x} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^{5/2}}{x},x\right)",0,"Integrate[ArcSin[a*x]^(5/2)/x, x]","A",-1
92,1,193,106,0.0505086,"\int \frac{x^4}{\sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[x^4/Sqrt[ArcSin[a*x]],x]","-\frac{i \left(10 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)-10 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)-5 \sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)+5 \sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)+\sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 i \sin ^{-1}(a x)\right)-\sqrt{5} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},5 i \sin ^{-1}(a x)\right)\right)}{160 a^5 \sqrt{\sin ^{-1}(a x)}}","\frac{\sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{3 \pi }{2}} C\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}+\frac{\sqrt{\frac{\pi }{10}} C\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}",1,"((-1/160*I)*(10*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]] - 10*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]] - 5*Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-3*I)*ArcSin[a*x]] + 5*Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (3*I)*ArcSin[a*x]] + Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-5*I)*ArcSin[a*x]] - Sqrt[5]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (5*I)*ArcSin[a*x]]))/(a^5*Sqrt[ArcSin[a*x]])","C",0
93,1,128,65,0.0356309,"\int \frac{x^3}{\sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[x^3/Sqrt[ArcSin[a*x]],x]","\frac{-2 \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)-2 \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 i \sin ^{-1}(a x)\right)}{32 a^4 \sqrt{\sin ^{-1}(a x)}}","\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{4 a^4}-\frac{\sqrt{\frac{\pi }{2}} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^4}",1,"(-2*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] - 2*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]] + Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-4*I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (4*I)*ArcSin[a*x]])/(32*a^4*Sqrt[ArcSin[a*x]])","C",0
94,1,128,71,0.0471792,"\int \frac{x^2}{\sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[x^2/Sqrt[ArcSin[a*x]],x]","-\frac{i \left(3 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)-3 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)+\sqrt{3} \left(\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)\right)\right)}{24 a^3 \sqrt{\sin ^{-1}(a x)}}","\frac{\sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\frac{\pi }{6}} C\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^3}",1,"((-1/24*I)*(3*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]] - 3*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]] + Sqrt[3]*(-(Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-3*I)*ArcSin[a*x]]) + Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (3*I)*ArcSin[a*x]])))/(a^3*Sqrt[ArcSin[a*x]])","C",0
95,1,71,28,0.0170359,"\int \frac{x}{\sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[x/Sqrt[ArcSin[a*x]],x]","-\frac{\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)}{4 \sqrt{2} a^2 \sqrt{\sin ^{-1}(a x)}}","\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a^2}",1,"-1/4*(Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]])/(Sqrt[2]*a^2*Sqrt[ArcSin[a*x]])","C",0
96,1,69,30,0.0246131,"\int \frac{1}{\sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[1/Sqrt[ArcSin[a*x]],x]","-\frac{i \left(\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)\right)}{2 a \sqrt{\sin ^{-1}(a x)}}","\frac{\sqrt{2 \pi } C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a}",1,"((-1/2*I)*(Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]] - Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]]))/(a*Sqrt[ArcSin[a*x]])","C",0
97,0,0,15,0.3540775,"\int \frac{1}{x \sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[1/(x*Sqrt[ArcSin[a*x]]),x]","\int \frac{1}{x \sqrt{\sin ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{\sin ^{-1}(a x)}},x\right)",0,"Integrate[1/(x*Sqrt[ArcSin[a*x]]), x]","A",-1
98,0,0,15,2.9732326,"\int \frac{1}{x^2 \sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[1/(x^2*Sqrt[ArcSin[a*x]]),x]","\int \frac{1}{x^2 \sqrt{\sin ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{\sin ^{-1}(a x)}},x\right)",0,"Integrate[1/(x^2*Sqrt[ArcSin[a*x]]), x]","A",-1
99,1,427,171,0.2187408,"\int \frac{x^6}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[x^6/ArcSin[a*x]^(3/2),x]","\frac{-\frac{5 \left(e^{i \sin ^{-1}(a x)}-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)\right)}{64 \sqrt{\sin ^{-1}(a x)}}-\frac{5 \left(e^{-i \sin ^{-1}(a x)}-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)\right)}{64 \sqrt{\sin ^{-1}(a x)}}+\frac{9 \left(e^{3 i \sin ^{-1}(a x)}-\sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)\right)}{64 \sqrt{\sin ^{-1}(a x)}}+\frac{9 \left(e^{-3 i \sin ^{-1}(a x)}-\sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)\right)}{64 \sqrt{\sin ^{-1}(a x)}}-\frac{5 \left(e^{5 i \sin ^{-1}(a x)}-\sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 i \sin ^{-1}(a x)\right)\right)}{64 \sqrt{\sin ^{-1}(a x)}}-\frac{5 \left(e^{-5 i \sin ^{-1}(a x)}-\sqrt{5} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},5 i \sin ^{-1}(a x)\right)\right)}{64 \sqrt{\sin ^{-1}(a x)}}+\frac{e^{7 i \sin ^{-1}(a x)}-\sqrt{7} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-7 i \sin ^{-1}(a x)\right)}{64 \sqrt{\sin ^{-1}(a x)}}+\frac{e^{-7 i \sin ^{-1}(a x)}-\sqrt{7} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},7 i \sin ^{-1}(a x)\right)}{64 \sqrt{\sin ^{-1}(a x)}}}{a^7}","-\frac{5 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^7}+\frac{9 \sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^7}-\frac{5 \sqrt{\frac{5 \pi }{2}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^7}+\frac{\sqrt{\frac{7 \pi }{2}} S\left(\sqrt{\frac{14}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^7}-\frac{2 x^6 \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"((-5*(E^(I*ArcSin[a*x]) - Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]]))/(64*Sqrt[ArcSin[a*x]]) - (5*(E^((-I)*ArcSin[a*x]) - Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]]))/(64*Sqrt[ArcSin[a*x]]) + (9*(E^((3*I)*ArcSin[a*x]) - Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-3*I)*ArcSin[a*x]]))/(64*Sqrt[ArcSin[a*x]]) + (9*(E^((-3*I)*ArcSin[a*x]) - Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (3*I)*ArcSin[a*x]]))/(64*Sqrt[ArcSin[a*x]]) - (5*(E^((5*I)*ArcSin[a*x]) - Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-5*I)*ArcSin[a*x]]))/(64*Sqrt[ArcSin[a*x]]) - (5*(E^((-5*I)*ArcSin[a*x]) - Sqrt[5]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (5*I)*ArcSin[a*x]]))/(64*Sqrt[ArcSin[a*x]]) + (E^((7*I)*ArcSin[a*x]) - Sqrt[7]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-7*I)*ArcSin[a*x]])/(64*Sqrt[ArcSin[a*x]]) + (E^((-7*I)*ArcSin[a*x]) - Sqrt[7]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (7*I)*ArcSin[a*x]])/(64*Sqrt[ArcSin[a*x]]))/a^7","C",0
100,1,231,127,0.1417129,"\int \frac{x^5}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[x^5/ArcSin[a*x]^(3/2),x]","-\frac{10 \sin \left(2 \sin ^{-1}(a x)\right)-8 \sin \left(4 \sin ^{-1}(a x)\right)+2 \sin \left(6 \sin ^{-1}(a x)\right)+5 i \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)-5 i \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)-8 i \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 i \sin ^{-1}(a x)\right)+8 i \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 i \sin ^{-1}(a x)\right)+i \sqrt{6} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-6 i \sin ^{-1}(a x)\right)-i \sqrt{6} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},6 i \sin ^{-1}(a x)\right)}{32 a^6 \sqrt{\sin ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} C\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^6}+\frac{\sqrt{3 \pi } C\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^6}+\frac{5 \sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a^6}-\frac{2 x^5 \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"-1/32*((5*I)*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] - (5*I)*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]] - (8*I)*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-4*I)*ArcSin[a*x]] + (8*I)*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (4*I)*ArcSin[a*x]] + I*Sqrt[6]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-6*I)*ArcSin[a*x]] - I*Sqrt[6]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (6*I)*ArcSin[a*x]] + 10*Sin[2*ArcSin[a*x]] - 8*Sin[4*ArcSin[a*x]] + 2*Sin[6*ArcSin[a*x]])/(a^6*Sqrt[ArcSin[a*x]])","C",0
101,1,319,136,0.1153306,"\int \frac{x^4}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[x^4/ArcSin[a*x]^(3/2),x]","\frac{-\frac{e^{i \sin ^{-1}(a x)}-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)}{8 \sqrt{\sin ^{-1}(a x)}}-\frac{e^{-i \sin ^{-1}(a x)}-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)}{8 \sqrt{\sin ^{-1}(a x)}}+\frac{3 \left(e^{3 i \sin ^{-1}(a x)}-\sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)\right)}{16 \sqrt{\sin ^{-1}(a x)}}+\frac{3 \left(e^{-3 i \sin ^{-1}(a x)}-\sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)\right)}{16 \sqrt{\sin ^{-1}(a x)}}-\frac{e^{5 i \sin ^{-1}(a x)}-\sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 i \sin ^{-1}(a x)\right)}{16 \sqrt{\sin ^{-1}(a x)}}-\frac{e^{-5 i \sin ^{-1}(a x)}-\sqrt{5} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},5 i \sin ^{-1}(a x)\right)}{16 \sqrt{\sin ^{-1}(a x)}}}{a^5}","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^5}+\frac{3 \sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{5 \pi }{2}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a^5}-\frac{2 x^4 \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"(-1/8*(E^(I*ArcSin[a*x]) - Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]])/Sqrt[ArcSin[a*x]] - (E^((-I)*ArcSin[a*x]) - Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]])/(8*Sqrt[ArcSin[a*x]]) + (3*(E^((3*I)*ArcSin[a*x]) - Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-3*I)*ArcSin[a*x]]))/(16*Sqrt[ArcSin[a*x]]) + (3*(E^((-3*I)*ArcSin[a*x]) - Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (3*I)*ArcSin[a*x]]))/(16*Sqrt[ArcSin[a*x]]) - (E^((5*I)*ArcSin[a*x]) - Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-5*I)*ArcSin[a*x]])/(16*Sqrt[ArcSin[a*x]]) - (E^((-5*I)*ArcSin[a*x]) - Sqrt[5]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (5*I)*ArcSin[a*x]])/(16*Sqrt[ArcSin[a*x]]))/a^5","C",0
102,1,154,90,0.0426609,"\int \frac{x^3}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[x^3/ArcSin[a*x]^(3/2),x]","\frac{-2 \sin \left(2 \sin ^{-1}(a x)\right)+\sin \left(4 \sin ^{-1}(a x)\right)-i \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)+i \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)+i \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 i \sin ^{-1}(a x)\right)-i \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 i \sin ^{-1}(a x)\right)}{4 a^4 \sqrt{\sin ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} C\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^4}+\frac{\sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a^4}-\frac{2 x^3 \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"((-I)*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] + I*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]] + I*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-4*I)*ArcSin[a*x]] - I*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (4*I)*ArcSin[a*x]] - 2*Sin[2*ArcSin[a*x]] + Sin[4*ArcSin[a*x]])/(4*a^4*Sqrt[ArcSin[a*x]])","C",0
103,1,211,96,0.0668544,"\int \frac{x^2}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[x^2/ArcSin[a*x]^(3/2),x]","\frac{-\frac{e^{i \sin ^{-1}(a x)}-\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)}{4 \sqrt{\sin ^{-1}(a x)}}-\frac{e^{-i \sin ^{-1}(a x)}-\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)}{4 \sqrt{\sin ^{-1}(a x)}}+\frac{e^{3 i \sin ^{-1}(a x)}-\sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)}{4 \sqrt{\sin ^{-1}(a x)}}+\frac{e^{-3 i \sin ^{-1}(a x)}-\sqrt{3} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)}{4 \sqrt{\sin ^{-1}(a x)}}}{a^3}","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^3}+\frac{\sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^3}-\frac{2 x^2 \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"(-1/4*(E^(I*ArcSin[a*x]) - Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]])/Sqrt[ArcSin[a*x]] - (E^((-I)*ArcSin[a*x]) - Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]])/(4*Sqrt[ArcSin[a*x]]) + (E^((3*I)*ArcSin[a*x]) - Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-3*I)*ArcSin[a*x]])/(4*Sqrt[ArcSin[a*x]]) + (E^((-3*I)*ArcSin[a*x]) - Sqrt[3]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (3*I)*ArcSin[a*x]])/(4*Sqrt[ArcSin[a*x]]))/a^3","C",0
