1,1,179,0,0.1823254,"\int (d+e x)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcSin[c*x]),x]","\frac{(d+e x)^4 \left(a+b \sin ^{-1}(c x)\right)}{4 e}+\frac{b \sqrt{1-c^2 x^2} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{b \left(24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \sin ^{-1}(c x)}{32 c^4 e}+\frac{b \sqrt{1-c^2 x^2} (d+e x)^3}{16 c}+\frac{7 b d \sqrt{1-c^2 x^2} (d+e x)^2}{48 c}","\frac{(d+e x)^4 \left(a+b \sin ^{-1}(c x)\right)}{4 e}+\frac{b \sqrt{1-c^2 x^2} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{b \left(24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \sin ^{-1}(c x)}{32 c^4 e}+\frac{b \sqrt{1-c^2 x^2} (d+e x)^3}{16 c}+\frac{7 b d \sqrt{1-c^2 x^2} (d+e x)^2}{48 c}",1,"(7*b*d*(d + e*x)^2*Sqrt[1 - c^2*x^2])/(48*c) + (b*(d + e*x)^3*Sqrt[1 - c^2*x^2])/(16*c) + (b*(4*d*(19*c^2*d^2 + 16*e^2) + e*(26*c^2*d^2 + 9*e^2)*x)*Sqrt[1 - c^2*x^2])/(96*c^3) - (b*(8*c^4*d^4 + 24*c^2*d^2*e^2 + 3*e^4)*ArcSin[c*x])/(32*c^4*e) + ((d + e*x)^4*(a + b*ArcSin[c*x]))/(4*e)","A",5,5,16,0.3125,1,"{4743, 743, 833, 780, 216}"
2,1,124,0,0.0950745,"\int (d+e x)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcSin[c*x]),x]","\frac{(d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)}{3 e}+\frac{b \sqrt{1-c^2 x^2} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b d \left(\frac{3 e^2}{c^2}+2 d^2\right) \sin ^{-1}(c x)}{6 e}+\frac{b \sqrt{1-c^2 x^2} (d+e x)^2}{9 c}","\frac{(d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)}{3 e}+\frac{b \sqrt{1-c^2 x^2} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b d \left(\frac{3 e^2}{c^2}+2 d^2\right) \sin ^{-1}(c x)}{6 e}+\frac{b \sqrt{1-c^2 x^2} (d+e x)^2}{9 c}",1,"(b*(d + e*x)^2*Sqrt[1 - c^2*x^2])/(9*c) + (b*(4*(4*c^2*d^2 + e^2) + 5*c^2*d*e*x)*Sqrt[1 - c^2*x^2])/(18*c^3) - (b*d*(2*d^2 + (3*e^2)/c^2)*ArcSin[c*x])/(6*e) + ((d + e*x)^3*(a + b*ArcSin[c*x]))/(3*e)","A",4,4,16,0.2500,1,"{4743, 743, 780, 216}"
3,1,98,0,0.0510849,"\int (d+e x) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcSin[c*x]),x]","\frac{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e}-\frac{b \left(\frac{e^2}{c^2}+2 d^2\right) \sin ^{-1}(c x)}{4 e}+\frac{b \sqrt{1-c^2 x^2} (d+e x)}{4 c}+\frac{3 b d \sqrt{1-c^2 x^2}}{4 c}","\frac{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e}-\frac{b \left(\frac{e^2}{c^2}+2 d^2\right) \sin ^{-1}(c x)}{4 e}+\frac{b \sqrt{1-c^2 x^2} (d+e x)}{4 c}+\frac{3 b d \sqrt{1-c^2 x^2}}{4 c}",1,"(3*b*d*Sqrt[1 - c^2*x^2])/(4*c) + (b*(d + e*x)*Sqrt[1 - c^2*x^2])/(4*c) - (b*(2*d^2 + e^2/c^2)*ArcSin[c*x])/(4*e) + ((d + e*x)^2*(a + b*ArcSin[c*x]))/(2*e)","A",4,4,14,0.2857,1,"{4743, 743, 641, 216}"
4,1,30,0,0.0132206,"\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}"
5,1,229,0,0.3025853,"\int \frac{a+b \sin ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x),x]","-\frac{i b \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{i b \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e}","-\frac{i b \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{i b \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e}",1,"((-I/2)*(a + b*ArcSin[c*x])^2)/(b*e) + ((a + b*ArcSin[c*x])*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e + ((a + b*ArcSin[c*x])*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e - (I*b*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e - (I*b*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e","A",8,5,16,0.3125,1,"{4741, 4519, 2190, 2279, 2391}"
6,1,85,0,0.0534458,"\int \frac{a+b \sin ^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x)^2,x]","\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{a+b \sin ^{-1}(c x)}{e (d+e x)}","\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{a+b \sin ^{-1}(c x)}{e (d+e x)}",1,"-((a + b*ArcSin[c*x])/(e*(d + e*x))) + (b*c*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e*Sqrt[c^2*d^2 - e^2])","A",3,3,16,0.1875,1,"{4743, 725, 204}"
7,1,135,0,0.0852537,"\int \frac{a+b \sin ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x)^3,x]","-\frac{a+b \sin ^{-1}(c x)}{2 e (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2}}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 e \left(c^2 d^2-e^2\right)^{3/2}}","-\frac{a+b \sin ^{-1}(c x)}{2 e (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2}}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 e \left(c^2 d^2-e^2\right)^{3/2}}",1,"(b*c*Sqrt[1 - c^2*x^2])/(2*(c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcSin[c*x])/(2*e*(d + e*x)^2) + (b*c^3*d*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e*(c^2*d^2 - e^2)^(3/2))","A",4,4,16,0.2500,1,"{4743, 731, 725, 204}"
8,1,191,0,0.1402138,"\int \frac{a+b \sin ^{-1}(c x)}{(d+e x)^4} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x)^4,x]","-\frac{a+b \sin ^{-1}(c x)}{3 e (d+e x)^3}+\frac{b c^3 d \sqrt{1-c^2 x^2}}{2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(2 c^2 d^2+e^2\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{6 e \left(c^2 d^2-e^2\right)^{5/2}}","-\frac{a+b \sin ^{-1}(c x)}{3 e (d+e x)^3}+\frac{b c^3 d \sqrt{1-c^2 x^2}}{2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(2 c^2 d^2+e^2\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{6 e \left(c^2 d^2-e^2\right)^{5/2}}",1,"(b*c*Sqrt[1 - c^2*x^2])/(6*(c^2*d^2 - e^2)*(d + e*x)^2) + (b*c^3*d*Sqrt[1 - c^2*x^2])/(2*(c^2*d^2 - e^2)^2*(d + e*x)) - (a + b*ArcSin[c*x])/(3*e*(d + e*x)^3) + (b*c^3*(2*c^2*d^2 + e^2)*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(6*e*(c^2*d^2 - e^2)^(5/2))","A",5,5,16,0.3125,1,"{4743, 745, 807, 725, 204}"
9,1,374,0,0.7123874,"\int (d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^3*(a + b*ArcSin[c*x])^2,x]","\frac{3 b d^2 e x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{3 d^2 e \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{2 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{4 b d e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^3}+\frac{2 b d e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{b e^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b e^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^3}-\frac{3 e^3 \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}-\frac{d^4 \left(a+b \sin ^{-1}(c x)\right)^2}{4 e}+\frac{(d+e x)^4 \left(a+b \sin ^{-1}(c x)\right)^2}{4 e}-\frac{4 b^2 d e^2 x}{3 c^2}-\frac{3 b^2 e^3 x^2}{32 c^2}-\frac{3}{4} b^2 d^2 e x^2-2 b^2 d^3 x-\frac{2}{9} b^2 d e^2 x^3-\frac{1}{32} b^2 e^3 x^4","\frac{3 b d^2 e x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{3 d^2 e \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{2 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{4 b d e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^3}+\frac{2 b d e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{b e^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b e^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^3}-\frac{3 e^3 \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}-\frac{d^4 \left(a+b \sin ^{-1}(c x)\right)^2}{4 e}+\frac{(d+e x)^4 \left(a+b \sin ^{-1}(c x)\right)^2}{4 e}-\frac{4 b^2 d e^2 x}{3 c^2}-\frac{3 b^2 e^3 x^2}{32 c^2}-\frac{3}{4} b^2 d^2 e x^2-2 b^2 d^3 x-\frac{2}{9} b^2 d e^2 x^3-\frac{1}{32} b^2 e^3 x^4",1,"-2*b^2*d^3*x - (4*b^2*d*e^2*x)/(3*c^2) - (3*b^2*d^2*e*x^2)/4 - (3*b^2*e^3*x^2)/(32*c^2) - (2*b^2*d*e^2*x^3)/9 - (b^2*e^3*x^4)/32 + (2*b*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (4*b*d*e^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c^3) + (3*b*d^2*e*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c) + (3*b*e^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(16*c^3) + (2*b*d*e^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c) + (b*e^3*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) - (d^4*(a + b*ArcSin[c*x])^2)/(4*e) - (3*d^2*e*(a + b*ArcSin[c*x])^2)/(4*c^2) - (3*e^3*(a + b*ArcSin[c*x])^2)/(32*c^4) + ((d + e*x)^4*(a + b*ArcSin[c*x])^2)/(4*e)","A",18,7,18,0.3889,1,"{4743, 4763, 4641, 4677, 8, 4707, 30}"
10,1,242,0,0.4793423,"\int (d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^2*(a + b*ArcSin[c*x])^2,x]","\frac{2 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{b d e x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}-\frac{d e \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2}+\frac{4 b e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{2 b e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 e}+\frac{(d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 e}-\frac{4 b^2 e^2 x}{9 c^2}-2 b^2 d^2 x-\frac{1}{2} b^2 d e x^2-\frac{2}{27} b^2 e^2 x^3","\frac{2 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{b d e x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}-\frac{d e \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2}+\frac{4 b e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{2 b e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 e}+\frac{(d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 e}-\frac{4 b^2 e^2 x}{9 c^2}-2 b^2 d^2 x-\frac{1}{2} b^2 d e x^2-\frac{2}{27} b^2 e^2 x^3",1,"-2*b^2*d^2*x - (4*b^2*e^2*x)/(9*c^2) - (b^2*d*e*x^2)/2 - (2*b^2*e^2*x^3)/27 + (2*b*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (4*b*e^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (b*d*e*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (2*b*e^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) - (d^3*(a + b*ArcSin[c*x])^2)/(3*e) - (d*e*(a + b*ArcSin[c*x])^2)/(2*c^2) + ((d + e*x)^3*(a + b*ArcSin[c*x])^2)/(3*e)","A",13,7,18,0.3889,1,"{4743, 4763, 4641, 4677, 8, 4707, 30}"
11,1,142,0,0.3093507,"\int (d+e x) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)*(a + b*ArcSin[c*x])^2,x]","\frac{2 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{b e x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{e \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 e}-2 b^2 d x-\frac{1}{4} b^2 e x^2","\frac{2 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{b e x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{e \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 e}-2 b^2 d x-\frac{1}{4} b^2 e x^2",1,"-2*b^2*d*x - (b^2*e*x^2)/4 + (2*b*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (b*e*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c) - (d^2*(a + b*ArcSin[c*x])^2)/(2*e) - (e*(a + b*ArcSin[c*x])^2)/(4*c^2) + ((d + e*x)^2*(a + b*ArcSin[c*x])^2)/(2*e)","A",9,7,16,0.4375,1,"{4743, 4763, 4641, 4677, 8, 4707, 30}"
12,1,47,0,0.0605806,"\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}"
13,1,347,0,0.5089776,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(a + b*ArcSin[c*x])^2/(d + e*x),x]","-\frac{2 i b \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 i b \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{2 b^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 b^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b e}","-\frac{2 i b \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 i b \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{2 b^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 b^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b e}",1,"((-I/3)*(a + b*ArcSin[c*x])^3)/(b*e) + ((a + b*ArcSin[c*x])^2*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e + ((a + b*ArcSin[c*x])^2*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e - ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e - ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e + (2*b^2*PolyLog[3, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e + (2*b^2*PolyLog[3, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e","A",10,6,18,0.3333,1,"{4741, 4519, 2190, 2531, 2282, 6589}"
14,1,309,0,0.5288952,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(d + e*x)^2,x]","-\frac{2 b^2 c \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 c \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 i b c \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 i b c \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{e (d+e x)}","-\frac{2 b^2 c \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 c \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 i b c \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 i b c \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{e (d+e x)}",1,"-((a + b*ArcSin[c*x])^2/(e*(d + e*x))) - ((2*I)*b*c*(a + b*ArcSin[c*x])*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) + ((2*I)*b*c*(a + b*ArcSin[c*x])*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) - (2*b^2*c*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) + (2*b^2*c*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2])","A",10,7,18,0.3889,1,"{4743, 4773, 3323, 2264, 2190, 2279, 2391}"
15,1,401,0,0.6355373,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[(a + b*ArcSin[c*x])^2/(d + e*x)^3,x]","-\frac{b^2 c^3 d \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b^2 c^3 d \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}-\frac{i b c^3 d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{i b c^3 d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 e (d+e x)^2}-\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}","-\frac{b^2 c^3 d \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b^2 c^3 d \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}-\frac{i b c^3 d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{i b c^3 d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 e (d+e x)^2}-\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}",1,"(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/((c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcSin[c*x])^2/(2*e*(d + e*x)^2) - (I*b*c^3*d*(a + b*ArcSin[c*x])*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) + (I*b*c^3*d*(a + b*ArcSin[c*x])*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) - (b^2*c^2*Log[d + e*x])/(e*(c^2*d^2 - e^2)) - (b^2*c^3*d*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) + (b^2*c^3*d*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2))","A",13,10,18,0.5556,1,"{4743, 4773, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
16,1,393,0,1.1335027,"\int \frac{(d+e x)^3}{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x)^3/(a + b*ArcSin[c*x]),x]","-\frac{3 d^2 e \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{3 d e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \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{e^3 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^4}+\frac{3 d^2 e \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{3 d e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \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{e^3 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^4}+\frac{d^3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}+\frac{d^3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}","-\frac{3 d^2 e \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{3 d e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \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{e^3 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^4}+\frac{3 d^2 e \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{3 d e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \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{e^3 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^4}+\frac{d^3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}+\frac{d^3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}",1,"(d^3*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(b*c) + (3*d*e^2*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) - (3*d*e^2*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3) - (3*d^2*e*CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(2*b*c^2) - (e^3*CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(4*b*c^4) + (e^3*CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(8*b*c^4) + (d^3*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b*c) + (3*d*e^2*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) + (3*d^2*e*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^2) + (e^3*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(4*b*c^4) - (3*d*e^2*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3) - (e^3*Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c^4)","A",27,7,18,0.3889,1,"{4747, 6742, 3303, 3299, 3302, 4406, 12}"
17,1,244,0,0.6667475,"\int \frac{(d+e x)^2}{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x)^2/(a + b*ArcSin[c*x]),x]","-\frac{d e \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \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{d e \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \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{d^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}+\frac{d^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}","-\frac{d e \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \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{d e \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \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{d^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}+\frac{d^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}",1,"(d^2*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(b*c) + (e^2*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) - (e^2*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3) - (d*e*CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(b*c^2) + (d^2*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b*c) + (e^2*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) + (d*e*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b*c^2) - (e^2*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3)","A",17,6,18,0.3333,1,"{4747, 6742, 3303, 3299, 3302, 4406}"
18,1,115,0,0.3064741,"\int \frac{d+e x}{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x)/(a + b*ArcSin[c*x]),x]","-\frac{e \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{e \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{d \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}+\frac{d \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}","-\frac{e \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{e \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{d \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}+\frac{d \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c}",1,"(d*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(b*c) - (e*CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(2*b*c^2) + (d*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b*c) + (e*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^2)","A",11,7,16,0.4375,1,"{4747, 6742, 3303, 3299, 3302, 4406, 12}"
19,1,53,0,0.0655422,"\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}"
20,0,0,0,0.0309113,"\int \frac{1}{(d+e x) \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{(d+e x) \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
21,0,0,0,0.0290262,"\int \frac{1}{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)^2*(a + b*ArcSin[c*x])),x]","\int \frac{1}{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x)^2*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
22,1,354,0,0.5459858,"\int \frac{(d+e x)^2}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)^2/(a + b*ArcSin[c*x])^2,x]","\frac{2 d e \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{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 e^2 \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{2 d e \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{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{3 e^2 \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{d^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}-\frac{d^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}-\frac{d^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{2 d e x \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{e^2 x^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{2 d e \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{e^2 \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 e^2 \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{2 d e \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{e^2 \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 e^2 \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{d^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{2 d e x \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{e^2 x^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((d^2*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x]))) - (2*d*e*x*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x])) - (e^2*x^2*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x])) + (2*d*e*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^2) + (d^2*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(b^2*c) + (e^2*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(4*b^2*c^3) - (3*e^2*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(4*b^2*c^3) - (d^2*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b^2*c) - (e^2*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^3) + (2*d*e*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^2) + (3*e^2*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^3)","A",19,7,18,0.3889,1,"{4745, 4621, 4723, 3303, 3299, 3302, 4631}"
23,1,177,0,0.3120241,"\int \frac{d+e x}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)/(a + b*ArcSin[c*x])^2,x]","\frac{e \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{e \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{d \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}-\frac{d \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b^2 c}-\frac{d \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{e x \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{e \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{e \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{d \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{e x \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((d*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x]))) - (e*x*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x])) + (e*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^2) + (d*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(b^2*c) - (d*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b^2*c) + (e*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^2)","A",11,7,16,0.4375,1,"{4745, 4621, 4723, 3303, 3299, 3302, 4631}"
24,1,82,0,0.1728255,"\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}"
25,0,0,0,0.028645,"\int \frac{1}{(d+e x) \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{(d+e x) \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
26,0,0,0,0.0274703,"\int \frac{1}{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x)^2*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x)^2*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
27,0,0,0,0.1961378,"\int (d+e x)^m \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^m*(a + b*ArcSin[c*x])^2,x]","\int (d+e x)^m \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{(d+e x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{e (m+1)}-\frac{2 b c \text{Int}\left(\frac{(d+e x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}},x\right)}{e (m+1)}",0,"((d + e*x)^(1 + m)*(a + b*ArcSin[c*x])^2)/(e*(1 + m)) - (2*b*c*Defer[Int][((d + e*x)^(1 + m)*(a + b*ArcSin[c*x]))/Sqrt[1 - c^2*x^2], x])/(e*(1 + m))","A",0,0,0,0,-1,"{}"
28,1,154,0,0.0856186,"\int (d+e x)^m \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^m*(a + b*ArcSin[c*x]),x]","\frac{(d+e x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{e (m+1)}-\frac{b c \sqrt{1-\frac{c (d+e x)}{c d-e}} \sqrt{1-\frac{c (d+e x)}{c d+e}} (d+e x)^{m+2} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{c (d+e x)}{c d-e},\frac{c (d+e x)}{c d+e}\right)}{e^2 (m+1) (m+2) \sqrt{1-c^2 x^2}}","\frac{(d+e x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{e (m+1)}-\frac{b c \sqrt{1-\frac{c (d+e x)}{c d-e}} \sqrt{1-\frac{c (d+e x)}{c d+e}} (d+e x)^{m+2} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{c (d+e x)}{c d-e},\frac{c (d+e x)}{c d+e}\right)}{e^2 (m+1) (m+2) \sqrt{1-c^2 x^2}}",1,"-((b*c*(d + e*x)^(2 + m)*Sqrt[1 - (c*(d + e*x))/(c*d - e)]*Sqrt[1 - (c*(d + e*x))/(c*d + e)]*AppellF1[2 + m, 1/2, 1/2, 3 + m, (c*(d + e*x))/(c*d - e), (c*(d + e*x))/(c*d + e)])/(e^2*(1 + m)*(2 + m)*Sqrt[1 - c^2*x^2])) + ((d + e*x)^(1 + m)*(a + b*ArcSin[c*x]))/(e*(1 + m))","A",3,3,16,0.1875,1,"{4743, 760, 133}"
29,0,0,0,0.0274455,"\int \frac{(d+e x)^m}{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x)^m/(a + b*ArcSin[c*x]),x]","\int \frac{(d+e x)^m}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d+e x)^m}{a+b \sin ^{-1}(c x)},x\right)",0,"Defer[Int][(d + e*x)^m/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
30,0,0,0,0.0274853,"\int \frac{(d+e x)^m}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)^m/(a + b*ArcSin[c*x])^2,x]","\int \frac{(d+e x)^m}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d+e x)^m}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d + e*x)^m/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
31,1,669,0,0.6925497,"\int (f+g x)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","-\frac{f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}+\frac{g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4}-\frac{g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4}-\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}+\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{1-c^2 x^2}}-\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}-\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{1-c^2 x^2}}+\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}","-\frac{f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}+\frac{g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4}-\frac{g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4}-\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}+\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{1-c^2 x^2}}-\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}-\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{1-c^2 x^2}}+\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}",1,"(b*f^2*g*x*Sqrt[d - c^2*d*x^2])/(c*Sqrt[1 - c^2*x^2]) + (2*b*g^3*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[1 - c^2*x^2]) - (b*c*f^3*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) + (3*b*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[1 - c^2*x^2]) - (b*c*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(3*Sqrt[1 - c^2*x^2]) + (b*g^3*x^3*Sqrt[d - c^2*d*x^2])/(45*c*Sqrt[1 - c^2*x^2]) - (3*b*c*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (b*c*g^3*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + (f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - (3*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c^2) + (3*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/4 - (f^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/c^2 - (g^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^4) + (g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c^4) + (f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2]) + (3*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c^3*Sqrt[1 - c^2*x^2])","A",16,12,31,0.3871,1,"{4777, 4763, 4647, 4641, 30, 4677, 4697, 4707, 266, 43, 4689, 12}"
32,1,450,0,0.5232951,"\int (f+g x)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}",1,"(2*b*f*g*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[1 - c^2*x^2]) - (b*c*f^2*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) + (b*g^2*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[1 - c^2*x^2]) - (2*b*c*f*g*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) - (b*c*g^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - (g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c^2) + (g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/4 - (2*f*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^2) + (f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2]) + (g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c^3*Sqrt[1 - c^2*x^2])","A",13,8,31,0.2581,1,"{4777, 4763, 4647, 4641, 30, 4677, 4697, 4707}"
33,1,238,0,0.2421495,"\int (f+g x) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}",1,"(b*g*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[1 - c^2*x^2]) - (b*c*f*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) - (b*c*g*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) + (f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - (g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^2) + (f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",8,6,29,0.2069,1,"{4777, 4763, 4647, 4641, 30, 4677}"
