1,1,75,0,0.0489039,"\int x^4 \sin ^{-1}(a x) \, dx","Int[x^4*ArcSin[a*x],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)","\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]/(5*a^5) - (2*(1 - a^2*x^2)^(3/2))/(15*a^5) + (1 - a^2*x^2)^(5/2)/(25*a^5) + (x^5*ArcSin[a*x])/5","A",4,3,8,0.3750,1,"{4627, 266, 43}"
2,1,69,0,0.0285116,"\int x^3 \sin ^{-1}(a x) \, dx","Int[x^3*ArcSin[a*x],x]","\frac{x^3 \sqrt{1-a^2 x^2}}{16 a}+\frac{3 x \sqrt{1-a^2 x^2}}{32 a^3}-\frac{3 \sin ^{-1}(a x)}{32 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)","\frac{x^3 \sqrt{1-a^2 x^2}}{16 a}+\frac{3 x \sqrt{1-a^2 x^2}}{32 a^3}-\frac{3 \sin ^{-1}(a x)}{32 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)",1,"(3*x*Sqrt[1 - a^2*x^2])/(32*a^3) + (x^3*Sqrt[1 - a^2*x^2])/(16*a) - (3*ArcSin[a*x])/(32*a^4) + (x^4*ArcSin[a*x])/4","A",4,3,8,0.3750,1,"{4627, 321, 216}"
3,1,54,0,0.034606,"\int x^2 \sin ^{-1}(a x) \, dx","Int[x^2*ArcSin[a*x],x]","-\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)","-\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]/(3*a^3) - (1 - a^2*x^2)^(3/2)/(9*a^3) + (x^3*ArcSin[a*x])/3","A",4,3,8,0.3750,1,"{4627, 266, 43}"
4,1,45,0,0.0158949,"\int x \sin ^{-1}(a x) \, dx","Int[x*ArcSin[a*x],x]","\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)","\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,"(x*Sqrt[1 - a^2*x^2])/(4*a) - ArcSin[a*x]/(4*a^2) + (x^2*ArcSin[a*x])/2","A",3,3,6,0.5000,1,"{4627, 321, 216}"
5,1,25,0,0.0075506,"\int \sin ^{-1}(a x) \, dx","Int[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",2,2,4,0.5000,1,"{4619, 261}"
6,1,51,0,0.0584378,"\int \frac{\sin ^{-1}(a x)}{x} \, dx","Int[ArcSin[a*x]/x,x]","-\frac{1}{2} i \text{PolyLog}\left(2,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)","-\frac{1}{2} i \text{PolyLog}\left(2,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,"(-I/2)*ArcSin[a*x]^2 + ArcSin[a*x]*Log[1 - E^((2*I)*ArcSin[a*x])] - (I/2)*PolyLog[2, E^((2*I)*ArcSin[a*x])]","A",5,5,8,0.6250,1,"{4625, 3717, 2190, 2279, 2391}"
7,1,28,0,0.0218774,"\int \frac{\sin ^{-1}(a x)}{x^2} \, dx","Int[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",4,4,8,0.5000,1,"{4627, 266, 63, 208}"
8,1,34,0,0.01436,"\int \frac{\sin ^{-1}(a x)}{x^3} \, dx","Int[ArcSin[a*x]/x^3,x]","-\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\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,"-(a*Sqrt[1 - a^2*x^2])/(2*x) - ArcSin[a*x]/(2*x^2)","A",2,2,8,0.2500,1,"{4627, 264}"
9,1,56,0,0.0328187,"\int \frac{\sin ^{-1}(a x)}{x^4} \, dx","Int[ArcSin[a*x]/x^4,x]","-\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}","-\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,"-(a*Sqrt[1 - a^2*x^2])/(6*x^2) - ArcSin[a*x]/(3*x^3) - (a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/6","A",5,5,8,0.6250,1,"{4627, 266, 51, 63, 208}"
10,1,58,0,0.0224819,"\int \frac{\sin ^{-1}(a x)}{x^5} \, dx","Int[ArcSin[a*x]/x^5,x]","-\frac{a^3 \sqrt{1-a^2 x^2}}{6 x}-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}-\frac{\sin ^{-1}(a x)}{4 x^4}","-\frac{a^3 \sqrt{1-a^2 x^2}}{6 x}-\frac{a \sqrt{1-a^2 x^2}}{12 x^3}-\frac{\sin ^{-1}(a x)}{4 x^4}",1,"-(a*Sqrt[1 - a^2*x^2])/(12*x^3) - (a^3*Sqrt[1 - a^2*x^2])/(6*x) - ArcSin[a*x]/(4*x^4)","A",3,3,8,0.3750,1,"{4627, 271, 264}"
11,1,80,0,0.0454824,"\int \frac{\sin ^{-1}(a x)}{x^6} \, dx","Int[ArcSin[a*x]/x^6,x]","-\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}-\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{\sin ^{-1}(a x)}{5 x^5}","-\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}-\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{\sin ^{-1}(a x)}{5 x^5}",1,"-(a*Sqrt[1 - a^2*x^2])/(20*x^4) - (3*a^3*Sqrt[1 - a^2*x^2])/(40*x^2) - ArcSin[a*x]/(5*x^5) - (3*a^5*ArcTanh[Sqrt[1 - a^2*x^2]])/40","A",6,5,8,0.6250,1,"{4627, 266, 51, 63, 208}"
12,1,120,0,0.1939855,"\int x^4 \sin ^{-1}(a x)^2 \, dx","Int[x^4*ArcSin[a*x]^2,x]","-\frac{8 x^3}{225 a^2}+\frac{2 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{25 a}+\frac{8 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{75 a^3}+\frac{16 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{75 a^5}-\frac{16 x}{75 a^4}+\frac{1}{5} x^5 \sin ^{-1}(a x)^2-\frac{2 x^5}{125}","-\frac{8 x^3}{225 a^2}+\frac{2 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{25 a}+\frac{8 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{75 a^3}+\frac{16 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{75 a^5}-\frac{16 x}{75 a^4}+\frac{1}{5} x^5 \sin ^{-1}(a x)^2-\frac{2 x^5}{125}",1,"(-16*x)/(75*a^4) - (8*x^3)/(225*a^2) - (2*x^5)/125 + (16*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(75*a^5) + (8*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(75*a^3) + (2*x^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(25*a) + (x^5*ArcSin[a*x]^2)/5","A",7,5,10,0.5000,1,"{4627, 4707, 4677, 8, 30}"
13,1,98,0,0.1625771,"\int x^3 \sin ^{-1}(a x)^2 \, dx","Int[x^3*ArcSin[a*x]^2,x]","-\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{3 \sin ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^2-\frac{x^4}{32}","-\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{3 \sin ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^2-\frac{x^4}{32}",1,"(-3*x^2)/(32*a^2) - x^4/32 + (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(16*a^3) + (x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(8*a) - (3*ArcSin[a*x]^2)/(32*a^4) + (x^4*ArcSin[a*x]^2)/4","A",6,4,10,0.4000,1,"{4627, 4707, 4641, 30}"
14,1,82,0,0.1214342,"\int x^2 \sin ^{-1}(a x)^2 \, dx","Int[x^2*ArcSin[a*x]^2,x]","\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^3}-\frac{4 x}{9 a^2}+\frac{1}{3} x^3 \sin ^{-1}(a x)^2-\frac{2 x^3}{27}","\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^3}-\frac{4 x}{9 a^2}+\frac{1}{3} x^3 \sin ^{-1}(a x)^2-\frac{2 x^3}{27}",1,"(-4*x)/(9*a^2) - (2*x^3)/27 + (4*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(9*a^3) + (2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(9*a) + (x^3*ArcSin[a*x]^2)/3","A",5,5,10,0.5000,1,"{4627, 4707, 4677, 8, 30}"
15,1,60,0,0.0932273,"\int x \sin ^{-1}(a x)^2 \, dx","Int[x*ArcSin[a*x]^2,x]","\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}","\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,"-x^2/4 + (x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(2*a) - ArcSin[a*x]^2/(4*a^2) + (x^2*ArcSin[a*x]^2)/2","A",4,4,8,0.5000,1,"{4627, 4707, 4641, 30}"
16,1,35,0,0.0449068,"\int \sin ^{-1}(a x)^2 \, dx","Int[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",3,3,6,0.5000,1,"{4619, 4677, 8}"
17,1,71,0,0.0945688,"\int \frac{\sin ^{-1}(a x)^2}{x} \, dx","Int[ArcSin[a*x]^2/x,x]","-i \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,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{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,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",6,6,10,0.6000,1,"{4625, 3717, 2190, 2531, 2282, 6589}"
18,1,66,0,0.1025224,"\int \frac{\sin ^{-1}(a x)^2}{x^2} \, dx","Int[ArcSin[a*x]^2/x^2,x]","2 i a \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-2 i a \text{PolyLog}\left(2,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)","2 i a \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-2 i a \text{PolyLog}\left(2,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,"-(ArcSin[a*x]^2/x) - 4*a*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])] + (2*I)*a*PolyLog[2, -E^(I*ArcSin[a*x])] - (2*I)*a*PolyLog[2, E^(I*ArcSin[a*x])]","A",7,5,10,0.5000,1,"{4627, 4709, 4183, 2279, 2391}"
19,1,44,0,0.0798736,"\int \frac{\sin ^{-1}(a x)^2}{x^3} \, dx","Int[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",3,3,10,0.3000,1,"{4627, 4681, 29}"
20,1,116,0,0.169508,"\int \frac{\sin ^{-1}(a x)^2}{x^4} \, dx","Int[ArcSin[a*x]^2/x^4,x]","\frac{1}{3} i a^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-\frac{1}{3} i a^3 \text{PolyLog}\left(2,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{2}{3} a^3 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^2}{3 x^3}","\frac{1}{3} i a^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-\frac{1}{3} i a^3 \text{PolyLog}\left(2,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{2}{3} a^3 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^2}{3 x^3}",1,"-a^2/(3*x) - (a*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*x^2) - ArcSin[a*x]^2/(3*x^3) - (2*a^3*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])])/3 + (I/3)*a^3*PolyLog[2, -E^(I*ArcSin[a*x])] - (I/3)*a^3*PolyLog[2, E^(I*ArcSin[a*x])]","A",9,7,10,0.7000,1,"{4627, 4701, 4709, 4183, 2279, 2391, 30}"
21,1,87,0,0.1403841,"\int \frac{\sin ^{-1}(a x)^2}{x^5} \, dx","Int[ArcSin[a*x]^2/x^5,x]","-\frac{a^2}{12 x^2}-\frac{a^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 x}-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{6 x^3}+\frac{1}{3} a^4 \log (x)-\frac{\sin ^{-1}(a x)^2}{4 x^4}","-\frac{a^2}{12 x^2}-\frac{a^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 x}-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{6 x^3}+\frac{1}{3} a^4 \log (x)-\frac{\sin ^{-1}(a x)^2}{4 x^4}",1,"-a^2/(12*x^2) - (a*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(6*x^3) - (a^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*x) - ArcSin[a*x]^2/(4*x^4) + (a^4*Log[x])/3","A",5,5,10,0.5000,1,"{4627, 4701, 4681, 29, 30}"
22,1,201,0,0.3845144,"\int x^4 \sin ^{-1}(a x)^3 \, dx","Int[x^4*ArcSin[a*x]^3,x]","-\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{3 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a}-\frac{8 x^3 \sin ^{-1}(a x)}{75 a^2}+\frac{4 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a^3}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a^5}-\frac{16 x \sin ^{-1}(a x)}{25 a^4}+\frac{1}{5} x^5 \sin ^{-1}(a x)^3-\frac{6}{125} x^5 \sin ^{-1}(a x)","-\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{3 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a}-\frac{8 x^3 \sin ^{-1}(a x)}{75 a^2}+\frac{4 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a^3}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{25 a^5}-\frac{16 x \sin ^{-1}(a x)}{25 a^4}+\frac{1}{5} x^5 \sin ^{-1}(a x)^3-\frac{6}{125} x^5 \sin ^{-1}(a x)",1,"(-298*Sqrt[1 - a^2*x^2])/(375*a^5) + (76*(1 - a^2*x^2)^(3/2))/(1125*a^5) - (6*(1 - a^2*x^2)^(5/2))/(625*a^5) - (16*x*ArcSin[a*x])/(25*a^4) - (8*x^3*ArcSin[a*x])/(75*a^2) - (6*x^5*ArcSin[a*x])/125 + (8*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(25*a^5) + (4*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(25*a^3) + (3*x^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(25*a) + (x^5*ArcSin[a*x]^3)/5","A",14,7,10,0.7000,1,"{4627, 4707, 4677, 4619, 261, 266, 43}"
23,1,167,0,0.2970968,"\int x^3 \sin ^{-1}(a x)^3 \, dx","Int[x^3*ArcSin[a*x]^3,x]","-\frac{3 x^3 \sqrt{1-a^2 x^2}}{128 a}-\frac{45 x \sqrt{1-a^2 x^2}}{256 a^3}+\frac{3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{16 a}-\frac{9 x^2 \sin ^{-1}(a x)}{32 a^2}+\frac{9 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{32 a^3}-\frac{3 \sin ^{-1}(a x)^3}{32 a^4}+\frac{45 \sin ^{-1}(a x)}{256 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^3-\frac{3}{32} x^4 \sin ^{-1}(a x)","-\frac{3 x^3 \sqrt{1-a^2 x^2}}{128 a}-\frac{45 x \sqrt{1-a^2 x^2}}{256 a^3}+\frac{3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{16 a}-\frac{9 x^2 \sin ^{-1}(a x)}{32 a^2}+\frac{9 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{32 a^3}-\frac{3 \sin ^{-1}(a x)^3}{32 a^4}+\frac{45 \sin ^{-1}(a x)}{256 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^3-\frac{3}{32} x^4 \sin ^{-1}(a x)",1,"(-45*x*Sqrt[1 - a^2*x^2])/(256*a^3) - (3*x^3*Sqrt[1 - a^2*x^2])/(128*a) + (45*ArcSin[a*x])/(256*a^4) - (9*x^2*ArcSin[a*x])/(32*a^2) - (3*x^4*ArcSin[a*x])/32 + (9*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(32*a^3) + (3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(16*a) - (3*ArcSin[a*x]^3)/(32*a^4) + (x^4*ArcSin[a*x]^3)/4","A",11,5,10,0.5000,1,"{4627, 4707, 4641, 321, 216}"
24,1,136,0,0.2247474,"\int x^2 \sin ^{-1}(a x)^3 \, dx","Int[x^2*ArcSin[a*x]^3,x]","\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{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^3}-\frac{4 x \sin ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \sin ^{-1}(a x)^3-\frac{2}{9} x^3 \sin ^{-1}(a x)","\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{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^3}-\frac{4 x \sin ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \sin ^{-1}(a x)^3-\frac{2}{9} x^3 \sin ^{-1}(a x)",1,"(-14*Sqrt[1 - a^2*x^2])/(9*a^3) + (2*(1 - a^2*x^2)^(3/2))/(27*a^3) - (4*x*ArcSin[a*x])/(3*a^2) - (2*x^3*ArcSin[a*x])/9 + (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(3*a^3) + (x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(3*a) + (x^3*ArcSin[a*x]^3)/3","A",9,7,10,0.7000,1,"{4627, 4707, 4677, 4619, 261, 266, 43}"
25,1,99,0,0.1559878,"\int x \sin ^{-1}(a x)^3 \, dx","Int[x*ArcSin[a*x]^3,x]","-\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)","-\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*x*Sqrt[1 - a^2*x^2])/(8*a) + (3*ArcSin[a*x])/(8*a^2) - (3*x^2*ArcSin[a*x])/4 + (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(4*a) - ArcSin[a*x]^3/(4*a^2) + (x^2*ArcSin[a*x]^3)/2","A",6,5,8,0.6250,1,"{4627, 4707, 4641, 321, 216}"
26,1,60,0,0.0801758,"\int \sin ^{-1}(a x)^3 \, dx","Int[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",4,3,6,0.5000,1,"{4619, 4677, 261}"
27,1,97,0,0.1089985,"\int \frac{\sin ^{-1}(a x)^3}{x} \, dx","Int[ArcSin[a*x]^3/x,x]","-\frac{3}{2} i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{2} \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{4} i \text{PolyLog}\left(4,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)","-\frac{3}{2} i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{2} \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{4} i \text{PolyLog}\left(4,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,"(-I/4)*ArcSin[a*x]^4 + ArcSin[a*x]^3*Log[1 - E^((2*I)*ArcSin[a*x])] - ((3*I)/2)*ArcSin[a*x]^2*PolyLog[2, E^((2*I)*ArcSin[a*x])] + (3*ArcSin[a*x]*PolyLog[3, E^((2*I)*ArcSin[a*x])])/2 + ((3*I)/4)*PolyLog[4, E^((2*I)*ArcSin[a*x])]","A",7,7,10,0.7000,1,"{4625, 3717, 2190, 2531, 6609, 2282, 6589}"