104,1,91,55,0.0289201,"\int \frac{x}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[x/ArcSin[a*x]^(3/2),x]","-\frac{2 \sin \left(2 \sin ^{-1}(a x)\right)+i \sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)-i \sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)}{2 a^2 \sqrt{\sin ^{-1}(a x)}}","\frac{2 \sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a^2}-\frac{2 x \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"-1/2*(I*Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] - I*Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]] + 2*Sin[2*ArcSin[a*x]])/(a^2*Sqrt[ArcSin[a*x]])","C",0
105,1,87,59,0.0919972,"\int \frac{1}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[ArcSin[a*x]^(-3/2),x]","\frac{-e^{-i \sin ^{-1}(a x)} \left(1+e^{2 i \sin ^{-1}(a x)}\right)+\sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)+\sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)}{a \sqrt{\sin ^{-1}(a x)}}","-\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{\sin ^{-1}(a x)}}-\frac{2 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a}",1,"(-((1 + E^((2*I)*ArcSin[a*x]))/E^(I*ArcSin[a*x])) + Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-I)*ArcSin[a*x]] + Sqrt[I*ArcSin[a*x]]*Gamma[1/2, I*ArcSin[a*x]])/(a*Sqrt[ArcSin[a*x]])","C",0
106,0,0,15,0.4490025,"\int \frac{1}{x \sin ^{-1}(a x)^{3/2}} \, dx","Integrate[1/(x*ArcSin[a*x]^(3/2)),x]","\int \frac{1}{x \sin ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)^{3/2}},x\right)",0,"Integrate[1/(x*ArcSin[a*x]^(3/2)), x]","A",-1
107,1,418,171,0.2952454,"\int \frac{x^4}{\sin ^{-1}(a x)^{5/2}} \, dx","Integrate[x^4/ArcSin[a*x]^(5/2),x]","\frac{\frac{i e^{i \sin ^{-1}(a x)} \left(-2 \sin ^{-1}(a x)+i\right)-2 \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)}{24 \sin ^{-1}(a x)^{3/2}}-\frac{e^{-i \sin ^{-1}(a x)} \left(-2 i \sin ^{-1}(a x)+2 e^{i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)+1\right)}{24 \sin ^{-1}(a x)^{3/2}}-\frac{i e^{3 i \sin ^{-1}(a x)} \left(-6 \sin ^{-1}(a x)+i\right)-6 \sqrt{3} \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)}{16 \sin ^{-1}(a x)^{3/2}}+\frac{e^{-3 i \sin ^{-1}(a x)} \left(-6 i \sin ^{-1}(a x)+6 \sqrt{3} e^{3 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)+1\right)}{16 \sin ^{-1}(a x)^{3/2}}+\frac{i e^{5 i \sin ^{-1}(a x)} \left(-10 \sin ^{-1}(a x)+i\right)-10 \sqrt{5} \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-5 i \sin ^{-1}(a x)\right)}{48 \sin ^{-1}(a x)^{3/2}}-\frac{e^{-5 i \sin ^{-1}(a x)} \left(-10 i \sin ^{-1}(a x)+10 \sqrt{5} e^{5 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},5 i \sin ^{-1}(a x)\right)+1\right)}{48 \sin ^{-1}(a x)^{3/2}}}{a^5}","-\frac{\sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^5}+\frac{3 \sqrt{\frac{3 \pi }{2}} C\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^5}-\frac{5 \sqrt{\frac{5 \pi }{2}} C\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{6 a^5}-\frac{16 x^3}{3 a^2 \sqrt{\sin ^{-1}(a x)}}-\frac{2 x^4 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}+\frac{20 x^5}{3 \sqrt{\sin ^{-1}(a x)}}",1,"((I*E^(I*ArcSin[a*x])*(I - 2*ArcSin[a*x]) - 2*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-I)*ArcSin[a*x]])/(24*ArcSin[a*x]^(3/2)) - (1 - (2*I)*ArcSin[a*x] + 2*E^(I*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, I*ArcSin[a*x]])/(24*E^(I*ArcSin[a*x])*ArcSin[a*x]^(3/2)) - (I*E^((3*I)*ArcSin[a*x])*(I - 6*ArcSin[a*x]) - 6*Sqrt[3]*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-3*I)*ArcSin[a*x]])/(16*ArcSin[a*x]^(3/2)) + (1 - (6*I)*ArcSin[a*x] + 6*Sqrt[3]*E^((3*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, (3*I)*ArcSin[a*x]])/(16*E^((3*I)*ArcSin[a*x])*ArcSin[a*x]^(3/2)) + (I*E^((5*I)*ArcSin[a*x])*(I - 10*ArcSin[a*x]) - 10*Sqrt[5]*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-5*I)*ArcSin[a*x]])/(48*ArcSin[a*x]^(3/2)) - (1 - (10*I)*ArcSin[a*x] + 10*Sqrt[5]*E^((5*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, (5*I)*ArcSin[a*x]])/(48*E^((5*I)*ArcSin[a*x])*ArcSin[a*x]^(3/2)))/a^5","C",0
108,1,200,126,0.3796232,"\int \frac{x^3}{\sin ^{-1}(a x)^{5/2}} \, dx","Integrate[x^3/ArcSin[a*x]^(5/2),x]","\frac{-2 \sin \left(2 \sin ^{-1}(a x)\right)+\sin \left(4 \sin ^{-1}(a x)\right)-4 \sin ^{-1}(a x) \left(e^{-2 i \sin ^{-1}(a x)}+e^{2 i \sin ^{-1}(a x)}-\sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)-\sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)\right)+4 \sin ^{-1}(a x) \left(e^{-4 i \sin ^{-1}(a x)}+e^{4 i \sin ^{-1}(a x)}-2 \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 i \sin ^{-1}(a x)\right)-2 \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 i \sin ^{-1}(a x)\right)\right)}{12 a^4 \sin ^{-1}(a x)^{3/2}}","\frac{4 \sqrt{2 \pi } S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^4}-\frac{4 \sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a^4}-\frac{4 x^2}{a^2 \sqrt{\sin ^{-1}(a x)}}-\frac{2 x^3 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}+\frac{16 x^4}{3 \sqrt{\sin ^{-1}(a x)}}",1,"(-4*ArcSin[a*x]*(E^((-2*I)*ArcSin[a*x]) + E^((2*I)*ArcSin[a*x]) - Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] - Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]]) + 4*ArcSin[a*x]*(E^((-4*I)*ArcSin[a*x]) + E^((4*I)*ArcSin[a*x]) - 2*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-4*I)*ArcSin[a*x]] - 2*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (4*I)*ArcSin[a*x]]) - 2*Sin[2*ArcSin[a*x]] + Sin[4*ArcSin[a*x]])/(12*a^4*ArcSin[a*x]^(3/2))","C",0
109,1,277,125,0.1495391,"\int \frac{x^2}{\sin ^{-1}(a x)^{5/2}} \, dx","Integrate[x^2/ArcSin[a*x]^(5/2),x]","\frac{\frac{i e^{i \sin ^{-1}(a x)} \left(-2 \sin ^{-1}(a x)+i\right)-2 \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)}{12 \sin ^{-1}(a x)^{3/2}}-\frac{e^{-i \sin ^{-1}(a x)} \left(-2 i \sin ^{-1}(a x)+2 e^{i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)+1\right)}{12 \sin ^{-1}(a x)^{3/2}}-\frac{i e^{3 i \sin ^{-1}(a x)} \left(-6 \sin ^{-1}(a x)+i\right)-6 \sqrt{3} \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)}{12 \sin ^{-1}(a x)^{3/2}}+\frac{e^{-3 i \sin ^{-1}(a x)} \left(-6 i \sin ^{-1}(a x)+6 \sqrt{3} e^{3 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)+1\right)}{12 \sin ^{-1}(a x)^{3/2}}}{a^3}","-\frac{\sqrt{2 \pi } C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^3}+\frac{\sqrt{6 \pi } C\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^3}-\frac{2 x^2 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{8 x}{3 a^2 \sqrt{\sin ^{-1}(a x)}}+\frac{4 x^3}{\sqrt{\sin ^{-1}(a x)}}",1,"((I*E^(I*ArcSin[a*x])*(I - 2*ArcSin[a*x]) - 2*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-I)*ArcSin[a*x]])/(12*ArcSin[a*x]^(3/2)) - (1 - (2*I)*ArcSin[a*x] + 2*E^(I*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, I*ArcSin[a*x]])/(12*E^(I*ArcSin[a*x])*ArcSin[a*x]^(3/2)) - (I*E^((3*I)*ArcSin[a*x])*(I - 6*ArcSin[a*x]) - 6*Sqrt[3]*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-3*I)*ArcSin[a*x]])/(12*ArcSin[a*x]^(3/2)) + (1 - (6*I)*ArcSin[a*x] + 6*Sqrt[3]*E^((3*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, (3*I)*ArcSin[a*x]])/(12*E^((3*I)*ArcSin[a*x])*ArcSin[a*x]^(3/2)))/a^3","C",0
110,1,112,89,0.2116492,"\int \frac{x}{\sin ^{-1}(a x)^{5/2}} \, dx","Integrate[x/ArcSin[a*x]^(5/2),x]","-\frac{\sin \left(2 \sin ^{-1}(a x)\right)+2 \sin ^{-1}(a x) \left(e^{-2 i \sin ^{-1}(a x)}+e^{2 i \sin ^{-1}(a x)}-\sqrt{2} \sqrt{-i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)-\sqrt{2} \sqrt{i \sin ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)\right)}{3 a^2 \sin ^{-1}(a x)^{3/2}}","-\frac{8 \sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a^2}-\frac{2 x \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{4}{3 a^2 \sqrt{\sin ^{-1}(a x)}}+\frac{8 x^2}{3 \sqrt{\sin ^{-1}(a x)}}",1,"-1/3*(2*ArcSin[a*x]*(E^((-2*I)*ArcSin[a*x]) + E^((2*I)*ArcSin[a*x]) - Sqrt[2]*Sqrt[(-I)*ArcSin[a*x]]*Gamma[1/2, (-2*I)*ArcSin[a*x]] - Sqrt[2]*Sqrt[I*ArcSin[a*x]]*Gamma[1/2, (2*I)*ArcSin[a*x]]) + Sin[2*ArcSin[a*x]])/(a^2*ArcSin[a*x]^(3/2))","C",0
111,1,138,76,0.1738814,"\int \frac{1}{\sin ^{-1}(a x)^{5/2}} \, dx","Integrate[ArcSin[a*x]^(-5/2),x]","\frac{-2 i e^{i \sin ^{-1}(a x)} \left(2 \sin ^{-1}(a x)-i\right)-4 \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)}{6 a \sin ^{-1}(a x)^{3/2}}+\frac{e^{-i \sin ^{-1}(a x)} \left(4 i \sin ^{-1}(a x)-4 e^{i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)-2\right)}{6 a \sin ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{4 \sqrt{2 \pi } C\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a}+\frac{4 x}{3 \sqrt{\sin ^{-1}(a x)}}",1,"((-2*I)*E^(I*ArcSin[a*x])*(-I + 2*ArcSin[a*x]) - 4*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-I)*ArcSin[a*x]])/(6*a*ArcSin[a*x]^(3/2)) + (-2 + (4*I)*ArcSin[a*x] - 4*E^(I*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, I*ArcSin[a*x]])/(6*a*E^(I*ArcSin[a*x])*ArcSin[a*x]^(3/2))","C",0
112,0,0,15,0.5202049,"\int \frac{1}{x \sin ^{-1}(a x)^{5/2}} \, dx","Integrate[1/(x*ArcSin[a*x]^(5/2)),x]","\int \frac{1}{x \sin ^{-1}(a x)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)^{5/2}},x\right)",0,"Integrate[1/(x*ArcSin[a*x]^(5/2)), x]","A",-1
113,1,417,264,0.7414887,"\int \frac{x^4}{\sin ^{-1}(a x)^{7/2}} \, dx","Integrate[x^4/ArcSin[a*x]^(7/2),x]","\frac{9 e^{3 i \sin ^{-1}(a x)} \left(-12 \sin ^{-1}(a x)^2+2 i \sin ^{-1}(a x)+1\right)+2 e^{i \sin ^{-1}(a x)} \left(4 \sin ^{-1}(a x)^2-2 i \sin ^{-1}(a x)-3\right)+e^{5 i \sin ^{-1}(a x)} \left(100 \sin ^{-1}(a x)^2-10 i \sin ^{-1}(a x)-3\right)-8 \sqrt{-i \sin ^{-1}(a x)} \sin ^{-1}(a x)^2 \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)+108 \sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \sin ^{-1}(a x)^2 \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)-100 \sqrt{5} \sqrt{-i \sin ^{-1}(a x)} \sin ^{-1}(a x)^2 \Gamma \left(\frac{1}{2},-5 i \sin ^{-1}(a x)\right)+e^{-i \sin ^{-1}(a x)} \left(8 \sin ^{-1}(a x)^2+4 i \sin ^{-1}(a x)+8 e^{i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)-6\right)-9 e^{-3 i \sin ^{-1}(a x)} \left(12 \sin ^{-1}(a x)^2+2 i \sin ^{-1}(a x)+12 \sqrt{3} e^{3 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)-1\right)+e^{-5 i \sin ^{-1}(a x)} \left(100 \sin ^{-1}(a x)^2+10 i \sin ^{-1}(a x)+100 \sqrt{5} e^{5 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},5 i \sin ^{-1}(a x)\right)-3\right)}{240 a^5 \sin ^{-1}(a x)^{5/2}}","\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{15 a^5}+\frac{8 \sqrt{6 \pi } S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{5 a^5}-\frac{5 \sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^5}+\frac{5 \sqrt{\frac{5 \pi }{2}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^5}-\frac{16 x^3}{15 a^2 \sin ^{-1}(a x)^{3/2}}+\frac{40 x^4 \sqrt{1-a^2 x^2}}{3 a \sqrt{\sin ^{-1}(a x)}}-\frac{2 x^4 \sqrt{1-a^2 x^2}}{5 a \sin ^{-1}(a x)^{5/2}}-\frac{32 x^2 \sqrt{1-a^2 x^2}}{5 a^3 \sqrt{\sin ^{-1}(a x)}}+\frac{4 x^5}{3 \sin ^{-1}(a x)^{3/2}}",1,"(9*E^((3*I)*ArcSin[a*x])*(1 + (2*I)*ArcSin[a*x] - 12*ArcSin[a*x]^2) + 2*E^(I*ArcSin[a*x])*(-3 - (2*I)*ArcSin[a*x] + 4*ArcSin[a*x]^2) + E^((5*I)*ArcSin[a*x])*(-3 - (10*I)*ArcSin[a*x] + 100*ArcSin[a*x]^2) - 8*Sqrt[(-I)*ArcSin[a*x]]*ArcSin[a*x]^2*Gamma[1/2, (-I)*ArcSin[a*x]] + (-6 + (4*I)*ArcSin[a*x] + 8*ArcSin[a*x]^2 + 8*E^(I*ArcSin[a*x])*(I*ArcSin[a*x])^(5/2)*Gamma[1/2, I*ArcSin[a*x]])/E^(I*ArcSin[a*x]) + 108*Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*ArcSin[a*x]^2*Gamma[1/2, (-3*I)*ArcSin[a*x]] - (9*(-1 + (2*I)*ArcSin[a*x] + 12*ArcSin[a*x]^2 + 12*Sqrt[3]*E^((3*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(5/2)*Gamma[1/2, (3*I)*ArcSin[a*x]]))/E^((3*I)*ArcSin[a*x]) - 100*Sqrt[5]*Sqrt[(-I)*ArcSin[a*x]]*ArcSin[a*x]^2*Gamma[1/2, (-5*I)*ArcSin[a*x]] + (-3 + (10*I)*ArcSin[a*x] + 100*ArcSin[a*x]^2 + 100*Sqrt[5]*E^((5*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(5/2)*Gamma[1/2, (5*I)*ArcSin[a*x]])/E^((5*I)*ArcSin[a*x]))/(240*a^5*ArcSin[a*x]^(5/2))","C",0