34,1,736,0,1.8763902,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{f+g x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(f + g*x),x]","\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{1-c^2 x^2} (f+g x)}+\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (f+g x)}+\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g \sqrt{1-c^2 x^2}}-\frac{a \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tan ^{-1}\left(\frac{c^2 f x+g}{\sqrt{1-c^2 x^2} \sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{a \sqrt{d-c^2 d x^2}}{g}+\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g}","\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{1-c^2 x^2} (f+g x)}+\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (f+g x)}+\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g \sqrt{1-c^2 x^2}}-\frac{a \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tan ^{-1}\left(\frac{c^2 f x+g}{\sqrt{1-c^2 x^2} \sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{a \sqrt{d-c^2 d x^2}}{g}+\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g}",1,"(a*Sqrt[d - c^2*d*x^2])/g - (b*c*x*Sqrt[d - c^2*d*x^2])/(g*Sqrt[1 - c^2*x^2]) + (b*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/g + (c*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*g*Sqrt[1 - c^2*x^2]) - ((1 - (c^2*f^2)/g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*(f + g*x)*Sqrt[1 - c^2*x^2]) + (Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*(f + g*x)) - (a*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^2*Sqrt[1 - c^2*x^2]) + (I*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (I*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) + (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2])","A",22,19,31,0.6129,1,"{4777, 4765, 683, 4757, 6742, 725, 204, 1654, 12, 4799, 4797, 4677, 8, 4773, 3323, 2264, 2190, 2279, 2391}"
35,1,860,0,2.7148843,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{(f+g x)^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(f + g*x)^2,x]","-\frac{b f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}-\frac{a f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}+\frac{a f \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{i b f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{i b f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}+\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b (f+g x)^2 c}+\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) (f+g x)^2 \sqrt{1-c^2 x^2} c}","-\frac{b f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}-\frac{a f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}+\frac{a f \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{i b f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{i b f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}+\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b (f+g x)^2 c}+\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) (f+g x)^2 \sqrt{1-c^2 x^2} c}",1,"-((a*Sqrt[d - c^2*d*x^2])/(g*(f + g*x))) - (b*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(g*(f + g*x)) - (a*c^3*f^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(g^2*(c^2*f^2 - g^2)*Sqrt[1 - c^2*x^2]) - (b*c^3*f^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2)/(2*g^2*(c^2*f^2 - g^2)*Sqrt[1 - c^2*x^2]) + ((g + c^2*f*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*(c^2*f^2 - g^2)*(f + g*x)^2*Sqrt[1 - c^2*x^2]) + (Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*(f + g*x)^2) + (a*c^2*f*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) - (I*b*c^2*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) + (I*b*c^2*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) + (b*c*Sqrt[d - c^2*d*x^2]*Log[f + g*x])/(g^2*Sqrt[1 - c^2*x^2]) - (b*c^2*f*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) + (b*c^2*f*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])","A",35,22,31,0.7097,1,"{4777, 4765, 37, 4755, 12, 1651, 844, 216, 725, 204, 4799, 4797, 4641, 4773, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
36,1,959,0,0.9398587,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{1-c^2 x^2}}-\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{1-c^2 x^2}}-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{1-c^2 x^2}}-\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{1-c^2 x^2}}-\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{1-c^2 x^2}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{1-c^2 x^2}}+\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}+\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}+\frac{d g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4}-\frac{d g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4}-\frac{3 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2}","\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{1-c^2 x^2}}-\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{1-c^2 x^2}}-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{1-c^2 x^2}}-\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{1-c^2 x^2}}-\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{1-c^2 x^2}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{1-c^2 x^2}}+\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}+\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}+\frac{d g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4}-\frac{d g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4}-\frac{3 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2}",1,"(3*b*d*f^2*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) + (2*b*d*g^3*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[1 - c^2*x^2]) - (5*b*c*d*f^3*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (3*b*d*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[1 - c^2*x^2]) - (2*b*c*d*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(5*Sqrt[1 - c^2*x^2]) + (b*d*g^3*x^3*Sqrt[d - c^2*d*x^2])/(105*c*Sqrt[1 - c^2*x^2]) + (b*c^3*d*f^3*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (7*b*c*d*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(32*Sqrt[1 - c^2*x^2]) + (3*b*c^3*d*f^2*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) - (8*b*c*d*g^3*x^5*Sqrt[d - c^2*d*x^2])/(175*Sqrt[1 - c^2*x^2]) + (b*c^3*d*f*g^2*x^6*Sqrt[d - c^2*d*x^2])/(12*Sqrt[1 - c^2*x^2]) + (b*c^3*d*g^3*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) + (3*d*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 - (3*d*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c^2) + (3*d*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 + (d*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/4 + (d*f*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - (3*d*f^2*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c^2) - (d*g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c^4) + (d*g^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c^4) + (3*d*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2]) + (3*d*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c^3*Sqrt[1 - c^2*x^2])","A",24,17,31,0.5484,1,"{4777, 4763, 4649, 4647, 4641, 30, 14, 4677, 194, 4699, 4697, 4707, 266, 43, 4689, 12, 373}"
37,1,680,0,0.7326716,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d f^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^2}+\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}+\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}+\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}-\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{1-c^2 x^2}}","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d f^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^2}+\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}+\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}+\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}-\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{1-c^2 x^2}}",1,"(2*b*d*f*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) - (5*b*c*d*f^2*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (b*d*g^2*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[1 - c^2*x^2]) - (4*b*c*d*f*g*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[1 - c^2*x^2]) + (b*c^3*d*f^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (7*b*c*d*g^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*f*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + (b*c^3*d*g^2*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[1 - c^2*x^2]) + (3*d*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 - (d*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c^2) + (d*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 + (d*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/4 + (d*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/6 - (2*d*f*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c^2) + (3*d*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2]) + (d*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c^3*Sqrt[1 - c^2*x^2])","A",20,12,31,0.3871,1,"{4777, 4763, 4649, 4647, 4641, 30, 14, 4677, 194, 4699, 4697, 4707}"
38,1,370,0,0.3263037,"\int (f+g x) \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2}+\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}+\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2}+\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}+\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}",1,"(b*d*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) - (5*b*c*d*f*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (2*b*c*d*g*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[1 - c^2*x^2]) + (b*c^3*d*f*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (b*c^3*d*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + (3*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 + (d*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/4 - (d*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c^2) + (3*d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2])","A",12,9,29,0.3103,1,"{4777, 4763, 4649, 4647, 4641, 30, 14, 4677, 194}"
39,1,1073,0,2.2241906,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(f + g*x),x]","\frac{b d x^3 \sqrt{d-c^2 d x^2} c^3}{9 g \sqrt{1-c^2 x^2}}-\frac{b d f x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^2 \sqrt{1-c^2 x^2}}+\frac{d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^2}{2 g^2}-\frac{d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{2 b g^3 \sqrt{1-c^2 x^2}}+\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{4 b g^2 \sqrt{1-c^2 x^2}}+\frac{b d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} c}{g^3 \sqrt{1-c^2 x^2}}-\frac{b d x \sqrt{d-c^2 d x^2} c}{3 g \sqrt{1-c^2 x^2}}-\frac{b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^3}+\frac{d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 g}+\frac{a d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{a d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}-\frac{d (c f-g) (c f+g) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^2 (f+g x) c}-\frac{d \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) \sqrt{1-c^2 x^2} c}","\frac{b d x^3 \sqrt{d-c^2 d x^2} c^3}{9 g \sqrt{1-c^2 x^2}}-\frac{b d f x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^2 \sqrt{1-c^2 x^2}}+\frac{d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^2}{2 g^2}-\frac{d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{2 b g^3 \sqrt{1-c^2 x^2}}+\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{4 b g^2 \sqrt{1-c^2 x^2}}+\frac{b d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} c}{g^3 \sqrt{1-c^2 x^2}}-\frac{b d x \sqrt{d-c^2 d x^2} c}{3 g \sqrt{1-c^2 x^2}}-\frac{b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^3}+\frac{d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 g}+\frac{a d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{a d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}-\frac{d (c f-g) (c f+g) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^2 (f+g x) c}-\frac{d \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) \sqrt{1-c^2 x^2} c}",1,"-((a*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2])/g^3) - (b*c*d*x*Sqrt[d - c^2*d*x^2])/(3*g*Sqrt[1 - c^2*x^2]) + (b*c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2])/(g^3*Sqrt[1 - c^2*x^2]) - (b*c^3*d*f*x^2*Sqrt[d - c^2*d*x^2])/(4*g^2*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^3*Sqrt[d - c^2*d*x^2])/(9*g*Sqrt[1 - c^2*x^2]) - (b*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/g^3 + (c^2*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*g^2) + (d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*g) + (c*d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*g^2*Sqrt[1 - c^2*x^2]) - (c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*g^3*Sqrt[1 - c^2*x^2]) - (d*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*g^4*(f + g*x)*Sqrt[1 - c^2*x^2]) - (d*(c*f - g)*(c*f + g)*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*g^2*(f + g*x)) + (a*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^4*Sqrt[1 - c^2*x^2]) - (I*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (I*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) - (b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2])","A",29,23,31,0.7419,1,"{4777, 4767, 4647, 4641, 30, 4677, 4765, 683, 4757, 6742, 725, 204, 1654, 12, 4799, 4797, 8, 4773, 3323, 2264, 2190, 2279, 2391}"
40,1,1281,0,1.1337837,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","-\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{1-c^2 x^2}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}+\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{1-c^2 x^2}}-\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{1-c^2 x^2}}-\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{1-c^2 x^2}}+\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{1-c^2 x^2}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{1-c^2 x^2}}-\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{1-c^2 x^2}}+\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}+\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}+\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}+\frac{d^2 g^3 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^4}-\frac{d^2 g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4}-\frac{3 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}","-\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{1-c^2 x^2}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}+\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{1-c^2 x^2}}-\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{1-c^2 x^2}}-\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{1-c^2 x^2}}+\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{1-c^2 x^2}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{1-c^2 x^2}}-\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{1-c^2 x^2}}+\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}+\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}+\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}+\frac{d^2 g^3 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^4}-\frac{d^2 g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4}-\frac{3 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}",1,"(3*b*d^2*f^2*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) + (2*b*d^2*g^3*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[1 - c^2*x^2]) - (25*b*c*d^2*f^3*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (15*b*d^2*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[1 - c^2*x^2]) - (3*b*c*d^2*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) + (b*d^2*g^3*x^3*Sqrt[d - c^2*d*x^2])/(189*c*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d^2*f^3*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (59*b*c*d^2*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(256*Sqrt[1 - c^2*x^2]) + (9*b*c^3*d^2*f^2*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) - (b*c*d^2*g^3*x^5*Sqrt[d - c^2*d*x^2])/(21*Sqrt[1 - c^2*x^2]) + (17*b*c^3*d^2*f*g^2*x^6*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (3*b*c^5*d^2*f^2*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) + (19*b*c^3*d^2*g^3*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[1 - c^2*x^2]) - (3*b*c^5*d^2*f*g^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*g^3*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[1 - c^2*x^2]) + (b*d^2*f^3*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/16 - (15*d^2*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c^2) + (15*d^2*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/64 + (5*d^2*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/24 + (5*d^2*f*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/16 + (d^2*f^3*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/6 + (3*d^2*f*g^2*x^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 - (3*d^2*f^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c^2) - (d^2*g^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c^4) + (d^2*g^3*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*c^4) + (5*d^2*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2]) + (15*d^2*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(256*b*c^3*Sqrt[1 - c^2*x^2])","A",30,18,31,0.5806,1,"{4777, 4763, 4649, 4647, 4641, 30, 14, 261, 4677, 194, 4699, 4697, 4707, 266, 43, 4689, 12, 373}"
41,1,940,0,0.919956,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}+\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}+\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x+\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}+\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}+\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}",1,"(2*b*d^2*f*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) - (25*b*c*d^2*f^2*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (5*b*d^2*g^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[1 - c^2*x^2]) - (2*b*c*d^2*f*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d^2*f^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (59*b*c*d^2*g^2*x^4*Sqrt[d - c^2*d*x^2])/(768*Sqrt[1 - c^2*x^2]) + (6*b*c^3*d^2*f*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) + (17*b*c^3*d^2*g^2*x^6*Sqrt[d - c^2*d*x^2])/(288*Sqrt[1 - c^2*x^2]) - (2*b*c^5*d^2*f*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*g^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[1 - c^2*x^2]) + (b*d^2*f^2*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/16 - (5*d^2*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c^2) + (5*d^2*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/64 + (5*d^2*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/24 + (5*d^2*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/48 + (d^2*f^2*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/6 + (d^2*g^2*x^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 - (2*d^2*f*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c^2) + (5*d^2*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2]) + (5*d^2*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(256*b*c^3*Sqrt[1 - c^2*x^2])","A",26,15,31,0.4839,1,"{4777, 4763, 4649, 4647, 4641, 30, 14, 261, 4677, 194, 4699, 4697, 4707, 266, 43}"
42,1,517,0,0.394001,"\int (f+g x) \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{1}{6} d^2 f x \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{24} d^2 f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2}+\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}-\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}-\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}+\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{1-c^2 x^2}}","\frac{1}{6} d^2 f x \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{24} d^2 f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2}+\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}-\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}-\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}+\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{1-c^2 x^2}}",1,"(b*d^2*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) - (25*b*c*d^2*f*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (b*c*d^2*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d^2*f*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (3*b*c^3*d^2*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) + (b*d^2*f*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/16 + (5*d^2*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/24 + (d^2*f*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/6 - (d^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c^2) + (5*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2])","A",14,10,29,0.3448,1,"{4777, 4763, 4649, 4647, 4641, 30, 14, 261, 4677, 194}"
43,1,1648,0,2.6874362,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(f + g*x),x]","-\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{1-c^2 x^2}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{1-c^2 x^2}}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{1-c^2 x^2}}-\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^5}+\frac{d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 g}-\frac{d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 g^3}-\frac{d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) c}+\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^6 (f+g x) \sqrt{1-c^2 x^2} c}","-\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{1-c^2 x^2}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{1-c^2 x^2}}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{1-c^2 x^2}}-\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^5}+\frac{d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 g}-\frac{d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 g^3}-\frac{d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) c}+\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b g^6 (f+g x) \sqrt{1-c^2 x^2} c}",1,"(a*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2])/g^5 + (2*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(15*g*Sqrt[1 - c^2*x^2]) + (b*c*d^2*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2])/(3*g^3*Sqrt[1 - c^2*x^2]) - (b*c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2])/(g^5*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*f*x^2*Sqrt[d - c^2*d*x^2])/(16*g^2*Sqrt[1 - c^2*x^2]) + (b*c^3*d^2*f*(c^2*f^2 - 2*g^2)*x^2*Sqrt[d - c^2*d*x^2])/(4*g^4*Sqrt[1 - c^2*x^2]) + (b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2])/(45*g*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*(c^2*f^2 - 2*g^2)*x^3*Sqrt[d - c^2*d*x^2])/(9*g^3*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*f*x^4*Sqrt[d - c^2*d*x^2])/(16*g^2*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2])/(25*g*Sqrt[1 - c^2*x^2]) + (b*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/g^5 + (c^2*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*g^2) - (c^2*d^2*f*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*g^4) - (c^4*d^2*f*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(4*g^2) - (d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*g) - (d^2*(c^2*f^2 - 2*g^2)*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*g^3) + (d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*g) - (c*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*g^2*Sqrt[1 - c^2*x^2]) - (c*d^2*f*(c^2*f^2 - 2*g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*g^4*Sqrt[1 - c^2*x^2]) + (c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*g^5*Sqrt[1 - c^2*x^2]) + (d^2*(c^2*f^2 - g^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*g^6*(f + g*x)*Sqrt[1 - c^2*x^2]) + (d^2*(c^2*f^2 - g^2)^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*g^4*(f + g*x)) - (a*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^6*Sqrt[1 - c^2*x^2]) + (I*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (I*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) + (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2])","A",37,28,31,0.9032,1,"{4777, 4767, 4647, 4641, 30, 4677, 4697, 4707, 266, 43, 4689, 12, 4765, 683, 4757, 6742, 725, 204, 1654, 4799, 4797, 8, 4773, 3323, 2264, 2190, 2279, 2391}"
44,1,450,0,0.5835743,"\int \frac{(f+g x)^3 \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{3 f^2 g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{f^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}+\frac{3 f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}+\frac{3 b f^2 g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}+\frac{3 b f g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}+\frac{b g^3 x^3 \sqrt{1-c^2 x^2}}{9 c \sqrt{d-c^2 d x^2}}+\frac{2 b g^3 x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}","-\frac{3 f^2 g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{f^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}+\frac{3 f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}+\frac{3 b f^2 g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}+\frac{3 b f g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}+\frac{b g^3 x^3 \sqrt{1-c^2 x^2}}{9 c \sqrt{d-c^2 d x^2}}+\frac{2 b g^3 x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(3*b*f^2*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) + (2*b*g^3*x*Sqrt[1 - c^2*x^2])/(3*c^3*Sqrt[d - c^2*d*x^2]) + (3*b*f*g^2*x^2*Sqrt[1 - c^2*x^2])/(4*c*Sqrt[d - c^2*d*x^2]) + (b*g^3*x^3*Sqrt[1 - c^2*x^2])/(9*c*Sqrt[d - c^2*d*x^2]) - (3*f^2*g*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (2*g^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c^4*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^2]) - (g^3*x^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c^2*Sqrt[d - c^2*d*x^2]) + (f^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2]) + (3*f*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",13,7,31,0.2258,1,"{4777, 4763, 4641, 4677, 8, 4707, 30}"
45,1,270,0,0.4332637,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b f g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}+\frac{b g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}","\frac{f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b f g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}+\frac{b g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}",1,"(2*b*f*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) + (b*g^2*x^2*Sqrt[1 - c^2*x^2])/(4*c*Sqrt[d - c^2*d*x^2]) - (2*f*g*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (g^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^2]) + (f^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2]) + (g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",9,7,31,0.2258,1,"{4777, 4763, 4641, 4677, 8, 4707, 30}"
46,1,126,0,0.222273,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{b g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}","\frac{f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{b g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}",1,"(b*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) - (g*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) + (f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2])","A",6,5,29,0.1724,1,"{4777, 4763, 4641, 4677, 8}"
47,1,380,0,0.6083531,"\int \frac{a+b \sin ^{-1}(c x)}{(f+g x) \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/((f + g*x)*Sqrt[d - c^2*d*x^2]),x]","-\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}","-\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}",1,"((-I)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (I*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2])","A",10,7,31,0.2258,1,"{4777, 4773, 3323, 2264, 2190, 2279, 2391}"
48,1,507,0,0.709962,"\int \frac{a+b \sin ^{-1}(c x)}{(f+g x)^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/((f + g*x)^2*Sqrt[d - c^2*d*x^2]),x]","-\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}-\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c \sqrt{1-c^2 x^2} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}","-\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}-\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c \sqrt{1-c^2 x^2} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}",1,"(g*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/((c^2*f^2 - g^2)*(f + g*x)*Sqrt[d - c^2*d*x^2]) - (I*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (I*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[1 - c^2*x^2]*Log[f + g*x])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) - (b*c^2*f*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (b*c^2*f*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2])","A",13,10,31,0.3226,1,"{4777, 4773, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
49,1,315,0,0.5556829,"\int \frac{(f+g x)^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{\left(c^2 f x \left(c^2 f^2+3 g^2\right)+g \left(3 c^2 f^2+g^2\right)\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}+\frac{g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g)^3 \log (c x+1)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g)^3 \log (1-c x)}{2 c^4 d \sqrt{d-c^2 d x^2}}-\frac{b g^3 x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}","\frac{\left(c^2 f x \left(c^2 f^2+3 g^2\right)+g \left(3 c^2 f^2+g^2\right)\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}+\frac{g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g)^3 \log (c x+1)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g)^3 \log (1-c x)}{2 c^4 d \sqrt{d-c^2 d x^2}}-\frac{b g^3 x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}",1,"-((b*g^3*x*Sqrt[1 - c^2*x^2])/(c^3*d*Sqrt[d - c^2*d*x^2])) + ((g*(3*c^2*f^2 + g^2) + c^2*f*(c^2*f^2 + 3*g^2)*x)*(a + b*ArcSin[c*x]))/(c^4*d*Sqrt[d - c^2*d*x^2]) + (g^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c^4*d*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c^3*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f + g)^3*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(2*c^4*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^3*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(2*c^4*d*Sqrt[d - c^2*d*x^2])","A",11,10,31,0.3226,1,"{4777, 4775, 637, 4761, 12, 633, 31, 4641, 4677, 8}"