28,1,108,0,0.1631995,"\int \frac{\sin ^{-1}(a x)^3}{x^2} \, dx","Int[ArcSin[a*x]^3/x^2,x]","6 i a \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-6 i a \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,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)","6 i a \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-6 i a \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,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,"-(ArcSin[a*x]^3/x) - 6*a*ArcSin[a*x]^2*ArcTanh[E^(I*ArcSin[a*x])] + (6*I)*a*ArcSin[a*x]*PolyLog[2, -E^(I*ArcSin[a*x])] - (6*I)*a*ArcSin[a*x]*PolyLog[2, E^(I*ArcSin[a*x])] - 6*a*PolyLog[3, -E^(I*ArcSin[a*x])] + 6*a*PolyLog[3, E^(I*ArcSin[a*x])]","A",9,6,10,0.6000,1,"{4627, 4709, 4183, 2531, 2282, 6589}"
29,1,102,0,0.1693306,"\int \frac{\sin ^{-1}(a x)^3}{x^3} \, dx","Int[ArcSin[a*x]^3/x^3,x]","-\frac{3}{2} i a^2 \text{PolyLog}\left(2,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}","-\frac{3}{2} i a^2 \text{PolyLog}\left(2,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,"((-3*I)/2)*a^2*ArcSin[a*x]^2 - (3*a*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(2*x) - ArcSin[a*x]^3/(2*x^2) + 3*a^2*ArcSin[a*x]*Log[1 - E^((2*I)*ArcSin[a*x])] - ((3*I)/2)*a^2*PolyLog[2, E^((2*I)*ArcSin[a*x])]","A",7,7,10,0.7000,1,"{4627, 4681, 4625, 3717, 2190, 2279, 2391}"
30,1,179,0,0.2845811,"\int \frac{\sin ^{-1}(a x)^3}{x^4} \, dx","Int[ArcSin[a*x]^3/x^4,x]","i a^3 \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-i a^3 \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-a^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+a^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x^2}-a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a^2 \sin ^{-1}(a x)}{x}+a^3 \left(-\sin ^{-1}(a x)^2\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^3}{3 x^3}","i a^3 \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-i a^3 \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-a^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+a^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-\frac{a \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x^2}-a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a^2 \sin ^{-1}(a x)}{x}+a^3 \left(-\sin ^{-1}(a x)^2\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{\sin ^{-1}(a x)^3}{3 x^3}",1,"-((a^2*ArcSin[a*x])/x) - (a*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(2*x^2) - ArcSin[a*x]^3/(3*x^3) - a^3*ArcSin[a*x]^2*ArcTanh[E^(I*ArcSin[a*x])] - a^3*ArcTanh[Sqrt[1 - a^2*x^2]] + I*a^3*ArcSin[a*x]*PolyLog[2, -E^(I*ArcSin[a*x])] - I*a^3*ArcSin[a*x]*PolyLog[2, E^(I*ArcSin[a*x])] - a^3*PolyLog[3, -E^(I*ArcSin[a*x])] + a^3*PolyLog[3, E^(I*ArcSin[a*x])]","A",14,10,10,1.000,1,"{4627, 4701, 4709, 4183, 2531, 2282, 6589, 266, 63, 208}"
31,1,169,0,0.2917723,"\int \frac{\sin ^{-1}(a x)^3}{x^5} \, dx","Int[ArcSin[a*x]^3/x^5,x]","-\frac{1}{2} i a^4 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)-\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{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{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{\sin ^{-1}(a x)^3}{4 x^4}","-\frac{1}{2} i a^4 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)-\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{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{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{\sin ^{-1}(a x)^3}{4 x^4}",1,"-(a^3*Sqrt[1 - a^2*x^2])/(4*x) - (a^2*ArcSin[a*x])/(4*x^2) - (I/2)*a^4*ArcSin[a*x]^2 - (a*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(4*x^3) - (a^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(2*x) - ArcSin[a*x]^3/(4*x^4) + a^4*ArcSin[a*x]*Log[1 - E^((2*I)*ArcSin[a*x])] - (I/2)*a^4*PolyLog[2, E^((2*I)*ArcSin[a*x])]","A",10,9,10,0.9000,1,"{4627, 4701, 4681, 4625, 3717, 2190, 2279, 2391, 264}"
32,1,282,0,0.8692462,"\int x^5 \sin ^{-1}(a x)^4 \, dx","Int[x^5*ArcSin[a*x]^4,x]","\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}+\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^4 \sin ^{-1}(a x)^2}{48 a^2}+\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{5 x^2 \sin ^{-1}(a x)^2}{16 a^4}+\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 \sin ^{-1}(a x)^4}{96 a^6}+\frac{245 \sin ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \sin ^{-1}(a x)^4-\frac{1}{18} x^6 \sin ^{-1}(a x)^2+\frac{x^6}{324}","\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}+\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^4 \sin ^{-1}(a x)^2}{48 a^2}+\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{5 x^2 \sin ^{-1}(a x)^2}{16 a^4}+\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 \sin ^{-1}(a x)^4}{96 a^6}+\frac{245 \sin ^{-1}(a x)^2}{1152 a^6}+\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,"(245*x^2)/(1152*a^4) + (65*x^4)/(3456*a^2) + x^6/324 - (245*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(576*a^5) - (65*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(864*a^3) - (x^5*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(54*a) + (245*ArcSin[a*x]^2)/(1152*a^6) - (5*x^2*ArcSin[a*x]^2)/(16*a^4) - (5*x^4*ArcSin[a*x]^2)/(48*a^2) - (x^6*ArcSin[a*x]^2)/18 + (5*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(24*a^5) + (5*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(36*a^3) + (x^5*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(9*a) - (5*ArcSin[a*x]^4)/(96*a^6) + (x^6*ArcSin[a*x]^4)/6","A",23,4,10,0.4000,1,"{4627, 4707, 4641, 30}"
33,1,250,0,0.662997,"\int x^4 \sin ^{-1}(a x)^4 \, dx","Int[x^4*ArcSin[a*x]^4,x]","\frac{1088 x^3}{16875 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{16 x^3 \sin ^{-1}(a x)^2}{75 a^2}+\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{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{16576 x}{5625 a^4}-\frac{32 x \sin ^{-1}(a x)^2}{25 a^4}+\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}","\frac{1088 x^3}{16875 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{16 x^3 \sin ^{-1}(a x)^2}{75 a^2}+\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{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{16576 x}{5625 a^4}-\frac{32 x \sin ^{-1}(a x)^2}{25 a^4}+\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,"(16576*x)/(5625*a^4) + (1088*x^3)/(16875*a^2) + (24*x^5)/3125 - (16576*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(5625*a^5) - (1088*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(5625*a^3) - (24*x^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(625*a) - (32*x*ArcSin[a*x]^2)/(25*a^4) - (16*x^3*ArcSin[a*x]^2)/(75*a^2) - (12*x^5*ArcSin[a*x]^2)/125 + (32*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(75*a^5) + (16*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(75*a^3) + (4*x^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(25*a) + (x^5*ArcSin[a*x]^4)/5","A",19,6,10,0.6000,1,"{4627, 4707, 4677, 4619, 8, 30}"
34,1,198,0,0.5160773,"\int x^3 \sin ^{-1}(a x)^4 \, dx","Int[x^3*ArcSin[a*x]^4,x]","\frac{45 x^2}{128 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{9 x^2 \sin ^{-1}(a x)^2}{16 a^2}+\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{3 \sin ^{-1}(a x)^4}{32 a^4}+\frac{45 \sin ^{-1}(a x)^2}{128 a^4}+\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}","\frac{45 x^2}{128 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{9 x^2 \sin ^{-1}(a x)^2}{16 a^2}+\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{3 \sin ^{-1}(a x)^4}{32 a^4}+\frac{45 \sin ^{-1}(a x)^2}{128 a^4}+\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,"(45*x^2)/(128*a^2) + (3*x^4)/128 - (45*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(64*a^3) - (3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(32*a) + (45*ArcSin[a*x]^2)/(128*a^4) - (9*x^2*ArcSin[a*x]^2)/(16*a^2) - (3*x^4*ArcSin[a*x]^2)/16 + (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(8*a^3) + (x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(4*a) - (3*ArcSin[a*x]^4)/(32*a^4) + (x^4*ArcSin[a*x]^4)/4","A",14,4,10,0.4000,1,"{4627, 4707, 4641, 30}"
35,1,166,0,0.3530411,"\int x^2 \sin ^{-1}(a x)^4 \, dx","Int[x^2*ArcSin[a*x]^4,x]","\frac{4 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a^3}-\frac{8 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a}-\frac{160 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a^3}+\frac{160 x}{27 a^2}-\frac{8 x \sin ^{-1}(a x)^2}{3 a^2}+\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}","\frac{4 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{9 a^3}-\frac{8 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a}-\frac{160 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a^3}+\frac{160 x}{27 a^2}-\frac{8 x \sin ^{-1}(a x)^2}{3 a^2}+\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,"(160*x)/(27*a^2) + (8*x^3)/81 - (160*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(27*a^3) - (8*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(27*a) - (8*x*ArcSin[a*x]^2)/(3*a^2) - (4*x^3*ArcSin[a*x]^2)/9 + (8*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(9*a^3) + (4*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(9*a) + (x^3*ArcSin[a*x]^4)/3","A",11,6,10,0.6000,1,"{4627, 4707, 4677, 4619, 8, 30}"
36,1,111,0,0.2376923,"\int x \sin ^{-1}(a x)^4 \, dx","Int[x*ArcSin[a*x]^4,x]","\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}","\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*x^2)/4 - (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(2*a) + (3*ArcSin[a*x]^2)/(4*a^2) - (3*x^2*ArcSin[a*x]^2)/2 + (x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/a - ArcSin[a*x]^4/(4*a^2) + (x^2*ArcSin[a*x]^4)/2","A",7,4,8,0.5000,1,"{4627, 4707, 4641, 30}"
37,1,69,0,0.1178542,"\int \sin ^{-1}(a x)^4 \, dx","Int[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",5,3,6,0.5000,1,"{4619, 4677, 8}"
38,1,113,0,0.122287,"\int \frac{\sin ^{-1}(a x)^4}{x} \, dx","Int[ArcSin[a*x]^4/x,x]","-2 i \sin ^{-1}(a x)^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+3 \sin ^{-1}(a x)^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(a x)}\right)+3 i \sin ^{-1}(a x) \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,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{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+3 \sin ^{-1}(a x)^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(a x)}\right)+3 i \sin ^{-1}(a x) \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,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",8,7,10,0.7000,1,"{4625, 3717, 2190, 2531, 6609, 2282, 6589}"
39,1,156,0,0.1937636,"\int \frac{\sin ^{-1}(a x)^4}{x^2} \, dx","Int[ArcSin[a*x]^4/x^2,x]","12 i a \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-12 i a \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-24 a \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+24 a \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-24 i a \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+24 i a \text{PolyLog}\left(4,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)","12 i a \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-12 i a \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-24 a \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+24 a \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-24 i a \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+24 i a \text{PolyLog}\left(4,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,"-(ArcSin[a*x]^4/x) - 8*a*ArcSin[a*x]^3*ArcTanh[E^(I*ArcSin[a*x])] + (12*I)*a*ArcSin[a*x]^2*PolyLog[2, -E^(I*ArcSin[a*x])] - (12*I)*a*ArcSin[a*x]^2*PolyLog[2, E^(I*ArcSin[a*x])] - 24*a*ArcSin[a*x]*PolyLog[3, -E^(I*ArcSin[a*x])] + 24*a*ArcSin[a*x]*PolyLog[3, E^(I*ArcSin[a*x])] - (24*I)*a*PolyLog[4, -E^(I*ArcSin[a*x])] + (24*I)*a*PolyLog[4, E^(I*ArcSin[a*x])]","A",11,7,10,0.7000,1,"{4627, 4709, 4183, 2531, 6609, 2282, 6589}"
40,1,119,0,0.2161415,"\int \frac{\sin ^{-1}(a x)^4}{x^3} \, dx","Int[ArcSin[a*x]^4/x^3,x]","-6 i a^2 \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,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}","-6 i a^2 \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,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,"(-2*I)*a^2*ArcSin[a*x]^3 - (2*a*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/x - ArcSin[a*x]^4/(2*x^2) + 6*a^2*ArcSin[a*x]^2*Log[1 - E^((2*I)*ArcSin[a*x])] - (6*I)*a^2*ArcSin[a*x]*PolyLog[2, E^((2*I)*ArcSin[a*x])] + 3*a^2*PolyLog[3, E^((2*I)*ArcSin[a*x])]","A",8,8,10,0.8000,1,"{4627, 4681, 4625, 3717, 2190, 2531, 2282, 6589}"
41,1,276,0,0.410257,"\int \frac{\sin ^{-1}(a x)^4}{x^4} \, dx","Int[ArcSin[a*x]^4/x^4,x]","2 i a^3 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-2 i a^3 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-4 a^3 \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+4 a^3 \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(4,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{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{\sin ^{-1}(a x)^4}{3 x^3}","2 i a^3 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-2 i a^3 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-4 a^3 \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+4 a^3 \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(4,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{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{\sin ^{-1}(a x)^4}{3 x^3}",1,"(-2*a^2*ArcSin[a*x]^2)/x - (2*a*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(3*x^2) - ArcSin[a*x]^4/(3*x^3) - 8*a^3*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])] - (4*a^3*ArcSin[a*x]^3*ArcTanh[E^(I*ArcSin[a*x])])/3 + (4*I)*a^3*PolyLog[2, -E^(I*ArcSin[a*x])] + (2*I)*a^3*ArcSin[a*x]^2*PolyLog[2, -E^(I*ArcSin[a*x])] - (4*I)*a^3*PolyLog[2, E^(I*ArcSin[a*x])] - (2*I)*a^3*ArcSin[a*x]^2*PolyLog[2, E^(I*ArcSin[a*x])] - 4*a^3*ArcSin[a*x]*PolyLog[3, -E^(I*ArcSin[a*x])] + 4*a^3*ArcSin[a*x]*PolyLog[3, E^(I*ArcSin[a*x])] - (4*I)*a^3*PolyLog[4, -E^(I*ArcSin[a*x])] + (4*I)*a^3*PolyLog[4, E^(I*ArcSin[a*x])]","A",19,10,10,1.000,1,"{4627, 4701, 4709, 4183, 2531, 6609, 2282, 6589, 2279, 2391}"
42,1,55,0,0.0965148,"\int \frac{x^6}{\sin ^{-1}(a x)} \, dx","Int[x^6/ArcSin[a*x],x]","\frac{5 \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{64 a^7}-\frac{9 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{64 a^7}+\frac{5 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{64 a^7}-\frac{\text{CosIntegral}\left(7 \sin ^{-1}(a x)\right)}{64 a^7}","\frac{5 \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{64 a^7}-\frac{9 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{64 a^7}+\frac{5 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{64 a^7}-\frac{\text{CosIntegral}\left(7 \sin ^{-1}(a x)\right)}{64 a^7}",1,"(5*CosIntegral[ArcSin[a*x]])/(64*a^7) - (9*CosIntegral[3*ArcSin[a*x]])/(64*a^7) + (5*CosIntegral[5*ArcSin[a*x]])/(64*a^7) - CosIntegral[7*ArcSin[a*x]]/(64*a^7)","A",7,3,10,0.3000,1,"{4635, 4406, 3302}"