114,1,272,190,1.107145,"\int \frac{x^3}{\sin ^{-1}(a x)^{7/2}} \, dx","Integrate[x^3/ArcSin[a*x]^(7/2),x]","\frac{-6 \sin \left(2 \sin ^{-1}(a x)\right)+3 \sin \left(4 \sin ^{-1}(a x)\right)+4 \sin ^{-1}(a x) \left(i e^{2 i \sin ^{-1}(a x)} \left(-4 \sin ^{-1}(a x)+i\right)-4 \sqrt{2} \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)+e^{-2 i \sin ^{-1}(a x)} \left(4 i \sin ^{-1}(a x)-4 \sqrt{2} e^{2 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)-1\right)\right)-4 \sin ^{-1}(a x) \left(i e^{4 i \sin ^{-1}(a x)} \left(-8 \sin ^{-1}(a x)+i\right)-16 \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-4 i \sin ^{-1}(a x)\right)+e^{-4 i \sin ^{-1}(a x)} \left(8 i \sin ^{-1}(a x)-16 e^{4 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},4 i \sin ^{-1}(a x)\right)-1\right)\right)}{60 a^4 \sin ^{-1}(a x)^{5/2}}","\frac{32 \sqrt{2 \pi } C\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{15 a^4}-\frac{16 \sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^4}-\frac{4 x^2}{5 a^2 \sin ^{-1}(a x)^{3/2}}+\frac{128 x^3 \sqrt{1-a^2 x^2}}{15 a \sqrt{\sin ^{-1}(a x)}}-\frac{2 x^3 \sqrt{1-a^2 x^2}}{5 a \sin ^{-1}(a x)^{5/2}}-\frac{16 x \sqrt{1-a^2 x^2}}{5 a^3 \sqrt{\sin ^{-1}(a x)}}+\frac{16 x^4}{15 \sin ^{-1}(a x)^{3/2}}",1,"(4*ArcSin[a*x]*(I*E^((2*I)*ArcSin[a*x])*(I - 4*ArcSin[a*x]) - 4*Sqrt[2]*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-2*I)*ArcSin[a*x]] + (-1 + (4*I)*ArcSin[a*x] - 4*Sqrt[2]*E^((2*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, (2*I)*ArcSin[a*x]])/E^((2*I)*ArcSin[a*x])) - 4*ArcSin[a*x]*(I*E^((4*I)*ArcSin[a*x])*(I - 8*ArcSin[a*x]) - 16*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-4*I)*ArcSin[a*x]] + (-1 + (8*I)*ArcSin[a*x] - 16*E^((4*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, (4*I)*ArcSin[a*x]])/E^((4*I)*ArcSin[a*x])) - 6*Sin[2*ArcSin[a*x]] + 3*Sin[4*ArcSin[a*x]])/(60*a^4*ArcSin[a*x]^(5/2))","C",0
115,1,280,191,0.3444657,"\int \frac{x^2}{\sin ^{-1}(a x)^{7/2}} \, dx","Integrate[x^2/ArcSin[a*x]^(7/2),x]","\frac{3 e^{3 i \sin ^{-1}(a x)} \left(-12 \sin ^{-1}(a x)^2+2 i \sin ^{-1}(a x)+1\right)+e^{i \sin ^{-1}(a x)} \left(4 \sin ^{-1}(a x)^2-2 i \sin ^{-1}(a x)-3\right)-4 \sqrt{-i \sin ^{-1}(a x)} \sin ^{-1}(a x)^2 \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)+36 \sqrt{3} \sqrt{-i \sin ^{-1}(a x)} \sin ^{-1}(a x)^2 \Gamma \left(\frac{1}{2},-3 i \sin ^{-1}(a x)\right)+e^{-i \sin ^{-1}(a x)} \left(4 \sin ^{-1}(a x)^2+2 i \sin ^{-1}(a x)+4 e^{i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)-3\right)-3 e^{-3 i \sin ^{-1}(a x)} \left(12 \sin ^{-1}(a x)^2+2 i \sin ^{-1}(a x)+12 \sqrt{3} e^{3 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},3 i \sin ^{-1}(a x)\right)-1\right)}{60 a^3 \sin ^{-1}(a x)^{5/2}}","\frac{2 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{15 a^3}-\frac{6 \sqrt{6 \pi } S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{5 a^3}+\frac{24 x^2 \sqrt{1-a^2 x^2}}{5 a \sqrt{\sin ^{-1}(a x)}}-\frac{2 x^2 \sqrt{1-a^2 x^2}}{5 a \sin ^{-1}(a x)^{5/2}}-\frac{8 x}{15 a^2 \sin ^{-1}(a x)^{3/2}}-\frac{16 \sqrt{1-a^2 x^2}}{15 a^3 \sqrt{\sin ^{-1}(a x)}}+\frac{4 x^3}{5 \sin ^{-1}(a x)^{3/2}}",1,"(3*E^((3*I)*ArcSin[a*x])*(1 + (2*I)*ArcSin[a*x] - 12*ArcSin[a*x]^2) + E^(I*ArcSin[a*x])*(-3 - (2*I)*ArcSin[a*x] + 4*ArcSin[a*x]^2) - 4*Sqrt[(-I)*ArcSin[a*x]]*ArcSin[a*x]^2*Gamma[1/2, (-I)*ArcSin[a*x]] + (-3 + (2*I)*ArcSin[a*x] + 4*ArcSin[a*x]^2 + 4*E^(I*ArcSin[a*x])*(I*ArcSin[a*x])^(5/2)*Gamma[1/2, I*ArcSin[a*x]])/E^(I*ArcSin[a*x]) + 36*Sqrt[3]*Sqrt[(-I)*ArcSin[a*x]]*ArcSin[a*x]^2*Gamma[1/2, (-3*I)*ArcSin[a*x]] - (3*(-1 + (2*I)*ArcSin[a*x] + 12*ArcSin[a*x]^2 + 12*Sqrt[3]*E^((3*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(5/2)*Gamma[1/2, (3*I)*ArcSin[a*x]]))/E^((3*I)*ArcSin[a*x]))/(60*a^3*ArcSin[a*x]^(5/2))","C",0
116,1,146,119,0.3682445,"\int \frac{x}{\sin ^{-1}(a x)^{7/2}} \, dx","Integrate[x/ArcSin[a*x]^(7/2),x]","-\frac{3 \sin \left(2 \sin ^{-1}(a x)\right)+\sin ^{-1}(a x) \left(2 e^{2 i \sin ^{-1}(a x)} \left(1+4 i \sin ^{-1}(a x)\right)+8 \sqrt{2} \left(-i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-2 i \sin ^{-1}(a x)\right)+e^{-2 i \sin ^{-1}(a x)} \left(-8 i \sin ^{-1}(a x)+8 \sqrt{2} e^{2 i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},2 i \sin ^{-1}(a x)\right)+2\right)\right)}{15 a^2 \sin ^{-1}(a x)^{5/2}}","-\frac{32 \sqrt{\pi } C\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^2}+\frac{32 x \sqrt{1-a^2 x^2}}{15 a \sqrt{\sin ^{-1}(a x)}}-\frac{2 x \sqrt{1-a^2 x^2}}{5 a \sin ^{-1}(a x)^{5/2}}-\frac{4}{15 a^2 \sin ^{-1}(a x)^{3/2}}+\frac{8 x^2}{15 \sin ^{-1}(a x)^{3/2}}",1,"-1/15*(ArcSin[a*x]*(2*E^((2*I)*ArcSin[a*x])*(1 + (4*I)*ArcSin[a*x]) + 8*Sqrt[2]*((-I)*ArcSin[a*x])^(3/2)*Gamma[1/2, (-2*I)*ArcSin[a*x]] + (2 - (8*I)*ArcSin[a*x] + 8*Sqrt[2]*E^((2*I)*ArcSin[a*x])*(I*ArcSin[a*x])^(3/2)*Gamma[1/2, (2*I)*ArcSin[a*x]])/E^((2*I)*ArcSin[a*x])) + 3*Sin[2*ArcSin[a*x]])/(a^2*ArcSin[a*x]^(5/2))","C",0
117,1,143,105,0.2420261,"\int \frac{1}{\sin ^{-1}(a x)^{7/2}} \, dx","Integrate[ArcSin[a*x]^(-7/2),x]","\frac{2 e^{i \sin ^{-1}(a x)} \left(4 \sin ^{-1}(a x)^2-2 i \sin ^{-1}(a x)-3\right)-8 \sqrt{-i \sin ^{-1}(a x)} \sin ^{-1}(a x)^2 \Gamma \left(\frac{1}{2},-i \sin ^{-1}(a x)\right)+e^{-i \sin ^{-1}(a x)} \left(8 \sin ^{-1}(a x)^2+4 i \sin ^{-1}(a x)+8 e^{i \sin ^{-1}(a x)} \left(i \sin ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},i \sin ^{-1}(a x)\right)-6\right)}{30 a \sin ^{-1}(a x)^{5/2}}","\frac{8 \sqrt{1-a^2 x^2}}{15 a \sqrt{\sin ^{-1}(a x)}}-\frac{2 \sqrt{1-a^2 x^2}}{5 a \sin ^{-1}(a x)^{5/2}}+\frac{8 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{15 a}+\frac{4 x}{15 \sin ^{-1}(a x)^{3/2}}",1,"(2*E^(I*ArcSin[a*x])*(-3 - (2*I)*ArcSin[a*x] + 4*ArcSin[a*x]^2) - 8*Sqrt[(-I)*ArcSin[a*x]]*ArcSin[a*x]^2*Gamma[1/2, (-I)*ArcSin[a*x]] + (-6 + (4*I)*ArcSin[a*x] + 8*ArcSin[a*x]^2 + 8*E^(I*ArcSin[a*x])*(I*ArcSin[a*x])^(5/2)*Gamma[1/2, I*ArcSin[a*x]])/E^(I*ArcSin[a*x]))/(30*a*ArcSin[a*x]^(5/2))","C",0
118,0,0,15,0.469474,"\int \frac{1}{x \sin ^{-1}(a x)^{7/2}} \, dx","Integrate[1/(x*ArcSin[a*x]^(7/2)),x]","\int \frac{1}{x \sin ^{-1}(a x)^{7/2}} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a x)^{7/2}},x\right)",0,"Integrate[1/(x*ArcSin[a*x]^(7/2)), x]","A",-1
119,0,0,65,1.0625227,"\int (b x)^m \sin ^{-1}(a x)^4 \, dx","Integrate[(b*x)^m*ArcSin[a*x]^4,x]","\int (b x)^m \sin ^{-1}(a x)^4 \, dx","\frac{\sin ^{-1}(a x)^4 (b x)^{m+1}}{b (m+1)}-\frac{4 a \text{Int}\left(\frac{\sin ^{-1}(a x)^3 (b x)^{m+1}}{\sqrt{1-a^2 x^2}},x\right)}{b (m+1)}",0,"Integrate[(b*x)^m*ArcSin[a*x]^4, x]","A",-1
120,0,0,65,0.9765426,"\int (b x)^m \sin ^{-1}(a x)^3 \, dx","Integrate[(b*x)^m*ArcSin[a*x]^3,x]","\int (b x)^m \sin ^{-1}(a x)^3 \, dx","\frac{\sin ^{-1}(a x)^3 (b x)^{m+1}}{b (m+1)}-\frac{3 a \text{Int}\left(\frac{\sin ^{-1}(a x)^2 (b x)^{m+1}}{\sqrt{1-a^2 x^2}},x\right)}{b (m+1)}",0,"Integrate[(b*x)^m*ArcSin[a*x]^3, x]","A",-1
121,1,122,150,0.0390084,"\int (b x)^m \sin ^{-1}(a x)^2 \, dx","Integrate[(b*x)^m*ArcSin[a*x]^2,x]","\frac{x (b x)^m \left(2 a^2 x^2 \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};a^2 x^2\right)+(m+3) \sin ^{-1}(a x) \left((m+2) \sin ^{-1}(a x)-2 a x \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)\right)\right)}{(m+1) (m+2) (m+3)}","\frac{2 a^2 (b x)^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};a^2 x^2\right)}{b^3 (m+1) (m+2) (m+3)}-\frac{2 a \sin ^{-1}(a x) (b x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{b^2 (m+1) (m+2)}+\frac{\sin ^{-1}(a x)^2 (b x)^{m+1}}{b (m+1)}",1,"(x*(b*x)^m*((3 + m)*ArcSin[a*x]*((2 + m)*ArcSin[a*x] - 2*a*x*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2]) + 2*a^2*x^2*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, a^2*x^2]))/((1 + m)*(2 + m)*(3 + m))","A",1
122,1,56,69,0.0186629,"\int (b x)^m \sin ^{-1}(a x) \, dx","Integrate[(b*x)^m*ArcSin[a*x],x]","-\frac{x (b x)^m \left(a x \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)-(m+2) \sin ^{-1}(a x)\right)}{(m+1) (m+2)}","\frac{\sin ^{-1}(a x) (b x)^{m+1}}{b (m+1)}-\frac{a (b x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{b^2 (m+1) (m+2)}",1,"-((x*(b*x)^m*(-((2 + m)*ArcSin[a*x]) + a*x*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2]))/((1 + m)*(2 + m)))","A",1
123,0,0,15,0.5582407,"\int \frac{(b x)^m}{\sin ^{-1}(a x)} \, dx","Integrate[(b*x)^m/ArcSin[a*x],x]","\int \frac{(b x)^m}{\sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{(b x)^m}{\sin ^{-1}(a x)},x\right)",0,"Integrate[(b*x)^m/ArcSin[a*x], x]","A",-1
124,0,0,15,0.585089,"\int \frac{(b x)^m}{\sin ^{-1}(a x)^2} \, dx","Integrate[(b*x)^m/ArcSin[a*x]^2,x]","\int \frac{(b x)^m}{\sin ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{(b x)^m}{\sin ^{-1}(a x)^2},x\right)",0,"Integrate[(b*x)^m/ArcSin[a*x]^2, x]","A",-1
125,0,0,17,2.6929226,"\int (b x)^m \sin ^{-1}(a x)^{3/2} \, dx","Integrate[(b*x)^m*ArcSin[a*x]^(3/2),x]","\int (b x)^m \sin ^{-1}(a x)^{3/2} \, dx","\text{Int}\left(\sin ^{-1}(a x)^{3/2} (b x)^m,x\right)",0,"Integrate[(b*x)^m*ArcSin[a*x]^(3/2), x]","A",-1
126,0,0,17,2.9748684,"\int (b x)^m \sqrt{\sin ^{-1}(a x)} \, dx","Integrate[(b*x)^m*Sqrt[ArcSin[a*x]],x]","\int (b x)^m \sqrt{\sin ^{-1}(a x)} \, dx","\text{Int}\left(\sqrt{\sin ^{-1}(a x)} (b x)^m,x\right)",0,"Integrate[(b*x)^m*Sqrt[ArcSin[a*x]], x]","A",-1
127,0,0,17,2.2517723,"\int \frac{(b x)^m}{\sqrt{\sin ^{-1}(a x)}} \, dx","Integrate[(b*x)^m/Sqrt[ArcSin[a*x]],x]","\int \frac{(b x)^m}{\sqrt{\sin ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{(b x)^m}{\sqrt{\sin ^{-1}(a x)}},x\right)",0,"Integrate[(b*x)^m/Sqrt[ArcSin[a*x]], x]","A",-1
128,0,0,17,2.2787234,"\int \frac{(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx","Integrate[(b*x)^m/ArcSin[a*x]^(3/2),x]","\int \frac{(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{(b x)^m}{\sin ^{-1}(a x)^{3/2}},x\right)",0,"Integrate[(b*x)^m/ArcSin[a*x]^(3/2), x]","A",-1
129,0,0,15,0.8500796,"\int (b x)^m \sin ^{-1}(a x)^n \, dx","Integrate[(b*x)^m*ArcSin[a*x]^n,x]","\int (b x)^m \sin ^{-1}(a x)^n \, dx","\text{Int}\left((b x)^m \sin ^{-1}(a x)^n,x\right)",0,"Integrate[(b*x)^m*ArcSin[a*x]^n, x]","A",-1
130,1,132,167,0.0999092,"\int x^3 \sin ^{-1}(a x)^n \, dx","Integrate[x^3*ArcSin[a*x]^n,x]","\frac{4^{-n-3} \sin ^{-1}(a x)^n \left(\sin ^{-1}(a x)^2\right)^{-n} \left(-2^{n+2} \left(-i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,2 i \sin ^{-1}(a x)\right)+\left(-i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,4 i \sin ^{-1}(a x)\right)-2^{n+2} \left(i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,-2 i \sin ^{-1}(a x)\right)+\left(i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,-4 i \sin ^{-1}(a x)\right)\right)}{a^4}","-\frac{2^{-n-4} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-2 i \sin ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-4 i \sin ^{-1}(a x)\right)}{a^4}-\frac{2^{-n-4} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,2 i \sin ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,4 i \sin ^{-1}(a x)\right)}{a^4}",1,"(4^(-3 - n)*ArcSin[a*x]^n*(-(2^(2 + n)*(I*ArcSin[a*x])^n*Gamma[1 + n, (-2*I)*ArcSin[a*x]]) - 2^(2 + n)*((-I)*ArcSin[a*x])^n*Gamma[1 + n, (2*I)*ArcSin[a*x]] + (I*ArcSin[a*x])^n*Gamma[1 + n, (-4*I)*ArcSin[a*x]] + ((-I)*ArcSin[a*x])^n*Gamma[1 + n, (4*I)*ArcSin[a*x]]))/(a^4*(ArcSin[a*x]^2)^n)","A",1
131,1,137,171,0.0735331,"\int x^2 \sin ^{-1}(a x)^n \, dx","Integrate[x^2*ArcSin[a*x]^n,x]","\frac{i 3^{-n-1} \sin ^{-1}(a x)^n \left(\sin ^{-1}(a x)^2\right)^{-n} \left(3^{n+1} \left(-i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,i \sin ^{-1}(a x)\right)-\left(-i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,3 i \sin ^{-1}(a x)\right)-3^{n+1} \left(i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,-i \sin ^{-1}(a x)\right)+\left(i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,-3 i \sin ^{-1}(a x)\right)\right)}{8 a^3}","-\frac{i \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-i \sin ^{-1}(a x)\right)}{8 a^3}+\frac{i 3^{-n-1} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-3 i \sin ^{-1}(a x)\right)}{8 a^3}+\frac{i \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,i \sin ^{-1}(a x)\right)}{8 a^3}-\frac{i 3^{-n-1} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,3 i \sin ^{-1}(a x)\right)}{8 a^3}",1,"((I/8)*3^(-1 - n)*ArcSin[a*x]^n*(-(3^(1 + n)*(I*ArcSin[a*x])^n*Gamma[1 + n, (-I)*ArcSin[a*x]]) + 3^(1 + n)*((-I)*ArcSin[a*x])^n*Gamma[1 + n, I*ArcSin[a*x]] + (I*ArcSin[a*x])^n*Gamma[1 + n, (-3*I)*ArcSin[a*x]] - ((-I)*ArcSin[a*x])^n*Gamma[1 + n, (3*I)*ArcSin[a*x]]))/(a^3*(ArcSin[a*x]^2)^n)","A",1
132,1,75,85,0.0197529,"\int x \sin ^{-1}(a x)^n \, dx","Integrate[x*ArcSin[a*x]^n,x]","-\frac{2^{-n-3} \sin ^{-1}(a x)^n \left(\sin ^{-1}(a x)^2\right)^{-n} \left(\left(-i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,2 i \sin ^{-1}(a x)\right)+\left(i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,-2 i \sin ^{-1}(a x)\right)\right)}{a^2}","-\frac{2^{-n-3} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-2 i \sin ^{-1}(a x)\right)}{a^2}-\frac{2^{-n-3} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,2 i \sin ^{-1}(a x)\right)}{a^2}",1,"-((2^(-3 - n)*ArcSin[a*x]^n*((I*ArcSin[a*x])^n*Gamma[1 + n, (-2*I)*ArcSin[a*x]] + ((-I)*ArcSin[a*x])^n*Gamma[1 + n, (2*I)*ArcSin[a*x]]))/(a^2*(ArcSin[a*x]^2)^n))","A",1