50,1,213,0,0.4282208,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{\left(x \left(c^2 f^2+g^2\right)+2 f g\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g)^2 \log (c x+1)}{2 c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g)^2 \log (1-c x)}{2 c^3 d \sqrt{d-c^2 d x^2}}","\frac{\left(x \left(c^2 f^2+g^2\right)+2 f g\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g)^2 \log (c x+1)}{2 c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g)^2 \log (1-c x)}{2 c^3 d \sqrt{d-c^2 d x^2}}",1,"((2*f*g + (c^2*f^2 + g^2)*x)*(a + b*ArcSin[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) - (g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c^3*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f + g)^2*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(2*c^3*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^2*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(2*c^3*d*Sqrt[d - c^2*d*x^2])","A",8,7,31,0.2258,1,"{4777, 4775, 637, 4761, 633, 31, 4641}"
51,1,144,0,0.186609,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{\left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g) \log (1-c x)}{2 c^2 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g) \log (c x+1)}{2 c^2 d \sqrt{d-c^2 d x^2}}","\frac{\left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g) \log (1-c x)}{2 c^2 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g) \log (c x+1)}{2 c^2 d \sqrt{d-c^2 d x^2}}",1,"((g + c^2*f*x)*(a + b*ArcSin[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f + g)*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(2*c^2*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(2*c^2*d*Sqrt[d - c^2*d*x^2])","A",6,6,29,0.2069,1,"{4777, 637, 4761, 12, 633, 31}"
52,1,654,0,1.1598506,"\int \frac{a+b \sin ^{-1}(c x)}{(f+g x) \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/((f + g*x)*(d - c^2*d*x^2)^(3/2)),x]","\frac{b g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{\sqrt{1-c^2 x^2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f+g)}-\frac{\sqrt{1-c^2 x^2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{b \sqrt{1-c^2 x^2} \log \left(\sin \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{b \sqrt{1-c^2 x^2} \log \left(\cos \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{d \sqrt{d-c^2 d x^2} (c f+g)}","\frac{b g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{\sqrt{1-c^2 x^2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f+g)}-\frac{\sqrt{1-c^2 x^2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{b \sqrt{1-c^2 x^2} \log \left(\sin \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{b \sqrt{1-c^2 x^2} \log \left(\cos \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{d \sqrt{d-c^2 d x^2} (c f+g)}",1,"-(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Cot[Pi/4 + ArcSin[c*x]/2])/(2*d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + (I*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (I*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[Cos[Pi/4 + ArcSin[c*x]/2]])/(d*(c*f + g)*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[Sin[Pi/4 + ArcSin[c*x]/2]])/(d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + (b*g^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (b*g^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Tan[Pi/4 + ArcSin[c*x]/2])/(2*d*(c*f + g)*Sqrt[d - c^2*d*x^2])","A",20,11,31,0.3548,1,"{4777, 4775, 4773, 3318, 4184, 3475, 3323, 2264, 2190, 2279, 2391}"
53,1,754,0,0.752741,"\int \frac{(f+g x)^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)^4*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{f g \left(1-c^2 x^2\right) \left(2 c^2 f^2-5 g^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(f+g x) \left(2 c^2 f x \left(c^2 f^2-2 g^2\right)+g \left(c^2 f^2-3 g^2\right)\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(f+g x)^3 \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{g^4 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b f g x \sqrt{1-c^2 x^2} \left(2 c^2 f^2-5 g^2\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b f g x \sqrt{1-c^2 x^2} \left(c^2 f^2-2 g^2\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (f+g x)^2 \left(c^2 f^2+2 c^2 f g x+g^2\right)}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{2 b f g^3 x \sqrt{1-c^2 x^2}}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b g \sqrt{1-c^2 x^2} (c f+g)^3 \log (1-c x)}{6 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b g \sqrt{1-c^2 x^2} (c f-g)^3 \log (c x+1)}{6 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (2 c f-3 g) (c f+g)^3 \log (1-c x)}{6 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g)^3 (2 c f+3 g) \log (c x+1)}{6 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b g^4 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 c^5 d^2 \sqrt{d-c^2 d x^2}}","\frac{f g \left(1-c^2 x^2\right) \left(2 c^2 f^2-5 g^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(f+g x) \left(2 c^2 f x \left(c^2 f^2-2 g^2\right)+g \left(c^2 f^2-3 g^2\right)\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(f+g x)^3 \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{g^4 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (f+g x)^2 \left(c^2 f^2+2 c^2 f g x+g^2\right)}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{b f g^3 x \sqrt{1-c^2 x^2}}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-2 g) (c f+g)^3 \log (1-c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g)^3 (c f+2 g) \log (c x+1)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b g^4 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 c^5 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b*(f + g*x)^2*(c^2*f^2 + g^2 + 2*c^2*f*g*x))/(6*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (2*b*f*g^3*x*Sqrt[1 - c^2*x^2])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) - (b*f*g*(2*c^2*f^2 - 5*g^2)*x*Sqrt[1 - c^2*x^2])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (2*b*f*g*(c^2*f^2 - 2*g^2)*x*Sqrt[1 - c^2*x^2])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) - (b*g^4*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(2*c^5*d^2*Sqrt[d - c^2*d*x^2]) + ((f + g*x)*(g*(c^2*f^2 - 3*g^2) + 2*c^2*f*(c^2*f^2 - 2*g^2)*x)*(a + b*ArcSin[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((g + c^2*f*x)*(f + g*x)^3*(a + b*ArcSin[c*x]))/(3*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (f*g*(2*c^2*f^2 - 5*g^2)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (g^4*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b*(2*c*f - 3*g)*(c*f + g)^3*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(6*c^5*d^2*Sqrt[d - c^2*d*x^2]) - (b*g*(c*f + g)^3*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(6*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^3*g*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(6*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^3*(2*c*f + 3*g)*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(6*c^5*d^2*Sqrt[d - c^2*d*x^2])","A",13,10,31,0.3226,1,"{4777, 739, 819, 641, 216, 4761, 774, 633, 31, 4641}"
54,1,410,0,0.4326802,"\int \frac{(f+g x)^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{2 (c f+g) (c f-g) \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(f+g x)^2 \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b (f+g x) \left(c^2 f^2+2 c^2 f g x+g^2\right)}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b g \sqrt{1-c^2 x^2} (c f-g)^2 \log (c x+1)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g) (c f-g)^2 \log (c x+1)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g)^2 (c f-g) \log (1-c x)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b g \sqrt{1-c^2 x^2} (c f+g)^2 \log (1-c x)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}","\frac{2 (c f+g) (c f-g) \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(f+g x)^2 \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b (f+g x) \left(c^2 f^2+2 c^2 f g x+g^2\right)}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b g \sqrt{1-c^2 x^2} (c f-g)^2 \log (c x+1)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g) (c f-g)^2 \log (c x+1)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f+g)^2 (c f-g) \log (1-c x)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b g \sqrt{1-c^2 x^2} (c f+g)^2 \log (1-c x)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b*(f + g*x)*(c^2*f^2 + g^2 + 2*c^2*f*g*x))/(6*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (2*(c*f - g)*(c*f + g)*(g + c^2*f*x)*(a + b*ArcSin[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((g + c^2*f*x)*(f + g*x)^2*(a + b*ArcSin[c*x]))/(3*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)*(c*f + g)^2*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (b*g*(c*f + g)^2*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(12*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^2*g*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(12*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^2*(c*f + g)*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2])","A",10,7,31,0.2258,1,"{4777, 723, 637, 4761, 819, 633, 31}"
55,1,354,0,0.3902608,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{x (f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 f \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (f+g x)^2}{6 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b f \sqrt{1-c^2 x^2} (c f+g) \log (1-c x)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b g \sqrt{1-c^2 x^2} (c f+g) \log (1-c x)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b f \sqrt{1-c^2 x^2} (c f-g) \log (c x+1)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{b g \sqrt{1-c^2 x^2} (c f-g) \log (c x+1)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}","\frac{x (f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 f \left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b x \left(x \left(c^2 f^2+g^2\right)+2 f g\right)}{6 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (2 c f-g) (c f+g) \log (1-c x)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} (c f-g) (2 c f+g) \log (c x+1)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b*(f + g*x)^2)/(6*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (2*f*(g + c^2*f*x)*(a + b*ArcSin[c*x]))/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (x*(f + g*x)^2*(a + b*ArcSin[c*x]))/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (b*f*(c*f + g)*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) - (b*g*(c*f + g)*Sqrt[1 - c^2*x^2]*Log[1 - c*x])/(6*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (b*f*(c*f - g)*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)*g*Sqrt[1 - c^2*x^2]*Log[1 + c*x])/(6*c^3*d^2*Sqrt[d - c^2*d*x^2])","A",10,7,31,0.2258,1,"{4777, 729, 637, 4761, 819, 633, 31}"
56,1,228,0,0.1947994,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{\left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 f x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (f+g x)}{6 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b f \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{b g \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 c^2 d^2 \sqrt{d-c^2 d x^2}}","\frac{\left(c^2 f x+g\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 f x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (f+g x)}{6 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b f \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{b g \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 c^2 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b*(f + g*x))/(6*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (2*f*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) + ((g + c^2*f*x)*(a + b*ArcSin[c*x]))/(3*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (b*g*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(6*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (b*f*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(3*c*d^2*Sqrt[d - c^2*d*x^2])","A",6,6,29,0.2069,1,"{4777, 639, 191, 4761, 206, 260}"
57,1,1300,0,1.7673451,"\int \frac{a+b \sin ^{-1}(c x)}{(f+g x) \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/((f + g*x)*(d - c^2*d*x^2)^(5/2)),x]","-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f-g) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f-g) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f+g) \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 d^2 (c f-g) \sqrt{d-c^2 d x^2}}-\frac{(c f-2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{4 d^2 (c f-g)^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f+2 g) \sqrt{1-c^2 x^2} \log \left(\cos \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{2 d^2 (c f+g)^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(\cos \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{6 d^2 (c f+g) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(\sin \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{6 d^2 (c f-g) \sqrt{d-c^2 d x^2}}+\frac{b (c f-2 g) \sqrt{1-c^2 x^2} \log \left(\sin \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{2 d^2 (c f-g)^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f+g) \sqrt{d-c^2 d x^2}}+\frac{(c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{4 d^2 (c f+g)^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 d^2 (c f+g) \sqrt{d-c^2 d x^2}}","-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) g^4}{d^2 (c f-g)^2 (c f+g)^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f-g) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f-g) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f+g) \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 d^2 (c f-g) \sqrt{d-c^2 d x^2}}-\frac{(c f-2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{4 d^2 (c f-g)^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f+2 g) \sqrt{1-c^2 x^2} \log \left(\cos \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{2 d^2 (c f+g)^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(\cos \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{6 d^2 (c f+g) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(\sin \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{6 d^2 (c f-g) \sqrt{d-c^2 d x^2}}+\frac{b (c f-2 g) \sqrt{1-c^2 x^2} \log \left(\sin \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)\right)}{2 d^2 (c f-g)^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 d^2 (c f+g) \sqrt{d-c^2 d x^2}}+\frac{(c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{4 d^2 (c f+g)^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 d^2 (c f+g) \sqrt{d-c^2 d x^2}}",1,"-((c*f - 2*g)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Cot[Pi/4 + ArcSin[c*x]/2])/(4*d^2*(c*f - g)^2*Sqrt[d - c^2*d*x^2]) - (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Cot[Pi/4 + ArcSin[c*x]/2])/(12*d^2*(c*f - g)*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[1 - c^2*x^2]*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(24*d^2*(c*f - g)*Sqrt[d - c^2*d*x^2]) - (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Cot[Pi/4 + ArcSin[c*x]/2]*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(24*d^2*(c*f - g)*Sqrt[d - c^2*d*x^2]) - (I*g^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d^2*(c*f - g)^2*(c*f + g)^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (I*g^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d^2*(c*f - g)^2*(c*f + g)^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[Cos[Pi/4 + ArcSin[c*x]/2]])/(6*d^2*(c*f + g)*Sqrt[d - c^2*d*x^2]) + (b*(c*f + 2*g)*Sqrt[1 - c^2*x^2]*Log[Cos[Pi/4 + ArcSin[c*x]/2]])/(2*d^2*(c*f + g)^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - 2*g)*Sqrt[1 - c^2*x^2]*Log[Sin[Pi/4 + ArcSin[c*x]/2]])/(2*d^2*(c*f - g)^2*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[Sin[Pi/4 + ArcSin[c*x]/2]])/(6*d^2*(c*f - g)*Sqrt[d - c^2*d*x^2]) - (b*g^4*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d^2*(c*f - g)^2*(c*f + g)^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (b*g^4*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d^2*(c*f - g)^2*(c*f + g)^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[1 - c^2*x^2]*Sec[Pi/4 + ArcSin[c*x]/2]^2)/(24*d^2*(c*f + g)*Sqrt[d - c^2*d*x^2]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Tan[Pi/4 + ArcSin[c*x]/2])/(12*d^2*(c*f + g)*Sqrt[d - c^2*d*x^2]) + ((c*f + 2*g)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Tan[Pi/4 + ArcSin[c*x]/2])/(4*d^2*(c*f + g)^2*Sqrt[d - c^2*d*x^2]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Sec[Pi/4 + ArcSin[c*x]/2]^2*Tan[Pi/4 + ArcSin[c*x]/2])/(24*d^2*(c*f + g)*Sqrt[d - c^2*d*x^2])","A",30,12,31,0.3871,1,"{4777, 4775, 4773, 3318, 4185, 4184, 3475, 3323, 2264, 2190, 2279, 2391}"
58,1,1154,0,1.554798,"\int (f+g x)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{25 \sqrt{1-c^2 x^2}}+\frac{1}{5} g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{3 b c f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{8 \sqrt{1-c^2 x^2}}+\frac{3}{4} f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{2 b g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{45 c \sqrt{1-c^2 x^2}}-\frac{2 b c f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{3 \sqrt{1-c^2 x^2}}-\frac{3}{32} b^2 f g^2 \sqrt{d-c^2 d x^2} x^3-\frac{g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^2}{15 c^2}-\frac{b c f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{2 \sqrt{1-c^2 x^2}}+\frac{3 b f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{8 c \sqrt{1-c^2 x^2}}+\frac{1}{2} f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{8 c^2}+\frac{4 b^2 g^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) x}{15 c^3 \sqrt{1-c^2 x^2}}+\frac{2 b f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 f^3 \sqrt{d-c^2 d x^2} x+\frac{3 b^2 f g^2 \sqrt{d-c^2 d x^2} x}{64 c^2}+\frac{4 a b g^3 \sqrt{d-c^2 d x^2} x}{15 c^3 \sqrt{1-c^2 x^2}}+\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}+\frac{f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^4}-\frac{f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^2}+\frac{b^2 f^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{3 b^2 f g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}+\frac{52 b^2 g^3 \sqrt{d-c^2 d x^2}}{225 c^4}-\frac{2 b^2 g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^4}+\frac{4 b^2 f^2 g \sqrt{d-c^2 d x^2}}{3 c^2}+\frac{26 b^2 g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{675 c^4}+\frac{2 b^2 f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{9 c^2}","-\frac{2 b c g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{25 \sqrt{1-c^2 x^2}}+\frac{1}{5} g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{3 b c f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{8 \sqrt{1-c^2 x^2}}+\frac{3}{4} f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{2 b g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{45 c \sqrt{1-c^2 x^2}}-\frac{2 b c f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{3 \sqrt{1-c^2 x^2}}-\frac{3}{32} b^2 f g^2 \sqrt{d-c^2 d x^2} x^3-\frac{g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^2}{15 c^2}-\frac{b c f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{2 \sqrt{1-c^2 x^2}}+\frac{3 b f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{8 c \sqrt{1-c^2 x^2}}+\frac{1}{2} f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{8 c^2}+\frac{4 b^2 g^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) x}{15 c^3 \sqrt{1-c^2 x^2}}+\frac{2 b f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 f^3 \sqrt{d-c^2 d x^2} x+\frac{3 b^2 f g^2 \sqrt{d-c^2 d x^2} x}{64 c^2}+\frac{4 a b g^3 \sqrt{d-c^2 d x^2} x}{15 c^3 \sqrt{1-c^2 x^2}}+\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}+\frac{f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^4}-\frac{f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^2}+\frac{b^2 f^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{3 b^2 f g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}+\frac{52 b^2 g^3 \sqrt{d-c^2 d x^2}}{225 c^4}-\frac{2 b^2 g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^4}+\frac{4 b^2 f^2 g \sqrt{d-c^2 d x^2}}{3 c^2}+\frac{26 b^2 g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{675 c^4}+\frac{2 b^2 f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{9 c^2}",1,"(4*b^2*f^2*g*Sqrt[d - c^2*d*x^2])/(3*c^2) + (52*b^2*g^3*Sqrt[d - c^2*d*x^2])/(225*c^4) - (b^2*f^3*x*Sqrt[d - c^2*d*x^2])/4 + (3*b^2*f*g^2*x*Sqrt[d - c^2*d*x^2])/(64*c^2) - (3*b^2*f*g^2*x^3*Sqrt[d - c^2*d*x^2])/32 + (4*a*b*g^3*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[1 - c^2*x^2]) + (2*b^2*f^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(9*c^2) + (26*b^2*g^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(675*c^4) - (2*b^2*g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*c^4) + (b^2*f^3*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) - (3*b^2*f*g^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c^3*Sqrt[1 - c^2*x^2]) + (4*b^2*g^3*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(15*c^3*Sqrt[1 - c^2*x^2]) + (2*b*f^2*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(c*Sqrt[1 - c^2*x^2]) - (b*c*f^3*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + (3*b*f*g^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c*Sqrt[1 - c^2*x^2]) - (2*b*c*f^2*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) + (2*b*g^3*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(45*c*Sqrt[1 - c^2*x^2]) - (3*b*c*f*g^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) - (2*b*c*g^3*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) - (2*g^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*c^4) + (f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 - (3*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(8*c^2) - (g^3*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*c^2) + (3*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/4 + (g^3*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/5 - (f^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/c^2 + (f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2]) + (f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*c^3*Sqrt[1 - c^2*x^2])","A",37,16,33,0.4848,1,"{4777, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43, 4697, 4707, 4619, 261, 266}"
59,1,737,0,1.0271317,"\int (f+g x)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{4 b c f g x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}+\frac{4 b f g x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{1-c^2 x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c \sqrt{1-c^2 x^2}}-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 f^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}+\frac{8 b^2 f g \sqrt{d-c^2 d x^2}}{9 c^2}+\frac{4 b^2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 c^2}-\frac{1}{32} b^2 g^2 x^3 \sqrt{d-c^2 d x^2}+\frac{b^2 g^2 x \sqrt{d-c^2 d x^2}}{64 c^2}-\frac{b^2 g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}","-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{4 b c f g x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}+\frac{4 b f g x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{1-c^2 x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c \sqrt{1-c^2 x^2}}-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 f^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}+\frac{8 b^2 f g \sqrt{d-c^2 d x^2}}{9 c^2}+\frac{4 b^2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 c^2}-\frac{1}{32} b^2 g^2 x^3 \sqrt{d-c^2 d x^2}+\frac{b^2 g^2 x \sqrt{d-c^2 d x^2}}{64 c^2}-\frac{b^2 g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}",1,"(8*b^2*f*g*Sqrt[d - c^2*d*x^2])/(9*c^2) - (b^2*f^2*x*Sqrt[d - c^2*d*x^2])/4 + (b^2*g^2*x*Sqrt[d - c^2*d*x^2])/(64*c^2) - (b^2*g^2*x^3*Sqrt[d - c^2*d*x^2])/32 + (4*b^2*f*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(27*c^2) + (b^2*f^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) - (b^2*g^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c^3*Sqrt[1 - c^2*x^2]) + (4*b*f*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c*Sqrt[1 - c^2*x^2]) - (b*c*f^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + (b*g^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c*Sqrt[1 - c^2*x^2]) - (4*b*c*f*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) - (b*c*g^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 - (g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(8*c^2) + (g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/4 - (2*f*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^2) + (f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2]) + (g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(24*b*c^3*Sqrt[1 - c^2*x^2])","A",23,13,33,0.3939,1,"{4777, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43, 4697, 4707}"
60,1,396,0,0.5038081,"\int (f+g x) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","-\frac{b c f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{2 b c g x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}+\frac{2 b g x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{1-c^2 x^2}}-\frac{g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2}-\frac{1}{4} b^2 f x \sqrt{d-c^2 d x^2}+\frac{b^2 f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}+\frac{4 b^2 g \sqrt{d-c^2 d x^2}}{9 c^2}+\frac{2 b^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 c^2}","-\frac{b c f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{2 b c g x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}+\frac{2 b g x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{1-c^2 x^2}}-\frac{g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2}-\frac{1}{4} b^2 f x \sqrt{d-c^2 d x^2}+\frac{b^2 f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}+\frac{4 b^2 g \sqrt{d-c^2 d x^2}}{9 c^2}+\frac{2 b^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 c^2}",1,"(4*b^2*g*Sqrt[d - c^2*d*x^2])/(9*c^2) - (b^2*f*x*Sqrt[d - c^2*d*x^2])/4 + (2*b^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(27*c^2) + (b^2*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) + (2*b*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c*Sqrt[1 - c^2*x^2]) - (b*c*f*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) - (2*b*c*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) + (f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 - (g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^2) + (f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2])","A",13,11,31,0.3548,1,"{4777, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43}"
61,1,1442,0,3.0546733,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{f+g x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(f + g*x),x]","\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (f+g x)}+\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g \sqrt{1-c^2 x^2}}-\frac{\left(1-\frac{c^2 f^2}{g^2}\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (f+g x) \sqrt{1-c^2 x^2}}+\frac{b^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2}{g}-\frac{2 b^2 c x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g \sqrt{1-c^2 x^2}}+\frac{2 a b \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g}-\frac{a^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 i a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 i a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 a b c x \sqrt{d-c^2 d x^2}}{g \sqrt{1-c^2 x^2}}+\frac{a^2 \sqrt{d-c^2 d x^2}}{g}-\frac{2 b^2 \sqrt{d-c^2 d x^2}}{g}","\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (f+g x)}+\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g \sqrt{1-c^2 x^2}}-\frac{\left(1-\frac{c^2 f^2}{g^2}\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (f+g x) \sqrt{1-c^2 x^2}}+\frac{b^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2}{g}-\frac{2 b^2 c x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g \sqrt{1-c^2 x^2}}+\frac{2 a b \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g}-\frac{a^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 i a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 i a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 a b \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{2 i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 i b^2 \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}-\frac{2 a b c x \sqrt{d-c^2 d x^2}}{g \sqrt{1-c^2 x^2}}+\frac{a^2 \sqrt{d-c^2 d x^2}}{g}-\frac{2 b^2 \sqrt{d-c^2 d x^2}}{g}",1,"(a^2*Sqrt[d - c^2*d*x^2])/g - (2*b^2*Sqrt[d - c^2*d*x^2])/g - (2*a*b*c*x*Sqrt[d - c^2*d*x^2])/(g*Sqrt[1 - c^2*x^2]) + (2*a*b*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/g - (2*b^2*c*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(g*Sqrt[1 - c^2*x^2]) + (b^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2)/g + (c*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*g*Sqrt[1 - c^2*x^2]) - ((1 - (c^2*f^2)/g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*(f + g*x)*Sqrt[1 - c^2*x^2]) + (Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*(f + g*x)) - (a^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^2*Sqrt[1 - c^2*x^2]) + ((2*I)*a*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) + (I*b^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - ((2*I)*a*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (I*b^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) + (2*a*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) + (2*b^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (2*a*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (2*b^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) + ((2*I)*b^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - ((2*I)*b^2*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2])","A",38,23,33,0.6970,1,"{4777, 4765, 683, 4757, 4799, 1654, 12, 725, 204, 4797, 4677, 8, 4773, 3323, 2264, 2190, 2279, 2391, 4619, 261, 2531, 2282, 6589}"