43,1,43,0,0.0803015,"\int \frac{x^5}{\sin ^{-1}(a x)} \, dx","Int[x^5/ArcSin[a*x],x]","\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}","\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]])/(32*a^6) - SinIntegral[4*ArcSin[a*x]]/(8*a^6) + SinIntegral[6*ArcSin[a*x]]/(32*a^6)","A",6,3,10,0.3000,1,"{4635, 4406, 3299}"
44,1,41,0,0.080892,"\int \frac{x^4}{\sin ^{-1}(a x)} \, dx","Int[x^4/ArcSin[a*x],x]","\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{16 a^5}+\frac{\text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{16 a^5}","\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{16 a^5}+\frac{\text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{16 a^5}",1,"CosIntegral[ArcSin[a*x]]/(8*a^5) - (3*CosIntegral[3*ArcSin[a*x]])/(16*a^5) + CosIntegral[5*ArcSin[a*x]]/(16*a^5)","A",6,3,10,0.3000,1,"{4635, 4406, 3302}"
45,1,29,0,0.0623942,"\int \frac{x^3}{\sin ^{-1}(a x)} \, dx","Int[x^3/ArcSin[a*x],x]","\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}","\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,"SinIntegral[2*ArcSin[a*x]]/(4*a^4) - SinIntegral[4*ArcSin[a*x]]/(8*a^4)","A",5,3,10,0.3000,1,"{4635, 4406, 3299}"
46,1,27,0,0.0631485,"\int \frac{x^2}{\sin ^{-1}(a x)} \, dx","Int[x^2/ArcSin[a*x],x]","\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{4 a^3}-\frac{\text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{4 a^3}","\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{4 a^3}-\frac{\text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{4 a^3}",1,"CosIntegral[ArcSin[a*x]]/(4*a^3) - CosIntegral[3*ArcSin[a*x]]/(4*a^3)","A",5,3,10,0.3000,1,"{4635, 4406, 3302}"
47,1,14,0,0.0349063,"\int \frac{x}{\sin ^{-1}(a x)} \, dx","Int[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",4,4,8,0.5000,1,"{4635, 4406, 12, 3299}"
48,1,9,0,0.0168823,"\int \frac{1}{\sin ^{-1}(a x)} \, dx","Int[ArcSin[a*x]^(-1),x]","\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{a}","\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{a}",1,"CosIntegral[ArcSin[a*x]]/a","A",2,2,6,0.3333,1,"{4623, 3302}"
49,0,0,0,0.0131449,"\int \frac{1}{x \sin ^{-1}(a x)} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.0141847,"\int \frac{1}{x^2 \sin ^{-1}(a x)} \, dx","Int[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,"Defer[Int][1/(x^2*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
51,1,83,0,0.0744056,"\int \frac{x^6}{\sin ^{-1}(a x)^2} \, dx","Int[x^6/ArcSin[a*x]^2,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)}","-\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,"-((x^6*Sqrt[1 - a^2*x^2])/(a*ArcSin[a*x])) - (5*SinIntegral[ArcSin[a*x]])/(64*a^7) + (27*SinIntegral[3*ArcSin[a*x]])/(64*a^7) - (25*SinIntegral[5*ArcSin[a*x]])/(64*a^7) + (7*SinIntegral[7*ArcSin[a*x]])/(64*a^7)","A",6,2,10,0.2000,1,"{4631, 3299}"
52,1,71,0,0.0634923,"\int \frac{x^5}{\sin ^{-1}(a x)^2} \, dx","Int[x^5/ArcSin[a*x]^2,x]","\frac{5 \text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{16 a^6}-\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{2 a^6}+\frac{3 \text{CosIntegral}\left(6 \sin ^{-1}(a x)\right)}{16 a^6}-\frac{x^5 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}","\frac{5 \text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{16 a^6}-\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{2 a^6}+\frac{3 \text{CosIntegral}\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,"-((x^5*Sqrt[1 - a^2*x^2])/(a*ArcSin[a*x])) + (5*CosIntegral[2*ArcSin[a*x]])/(16*a^6) - CosIntegral[4*ArcSin[a*x]]/(2*a^6) + (3*CosIntegral[6*ArcSin[a*x]])/(16*a^6)","A",5,2,10,0.2000,1,"{4631, 3302}"
53,1,69,0,0.0576204,"\int \frac{x^4}{\sin ^{-1}(a x)^2} \, dx","Int[x^4/ArcSin[a*x]^2,x]","-\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)}","-\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,"-((x^4*Sqrt[1 - a^2*x^2])/(a*ArcSin[a*x])) - SinIntegral[ArcSin[a*x]]/(8*a^5) + (9*SinIntegral[3*ArcSin[a*x]])/(16*a^5) - (5*SinIntegral[5*ArcSin[a*x]])/(16*a^5)","A",5,2,10,0.2000,1,"{4631, 3299}"
54,1,57,0,0.0486051,"\int \frac{x^3}{\sin ^{-1}(a x)^2} \, dx","Int[x^3/ArcSin[a*x]^2,x]","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^4}-\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{2 a^4}-\frac{x^3 \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^4}-\frac{\text{CosIntegral}\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,"-((x^3*Sqrt[1 - a^2*x^2])/(a*ArcSin[a*x])) + CosIntegral[2*ArcSin[a*x]]/(2*a^4) - CosIntegral[4*ArcSin[a*x]]/(2*a^4)","A",4,2,10,0.2000,1,"{4631, 3302}"
55,1,55,0,0.0439644,"\int \frac{x^2}{\sin ^{-1}(a x)^2} \, dx","Int[x^2/ArcSin[a*x]^2,x]","-\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)}","-\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,"-((x^2*Sqrt[1 - a^2*x^2])/(a*ArcSin[a*x])) - SinIntegral[ArcSin[a*x]]/(4*a^3) + (3*SinIntegral[3*ArcSin[a*x]])/(4*a^3)","A",4,2,10,0.2000,1,"{4631, 3299}"
56,1,38,0,0.0247518,"\int \frac{x}{\sin ^{-1}(a x)^2} \, dx","Int[x/ArcSin[a*x]^2,x]","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}",1,"-((x*Sqrt[1 - a^2*x^2])/(a*ArcSin[a*x])) + CosIntegral[2*ArcSin[a*x]]/a^2","A",2,2,8,0.2500,1,"{4631, 3302}"
57,1,36,0,0.0779915,"\int \frac{1}{\sin ^{-1}(a x)^2} \, dx","Int[ArcSin[a*x]^(-2),x]","-\frac{\sqrt{1-a^2 x^2}}{a \sin ^{-1}(a x)}-\frac{\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]/(a*ArcSin[a*x])) - SinIntegral[ArcSin[a*x]]/a","A",3,3,6,0.5000,1,"{4621, 4723, 3299}"
58,0,0,0,0.0120926,"\int \frac{1}{x \sin ^{-1}(a x)^2} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]^2), x]","A",0,0,0,0,-1,"{}"
59,0,0,0,0.0136797,"\int \frac{1}{x^2 \sin ^{-1}(a x)^2} \, dx","Int[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,"Defer[Int][1/(x^2*ArcSin[a*x]^2), x]","A",0,0,0,0,-1,"{}"
60,1,98,0,0.3428069,"\int \frac{x^4}{\sin ^{-1}(a x)^3} \, dx","Int[x^4/ArcSin[a*x]^3,x]","-\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{32 a^5}-\frac{25 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{32 a^5}-\frac{x^4 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{2 x^3}{a^2 \sin ^{-1}(a x)}+\frac{5 x^5}{2 \sin ^{-1}(a x)}","-\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{32 a^5}-\frac{25 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{32 a^5}-\frac{x^4 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{2 x^3}{a^2 \sin ^{-1}(a x)}+\frac{5 x^5}{2 \sin ^{-1}(a x)}",1,"-(x^4*Sqrt[1 - a^2*x^2])/(2*a*ArcSin[a*x]^2) - (2*x^3)/(a^2*ArcSin[a*x]) + (5*x^5)/(2*ArcSin[a*x]) - CosIntegral[ArcSin[a*x]]/(16*a^5) + (27*CosIntegral[3*ArcSin[a*x]])/(32*a^5) - (25*CosIntegral[5*ArcSin[a*x]])/(32*a^5)","A",14,5,10,0.5000,1,"{4633, 4719, 4635, 4406, 3302}"
61,1,83,0,0.2998427,"\int \frac{x^3}{\sin ^{-1}(a x)^3} \, dx","Int[x^3/ArcSin[a*x]^3,x]","-\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{x^3 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \sin ^{-1}(a x)}+\frac{2 x^4}{\sin ^{-1}(a x)}","-\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{x^3 \sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \sin ^{-1}(a x)}+\frac{2 x^4}{\sin ^{-1}(a x)}",1,"-(x^3*Sqrt[1 - a^2*x^2])/(2*a*ArcSin[a*x]^2) - (3*x^2)/(2*a^2*ArcSin[a*x]) + (2*x^4)/ArcSin[a*x] - SinIntegral[2*ArcSin[a*x]]/(2*a^4) + SinIntegral[4*ArcSin[a*x]]/a^4","A",12,6,10,0.6000,1,"{4633, 4719, 4635, 4406, 3299, 12}"
62,1,82,0,0.2486645,"\int \frac{x^2}{\sin ^{-1}(a x)^3} \, dx","Int[x^2/ArcSin[a*x]^3,x]","-\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{CosIntegral}\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)}","-\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{CosIntegral}\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,"-(x^2*Sqrt[1 - a^2*x^2])/(2*a*ArcSin[a*x]^2) - x/(a^2*ArcSin[a*x]) + (3*x^3)/(2*ArcSin[a*x]) - CosIntegral[ArcSin[a*x]]/(8*a^3) + (9*CosIntegral[3*ArcSin[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{4633, 4719, 4635, 4406, 3302, 4623}"
63,1,64,0,0.168357,"\int \frac{x}{\sin ^{-1}(a x)^3} \, dx","Int[x/ArcSin[a*x]^3,x]","-\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)}","-\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,"-(x*Sqrt[1 - a^2*x^2])/(2*a*ArcSin[a*x]^2) - 1/(2*a^2*ArcSin[a*x]) + x^2/ArcSin[a*x] - SinIntegral[2*ArcSin[a*x]]/a^2","A",7,7,8,0.8750,1,"{4633, 4719, 4635, 4406, 12, 3299, 4641}"
64,1,51,0,0.0845015,"\int \frac{1}{\sin ^{-1}(a x)^3} \, dx","Int[ArcSin[a*x]^(-3),x]","-\frac{\sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{2 a}+\frac{x}{2 \sin ^{-1}(a x)}","-\frac{\sqrt{1-a^2 x^2}}{2 a \sin ^{-1}(a x)^2}-\frac{\text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{2 a}+\frac{x}{2 \sin ^{-1}(a x)}",1,"-Sqrt[1 - a^2*x^2]/(2*a*ArcSin[a*x]^2) + x/(2*ArcSin[a*x]) - CosIntegral[ArcSin[a*x]]/(2*a)","A",4,4,6,0.6667,1,"{4621, 4719, 4623, 3302}"
65,0,0,0,0.0124023,"\int \frac{1}{x \sin ^{-1}(a x)^3} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]^3), x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0133543,"\int \frac{1}{x^2 \sin ^{-1}(a x)^3} \, dx","Int[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,"Defer[Int][1/(x^2*ArcSin[a*x]^3), x]","A",0,0,0,0,-1,"{}"
67,1,158,0,0.3142408,"\int \frac{x^4}{\sin ^{-1}(a x)^4} \, dx","Int[x^4/ArcSin[a*x]^4,x]","\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{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^3}{3 a^2 \sin ^{-1}(a x)^2}-\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}","\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{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^3}{3 a^2 \sin ^{-1}(a x)^2}-\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,"-(x^4*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^3) - (2*x^3)/(3*a^2*ArcSin[a*x]^2) + (5*x^5)/(6*ArcSin[a*x]^2) - (2*x^2*Sqrt[1 - a^2*x^2])/(a^3*ArcSin[a*x]) + (25*x^4*Sqrt[1 - a^2*x^2])/(6*a*ArcSin[a*x]) + SinIntegral[ArcSin[a*x]]/(48*a^5) - (27*SinIntegral[3*ArcSin[a*x]])/(32*a^5) + (125*SinIntegral[5*ArcSin[a*x]])/(96*a^5)","A",12,4,10,0.4000,1,"{4633, 4719, 4631, 3299}"
68,1,144,0,0.2816779,"\int \frac{x^3}{\sin ^{-1}(a x)^4} \, dx","Int[x^3/ArcSin[a*x]^4,x]","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{3 a^4}+\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^2}{2 a^2 \sin ^{-1}(a x)^2}-\frac{x \sqrt{1-a^2 x^2}}{a^3 \sin ^{-1}(a x)}+\frac{2 x^4}{3 \sin ^{-1}(a x)^2}","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{3 a^4}+\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^2}{2 a^2 \sin ^{-1}(a x)^2}-\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,"-(x^3*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^3) - x^2/(2*a^2*ArcSin[a*x]^2) + (2*x^4)/(3*ArcSin[a*x]^2) - (x*Sqrt[1 - a^2*x^2])/(a^3*ArcSin[a*x]) + (8*x^3*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]) - CosIntegral[2*ArcSin[a*x]]/(3*a^4) + (4*CosIntegral[4*ArcSin[a*x]])/(3*a^4)","A",9,4,10,0.4000,1,"{4633, 4719, 4631, 3302}"
69,1,141,0,0.3034095,"\int \frac{x^2}{\sin ^{-1}(a x)^4} \, dx","Int[x^2/ArcSin[a*x]^4,x]","\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{\sqrt{1-a^2 x^2}}{3 a^3 \sin ^{-1}(a x)}-\frac{x}{3 a^2 \sin ^{-1}(a x)^2}+\frac{x^3}{2 \sin ^{-1}(a x)^2}","\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{\sqrt{1-a^2 x^2}}{3 a^3 \sin ^{-1}(a x)}-\frac{x}{3 a^2 \sin ^{-1}(a x)^2}+\frac{x^3}{2 \sin ^{-1}(a x)^2}",1,"-(x^2*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^3) - x/(3*a^2*ArcSin[a*x]^2) + x^3/(2*ArcSin[a*x]^2) - Sqrt[1 - a^2*x^2]/(3*a^3*ArcSin[a*x]) + (3*x^2*Sqrt[1 - a^2*x^2])/(2*a*ArcSin[a*x]) + SinIntegral[ArcSin[a*x]]/(24*a^3) - (9*SinIntegral[3*ArcSin[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{4633, 4719, 4631, 3299, 4621, 4723}"
70,1,97,0,0.1636074,"\int \frac{x}{\sin ^{-1}(a x)^4} \, dx","Int[x/ArcSin[a*x]^4,x]","-\frac{2 \text{CosIntegral}\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}","-\frac{2 \text{CosIntegral}\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,"-(x*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^3) - 1/(6*a^2*ArcSin[a*x]^2) + x^2/(3*ArcSin[a*x]^2) + (2*x*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]) - (2*CosIntegral[2*ArcSin[a*x]])/(3*a^2)","A",5,5,8,0.6250,1,"{4633, 4719, 4631, 3302, 4641}"
71,1,78,0,0.1527118,"\int \frac{1}{\sin ^{-1}(a x)^4} \, dx","Int[ArcSin[a*x]^(-4),x]","\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}","\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,"-Sqrt[1 - a^2*x^2]/(3*a*ArcSin[a*x]^3) + x/(6*ArcSin[a*x]^2) + Sqrt[1 - a^2*x^2]/(6*a*ArcSin[a*x]) + SinIntegral[ArcSin[a*x]]/(6*a)","A",5,4,6,0.6667,1,"{4621, 4719, 4723, 3299}"
72,0,0,0,0.0124201,"\int \frac{1}{x \sin ^{-1}(a x)^4} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]^4), x]","A",0,0,0,0,-1,"{}"
73,0,0,0,0.0140271,"\int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx","Int[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,"Defer[Int][1/(x^2*ArcSin[a*x]^4), x]","A",0,0,0,0,-1,"{}"
74,1,121,0,0.2415091,"\int x^4 \sqrt{\sin ^{-1}(a x)} \, dx","Int[x^4*Sqrt[ArcSin[a*x]],x]","-\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)}","-\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,"(x^5*Sqrt[ArcSin[a*x]])/5 - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^5) - (Sqrt[Pi/10]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(80*a^5)","A",10,5,12,0.4167,1,"{4629, 4723, 3312, 3305, 3351}"
75,1,95,0,0.1894162,"\int x^3 \sqrt{\sin ^{-1}(a x)} \, dx","Int[x^3*Sqrt[ArcSin[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{64 a^4}+\frac{\sqrt{\pi } \text{FresnelC}\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)}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{64 a^4}+\frac{\sqrt{\pi } \text{FresnelC}\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,"(-3*Sqrt[ArcSin[a*x]])/(32*a^4) + (x^4*Sqrt[ArcSin[a*x]])/4 - (Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(64*a^4) + (Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(16*a^4)","A",8,5,12,0.4167,1,"{4629, 4723, 3312, 3304, 3352}"
76,1,86,0,0.1808751,"\int x^2 \sqrt{\sin ^{-1}(a x)} \, dx","Int[x^2*Sqrt[ArcSin[a*x]],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)}","-\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,"(x^3*Sqrt[ArcSin[a*x]])/3 - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^3) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(12*a^3)","A",8,5,12,0.4167,1,"{4629, 4723, 3312, 3305, 3351}"
77,1,59,0,0.1507847,"\int x \sqrt{\sin ^{-1}(a x)} \, dx","Int[x*Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\pi } \text{FresnelC}\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)}","\frac{\sqrt{\pi } \text{FresnelC}\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,"-Sqrt[ArcSin[a*x]]/(4*a^2) + (x^2*Sqrt[ArcSin[a*x]])/2 + (Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(8*a^2)","A",6,5,10,0.5000,1,"{4629, 4723, 3312, 3304, 3352}"