133,1,73,79,0.0363472,"\int \sin ^{-1}(a x)^n \, dx","Integrate[ArcSin[a*x]^n,x]","\frac{i \sin ^{-1}(a x)^n \left(\sin ^{-1}(a x)^2\right)^{-n} \left(\left(-i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,i \sin ^{-1}(a x)\right)-\left(i \sin ^{-1}(a x)\right)^n \Gamma \left(n+1,-i \sin ^{-1}(a x)\right)\right)}{2 a}","\frac{i \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,i \sin ^{-1}(a x)\right)}{2 a}-\frac{i \left(-i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \Gamma \left(n+1,-i \sin ^{-1}(a x)\right)}{2 a}",1,"((I/2)*ArcSin[a*x]^n*(-((I*ArcSin[a*x])^n*Gamma[1 + n, (-I)*ArcSin[a*x]]) + ((-I)*ArcSin[a*x])^n*Gamma[1 + n, I*ArcSin[a*x]]))/(a*(ArcSin[a*x]^2)^n)","A",1
134,0,0,13,0.3084132,"\int \frac{\sin ^{-1}(a x)^n}{x} \, dx","Integrate[ArcSin[a*x]^n/x,x]","\int \frac{\sin ^{-1}(a x)^n}{x} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^n}{x},x\right)",0,"Integrate[ArcSin[a*x]^n/x, x]","A",-1
135,0,0,13,0.6734284,"\int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx","Integrate[ArcSin[a*x]^n/x^2,x]","\int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^n}{x^2},x\right)",0,"Integrate[ArcSin[a*x]^n/x^2, x]","A",-1
136,0,0,17,3.5800443,"\int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx","Integrate[(b*x)^(3/2)*ArcSin[a*x]^n,x]","\int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx","\text{Int}\left((b x)^{3/2} \sin ^{-1}(a x)^n,x\right)",0,"Integrate[(b*x)^(3/2)*ArcSin[a*x]^n, x]","A",-1
137,0,0,17,4.2824055,"\int \sqrt{b x} \sin ^{-1}(a x)^n \, dx","Integrate[Sqrt[b*x]*ArcSin[a*x]^n,x]","\int \sqrt{b x} \sin ^{-1}(a x)^n \, dx","\text{Int}\left(\sqrt{b x} \sin ^{-1}(a x)^n,x\right)",0,"Integrate[Sqrt[b*x]*ArcSin[a*x]^n, x]","A",-1
138,0,0,17,1.5992348,"\int \frac{\sin ^{-1}(a x)^n}{\sqrt{b x}} \, dx","Integrate[ArcSin[a*x]^n/Sqrt[b*x],x]","\int \frac{\sin ^{-1}(a x)^n}{\sqrt{b x}} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^n}{\sqrt{b x}},x\right)",0,"Integrate[ArcSin[a*x]^n/Sqrt[b*x], x]","A",-1
139,0,0,17,1.9272314,"\int \frac{\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx","Integrate[ArcSin[a*x]^n/(b*x)^(3/2),x]","\int \frac{\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^n}{(b x)^{3/2}},x\right)",0,"Integrate[ArcSin[a*x]^n/(b*x)^(3/2), x]","A",-1
140,1,81,76,0.0304059,"\int x^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[x^3*(a + b*ArcSin[c*x]),x]","\frac{a x^4}{4}-\frac{3 b \sin ^{-1}(c x)}{32 c^4}+\frac{b x^3 \sqrt{1-c^2 x^2}}{16 c}+\frac{3 b x \sqrt{1-c^2 x^2}}{32 c^3}+\frac{1}{4} b x^4 \sin ^{-1}(c x)","\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right)-\frac{3 b \sin ^{-1}(c x)}{32 c^4}+\frac{b x^3 \sqrt{1-c^2 x^2}}{16 c}+\frac{3 b x \sqrt{1-c^2 x^2}}{32 c^3}",1,"(a*x^4)/4 + (3*b*x*Sqrt[1 - c^2*x^2])/(32*c^3) + (b*x^3*Sqrt[1 - c^2*x^2])/(16*c) - (3*b*ArcSin[c*x])/(32*c^4) + (b*x^4*ArcSin[c*x])/4","A",1
141,1,49,60,0.0410054,"\int x^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[x^2*(a + b*ArcSin[c*x]),x]","\frac{1}{9} \left(3 a x^3+\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+2\right)}{c^3}+3 b x^3 \sin ^{-1}(c x)\right)","\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^3}+\frac{b \sqrt{1-c^2 x^2}}{3 c^3}",1,"(3*a*x^3 + (b*Sqrt[1 - c^2*x^2]*(2 + c^2*x^2))/c^3 + 3*b*x^3*ArcSin[c*x])/9","A",1
142,1,56,51,0.0200181,"\int x \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[x*(a + b*ArcSin[c*x]),x]","\frac{a x^2}{2}+\frac{b x \sqrt{1-c^2 x^2}}{4 c}-\frac{b \sin ^{-1}(c x)}{4 c^2}+\frac{1}{2} b x^2 \sin ^{-1}(c x)","\frac{1}{2} x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x \sqrt{1-c^2 x^2}}{4 c}-\frac{b \sin ^{-1}(c x)}{4 c^2}",1,"(a*x^2)/2 + (b*x*Sqrt[1 - c^2*x^2])/(4*c) - (b*ArcSin[c*x])/(4*c^2) + (b*x^2*ArcSin[c*x])/2","A",1
143,1,30,30,0.0140001,"\int \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[a + b*ArcSin[c*x],x]","a x+\frac{b \sqrt{1-c^2 x^2}}{c}+b x \sin ^{-1}(c x)","a x+\frac{b \sqrt{1-c^2 x^2}}{c}+b x \sin ^{-1}(c x)",1,"a*x + (b*Sqrt[1 - c^2*x^2])/c + b*x*ArcSin[c*x]","A",1
144,1,52,63,0.0321167,"\int \frac{a+b \sin ^{-1}(c x)}{x} \, dx","Integrate[(a + b*ArcSin[c*x])/x,x]","a \log (x)-\frac{1}{2} i b \left(\sin ^{-1}(c x)^2+\text{Li}_2\left(e^{2 i \sin ^{-1}(c x)}\right)\right)+b \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)","-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{2} i b \text{Li}_2\left(e^{2 i \sin ^{-1}(c x)}\right)",1,"b*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] + a*Log[x] - (I/2)*b*(ArcSin[c*x]^2 + PolyLog[2, E^((2*I)*ArcSin[c*x])])","A",0
145,1,36,33,0.0031045,"\int \frac{a+b \sin ^{-1}(c x)}{x^2} \, dx","Integrate[(a + b*ArcSin[c*x])/x^2,x]","-\frac{a}{x}-b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b \sin ^{-1}(c x)}{x}","-\frac{a+b \sin ^{-1}(c x)}{x}-b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"-(a/x) - (b*ArcSin[c*x])/x - b*c*ArcTanh[Sqrt[1 - c^2*x^2]]","A",1
146,1,44,39,0.0122017,"\int \frac{a+b \sin ^{-1}(c x)}{x^3} \, dx","Integrate[(a + b*ArcSin[c*x])/x^3,x]","-\frac{a}{2 x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 x}-\frac{b \sin ^{-1}(c x)}{2 x^2}","-\frac{a+b \sin ^{-1}(c x)}{2 x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 x}",1,"-1/2*a/x^2 - (b*c*Sqrt[1 - c^2*x^2])/(2*x) - (b*ArcSin[c*x])/(2*x^2)","A",1
147,1,67,62,0.0182204,"\int \frac{a+b \sin ^{-1}(c x)}{x^4} \, dx","Integrate[(a + b*ArcSin[c*x])/x^4,x]","-\frac{a}{3 x^3}-\frac{b c \sqrt{1-c^2 x^2}}{6 x^2}-\frac{1}{6} b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b \sin ^{-1}(c x)}{3 x^3}","-\frac{a+b \sin ^{-1}(c x)}{3 x^3}-\frac{b c \sqrt{1-c^2 x^2}}{6 x^2}-\frac{1}{6} b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"-1/3*a/x^3 - (b*c*Sqrt[1 - c^2*x^2])/(6*x^2) - (b*ArcSin[c*x])/(3*x^3) - (b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",1
148,1,95,102,0.1775283,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Integrate[x^2*(a + b*ArcSin[c*x])^2,x]","\frac{1}{3} \left(x^3 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b \left(-3 c^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-6 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+b c^3 x^3+6 b c x\right)}{9 c^3}\right)","\frac{2 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 x}{9 c^2}-\frac{2}{27} b^2 x^3",1,"(x^3*(a + b*ArcSin[c*x])^2 - (2*b*(6*b*c*x + b*c^3*x^3 - 6*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]) - 3*c^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])))/(9*c^3))/3","A",1
149,1,73,76,0.0751889,"\int x \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Integrate[x*(a + b*ArcSin[c*x])^2,x]","-\frac{-2 c^2 x^2 \left(a+b \sin ^{-1}(c x)\right)^2-2 b c x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\left(a+b \sin ^{-1}(c x)\right)^2+b^2 c^2 x^2}{4 c^2}","\frac{b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{4} b^2 x^2",1,"-1/4*(b^2*c^2*x^2 - 2*b*c*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]) + (a + b*ArcSin[c*x])^2 - 2*c^2*x^2*(a + b*ArcSin[c*x])^2)/c^2","A",1
150,1,47,47,0.0442296,"\int \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Integrate[(a + b*ArcSin[c*x])^2,x]","\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+x \left(a+b \sin ^{-1}(c x)\right)^2-2 b^2 x","\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+x \left(a+b \sin ^{-1}(c x)\right)^2-2 b^2 x",1,"-2*b^2*x + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + x*(a + b*ArcSin[c*x])^2","A",1
151,1,143,90,0.1519364,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Integrate[(a + b*ArcSin[c*x])^2/x,x]","a^2 \log (c x)+2 a b \left(\sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{2} i \left(\sin ^{-1}(c x)^2+\text{Li}_2\left(e^{2 i \sin ^{-1}(c x)}\right)\right)\right)+b^2 \left(i \sin ^{-1}(c x) \text{Li}_2\left(e^{-2 i \sin ^{-1}(c x)}\right)+\frac{1}{2} \text{Li}_3\left(e^{-2 i \sin ^{-1}(c x)}\right)+\frac{1}{3} i \sin ^{-1}(c x)^3+\sin ^{-1}(c x)^2 \log \left(1-e^{-2 i \sin ^{-1}(c x)}\right)-\frac{i \pi ^3}{24}\right)","-i b \text{Li}_2\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}+\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{2} b^2 \text{Li}_3\left(e^{2 i \sin ^{-1}(c x)}\right)",1,"a^2*Log[c*x] + 2*a*b*(ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - (I/2)*(ArcSin[c*x]^2 + PolyLog[2, E^((2*I)*ArcSin[c*x])])) + b^2*((-1/24*I)*Pi^3 + (I/3)*ArcSin[c*x]^3 + ArcSin[c*x]^2*Log[1 - E^((-2*I)*ArcSin[c*x])] + I*ArcSin[c*x]*PolyLog[2, E^((-2*I)*ArcSin[c*x])] + PolyLog[3, E^((-2*I)*ArcSin[c*x])]/2)","A",0
152,1,126,81,0.2253074,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Integrate[(a + b*ArcSin[c*x])^2/x^2,x]","-\frac{a^2+2 a b \left(c x \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\sin ^{-1}(c x)\right)-i b^2 \left(2 c x \text{Li}_2\left(-e^{i \sin ^{-1}(c x)}\right)-2 c x \text{Li}_2\left(e^{i \sin ^{-1}(c x)}\right)+i \sin ^{-1}(c x) \left(\sin ^{-1}(c x)+2 c x \left(\log \left(1+e^{i \sin ^{-1}(c x)}\right)-\log \left(1-e^{i \sin ^{-1}(c x)}\right)\right)\right)\right)}{x}","-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x}-4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+2 i b^2 c \text{Li}_2\left(-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c \text{Li}_2\left(e^{i \sin ^{-1}(c x)}\right)",1,"-((a^2 + 2*a*b*(ArcSin[c*x] + c*x*ArcTanh[Sqrt[1 - c^2*x^2]]) - I*b^2*(I*ArcSin[c*x]*(ArcSin[c*x] + 2*c*x*(-Log[1 - E^(I*ArcSin[c*x])] + Log[1 + E^(I*ArcSin[c*x])])) + 2*c*x*PolyLog[2, -E^(I*ArcSin[c*x])] - 2*c*x*PolyLog[2, E^(I*ArcSin[c*x])]))/x)","A",0
153,1,163,178,0.3814506,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Integrate[x^2*(a + b*ArcSin[c*x])^3,x]","\frac{1}{27} \left(\frac{b \left(9 c^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2+18 \left(\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2-2 b \left(a c x+b \sqrt{1-c^2 x^2}+b c x \sin ^{-1}(c x)\right)\right)-2 b \left(3 c^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+b \sqrt{1-c^2 x^2} \left(c^2 x^2+2\right)\right)\right)}{c^3}+9 x^3 \left(a+b \sin ^{-1}(c x)\right)^3\right)","-\frac{4 a b^2 x}{3 c^2}-\frac{2}{9} b^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^3}+\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)^3-\frac{4 b^3 x \sin ^{-1}(c x)}{3 c^2}+\frac{2 b^3 \left(1-c^2 x^2\right)^{3/2}}{27 c^3}-\frac{14 b^3 \sqrt{1-c^2 x^2}}{9 c^3}",1,"(9*x^3*(a + b*ArcSin[c*x])^3 + (b*(9*c^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2 - 2*b*(b*Sqrt[1 - c^2*x^2]*(2 + c^2*x^2) + 3*c^3*x^3*(a + b*ArcSin[c*x])) + 18*(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2 - 2*b*(a*c*x + b*Sqrt[1 - c^2*x^2] + b*c*x*ArcSin[c*x]))))/c^3)/27","A",1
154,1,114,125,0.140435,"\int x \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Integrate[x*(a + b*ArcSin[c*x])^3,x]","\frac{-3 b^2 \left(c x \left(2 a c x+b \sqrt{1-c^2 x^2}\right)+b \left(2 c^2 x^2-1\right) \sin ^{-1}(c x)\right)+4 c^2 x^2 \left(a+b \sin ^{-1}(c x)\right)^3+6 b c x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2-2 \left(a+b \sin ^{-1}(c x)\right)^3}{8 c^2}","-\frac{3}{4} b^2 x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{3 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 c}-\frac{\left(a+b \sin ^{-1}(c x)\right)^3}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sin ^{-1}(c x)\right)^3-\frac{3 b^3 x \sqrt{1-c^2 x^2}}{8 c}+\frac{3 b^3 \sin ^{-1}(c x)}{8 c^2}",1,"(6*b*c*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2 - 2*(a + b*ArcSin[c*x])^3 + 4*c^2*x^2*(a + b*ArcSin[c*x])^3 - 3*b^2*(c*x*(2*a*c*x + b*Sqrt[1 - c^2*x^2]) + b*(-1 + 2*c^2*x^2)*ArcSin[c*x]))/(8*c^2)","A",1
155,1,77,82,0.0816917,"\int \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Integrate[(a + b*ArcSin[c*x])^3,x]","\frac{3 b \left(\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2-2 b \left(a c x+b \sqrt{1-c^2 x^2}+b c x \sin ^{-1}(c x)\right)\right)}{c}+x \left(a+b \sin ^{-1}(c x)\right)^3","-6 a b^2 x+\frac{3 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c}+x \left(a+b \sin ^{-1}(c x)\right)^3-\frac{6 b^3 \sqrt{1-c^2 x^2}}{c}-6 b^3 x \sin ^{-1}(c x)",1,"x*(a + b*ArcSin[c*x])^3 + (3*b*(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2 - 2*b*(a*c*x + b*Sqrt[1 - c^2*x^2] + b*c*x*ArcSin[c*x])))/c","A",1