62,1,1685,0,2.4691146,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2 b c^3 d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{6 \sqrt{1-c^2 x^2}}-\frac{16 b c d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{175 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{25 \sqrt{1-c^2 x^2}}+\frac{1}{36} b^2 c^2 d f g^2 \sqrt{d-c^2 d x^2} x^5+\frac{3}{35} d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4+\frac{1}{7} d g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{16 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{1}{2} d f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{105 c \sqrt{1-c^2 x^2}}-\frac{4 b c d f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{5 \sqrt{1-c^2 x^2}}-\frac{43}{576} b^2 d f g^2 \sqrt{d-c^2 d x^2} x^3-\frac{d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^2}{35 c^2}-\frac{3 b c d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{8 \sqrt{1-c^2 x^2}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{16 c^2}+\frac{1}{4} d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b^2 d g^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) x}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{6 b d f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{5 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 d f^3 \sqrt{d-c^2 d x^2} x-\frac{7 b^2 d f g^2 \sqrt{d-c^2 d x^2} x}{384 c^2}-\frac{1}{32} b^2 d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x+\frac{4 a b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \sqrt{1-c^2 x^2}}+\frac{d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{16 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{35 c^4}-\frac{3 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}+\frac{9 b^2 d f^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}+\frac{7 b^2 d f g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{384 c^3 \sqrt{1-c^2 x^2}}+\frac{b d f^3 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{304 b^2 d g^3 \sqrt{d-c^2 d x^2}}{3675 c^4}-\frac{2 b^2 d g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^4}+\frac{38 b^2 d g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{6125 c^4}+\frac{6 b^2 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{16 b^2 d f^2 g \sqrt{d-c^2 d x^2}}{25 c^2}+\frac{152 b^2 d g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11025 c^4}+\frac{8 b^2 d f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{75 c^2}","\frac{2 b c^3 d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{6 \sqrt{1-c^2 x^2}}-\frac{16 b c d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{175 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{25 \sqrt{1-c^2 x^2}}+\frac{1}{36} b^2 c^2 d f g^2 \sqrt{d-c^2 d x^2} x^5+\frac{3}{35} d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4+\frac{1}{7} d g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{16 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{1}{2} d f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{105 c \sqrt{1-c^2 x^2}}-\frac{4 b c d f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{5 \sqrt{1-c^2 x^2}}-\frac{43}{576} b^2 d f g^2 \sqrt{d-c^2 d x^2} x^3-\frac{d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^2}{35 c^2}-\frac{3 b c d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{8 \sqrt{1-c^2 x^2}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{16 c^2}+\frac{1}{4} d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b^2 d g^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) x}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{6 b d f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{5 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 d f^3 \sqrt{d-c^2 d x^2} x-\frac{7 b^2 d f g^2 \sqrt{d-c^2 d x^2} x}{384 c^2}-\frac{1}{32} b^2 d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x+\frac{4 a b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{d f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \sqrt{1-c^2 x^2}}+\frac{d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{16 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{35 c^4}-\frac{3 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}+\frac{9 b^2 d f^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}+\frac{7 b^2 d f g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{384 c^3 \sqrt{1-c^2 x^2}}+\frac{b d f^3 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{304 b^2 d g^3 \sqrt{d-c^2 d x^2}}{3675 c^4}-\frac{2 b^2 d g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^4}+\frac{38 b^2 d g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{6125 c^4}+\frac{6 b^2 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{16 b^2 d f^2 g \sqrt{d-c^2 d x^2}}{25 c^2}+\frac{152 b^2 d g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11025 c^4}+\frac{8 b^2 d f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{75 c^2}",1,"(16*b^2*d*f^2*g*Sqrt[d - c^2*d*x^2])/(25*c^2) + (304*b^2*d*g^3*Sqrt[d - c^2*d*x^2])/(3675*c^4) - (15*b^2*d*f^3*x*Sqrt[d - c^2*d*x^2])/64 - (7*b^2*d*f*g^2*x*Sqrt[d - c^2*d*x^2])/(384*c^2) - (43*b^2*d*f*g^2*x^3*Sqrt[d - c^2*d*x^2])/576 + (b^2*c^2*d*f*g^2*x^5*Sqrt[d - c^2*d*x^2])/36 + (4*a*b*d*g^3*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[1 - c^2*x^2]) + (8*b^2*d*f^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(75*c^2) + (152*b^2*d*g^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(11025*c^4) - (b^2*d*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/32 + (6*b^2*d*f^2*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*c^2) + (38*b^2*d*g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(6125*c^4) - (2*b^2*d*g^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(343*c^4) + (9*b^2*d*f^3*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c*Sqrt[1 - c^2*x^2]) + (7*b^2*d*f*g^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(384*c^3*Sqrt[1 - c^2*x^2]) + (4*b^2*d*g^3*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(35*c^3*Sqrt[1 - c^2*x^2]) + (6*b*d*f^2*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c*Sqrt[1 - c^2*x^2]) - (3*b*c*d*f^3*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (3*b*d*f*g^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c*Sqrt[1 - c^2*x^2]) - (4*b*c*d*f^2*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*Sqrt[1 - c^2*x^2]) + (2*b*d*g^3*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(105*c*Sqrt[1 - c^2*x^2]) - (7*b*c*d*f*g^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*Sqrt[1 - c^2*x^2]) + (6*b*c^3*d*f^2*g*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) - (16*b*c*d*g^3*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(175*Sqrt[1 - c^2*x^2]) + (b*c^3*d*f*g^2*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(6*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*g^3*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(49*Sqrt[1 - c^2*x^2]) + (b*d*f^3*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c) - (2*d*g^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(35*c^4) + (3*d*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 - (3*d*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*c^2) - (d*g^3*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(35*c^2) + (3*d*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 + (3*d*g^3*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/35 + (d*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/4 + (d*f*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 + (d*g^3*x^4*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/7 - (3*d*f^2*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(5*c^2) + (d*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*c*Sqrt[1 - c^2*x^2]) + (d*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(16*b*c^3*Sqrt[1 - c^2*x^2])","A",56,27,33,0.8182,1,"{4777, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1247, 698, 4699, 4697, 4707, 14, 4687, 459, 4619, 261, 266, 43, 446, 77}"
63,1,1108,0,1.5236659,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{b c^3 d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{18 \sqrt{1-c^2 x^2}}+\frac{4 b c^3 d f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{25 \sqrt{1-c^2 x^2}}+\frac{1}{108} b^2 c^2 d g^2 \sqrt{d-c^2 d x^2} x^5-\frac{7 b c d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{48 \sqrt{1-c^2 x^2}}+\frac{1}{8} d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{1}{6} d g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3-\frac{8 b c d f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{15 \sqrt{1-c^2 x^2}}-\frac{43 b^2 d g^2 \sqrt{d-c^2 d x^2} x^3}{1728}-\frac{3 b c d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{8 \sqrt{1-c^2 x^2}}+\frac{b d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{16 c^2}+\frac{1}{4} d f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b d f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{5 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 d f^2 \sqrt{d-c^2 d x^2} x-\frac{7 b^2 d g^2 \sqrt{d-c^2 d x^2} x}{1152 c^2}-\frac{1}{32} b^2 d f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x+\frac{d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \sqrt{1-c^2 x^2}}+\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}+\frac{9 b^2 d f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}+\frac{7 b^2 d g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c^3 \sqrt{1-c^2 x^2}}+\frac{b d f^2 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{4 b^2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{32 b^2 d f g \sqrt{d-c^2 d x^2}}{75 c^2}+\frac{16 b^2 d f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{225 c^2}","\frac{b c^3 d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{18 \sqrt{1-c^2 x^2}}+\frac{4 b c^3 d f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{25 \sqrt{1-c^2 x^2}}+\frac{1}{108} b^2 c^2 d g^2 \sqrt{d-c^2 d x^2} x^5-\frac{7 b c d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{48 \sqrt{1-c^2 x^2}}+\frac{1}{8} d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{1}{6} d g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3-\frac{8 b c d f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{15 \sqrt{1-c^2 x^2}}-\frac{43 b^2 d g^2 \sqrt{d-c^2 d x^2} x^3}{1728}-\frac{3 b c d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{8 \sqrt{1-c^2 x^2}}+\frac{b d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{16 c^2}+\frac{1}{4} d f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b d f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{5 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 d f^2 \sqrt{d-c^2 d x^2} x-\frac{7 b^2 d g^2 \sqrt{d-c^2 d x^2} x}{1152 c^2}-\frac{1}{32} b^2 d f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x+\frac{d f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \sqrt{1-c^2 x^2}}+\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}+\frac{9 b^2 d f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}+\frac{7 b^2 d g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c^3 \sqrt{1-c^2 x^2}}+\frac{b d f^2 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{4 b^2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{32 b^2 d f g \sqrt{d-c^2 d x^2}}{75 c^2}+\frac{16 b^2 d f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{225 c^2}",1,"(32*b^2*d*f*g*Sqrt[d - c^2*d*x^2])/(75*c^2) - (15*b^2*d*f^2*x*Sqrt[d - c^2*d*x^2])/64 - (7*b^2*d*g^2*x*Sqrt[d - c^2*d*x^2])/(1152*c^2) - (43*b^2*d*g^2*x^3*Sqrt[d - c^2*d*x^2])/1728 + (b^2*c^2*d*g^2*x^5*Sqrt[d - c^2*d*x^2])/108 + (16*b^2*d*f*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(225*c^2) - (b^2*d*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/32 + (4*b^2*d*f*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*c^2) + (9*b^2*d*f^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c*Sqrt[1 - c^2*x^2]) + (7*b^2*d*g^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(1152*c^3*Sqrt[1 - c^2*x^2]) + (4*b*d*f*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c*Sqrt[1 - c^2*x^2]) - (3*b*c*d*f^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (b*d*g^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c*Sqrt[1 - c^2*x^2]) - (8*b*c*d*f*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(15*Sqrt[1 - c^2*x^2]) - (7*b*c*d*g^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*Sqrt[1 - c^2*x^2]) + (4*b*c^3*d*f*g*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) + (b*c^3*d*g^2*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(18*Sqrt[1 - c^2*x^2]) + (b*d*f^2*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (3*d*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 - (d*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*c^2) + (d*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 + (d*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/4 + (d*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/6 - (2*d*f*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(5*c^2) + (d*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*c*Sqrt[1 - c^2*x^2]) + (d*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(48*b*c^3*Sqrt[1 - c^2*x^2])","A",36,21,33,0.6364,1,"{4777, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1247, 698, 4699, 4697, 4707, 14, 4687, 459}"
64,1,621,0,0.7168909,"\int (f+g x) \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{3 b c d f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \sqrt{1-c^2 x^2}}+\frac{b d f \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{2 b c^3 d g x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 \sqrt{1-c^2 x^2}}-\frac{4 b c d g x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 \sqrt{1-c^2 x^2}}+\frac{2 b d g x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c \sqrt{1-c^2 x^2}}-\frac{d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}-\frac{15}{64} b^2 d f x \sqrt{d-c^2 d x^2}-\frac{1}{32} b^2 d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}+\frac{9 b^2 d f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}+\frac{2 b^2 d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{16 b^2 d g \sqrt{d-c^2 d x^2}}{75 c^2}+\frac{8 b^2 d g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{225 c^2}","-\frac{3 b c d f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \sqrt{1-c^2 x^2}}+\frac{b d f \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{2 b c^3 d g x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 \sqrt{1-c^2 x^2}}-\frac{4 b c d g x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 \sqrt{1-c^2 x^2}}+\frac{2 b d g x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c \sqrt{1-c^2 x^2}}-\frac{d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}-\frac{15}{64} b^2 d f x \sqrt{d-c^2 d x^2}-\frac{1}{32} b^2 d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}+\frac{9 b^2 d f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}+\frac{2 b^2 d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{16 b^2 d g \sqrt{d-c^2 d x^2}}{75 c^2}+\frac{8 b^2 d g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{225 c^2}",1,"(16*b^2*d*g*Sqrt[d - c^2*d*x^2])/(75*c^2) - (15*b^2*d*f*x*Sqrt[d - c^2*d*x^2])/64 + (8*b^2*d*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(225*c^2) - (b^2*d*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/32 + (2*b^2*d*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*c^2) + (9*b^2*d*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c*Sqrt[1 - c^2*x^2]) + (2*b*d*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c*Sqrt[1 - c^2*x^2]) - (3*b*c*d*f*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) - (4*b*c*d*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(15*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*g*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) + (b*d*f*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (3*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 + (d*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/4 - (d*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(5*c^2) + (d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*c*Sqrt[1 - c^2*x^2])","A",19,15,31,0.4839,1,"{4777, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1247, 698}"
65,1,1992,0,3.7799531,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(f + g*x),x]","\frac{2 b d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{9 g \sqrt{1-c^2 x^2}}-\frac{b d f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{2 g^2 \sqrt{1-c^2 x^2}}+\frac{d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{2 g^2}-\frac{b^2 d f x \sqrt{d-c^2 d x^2} c^2}{4 g^2}-\frac{d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{3 b g^3 \sqrt{1-c^2 x^2}}+\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{6 b g^2 \sqrt{1-c^2 x^2}}+\frac{2 b^2 d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{g^3 \sqrt{1-c^2 x^2}}+\frac{b^2 d f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{4 g^2 \sqrt{1-c^2 x^2}}-\frac{2 b d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c}{3 g \sqrt{1-c^2 x^2}}+\frac{2 a b d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} c}{g^3 \sqrt{1-c^2 x^2}}-\frac{b^2 d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2}{g^3}+\frac{d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 g}-\frac{2 a b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^3}+\frac{a^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 i a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 i a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{a^2 d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}+\frac{2 b^2 d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}-\frac{2 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 g}-\frac{4 b^2 d \sqrt{d-c^2 d x^2}}{9 g}-\frac{d (c f-g) (c f+g) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^2 (f+g x) c}-\frac{d \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^4 (f+g x) \sqrt{1-c^2 x^2} c}","\frac{2 b d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{9 g \sqrt{1-c^2 x^2}}-\frac{b d f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{2 g^2 \sqrt{1-c^2 x^2}}+\frac{d f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{2 g^2}-\frac{b^2 d f x \sqrt{d-c^2 d x^2} c^2}{4 g^2}-\frac{d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{3 b g^3 \sqrt{1-c^2 x^2}}+\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{6 b g^2 \sqrt{1-c^2 x^2}}+\frac{2 b^2 d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{g^3 \sqrt{1-c^2 x^2}}+\frac{b^2 d f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{4 g^2 \sqrt{1-c^2 x^2}}-\frac{2 b d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c}{3 g \sqrt{1-c^2 x^2}}+\frac{2 a b d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} c}{g^3 \sqrt{1-c^2 x^2}}-\frac{b^2 d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2}{g^3}+\frac{d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 g}-\frac{2 a b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^3}+\frac{a^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 i a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 i a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 a b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{2 i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{2 i b^2 d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{a^2 d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}+\frac{2 b^2 d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}-\frac{2 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 g}-\frac{4 b^2 d \sqrt{d-c^2 d x^2}}{9 g}-\frac{d (c f-g) (c f+g) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^2 (f+g x) c}-\frac{d \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^4 (f+g x) \sqrt{1-c^2 x^2} c}",1,"(-4*b^2*d*Sqrt[d - c^2*d*x^2])/(9*g) - (a^2*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2])/g^3 + (2*b^2*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2])/g^3 - (b^2*c^2*d*f*x*Sqrt[d - c^2*d*x^2])/(4*g^2) + (2*a*b*c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2])/(g^3*Sqrt[1 - c^2*x^2]) - (2*b^2*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(27*g) - (2*a*b*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/g^3 + (b^2*c*d*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*g^2*Sqrt[1 - c^2*x^2]) + (2*b^2*c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(g^3*Sqrt[1 - c^2*x^2]) - (b^2*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2)/g^3 - (2*b*c*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*g*Sqrt[1 - c^2*x^2]) - (b*c^3*d*f*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*g^2*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*g*Sqrt[1 - c^2*x^2]) + (c^2*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*g^2) + (d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*g) + (c*d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*g^2*Sqrt[1 - c^2*x^2]) - (c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*g^3*Sqrt[1 - c^2*x^2]) - (d*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*g^4*(f + g*x)*Sqrt[1 - c^2*x^2]) - (d*(c*f - g)*(c*f + g)*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*g^2*(f + g*x)) + (a^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^4*Sqrt[1 - c^2*x^2]) - ((2*I)*a*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) - (I*b^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + ((2*I)*a*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (I*b^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) - (2*a*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) - (2*b^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (2*a*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (2*b^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) - ((2*I)*b^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + ((2*I)*b^2*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2])","A",50,32,33,0.9697,1,"{4777, 4767, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43, 4765, 683, 4757, 4799, 1654, 12, 725, 204, 4797, 8, 4773, 3323, 2264, 2190, 2279, 2391, 4619, 261, 2531, 2282, 6589}"
66,1,2290,0,3.2867498,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^9}{81 \sqrt{1-c^2 x^2}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^8}{32 \sqrt{1-c^2 x^2}}+\frac{38 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{441 \sqrt{1-c^2 x^2}}-\frac{6 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}-\frac{3}{256} b^2 c^4 d^2 f g^2 \sqrt{d-c^2 d x^2} x^7+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{48 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{21 \sqrt{1-c^2 x^2}}+\frac{18 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{35 \sqrt{1-c^2 x^2}}+\frac{209 b^2 c^2 d^2 f g^2 \sqrt{d-c^2 d x^2} x^5}{4608}+\frac{1}{21} d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4+\frac{1}{9} d^2 g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4+\frac{5}{63} d^2 g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{128 \sqrt{1-c^2 x^2}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{3}{8} d^2 f g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{5}{16} d^2 f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{189 c \sqrt{1-c^2 x^2}}-\frac{6 b c d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{7 \sqrt{1-c^2 x^2}}-\frac{1079 b^2 d^2 f g^2 \sqrt{d-c^2 d x^2} x^3}{18432}-\frac{d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^2}{63 c^2}-\frac{5 b c d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 \sqrt{1-c^2 x^2}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{128 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{24} d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b^2 d^2 g^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) x}{63 c^3 \sqrt{1-c^2 x^2}}+\frac{6 b d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{7 c \sqrt{1-c^2 x^2}}-\frac{245 b^2 d^2 f^3 \sqrt{d-c^2 d x^2} x}{1152}-\frac{359 b^2 d^2 f g^2 \sqrt{d-c^2 d x^2} x}{12288 c^2}-\frac{1}{108} b^2 d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} x-\frac{65 b^2 d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{1728}+\frac{4 a b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{1-c^2 x^2}}+\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \sqrt{1-c^2 x^2}}+\frac{5 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{128 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{63 c^4}-\frac{3 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2}+\frac{115 b^2 d^2 f^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}+\frac{359 b^2 d^2 f g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{12288 c^3 \sqrt{1-c^2 x^2}}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 f^3 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}-\frac{2 b^2 d^2 g^3 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{729 c^4}+\frac{160 b^2 d^2 g^3 \sqrt{d-c^2 d x^2}}{3969 c^4}+\frac{50 b^2 d^2 g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{27783 c^4}+\frac{6 b^2 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{4 b^2 d^2 g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1323 c^4}+\frac{36 b^2 d^2 f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{96 b^2 d^2 f^2 g \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{80 b^2 d^2 g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11907 c^4}+\frac{16 b^2 d^2 f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{245 c^2}","-\frac{2 b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^9}{81 \sqrt{1-c^2 x^2}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^8}{32 \sqrt{1-c^2 x^2}}+\frac{38 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{441 \sqrt{1-c^2 x^2}}-\frac{6 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}-\frac{3}{256} b^2 c^4 d^2 f g^2 \sqrt{d-c^2 d x^2} x^7+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{48 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{21 \sqrt{1-c^2 x^2}}+\frac{18 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{35 \sqrt{1-c^2 x^2}}+\frac{209 b^2 c^2 d^2 f g^2 \sqrt{d-c^2 d x^2} x^5}{4608}+\frac{1}{21} d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4+\frac{1}{9} d^2 g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4+\frac{5}{63} d^2 g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{128 \sqrt{1-c^2 x^2}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{3}{8} d^2 f g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{5}{16} d^2 f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{189 c \sqrt{1-c^2 x^2}}-\frac{6 b c d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{7 \sqrt{1-c^2 x^2}}-\frac{1079 b^2 d^2 f g^2 \sqrt{d-c^2 d x^2} x^3}{18432}-\frac{d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^2}{63 c^2}-\frac{5 b c d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 \sqrt{1-c^2 x^2}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{128 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{24} d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b^2 d^2 g^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) x}{63 c^3 \sqrt{1-c^2 x^2}}+\frac{6 b d^2 f^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{7 c \sqrt{1-c^2 x^2}}-\frac{245 b^2 d^2 f^3 \sqrt{d-c^2 d x^2} x}{1152}-\frac{359 b^2 d^2 f g^2 \sqrt{d-c^2 d x^2} x}{12288 c^2}-\frac{1}{108} b^2 d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} x-\frac{65 b^2 d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{1728}+\frac{4 a b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{1-c^2 x^2}}+\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \sqrt{1-c^2 x^2}}+\frac{5 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{128 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 g^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{63 c^4}-\frac{3 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2}+\frac{115 