78,1,44,0,0.0896557,"\int \sqrt{\sin ^{-1}(a x)} \, dx","Int[Sqrt[ArcSin[a*x]],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}","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,"x*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a","A",4,4,8,0.5000,1,"{4619, 4723, 3305, 3351}"
79,0,0,0,0.0127665,"\int \frac{\sqrt{\sin ^{-1}(a x)}}{x} \, dx","Int[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,"Defer[Int][Sqrt[ArcSin[a*x]]/x, x]","A",0,0,0,0,-1,"{}"
80,1,282,0,0.5325585,"\int x^4 \sin ^{-1}(a x)^{3/2} \, dx","Int[x^4*ArcSin[a*x]^(3/2),x]","-\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{25 a^5}-\frac{11 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{400 a^5}+\frac{3 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{800 a^5}+\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{50 a^5}-\frac{3 \sqrt{\frac{\pi }{10}} \text{FresnelC}\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{2 x^2 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{25 a^3}+\frac{4 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \sin ^{-1}(a x)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{32 a^5}-\frac{3 \sqrt{\frac{\pi }{10}} \text{FresnelC}\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{2 x^2 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{25 a^3}+\frac{4 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \sin ^{-1}(a x)^{3/2}",1,"(4*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(25*a^5) + (2*x^2*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(25*a^3) + (3*x^4*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(50*a) + (x^5*ArcSin[a*x]^(3/2))/5 - (11*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(400*a^5) - (2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(25*a^5) + (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(50*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(800*a^5) - (3*Sqrt[Pi/10]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(800*a^5)","A",23,8,12,0.6667,1,"{4629, 4707, 4677, 4623, 3304, 3352, 4635, 4406}"
81,1,157,0,0.378891,"\int x^3 \sin ^{-1}(a x)^{3/2} \, dx","Int[x^3*ArcSin[a*x]^(3/2),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 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{3 \sin ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^{3/2}","\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 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{3 \sin ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^{3/2}",1,"(9*x*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(64*a^3) + (3*x^3*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(32*a) - (3*ArcSin[a*x]^(3/2))/(32*a^4) + (x^4*ArcSin[a*x]^(3/2))/4 + (3*Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(512*a^4) - (3*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(64*a^4)","A",16,8,12,0.6667,1,"{4629, 4707, 4641, 4635, 4406, 12, 3305, 3351}"
82,1,147,0,0.302717,"\int x^2 \sin ^{-1}(a x)^{3/2} \, dx","Int[x^2*ArcSin[a*x]^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\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}","-\frac{3 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\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[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(3*a^3) + (x^2*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(6*a) + (x^3*ArcSin[a*x]^(3/2))/3 - (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^3) + (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(24*a^3)","A",13,8,12,0.6667,1,"{4629, 4707, 4677, 4623, 3304, 3352, 4635, 4406}"
83,1,89,0,0.1827851,"\int x \sin ^{-1}(a x)^{3/2} \, dx","Int[x*ArcSin[a*x]^(3/2),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}","-\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,"(3*x*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(8*a) - ArcSin[a*x]^(3/2)/(4*a^2) + (x^2*ArcSin[a*x]^(3/2))/2 - (3*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(32*a^2)","A",8,8,10,0.8000,1,"{4629, 4707, 4641, 4635, 4406, 12, 3305, 3351}"
84,1,75,0,0.0991487,"\int \sin ^{-1}(a x)^{3/2} \, dx","Int[ArcSin[a*x]^(3/2),x]","\frac{3 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{2 a}-\frac{3 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a}+x \sin ^{-1}(a x)^{3/2}","\frac{3 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{2 a}-\frac{3 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a}+x \sin ^{-1}(a x)^{3/2}",1,"(3*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(2*a) + x*ArcSin[a*x]^(3/2) - (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a)","A",5,5,8,0.6250,1,"{4619, 4677, 4623, 3304, 3352}"
85,0,0,0,0.0131838,"\int \frac{\sin ^{-1}(a x)^{3/2}}{x} \, dx","Int[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,"Defer[Int][ArcSin[a*x]^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
86,1,298,0,0.803417,"\int x^4 \sin ^{-1}(a x)^{5/2} \, dx","Int[x^4*ArcSin[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{320 a^5}-\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{60 a^5}+\frac{3 \sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{1600 a^5}+\frac{x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{10 a}-\frac{x^3 \sqrt{\sin ^{-1}(a x)}}{15 a^2}+\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{15 a^3}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{15 a^5}-\frac{2 x \sqrt{\sin ^{-1}(a x)}}{5 a^4}+\frac{1}{5} x^5 \sin ^{-1}(a x)^{5/2}-\frac{3}{100} x^5 \sqrt{\sin ^{-1}(a x)}","\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{x^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{10 a}-\frac{x^3 \sqrt{\sin ^{-1}(a x)}}{15 a^2}+\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{15 a^3}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{15 a^5}-\frac{2 x \sqrt{\sin ^{-1}(a x)}}{5 a^4}+\frac{1}{5} x^5 \sin ^{-1}(a x)^{5/2}-\frac{3}{100} x^5 \sqrt{\sin ^{-1}(a x)}",1,"(-2*x*Sqrt[ArcSin[a*x]])/(5*a^4) - (x^3*Sqrt[ArcSin[a*x]])/(15*a^2) - (3*x^5*Sqrt[ArcSin[a*x]])/100 + (4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(15*a^5) + (2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(15*a^3) + (x^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(10*a) + (x^5*ArcSin[a*x]^(5/2))/5 + (15*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(32*a^5) - (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(60*a^5) - (Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(320*a^5) + (3*Sqrt[Pi/10]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(1600*a^5)","A",26,8,12,0.6667,1,"{4629, 4707, 4677, 4619, 4723, 3305, 3351, 3312}"
87,1,205,0,0.6003908,"\int x^3 \sin ^{-1}(a x)^{5/2} \, dx","Int[x^3*ArcSin[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4096 a^4}-\frac{15 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{256 a^4}+\frac{5 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{32 a}-\frac{45 x^2 \sqrt{\sin ^{-1}(a x)}}{256 a^2}+\frac{15 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \sin ^{-1}(a x)^{5/2}}{32 a^4}+\frac{225 \sqrt{\sin ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^{5/2}-\frac{15}{256} x^4 \sqrt{\sin ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4096 a^4}-\frac{15 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{256 a^4}+\frac{5 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{32 a}-\frac{45 x^2 \sqrt{\sin ^{-1}(a x)}}{256 a^2}+\frac{15 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \sin ^{-1}(a x)^{5/2}}{32 a^4}+\frac{225 \sqrt{\sin ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \sin ^{-1}(a x)^{5/2}-\frac{15}{256} x^4 \sqrt{\sin ^{-1}(a x)}",1,"(225*Sqrt[ArcSin[a*x]])/(2048*a^4) - (45*x^2*Sqrt[ArcSin[a*x]])/(256*a^2) - (15*x^4*Sqrt[ArcSin[a*x]])/256 + (15*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(64*a^3) + (5*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(32*a) - (3*ArcSin[a*x]^(5/2))/(32*a^4) + (x^4*ArcSin[a*x]^(5/2))/4 + (15*Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4096*a^4) - (15*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(256*a^4)","A",18,7,12,0.5833,1,"{4629, 4707, 4641, 4723, 3312, 3304, 3352}"
88,1,178,0,0.4691996,"\int x^2 \sin ^{-1}(a x)^{5/2} \, dx","Int[x^2*ArcSin[a*x]^(5/2),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 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{9 a^3}-\frac{5 x \sqrt{\sin ^{-1}(a x)}}{6 a^2}+\frac{1}{3} x^3 \sin ^{-1}(a x)^{5/2}-\frac{5}{36} x^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 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{9 a^3}-\frac{5 x \sqrt{\sin ^{-1}(a x)}}{6 a^2}+\frac{1}{3} x^3 \sin ^{-1}(a x)^{5/2}-\frac{5}{36} x^3 \sqrt{\sin ^{-1}(a x)}",1,"(-5*x*Sqrt[ArcSin[a*x]])/(6*a^2) - (5*x^3*Sqrt[ArcSin[a*x]])/36 + (5*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(9*a^3) + (5*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(18*a) + (x^3*ArcSin[a*x]^(5/2))/3 + (15*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^3) - (5*Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(144*a^3)","A",15,8,12,0.6667,1,"{4629, 4707, 4677, 4619, 4723, 3305, 3351, 3312}"
89,1,119,0,0.312713,"\int x \sin ^{-1}(a x)^{5/2} \, dx","Int[x*ArcSin[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{FresnelC}\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)}","-\frac{15 \sqrt{\pi } \text{FresnelC}\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,"(15*Sqrt[ArcSin[a*x]])/(64*a^2) - (15*x^2*Sqrt[ArcSin[a*x]])/32 + (5*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(8*a) - ArcSin[a*x]^(5/2)/(4*a^2) + (x^2*ArcSin[a*x]^(5/2))/2 - (15*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(128*a^2)","A",9,7,10,0.7000,1,"{4629, 4707, 4641, 4723, 3312, 3304, 3352}"
90,1,88,0,0.1649649,"\int \sin ^{-1}(a x)^{5/2} \, dx","Int[ArcSin[a*x]^(5/2),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)}","\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,"(-15*x*Sqrt[ArcSin[a*x]])/4 + (5*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(2*a) + x*ArcSin[a*x]^(5/2) + (15*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a)","A",6,5,8,0.6250,1,"{4619, 4677, 4723, 3305, 3351}"
91,0,0,0,0.0125499,"\int \frac{\sin ^{-1}(a x)^{5/2}}{x} \, dx","Int[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,"Defer[Int][ArcSin[a*x]^(5/2)/x, x]","A",0,0,0,0,-1,"{}"
92,1,106,0,0.1116078,"\int \frac{x^4}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[x^4/Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}+\frac{\sqrt{\frac{\pi }{10}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}","\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}+\frac{\sqrt{\frac{\pi }{10}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^5}",1,"(Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^5) - (Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5) + (Sqrt[Pi/10]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5)","A",9,4,12,0.3333,1,"{4635, 4406, 3304, 3352}"
93,1,65,0,0.0826256,"\int \frac{x^3}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[x^3/Sqrt[ArcSin[a*x]],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}","\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,"-(Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^4) + (Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(4*a^4)","A",7,4,12,0.3333,1,"{4635, 4406, 3305, 3351}"
94,1,71,0,0.0892158,"\int \frac{x^2}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[x^2/Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^3}","\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^3}",1,"(Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^3) - (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^3)","A",7,4,12,0.3333,1,"{4635, 4406, 3304, 3352}"
95,1,28,0,0.0447623,"\int \frac{x}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[x/Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a^2}","\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a^2}",1,"(Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a^2)","A",5,5,10,0.5000,1,"{4635, 4406, 12, 3305, 3351}"
96,1,30,0,0.0244487,"\int \frac{1}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[1/Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a}","\frac{\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a}",1,"(Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a","A",3,3,8,0.3750,1,"{4623, 3304, 3352}"
97,0,0,0,0.0141105,"\int \frac{1}{x \sqrt{\sin ^{-1}(a x)}} \, dx","Int[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,"Defer[Int][1/(x*Sqrt[ArcSin[a*x]]), x]","A",0,0,0,0,-1,"{}"
98,0,0,0,0.0131443,"\int \frac{1}{x^2 \sqrt{\sin ^{-1}(a x)}} \, dx","Int[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,"Defer[Int][1/(x^2*Sqrt[ArcSin[a*x]]), x]","A",0,0,0,0,-1,"{}"
99,1,171,0,0.1441803,"\int \frac{x^6}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[x^6/ArcSin[a*x]^(3/2),x]","-\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)}}","-\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,"(-2*x^6*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) - (5*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^7) + (9*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^7) - (5*Sqrt[(5*Pi)/2]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^7) + (Sqrt[(7*Pi)/2]*FresnelS[Sqrt[14/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^7)","A",10,3,12,0.2500,1,"{4631, 3305, 3351}"
100,1,127,0,0.1066074,"\int \frac{x^5}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[x^5/ArcSin[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^6}+\frac{\sqrt{3 \pi } \text{FresnelC}\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^6}+\frac{5 \sqrt{\pi } \text{FresnelC}\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)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^6}+\frac{\sqrt{3 \pi } \text{FresnelC}\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a^6}+\frac{5 \sqrt{\pi } \text{FresnelC}\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,"(-2*x^5*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) - (Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^6 + (Sqrt[3*Pi]*FresnelC[2*Sqrt[3/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^6) + (5*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(8*a^6)","A",8,3,12,0.2500,1,"{4631, 3304, 3352}"
101,1,136,0,0.098155,"\int \frac{x^4}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[x^4/ArcSin[a*x]^(3/2),x]","-\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)}}","-\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,"(-2*x^4*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^5) - (Sqrt[(5*Pi)/2]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^5)","A",8,3,12,0.2500,1,"{4631, 3305, 3351}"