156,1,244,123,0.2340628,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{x} \, dx","Integrate[(a + b*ArcSin[c*x])^3/x,x]","a^3 \log (c x)+3 a^2 b \left(\sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{2} i \left(\sin ^{-1}(c x)^2+\text{Li}_2\left(e^{2 i \sin ^{-1}(c x)}\right)\right)\right)+\frac{1}{8} a b^2 \left(24 i \sin ^{-1}(c x) \text{Li}_2\left(e^{-2 i \sin ^{-1}(c x)}\right)+12 \text{Li}_3\left(e^{-2 i \sin ^{-1}(c x)}\right)+8 i \sin ^{-1}(c x)^3+24 \sin ^{-1}(c x)^2 \log \left(1-e^{-2 i \sin ^{-1}(c x)}\right)-i \pi ^3\right)-\frac{1}{64} i b^3 \left(-96 \sin ^{-1}(c x)^2 \text{Li}_2\left(e^{-2 i \sin ^{-1}(c x)}\right)+96 i \sin ^{-1}(c x) \text{Li}_3\left(e^{-2 i \sin ^{-1}(c x)}\right)+48 \text{Li}_4\left(e^{-2 i \sin ^{-1}(c x)}\right)-16 \sin ^{-1}(c x)^4+64 i \sin ^{-1}(c x)^3 \log \left(1-e^{-2 i \sin ^{-1}(c x)}\right)+\pi ^4\right)","\frac{3}{2} b^2 \text{Li}_3\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} i b \text{Li}_2\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{i \left(a+b \sin ^{-1}(c x)\right)^4}{4 b}+\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^3+\frac{3}{4} i b^3 \text{Li}_4\left(e^{2 i \sin ^{-1}(c x)}\right)",1,"a^3*Log[c*x] + 3*a^2*b*(ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - (I/2)*(ArcSin[c*x]^2 + PolyLog[2, E^((2*I)*ArcSin[c*x])])) + (a*b^2*((-I)*Pi^3 + (8*I)*ArcSin[c*x]^3 + 24*ArcSin[c*x]^2*Log[1 - E^((-2*I)*ArcSin[c*x])] + (24*I)*ArcSin[c*x]*PolyLog[2, E^((-2*I)*ArcSin[c*x])] + 12*PolyLog[3, E^((-2*I)*ArcSin[c*x])]))/8 - (I/64)*b^3*(Pi^4 - 16*ArcSin[c*x]^4 + (64*I)*ArcSin[c*x]^3*Log[1 - E^((-2*I)*ArcSin[c*x])] - 96*ArcSin[c*x]^2*PolyLog[2, E^((-2*I)*ArcSin[c*x])] + (96*I)*ArcSin[c*x]*PolyLog[3, E^((-2*I)*ArcSin[c*x])] + 48*PolyLog[4, E^((-2*I)*ArcSin[c*x])])","A",0
157,1,283,137,0.3162494,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{x^2} \, dx","Integrate[(a + b*ArcSin[c*x])^3/x^2,x]","-\frac{a^3}{x}-3 a^2 b c \log \left(\sqrt{1-c^2 x^2}+1\right)+3 a^2 b c \log (x)-\frac{3 a^2 b \sin ^{-1}(c x)}{x}+3 a b^2 c \left(2 i \text{Li}_2\left(-e^{i \sin ^{-1}(c x)}\right)-2 i \text{Li}_2\left(e^{i \sin ^{-1}(c x)}\right)-\sin ^{-1}(c x) \left(\frac{\sin ^{-1}(c x)}{c x}-2 \log \left(1-e^{i \sin ^{-1}(c x)}\right)+2 \log \left(1+e^{i \sin ^{-1}(c x)}\right)\right)\right)+b^3 c \left(6 i \sin ^{-1}(c x) \text{Li}_2\left(-e^{i \sin ^{-1}(c x)}\right)-6 i \sin ^{-1}(c x) \text{Li}_2\left(e^{i \sin ^{-1}(c x)}\right)-6 \text{Li}_3\left(-e^{i \sin ^{-1}(c x)}\right)+6 \text{Li}_3\left(e^{i \sin ^{-1}(c x)}\right)-\frac{\sin ^{-1}(c x)^3}{c x}+3 \sin ^{-1}(c x)^2 \log \left(1-e^{i \sin ^{-1}(c x)}\right)-3 \sin ^{-1}(c x)^2 \log \left(1+e^{i \sin ^{-1}(c x)}\right)\right)","6 i b^2 c \text{Li}_2\left(-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-6 i b^2 c \text{Li}_2\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(a+b \sin ^{-1}(c x)\right)^3}{x}-6 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-6 b^3 c \text{Li}_3\left(-e^{i \sin ^{-1}(c x)}\right)+6 b^3 c \text{Li}_3\left(e^{i \sin ^{-1}(c x)}\right)",1,"-(a^3/x) - (3*a^2*b*ArcSin[c*x])/x + 3*a^2*b*c*Log[x] - 3*a^2*b*c*Log[1 + Sqrt[1 - c^2*x^2]] + 3*a*b^2*c*(-(ArcSin[c*x]*(ArcSin[c*x]/(c*x) - 2*Log[1 - E^(I*ArcSin[c*x])] + 2*Log[1 + E^(I*ArcSin[c*x])])) + (2*I)*PolyLog[2, -E^(I*ArcSin[c*x])] - (2*I)*PolyLog[2, E^(I*ArcSin[c*x])]) + b^3*c*(-(ArcSin[c*x]^3/(c*x)) + 3*ArcSin[c*x]^2*Log[1 - E^(I*ArcSin[c*x])] - 3*ArcSin[c*x]^2*Log[1 + E^(I*ArcSin[c*x])] + (6*I)*ArcSin[c*x]*PolyLog[2, -E^(I*ArcSin[c*x])] - (6*I)*ArcSin[c*x]*PolyLog[2, E^(I*ArcSin[c*x])] - 6*PolyLog[3, -E^(I*ArcSin[c*x])] + 6*PolyLog[3, E^(I*ArcSin[c*x])])","B",0
158,1,91,121,0.2014014,"\int \frac{x^2}{a+b \sin ^{-1}(c x)} \, dx","Integrate[x^2/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)-\cos \left(\frac{3 a}{b}\right) \text{Ci}\left(3 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)+\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)-\sin \left(\frac{3 a}{b}\right) \text{Si}\left(3 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)}{4 b c^3}","\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{\cos \left(\frac{3 a}{b}\right) \text{Ci}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{\sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^3}",1,"(Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]] - Cos[(3*a)/b]*CosIntegral[3*(a/b + ArcSin[c*x])] + Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]] - Sin[(3*a)/b]*SinIntegral[3*(a/b + ArcSin[c*x])])/(4*b*c^3)","A",1
159,1,56,63,0.0789262,"\int \frac{x}{a+b \sin ^{-1}(c x)} \, dx","Integrate[x/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)-\sin \left(\frac{2 a}{b}\right) \text{Ci}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c^2}","\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^2}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Ci}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^2}",1,"(-(CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b]) + Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^2)","A",1
160,1,44,53,0.073096,"\int \frac{1}{a+b \sin ^{-1}(c x)} \, dx","Integrate[(a + b*ArcSin[c*x])^(-1),x]","\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)+\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}","\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}",1,"(Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]] + Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b*c)","A",1
161,0,0,17,0.2513596,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","Integrate[1/(x*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Integrate[1/(x*(a + b*ArcSin[c*x])), x]","A",-1
162,0,0,17,2.1794414,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Integrate[1/(x^2*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*ArcSin[c*x])), x]","A",-1
163,1,125,156,0.5606448,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[x^2/(a + b*ArcSin[c*x])^2,x]","\frac{-\frac{4 b c^2 x^2 \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)}+\sin \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)-3 \sin \left(\frac{3 a}{b}\right) \text{Ci}\left(3 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)-\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)+3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(3 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)}{4 b^2 c^3}","\frac{\sin \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2 c^3}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Ci}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2 c^3}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{x^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"((-4*b*c^2*x^2*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]) + CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b] - 3*CosIntegral[3*(a/b + ArcSin[c*x])]*Sin[(3*a)/b] - Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]] + 3*Cos[(3*a)/b]*SinIntegral[3*(a/b + ArcSin[c*x])])/(4*b^2*c^3)","A",1
164,1,79,90,0.2944293,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[x/(a + b*ArcSin[c*x])^2,x]","\frac{-\frac{b c x \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)}+\cos \left(\frac{2 a}{b}\right) \text{Ci}\left(2 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)+\sin \left(\frac{2 a}{b}\right) \text{Si}\left(2 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)}{b^2 c^2}","\frac{\cos \left(\frac{2 a}{b}\right) \text{Ci}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{x \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"(-((b*c*x*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])) + Cos[(2*a)/b]*CosIntegral[2*(a/b + ArcSin[c*x])] + Sin[(2*a)/b]*SinIntegral[2*(a/b + ArcSin[c*x])])/(b^2*c^2)","A",1
165,1,72,86,0.1506045,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[(a + b*ArcSin[c*x])^(-2),x]","\frac{-\frac{b \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)}+\sin \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)-\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}","\frac{\sin \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{\sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"(-((b*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])) + CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b] - Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b^2*c)","A",1
166,0,0,17,4.1172291,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[1/(x*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*ArcSin[c*x])^2), x]","A",-1
167,0,0,17,34.2497822,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[1/(x^2*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*ArcSin[c*x])^2), x]","A",-1
168,1,168,197,0.8741043,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Integrate[x^2/(a + b*ArcSin[c*x])^3,x]","-\frac{\frac{4 b^2 x^2 \sqrt{1-c^2 x^2}}{c \left(a+b \sin ^{-1}(c x)\right)^2}+\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{c^3}-\frac{9 \cos \left(\frac{3 a}{b}\right) \text{Ci}\left(3 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)}{c^3}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{c^3}-\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(3 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)}{c^3}+\frac{8 b x}{c^2 \left(a+b \sin ^{-1}(c x)\right)}-\frac{12 b x^3}{a+b \sin ^{-1}(c x)}}{8 b^3}","-\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^3 c^3}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{Ci}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b^3 c^3}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^3 c^3}+\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b^3 c^3}-\frac{x}{b^2 c^2 \left(a+b \sin ^{-1}(c x)\right)}+\frac{3 x^3}{2 b^2 \left(a+b \sin ^{-1}(c x)\right)}-\frac{x^2 \sqrt{1-c^2 x^2}}{2 b c \left(a+b \sin ^{-1}(c x)\right)^2}",1,"-1/8*((4*b^2*x^2*Sqrt[1 - c^2*x^2])/(c*(a + b*ArcSin[c*x])^2) + (8*b*x)/(c^2*(a + b*ArcSin[c*x])) - (12*b*x^3)/(a + b*ArcSin[c*x]) + (Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/c^3 - (9*Cos[(3*a)/b]*CosIntegral[3*(a/b + ArcSin[c*x])])/c^3 + (Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/c^3 - (9*Sin[(3*a)/b]*SinIntegral[3*(a/b + ArcSin[c*x])])/c^3)/b^3","A",1
169,1,108,130,0.3860317,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Integrate[x/(a + b*ArcSin[c*x])^3,x]","\frac{-\frac{b^2 c x \sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2}+\frac{b \left(2 c^2 x^2-1\right)}{a+b \sin ^{-1}(c x)}+2 \sin \left(\frac{2 a}{b}\right) \text{Ci}\left(2 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)-2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(2 \left(\frac{a}{b}+\sin ^{-1}(c x)\right)\right)}{2 b^3 c^2}","\frac{\sin \left(\frac{2 a}{b}\right) \text{Ci}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^3 c^2}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^3 c^2}-\frac{1}{2 b^2 c^2 \left(a+b \sin ^{-1}(c x)\right)}+\frac{x^2}{b^2 \left(a+b \sin ^{-1}(c x)\right)}-\frac{x \sqrt{1-c^2 x^2}}{2 b c \left(a+b \sin ^{-1}(c x)\right)^2}",1,"(-((b^2*c*x*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])^2) + (b*(-1 + 2*c^2*x^2))/(a + b*ArcSin[c*x]) + 2*CosIntegral[2*(a/b + ArcSin[c*x])]*Sin[(2*a)/b] - 2*Cos[(2*a)/b]*SinIntegral[2*(a/b + ArcSin[c*x])])/(2*b^3*c^2)","A",1
170,1,93,111,0.464395,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Integrate[(a + b*ArcSin[c*x])^(-3),x]","-\frac{\frac{b \left(\frac{b \sqrt{1-c^2 x^2}}{c}-x \left(a+b \sin ^{-1}(c x)\right)\right)}{\left(a+b \sin ^{-1}(c x)\right)^2}+\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{c}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{c}}{2 b^3}","-\frac{\cos \left(\frac{a}{b}\right) \text{Ci}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{2 b^3 c}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{2 b^3 c}+\frac{x}{2 b^2 \left(a+b \sin ^{-1}(c x)\right)}-\frac{\sqrt{1-c^2 x^2}}{2 b c \left(a+b \sin ^{-1}(c x)\right)^2}",1,"-1/2*((b*((b*Sqrt[1 - c^2*x^2])/c - x*(a + b*ArcSin[c*x])))/(a + b*ArcSin[c*x])^2 + (Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/c + (Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/c)/b^3","A",1
171,0,0,17,2.405299,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Integrate[1/(x*(a + b*ArcSin[c*x])^3),x]","\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^3},x\right)",0,"Integrate[1/(x*(a + b*ArcSin[c*x])^3), x]","A",-1
172,0,0,17,19.1171483,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Integrate[1/(x^2*(a + b*ArcSin[c*x])^3),x]","\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^3},x\right)",0,"Integrate[1/(x^2*(a + b*ArcSin[c*x])^3), x]","A",-1