b^2 d^2 f^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}+\frac{359 b^2 d^2 f g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{12288 c^3 \sqrt{1-c^2 x^2}}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 f^3 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}-\frac{2 b^2 d^2 g^3 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{729 c^4}+\frac{160 b^2 d^2 g^3 \sqrt{d-c^2 d x^2}}{3969 c^4}+\frac{50 b^2 d^2 g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{27783 c^4}+\frac{6 b^2 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{4 b^2 d^2 g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1323 c^4}+\frac{36 b^2 d^2 f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{96 b^2 d^2 f^2 g \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{80 b^2 d^2 g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11907 c^4}+\frac{16 b^2 d^2 f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{245 c^2}",1,"(96*b^2*d^2*f^2*g*Sqrt[d - c^2*d*x^2])/(245*c^2) + (160*b^2*d^2*g^3*Sqrt[d - c^2*d*x^2])/(3969*c^4) - (245*b^2*d^2*f^3*x*Sqrt[d - c^2*d*x^2])/1152 - (359*b^2*d^2*f*g^2*x*Sqrt[d - c^2*d*x^2])/(12288*c^2) - (1079*b^2*d^2*f*g^2*x^3*Sqrt[d - c^2*d*x^2])/18432 + (209*b^2*c^2*d^2*f*g^2*x^5*Sqrt[d - c^2*d*x^2])/4608 - (3*b^2*c^4*d^2*f*g^2*x^7*Sqrt[d - c^2*d*x^2])/256 + (4*a*b*d^2*g^3*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[1 - c^2*x^2]) + (16*b^2*d^2*f^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(245*c^2) + (80*b^2*d^2*g^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(11907*c^4) - (65*b^2*d^2*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/1728 + (36*b^2*d^2*f^2*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(1225*c^2) + (4*b^2*d^2*g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(1323*c^4) - (b^2*d^2*f^3*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/108 + (6*b^2*d^2*f^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(343*c^2) + (50*b^2*d^2*g^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(27783*c^4) - (2*b^2*d^2*g^3*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2])/(729*c^4) + (115*b^2*d^2*f^3*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(1152*c*Sqrt[1 - c^2*x^2]) + (359*b^2*d^2*f*g^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(12288*c^3*Sqrt[1 - c^2*x^2]) + (4*b^2*d^2*g^3*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(63*c^3*Sqrt[1 - c^2*x^2]) + (6*b*d^2*f^2*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c*Sqrt[1 - c^2*x^2]) - (5*b*c*d^2*f^3*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*Sqrt[1 - c^2*x^2]) + (15*b*d^2*f*g^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c*Sqrt[1 - c^2*x^2]) - (6*b*c*d^2*f^2*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*Sqrt[1 - c^2*x^2]) + (2*b*d^2*g^3*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(189*c*Sqrt[1 - c^2*x^2]) - (59*b*c*d^2*f*g^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*Sqrt[1 - c^2*x^2]) + (18*b*c^3*d^2*f^2*g*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(35*Sqrt[1 - c^2*x^2]) - (2*b*c*d^2*g^3*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(21*Sqrt[1 - c^2*x^2]) + (17*b*c^3*d^2*f*g^2*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*Sqrt[1 - c^2*x^2]) - (6*b*c^5*d^2*f^2*g*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(49*Sqrt[1 - c^2*x^2]) + (38*b*c^3*d^2*g^3*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(441*Sqrt[1 - c^2*x^2]) - (3*b*c^5*d^2*f*g^2*x^8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(32*Sqrt[1 - c^2*x^2]) - (2*b*c^5*d^2*g^3*x^9*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(81*Sqrt[1 - c^2*x^2]) + (5*b*d^2*f^3*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*c) + (b*d^2*f^3*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(18*c) - (2*d^2*g^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(63*c^4) + (5*d^2*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/16 - (15*d^2*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(128*c^2) - (d^2*g^3*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(63*c^2) + (15*d^2*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/64 + (d^2*g^3*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/21 + (5*d^2*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/24 + (5*d^2*f*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/16 + (5*d^2*g^3*x^4*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/63 + (d^2*f^3*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/6 + (3*d^2*f*g^2*x^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 + (d^2*g^3*x^4*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/9 - (3*d^2*f^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(7*c^2) + (5*d^2*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(48*b*c*Sqrt[1 - c^2*x^2]) + (5*d^2*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(128*b*c^3*Sqrt[1 - c^2*x^2])","A",77,32,33,0.9697,1,"{4777, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1799, 1850, 4699, 4697, 4707, 14, 4687, 459, 266, 43, 1267, 4619, 261, 446, 77, 270, 1251, 897, 1153}"
67,1,1533,0,2.052702,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^8}{32 \sqrt{1-c^2 x^2}}-\frac{4 b c^5 d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}-\frac{1}{256} b^2 c^4 d^2 g^2 \sqrt{d-c^2 d x^2} x^7+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{144 \sqrt{1-c^2 x^2}}+\frac{12 b c^3 d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{35 \sqrt{1-c^2 x^2}}+\frac{209 b^2 c^2 d^2 g^2 \sqrt{d-c^2 d x^2} x^5}{13824}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{384 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{1}{8} d^2 g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{5}{48} d^2 g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3-\frac{4 b c d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{7 \sqrt{1-c^2 x^2}}-\frac{1079 b^2 d^2 g^2 \sqrt{d-c^2 d x^2} x^3}{55296}-\frac{5 b c d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 \sqrt{1-c^2 x^2}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{128 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{24} d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{7 c \sqrt{1-c^2 x^2}}-\frac{245 b^2 d^2 f^2 \sqrt{d-c^2 d x^2} x}{1152}-\frac{359 b^2 d^2 g^2 \sqrt{d-c^2 d x^2} x}{36864 c^2}-\frac{1}{108} b^2 d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} x-\frac{65 b^2 d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{1728}+\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \sqrt{1-c^2 x^2}}+\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{384 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2}+\frac{115 b^2 d^2 f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}+\frac{359 b^2 d^2 g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{36864 c^3 \sqrt{1-c^2 x^2}}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 f^2 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}+\frac{4 b^2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{24 b^2 d^2 f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{64 b^2 d^2 f g \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{32 b^2 d^2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{735 c^2}","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^8}{32 \sqrt{1-c^2 x^2}}-\frac{4 b c^5 d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}-\frac{1}{256} b^2 c^4 d^2 g^2 \sqrt{d-c^2 d x^2} x^7+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^6}{144 \sqrt{1-c^2 x^2}}+\frac{12 b c^3 d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{35 \sqrt{1-c^2 x^2}}+\frac{209 b^2 c^2 d^2 g^2 \sqrt{d-c^2 d x^2} x^5}{13824}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{384 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{1}{8} d^2 g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3+\frac{5}{48} d^2 g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^3-\frac{4 b c d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{7 \sqrt{1-c^2 x^2}}-\frac{1079 b^2 d^2 g^2 \sqrt{d-c^2 d x^2} x^3}{55296}-\frac{5 b c d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 \sqrt{1-c^2 x^2}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{128 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{24} d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{4 b d^2 f g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{7 c \sqrt{1-c^2 x^2}}-\frac{245 b^2 d^2 f^2 \sqrt{d-c^2 d x^2} x}{1152}-\frac{359 b^2 d^2 g^2 \sqrt{d-c^2 d x^2} x}{36864 c^2}-\frac{1}{108} b^2 d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} x-\frac{65 b^2 d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{1728}+\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \sqrt{1-c^2 x^2}}+\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{384 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2}+\frac{115 b^2 d^2 f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}+\frac{359 b^2 d^2 g^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{36864 c^3 \sqrt{1-c^2 x^2}}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 f^2 \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}+\frac{4 b^2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{24 b^2 d^2 f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{64 b^2 d^2 f g \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{32 b^2 d^2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{735 c^2}",1,"(64*b^2*d^2*f*g*Sqrt[d - c^2*d*x^2])/(245*c^2) - (245*b^2*d^2*f^2*x*Sqrt[d - c^2*d*x^2])/1152 - (359*b^2*d^2*g^2*x*Sqrt[d - c^2*d*x^2])/(36864*c^2) - (1079*b^2*d^2*g^2*x^3*Sqrt[d - c^2*d*x^2])/55296 + (209*b^2*c^2*d^2*g^2*x^5*Sqrt[d - c^2*d*x^2])/13824 - (b^2*c^4*d^2*g^2*x^7*Sqrt[d - c^2*d*x^2])/256 + (32*b^2*d^2*f*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(735*c^2) - (65*b^2*d^2*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/1728 + (24*b^2*d^2*f*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(1225*c^2) - (b^2*d^2*f^2*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/108 + (4*b^2*d^2*f*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(343*c^2) + (115*b^2*d^2*f^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(1152*c*Sqrt[1 - c^2*x^2]) + (359*b^2*d^2*g^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(36864*c^3*Sqrt[1 - c^2*x^2]) + (4*b*d^2*f*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c*Sqrt[1 - c^2*x^2]) - (5*b*c*d^2*f^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*Sqrt[1 - c^2*x^2]) + (5*b*d^2*g^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c*Sqrt[1 - c^2*x^2]) - (4*b*c*d^2*f*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*Sqrt[1 - c^2*x^2]) - (59*b*c*d^2*g^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(384*Sqrt[1 - c^2*x^2]) + (12*b*c^3*d^2*f*g*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(35*Sqrt[1 - c^2*x^2]) + (17*b*c^3*d^2*g^2*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(144*Sqrt[1 - c^2*x^2]) - (4*b*c^5*d^2*f*g*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(49*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*g^2*x^8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(32*Sqrt[1 - c^2*x^2]) + (5*b*d^2*f^2*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*c) + (b*d^2*f^2*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(18*c) + (5*d^2*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/16 - (5*d^2*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(128*c^2) + (5*d^2*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/64 + (5*d^2*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/24 + (5*d^2*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/48 + (d^2*f^2*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/6 + (d^2*g^2*x^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 - (2*d^2*f*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(7*c^2) + (5*d^2*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(48*b*c*Sqrt[1 - c^2*x^2]) + (5*d^2*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(384*b*c^3*Sqrt[1 - c^2*x^2])","A",50,24,33,0.7273,1,"{4777, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1799, 1850, 4699, 4697, 4707, 14, 4687, 459, 266, 43, 1267}"
68,1,878,0,0.9412681,"\int (f+g x) \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c^5 d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{35 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{7 \sqrt{1-c^2 x^2}}-\frac{5 b c d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 \sqrt{1-c^2 x^2}}+\frac{1}{6} d^2 f \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{16} d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{24} d^2 f \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{2 b d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{7 c \sqrt{1-c^2 x^2}}-\frac{1}{108} b^2 d^2 f \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} x-\frac{245 b^2 d^2 f \sqrt{d-c^2 d x^2} x}{1152}-\frac{65 b^2 d^2 f \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{1728}+\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \sqrt{1-c^2 x^2}}-\frac{d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2}+\frac{115 b^2 d^2 f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 f \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}+\frac{2 b^2 d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{12 b^2 d^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{32 b^2 d^2 g \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{16 b^2 d^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{735 c^2}","-\frac{2 b c^5 d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^7}{49 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{35 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{7 \sqrt{1-c^2 x^2}}-\frac{5 b c d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{16 \sqrt{1-c^2 x^2}}+\frac{1}{6} d^2 f \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{16} d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{5}{24} d^2 f \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x+\frac{2 b d^2 g \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x}{7 c \sqrt{1-c^2 x^2}}-\frac{1}{108} b^2 d^2 f \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} x-\frac{245 b^2 d^2 f \sqrt{d-c^2 d x^2} x}{1152}-\frac{65 b^2 d^2 f \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{1728}+\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \sqrt{1-c^2 x^2}}-\frac{d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2}+\frac{115 b^2 d^2 f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 f \left(1-c^2 x^2\right)^{3/2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}+\frac{2 b^2 d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{12 b^2 d^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{32 b^2 d^2 g \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{16 b^2 d^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{735 c^2}",1,"(32*b^2*d^2*g*Sqrt[d - c^2*d*x^2])/(245*c^2) - (245*b^2*d^2*f*x*Sqrt[d - c^2*d*x^2])/1152 + (16*b^2*d^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(735*c^2) - (65*b^2*d^2*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/1728 + (12*b^2*d^2*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(1225*c^2) - (b^2*d^2*f*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/108 + (2*b^2*d^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(343*c^2) + (115*b^2*d^2*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(1152*c*Sqrt[1 - c^2*x^2]) + (2*b*d^2*g*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c*Sqrt[1 - c^2*x^2]) - (5*b*c*d^2*f*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*Sqrt[1 - c^2*x^2]) - (2*b*c*d^2*g*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*Sqrt[1 - c^2*x^2]) + (6*b*c^3*d^2*g*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(35*Sqrt[1 - c^2*x^2]) - (2*b*c^5*d^2*g*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(49*Sqrt[1 - c^2*x^2]) + (5*b*d^2*f*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*c) + (b*d^2*f*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(18*c) + (5*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/16 + (5*d^2*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/24 + (d^2*f*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/6 - (d^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(7*c^2) + (5*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(48*b*c*Sqrt[1 - c^2*x^2])","A",25,15,31,0.4839,1,"{4777, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1799, 1850}"
69,1,2989,0,4.9407733,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(f + g*x),x]","-\frac{2 b d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^5}{25 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^5}{8 g^2 \sqrt{1-c^2 x^2}}+\frac{d^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^4}{5 g}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^4}{4 g^2}+\frac{b^2 d^2 f x^3 \sqrt{d-c^2 d x^2} c^4}{32 g^2}-\frac{2 b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{9 g^3 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{45 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{2 g^4 \sqrt{1-c^2 x^2}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{8 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{15 g}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{8 g^2}+\frac{b^2 d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c^2}{4 g^4}-\frac{b^2 d^2 f x \sqrt{d-c^2 d x^2} c^2}{64 g^2}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{6 b g^4 \sqrt{1-c^2 x^2}}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{3 b g^5 \sqrt{1-c^2 x^2}}-\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{24 b g^2 \sqrt{1-c^2 x^2}}-\frac{b^2 d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{4 g^4 \sqrt{1-c^2 x^2}}-\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{g^5 \sqrt{1-c^2 x^2}}+\frac{4 b^2 d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{15 g \sqrt{1-c^2 x^2}}+\frac{b^2 d^2 f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{64 g^2 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c}{3 g^3 \sqrt{1-c^2 x^2}}-\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{1-c^2 x^2}}+\frac{4 a b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{1-c^2 x^2}}+\frac{b^2 d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2}{g^5}-\frac{d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 g^3}-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 g}+\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^5}-\frac{a^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 i a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 i a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{a^2 d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}-\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}-\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 g}+\frac{4 b^2 d^2 \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2}}{9 g^3}+\frac{2 b^2 d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 g^3}+\frac{26 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{675 g}+\frac{52 b^2 d^2 \sqrt{d-c^2 d x^2}}{225 g}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^4 (f+g x) c}+\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^6 (f+g x) \sqrt{1-c^2 x^2} c}","-\frac{2 b d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^5}{25 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^5}{8 g^2 \sqrt{1-c^2 x^2}}+\frac{d^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^4}{5 g}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^4}{4 g^2}+\frac{b^2 d^2 f x^3 \sqrt{d-c^2 d x^2} c^4}{32 g^2}-\frac{2 b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{9 g^3 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{45 g \sqrt{1-c^2 x^2}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{2 g^4 \sqrt{1-c^2 x^2}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c^3}{8 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{15 g}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 c^2}{8 g^2}+\frac{b^2 d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c^2}{4 g^4}-\frac{b^2 d^2 f x \sqrt{d-c^2 d x^2} c^2}{64 g^2}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{6 b g^4 \sqrt{1-c^2 x^2}}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{3 b g^5 \sqrt{1-c^2 x^2}}-\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3 c}{24 b g^2 \sqrt{1-c^2 x^2}}-\frac{b^2 d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{4 g^4 \sqrt{1-c^2 x^2}}-\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{g^5 \sqrt{1-c^2 x^2}}+\frac{4 b^2 d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{15 g \sqrt{1-c^2 x^2}}+\frac{b^2 d^2 f \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c}{64 g^2 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) c}{3 g^3 \sqrt{1-c^2 x^2}}-\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{1-c^2 x^2}}+\frac{4 a b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{1-c^2 x^2}}+\frac{b^2 d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2}{g^5}-\frac{d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 g^3}-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 g}+\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{g^5}-\frac{a^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 i a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 i a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 a b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{2 i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{2 i b^2 d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{a^2 d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}-\frac{2 b^2 d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}-\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 g}+\frac{4 b^2 d^2 \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2}}{9 g^3}+\frac{2 b^2 d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 g^3}+\frac{26 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{675 g}+\frac{52 b^2 d^2 \sqrt{d-c^2 d x^2}}{225 g}+\frac{d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^4 (f+g x) c}+\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b g^6 (f+g x) \sqrt{1-c^2 x^2} c}",1,"(52*b^2*d^2*Sqrt[d - c^2*d*x^2])/(225*g) + (4*b^2*d^2*(c^2*f^2 - 2*g^2)*Sqrt[d - c^2*d*x^2])/(9*g^3) + (a^2*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2])/g^5 - (2*b^2*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2])/g^5 - (b^2*c^2*d^2*f*x*Sqrt[d - c^2*d*x^2])/(64*g^2) + (b^2*c^2*d^2*f*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2])/(4*g^4) + (b^2*c^4*d^2*f*x^3*Sqrt[d - c^2*d*x^2])/(32*g^2) + (4*a*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(15*g*Sqrt[1 - c^2*x^2]) - (2*a*b*c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2])/(g^5*Sqrt[1 - c^2*x^2]) + (26*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(675*g) + (2*b^2*d^2*(c^2*f^2 - 2*g^2)*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(27*g^3) - (2*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*g) + (2*a*b*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/g^5 + (b^2*c*d^2*f*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*g^2*Sqrt[1 - c^2*x^2]) - (b^2*c*d^2*f*(c^2*f^2 - 2*g^2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*g^4*Sqrt[1 - c^2*x^2]) + (4*b^2*c*d^2*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(15*g*Sqrt[1 - c^2*x^2]) - (2*b^2*c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(g^5*Sqrt[1 - c^2*x^2]) + (b^2*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2)/g^5 + (2*b*c*d^2*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*g^3*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*f*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*g^2*Sqrt[1 - c^2*x^2]) + (b*c^3*d^2*f*(c^2*f^2 - 2*g^2)*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*g^4*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(45*g*Sqrt[1 - c^2*x^2]) - (2*b*c^3*d^2*(c^2*f^2 - 2*g^2)*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*g^3*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*f*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*g^2*Sqrt[1 - c^2*x^2]) - (2*b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*g*Sqrt[1 - c^2*x^2]) - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*g) + (c^2*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(8*g^2) - (c^2*d^2*f*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*g^4) - (c^2*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*g) - (c^4*d^2*f*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*g^2) + (c^4*d^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(5*g) - (d^2*(c^2*f^2 - 2*g^2)*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*g^3) - (c*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(24*b*g^2*Sqrt[1 - c^2*x^2]) - (c*d^2*f*(c^2*f^2 - 2*g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*g^4*Sqrt[1 - c^2*x^2]) + (c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*g^5*Sqrt[1 - c^2*x^2]) + (d^2*(c^2*f^2 - g^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*g^6*(f + g*x)*Sqrt[1 - c^2*x^2]) + (d^2*(c^2*f^2 - g^2)^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*g^4*(f + g*x)) - (a^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^6*Sqrt[1 - c^2*x^2]) + ((2*I)*a*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) + (I*b^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - ((2*I)*a*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (I*b^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) + (2*a*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) + (2*b^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (2*a*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (2*b^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) + ((2*I)*b^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - ((2*I)*b^2*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2])","A",74,35,33,1.061,1,"{4777, 4767, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43, 4697, 4707, 4619, 261, 266, 4765, 683, 4757, 4799, 1654, 12, 725, 204, 4797, 8, 4773, 3323, 2264, 2190, 2279, 2391, 2531, 2282, 6589}"
70,1,692,0,0.7020421,"\int \frac{(f+g x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","-\frac{3 f^2 g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{d-c^2 d x^2}}+\frac{6 b f^2 g x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{d-c^2 d x^2}}+\frac{f^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}+\frac{f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{3 b f g^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 \sqrt{d-c^2 d x^2}}+\frac{2 b g^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c \sqrt{d-c^2 d x^2}}+\frac{4 b g^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 \sqrt{d-c^2 d x^2}}+\frac{6 b^2 f^2 g \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{3 b^2 f g^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b^2 f g^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 g^3 \left(1-c^2 x^2\right)^2}{27 c^4 \sqrt{d-c^2 d x^2}}+\frac{14 b^2 g^3 \left(1-c^2 x^2\right)}{9 c^4 \sqrt{d-c^2 d x^2}}","-\frac{3 f^2 g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{d-c^2 d x^2}}+\frac{6 b f^2 g x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{d-c^2 d x^2}}+\frac{f^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}+\frac{f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{3 b f g^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 \sqrt{d-c^2 d x^2}}+\frac{2 b g^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c \sqrt{d-c^2 d x^2}}+\frac{4 b g^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 \sqrt{d-c^2 d x^2}}+\frac{6 b^2 f^2 g \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{3 b^2 f g^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b^2 f g^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 g^3 \left(1-c^2 x^2\right)^2}{27 c^4 \sqrt{d-c^2 d x^2}}+\frac{14 b^2 g^3 \left(1-c^2 x^2\right)}{9 c^4 \sqrt{d-c^2 d x^2}}",1,"(6*b^2*f^2*g*(1 - c^2*x^2))/(c^2*Sqrt[d - c^2*d*x^2]) + (14*b^2*g^3*(1 - c^2*x^2))/(9*c^4*Sqrt[d - c^2*d*x^2]) + (3*b^2*f*g^2*x*(1 - c^2*x^2))/(4*c^2*Sqrt[d - c^2*d*x^2]) - (2*b^2*g^3*(1 - c^2*x^2)^2)/(27*c^4*Sqrt[d - c^2*d*x^2]) - (3*b^2*f*g^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c^3*Sqrt[d - c^2*d*x^2]) + (6*b*f^2*g*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(c*Sqrt[d - c^2*d*x^2]) + (4*b*g^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c^3*Sqrt[d - c^2*d*x^2]) + (3*b*f*g^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c*Sqrt[d - c^2*d*x^2]) + (2*b*g^3*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c*Sqrt[d - c^2*d*x^2]) - (3*f^2*g*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c^2*Sqrt[d - c^2*d*x^2]) - (2*g^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c^4*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*c^2*Sqrt[d - c^2*d*x^2]) - (g^3*x^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c^2*Sqrt[d - c^2*d*x^2]) + (f^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d - c^2*d*x^2]) + (f*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(2*b*c^3*Sqrt[d - c^2*d*x^2])","A",17,10,33,0.3030,1,"{4777, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8, 2633}"