102,1,90,0,0.0696889,"\int \frac{x^3}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[x^3/ArcSin[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^4}+\frac{\sqrt{\pi } \text{FresnelC}\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)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^4}+\frac{\sqrt{\pi } \text{FresnelC}\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,"(-2*x^3*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) - (Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^4 + (Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/a^4","A",6,3,12,0.2500,1,"{4631, 3304, 3352}"
103,1,96,0,0.0692069,"\int \frac{x^2}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[x^2/ArcSin[a*x]^(3/2),x]","-\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)}}","-\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,"(-2*x^2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^3 + (Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/a^3","A",6,3,12,0.2500,1,"{4631, 3305, 3351}"
104,1,55,0,0.031562,"\int \frac{x}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[x/ArcSin[a*x]^(3/2),x]","\frac{2 \sqrt{\pi } \text{FresnelC}\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)}}","\frac{2 \sqrt{\pi } \text{FresnelC}\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,"(-2*x*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) + (2*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/a^2","A",3,3,10,0.3000,1,"{4631, 3304, 3352}"
105,1,59,0,0.0904898,"\int \frac{1}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[ArcSin[a*x]^(-3/2),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}","-\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,"(-2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]]) - (2*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a","A",4,4,8,0.5000,1,"{4621, 4723, 3305, 3351}"
106,0,0,0,0.0136693,"\int \frac{1}{x \sin ^{-1}(a x)^{3/2}} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]^(3/2)), x]","A",0,0,0,0,-1,"{}"
107,1,235,0,0.4343862,"\int \frac{x^4}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[x^4/ArcSin[a*x]^(5/2),x]","\frac{4 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^5}-\frac{25 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^5}-\frac{4 \sqrt{\frac{2 \pi }{3}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a^5}+\frac{25 \sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^5}-\frac{5 \sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{6 a^5}-\frac{2 x^4 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{16 x^3}{3 a^2 \sqrt{\sin ^{-1}(a x)}}+\frac{20 x^5}{3 \sqrt{\sin ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^5}+\frac{3 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a^5}-\frac{5 \sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{6 a^5}-\frac{2 x^4 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{16 x^3}{3 a^2 \sqrt{\sin ^{-1}(a x)}}+\frac{20 x^5}{3 \sqrt{\sin ^{-1}(a x)}}",1,"(-2*x^4*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^(3/2)) - (16*x^3)/(3*a^2*Sqrt[ArcSin[a*x]]) + (20*x^5)/(3*Sqrt[ArcSin[a*x]]) - (25*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^5) + (4*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^5 + (25*Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^5) - (4*Sqrt[(2*Pi)/3]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/a^5 - (5*Sqrt[(5*Pi)/2]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(6*a^5)","A",19,6,12,0.5000,1,"{4633, 4719, 4635, 4406, 3304, 3352}"
108,1,126,0,0.338175,"\int \frac{x^3}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[x^3/ArcSin[a*x]^(5/2),x]","\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{2 x^3 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{4 x^2}{a^2 \sqrt{\sin ^{-1}(a x)}}+\frac{16 x^4}{3 \sqrt{\sin ^{-1}(a x)}}","\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{2 x^3 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{4 x^2}{a^2 \sqrt{\sin ^{-1}(a x)}}+\frac{16 x^4}{3 \sqrt{\sin ^{-1}(a x)}}",1,"(-2*x^3*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^(3/2)) - (4*x^2)/(a^2*Sqrt[ArcSin[a*x]]) + (16*x^4)/(3*Sqrt[ArcSin[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^4) - (4*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(3*a^4)","A",15,7,12,0.5833,1,"{4633, 4719, 4635, 4406, 3305, 3351, 12}"
109,1,125,0,0.3012039,"\int \frac{x^2}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[x^2/ArcSin[a*x]^(5/2),x]","-\frac{\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^3}+\frac{\sqrt{6 \pi } \text{FresnelC}\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)}}","-\frac{\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a^3}+\frac{\sqrt{6 \pi } \text{FresnelC}\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,"(-2*x^2*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^(3/2)) - (8*x)/(3*a^2*Sqrt[ArcSin[a*x]]) + (4*x^3)/Sqrt[ArcSin[a*x]] - (Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^3) + (Sqrt[6*Pi]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/a^3","A",13,7,12,0.5833,1,"{4633, 4719, 4635, 4406, 3304, 3352, 4623}"
110,1,89,0,0.1795316,"\int \frac{x}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[x/ArcSin[a*x]^(5/2),x]","-\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)}}","-\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,"(-2*x*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^(3/2)) - 4/(3*a^2*Sqrt[ArcSin[a*x]]) + (8*x^2)/(3*Sqrt[ArcSin[a*x]]) - (8*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(3*a^2)","A",8,8,10,0.8000,1,"{4633, 4719, 4635, 4406, 12, 3305, 3351, 4641}"
111,1,76,0,0.0989886,"\int \frac{1}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[ArcSin[a*x]^(-5/2),x]","-\frac{2 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{4 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a}+\frac{4 x}{3 \sqrt{\sin ^{-1}(a x)}}","-\frac{2 \sqrt{1-a^2 x^2}}{3 a \sin ^{-1}(a x)^{3/2}}-\frac{4 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a}+\frac{4 x}{3 \sqrt{\sin ^{-1}(a x)}}",1,"(-2*Sqrt[1 - a^2*x^2])/(3*a*ArcSin[a*x]^(3/2)) + (4*x)/(3*Sqrt[ArcSin[a*x]]) - (4*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a)","A",5,5,8,0.6250,1,"{4621, 4719, 4623, 3304, 3352}"
112,0,0,0,0.0133551,"\int \frac{1}{x \sin ^{-1}(a x)^{5/2}} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]^(5/2)), x]","A",0,0,0,0,-1,"{}"
113,1,264,0,0.3958697,"\int \frac{x^4}{\sin ^{-1}(a x)^{7/2}} \, dx","Int[x^4/ArcSin[a*x]^(7/2),x]","\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{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{16 x^3}{15 a^2 \sin ^{-1}(a x)^{3/2}}-\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}}","\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{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{16 x^3}{15 a^2 \sin ^{-1}(a x)^{3/2}}-\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,"(-2*x^4*Sqrt[1 - a^2*x^2])/(5*a*ArcSin[a*x]^(5/2)) - (16*x^3)/(15*a^2*ArcSin[a*x]^(3/2)) + (4*x^5)/(3*ArcSin[a*x]^(3/2)) - (32*x^2*Sqrt[1 - a^2*x^2])/(5*a^3*Sqrt[ArcSin[a*x]]) + (40*x^4*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[ArcSin[a*x]]) + (Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(15*a^5) - (5*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/a^5 + (8*Sqrt[6*Pi]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(5*a^5) + (5*Sqrt[(5*Pi)/2]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^5)","A",17,5,12,0.4167,1,"{4633, 4719, 4631, 3305, 3351}"
114,1,190,0,0.3187817,"\int \frac{x^3}{\sin ^{-1}(a x)^{7/2}} \, dx","Int[x^3/ArcSin[a*x]^(7/2),x]","\frac{32 \sqrt{2 \pi } \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{15 a^4}-\frac{16 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^4}+\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{4 x^2}{5 a^2 \sin ^{-1}(a x)^{3/2}}-\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}}","\frac{32 \sqrt{2 \pi } \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{15 a^4}-\frac{16 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^4}+\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{4 x^2}{5 a^2 \sin ^{-1}(a x)^{3/2}}-\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,"(-2*x^3*Sqrt[1 - a^2*x^2])/(5*a*ArcSin[a*x]^(5/2)) - (4*x^2)/(5*a^2*ArcSin[a*x]^(3/2)) + (16*x^4)/(15*ArcSin[a*x]^(3/2)) - (16*x*Sqrt[1 - a^2*x^2])/(5*a^3*Sqrt[ArcSin[a*x]]) + (128*x^3*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[ArcSin[a*x]]) + (32*Sqrt[2*Pi]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(15*a^4) - (16*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(15*a^4)","A",12,5,12,0.4167,1,"{4633, 4719, 4631, 3304, 3352}"
115,1,191,0,0.3476935,"\int \frac{x^2}{\sin ^{-1}(a x)^{7/2}} \, dx","Int[x^2/ArcSin[a*x]^(7/2),x]","\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{16 \sqrt{1-a^2 x^2}}{15 a^3 \sqrt{\sin ^{-1}(a x)}}-\frac{8 x}{15 a^2 \sin ^{-1}(a x)^{3/2}}+\frac{4 x^3}{5 \sin ^{-1}(a x)^{3/2}}","\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{16 \sqrt{1-a^2 x^2}}{15 a^3 \sqrt{\sin ^{-1}(a x)}}-\frac{8 x}{15 a^2 \sin ^{-1}(a x)^{3/2}}+\frac{4 x^3}{5 \sin ^{-1}(a x)^{3/2}}",1,"(-2*x^2*Sqrt[1 - a^2*x^2])/(5*a*ArcSin[a*x]^(5/2)) - (8*x)/(15*a^2*ArcSin[a*x]^(3/2)) + (4*x^3)/(5*ArcSin[a*x]^(3/2)) - (16*Sqrt[1 - a^2*x^2])/(15*a^3*Sqrt[ArcSin[a*x]]) + (24*x^2*Sqrt[1 - a^2*x^2])/(5*a*Sqrt[ArcSin[a*x]]) + (2*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(15*a^3) - (6*Sqrt[6*Pi]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcSin[a*x]]])/(5*a^3)","A",13,7,12,0.5833,1,"{4633, 4719, 4631, 3305, 3351, 4621, 4723}"
116,1,119,0,0.1716349,"\int \frac{x}{\sin ^{-1}(a x)^{7/2}} \, dx","Int[x/ArcSin[a*x]^(7/2),x]","-\frac{32 \sqrt{\pi } \text{FresnelC}\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}}","-\frac{32 \sqrt{\pi } \text{FresnelC}\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,"(-2*x*Sqrt[1 - a^2*x^2])/(5*a*ArcSin[a*x]^(5/2)) - 4/(15*a^2*ArcSin[a*x]^(3/2)) + (8*x^2)/(15*ArcSin[a*x]^(3/2)) + (32*x*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[ArcSin[a*x]]) - (32*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(15*a^2)","A",6,6,10,0.6000,1,"{4633, 4719, 4631, 3304, 3352, 4641}"
117,1,105,0,0.165702,"\int \frac{1}{\sin ^{-1}(a x)^{7/2}} \, dx","Int[ArcSin[a*x]^(-7/2),x]","\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}}","\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*Sqrt[1 - a^2*x^2])/(5*a*ArcSin[a*x]^(5/2)) + (4*x)/(15*ArcSin[a*x]^(3/2)) + (8*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[ArcSin[a*x]]) + (8*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(15*a)","A",6,5,8,0.6250,1,"{4621, 4719, 4723, 3305, 3351}"
118,0,0,0,0.0127218,"\int \frac{1}{x \sin ^{-1}(a x)^{7/2}} \, dx","Int[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,"Defer[Int][1/(x*ArcSin[a*x]^(7/2)), x]","A",0,0,0,0,-1,"{}"
119,0,0,0,0.1219135,"\int (b x)^m \sin ^{-1}(a x)^4 \, dx","Int[(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,"((b*x)^(1 + m)*ArcSin[a*x]^4)/(b*(1 + m)) - (4*a*Defer[Int][((b*x)^(1 + m)*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2], x])/(b*(1 + m))","A",0,0,0,0,-1,"{}"
120,0,0,0,0.1182263,"\int (b x)^m \sin ^{-1}(a x)^3 \, dx","Int[(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,"((b*x)^(1 + m)*ArcSin[a*x]^3)/(b*(1 + m)) - (3*a*Defer[Int][((b*x)^(1 + m)*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2], x])/(b*(1 + m))","A",0,0,0,0,-1,"{}"
121,1,150,0,0.1140862,"\int (b x)^m \sin ^{-1}(a x)^2 \, dx","Int[(b*x)^m*ArcSin[a*x]^2,x]","\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)}","\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,"((b*x)^(1 + m)*ArcSin[a*x]^2)/(b*(1 + m)) - (2*a*(b*x)^(2 + m)*ArcSin[a*x]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(b^2*(1 + m)*(2 + m)) + (2*a^2*(b*x)^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, a^2*x^2])/(b^3*(1 + m)*(2 + m)*(3 + m))","A",2,2,12,0.1667,1,"{4627, 4711}"
122,1,69,0,0.0252512,"\int (b x)^m \sin ^{-1}(a x) \, dx","Int[(b*x)^m*ArcSin[a*x],x]","\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)}","\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,"((b*x)^(1 + m)*ArcSin[a*x])/(b*(1 + m)) - (a*(b*x)^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(b^2*(1 + m)*(2 + m))","A",2,2,10,0.2000,1,"{4627, 364}"
123,0,0,0,0.0165568,"\int \frac{(b x)^m}{\sin ^{-1}(a x)} \, dx","Int[(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,"Defer[Int][(b*x)^m/ArcSin[a*x], x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.0153909,"\int \frac{(b x)^m}{\sin ^{-1}(a x)^2} \, dx","Int[(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,"Defer[Int][(b*x)^m/ArcSin[a*x]^2, x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.016084,"\int (b x)^m \sin ^{-1}(a x)^{3/2} \, dx","Int[(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,"Defer[Int][(b*x)^m*ArcSin[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
126,0,0,0,0.0152887,"\int (b x)^m \sqrt{\sin ^{-1}(a x)} \, dx","Int[(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,"Defer[Int][(b*x)^m*Sqrt[ArcSin[a*x]], x]","A",0,0,0,0,-1,"{}"
127,0,0,0,0.0153915,"\int \frac{(b x)^m}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[(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,"Defer[Int][(b*x)^m/Sqrt[ArcSin[a*x]], x]","A",0,0,0,0,-1,"{}"
128,0,0,0,0.0151034,"\int \frac{(b x)^m}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[(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,"Defer[Int][(b*x)^m/ArcSin[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
129,0,0,0,0.0156084,"\int (b x)^m \sin ^{-1}(a x)^n \, dx","Int[(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,"Defer[Int][(b*x)^m*ArcSin[a*x]^n, x]","A",0,0,0,0,-1,"{}"
130,1,167,0,0.1768532,"\int x^3 \sin ^{-1}(a x)^n \, dx","Int[x^3*ArcSin[a*x]^n,x]","-\frac{2^{-n-4} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{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} \text{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 \text{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 \text{Gamma}\left(n+1,4 i \sin ^{-1}(a x)\right)}{a^4}","-\frac{2^{-n-4} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{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} \text{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 \text{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 \text{Gamma}\left(n+1,4 i \sin ^{-1}(a x)\right)}{a^4}",1,"-((2^(-4 - n)*ArcSin[a*x]^n*Gamma[1 + n, (-2*I)*ArcSin[a*x]])/(a^4*((-I)*ArcSin[a*x])^n)) - (2^(-4 - n)*ArcSin[a*x]^n*Gamma[1 + n, (2*I)*ArcSin[a*x]])/(a^4*(I*ArcSin[a*x])^n) + (ArcSin[a*x]^n*Gamma[1 + n, (-4*I)*ArcSin[a*x]])/(2^(2*(3 + n))*a^4*((-I)*ArcSin[a*x])^n) + (ArcSin[a*x]^n*Gamma[1 + n, (4*I)*ArcSin[a*x]])/(2^(2*(3 + n))*a^4*(I*ArcSin[a*x])^n)","A",9,4,10,0.4000,1,"{4635, 4406, 3308, 2181}"