173,1,246,242,0.3196236,"\int x^2 \sqrt{a+b \sin ^{-1}(c x)} \, dx","Integrate[x^2*Sqrt[a + b*ArcSin[c*x]],x]","-\frac{i e^{-\frac{3 i a}{b}} \sqrt{a+b \sin ^{-1}(c x)} \left(9 e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-9 e^{\frac{4 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+\sqrt{3} \left(e^{\frac{6 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)\right)}{72 c^3 \sqrt{\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{b^2}}}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} \sin \left(\frac{3 a}{b}\right) C\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}+\frac{1}{3} x^3 \sqrt{a+b \sin ^{-1}(c x)}",1,"((-1/72*I)*Sqrt[a + b*ArcSin[c*x]]*(9*E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((-I)*(a + b*ArcSin[c*x]))/b] - 9*E^(((4*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, (I*(a + b*ArcSin[c*x]))/b] + Sqrt[3]*(-(Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((-3*I)*(a + b*ArcSin[c*x]))/b]) + E^(((6*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((3*I)*(a + b*ArcSin[c*x]))/b])))/(c^3*E^(((3*I)*a)/b)*Sqrt[(a + b*ArcSin[c*x])^2/b^2])","C",0
174,1,141,137,0.0756818,"\int x \sqrt{a+b \sin ^{-1}(c x)} \, dx","Integrate[x*Sqrt[a + b*ArcSin[c*x]],x]","-\frac{e^{-\frac{2 i a}{b}} \sqrt{a+b \sin ^{-1}(c x)} \left(\sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{8 \sqrt{2} c^2 \sqrt{\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{b^2}}}","\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) C\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 c^2}+\frac{\sqrt{\pi } \sqrt{b} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 c^2}-\frac{\sqrt{a+b \sin ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \sin ^{-1}(c x)}",1,"-1/8*(Sqrt[a + b*ArcSin[c*x]]*(Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((-2*I)*(a + b*ArcSin[c*x]))/b] + E^(((4*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((2*I)*(a + b*ArcSin[c*x]))/b]))/(Sqrt[2]*c^2*E^(((2*I)*a)/b)*Sqrt[(a + b*ArcSin[c*x])^2/b^2])","C",0
175,1,119,120,0.0985946,"\int \sqrt{a+b \sin ^{-1}(c x)} \, dx","Integrate[Sqrt[a + b*ArcSin[c*x]],x]","\frac{b e^{-\frac{i a}{b}} \left(\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{2 c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+x \sqrt{a+b \sin ^{-1}(c x)}",1,"(b*(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((-I)*(a + b*ArcSin[c*x]))/b] + E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, (I*(a + b*ArcSin[c*x]))/b]))/(2*c*E^((I*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
176,0,0,19,3.4868782,"\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{x} \, dx","Integrate[Sqrt[a + b*ArcSin[c*x]]/x,x]","\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{a+b \sin ^{-1}(c x)}}{x},x\right)",0,"Integrate[Sqrt[a + b*ArcSin[c*x]]/x, x]","A",-1
177,0,0,19,11.9038307,"\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{x^2} \, dx","Integrate[Sqrt[a + b*ArcSin[c*x]]/x^2,x]","\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \sin ^{-1}(c x)}}{x^2},x\right)",0,"Integrate[Sqrt[a + b*ArcSin[c*x]]/x^2, x]","A",-1
178,1,245,313,0.3064109,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Integrate[x^2*(a + b*ArcSin[c*x])^(3/2),x]","\frac{b e^{-\frac{3 i a}{b}} \sqrt{a+b \sin ^{-1}(c x)} \left(27 e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{5}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+27 e^{\frac{4 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{5}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{3} \left(\sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{5}{2},-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{6 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{5}{2},\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)\right)}{216 c^3 \sqrt{\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{b^2}}}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} \cos \left(\frac{3 a}{b}\right) C\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}+\frac{b x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{6 c}+\frac{b \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)^{3/2}",1,"(b*Sqrt[a + b*ArcSin[c*x]]*(27*E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[5/2, ((-I)*(a + b*ArcSin[c*x]))/b] + 27*E^(((4*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[5/2, (I*(a + b*ArcSin[c*x]))/b] - Sqrt[3]*(Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[5/2, ((-3*I)*(a + b*ArcSin[c*x]))/b] + E^(((6*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[5/2, ((3*I)*(a + b*ArcSin[c*x]))/b])))/(216*c^3*E^(((3*I)*a)/b)*Sqrt[(a + b*ArcSin[c*x])^2/b^2])","C",0
179,1,126,172,0.066203,"\int x \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Integrate[x*(a + b*ArcSin[c*x])^(3/2),x]","\frac{b^2 e^{-\frac{2 i a}{b}} \left(\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{5}{2},-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{5}{2},\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{16 \sqrt{2} c^2 \sqrt{a+b \sin ^{-1}(c x)}}","\frac{3 \sqrt{\pi } b^{3/2} \sin \left(\frac{2 a}{b}\right) C\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 c^2}-\frac{3 \sqrt{\pi } b^{3/2} \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 c^2}+\frac{3 b x \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{8 c}-\frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}",1,"(b^2*(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[5/2, ((-2*I)*(a + b*ArcSin[c*x]))/b] + E^(((4*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[5/2, ((2*I)*(a + b*ArcSin[c*x]))/b]))/(16*Sqrt[2]*c^2*E^(((2*I)*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
180,1,291,159,2.9758394,"\int \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Integrate[(a + b*ArcSin[c*x])^(3/2),x]","\frac{b \left(2 \left(3 \sqrt{1-c^2 x^2}+2 c x \sin ^{-1}(c x)\right) \sqrt{a+b \sin ^{-1}(c x)}-\sqrt{2 \pi } \sqrt{\frac{1}{b}} \left(2 a \sin \left(\frac{a}{b}\right)+3 b \cos \left(\frac{a}{b}\right)\right) C\left(\sqrt{\frac{1}{b}} \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}\right)+\sqrt{2 \pi } \sqrt{\frac{1}{b}} \left(2 a \cos \left(\frac{a}{b}\right)-3 b \sin \left(\frac{a}{b}\right)\right) S\left(\sqrt{\frac{1}{b}} \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}\right)+\frac{2 a e^{-\frac{i a}{b}} \left(\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{\sqrt{a+b \sin ^{-1}(c x)}}\right)}{4 c}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 b \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{2 c}+x \left(a+b \sin ^{-1}(c x)\right)^{3/2}",1,"(b*(2*Sqrt[a + b*ArcSin[c*x]]*(3*Sqrt[1 - c^2*x^2] + 2*c*x*ArcSin[c*x]) + (2*a*(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((-I)*(a + b*ArcSin[c*x]))/b] + E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, (I*(a + b*ArcSin[c*x]))/b]))/(E^((I*a)/b)*Sqrt[a + b*ArcSin[c*x]]) - Sqrt[b^(-1)]*Sqrt[2*Pi]*FresnelC[Sqrt[b^(-1)]*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]]]*(3*b*Cos[a/b] + 2*a*Sin[a/b]) + Sqrt[b^(-1)]*Sqrt[2*Pi]*FresnelS[Sqrt[b^(-1)]*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]]]*(2*a*Cos[a/b] - 3*b*Sin[a/b])))/(4*c)","C",0
181,0,0,19,3.1228312,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x} \, dx","Integrate[(a + b*ArcSin[c*x])^(3/2)/x,x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x},x\right)",0,"Integrate[(a + b*ArcSin[c*x])^(3/2)/x, x]","A",-1
182,0,0,19,10.5746288,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x^2} \, dx","Integrate[(a + b*ArcSin[c*x])^(3/2)/x^2,x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x^2},x\right)",0,"Integrate[(a + b*ArcSin[c*x])^(3/2)/x^2, x]","A",-1
183,1,228,358,0.2842982,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2} \, dx","Integrate[x^2*(a + b*ArcSin[c*x])^(5/2),x]","\frac{b^3 e^{-\frac{3 i a}{b}} \left(-81 e^{\frac{2 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{7}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-81 e^{\frac{4 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{7}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+\sqrt{3} \left(\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{7}{2},-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{6 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{7}{2},\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)\right)}{648 c^3 \sqrt{a+b \sin ^{-1}(c x)}}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} \sin \left(\frac{3 a}{b}\right) C\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{144 c^3}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{144 c^3}-\frac{5 b^2 x \sqrt{a+b \sin ^{-1}(c x)}}{6 c^2}-\frac{5}{36} b^2 x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{5 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{3/2}}{18 c}+\frac{5 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)^{5/2}",1,"(b^3*(-81*E^(((2*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[7/2, ((-I)*(a + b*ArcSin[c*x]))/b] - 81*E^(((4*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[7/2, (I*(a + b*ArcSin[c*x]))/b] + Sqrt[3]*(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[7/2, ((-3*I)*(a + b*ArcSin[c*x]))/b] + E^(((6*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[7/2, ((3*I)*(a + b*ArcSin[c*x]))/b])))/(648*c^3*E^(((3*I)*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
184,1,141,216,0.1003555,"\int x \left(a+b \sin ^{-1}(c x)\right)^{5/2} \, dx","Integrate[x*(a + b*ArcSin[c*x])^(5/2),x]","\frac{e^{-\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c x)\right)^{5/2} \left(\sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{7}{2},-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{7}{2},\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{32 \sqrt{2} c^2 \left(\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{b^2}\right)^{3/2}}","-\frac{15 \sqrt{\pi } b^{5/2} \cos \left(\frac{2 a}{b}\right) C\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 c^2}-\frac{15 \sqrt{\pi } b^{5/2} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 c^2}+\frac{15 b^2 \sqrt{a+b \sin ^{-1}(c x)}}{64 c^2}-\frac{15}{32} b^2 x^2 \sqrt{a+b \sin ^{-1}(c x)}+\frac{5 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{3/2}}{8 c}-\frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2}",1,"((a + b*ArcSin[c*x])^(5/2)*(Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[7/2, ((-2*I)*(a + b*ArcSin[c*x]))/b] + E^(((4*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[7/2, ((2*I)*(a + b*ArcSin[c*x]))/b]))/(32*Sqrt[2]*c^2*E^(((2*I)*a)/b)*((a + b*ArcSin[c*x])^2/b^2)^(3/2))","C",0
185,1,379,179,3.1903436,"\int \left(a+b \sin ^{-1}(c x)\right)^{5/2} \, dx","Integrate[(a + b*ArcSin[c*x])^(5/2),x]","\frac{e^{-\frac{i a}{b}} \left(\frac{i \sqrt{\frac{\pi }{2}} \left(4 a^2+15 b^2\right) \left(-1+e^{\frac{2 i a}{b}}\right) \sqrt{a+b \sin ^{-1}(c x)} C\left(\sqrt{\frac{1}{b}} \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}\right)}{\sqrt{\frac{1}{b}}}+\frac{\sqrt{\frac{\pi }{2}} \left(4 a^2+15 b^2\right) \left(1+e^{\frac{2 i a}{b}}\right) \sqrt{a+b \sin ^{-1}(c x)} S\left(\sqrt{\frac{1}{b}} \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}\right)}{\sqrt{\frac{1}{b}}}+2 b \left(2 a^2 \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+2 a^2 e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{3}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c x)\right) \left(2 \sin ^{-1}(c x) \left(4 a c x+5 b \sqrt{1-c^2 x^2}\right)+10 a \sqrt{1-c^2 x^2}-15 b c x+4 b c x \sin ^{-1}(c x)^2\right)\right)\right)}{8 c \sqrt{a+b \sin ^{-1}(c x)}}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{15}{4} b^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{5 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \sin ^{-1}(c x)\right)^{5/2}",1,"((I*(4*a^2 + 15*b^2)*(-1 + E^(((2*I)*a)/b))*Sqrt[Pi/2]*Sqrt[a + b*ArcSin[c*x]]*FresnelC[Sqrt[b^(-1)]*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]]])/Sqrt[b^(-1)] + ((4*a^2 + 15*b^2)*(1 + E^(((2*I)*a)/b))*Sqrt[Pi/2]*Sqrt[a + b*ArcSin[c*x]]*FresnelS[Sqrt[b^(-1)]*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]]])/Sqrt[b^(-1)] + 2*b*(E^((I*a)/b)*(a + b*ArcSin[c*x])*(-15*b*c*x + 10*a*Sqrt[1 - c^2*x^2] + 2*(4*a*c*x + 5*b*Sqrt[1 - c^2*x^2])*ArcSin[c*x] + 4*b*c*x*ArcSin[c*x]^2) + 2*a^2*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, ((-I)*(a + b*ArcSin[c*x]))/b] + 2*a^2*E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[3/2, (I*(a + b*ArcSin[c*x]))/b]))/(8*c*E^((I*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
186,0,0,19,3.2478189,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x} \, dx","Integrate[(a + b*ArcSin[c*x])^(5/2)/x,x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x},x\right)",0,"Integrate[(a + b*ArcSin[c*x])^(5/2)/x, x]","A",-1