71,1,410,0,0.5530557,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{d-c^2 d x^2}}+\frac{4 b f g x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{b g^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c \sqrt{d-c^2 d x^2}}+\frac{4 b^2 f g \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 g^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 g^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}","\frac{f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{d-c^2 d x^2}}+\frac{4 b f g x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{b g^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c \sqrt{d-c^2 d x^2}}+\frac{4 b^2 f g \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 g^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 g^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}",1,"(4*b^2*f*g*(1 - c^2*x^2))/(c^2*Sqrt[d - c^2*d*x^2]) + (b^2*g^2*x*(1 - c^2*x^2))/(4*c^2*Sqrt[d - c^2*d*x^2]) - (b^2*g^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c^3*Sqrt[d - c^2*d*x^2]) + (4*b*f*g*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(c*Sqrt[d - c^2*d*x^2]) + (b*g^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c*Sqrt[d - c^2*d*x^2]) - (2*f*g*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c^2*Sqrt[d - c^2*d*x^2]) - (g^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*c^2*Sqrt[d - c^2*d*x^2]) + (f^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d - c^2*d*x^2]) + (g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c^3*Sqrt[d - c^2*d*x^2])","A",11,9,33,0.2727,1,"{4777, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8}"
72,1,207,0,0.3687332,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}+\frac{2 a b g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 g \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 g x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c \sqrt{d-c^2 d x^2}}","\frac{f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}-\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b g x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{d-c^2 d x^2}}+\frac{2 b^2 g \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}",1,"(2*a*b*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) + (2*b^2*g*(1 - c^2*x^2))/(c^2*Sqrt[d - c^2*d*x^2]) + (2*b^2*g*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*Sqrt[d - c^2*d*x^2]) - (g*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c^2*Sqrt[d - c^2*d*x^2]) + (f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d - c^2*d*x^2])","A",8,6,31,0.1935,1,"{4777, 4763, 4641, 4677, 4619, 261}"
73,1,589,0,1.0178138,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(f+g x) \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((f + g*x)*Sqrt[d - c^2*d*x^2]),x]","-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}","-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}",1,"((-I)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (I*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2])","A",12,8,33,0.2424,1,"{4777, 4773, 3323, 2264, 2190, 2531, 2282, 6589}"
74,1,1113,0,1.4756604,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(f+g x)^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((f + g*x)^2*Sqrt[d - c^2*d*x^2]),x]","\frac{2 i c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 i c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 i c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{2 i c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{2 c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{2 c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\left(c^2 f^2-g^2\right) (f+g x) \sqrt{d-c^2 d x^2}}+\frac{i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}","\frac{2 i c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 i c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 i c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{2 i c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b^2}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{2 c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{2 c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{g \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\left(c^2 f^2-g^2\right) (f+g x) \sqrt{d-c^2 d x^2}}+\frac{i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\left(c^2 f^2-g^2\right) \sqrt{d-c^2 d x^2}}-\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{\left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}",1,"(I*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) + (g*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((c^2*f^2 - g^2)*(f + g*x)*Sqrt[d - c^2*d*x^2]) - (2*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) - (I*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (2*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) + (I*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) - (2*b*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) + (2*b*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*c^2*f*Sqrt[1 - c^2*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*c^2*f*Sqrt[1 - c^2*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2])","A",20,12,33,0.3636,1,"{4777, 4773, 3324, 3323, 2264, 2190, 2531, 2282, 6589, 4519, 2279, 2391}"
75,1,738,0,1.1911608,"\int \frac{(f+g x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{2 i b^2 g \sqrt{1-c^2 x^2} \left(3 c^2 f^2+g^2\right) \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 g \sqrt{1-c^2 x^2} \left(3 c^2 f^2+g^2\right) \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{i b^2 f \sqrt{1-c^2 x^2} \left(c^2 f^2+3 g^2\right) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{g \left(3 c^2 f^2+g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{f x \left(\frac{3 g^2}{c^2}+f^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{i f \sqrt{1-c^2 x^2} \left(c^2 f^2+3 g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b f \sqrt{1-c^2 x^2} \left(c^2 f^2+3 g^2\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{4 i b g \sqrt{1-c^2 x^2} \left(3 c^2 f^2+g^2\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{b c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 a b g^3 x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 g^3 \left(1-c^2 x^2\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 g^3 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c^3 d \sqrt{d-c^2 d x^2}}","-\frac{2 i b^2 g \sqrt{1-c^2 x^2} \left(3 c^2 f^2+g^2\right) \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 g \sqrt{1-c^2 x^2} \left(3 c^2 f^2+g^2\right) \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{i b^2 f \sqrt{1-c^2 x^2} \left(c^2 f^2+3 g^2\right) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{g \left(3 c^2 f^2+g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{f x \left(\frac{3 g^2}{c^2}+f^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{i f \sqrt{1-c^2 x^2} \left(c^2 f^2+3 g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b f \sqrt{1-c^2 x^2} \left(c^2 f^2+3 g^2\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{4 i b g \sqrt{1-c^2 x^2} \left(3 c^2 f^2+g^2\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{f g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{b c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 a b g^3 x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{g^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 g^3 \left(1-c^2 x^2\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 g^3 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c^3 d \sqrt{d-c^2 d x^2}}",1,"(-2*a*b*g^3*x*Sqrt[1 - c^2*x^2])/(c^3*d*Sqrt[d - c^2*d*x^2]) - (2*b^2*g^3*(1 - c^2*x^2))/(c^4*d*Sqrt[d - c^2*d*x^2]) - (2*b^2*g^3*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c^3*d*Sqrt[d - c^2*d*x^2]) + (g*(3*c^2*f^2 + g^2)*(a + b*ArcSin[c*x])^2)/(c^4*d*Sqrt[d - c^2*d*x^2]) + (f*(f^2 + (3*g^2)/c^2)*x*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - (I*f*(c^2*f^2 + 3*g^2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^3*d*Sqrt[d - c^2*d*x^2]) + (g^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c^4*d*Sqrt[d - c^2*d*x^2]) - (f*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(b*c^3*d*Sqrt[d - c^2*d*x^2]) + ((4*I)*b*g*(3*c^2*f^2 + g^2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^4*d*Sqrt[d - c^2*d*x^2]) + (2*b*f*(c^2*f^2 + 3*g^2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^3*d*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*g*(3*c^2*f^2 + g^2)*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^4*d*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*g*(3*c^2*f^2 + g^2)*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^4*d*Sqrt[d - c^2*d*x^2]) - (I*b^2*f*(c^2*f^2 + 3*g^2)*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^3*d*Sqrt[d - c^2*d*x^2])","A",23,15,33,0.4545,1,"{4777, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641, 4619, 261}"
76,1,513,0,0.9802226,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{i b^2 \sqrt{1-c^2 x^2} \left(c^2 f^2+g^2\right) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{4 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{x \left(c^2 f^2+g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{i \sqrt{1-c^2 x^2} \left(c^2 f^2+g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{1-c^2 x^2} \left(c^2 f^2+g^2\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 f g \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{8 i b f g \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^3 d \sqrt{d-c^2 d x^2}}","-\frac{i b^2 \sqrt{1-c^2 x^2} \left(c^2 f^2+g^2\right) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{4 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{x \left(c^2 f^2+g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{i \sqrt{1-c^2 x^2} \left(c^2 f^2+g^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{1-c^2 x^2} \left(c^2 f^2+g^2\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 f g \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{8 i b f g \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^3 d \sqrt{d-c^2 d x^2}}",1,"(2*f*g*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + ((c^2*f^2 + g^2)*x*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) - (I*(c^2*f^2 + g^2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^3*d*Sqrt[d - c^2*d*x^2]) - (g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c^3*d*Sqrt[d - c^2*d*x^2]) + ((8*I)*b*f*g*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*b*(c^2*f^2 + g^2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^3*d*Sqrt[d - c^2*d*x^2]) - ((4*I)*b^2*f*g*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2]) + ((4*I)*b^2*f*g*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2]) - (I*b^2*(c^2*f^2 + g^2)*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^3*d*Sqrt[d - c^2*d*x^2])","A",19,13,33,0.3939,1,"{4777, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641}"
77,1,410,0,0.5728835,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{i b^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{f x \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{i f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c d \sqrt{d-c^2 d x^2}}+\frac{2 b f \sqrt{1-c^2 x^2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d \sqrt{d-c^2 d x^2}}+\frac{g \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b g \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}","-\frac{i b^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{f x \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{i f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c d \sqrt{d-c^2 d x^2}}+\frac{2 b f \sqrt{1-c^2 x^2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d \sqrt{d-c^2 d x^2}}+\frac{g \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b g \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}",1,"(g*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (f*x*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - (I*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c*d*Sqrt[d - c^2*d*x^2]) + ((4*I)*b*g*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*b*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*d*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*g*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*g*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2]) - (I*b^2*f*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*d*Sqrt[d - c^2*d*x^2])","A",16,11,31,0.3548,1,"{4777, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181}"
78,1,1137,0,1.9999431,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(f+g x) \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((f + g*x)*(d - c^2*d*x^2)^(3/2)),x]","\frac{2 i \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right) b^2}{d (c f+g) \sqrt{d-c^2 d x^2}}-\frac{2 i \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) b^2}{d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{2 i g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b^2}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{2 i g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b^2}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) b}{d (c f+g) \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{i \sin ^{-1}(c x)}\right) b}{d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{2 g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{2 g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d (c f+g) \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{2 d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{2 d (c f+g) \sqrt{d-c^2 d x^2}}","\frac{2 i \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right) b^2}{d (c f+g) \sqrt{d-c^2 d x^2}}-\frac{2 i \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) b^2}{d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{2 i g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b^2}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{2 i g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b^2}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) b}{d (c f+g) \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{i \sin ^{-1}(c x)}\right) b}{d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{2 g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) b}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{2 g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) b}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d (c f+g) \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{2 d (c f-g) \sqrt{d-c^2 d x^2}}+\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}-\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{2 d (c f+g) \sqrt{d-c^2 d x^2}}",1,"((-I/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + ((I/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d*(c*f + g)*Sqrt[d - c^2*d*x^2]) - (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2])/(2*d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - I/E^(I*ArcSin[c*x])])/(d*(c*f + g)*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - I*E^(I*ArcSin[c*x])])/(d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + (I*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (I*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I/E^(I*ArcSin[c*x])])/(d*(c*f + g)*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + (2*b*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (2*b*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*g^2*Sqrt[1 - c^2*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*g^2*Sqrt[1 - c^2*x^2]*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Tan[Pi/4 + ArcSin[c*x]/2])/(2*d*(c*f + g)*Sqrt[d - c^2*d*x^2])","A",28,14,33,0.4242,1,"{4777, 4775, 4773, 3318, 4184, 3717, 2190, 2279, 2391, 3323, 2264, 2531, 2282, 6589}"
79,1,1589,0,2.1115233,"\int \frac{(f+g x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 (c f-g)^3}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{24 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{6 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{i \sin ^{-1}(c x)}\right) (c f-g)^3}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) (c f-g)^3}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{i (c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 (c f-g)^2}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{(c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^2}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{i \sin ^{-1}(c x)}\right) (c f-g)^2}{c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 (c f+2 g) \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) (c f-g)^2}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i (c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i (c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{-i \sin ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{-i \sin ^{-1}(c x)}\right)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 (c f+g)^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 (c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 (c f+g)^3 \sqrt{1-c^2 x^2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{6 c^4 d^2 \sqrt{d-c^2 d x^2}}","-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 (c f-g)^3}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{24 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^3}{6 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{i \sin ^{-1}(c x)}\right) (c f-g)^3}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) (c f-g)^3}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{i (c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 (c f-g)^2}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{(c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) (c f-g)^2}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f+2 g) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{i \sin ^{-1}(c x)}\right) (c f-g)^2}{c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 (c f+2 g) \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) (c f-g)^2}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i (c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i (c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b (c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{-i \sin ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b (c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-i e^{-i \sin ^{-1}(c x)}\right)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 (c f+g)^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 (c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{12 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(c f-2 g) (c f+g)^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{4 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{(c f+g)^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{24 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 (c f+g)^3 \sqrt{1-c^2 x^2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{6 c^4 d^2 \sqrt{d-c^2 d x^2}}",1,"((-I/12)*(c*f - g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((I/4)*(c*f - 2*g)*(c*f + g)^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((I/12)*(c*f + g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^4*d^2*Sqrt[d - c^2*d*x^2]) - ((I/4)*(c*f - g)^2*(c*f + 2*g)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^4*d^2*Sqrt[d - c^2*d*x^2]) - (b^2*(c*f - g)^3*Sqrt[1 - c^2*x^2]*Cot[Pi/4 + ArcSin[c*x]/2])/(6*c^4*d^2*Sqrt[d - c^2*d*x^2]) - ((c*f - g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2])/(12*c^4*d^2*Sqrt[d - c^2*d*x^2]) - ((c*f - g)^2*(c*f + 2*g)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2])/(4*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (b*(c*f - g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(12*c^4*d^2*Sqrt[d - c^2*d*x^2]) - ((c*f - g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2]*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(24*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - 2*g)*(c*f + g)^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - I/E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f + g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - I/E^(I*ArcSin[c*x])])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - I*E^(I*ArcSin[c*x])])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*(c*f - g)^2*(c*f + 2*g)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - I*E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (I*b^2*(c*f - 2*g)*(c*f + g)^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I/E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((I/3)*b^2*(c*f + g)^3*Sqrt[1 - c^2*x^2]*PolyLog[2, I/E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) - ((I/3)*b^2*(c*f - g)^3*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) - (I*b^2*(c*f - g)^2*(c*f + 2*g)*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) - (b*(c*f + g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Sec[Pi/4 + ArcSin[c*x]/2]^2)/(12*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*(c*f + g)^3*Sqrt[1 - c^2*x^2]*Tan[Pi/4 + ArcSin[c*x]/2])/(6*c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((c*f - 2*g)*(c*f + g)^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Tan[Pi/4 + ArcSin[c*x]/2])/(4*c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((c*f + g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Tan[Pi/4 + ArcSin[c*x]/2])/(12*c^4*d^2*Sqrt[d - c^2*d*x^2]) + ((c*f + g)^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*Sec[Pi/4 + ArcSin[c*x]/2]^2*Tan[Pi/4 + ArcSin[c*x]/2])/(24*c^4*d^2*Sqrt[d - c^2*d*x^2])","A",37,12,33,0.3636,1,"{4777, 4775, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
80,1,1025,0,1.3071994,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{g^2 \left(a+b \sin ^{-1}(c x)\right)^2 x^3}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b g^2 \left(a+b \sin ^{-1}(c x)\right) x^2}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{2 f^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{f^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 b f g \left(a+b \sin ^{-1}(c x)\right) x}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b^2 f^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 g^2 x}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 f g \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b^2 g^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b f^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{4 i b f g \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 b f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{2 b g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 f^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 f g}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}","\frac{g^2 \left(a+b \sin ^{-1}(c x)\right)^2 x^3}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b g^2 \left(a+b \sin ^{-1}(c x)\right) x^2}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{2 f^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{f^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 b f g \left(a+b \sin ^{-1}(c x)\right) x}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b^2 f^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 g^2 x}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{i g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 f g \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b^2 g^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b f^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{4 i b f g \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 b f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{2 b g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 f g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 f^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 g^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 f g}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}",1,"(2*b^2*f*g)/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*f^2*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*g^2*x)/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) - (b^2*g^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) - (b*f^2*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (2*b*f*g*x*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (b*g^2*x^2*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (2*f^2*x*(a + b*ArcSin[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (2*f*g*(a + b*ArcSin[c*x])^2)/(3*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (f^2*x*(a + b*ArcSin[c*x])^2)/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (g^2*x^3*(a + b*ArcSin[c*x])^2)/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*f^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c*d^2*Sqrt[d - c^2*d*x^2]) + ((I/3)*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^3*d^2*Sqrt[d - c^2*d*x^2]) + (((4*I)/3)*b*f*g*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^2*d^2*Sqrt[d - c^2*d*x^2]) + (4*b*f^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*d^2*Sqrt[d - c^2*d*x^2]) - (2*b*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*b^2*f*g*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^2*d^2*Sqrt[d - c^2*d*x^2]) + (((2*I)/3)*b^2*f*g*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^2*d^2*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*b^2*f^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*d^2*Sqrt[d - c^2*d*x^2]) + ((I/3)*b^2*g^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^3*d^2*Sqrt[d - c^2*d*x^2])","A",30,18,33,0.5455,1,"{4777, 4763, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4657, 4181, 261, 4681, 4703, 288, 216}"
81,1,641,0,0.78413,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","-\frac{2 i b^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b f \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{2 f x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{f x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{4 b f \sqrt{1-c^2 x^2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{g \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 i b g \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 f x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 g}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}","-\frac{2 i b^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{i b^2 g \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b f \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{2 f x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{f x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{4 b f \sqrt{1-c^2 x^2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \left(a+b \sin ^{-1}(c x)\right)}{3 c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{g \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 i b g \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 f x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 g}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}",1,"(b^2*g)/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*f*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b*f*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (b*g*x*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (2*f*x*(a + b*ArcSin[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (g*(a + b*ArcSin[c*x])^2)/(3*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (f*x*(a + b*ArcSin[c*x])^2)/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c*d^2*Sqrt[d - c^2*d*x^2]) + (((2*I)/3)*b*g*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^2*d^2*Sqrt[d - c^2*d*x^2]) + (4*b*f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*d^2*Sqrt[d - c^2*d*x^2]) - ((I/3)*b^2*g*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^2*d^2*Sqrt[d - c^2*d*x^2]) + ((I/3)*b^2*g*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^2*d^2*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*b^2*f*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*d^2*Sqrt[d - c^2*d*x^2])","A",21,14,31,0.4516,1,"{4777, 4763, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4657, 4181, 261}"
82,0,0,0,0.1833664,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcSin[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}},x\right)",0,"Defer[Int][((a + b*ArcSin[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2], x]","A",0,0,0,0,-1,"{}"