131,1,171,0,0.1661408,"\int x^2 \sin ^{-1}(a x)^n \, dx","Int[x^2*ArcSin[a*x]^n,x]","-\frac{i \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{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} \text{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 \text{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 \text{Gamma}\left(n+1,3 i \sin ^{-1}(a x)\right)}{8 a^3}","-\frac{i \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{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} \text{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 \text{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 \text{Gamma}\left(n+1,3 i \sin ^{-1}(a x)\right)}{8 a^3}",1,"((-I/8)*ArcSin[a*x]^n*Gamma[1 + n, (-I)*ArcSin[a*x]])/(a^3*((-I)*ArcSin[a*x])^n) + ((I/8)*ArcSin[a*x]^n*Gamma[1 + n, I*ArcSin[a*x]])/(a^3*(I*ArcSin[a*x])^n) + ((I/8)*3^(-1 - n)*ArcSin[a*x]^n*Gamma[1 + n, (-3*I)*ArcSin[a*x]])/(a^3*((-I)*ArcSin[a*x])^n) - ((I/8)*3^(-1 - n)*ArcSin[a*x]^n*Gamma[1 + n, (3*I)*ArcSin[a*x]])/(a^3*(I*ArcSin[a*x])^n)","A",9,4,10,0.4000,1,"{4635, 4406, 3307, 2181}"
132,1,85,0,0.0819761,"\int x \sin ^{-1}(a x)^n \, dx","Int[x*ArcSin[a*x]^n,x]","-\frac{2^{-n-3} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{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 \text{Gamma}\left(n+1,2 i \sin ^{-1}(a x)\right)}{a^2}","-\frac{2^{-n-3} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{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 \text{Gamma}\left(n+1,2 i \sin ^{-1}(a x)\right)}{a^2}",1,"-((2^(-3 - n)*ArcSin[a*x]^n*Gamma[1 + n, (-2*I)*ArcSin[a*x]])/(a^2*((-I)*ArcSin[a*x])^n)) - (2^(-3 - n)*ArcSin[a*x]^n*Gamma[1 + n, (2*I)*ArcSin[a*x]])/(a^2*(I*ArcSin[a*x])^n)","A",6,5,8,0.6250,1,"{4635, 4406, 12, 3308, 2181}"
133,1,79,0,0.0546235,"\int \sin ^{-1}(a x)^n \, dx","Int[ArcSin[a*x]^n,x]","\frac{i \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{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 \text{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 \text{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 \text{Gamma}\left(n+1,-i \sin ^{-1}(a x)\right)}{2 a}",1,"((-I/2)*ArcSin[a*x]^n*Gamma[1 + n, (-I)*ArcSin[a*x]])/(a*((-I)*ArcSin[a*x])^n) + ((I/2)*ArcSin[a*x]^n*Gamma[1 + n, I*ArcSin[a*x]])/(a*(I*ArcSin[a*x])^n)","A",4,3,6,0.5000,1,"{4623, 3307, 2181}"
134,0,0,0,0.0147082,"\int \frac{\sin ^{-1}(a x)^n}{x} \, dx","Int[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,"Defer[Int][ArcSin[a*x]^n/x, x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.0159331,"\int \frac{\sin ^{-1}(a x)^n}{x^2} \, dx","Int[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,"Defer[Int][ArcSin[a*x]^n/x^2, x]","A",0,0,0,0,-1,"{}"
136,0,0,0,0.0214075,"\int (b x)^{3/2} \sin ^{-1}(a x)^n \, dx","Int[(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,"Defer[Int][(b*x)^(3/2)*ArcSin[a*x]^n, x]","A",0,0,0,0,-1,"{}"
137,0,0,0,0.0174957,"\int \sqrt{b x} \sin ^{-1}(a x)^n \, dx","Int[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,"Defer[Int][Sqrt[b*x]*ArcSin[a*x]^n, x]","A",0,0,0,0,-1,"{}"
138,0,0,0,0.0183719,"\int \frac{\sin ^{-1}(a x)^n}{\sqrt{b x}} \, dx","Int[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,"Defer[Int][ArcSin[a*x]^n/Sqrt[b*x], x]","A",0,0,0,0,-1,"{}"
139,0,0,0,0.0207741,"\int \frac{\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx","Int[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,"Defer[Int][ArcSin[a*x]^n/(b*x)^(3/2), x]","A",0,0,0,0,-1,"{}"
140,1,76,0,0.0345858,"\int x^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcSin[c*x]),x]","\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right)+\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{3 b \sin ^{-1}(c x)}{32 c^4}","\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right)+\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{3 b \sin ^{-1}(c x)}{32 c^4}",1,"(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) + (x^4*(a + b*ArcSin[c*x]))/4","A",4,3,12,0.2500,1,"{4627, 321, 216}"
141,1,60,0,0.0391678,"\int x^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcSin[c*x]),x]","\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}","\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,"(b*Sqrt[1 - c^2*x^2])/(3*c^3) - (b*(1 - c^2*x^2)^(3/2))/(9*c^3) + (x^3*(a + b*ArcSin[c*x]))/3","A",4,3,12,0.2500,1,"{4627, 266, 43}"
142,1,51,0,0.0189604,"\int x \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcSin[c*x]),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}","\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,"(b*x*Sqrt[1 - c^2*x^2])/(4*c) - (b*ArcSin[c*x])/(4*c^2) + (x^2*(a + b*ArcSin[c*x]))/2","A",3,3,10,0.3000,1,"{4627, 321, 216}"
143,1,30,0,0.0137527,"\int \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[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",3,2,8,0.2500,1,"{4619, 261}"
144,1,63,0,0.069963,"\int \frac{a+b \sin ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcSin[c*x])/x,x]","-\frac{1}{2} i b \text{PolyLog}\left(2,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{PolyLog}\left(2,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)",1,"((-I/2)*(a + b*ArcSin[c*x])^2)/b + (a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] - (I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",5,5,12,0.4167,1,"{4625, 3717, 2190, 2279, 2391}"
145,1,33,0,0.0265272,"\int \frac{a+b \sin ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcSin[c*x])/x^2,x]","-\frac{a+b \sin ^{-1}(c x)}{x}-b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","-\frac{a+b \sin ^{-1}(c x)}{x}-b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"-((a + b*ArcSin[c*x])/x) - b*c*ArcTanh[Sqrt[1 - c^2*x^2]]","A",4,4,12,0.3333,1,"{4627, 266, 63, 208}"
146,1,39,0,0.0189224,"\int \frac{a+b \sin ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcSin[c*x])/x^3,x]","-\frac{a+b \sin ^{-1}(c x)}{2 x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 x}","-\frac{a+b \sin ^{-1}(c x)}{2 x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 x}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*x) - (a + b*ArcSin[c*x])/(2*x^2)","A",2,2,12,0.1667,1,"{4627, 264}"
147,1,62,0,0.0382465,"\int \frac{a+b \sin ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcSin[c*x])/x^4,x]","-\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)","-\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,"-(b*c*Sqrt[1 - c^2*x^2])/(6*x^2) - (a + b*ArcSin[c*x])/(3*x^3) - (b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",5,5,12,0.4167,1,"{4627, 266, 51, 63, 208}"
148,1,102,0,0.1538687,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcSin[c*x])^2,x]","\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","\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,"(-4*b^2*x)/(9*c^2) - (2*b^2*x^3)/27 + (4*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (2*b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) + (x^3*(a + b*ArcSin[c*x])^2)/3","A",5,5,14,0.3571,1,"{4627, 4707, 4677, 8, 30}"
149,1,76,0,0.1187838,"\int x \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcSin[c*x])^2,x]","\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","\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,"-(b^2*x^2)/4 + (b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c) - (a + b*ArcSin[c*x])^2/(4*c^2) + (x^2*(a + b*ArcSin[c*x])^2)/2","A",4,4,12,0.3333,1,"{4627, 4707, 4641, 30}"
150,1,47,0,0.0602799,"\int \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(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",3,3,10,0.3000,1,"{4619, 4677, 8}"
151,1,90,0,0.1225931,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcSin[c*x])^2/x,x]","-i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,e^{2 i \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","-i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,e^{2 i \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",1,"((-I/3)*(a + b*ArcSin[c*x])^3)/b + (a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] - I*b*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] + (b^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2","A",6,6,14,0.4286,1,"{4625, 3717, 2190, 2531, 2282, 6589}"
152,1,81,0,0.1281707,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcSin[c*x])^2/x^2,x]","2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\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{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\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)",1,"-((a + b*ArcSin[c*x])^2/x) - 4*b*c*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])] + (2*I)*b^2*c*PolyLog[2, -E^(I*ArcSin[c*x])] - (2*I)*b^2*c*PolyLog[2, E^(I*ArcSin[c*x])]","A",7,5,14,0.3571,1,"{4627, 4709, 4183, 2279, 2391}"
153,1,178,0,0.2968774,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcSin[c*x])^3,x]","-\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{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}-\frac{4 b^3 x \sin ^{-1}(c x)}{3 c^2}","-\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{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}-\frac{4 b^3 x \sin ^{-1}(c x)}{3 c^2}",1,"(-4*a*b^2*x)/(3*c^2) - (14*b^3*Sqrt[1 - c^2*x^2])/(9*c^3) + (2*b^3*(1 - c^2*x^2)^(3/2))/(27*c^3) - (4*b^3*x*ArcSin[c*x])/(3*c^2) - (2*b^2*x^3*(a + b*ArcSin[c*x]))/9 + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^3) + (b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(3*c) + (x^3*(a + b*ArcSin[c*x])^3)/3","A",10,7,14,0.5000,1,"{4627, 4707, 4677, 4619, 261, 266, 43}"
154,1,125,0,0.2046218,"\int x \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcSin[c*x])^3,x]","-\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}","-\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,"(-3*b^3*x*Sqrt[1 - c^2*x^2])/(8*c) + (3*b^3*ArcSin[c*x])/(8*c^2) - (3*b^2*x^2*(a + b*ArcSin[c*x]))/4 + (3*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*c) - (a + b*ArcSin[c*x])^3/(4*c^2) + (x^2*(a + b*ArcSin[c*x])^3)/2","A",6,5,12,0.4167,1,"{4627, 4707, 4641, 321, 216}"
155,1,82,0,0.1087026,"\int \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcSin[c*x])^3,x]","-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)","-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,"-6*a*b^2*x - (6*b^3*Sqrt[1 - c^2*x^2])/c - 6*b^3*x*ArcSin[c*x] + (3*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/c + x*(a + b*ArcSin[c*x])^3","A",5,3,10,0.3000,1,"{4619, 4677, 261}"
156,1,123,0,0.1466186,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcSin[c*x])^3/x,x]","\frac{3}{2} b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{4} i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(c x)}\right)-\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}{2} b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{4} i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(c x)}\right)-\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",1,"((-I/4)*(a + b*ArcSin[c*x])^4)/b + (a + b*ArcSin[c*x])^3*Log[1 - E^((2*I)*ArcSin[c*x])] - ((3*I)/2)*b*(a + b*ArcSin[c*x])^2*PolyLog[2, E^((2*I)*ArcSin[c*x])] + (3*b^2*(a + b*ArcSin[c*x])*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2 + ((3*I)/4)*b^3*PolyLog[4, E^((2*I)*ArcSin[c*x])]","A",7,7,14,0.5000,1,"{4625, 3717, 2190, 2531, 6609, 2282, 6589}"
157,1,137,0,0.2128949,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcSin[c*x])^3/x^2,x]","6 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-6 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-6 b^3 c \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)+6 b^3 c \text{PolyLog}\left(3,e^{i \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 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-6 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-6 b^3 c \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)+6 b^3 c \text{PolyLog}\left(3,e^{i \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",1,"-((a + b*ArcSin[c*x])^3/x) - 6*b*c*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])] + (6*I)*b^2*c*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])] - (6*I)*b^2*c*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])] - 6*b^3*c*PolyLog[3, -E^(I*ArcSin[c*x])] + 6*b^3*c*PolyLog[3, E^(I*ArcSin[c*x])]","A",9,6,14,0.4286,1,"{4627, 4709, 4183, 2531, 2282, 6589}"
158,1,117,0,0.2537272,"\int \frac{x^2}{a+b \sin ^{-1}(c x)} \, dx","Int[x^2/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{\cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b c^3}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{\sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b c^3}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{\cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\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]])/(4*b*c^3) - (Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3) + (Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) - (Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3)","A",9,5,14,0.3571,1,"{4635, 4406, 3303, 3299, 3302}"
159,1,63,0,0.1318636,"\int \frac{x}{a+b \sin ^{-1}(c x)} \, dx","Int[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)}{2 b c^2}-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\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{CosIntegral}\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])/(2*b*c^2) + (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^2)","A",6,6,12,0.5000,1,"{4635, 4406, 12, 3303, 3299, 3302}"
160,1,53,0,0.066952,"\int \frac{1}{a+b \sin ^{-1}(c x)} \, dx","Int[(a + b*ArcSin[c*x])^(-1),x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\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}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\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])/b])/(b*c) + (Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(b*c)","A",4,4,10,0.4000,1,"{4623, 3303, 3299, 3302}"
161,0,0,0,0.0237117,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[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,"Defer[Int][1/(x*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
162,0,0,0,0.0245967,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