187,0,0,19,10.6009596,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x^2} \, dx","Integrate[(a + b*ArcSin[c*x])^(5/2)/x^2,x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x^2},x\right)",0,"Integrate[(a + b*ArcSin[c*x])^(5/2)/x^2, x]","A",-1
188,1,228,223,0.2887588,"\int \frac{x^2}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Integrate[x^2/Sqrt[a + b*ArcSin[c*x]],x]","-\frac{i e^{-\frac{3 i a}{b}} \left(3 e^{\frac{2 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-3 e^{\frac{4 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+\sqrt{3} \left(e^{\frac{6 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)\right)}{24 c^3 \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} \cos \left(\frac{3 a}{b}\right) C\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}",1,"((-1/24*I)*(3*E^(((2*I)*a)/b)*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-I)*(a + b*ArcSin[c*x]))/b] - 3*E^(((4*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, (I*(a + b*ArcSin[c*x]))/b] + Sqrt[3]*(-(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-3*I)*(a + b*ArcSin[c*x]))/b]) + E^(((6*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((3*I)*(a + b*ArcSin[c*x]))/b])))/(c^3*E^(((3*I)*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
189,1,123,99,0.0768044,"\int \frac{x}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Integrate[x/Sqrt[a + b*ArcSin[c*x]],x]","-\frac{e^{-\frac{2 i a}{b}} \left(\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{4 \sqrt{2} c^2 \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} c^2}-\frac{\sqrt{\pi } \sin \left(\frac{2 a}{b}\right) C\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} c^2}",1,"-1/4*(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-2*I)*(a + b*ArcSin[c*x]))/b] + E^(((4*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((2*I)*(a + b*ArcSin[c*x]))/b])/(Sqrt[2]*c^2*E^(((2*I)*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
190,1,121,101,0.0878994,"\int \frac{1}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Integrate[1/Sqrt[a + b*ArcSin[c*x]],x]","\frac{i e^{-\frac{i a}{b}} \left(e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{2 c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}",1,"((I/2)*(-(Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-I)*(a + b*ArcSin[c*x]))/b]) + E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, (I*(a + b*ArcSin[c*x]))/b]))/(c*E^((I*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
191,0,0,19,3.1186484,"\int \frac{1}{x \sqrt{a+b \sin ^{-1}(c x)}} \, dx","Integrate[1/(x*Sqrt[a + b*ArcSin[c*x]]),x]","\int \frac{1}{x \sqrt{a+b \sin ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a+b \sin ^{-1}(c x)}},x\right)",0,"Integrate[1/(x*Sqrt[a + b*ArcSin[c*x]]), x]","A",-1
192,0,0,19,11.7467812,"\int \frac{1}{x^2 \sqrt{a+b \sin ^{-1}(c x)}} \, dx","Integrate[1/(x^2*Sqrt[a + b*ArcSin[c*x]]),x]","\int \frac{1}{x^2 \sqrt{a+b \sin ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{a+b \sin ^{-1}(c x)}},x\right)",0,"Integrate[1/(x^2*Sqrt[a + b*ArcSin[c*x]]), x]","A",-1
193,1,343,250,0.4715009,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[x^2/(a + b*ArcSin[c*x])^(3/2),x]","\frac{e^{-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}} \left(-e^{\frac{3 i a}{b}+2 i \sin ^{-1}(c x)}-e^{\frac{3 i a}{b}+4 i \sin ^{-1}(c x)}+e^{\frac{3 i \left(a+2 b \sin ^{-1}(c x)\right)}{b}}+e^{\frac{2 i a}{b}+3 i \sin ^{-1}(c x)} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 i a}{b}+3 i \sin ^{-1}(c x)} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{3} e^{3 i \sin ^{-1}(c x)} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{3} e^{3 i \left(\frac{2 a}{b}+\sin ^{-1}(c x)\right)} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{3 i a}{b}}\right)}{4 b c^3 \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} \sin \left(\frac{3 a}{b}\right) C\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{\sqrt{\frac{3 \pi }{2}} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{2 x^2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(E^(((3*I)*a)/b) - E^(((3*I)*a)/b + (2*I)*ArcSin[c*x]) - E^(((3*I)*a)/b + (4*I)*ArcSin[c*x]) + E^(((3*I)*(a + 2*b*ArcSin[c*x]))/b) + E^(((2*I)*a)/b + (3*I)*ArcSin[c*x])*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-I)*(a + b*ArcSin[c*x]))/b] + E^(((4*I)*a)/b + (3*I)*ArcSin[c*x])*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, (I*(a + b*ArcSin[c*x]))/b] - Sqrt[3]*E^((3*I)*ArcSin[c*x])*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-3*I)*(a + b*ArcSin[c*x]))/b] - Sqrt[3]*E^((3*I)*((2*a)/b + ArcSin[c*x]))*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((3*I)*(a + b*ArcSin[c*x]))/b])/(4*b*c^3*E^(((3*I)*(a + b*ArcSin[c*x]))/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
194,1,155,130,0.1504029,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[x/(a + b*ArcSin[c*x])^(3/2),x]","\frac{i e^{-\frac{2 i a}{b}} \left(2 i e^{\frac{2 i a}{b}} \sin \left(2 \sin ^{-1}(c x)\right)-\sqrt{2} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+\sqrt{2} e^{\frac{4 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)\right)}{2 b c^2 \sqrt{a+b \sin ^{-1}(c x)}}","\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) C\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} c^2}+\frac{2 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} c^2}-\frac{2 x \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"((I/2)*(-(Sqrt[2]*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-2*I)*(a + b*ArcSin[c*x]))/b]) + Sqrt[2]*E^(((4*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((2*I)*(a + b*ArcSin[c*x]))/b] + (2*I)*E^(((2*I)*a)/b)*Sin[2*ArcSin[c*x]]))/(b*c^2*E^(((2*I)*a)/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
195,1,167,137,0.3293177,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[(a + b*ArcSin[c*x])^(-3/2),x]","\frac{e^{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \left(e^{i \sin ^{-1}(c x)} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{\frac{i a}{b}} \left(e^{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-e^{2 i \sin ^{-1}(c x)}-1\right)\right)}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(E^(I*ArcSin[c*x])*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-I)*(a + b*ArcSin[c*x]))/b] + E^((I*a)/b)*(-1 - E^((2*I)*ArcSin[c*x]) + E^((I*(a + b*ArcSin[c*x]))/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, (I*(a + b*ArcSin[c*x]))/b]))/(b*c*E^((I*(a + b*ArcSin[c*x]))/b)*Sqrt[a + b*ArcSin[c*x]])","C",0
196,0,0,19,3.8119347,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[1/(x*(a + b*ArcSin[c*x])^(3/2)),x]","\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}},x\right)",0,"Integrate[1/(x*(a + b*ArcSin[c*x])^(3/2)), x]","A",-1
197,0,0,19,11.524711,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[1/(x^2*(a + b*ArcSin[c*x])^(3/2)),x]","\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}},x\right)",0,"Integrate[1/(x^2*(a + b*ArcSin[c*x])^(3/2)), x]","A",-1
198,1,370,291,1.8772512,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[x^2/(a + b*ArcSin[c*x])^(5/2),x]","\frac{e^{3 i \sin ^{-1}(c x)} \left(6 i a+6 i b \sin ^{-1}(c x)+b\right)-i e^{i \sin ^{-1}(c x)} \left(2 a+2 b \sin ^{-1}(c x)-i b\right)-2 b e^{-\frac{i a}{b}} \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+6 \sqrt{3} b e^{-\frac{3 i a}{b}} \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+i e^{-i \sin ^{-1}(c x)} \left(2 i b e^{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+2 a+2 b \sin ^{-1}(c x)+i b\right)+6 \sqrt{3} b e^{\frac{3 i a}{b}} \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-6 i a e^{-3 i \sin ^{-1}(c x)}+b e^{-3 i \sin ^{-1}(c x)} \left(1-6 i \sin ^{-1}(c x)\right)}{12 b^2 c^3 \left(a+b \sin ^{-1}(c x)\right)^{3/2}}","-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^3}+\frac{\sqrt{6 \pi } \cos \left(\frac{3 a}{b}\right) C\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{5/2} c^3}-\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^3}+\frac{\sqrt{6 \pi } \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{5/2} c^3}-\frac{8 x}{3 b^2 c^2 \sqrt{a+b \sin ^{-1}(c x)}}+\frac{4 x^3}{b^2 \sqrt{a+b \sin ^{-1}(c x)}}-\frac{2 x^2 \sqrt{1-c^2 x^2}}{3 b c \left(a+b \sin ^{-1}(c x)\right)^{3/2}}",1,"(((-6*I)*a)/E^((3*I)*ArcSin[c*x]) + (b*(1 - (6*I)*ArcSin[c*x]))/E^((3*I)*ArcSin[c*x]) + E^((3*I)*ArcSin[c*x])*((6*I)*a + b + (6*I)*b*ArcSin[c*x]) - I*E^(I*ArcSin[c*x])*(2*a - I*b + 2*b*ArcSin[c*x]) - (2*b*(((-I)*(a + b*ArcSin[c*x]))/b)^(3/2)*Gamma[1/2, ((-I)*(a + b*ArcSin[c*x]))/b])/E^((I*a)/b) + (I*(2*a + I*b + 2*b*ArcSin[c*x] + (2*I)*b*E^((I*(a + b*ArcSin[c*x]))/b)*((I*(a + b*ArcSin[c*x]))/b)^(3/2)*Gamma[1/2, (I*(a + b*ArcSin[c*x]))/b]))/E^(I*ArcSin[c*x]) + (6*Sqrt[3]*b*(((-I)*(a + b*ArcSin[c*x]))/b)^(3/2)*Gamma[1/2, ((-3*I)*(a + b*ArcSin[c*x]))/b])/E^(((3*I)*a)/b) + 6*Sqrt[3]*b*E^(((3*I)*a)/b)*((I*(a + b*ArcSin[c*x]))/b)^(3/2)*Gamma[1/2, ((3*I)*(a + b*ArcSin[c*x]))/b])/(12*b^2*c^3*(a + b*ArcSin[c*x])^(3/2))","C",0
199,1,173,180,1.3587566,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[x/(a + b*ArcSin[c*x])^(5/2),x]","-\frac{b \sin \left(2 \sin ^{-1}(c x)\right)+2 \left(a+b \sin ^{-1}(c x)\right) \left(-\sqrt{2} e^{-\frac{2 i a}{b}} \sqrt{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-\sqrt{2} e^{\frac{2 i a}{b}} \sqrt{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \Gamma \left(\frac{1}{2},\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+e^{-2 i \sin ^{-1}(c x)}+e^{2 i \sin ^{-1}(c x)}\right)}{3 b^2 c^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}}","\frac{8 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) C\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} c^2}-\frac{8 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} c^2}-\frac{4}{3 b^2 c^2 \sqrt{a+b \sin ^{-1}(c x)}}+\frac{8 x^2}{3 b^2 \sqrt{a+b \sin ^{-1}(c x)}}-\frac{2 x \sqrt{1-c^2 x^2}}{3 b c \left(a+b \sin ^{-1}(c x)\right)^{3/2}}",1,"-1/3*(2*(a + b*ArcSin[c*x])*(E^((-2*I)*ArcSin[c*x]) + E^((2*I)*ArcSin[c*x]) - (Sqrt[2]*Sqrt[((-I)*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((-2*I)*(a + b*ArcSin[c*x]))/b])/E^(((2*I)*a)/b) - Sqrt[2]*E^(((2*I)*a)/b)*Sqrt[(I*(a + b*ArcSin[c*x]))/b]*Gamma[1/2, ((2*I)*(a + b*ArcSin[c*x]))/b]) + b*Sin[2*ArcSin[c*x]])/(b^2*c^2*(a + b*ArcSin[c*x])^(3/2))","C",0
200,1,214,163,0.9776652,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[(a + b*ArcSin[c*x])^(-5/2),x]","\frac{e^{-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \left(-2 b e^{i \sin ^{-1}(c x)} \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)-i e^{\frac{i a}{b}} \left(-2 i b e^{\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}} \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)+2 a \left(-1+e^{2 i \sin ^{-1}(c x)}\right)+b \left(-2 \sin ^{-1}(c x)+e^{2 i \sin ^{-1}(c x)} \left(2 \sin ^{-1}(c x)-i\right)-i\right)\right)\right)}{3 b^2 c \left(a+b \sin ^{-1}(c x)\right)^{3/2}}","-\frac{4 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) C\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{4 x}{3 b^2 \sqrt{a+b \sin ^{-1}(c x)}}-\frac{2 \sqrt{1-c^2 x^2}}{3 b c \left(a+b \sin ^{-1}(c x)\right)^{3/2}}",1,"(-2*b*E^(I*ArcSin[c*x])*(((-I)*(a + b*ArcSin[c*x]))/b)^(3/2)*Gamma[1/2, ((-I)*(a + b*ArcSin[c*x]))/b] - I*E^((I*a)/b)*(2*a*(-1 + E^((2*I)*ArcSin[c*x])) + b*(-I - 2*ArcSin[c*x] + E^((2*I)*ArcSin[c*x])*(-I + 2*ArcSin[c*x])) - (2*I)*b*E^((I*(a + b*ArcSin[c*x]))/b)*((I*(a + b*ArcSin[c*x]))/b)^(3/2)*Gamma[1/2, (I*(a + b*ArcSin[c*x]))/b]))/(3*b^2*c*E^((I*(a + b*ArcSin[c*x]))/b)*(a + b*ArcSin[c*x])^(3/2))","C",0
201,0,0,19,3.9502963,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[1/(x*(a + b*ArcSin[c*x])^(5/2)),x]","\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{5/2}},x\right)",0,"Integrate[1/(x*(a + b*ArcSin[c*x])^(5/2)), x]","A",-1
202,0,0,19,11.5646327,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[1/(x^2*(a + b*ArcSin[c*x])^(5/2)),x]","\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2}},x\right)",0,"Integrate[1/(x^2*(a + b*ArcSin[c*x])^(5/2)), x]","A",-1
203,1,100,120,0.0394406,"\int (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[(d*x)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{2 d^2 \sqrt{d x} \left(21 a c^3 x^3+21 b c^3 x^3 \sin ^{-1}(c x)-10 b \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)+6 b c^2 x^2 \sqrt{1-c^2 x^2}+10 b \sqrt{1-c^2 x^2}\right)}{147 c^3}","\frac{2 (d x)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d}-\frac{20 b d^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{147 c^{7/2}}+\frac{4 b \sqrt{1-c^2 x^2} (d x)^{5/2}}{49 c}+\frac{20 b d^2 \sqrt{1-c^2 x^2} \sqrt{d x}}{147 c^3}",1,"(2*d^2*Sqrt[d*x]*(21*a*c^3*x^3 + 10*b*Sqrt[1 - c^2*x^2] + 6*b*c^2*x^2*Sqrt[1 - c^2*x^2] + 21*b*c^3*x^3*ArcSin[c*x] - 10*b*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2]))/(147*c^3)","C",1