83,1,634,0,0.8713975,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcSin[c*x])^3*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","-\frac{6 i b^2 m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{6 i b^2 m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^3 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^3 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{3 b m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{3 b m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{6 b^3 m \text{PolyLog}\left(5,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{6 b^3 m \text{PolyLog}\left(5,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^5}{20 b^2 c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^4 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{4 b c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^4 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{4 b c}+\frac{\left(a+b \sin ^{-1}(c x)\right)^4 \log \left(h (f+g x)^m\right)}{4 b c}","-\frac{6 i b^2 m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{6 i b^2 m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^3 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^3 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{3 b m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{3 b m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{6 b^3 m \text{PolyLog}\left(5,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{6 b^3 m \text{PolyLog}\left(5,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^5}{20 b^2 c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^4 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{4 b c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^4 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{4 b c}+\frac{\left(a+b \sin ^{-1}(c x)\right)^4 \log \left(h (f+g x)^m\right)}{4 b c}",1,"((I/20)*m*(a + b*ArcSin[c*x])^5)/(b^2*c) - (m*(a + b*ArcSin[c*x])^4*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(4*b*c) - (m*(a + b*ArcSin[c*x])^4*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(4*b*c) + ((a + b*ArcSin[c*x])^4*Log[h*(f + g*x)^m])/(4*b*c) + (I*m*(a + b*ArcSin[c*x])^3*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*(a + b*ArcSin[c*x])^3*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c - (3*b*m*(a + b*ArcSin[c*x])^2*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - (3*b*m*(a + b*ArcSin[c*x])^2*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c - ((6*I)*b^2*m*(a + b*ArcSin[c*x])*PolyLog[4, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - ((6*I)*b^2*m*(a + b*ArcSin[c*x])*PolyLog[4, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c + (6*b^3*m*PolyLog[5, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (6*b^3*m*PolyLog[5, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",15,9,35,0.2571,1,"{4641, 4779, 4741, 4519, 2190, 2531, 6609, 2282, 6589}"
84,1,514,0,0.7528534,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcSin[c*x])^2*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\frac{i m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{2 b m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{2 b m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{2 i b^2 m \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{2 i b^2 m \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^4}{12 b^2 c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^3 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{3 b c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^3 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{3 b c}+\frac{\left(a+b \sin ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c}","\frac{i m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{2 b m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{2 b m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{2 i b^2 m \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{2 i b^2 m \text{PolyLog}\left(4,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^4}{12 b^2 c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^3 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{3 b c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^3 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{3 b c}+\frac{\left(a+b \sin ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c}",1,"((I/12)*m*(a + b*ArcSin[c*x])^4)/(b^2*c) - (m*(a + b*ArcSin[c*x])^3*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(3*b*c) - (m*(a + b*ArcSin[c*x])^3*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(3*b*c) + ((a + b*ArcSin[c*x])^3*Log[h*(f + g*x)^m])/(3*b*c) + (I*m*(a + b*ArcSin[c*x])^2*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*(a + b*ArcSin[c*x])^2*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c - (2*b*m*(a + b*ArcSin[c*x])*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - (2*b*m*(a + b*ArcSin[c*x])*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c - ((2*I)*b^2*m*PolyLog[4, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - ((2*I)*b^2*m*PolyLog[4, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",13,9,35,0.2571,1,"{4641, 4779, 4741, 4519, 2190, 2531, 6609, 2282, 6589}"
85,1,390,0,0.6231691,"\int \frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcSin[c*x])*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\frac{i m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{b m \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{b m \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^3}{6 b^2 c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{2 b c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{2 b c}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c}","\frac{i m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{b m \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{b m \text{PolyLog}\left(3,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{i m \left(a+b \sin ^{-1}(c x)\right)^3}{6 b^2 c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{2 b c}-\frac{m \left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{2 b c}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c}",1,"((I/6)*m*(a + b*ArcSin[c*x])^3)/(b^2*c) - (m*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(2*b*c) - (m*(a + b*ArcSin[c*x])^2*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(2*b*c) + ((a + b*ArcSin[c*x])^2*Log[h*(f + g*x)^m])/(2*b*c) + (I*m*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*(a + b*ArcSin[c*x])*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c - (b*m*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - (b*m*PolyLog[3, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",11,8,33,0.2424,1,"{4641, 4779, 4741, 4519, 2190, 2531, 2282, 6589}"
86,1,237,0,0.33166,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[Log[h*(f + g*x)^m]/Sqrt[1 - c^2*x^2],x]","\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}","\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}",1,"((I/2)*m*ArcSin[c*x]^2)/c - (m*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - (m*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c + (ArcSin[c*x]*Log[h*(f + g*x)^m])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",9,7,25,0.2800,1,"{216, 2404, 4741, 4519, 2190, 2279, 2391}"
87,0,0,0,0.1939487,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
88,1,351,0,0.9918713,"\int (d+e x)^3 (f+g x) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(f + g*x)*(a + b*ArcSin[c*x]),x]","\frac{1}{2} d^2 x^2 (d g+3 e f) \left(a+b \sin ^{-1}(c x)\right)+d^3 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 (3 d g+e f) \left(a+b \sin ^{-1}(c x)\right)+d e x^3 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^3 g x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(75 c^2 x \left(8 c^2 d^2 (d g+3 e f)+3 e^2 (3 d g+e f)\right)+32 \left(75 c^4 d^3 f+50 c^2 d e (d g+e f)+8 e^3 g\right)\right)}{2400 c^5}-\frac{b \sin ^{-1}(c x) \left(8 c^2 d^2 (d g+3 e f)+3 e^2 (3 d g+e f)\right)}{32 c^4}+\frac{b e^2 x^3 \sqrt{1-c^2 x^2} (3 d g+e f)}{16 c}+\frac{b e x^2 \sqrt{1-c^2 x^2} \left(25 c^2 d (d g+e f)+4 e^2 g\right)}{75 c^3}+\frac{b e^3 g x^4 \sqrt{1-c^2 x^2}}{25 c}","\frac{1}{2} d^2 x^2 (d g+3 e f) \left(a+b \sin ^{-1}(c x)\right)+d^3 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 (3 d g+e f) \left(a+b \sin ^{-1}(c x)\right)+d e x^3 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^3 g x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(75 c^2 x \left(8 c^2 d^2 (d g+3 e f)+3 e^2 (3 d g+e f)\right)+32 \left(75 c^4 d^3 f+50 c^2 d e (d g+e f)+8 e^3 g\right)\right)}{2400 c^5}-\frac{b \sin ^{-1}(c x) \left(8 c^2 d^2 (d g+3 e f)+3 e^2 (3 d g+e f)\right)}{32 c^4}+\frac{b e^2 x^3 \sqrt{1-c^2 x^2} (3 d g+e f)}{16 c}+\frac{b e x^2 \sqrt{1-c^2 x^2} \left(25 c^2 d (d g+e f)+4 e^2 g\right)}{75 c^3}+\frac{b e^3 g x^4 \sqrt{1-c^2 x^2}}{25 c}",1,"(b*e*(4*e^2*g + 25*c^2*d*(e*f + d*g))*x^2*Sqrt[1 - c^2*x^2])/(75*c^3) + (b*e^2*(e*f + 3*d*g)*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (b*e^3*g*x^4*Sqrt[1 - c^2*x^2])/(25*c) + (b*(32*(75*c^4*d^3*f + 8*e^3*g + 50*c^2*d*e*(e*f + d*g)) + 75*c^2*(8*c^2*d^2*(3*e*f + d*g) + 3*e^2*(e*f + 3*d*g))*x)*Sqrt[1 - c^2*x^2])/(2400*c^5) - (b*(8*c^2*d^2*(3*e*f + d*g) + 3*e^2*(e*f + 3*d*g))*ArcSin[c*x])/(32*c^4) + d^3*f*x*(a + b*ArcSin[c*x]) + (d^2*(3*e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + d*e*(e*f + d*g)*x^3*(a + b*ArcSin[c*x]) + (e^2*(e*f + 3*d*g)*x^4*(a + b*ArcSin[c*x]))/4 + (e^3*g*x^5*(a + b*ArcSin[c*x]))/5","A",6,4,21,0.1905,1,"{4749, 1809, 780, 216}"
89,1,248,0,0.535084,"\int (d+e x)^2 (f+g x) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(f + g*x)*(a + b*ArcSin[c*x]),x]","d^2 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e x^3 (2 d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d x^2 (d g+2 e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^2 g x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(32 \left(9 c^2 d^2 f+2 e (2 d g+e f)\right)+9 x \left(8 c^2 d (d g+2 e f)+3 e^2 g\right)\right)}{288 c^3}-\frac{b \sin ^{-1}(c x) \left(8 c^2 d (d g+2 e f)+3 e^2 g\right)}{32 c^4}+\frac{b e x^2 \sqrt{1-c^2 x^2} (2 d g+e f)}{9 c}+\frac{b e^2 g x^3 \sqrt{1-c^2 x^2}}{16 c}","d^2 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e x^3 (2 d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d x^2 (d g+2 e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^2 g x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(32 \left(9 c^2 d^2 f+2 e (2 d g+e f)\right)+9 x \left(8 c^2 d (d g+2 e f)+3 e^2 g\right)\right)}{288 c^3}-\frac{b \sin ^{-1}(c x) \left(8 c^2 d (d g+2 e f)+3 e^2 g\right)}{32 c^4}+\frac{b e x^2 \sqrt{1-c^2 x^2} (2 d g+e f)}{9 c}+\frac{b e^2 g x^3 \sqrt{1-c^2 x^2}}{16 c}",1,"(b*e*(e*f + 2*d*g)*x^2*Sqrt[1 - c^2*x^2])/(9*c) + (b*e^2*g*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (b*(32*(9*c^2*d^2*f + 2*e*(e*f + 2*d*g)) + 9*(3*e^2*g + 8*c^2*d*(2*e*f + d*g))*x)*Sqrt[1 - c^2*x^2])/(288*c^3) - (b*(3*e^2*g + 8*c^2*d*(2*e*f + d*g))*ArcSin[c*x])/(32*c^4) + d^2*f*x*(a + b*ArcSin[c*x]) + (d*(2*e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + (e*(e*f + 2*d*g)*x^3*(a + b*ArcSin[c*x]))/3 + (e^2*g*x^4*(a + b*ArcSin[c*x]))/4","A",6,5,21,0.2381,1,"{4749, 12, 1809, 780, 216}"
90,1,148,0,0.1929872,"\int (d+e x) (f+g x) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(f + g*x)*(a + b*ArcSin[c*x]),x]","\frac{1}{2} x^2 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+d f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e g x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(9 c^2 x (d g+e f)+4 \left(9 c^2 d f+2 e g\right)\right)}{36 c^3}-\frac{b \sin ^{-1}(c x) (d g+e f)}{4 c^2}+\frac{b e g x^2 \sqrt{1-c^2 x^2}}{9 c}","\frac{1}{2} x^2 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+d f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e g x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(9 c^2 x (d g+e f)+4 \left(9 c^2 d f+2 e g\right)\right)}{36 c^3}-\frac{b \sin ^{-1}(c x) (d g+e f)}{4 c^2}+\frac{b e g x^2 \sqrt{1-c^2 x^2}}{9 c}",1,"(b*e*g*x^2*Sqrt[1 - c^2*x^2])/(9*c) + (b*(4*(9*c^2*d*f + 2*e*g) + 9*c^2*(e*f + d*g)*x)*Sqrt[1 - c^2*x^2])/(36*c^3) - (b*(e*f + d*g)*ArcSin[c*x])/(4*c^2) + d*f*x*(a + b*ArcSin[c*x]) + ((e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + (e*g*x^3*(a + b*ArcSin[c*x]))/3","A",5,5,19,0.2632,1,"{4749, 12, 1809, 780, 216}"
91,1,344,0,0.6434942,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{d+e x} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d + e*x),x]","-\frac{i b (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}-\frac{i b (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}+\frac{(e f-d g) \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{g x \left(a+b \sin ^{-1}(c x)\right)}{e}+\frac{b \sin ^{-1}(c x) (e f-d g) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}+\frac{b \sin ^{-1}(c x) (e f-d g) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}+\frac{b g \sqrt{1-c^2 x^2}}{c e}-\frac{i b \sin ^{-1}(c x)^2 (e f-d g)}{2 e^2}-\frac{b \sin ^{-1}(c x) (e f-d g) \log (d+e x)}{e^2}","-\frac{i b (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}-\frac{i b (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}+\frac{(e f-d g) \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{g x \left(a+b \sin ^{-1}(c x)\right)}{e}+\frac{b \sin ^{-1}(c x) (e f-d g) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}+\frac{b \sin ^{-1}(c x) (e f-d g) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}+\frac{b g \sqrt{1-c^2 x^2}}{c e}-\frac{i b \sin ^{-1}(c x)^2 (e f-d g)}{2 e^2}-\frac{b \sin ^{-1}(c x) (e f-d g) \log (d+e x)}{e^2}",1,"(b*g*Sqrt[1 - c^2*x^2])/(c*e) - ((I/2)*b*(e*f - d*g)*ArcSin[c*x]^2)/e^2 + (g*x*(a + b*ArcSin[c*x]))/e + (b*(e*f - d*g)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^2 + (b*(e*f - d*g)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^2 - (b*(e*f - d*g)*ArcSin[c*x]*Log[d + e*x])/e^2 + ((e*f - d*g)*(a + b*ArcSin[c*x])*Log[d + e*x])/e^2 - (I*b*(e*f - d*g)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^2 - (I*b*(e*f - d*g)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^2","A",14,12,21,0.5714,1,"{43, 4753, 12, 6742, 261, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
92,1,358,0,0.9521153,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^2} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d + e*x)^2,x]","-\frac{i b g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}-\frac{i b g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{e^2 (d+e x)}+\frac{g \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{b c (e f-d g) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{b g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}+\frac{b g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}-\frac{b g \sin ^{-1}(c x) \log (d+e x)}{e^2}-\frac{i b g \sin ^{-1}(c x)^2}{2 e^2}","-\frac{i b g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}-\frac{i b g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{e^2 (d+e x)}+\frac{g \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{b c (e f-d g) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{b g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2}+\frac{b g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2}-\frac{b g \sin ^{-1}(c x) \log (d+e x)}{e^2}-\frac{i b g \sin ^{-1}(c x)^2}{2 e^2}",1,"((-I/2)*b*g*ArcSin[c*x]^2)/e^2 - ((e*f - d*g)*(a + b*ArcSin[c*x]))/(e^2*(d + e*x)) + (b*c*(e*f - d*g)*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) + (b*g*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^2 + (b*g*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^2 - (b*g*ArcSin[c*x]*Log[d + e*x])/e^2 + (g*(a + b*ArcSin[c*x])*Log[d + e*x])/e^2 - (I*b*g*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^2 - (I*b*g*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^2","A",15,13,21,0.6190,1,"{43, 4753, 12, 6742, 725, 204, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
93,1,202,0,0.3578126,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^3} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d + e*x)^3,x]","-\frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 (d+e x)^2 (e f-d g)}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{2 e \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c \left(2 e^2 g-c^2 d (d g+e f)\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 e^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b g^2 \sin ^{-1}(c x)}{2 e^2 (e f-d g)}","-\frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 (d+e x)^2 (e f-d g)}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{2 e \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c \left(2 e^2 g-c^2 d (d g+e f)\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{2 e^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b g^2 \sin ^{-1}(c x)}{2 e^2 (e f-d g)}",1,"(b*c*(e*f - d*g)*Sqrt[1 - c^2*x^2])/(2*e*(c^2*d^2 - e^2)*(d + e*x)) + (b*g^2*ArcSin[c*x])/(2*e^2*(e*f - d*g)) - ((f + g*x)^2*(a + b*ArcSin[c*x]))/(2*(e*f - d*g)*(d + e*x)^2) - (b*c*(2*e^2*g - c^2*d*(e*f + d*g))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e^2*(c^2*d^2 - e^2)^(3/2))","A",7,8,21,0.3810,1,"{37, 4753, 12, 1651, 844, 216, 725, 204}"
94,1,257,0,0.427468,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^4} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d + e*x)^4,x]","-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{3 e^2 (d+e x)^3}-\frac{g \left(a+b \sin ^{-1}(c x)\right)}{2 e^2 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} \left(c^2 d f-e g\right)}{2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{6 e \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(c^2 d^2 (d g+2 e f)+e^2 (e f-4 d g)\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{6 e^2 \left(c^2 d^2-e^2\right)^{5/2}}","-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{3 e^2 (d+e x)^3}-\frac{g \left(a+b \sin ^{-1}(c x)\right)}{2 e^2 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} \left(c^2 d f-e g\right)}{2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{6 e \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(c^2 d^2 (d g+2 e f)+e^2 (e f-4 d g)\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{6 e^2 \left(c^2 d^2-e^2\right)^{5/2}}",1,"(b*c*(e*f - d*g)*Sqrt[1 - c^2*x^2])/(6*e*(c^2*d^2 - e^2)*(d + e*x)^2) + (b*c*(c^2*d*f - e*g)*Sqrt[1 - c^2*x^2])/(2*(c^2*d^2 - e^2)^2*(d + e*x)) - ((e*f - d*g)*(a + b*ArcSin[c*x]))/(3*e^2*(d + e*x)^3) - (g*(a + b*ArcSin[c*x]))/(2*e^2*(d + e*x)^2) + (b*c^3*(e^2*(e*f - 4*d*g) + c^2*d^2*(2*e*f + d*g))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(6*e^2*(c^2*d^2 - e^2)^(5/2))","A",6,7,21,0.3333,1,"{43, 4753, 12, 835, 807, 725, 204}"
95,1,360,0,0.6951722,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^5} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d + e*x)^5,x]","-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{4 e^2 (d+e x)^4}-\frac{g \left(a+b \sin ^{-1}(c x)\right)}{3 e^2 (d+e x)^3}+\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^2 d^2 (d g+11 e f)+4 e^2 (e f-4 d g)\right)}{24 e \left(c^2 d^2-e^2\right)^3 (d+e x)}-\frac{b c \sqrt{1-c^2 x^2} \left(4 e^2 g-c^2 d (5 e f-d g)\right)}{24 e \left(c^2 d^2-e^2\right)^2 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{12 e \left(c^2 d^2-e^2\right) (d+e x)^3}-\frac{b c^3 \left(-2 c^4 d^3 (d g+3 e f)-c^2 d e^2 (9 e f-13 d g)+4 e^4 g\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{24 e^2 \left(c^2 d^2-e^2\right)^{7/2}}","-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{4 e^2 (d+e x)^4}-\frac{g \left(a+b \sin ^{-1}(c x)\right)}{3 e^2 (d+e x)^3}+\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^2 d^2 (d g+11 e f)+4 e^2 (e f-4 d g)\right)}{24 e \left(c^2 d^2-e^2\right)^3 (d+e x)}-\frac{b c \sqrt{1-c^2 x^2} \left(4 e^2 g-c^2 d (5 e f-d g)\right)}{24 e \left(c^2 d^2-e^2\right)^2 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{12 e \left(c^2 d^2-e^2\right) (d+e x)^3}-\frac{b c^3 \left(-2 c^4 d^3 (d g+3 e f)-c^2 d e^2 (9 e f-13 d g)+4 e^4 g\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{24 e^2 \left(c^2 d^2-e^2\right)^{7/2}}",1,"(b*c*(e*f - d*g)*Sqrt[1 - c^2*x^2])/(12*e*(c^2*d^2 - e^2)*(d + e*x)^3) - (b*c*(4*e^2*g - c^2*d*(5*e*f - d*g))*Sqrt[1 - c^2*x^2])/(24*e*(c^2*d^2 - e^2)^2*(d + e*x)^2) + (b*c^3*(4*e^2*(e*f - 4*d*g) + c^2*d^2*(11*e*f + d*g))*Sqrt[1 - c^2*x^2])/(24*e*(c^2*d^2 - e^2)^3*(d + e*x)) - ((e*f - d*g)*(a + b*ArcSin[c*x]))/(4*e^2*(d + e*x)^4) - (g*(a + b*ArcSin[c*x]))/(3*e^2*(d + e*x)^3) - (b*c^3*(4*e^4*g - c^2*d*e^2*(9*e*f - 13*d*g) - 2*c^4*d^3*(3*e*f + d*g))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(24*e^2*(c^2*d^2 - e^2)^(7/2))","A",7,7,21,0.3333,1,"{43, 4753, 12, 835, 807, 725, 204}"
96,1,457,0,0.9655647,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^6} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x]))/(d + e*x)^6,x]","-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{5 e^2 (d+e x)^5}-\frac{g \left(a+b \sin ^{-1}(c x)\right)}{4 e^2 (d+e x)^4}-\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^4 \left(-d^3\right) (d g+10 e f)-c^2 d e^2 (11 e f-18 d g)+4 e^4 g\right)}{24 e \left(c^2 d^2-e^2\right)^4 (d+e x)}+\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^2 d^2 (26 e f-d g)+e^2 (9 e f-34 d g)\right)}{120 e \left(c^2 d^2-e^2\right)^3 (d+e x)^2}-\frac{b c \sqrt{1-c^2 x^2} \left(5 e^2 g-c^2 d (7 e f-2 d g)\right)}{60 e \left(c^2 d^2-e^2\right)^2 (d+e x)^3}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{20 e \left(c^2 d^2-e^2\right) (d+e x)^4}+\frac{b c^5 \left(c^2 d^2 e^2 (24 e f-19 d g)+2 c^4 d^4 (d g+4 e f)+3 e^4 (e f-6 d g)\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{40 e^2 \left(c^2 d^2-e^2\right)^{9/2}}","-\frac{(e f-d g) \left(a+b \sin ^{-1}(c x)\right)}{5 e^2 (d+e x)^5}-\frac{g \left(a+b \sin ^{-1}(c x)\right)}{4 e^2 (d+e x)^4}-\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^4 \left(-d^3\right) (d g+10 e f)-c^2 d e^2 (11 e f-18 d g)+4 e^4 g\right)}{24 e \left(c^2 d^2-e^2\right)^4 (d+e x)}+\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^2 d^2 (26 e f-d g)+e^2 (9 e f-34 d g)\right)}{120 e \left(c^2 d^2-e^2\right)^3 (d+e x)^2}-\frac{b c \sqrt{1-c^2 x^2} \left(5 e^2 g-c^2 d (7 e f-2 d g)\right)}{60 e \left(c^2 d^2-e^2\right)^2 (d+e x)^3}+\frac{b c \sqrt{1-c^2 x^2} (e f-d g)}{20 e \left(c^2 d^2-e^2\right) (d+e x)^4}+\frac{b c^5 \left(c^2 d^2 e^2 (24 e f-19 d g)+2 c^4 d^4 (d g+4 e f)+3 e^4 (e f-6 d g)\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{40 e^2 \left(c^2 d^2-e^2\right)^{9/2}}",1,"(b*c*(e*f - d*g)*Sqrt[1 - c^2*x^2])/(20*e*(c^2*d^2 - e^2)*(d + e*x)^4) - (b*c*(5*e^2*g - c^2*d*(7*e*f - 2*d*g))*Sqrt[1 - c^2*x^2])/(60*e*(c^2*d^2 - e^2)^2*(d + e*x)^3) + (b*c^3*(e^2*(9*e*f - 34*d*g) + c^2*d^2*(26*e*f - d*g))*Sqrt[1 - c^2*x^2])/(120*e*(c^2*d^2 - e^2)^3*(d + e*x)^2) - (b*c^3*(4*e^4*g - c^2*d*e^2*(11*e*f - 18*d*g) - c^4*d^3*(10*e*f + d*g))*Sqrt[1 - c^2*x^2])/(24*e*(c^2*d^2 - e^2)^4*(d + e*x)) - ((e*f - d*g)*(a + b*ArcSin[c*x]))/(5*e^2*(d + e*x)^5) - (g*(a + b*ArcSin[c*x]))/(4*e^2*(d + e*x)^4) + (b*c^5*(c^2*d^2*e^2*(24*e*f - 19*d*g) + 3*e^4*(e*f - 6*d*g) + 2*c^4*d^4*(4*e*f + d*g))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(40*e^2*(c^2*d^2 - e^2)^(9/2))","A",8,7,21,0.3333,1,"{43, 4753, 12, 835, 807, 725, 204}"
97,1,509,0,2.5107772,"\int (d+e x)^3 \left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(f + g*x + h*x^2)*(a + b*ArcSin[c*x]),x]","\frac{1}{4} e x^4 \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 h+3 d e g+e^2 f\right)+\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+3 d e g+3 e^2 f\right)+\frac{1}{2} d^2 x^2 (d g+3 e f) \left(a+b \sin ^{-1}(c x)\right)+d^3 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 (3 d h+e g) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^3 h x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e x^3 \sqrt{1-c^2 x^2} \left(e^2 \left(\frac{5 h}{c^2}+9 f\right)+27 d^2 h+27 d e g\right)}{144 c}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 d \left(d^2 h+3 d e g+3 e^2 f\right)+12 e^2 (3 d h+e g)\right)}{225 c^3}+\frac{b \sqrt{1-c^2 x^2} \left(75 x \left(9 c^2 e \left(3 d^2 h+3 d e g+e^2 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^3 h\right)+32 \left(50 c^2 d \left(d^2 h+3 d e g+3 e^2 f\right)+225 c^4 d^3 f+24 e^2 (3 d h+e g)\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(9 c^2 e \left(3 d^2 h+3 d e g+e^2 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^3 h\right)}{96 c^6}+\frac{b e^2 x^4 \sqrt{1-c^2 x^2} (3 d h+e g)}{25 c}+\frac{b e^3 h x^5 \sqrt{1-c^2 x^2}}{36 c}","\frac{1}{4} e x^4 \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 h+3 d e g+e^2 f\right)+\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+3 d e g+3 e^2 f\right)+\frac{1}{2} d^2 x^2 (d g+3 e f) \left(a+b \sin ^{-1}(c x)\right)+d^3 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 (3 d h+e g) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^3 h x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e x^3 \sqrt{1-c^2 x^2} \left(9 c^2 \left(3 d^2 h+3 d e g+e^2 f\right)+5 e^2 h\right)}{144 c^3}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 d \left(d^2 h+3 d e g+3 e^2 f\right)+12 e^2 (3 d h+e g)\right)}{225 c^3}+\frac{b \sqrt{1-c^2 x^2} \left(75 x \left(9 c^2 e \left(3 d^2 h+3 d e g+e^2 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^3 h\right)+32 \left(50 c^2 d \left(d^2 h+3 d e g+3 e^2 f\right)+225 c^4 d^3 f+24 e^2 (3 d h+e g)\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(9 c^2 e \left(3 d^2 h+3 d e g+e^2 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^3 h\right)}{96 c^6}+\frac{b e^2 x^4 \sqrt{1-c^2 x^2} (3 d h+e g)}{25 c}+\frac{b e^3 h x^5 \sqrt{1-c^2 x^2}}{36 c}",1,"(b*(12*e^2*(e*g + 3*d*h) + 25*c^2*d*(3*e^2*f + 3*d*e*g + d^2*h))*x^2*Sqrt[1 - c^2*x^2])/(225*c^3) + (b*e*(27*d*e*g + 27*d^2*h + e^2*(9*f + (5*h)/c^2))*x^3*Sqrt[1 - c^2*x^2])/(144*c) + (b*e^2*(e*g + 3*d*h)*x^4*Sqrt[1 - c^2*x^2])/(25*c) + (b*e^3*h*x^5*Sqrt[1 - c^2*x^2])/(36*c) + (b*(32*(225*c^4*d^3*f + 24*e^2*(e*g + 3*d*h) + 50*c^2*d*(3*e^2*f + 3*d*e*g + d^2*h)) + 75*(24*c^4*d^2*(3*e*f + d*g) + 5*e^3*h + 9*c^2*e*(e^2*f + 3*d*e*g + 3*d^2*h))*x)*Sqrt[1 - c^2*x^2])/(7200*c^5) - (b*(24*c^4*d^2*(3*e*f + d*g) + 5*e^3*h + 9*c^2*e*(e^2*f + 3*d*e*g + 3*d^2*h))*ArcSin[c*x])/(96*c^6) + d^3*f*x*(a + b*ArcSin[c*x]) + (d^2*(3*e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + (d*(3*e^2*f + 3*d*e*g + d^2*h)*x^3*(a + b*ArcSin[c*x]))/3 + (e*(e^2*f + 3*d*e*g + 3*d^2*h)*x^4*(a + b*ArcSin[c*x]))/4 + (e^2*(e*g + 3*d*h)*x^5*(a + b*ArcSin[c*x]))/5 + (e^3*h*x^6*(a + b*ArcSin[c*x]))/6","A",8,5,26,0.1923,1,"{4749, 12, 1809, 780, 216}"
98,1,361,0,1.2152814,"\int (d+e x)^2 \left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(f + g*x + h*x^2)*(a + b*ArcSin[c*x]),x]","\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+2 d e g+e^2 f\right)+d^2 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d x^2 (d g+2 e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e x^4 (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^2 h x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 \left(d^2 h+2 d e g+e^2 f\right)+12 e^2 h\right)}{225 c^3}+\frac{b \sqrt{1-c^2 x^2} \left(32 \left(50 c^2 \left(d^2 h+2 d e g+e^2 f\right)+225 c^4 d^2 f+24 e^2 h\right)+225 c^2 x \left(8 c^2 d (d g+2 e f)+3 e (2 d h+e g)\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(8 c^2 d (d g+2 e f)+3 e (2 d h+e g)\right)}{32 c^4}+\frac{b e x^3 \sqrt{1-c^2 x^2} (2 d h+e g)}{16 c}+\frac{b e^2 h x^4 \sqrt{1-c^2 x^2}}{25 c}","\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+2 d e g+e^2 f\right)+d^2 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d x^2 (d g+2 e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e x^4 (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^2 h x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 \left(d^2 h+2 d e g+e^2 f\right)+12 e^2 h\right)}{225 c^3}+\frac{b \sqrt{1-c^2 x^2} \left(32 \left(50 c^2 \left(d^2 h+2 d e g+e^2 f\right)+225 c^4 d^2 f+24 e^2 h\right)+225 c^2 x \left(8 c^2 d (d g+2 e f)+3 e (2 d h+e g)\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(8 c^2 d (d g+2 e f)+3 e (2 d h+e g)\right)}{32 c^4}+\frac{b e x^3 \sqrt{1-c^2 x^2} (2 d h+e g)}{16 c}+\frac{b e^2 h x^4 \sqrt{1-c^2 x^2}}{25 c}",1,"(b*(12*e^2*h + 25*c^2*(e^2*f + 2*d*e*g + d^2*h))*x^2*Sqrt[1 - c^2*x^2])/(225*c^3) + (b*e*(e*g + 2*d*h)*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (b*e^2*h*x^4*Sqrt[1 - c^2*x^2])/(25*c) + (b*(32*(225*c^4*d^2*f + 24*e^2*h + 50*c^2*(e^2*f + 2*d*e*g + d^2*h)) + 225*c^2*(8*c^2*d*(2*e*f + d*g) + 3*e*(e*g + 2*d*h))*x)*Sqrt[1 - c^2*x^2])/(7200*c^5) - (b*(8*c^2*d*(2*e*f + d*g) + 3*e*(e*g + 2*d*h))*ArcSin[c*x])/(32*c^4) + d^2*f*x*(a + b*ArcSin[c*x]) + (d*(2*e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + ((e^2*f + 2*d*e*g + d^2*h)*x^3*(a + b*ArcSin[c*x]))/3 + (e*(e*g + 2*d*h)*x^4*(a + b*ArcSin[c*x]))/4 + (e^2*h*x^5*(a + b*ArcSin[c*x]))/5","A",7,5,26,0.1923,1,"{4749, 12, 1809, 780, 216}"
99,1,223,0,0.4476163,"\int (d+e x) \left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(f + g*x + h*x^2)*(a + b*ArcSin[c*x]),x]","\frac{1}{2} x^2 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} x^3 (d h+e g) \left(a+b \sin ^{-1}(c x)\right)+d f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e h x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(9 x \left(8 c^2 (d g+e f)+3 e h\right)+32 \left(9 c^2 d f+2 d h+2 e g\right)\right)}{288 c^3}-\frac{b \sin ^{-1}(c x) \left(8 c^2 (d g+e f)+3 e h\right)}{32 c^4}+\frac{b x^2 \sqrt{1-c^2 x^2} (d h+e g)}{9 c}+\frac{b e h x^3 \sqrt{1-c^2 x^2}}{16 c}","\frac{1}{2} x^2 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} x^3 (d h+e g) \left(a+b \sin ^{-1}(c x)\right)+d f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e h x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(9 x \left(8 c^2 (d g+e f)+3 e h\right)+32 \left(9 c^2 d f+2 d h+2 e g\right)\right)}{288 c^3}-\frac{b \sin ^{-1}(c x) \left(8 c^2 (d g+e f)+3 e h\right)}{32 c^4}+\frac{b x^2 \sqrt{1-c^2 x^2} (d h+e g)}{9 c}+\frac{b e h x^3 \sqrt{1-c^2 x^2}}{16 c}",1,"(b*(e*g + d*h)*x^2*Sqrt[1 - c^2*x^2])/(9*c) + (b*e*h*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (b*(32*(9*c^2*d*f + 2*e*g + 2*d*h) + 9*(8*c^2*(e*f + d*g) + 3*e*h)*x)*Sqrt[1 - c^2*x^2])/(288*c^3) - (b*(8*c^2*(e*f + d*g) + 3*e*h)*ArcSin[c*x])/(32*c^4) + d*f*x*(a + b*ArcSin[c*x]) + ((e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + ((e*g + d*h)*x^3*(a + b*ArcSin[c*x]))/3 + (e*h*x^4*(a + b*ArcSin[c*x]))/4","A",6,5,24,0.2083,1,"{4749, 12, 1809, 780, 216}"