163,1,152,0,0.1818897,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^2/(a + b*ArcSin[c*x])^2,x]","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\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)}","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\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{CosIntegral}\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,"-((x^2*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x]))) + (CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(4*b^2*c^3) - (3*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(4*b^2*c^3) - (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^3) + (3*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^3)","A",8,4,14,0.2857,1,"{4631, 3303, 3299, 3302}"
164,1,90,0,0.1003296,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x/(a + b*ArcSin[c*x])^2,x]","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c^2}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c^2}-\frac{x \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\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,"-((x*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x]))) + (Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^2) + (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^2)","A",4,4,12,0.3333,1,"{4631, 3303, 3299, 3302}"
165,1,82,0,0.1686473,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^(-2),x]","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}-\frac{\sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\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,"-(Sqrt[1 - c^2*x^2]/(b*c*(a + b*ArcSin[c*x]))) + (CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(b^2*c) - (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b^2*c)","A",5,5,10,0.5000,1,"{4621, 4723, 3303, 3299, 3302}"
166,0,0,0,0.0226791,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[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,"Defer[Int][1/(x*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
167,0,0,0,0.0228626,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
168,1,245,0,0.5424888,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Int[x^2/(a + b*ArcSin[c*x])^3,x]","-\frac{9 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^3 c^3}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{8 b^3 c^3}+\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^3 c^3}-\frac{9 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^3 c^3}+\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\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)}{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}","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\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{CosIntegral}\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,"-(x^2*Sqrt[1 - c^2*x^2])/(2*b*c*(a + b*ArcSin[c*x])^2) - x/(b^2*c^2*(a + b*ArcSin[c*x])) + (3*x^3)/(2*b^2*(a + b*ArcSin[c*x])) - (9*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(8*b^3*c^3) + (9*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(8*b^3*c^3) + (Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/(b^3*c^3) - (9*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b^3*c^3) + (9*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(8*b^3*c^3) + (Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(b^3*c^3)","A",16,8,14,0.5714,1,"{4633, 4719, 4635, 4406, 3303, 3299, 3302, 4623}"
169,1,130,0,0.3228319,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Int[x/(a + b*ArcSin[c*x])^3,x]","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^3 c^2}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\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}","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\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,"-(x*Sqrt[1 - c^2*x^2])/(2*b*c*(a + b*ArcSin[c*x])^2) - 1/(2*b^2*c^2*(a + b*ArcSin[c*x])) + x^2/(b^2*(a + b*ArcSin[c*x])) + (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(b^3*c^2) - (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^3*c^2)","A",9,9,12,0.7500,1,"{4633, 4719, 4635, 4406, 12, 3303, 3299, 3302, 4641}"
170,1,111,0,0.1723655,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Int[(a + b*ArcSin[c*x])^(-3),x]","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\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}","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\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,"-Sqrt[1 - c^2*x^2]/(2*b*c*(a + b*ArcSin[c*x])^2) + x/(2*b^2*(a + b*ArcSin[c*x])) - (Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/(2*b^3*c) - (Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(2*b^3*c)","A",6,6,10,0.6000,1,"{4621, 4719, 4623, 3303, 3299, 3302}"
171,0,0,0,0.0229314,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Int[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,"Defer[Int][1/(x*(a + b*ArcSin[c*x])^3), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.0229158,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^3} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*ArcSin[c*x])^3), x]","A",0,0,0,0,-1,"{}"
173,1,242,0,0.7556717,"\int x^2 \sqrt{a+b \sin ^{-1}(c x)} \, dx","Int[x^2*Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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,"(x^3*Sqrt[a + b*ArcSin[c*x]])/3 - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*c^3) + (Sqrt[b]*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(12*c^3) + (Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(4*c^3) - (Sqrt[b]*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(12*c^3)","A",14,8,16,0.5000,1,"{4629, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
174,1,137,0,0.453424,"\int x \sqrt{a+b \sin ^{-1}(c x)} \, dx","Int[x*Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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)}","\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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,"-Sqrt[a + b*ArcSin[c*x]]/(4*c^2) + (x^2*Sqrt[a + b*ArcSin[c*x]])/2 + (Sqrt[b]*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(8*c^2) + (Sqrt[b]*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(8*c^2)","A",9,8,14,0.5714,1,"{4629, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
175,1,120,0,0.3311212,"\int \sqrt{a+b \sin ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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,"x*Sqrt[a + b*ArcSin[c*x]] - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/c + (Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/c","A",7,7,12,0.5833,1,"{4619, 4723, 3306, 3305, 3351, 3304, 3352}"
176,0,0,0,0.0463406,"\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{x} \, dx","Int[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,"Defer[Int][Sqrt[a + b*ArcSin[c*x]]/x, x]","A",0,0,0,0,-1,"{}"
177,0,0,0,0.0373746,"\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{x^2} \, dx","Int[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,"Defer[Int][Sqrt[a + b*ArcSin[c*x]]/x^2, x]","A",0,0,0,0,-1,"{}"
178,1,313,0,1.0461848,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Int[x^2*(a + b*ArcSin[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(3*c^3) + (b*x^2*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(6*c) + (x^3*(a + b*ArcSin[c*x])^(3/2))/3 - (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*c^3) + (b^(3/2)*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(24*c^3) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(8*c^3) + (b^(3/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(24*c^3)","A",22,11,16,0.6875,1,"{4629, 4707, 4677, 4623, 3306, 3305, 3351, 3304, 3352, 4635, 4406}"
179,1,172,0,0.5249705,"\int x \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Int[x*(a + b*ArcSin[c*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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}","\frac{3 \sqrt{\pi } b^{3/2} \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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,"(3*b*x*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(8*c) - (a + b*ArcSin[c*x])^(3/2)/(4*c^2) + (x^2*(a + b*ArcSin[c*x])^(3/2))/2 - (3*b^(3/2)*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(32*c^2) + (3*b^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(32*c^2)","A",11,11,14,0.7857,1,"{4629, 4707, 4641, 4635, 4406, 12, 3306, 3305, 3351, 3304, 3352}"
180,1,159,0,0.2809821,"\int \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcSin[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\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}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\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,"(3*b*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(2*c) + x*(a + b*ArcSin[c*x])^(3/2) - (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*c) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*c)","A",8,8,12,0.6667,1,"{4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352}"
181,0,0,0,0.0451535,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x} \, dx","Int[(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,"Defer[Int][(a + b*ArcSin[c*x])^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
182,0,0,0,0.0420042,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{x^2} \, dx","Int[(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,"Defer[Int][(a + b*ArcSin[c*x])^(3/2)/x^2, x]","A",0,0,0,0,-1,"{}"
183,1,358,0,1.4091241,"\int x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2} \, dx","Int[x^2*(a + b*ArcSin[c*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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,"(-5*b^2*x*Sqrt[a + b*ArcSin[c*x]])/(6*c^2) - (5*b^2*x^3*Sqrt[a + b*ArcSin[c*x]])/36 + (5*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^(3/2))/(9*c^3) + (5*b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^(3/2))/(18*c) + (x^3*(a + b*ArcSin[c*x])^(5/2))/3 + (15*b^(5/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*c^3) - (5*b^(5/2)*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(144*c^3) - (15*b^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(16*c^3) + (5*b^(5/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(144*c^3)","A",24,11,16,0.6875,1,"{4629, 4707, 4677, 4619, 4723, 3306, 3305, 3351, 3304, 3352, 3312}"
184,1,216,0,0.7425189,"\int x \left(a+b \sin ^{-1}(c x)\right)^{5/2} \, dx","Int[x*(a + b*ArcSin[c*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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}","-\frac{15 \sqrt{\pi } b^{5/2} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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,"(15*b^2*Sqrt[a + b*ArcSin[c*x]])/(64*c^2) - (15*b^2*x^2*Sqrt[a + b*ArcSin[c*x]])/32 + (5*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^(3/2))/(8*c) - (a + b*ArcSin[c*x])^(5/2)/(4*c^2) + (x^2*(a + b*ArcSin[c*x])^(5/2))/2 - (15*b^(5/2)*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(128*c^2) - (15*b^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(128*c^2)","A",12,10,14,0.7143,1,"{4629, 4707, 4641, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
185,1,179,0,0.5019696,"\int \left(a+b \sin ^{-1}(c x)\right)^{5/2} \, dx","Int[(a + b*ArcSin[c*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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,"(-15*b^2*x*Sqrt[a + b*ArcSin[c*x]])/4 + (5*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^(3/2))/(2*c) + x*(a + b*ArcSin[c*x])^(5/2) + (15*b^(5/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*c) - (15*b^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(4*c)","A",9,8,12,0.6667,1,"{4619, 4677, 4723, 3306, 3305, 3351, 3304, 3352}"
186,0,0,0,0.0441739,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x} \, dx","Int[(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,"Defer[Int][(a + b*ArcSin[c*x])^(5/2)/x, x]","A",0,0,0,0,-1,"{}"
187,0,0,0,0.0433305,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{5/2}}{x^2} \, dx","Int[(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,"Defer[Int][(a + b*ArcSin[c*x])^(5/2)/x^2, x]","A",0,0,0,0,-1,"{}"
188,1,223,0,0.4208642,"\int \frac{x^2}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[x^2/Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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}","\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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,"(Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*Sqrt[b]*c^3) - (Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*Sqrt[b]*c^3) + (Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*Sqrt[b]*c^3) - (Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(2*Sqrt[b]*c^3)","A",13,7,16,0.4375,1,"{4635, 4406, 3306, 3305, 3351, 3304, 3352}"
189,1,99,0,0.1764397,"\int \frac{x}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[x/Sqrt[a + b*ArcSin[c*x]],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) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} c^2}","\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) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} c^2}",1,"(Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(2*Sqrt[b]*c^2) - (Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(2*Sqrt[b]*c^2)","A",8,8,14,0.5714,1,"{4635, 4406, 12, 3306, 3305, 3351, 3304, 3352}"
190,1,101,0,0.0909293,"\int \frac{1}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\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}","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\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,"(Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(Sqrt[b]*c) + (Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*c)","A",6,6,12,0.5000,1,"{4623, 3306, 3305, 3351, 3304, 3352}"
191,0,0,0,0.0373151,"\int \frac{1}{x \sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[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,"Defer[Int][1/(x*Sqrt[a + b*ArcSin[c*x]]), x]","A",0,0,0,0,-1,"{}"
192,0,0,0,0.0368645,"\int \frac{1}{x^2 \sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[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,"Defer[Int][1/(x^2*Sqrt[a + b*ArcSin[c*x]]), x]","A",0,0,0,0,-1,"{}"
193,1,250,0,0.418084,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[x^2/(a + b*ArcSin[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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)}}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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,"(-2*x^2*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) + (Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) + (Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c^3) - (Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(3/2)*c^3)","A",12,6,16,0.3750,1,"{4631, 3306, 3305, 3351, 3304, 3352}"