204,1,66,124,0.032485,"\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[(d*x)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{2 (d x)^{3/2} \left(5 a c x-2 b \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right)+2 b \sqrt{1-c^2 x^2}+5 b c x \sin ^{-1}(c x)\right)}{25 c}","\frac{2 (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 d}+\frac{12 b d^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{25 c^{5/2}}-\frac{12 b d^{3/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{25 c^{5/2}}+\frac{4 b \sqrt{1-c^2 x^2} (d x)^{3/2}}{25 c}",1,"(2*(d*x)^(3/2)*(5*a*c*x + 2*b*Sqrt[1 - c^2*x^2] + 5*b*c*x*ArcSin[c*x] - 2*b*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2]))/(25*c)","C",1
205,1,66,88,0.0172335,"\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right) \, dx","Integrate[Sqrt[d*x]*(a + b*ArcSin[c*x]),x]","\frac{2 \sqrt{d x} \left(3 a c x-2 b \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)+2 b \sqrt{1-c^2 x^2}+3 b c x \sin ^{-1}(c x)\right)}{9 c}","\frac{2 (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 d}-\frac{4 b \sqrt{d} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{9 c^{3/2}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d x}}{9 c}",1,"(2*Sqrt[d*x]*(3*a*c*x + 2*b*Sqrt[1 - c^2*x^2] + 3*b*c*x*ArcSin[c*x] - 2*b*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2]))/(9*c)","C",1
206,1,45,89,0.0123917,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d x}} \, dx","Integrate[(a + b*ArcSin[c*x])/Sqrt[d*x],x]","\frac{2 x \left(3 \left(a+b \sin ^{-1}(c x)\right)-2 b c x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right)\right)}{3 \sqrt{d x}}","\frac{2 \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)}{d}+\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{\sqrt{c} \sqrt{d}}-\frac{4 b E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{\sqrt{c} \sqrt{d}}",1,"(2*x*(3*(a + b*ArcSin[c*x]) - 2*b*c*x*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2]))/(3*Sqrt[d*x])","C",1
207,1,40,55,0.0137938,"\int \frac{a+b \sin ^{-1}(c x)}{(d x)^{3/2}} \, dx","Integrate[(a + b*ArcSin[c*x])/(d*x)^(3/2),x]","-\frac{2 x \left(a-2 b c x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)+b \sin ^{-1}(c x)\right)}{(d x)^{3/2}}","\frac{4 b \sqrt{c} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{d^{3/2}}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d x}}",1,"(-2*x*(a + b*ArcSin[c*x] - 2*b*c*x*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2]))/(d*x)^(3/2)","C",1
208,1,42,125,0.0155915,"\int \frac{a+b \sin ^{-1}(c x)}{(d x)^{5/2}} \, dx","Integrate[(a + b*ArcSin[c*x])/(d*x)^(5/2),x]","-\frac{2 x \left(a+2 b c x \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};c^2 x^2\right)+b \sin ^{-1}(c x)\right)}{3 (d x)^{5/2}}","-\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{3 d (d x)^{3/2}}+\frac{4 b c^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{3 d^{5/2}}-\frac{4 b c^{3/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{3 d^{5/2}}-\frac{4 b c \sqrt{1-c^2 x^2}}{3 d^2 \sqrt{d x}}",1,"(-2*x*(a + b*ArcSin[c*x] + 2*b*c*x*Hypergeometric2F1[-1/4, 1/2, 3/4, c^2*x^2]))/(3*(d*x)^(5/2))","C",1
209,1,90,109,0.062286,"\int (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Integrate[(d*x)^(5/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2}{693} x (d x)^{5/2} \left(8 b^2 c^2 x^2 \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};c^2 x^2\right)+11 \left(a+b \sin ^{-1}(c x)\right) \left(9 \left(a+b \sin ^{-1}(c x)\right)-4 b c x \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};c^2 x^2\right)\right)\right)","\frac{16 b^2 c^2 (d x)^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};c^2 x^2\right)}{693 d^3}-\frac{8 b c (d x)^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{63 d^2}+\frac{2 (d x)^{7/2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 d}",1,"(2*x*(d*x)^(5/2)*(11*(a + b*ArcSin[c*x])*(9*(a + b*ArcSin[c*x]) - 4*b*c*x*Hypergeometric2F1[1/2, 9/4, 13/4, c^2*x^2]) + 8*b^2*c^2*x^2*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, c^2*x^2]))/693","A",1
210,1,90,109,0.0745335,"\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Integrate[(d*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2}{315} x (d x)^{3/2} \left(8 b^2 c^2 x^2 \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};c^2 x^2\right)+9 \left(a+b \sin ^{-1}(c x)\right) \left(7 \left(a+b \sin ^{-1}(c x)\right)-4 b c x \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};c^2 x^2\right)\right)\right)","\frac{16 b^2 c^2 (d x)^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};c^2 x^2\right)}{315 d^3}-\frac{8 b c (d x)^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{35 d^2}+\frac{2 (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 d}",1,"(2*x*(d*x)^(3/2)*(9*(a + b*ArcSin[c*x])*(7*(a + b*ArcSin[c*x]) - 4*b*c*x*Hypergeometric2F1[1/2, 7/4, 11/4, c^2*x^2]) + 8*b^2*c^2*x^2*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, c^2*x^2]))/315","A",1
211,1,90,109,0.0519596,"\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Integrate[Sqrt[d*x]*(a + b*ArcSin[c*x])^2,x]","\frac{2}{105} x \sqrt{d x} \left(8 b^2 c^2 x^2 \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)+7 \left(a+b \sin ^{-1}(c x)\right) \left(5 \left(a+b \sin ^{-1}(c x)\right)-4 b c x \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right)\right)\right)","\frac{16 b^2 c^2 (d x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{105 d^3}-\frac{8 b c (d x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{15 d^2}+\frac{2 (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d}",1,"(2*x*Sqrt[d*x]*(7*(a + b*ArcSin[c*x])*(5*(a + b*ArcSin[c*x]) - 4*b*c*x*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2]) + 8*b^2*c^2*x^2*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2]))/105","A",1
212,1,90,107,0.0506208,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d x}} \, dx","Integrate[(a + b*ArcSin[c*x])^2/Sqrt[d*x],x]","\frac{2 x \left(8 b^2 c^2 x^2 \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};c^2 x^2\right)+5 \left(a+b \sin ^{-1}(c x)\right) \left(3 \left(a+b \sin ^{-1}(c x)\right)-4 b c x \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right)\right)\right)}{15 \sqrt{d x}}","\frac{16 b^2 c^2 (d x)^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};c^2 x^2\right)}{15 d^3}-\frac{8 b c (d x)^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2}+\frac{2 \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2}{d}",1,"(2*x*(5*(a + b*ArcSin[c*x])*(3*(a + b*ArcSin[c*x]) - 4*b*c*x*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2]) + 8*b^2*c^2*x^2*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, c^2*x^2]))/(15*Sqrt[d*x])","A",1
213,1,87,105,0.0514939,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d x)^{3/2}} \, dx","Integrate[(a + b*ArcSin[c*x])^2/(d*x)^(3/2),x]","-\frac{2 x \left(8 b^2 c^2 x^2 \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};c^2 x^2\right)+3 \left(a+b \sin ^{-1}(c x)\right) \left(a-4 b c x \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right)+b \sin ^{-1}(c x)\right)\right)}{3 (d x)^{3/2}}","-\frac{16 b^2 c^2 (d x)^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};c^2 x^2\right)}{3 d^3}+\frac{8 b c \sqrt{d x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d x}}",1,"(-2*x*(3*(a + b*ArcSin[c*x])*(a + b*ArcSin[c*x] - 4*b*c*x*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2]) + 8*b^2*c^2*x^2*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, c^2*x^2]))/(3*(d*x)^(3/2))","A",1
214,1,87,109,0.0595497,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d x)^{5/2}} \, dx","Integrate[(a + b*ArcSin[c*x])^2/(d*x)^(5/2),x]","\frac{x \left(16 b^2 c^2 x^2 \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};c^2 x^2\right)-2 \left(a+b \sin ^{-1}(c x)\right) \left(a+4 b c x \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};c^2 x^2\right)+b \sin ^{-1}(c x)\right)\right)}{3 (d x)^{5/2}}","\frac{16 b^2 c^2 \sqrt{d x} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};c^2 x^2\right)}{3 d^3}-\frac{8 b c \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d x}}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d (d x)^{3/2}}",1,"(x*(-2*(a + b*ArcSin[c*x])*(a + b*ArcSin[c*x] + 4*b*c*x*Hypergeometric2F1[-1/4, 1/2, 3/4, c^2*x^2]) + 16*b^2*c^2*x^2*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, c^2*x^2]))/(3*(d*x)^(5/2))","A",1
215,0,0,69,39.3680695,"\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Integrate[(d*x)^(3/2)*(a + b*ArcSin[c*x])^3,x]","\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","\frac{2 (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{5 d}-\frac{6 b c \text{Int}\left(\frac{(d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}},x\right)}{5 d}",0,"Integrate[(d*x)^(3/2)*(a + b*ArcSin[c*x])^3, x]","A",-1
216,-1,0,67,180.0029016,"\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Integrate[Sqrt[d*x]*(a + b*ArcSin[c*x])^3,x]","\text{\$Aborted}","\frac{2 (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 d}-\frac{2 b c \text{Int}\left(\frac{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}},x\right)}{d}",0,"$Aborted","F",-1
217,0,0,65,9.0108904,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{\sqrt{d x}} \, dx","Integrate[(a + b*ArcSin[c*x])^3/Sqrt[d*x],x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{\sqrt{d x}} \, dx","\frac{2 \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^3}{d}-\frac{6 b c \text{Int}\left(\frac{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}},x\right)}{d}",0,"Integrate[(a + b*ArcSin[c*x])^3/Sqrt[d*x], x]","A",-1
218,0,0,65,8.4429915,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{(d x)^{3/2}} \, dx","Integrate[(a + b*ArcSin[c*x])^3/(d*x)^(3/2),x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{(d x)^{3/2}} \, dx","\frac{6 b c \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2} \sqrt{d x}},x\right)}{d}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)^3}{d \sqrt{d x}}",0,"Integrate[(a + b*ArcSin[c*x])^3/(d*x)^(3/2), x]","A",-1
219,0,0,67,14.4105762,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{(d x)^{5/2}} \, dx","Integrate[(a + b*ArcSin[c*x])^3/(d*x)^(5/2),x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{(d x)^{5/2}} \, dx","\frac{2 b c \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2} (d x)^{3/2}},x\right)}{d}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)^3}{3 d (d x)^{3/2}}",0,"Integrate[(a + b*ArcSin[c*x])^3/(d*x)^(5/2), x]","A",-1
220,0,0,21,3.0685528,"\int \frac{(d x)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Integrate[(d*x)^(3/2)/(a + b*ArcSin[c*x]),x]","\int \frac{(d x)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^{3/2}}{a+b \sin ^{-1}(c x)},x\right)",0,"Integrate[(d*x)^(3/2)/(a + b*ArcSin[c*x]), x]","A",-1
221,0,0,21,2.8974992,"\int \frac{\sqrt{d x}}{a+b \sin ^{-1}(c x)} \, dx","Integrate[Sqrt[d*x]/(a + b*ArcSin[c*x]),x]","\int \frac{\sqrt{d x}}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{d x}}{a+b \sin ^{-1}(c x)},x\right)",0,"Integrate[Sqrt[d*x]/(a + b*ArcSin[c*x]), x]","A",-1
222,0,0,21,0.8581166,"\int \frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Integrate[1/(Sqrt[d*x]*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Integrate[1/(Sqrt[d*x]*(a + b*ArcSin[c*x])), x]","A",-1
223,0,0,21,4.2109701,"\int \frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Integrate[1/((d*x)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Integrate[1/((d*x)^(3/2)*(a + b*ArcSin[c*x])), x]","A",-1
224,0,0,21,6.2051866,"\int \frac{(d x)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[(d*x)^(3/2)/(a + b*ArcSin[c*x])^2,x]","\int \frac{(d x)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Integrate[(d*x)^(3/2)/(a + b*ArcSin[c*x])^2, x]","A",-1
225,0,0,21,5.2871353,"\int \frac{\sqrt{d x}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[Sqrt[d*x]/(a + b*ArcSin[c*x])^2,x]","\int \frac{\sqrt{d x}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{d x}}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Integrate[Sqrt[d*x]/(a + b*ArcSin[c*x])^2, x]","A",-1
226,0,0,21,9.3610161,"\int \frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[1/(Sqrt[d*x]*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Integrate[1/(Sqrt[d*x]*(a + b*ArcSin[c*x])^2), x]","A",-1
227,0,0,21,14.8133379,"\int \frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Integrate[1/((d*x)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Integrate[1/((d*x)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",-1