194,1,130,0,0.1628712,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[x/(a + b*ArcSin[c*x])^(3/2),x]","\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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)}}","\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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,"(-2*x*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcSin[c*x]]) + (2*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(b^(3/2)*c^2) + (2*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(b^(3/2)*c^2)","A",6,6,14,0.4286,1,"{4631, 3306, 3305, 3351, 3304, 3352}"
195,1,137,0,0.2942596,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^(-3/2),x]","\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\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)}}","\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\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,"(-2*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (2*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c) + (2*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c)","A",7,7,12,0.5833,1,"{4621, 4723, 3306, 3305, 3351, 3304, 3352}"
196,0,0,0,0.0442315,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[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,"Defer[Int][1/(x*(a + b*ArcSin[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
197,0,0,0,0.0428374,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*ArcSin[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
198,1,291,0,1.0071883,"\int \frac{x^2}{\left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Int[x^2/(a + b*ArcSin[c*x])^(5/2),x]","-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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}}","-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\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) \text{FresnelC}\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,"(-2*x^2*Sqrt[1 - c^2*x^2])/(3*b*c*(a + b*ArcSin[c*x])^(3/2)) - (8*x)/(3*b^2*c^2*Sqrt[a + b*ArcSin[c*x]]) + (4*x^3)/(b^2*Sqrt[a + b*ArcSin[c*x]]) - (Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(3*b^(5/2)*c^3) + (Sqrt[6*Pi]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(5/2)*c^3) - (Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*c^3) + (Sqrt[6*Pi]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(5/2)*c^3)","A",22,10,16,0.6250,1,"{4633, 4719, 4635, 4406, 3306, 3305, 3351, 3304, 3352, 4623}"
199,1,180,0,0.5061635,"\int \frac{x}{\left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Int[x/(a + b*ArcSin[c*x])^(5/2),x]","\frac{8 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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}}","\frac{8 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\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,"(-2*x*Sqrt[1 - c^2*x^2])/(3*b*c*(a + b*ArcSin[c*x])^(3/2)) - 4/(3*b^2*c^2*Sqrt[a + b*ArcSin[c*x]]) + (8*x^2)/(3*b^2*Sqrt[a + b*ArcSin[c*x]]) - (8*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(3*b^(5/2)*c^2) + (8*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(3*b^(5/2)*c^2)","A",11,11,14,0.7857,1,"{4633, 4719, 4635, 4406, 12, 3306, 3305, 3351, 3304, 3352, 4641}"
200,1,163,0,0.2759938,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^(-5/2),x]","-\frac{4 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\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}}","-\frac{4 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\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*Sqrt[1 - c^2*x^2])/(3*b*c*(a + b*ArcSin[c*x])^(3/2)) + (4*x)/(3*b^2*Sqrt[a + b*ArcSin[c*x]]) - (4*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(3*b^(5/2)*c) - (4*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*c)","A",8,8,12,0.6667,1,"{4621, 4719, 4623, 3306, 3305, 3351, 3304, 3352}"
201,0,0,0,0.0452953,"\int \frac{1}{x \left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Int[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,"Defer[Int][1/(x*(a + b*ArcSin[c*x])^(5/2)), x]","A",0,0,0,0,-1,"{}"
202,0,0,0,0.0451862,"\int \frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)^{5/2}} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*ArcSin[c*x])^(5/2)), x]","A",0,0,0,0,-1,"{}"
203,1,120,0,0.075921,"\int (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d*x)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{2 (d x)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d}+\frac{20 b d^2 \sqrt{1-c^2 x^2} \sqrt{d x}}{147 c^3}-\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{2 (d x)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d}+\frac{20 b d^2 \sqrt{1-c^2 x^2} \sqrt{d x}}{147 c^3}-\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}",1,"(20*b*d^2*Sqrt[d*x]*Sqrt[1 - c^2*x^2])/(147*c^3) + (4*b*(d*x)^(5/2)*Sqrt[1 - c^2*x^2])/(49*c) + (2*(d*x)^(7/2)*(a + b*ArcSin[c*x]))/(7*d) - (20*b*d^(5/2)*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(147*c^(7/2))","A",5,4,16,0.2500,1,"{4627, 321, 329, 221}"
204,1,124,0,0.0984692,"\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d*x)^(3/2)*(a + b*ArcSin[c*x]),x]","\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}","\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,"(4*b*(d*x)^(3/2)*Sqrt[1 - c^2*x^2])/(25*c) + (2*(d*x)^(5/2)*(a + b*ArcSin[c*x]))/(5*d) - (12*b*d^(3/2)*EllipticE[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(25*c^(5/2)) + (12*b*d^(3/2)*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(25*c^(5/2))","A",7,7,16,0.4375,1,"{4627, 321, 329, 307, 221, 1199, 424}"
205,1,88,0,0.044585,"\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[d*x]*(a + b*ArcSin[c*x]),x]","\frac{2 (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 d}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d x}}{9 c}-\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{2 (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 d}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d x}}{9 c}-\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}}",1,"(4*b*Sqrt[d*x]*Sqrt[1 - c^2*x^2])/(9*c) + (2*(d*x)^(3/2)*(a + b*ArcSin[c*x]))/(3*d) - (4*b*Sqrt[d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(9*c^(3/2))","A",4,4,16,0.2500,1,"{4627, 321, 329, 221}"
206,1,89,0,0.0780528,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d x}} \, dx","Int[(a + b*ArcSin[c*x])/Sqrt[d*x],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}}","\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*Sqrt[d*x]*(a + b*ArcSin[c*x]))/d - (4*b*EllipticE[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(Sqrt[c]*Sqrt[d]) + (4*b*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(Sqrt[c]*Sqrt[d])","A",6,6,16,0.3750,1,"{4627, 329, 307, 221, 1199, 424}"
207,1,55,0,0.0377391,"\int \frac{a+b \sin ^{-1}(c x)}{(d x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d*x)^(3/2),x]","\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}}","\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*(a + b*ArcSin[c*x]))/(d*Sqrt[d*x]) + (4*b*Sqrt[c]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/d^(3/2)","A",3,3,16,0.1875,1,"{4627, 329, 221}"
208,1,125,0,0.0968909,"\int \frac{a+b \sin ^{-1}(c x)}{(d x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d*x)^(5/2),x]","-\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{3 d (d x)^{3/2}}-\frac{4 b c \sqrt{1-c^2 x^2}}{3 d^2 \sqrt{d x}}+\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{2 \left(a+b \sin ^{-1}(c x)\right)}{3 d (d x)^{3/2}}-\frac{4 b c \sqrt{1-c^2 x^2}}{3 d^2 \sqrt{d x}}+\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}}",1,"(-4*b*c*Sqrt[1 - c^2*x^2])/(3*d^2*Sqrt[d*x]) - (2*(a + b*ArcSin[c*x]))/(3*d*(d*x)^(3/2)) - (4*b*c^(3/2)*EllipticE[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(3*d^(5/2)) + (4*b*c^(3/2)*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(3*d^(5/2))","A",7,7,16,0.4375,1,"{4627, 325, 329, 307, 221, 1199, 424}"
209,1,109,0,0.1407916,"\int (d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^(5/2)*(a + b*ArcSin[c*x])^2,x]","\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}","\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*(d*x)^(7/2)*(a + b*ArcSin[c*x])^2)/(7*d) - (8*b*c*(d*x)^(9/2)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, 9/4, 13/4, c^2*x^2])/(63*d^2) + (16*b^2*c^2*(d*x)^(11/2)*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, c^2*x^2])/(693*d^3)","A",2,2,18,0.1111,1,"{4627, 4711}"
210,1,109,0,0.1410346,"\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\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}","\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*(d*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(5*d) - (8*b*c*(d*x)^(7/2)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, 7/4, 11/4, c^2*x^2])/(35*d^2) + (16*b^2*c^2*(d*x)^(9/2)*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, c^2*x^2])/(315*d^3)","A",2,2,18,0.1111,1,"{4627, 4711}"
211,1,109,0,0.1426313,"\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d*x]*(a + b*ArcSin[c*x])^2,x]","\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}","\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*(d*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(3*d) - (8*b*c*(d*x)^(5/2)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(15*d^2) + (16*b^2*c^2*(d*x)^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(105*d^3)","A",2,2,18,0.1111,1,"{4627, 4711}"
212,1,107,0,0.1300817,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d x}} \, dx","Int[(a + b*ArcSin[c*x])^2/Sqrt[d*x],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}","\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*Sqrt[d*x]*(a + b*ArcSin[c*x])^2)/d - (8*b*c*(d*x)^(3/2)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2])/(3*d^2) + (16*b^2*c^2*(d*x)^(5/2)*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, c^2*x^2])/(15*d^3)","A",2,2,18,0.1111,1,"{4627, 4711}"
213,1,105,0,0.1349476,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(d*x)^(3/2),x]","-\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}}","-\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*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d*x]) + (8*b*c*Sqrt[d*x]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2])/d^2 - (16*b^2*c^2*(d*x)^(3/2)*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, c^2*x^2])/(3*d^3)","A",2,2,18,0.1111,1,"{4627, 4711}"
214,1,109,0,0.1454501,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(d*x)^(5/2),x]","\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}}","\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,"(-2*(a + b*ArcSin[c*x])^2)/(3*d*(d*x)^(3/2)) - (8*b*c*(a + b*ArcSin[c*x])*Hypergeometric2F1[-1/4, 1/2, 3/4, c^2*x^2])/(3*d^2*Sqrt[d*x]) + (16*b^2*c^2*Sqrt[d*x]*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, c^2*x^2])/(3*d^3)","A",2,2,18,0.1111,1,"{4627, 4711}"
215,0,0,0,0.169876,"\int (d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Int[(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,"(2*(d*x)^(5/2)*(a + b*ArcSin[c*x])^3)/(5*d) - (6*b*c*Defer[Int][((d*x)^(5/2)*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2], x])/(5*d)","A",0,0,0,0,-1,"{}"
216,0,0,0,0.1678825,"\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","Int[Sqrt[d*x]*(a + b*ArcSin[c*x])^3,x]","\int \sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^3 \, dx","\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,"(2*(d*x)^(3/2)*(a + b*ArcSin[c*x])^3)/(3*d) - (2*b*c*Defer[Int][((d*x)^(3/2)*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2], x])/d","A",0,0,0,0,-1,"{}"
217,0,0,0,0.160063,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{\sqrt{d x}} \, dx","Int[(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,"(2*Sqrt[d*x]*(a + b*ArcSin[c*x])^3)/d - (6*b*c*Defer[Int][(Sqrt[d*x]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2], x])/d","A",0,0,0,0,-1,"{}"
218,0,0,0,0.1591323,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{(d x)^{3/2}} \, dx","Int[(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,"(-2*(a + b*ArcSin[c*x])^3)/(d*Sqrt[d*x]) + (6*b*c*Defer[Int][(a + b*ArcSin[c*x])^2/(Sqrt[d*x]*Sqrt[1 - c^2*x^2]), x])/d","A",0,0,0,0,-1,"{}"
219,0,0,0,0.173453,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3}{(d x)^{5/2}} \, dx","Int[(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,"(-2*(a + b*ArcSin[c*x])^3)/(3*d*(d*x)^(3/2)) + (2*b*c*Defer[Int][(a + b*ArcSin[c*x])^2/((d*x)^(3/2)*Sqrt[1 - c^2*x^2]), x])/d","A",0,0,0,0,-1,"{}"
220,0,0,0,0.0296614,"\int \frac{(d x)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(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,"Defer[Int][(d*x)^(3/2)/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
221,0,0,0,0.0260333,"\int \frac{\sqrt{d x}}{a+b \sin ^{-1}(c x)} \, dx","Int[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,"Defer[Int][Sqrt[d*x]/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
222,0,0,0,0.0292444,"\int \frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[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,"Defer[Int][1/(Sqrt[d*x]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
223,0,0,0,0.0317726,"\int \frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[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,"Defer[Int][1/((d*x)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
224,0,0,0,0.0291117,"\int \frac{(d x)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(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,"Defer[Int][(d*x)^(3/2)/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
225,0,0,0,0.0256366,"\int \frac{\sqrt{d x}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[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,"Defer[Int][Sqrt[d*x]/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
226,0,0,0,0.0253785,"\int \frac{1}{\sqrt{d x} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[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,"Defer[Int][1/(Sqrt[d*x]*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
227,0,0,0,0.0279332,"\int \frac{1}{(d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[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,"Defer[Int][1/((d*x)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"