100,1,459,0,0.7866986,"\int \frac{\left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{d+e x} \, dx","Int[((f + g*x + h*x^2)*(a + b*ArcSin[c*x]))/(d + e*x),x]","-\frac{i b \left(d^2 h-d e g+e^2 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{i b \left(d^2 h-d e g+e^2 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}+\frac{\log (d+e x) \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{e^3}+\frac{x (e g-d h) \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{h x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e}+\frac{b \sin ^{-1}(c x) \left(d^2 h-d e g+e^2 f\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b \sin ^{-1}(c x) \left(d^2 h-d e g+e^2 f\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}+\frac{b \sqrt{1-c^2 x^2} (4 (e g-d h)+e h x)}{4 c e^2}-\frac{b h \sin ^{-1}(c x)}{4 c^2 e}-\frac{i b \sin ^{-1}(c x)^2 \left(d^2 h-d e g+e^2 f\right)}{2 e^3}-\frac{b \sin ^{-1}(c x) \log (d+e x) \left(d^2 h-d e g+e^2 f\right)}{e^3}","-\frac{i b \left(d^2 h-d e g+e^2 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{i b \left(d^2 h-d e g+e^2 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}+\frac{\log (d+e x) \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{e^3}+\frac{x (e g-d h) \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{h x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e}+\frac{b \sin ^{-1}(c x) \left(d^2 h-d e g+e^2 f\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b \sin ^{-1}(c x) \left(d^2 h-d e g+e^2 f\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}+\frac{b \sqrt{1-c^2 x^2} (4 (e g-d h)+e h x)}{4 c e^2}-\frac{b h \sin ^{-1}(c x)}{4 c^2 e}-\frac{i b \sin ^{-1}(c x)^2 \left(d^2 h-d e g+e^2 f\right)}{2 e^3}-\frac{b \sin ^{-1}(c x) \log (d+e x) \left(d^2 h-d e g+e^2 f\right)}{e^3}",1,"(b*(4*(e*g - d*h) + e*h*x)*Sqrt[1 - c^2*x^2])/(4*c*e^2) - (b*h*ArcSin[c*x])/(4*c^2*e) - ((I/2)*b*(e^2*f - d*e*g + d^2*h)*ArcSin[c*x]^2)/e^3 + ((e*g - d*h)*x*(a + b*ArcSin[c*x]))/e^2 + (h*x^2*(a + b*ArcSin[c*x]))/(2*e) + (b*(e^2*f - d*e*g + d^2*h)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 + (b*(e^2*f - d*e*g + d^2*h)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 - (b*(e^2*f - d*e*g + d^2*h)*ArcSin[c*x]*Log[d + e*x])/e^3 + ((e^2*f - d*e*g + d^2*h)*(a + b*ArcSin[c*x])*Log[d + e*x])/e^3 - (I*b*(e^2*f - d*e*g + d^2*h)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 - (I*b*(e^2*f - d*e*g + d^2*h)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3","A",15,12,26,0.4615,1,"{698, 4753, 12, 6742, 780, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
101,1,460,0,0.8473266,"\int \frac{\left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^2} \, dx","Int[((f + g*x + h*x^2)*(a + b*ArcSin[c*x]))/(d + e*x)^2,x]","-\frac{i b (e g-2 d h) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{i b (e g-2 d h) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{e^3 (d+e x)}+\frac{(e g-2 d h) \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^3}+\frac{h x \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(d^2 h-d e g+e^2 f\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{b \sin ^{-1}(c x) (e g-2 d h) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b \sin ^{-1}(c x) (e g-2 d h) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}+\frac{b h \sqrt{1-c^2 x^2}}{c e^2}-\frac{i b \sin ^{-1}(c x)^2 (e g-2 d h)}{2 e^3}-\frac{b \sin ^{-1}(c x) (e g-2 d h) \log (d+e x)}{e^3}","-\frac{i b (e g-2 d h) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{i b (e g-2 d h) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{e^3 (d+e x)}+\frac{(e g-2 d h) \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^3}+\frac{h x \left(a+b \sin ^{-1}(c x)\right)}{e^2}+\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(d^2 h-d e g+e^2 f\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{b \sin ^{-1}(c x) (e g-2 d h) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b \sin ^{-1}(c x) (e g-2 d h) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}+\frac{b h \sqrt{1-c^2 x^2}}{c e^2}-\frac{i b \sin ^{-1}(c x)^2 (e g-2 d h)}{2 e^3}-\frac{b \sin ^{-1}(c x) (e g-2 d h) \log (d+e x)}{e^3}",1,"(b*h*Sqrt[1 - c^2*x^2])/(c*e^2) - ((I/2)*b*(e*g - 2*d*h)*ArcSin[c*x]^2)/e^3 + (h*x*(a + b*ArcSin[c*x]))/e^2 - ((e^2*f - d*e*g + d^2*h)*(a + b*ArcSin[c*x]))/(e^3*(d + e*x)) + (b*c*(e^2*f - d*e*g + d^2*h)*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) + (b*(e*g - 2*d*h)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 + (b*(e*g - 2*d*h)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 - (b*(e*g - 2*d*h)*ArcSin[c*x]*Log[d + e*x])/e^3 + ((e*g - 2*d*h)*(a + b*ArcSin[c*x])*Log[d + e*x])/e^3 - (I*b*(e*g - 2*d*h)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 - (I*b*(e*g - 2*d*h)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3","A",16,14,26,0.5385,1,"{698, 4753, 12, 6742, 261, 725, 204, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
102,1,488,0,1.2620681,"\int \frac{\left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^3} \, dx","Int[((f + g*x + h*x^2)*(a + b*ArcSin[c*x]))/(d + e*x)^3,x]","-\frac{i b h \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{i b h \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{2 e^3 (d+e x)^2}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{e^3 (d+e x)}+\frac{h \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^3}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{2 e^2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(2 e^2 (e g-2 d h)-c^2 d \left(-3 d^2 h+d e g+e^2 f\right)\right)}{2 e^3 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b h \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b h \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}-\frac{b h \sin ^{-1}(c x) \log (d+e x)}{e^3}-\frac{i b h \sin ^{-1}(c x)^2}{2 e^3}","-\frac{i b h \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{i b h \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{2 e^3 (d+e x)^2}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{e^3 (d+e x)}+\frac{h \log (d+e x) \left(a+b \sin ^{-1}(c x)\right)}{e^3}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{2 e^2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(2 e^2 (e g-2 d h)-c^2 d \left(-3 d^2 h+d e g+e^2 f\right)\right)}{2 e^3 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b h \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b h \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^3}-\frac{b h \sin ^{-1}(c x) \log (d+e x)}{e^3}-\frac{i b h \sin ^{-1}(c x)^2}{2 e^3}",1,"(b*c*(e^2*f - d*e*g + d^2*h)*Sqrt[1 - c^2*x^2])/(2*e^2*(c^2*d^2 - e^2)*(d + e*x)) - ((I/2)*b*h*ArcSin[c*x]^2)/e^3 - ((e^2*f - d*e*g + d^2*h)*(a + b*ArcSin[c*x]))/(2*e^3*(d + e*x)^2) - ((e*g - 2*d*h)*(a + b*ArcSin[c*x]))/(e^3*(d + e*x)) - (b*c*(2*e^2*(e*g - 2*d*h) - c^2*d*(e^2*f + d*e*g - 3*d^2*h))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e^3*(c^2*d^2 - e^2)^(3/2)) + (b*h*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 + (b*h*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 - (b*h*ArcSin[c*x]*Log[d + e*x])/e^3 + (h*(a + b*ArcSin[c*x])*Log[d + e*x])/e^3 - (I*b*h*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 - (I*b*h*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3","A",16,14,26,0.5385,1,"{698, 4753, 12, 6742, 807, 725, 204, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
103,1,349,0,0.6170116,"\int \frac{\left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^4} \, dx","Int[((f + g*x + h*x^2)*(a + b*ArcSin[c*x]))/(d + e*x)^4,x]","-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{3 e^3 (d+e x)^3}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{2 e^3 (d+e x)^2}-\frac{h \left(a+b \sin ^{-1}(c x)\right)}{e^3 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{6 e^2 \left(c^2 d^2-e^2\right) (d+e x)^2}-\frac{b c \sqrt{1-c^2 x^2} \left(e^2 (e g-2 d h)-c^2 \left(d e^2 f-d^3 h\right)\right)}{2 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(c^4 d^2 \left(2 d^2 h+d e g+2 e^2 f\right)+c^2 e^2 \left(-5 d^2 h-4 d e g+e^2 f\right)+6 e^4 h\right)}{6 e^3 \left(c^2 d^2-e^2\right)^{5/2}}","-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{3 e^3 (d+e x)^3}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{2 e^3 (d+e x)^2}-\frac{h \left(a+b \sin ^{-1}(c x)\right)}{e^3 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{6 e^2 \left(c^2 d^2-e^2\right) (d+e x)^2}-\frac{b c \sqrt{1-c^2 x^2} \left(e^2 (e g-2 d h)-c^2 \left(d e^2 f-d^3 h\right)\right)}{2 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(c^4 d^2 \left(2 d^2 h+d e g+2 e^2 f\right)+c^2 e^2 \left(-5 d^2 h-4 d e g+e^2 f\right)+6 e^4 h\right)}{6 e^3 \left(c^2 d^2-e^2\right)^{5/2}}",1,"(b*c*(e^2*f - d*e*g + d^2*h)*Sqrt[1 - c^2*x^2])/(6*e^2*(c^2*d^2 - e^2)*(d + e*x)^2) - (b*c*(e^2*(e*g - 2*d*h) - c^2*(d*e^2*f - d^3*h))*Sqrt[1 - c^2*x^2])/(2*e^2*(c^2*d^2 - e^2)^2*(d + e*x)) - ((e^2*f - d*e*g + d^2*h)*(a + b*ArcSin[c*x]))/(3*e^3*(d + e*x)^3) - ((e*g - 2*d*h)*(a + b*ArcSin[c*x]))/(2*e^3*(d + e*x)^2) - (h*(a + b*ArcSin[c*x]))/(e^3*(d + e*x)) + (b*c*(6*e^4*h + c^2*e^2*(e^2*f - 4*d*e*g - 5*d^2*h) + c^4*d^2*(2*e^2*f + d*e*g + 2*d^2*h))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(6*e^3*(c^2*d^2 - e^2)^(5/2))","A",6,7,26,0.2692,1,"{698, 4753, 12, 1651, 807, 725, 204}"
104,1,470,0,0.9435019,"\int \frac{\left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^5} \, dx","Int[((f + g*x + h*x^2)*(a + b*ArcSin[c*x]))/(d + e*x)^5,x]","-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{4 e^3 (d+e x)^4}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{3 e^3 (d+e x)^3}-\frac{h \left(a+b \sin ^{-1}(c x)\right)}{2 e^3 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} \left(c^4 d^2 \left(d^2 (-h)+d e g+11 e^2 f\right)+4 c^2 e^2 \left(d^2 h-4 d e g+e^2 f\right)+12 e^4 h\right)}{24 e^2 \left(c^2 d^2-e^2\right)^3 (d+e x)}-\frac{b c \sqrt{1-c^2 x^2} \left(4 e^2 (e g-2 d h)-c^2 d \left(-3 d^2 h-d e g+5 e^2 f\right)\right)}{24 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{12 e^2 \left(c^2 d^2-e^2\right) (d+e x)^3}-\frac{b c^3 \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(-2 c^4 d^3 \left(d^2 h+d e g+3 e^2 f\right)-c^2 d e^2 \left(-7 d^2 h-13 d e g+9 e^2 f\right)+4 e^4 (e g-5 d h)\right)}{24 e^3 \left(c^2 d^2-e^2\right)^{7/2}}","-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{4 e^3 (d+e x)^4}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{3 e^3 (d+e x)^3}-\frac{h \left(a+b \sin ^{-1}(c x)\right)}{2 e^3 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} \left(c^4 d^2 \left(d^2 (-h)+d e g+11 e^2 f\right)+4 c^2 e^2 \left(d^2 h-4 d e g+e^2 f\right)+12 e^4 h\right)}{24 e^2 \left(c^2 d^2-e^2\right)^3 (d+e x)}-\frac{b c \sqrt{1-c^2 x^2} \left(4 e^2 (e g-2 d h)-c^2 d \left(-3 d^2 h-d e g+5 e^2 f\right)\right)}{24 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)^2}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{12 e^2 \left(c^2 d^2-e^2\right) (d+e x)^3}-\frac{b c^3 \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(-2 c^4 d^3 \left(d^2 h+d e g+3 e^2 f\right)-c^2 d e^2 \left(-7 d^2 h-13 d e g+9 e^2 f\right)+4 e^4 (e g-5 d h)\right)}{24 e^3 \left(c^2 d^2-e^2\right)^{7/2}}",1,"(b*c*(e^2*f - d*e*g + d^2*h)*Sqrt[1 - c^2*x^2])/(12*e^2*(c^2*d^2 - e^2)*(d + e*x)^3) - (b*c*(4*e^2*(e*g - 2*d*h) - c^2*d*(5*e^2*f - d*e*g - 3*d^2*h))*Sqrt[1 - c^2*x^2])/(24*e^2*(c^2*d^2 - e^2)^2*(d + e*x)^2) + (b*c*(12*e^4*h + c^4*d^2*(11*e^2*f + d*e*g - d^2*h) + 4*c^2*e^2*(e^2*f - 4*d*e*g + d^2*h))*Sqrt[1 - c^2*x^2])/(24*e^2*(c^2*d^2 - e^2)^3*(d + e*x)) - ((e^2*f - d*e*g + d^2*h)*(a + b*ArcSin[c*x]))/(4*e^3*(d + e*x)^4) - ((e*g - 2*d*h)*(a + b*ArcSin[c*x]))/(3*e^3*(d + e*x)^3) - (h*(a + b*ArcSin[c*x]))/(2*e^3*(d + e*x)^2) - (b*c^3*(4*e^4*(e*g - 5*d*h) - c^2*d*e^2*(9*e^2*f - 13*d*e*g - 7*d^2*h) - 2*c^4*d^3*(3*e^2*f + d*e*g + d^2*h))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(24*e^3*(c^2*d^2 - e^2)^(7/2))","A",7,8,26,0.3077,1,"{698, 4753, 12, 1651, 835, 807, 725, 204}"
105,1,593,0,1.2554874,"\int \frac{\left(f+g x+h x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^6} \, dx","Int[((f + g*x + h*x^2)*(a + b*ArcSin[c*x]))/(d + e*x)^6,x]","-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{5 e^3 (d+e x)^5}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{4 e^3 (d+e x)^4}-\frac{h \left(a+b \sin ^{-1}(c x)\right)}{3 e^3 (d+e x)^3}+\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^2 d e \left(d^2 h-18 d e g+11 e^2 f\right)+c^4 d^3 (d g+10 e f)-4 e^3 (e g-5 d h)\right)}{24 e \left(c^2 d^2-e^2\right)^4 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2} \left(c^4 d^2 \left(-4 d^2 h-d e g+26 e^2 f\right)+c^2 e^2 \left(19 d^2 h-34 d e g+9 e^2 f\right)+20 e^4 h\right)}{120 e^2 \left(c^2 d^2-e^2\right)^3 (d+e x)^2}-\frac{b c \sqrt{1-c^2 x^2} \left(5 e^2 (e g-2 d h)-c^2 d \left(-3 d^2 h-2 d e g+7 e^2 f\right)\right)}{60 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)^3}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{20 e^2 \left(c^2 d^2-e^2\right) (d+e x)^4}+\frac{b c^3 \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(2 c^6 d^4 \left(2 d^2 h+3 d e g+12 e^2 f\right)+3 c^4 d^2 e^2 \left(-6 d^2 h-19 d e g+24 e^2 f\right)+9 c^2 e^4 \left(11 d^2 h-6 d e g+e^2 f\right)+20 e^6 h\right)}{120 e^3 \left(c^2 d^2-e^2\right)^{9/2}}","-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 h-d e g+e^2 f\right)}{5 e^3 (d+e x)^5}-\frac{(e g-2 d h) \left(a+b \sin ^{-1}(c x)\right)}{4 e^3 (d+e x)^4}-\frac{h \left(a+b \sin ^{-1}(c x)\right)}{3 e^3 (d+e x)^3}+\frac{b c^3 \sqrt{1-c^2 x^2} \left(c^2 d e \left(d^2 h-18 d e g+11 e^2 f\right)+c^4 d^3 (d g+10 e f)-4 e^3 (e g-5 d h)\right)}{24 e \left(c^2 d^2-e^2\right)^4 (d+e x)}+\frac{b c \sqrt{1-c^2 x^2} \left(c^4 d^2 \left(-4 d^2 h-d e g+26 e^2 f\right)+c^2 e^2 \left(19 d^2 h-34 d e g+9 e^2 f\right)+20 e^4 h\right)}{120 e^2 \left(c^2 d^2-e^2\right)^3 (d+e x)^2}-\frac{b c \sqrt{1-c^2 x^2} \left(5 e^2 (e g-2 d h)-c^2 d \left(-3 d^2 h-2 d e g+7 e^2 f\right)\right)}{60 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)^3}+\frac{b c \sqrt{1-c^2 x^2} \left(d^2 h-d e g+e^2 f\right)}{20 e^2 \left(c^2 d^2-e^2\right) (d+e x)^4}+\frac{b c^3 \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(2 c^6 d^4 \left(2 d^2 h+3 d e g+12 e^2 f\right)+3 c^4 d^2 e^2 \left(-6 d^2 h-19 d e g+24 e^2 f\right)+9 c^2 e^4 \left(11 d^2 h-6 d e g+e^2 f\right)+20 e^6 h\right)}{120 e^3 \left(c^2 d^2-e^2\right)^{9/2}}",1,"(b*c*(e^2*f - d*e*g + d^2*h)*Sqrt[1 - c^2*x^2])/(20*e^2*(c^2*d^2 - e^2)*(d + e*x)^4) - (b*c*(5*e^2*(e*g - 2*d*h) - c^2*d*(7*e^2*f - 2*d*e*g - 3*d^2*h))*Sqrt[1 - c^2*x^2])/(60*e^2*(c^2*d^2 - e^2)^2*(d + e*x)^3) + (b*c*(20*e^4*h + c^4*d^2*(26*e^2*f - d*e*g - 4*d^2*h) + c^2*e^2*(9*e^2*f - 34*d*e*g + 19*d^2*h))*Sqrt[1 - c^2*x^2])/(120*e^2*(c^2*d^2 - e^2)^3*(d + e*x)^2) + (b*c^3*(c^4*d^3*(10*e*f + d*g) - 4*e^3*(e*g - 5*d*h) + c^2*d*e*(11*e^2*f - 18*d*e*g + d^2*h))*Sqrt[1 - c^2*x^2])/(24*e*(c^2*d^2 - e^2)^4*(d + e*x)) - ((e^2*f - d*e*g + d^2*h)*(a + b*ArcSin[c*x]))/(5*e^3*(d + e*x)^5) - ((e*g - 2*d*h)*(a + b*ArcSin[c*x]))/(4*e^3*(d + e*x)^4) - (h*(a + b*ArcSin[c*x]))/(3*e^3*(d + e*x)^3) + (b*c^3*(20*e^6*h + 3*c^4*d^2*e^2*(24*e^2*f - 19*d*e*g - 6*d^2*h) + 2*c^6*d^4*(12*e^2*f + 3*d*e*g + 2*d^2*h) + 9*c^2*e^4*(e^2*f - 6*d*e*g + 11*d^2*h))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(120*e^3*(c^2*d^2 - e^2)^(9/2))","A",8,8,26,0.3077,1,"{698, 4753, 12, 1651, 835, 807, 725, 204}"
106,1,684,0,6.2640883,"\int (d+e x)^3 \left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]),x]","\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+3 d e g+3 e^2 f\right)+\frac{1}{5} e x^5 \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 i+3 d e h+e^2 g\right)+\frac{1}{2} d^2 x^2 (d g+3 e f) \left(a+b \sin ^{-1}(c x)\right)+d^3 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^2 x^6 (3 d i+e h) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e^3 i x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-c^2 x^2} \left(9 c^2 \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+5 e^2 (3 d i+e h)\right)}{144 c^3}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(1225 c^4 d \left(d^2 h+3 d e g+3 e^2 f\right)+588 c^2 e \left(3 d^2 i+3 d e h+e^2 g\right)+360 e^3 i\right)}{11025 c^5}+\frac{b \sqrt{1-c^2 x^2} \left(3675 c^2 x \left(9 c^2 \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^2 (3 d i+e h)\right)+32 \left(2450 c^4 d \left(d^2 h+3 d e g+3 e^2 f\right)+1176 c^2 e \left(3 d^2 i+3 d e h+e^2 g\right)+11025 c^6 d^3 f+720 e^3 i\right)\right)}{352800 c^7}-\frac{b \sin ^{-1}(c x) \left(9 c^2 \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^2 (3 d i+e h)\right)}{96 c^6}+\frac{b e x^4 \sqrt{1-c^2 x^2} \left(49 c^2 \left(3 d^2 i+3 d e h+e^2 g\right)+30 e^2 i\right)}{1225 c^3}+\frac{b e^2 x^5 \sqrt{1-c^2 x^2} (3 d i+e h)}{36 c}+\frac{b e^3 i x^6 \sqrt{1-c^2 x^2}}{49 c}","\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+3 d e g+3 e^2 f\right)+\frac{1}{5} e x^5 \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 i+3 d e h+e^2 g\right)+\frac{1}{2} d^2 x^2 (d g+3 e f) \left(a+b \sin ^{-1}(c x)\right)+d^3 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^2 x^6 (3 d i+e h) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e^3 i x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-c^2 x^2} \left(9 c^2 \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+5 e^2 (3 d i+e h)\right)}{144 c^3}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(1225 c^4 d \left(d^2 h+3 d e g+3 e^2 f\right)+588 c^2 e \left(3 d^2 i+3 d e h+e^2 g\right)+360 e^3 i\right)}{11025 c^5}+\frac{b \sqrt{1-c^2 x^2} \left(3675 c^2 x \left(9 c^2 \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^2 (3 d i+e h)\right)+32 \left(2450 c^4 d \left(d^2 h+3 d e g+3 e^2 f\right)+1176 c^2 e \left(3 d^2 i+3 d e h+e^2 g\right)+11025 c^6 d^3 f+720 e^3 i\right)\right)}{352800 c^7}-\frac{b \sin ^{-1}(c x) \left(9 c^2 \left(3 d^2 e h+d^3 i+3 d e^2 g+e^3 f\right)+24 c^4 d^2 (d g+3 e f)+5 e^2 (3 d i+e h)\right)}{96 c^6}+\frac{b e x^4 \sqrt{1-c^2 x^2} \left(49 c^2 \left(3 d^2 i+3 d e h+e^2 g\right)+30 e^2 i\right)}{1225 c^3}+\frac{b e^2 x^5 \sqrt{1-c^2 x^2} (3 d i+e h)}{36 c}+\frac{b e^3 i x^6 \sqrt{1-c^2 x^2}}{49 c}",1,"(b*(1225*c^4*d*(3*e^2*f + 3*d*e*g + d^2*h) + 360*e^3*i + 588*c^2*e*(e^2*g + 3*d*e*h + 3*d^2*i))*x^2*Sqrt[1 - c^2*x^2])/(11025*c^5) + (b*(5*e^2*(e*h + 3*d*i) + 9*c^2*(e^3*f + 3*d*e^2*g + 3*d^2*e*h + d^3*i))*x^3*Sqrt[1 - c^2*x^2])/(144*c^3) + (b*e*(30*e^2*i + 49*c^2*(e^2*g + 3*d*e*h + 3*d^2*i))*x^4*Sqrt[1 - c^2*x^2])/(1225*c^3) + (b*e^2*(e*h + 3*d*i)*x^5*Sqrt[1 - c^2*x^2])/(36*c) + (b*e^3*i*x^6*Sqrt[1 - c^2*x^2])/(49*c) + (b*(32*(11025*c^6*d^3*f + 2450*c^4*d*(3*e^2*f + 3*d*e*g + d^2*h) + 720*e^3*i + 1176*c^2*e*(e^2*g + 3*d*e*h + 3*d^2*i)) + 3675*c^2*(24*c^4*d^2*(3*e*f + d*g) + 5*e^2*(e*h + 3*d*i) + 9*c^2*(e^3*f + 3*d*e^2*g + 3*d^2*e*h + d^3*i))*x)*Sqrt[1 - c^2*x^2])/(352800*c^7) - (b*(24*c^4*d^2*(3*e*f + d*g) + 5*e^2*(e*h + 3*d*i) + 9*c^2*(e^3*f + 3*d*e^2*g + 3*d^2*e*h + d^3*i))*ArcSin[c*x])/(96*c^6) + d^3*f*x*(a + b*ArcSin[c*x]) + (d^2*(3*e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + (d*(3*e^2*f + 3*d*e*g + d^2*h)*x^3*(a + b*ArcSin[c*x]))/3 + ((e^3*f + 3*d*e^2*g + 3*d^2*e*h + d^3*i)*x^4*(a + b*ArcSin[c*x]))/4 + (e*(e^2*g + 3*d*e*h + 3*d^2*i)*x^5*(a + b*ArcSin[c*x]))/5 + (e^2*(e*h + 3*d*i)*x^6*(a + b*ArcSin[c*x]))/6 + (e^3*i*x^7*(a + b*ArcSin[c*x]))/7","A",9,5,31,0.1613,1,"{4749, 12, 1809, 780, 216}"
107,1,482,0,2.5499519,"\int (d+e x)^2 \left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]),x]","\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+2 d e g+e^2 f\right)+\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 i+2 d e h+e^2 g\right)+d^2 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d x^2 (d g+2 e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e x^5 (2 d i+e h) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^2 i x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 \left(d^2 h+2 d e g+e^2 f\right)+12 e (2 d i+e h)\right)}{225 c^3}+\frac{b \sqrt{1-c^2 x^2} \left(75 x \left(9 c^2 \left(d^2 i+2 d e h+e^2 g\right)+24 c^4 d (d g+2 e f)+5 e^2 i\right)+32 \left(50 c^2 \left(d^2 h+2 d e g+e^2 f\right)+225 c^4 d^2 f+24 e (2 d i+e h)\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(9 c^2 \left(d^2 i+2 d e h+e^2 g\right)+24 c^4 d (d g+2 e f)+5 e^2 i\right)}{96 c^6}+\frac{b x^3 \sqrt{1-c^2 x^2} \left(e^2 \left(\frac{5 i}{c^2}+9 g\right)+9 d^2 i+18 d e h\right)}{144 c}+\frac{b e x^4 \sqrt{1-c^2 x^2} (2 d i+e h)}{25 c}+\frac{b e^2 i x^5 \sqrt{1-c^2 x^2}}{36 c}","\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 h+2 d e g+e^2 f\right)+\frac{1}{4} x^4 \left(a+b \sin ^{-1}(c x)\right) \left(d^2 i+2 d e h+e^2 g\right)+d^2 f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d x^2 (d g+2 e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e x^5 (2 d i+e h) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^2 i x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 \left(d^2 h+2 d e g+e^2 f\right)+12 e (2 d i+e h)\right)}{225 c^3}+\frac{b \sqrt{1-c^2 x^2} \left(75 x \left(9 c^2 \left(d^2 i+2 d e h+e^2 g\right)+24 c^4 d (d g+2 e f)+5 e^2 i\right)+32 \left(50 c^2 \left(d^2 h+2 d e g+e^2 f\right)+225 c^4 d^2 f+24 e (2 d i+e h)\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(9 c^2 \left(d^2 i+2 d e h+e^2 g\right)+24 c^4 d (d g+2 e f)+5 e^2 i\right)}{96 c^6}+\frac{b x^3 \sqrt{1-c^2 x^2} \left(9 c^2 \left(d^2 i+2 d e h+e^2 g\right)+5 e^2 i\right)}{144 c^3}+\frac{b e x^4 \sqrt{1-c^2 x^2} (2 d i+e h)}{25 c}+\frac{b e^2 i x^5 \sqrt{1-c^2 x^2}}{36 c}",1,"(b*(25*c^2*(e^2*f + 2*d*e*g + d^2*h) + 12*e*(e*h + 2*d*i))*x^2*Sqrt[1 - c^2*x^2])/(225*c^3) + (b*(18*d*e*h + 9*d^2*i + e^2*(9*g + (5*i)/c^2))*x^3*Sqrt[1 - c^2*x^2])/(144*c) + (b*e*(e*h + 2*d*i)*x^4*Sqrt[1 - c^2*x^2])/(25*c) + (b*e^2*i*x^5*Sqrt[1 - c^2*x^2])/(36*c) + (b*(32*(225*c^4*d^2*f + 50*c^2*(e^2*f + 2*d*e*g + d^2*h) + 24*e*(e*h + 2*d*i)) + 75*(24*c^4*d*(2*e*f + d*g) + 5*e^2*i + 9*c^2*(e^2*g + 2*d*e*h + d^2*i))*x)*Sqrt[1 - c^2*x^2])/(7200*c^5) - (b*(24*c^4*d*(2*e*f + d*g) + 5*e^2*i + 9*c^2*(e^2*g + 2*d*e*h + d^2*i))*ArcSin[c*x])/(96*c^6) + d^2*f*x*(a + b*ArcSin[c*x]) + (d*(2*e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + ((e^2*f + 2*d*e*g + d^2*h)*x^3*(a + b*ArcSin[c*x]))/3 + ((e^2*g + 2*d*e*h + d^2*i)*x^4*(a + b*ArcSin[c*x]))/4 + (e*(e*h + 2*d*i)*x^5*(a + b*ArcSin[c*x]))/5 + (e^2*i*x^6*(a + b*ArcSin[c*x]))/6","A",8,5,31,0.1613,1,"{4749, 12, 1809, 780, 216}"
108,1,308,0,0.9480632,"\int (d+e x) \left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]),x]","\frac{1}{2} x^2 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} x^3 (d h+e g) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} x^4 (d i+e h) \left(a+b \sin ^{-1}(c x)\right)+d f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e i x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(225 c^2 x \left(8 c^2 (d g+e f)+3 (d i+e h)\right)+32 \left(50 c^2 (d h+e g)+225 c^4 d f+24 e i\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(8 c^2 (d g+e f)+3 (d i+e h)\right)}{32 c^4}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 (d h+e g)+12 e i\right)}{225 c^3}+\frac{b x^3 \sqrt{1-c^2 x^2} (d i+e h)}{16 c}+\frac{b e i x^4 \sqrt{1-c^2 x^2}}{25 c}","\frac{1}{2} x^2 (d g+e f) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} x^3 (d h+e g) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} x^4 (d i+e h) \left(a+b \sin ^{-1}(c x)\right)+d f x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e i x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(225 c^2 x \left(8 c^2 (d g+e f)+3 (d i+e h)\right)+32 \left(50 c^2 (d h+e g)+225 c^4 d f+24 e i\right)\right)}{7200 c^5}-\frac{b \sin ^{-1}(c x) \left(8 c^2 (d g+e f)+3 (d i+e h)\right)}{32 c^4}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(25 c^2 (d h+e g)+12 e i\right)}{225 c^3}+\frac{b x^3 \sqrt{1-c^2 x^2} (d i+e h)}{16 c}+\frac{b e i x^4 \sqrt{1-c^2 x^2}}{25 c}",1,"(b*(25*c^2*(e*g + d*h) + 12*e*i)*x^2*Sqrt[1 - c^2*x^2])/(225*c^3) + (b*(e*h + d*i)*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (b*e*i*x^4*Sqrt[1 - c^2*x^2])/(25*c) + (b*(32*(225*c^4*d*f + 50*c^2*(e*g + d*h) + 24*e*i) + 225*c^2*(8*c^2*(e*f + d*g) + 3*(e*h + d*i))*x)*Sqrt[1 - c^2*x^2])/(7200*c^5) - (b*(8*c^2*(e*f + d*g) + 3*(e*h + d*i))*ArcSin[c*x])/(32*c^4) + d*f*x*(a + b*ArcSin[c*x]) + ((e*f + d*g)*x^2*(a + b*ArcSin[c*x]))/2 + ((e*g + d*h)*x^3*(a + b*ArcSin[c*x]))/3 + ((e*h + d*i)*x^4*(a + b*ArcSin[c*x]))/4 + (e*i*x^5*(a + b*ArcSin[c*x]))/5","A",7,5,29,0.1724,1,"{4749, 12, 1809, 780, 216}"
109,1,623,0,1.135704,"\int \frac{\left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right)}{d+e x} \, dx","Int[((f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]))/(d + e*x),x]","-\frac{i b \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^4}+\frac{\log (d+e x) \left(a+b \sin ^{-1}(c x)\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}+\frac{x \left(a+b \sin ^{-1}(c x)\right) \left(d^2 i-d e h+e^2 g\right)}{e^3}+\frac{x^2 (e h-d i) \left(a+b \sin ^{-1}(c x)\right)}{2 e^2}+\frac{i x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 e}+\frac{b \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}+\frac{b \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}+\frac{b \sqrt{1-c^2 x^2} \left(4 \left(9 c^2 \left(d^2 i-d e h+e^2 g\right)+2 e^2 i\right)+9 c^2 e x (e h-d i)\right)}{36 c^3 e^3}-\frac{b \sin ^{-1}(c x) (e h-d i)}{4 c^2 e^2}+\frac{b i x^2 \sqrt{1-c^2 x^2}}{9 c e}-\frac{i b \sin ^{-1}(c x)^2 \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{2 e^4}-\frac{b \sin ^{-1}(c x) \log (d+e x) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}","-\frac{i b \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^4}+\frac{\log (d+e x) \left(a+b \sin ^{-1}(c x)\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}+\frac{x \left(a+b \sin ^{-1}(c x)\right) \left(d^2 i-d e h+e^2 g\right)}{e^3}+\frac{x^2 (e h-d i) \left(a+b \sin ^{-1}(c x)\right)}{2 e^2}+\frac{i x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 e}+\frac{b \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}+\frac{b \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}+\frac{b \sqrt{1-c^2 x^2} \left(4 \left(9 c^2 \left(d^2 i-d e h+e^2 g\right)+2 e^2 i\right)+9 c^2 e x (e h-d i)\right)}{36 c^3 e^3}-\frac{b \sin ^{-1}(c x) (e h-d i)}{4 c^2 e^2}+\frac{b i x^2 \sqrt{1-c^2 x^2}}{9 c e}-\frac{i b \sin ^{-1}(c x)^2 \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{2 e^4}-\frac{b \sin ^{-1}(c x) \log (d+e x) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4}",1,"(b*i*x^2*Sqrt[1 - c^2*x^2])/(9*c*e) + (b*(4*(2*e^2*i + 9*c^2*(e^2*g - d*e*h + d^2*i)) + 9*c^2*e*(e*h - d*i)*x)*Sqrt[1 - c^2*x^2])/(36*c^3*e^3) - (b*(e*h - d*i)*ArcSin[c*x])/(4*c^2*e^2) - ((I/2)*b*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*ArcSin[c*x]^2)/e^4 + ((e^2*g - d*e*h + d^2*i)*x*(a + b*ArcSin[c*x]))/e^3 + ((e*h - d*i)*x^2*(a + b*ArcSin[c*x]))/(2*e^2) + (i*x^3*(a + b*ArcSin[c*x]))/(3*e) + (b*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 + (b*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4 - (b*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*ArcSin[c*x]*Log[d + e*x])/e^4 + ((e^3*f - d*e^2*g + d^2*e*h - d^3*i)*(a + b*ArcSin[c*x])*Log[d + e*x])/e^4 - (I*b*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 - (I*b*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4","A",16,13,31,0.4194,1,"{1850, 4753, 12, 6742, 1809, 780, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
110,1,617,0,1.7419729,"\int \frac{\left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^2} \, dx","Int[((f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]))/(d + e*x)^2,x]","-\frac{i b \left(3 d^2 i-2 d e h+e^2 g\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b \left(3 d^2 i-2 d e h+e^2 g\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^4}-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 i-2 d e h+e^2 g\right)}{e^4}+\frac{x (e h-2 d i) \left(a+b \sin ^{-1}(c x)\right)}{e^3}+\frac{i x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e^2}+\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4 \sqrt{c^2 d^2-e^2}}+\frac{b \sin ^{-1}(c x) \left(3 d^2 i-2 d e h+e^2 g\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b \sin ^{-1}(c x) \left(3 d^2 i-2 d e h+e^2 g\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^4}+\frac{b \sqrt{1-c^2 x^2} (e h-2 d i)}{c e^3}+\frac{b i x \sqrt{1-c^2 x^2}}{4 c e^2}-\frac{b i \sin ^{-1}(c x)}{4 c^2 e^2}-\frac{i b \sin ^{-1}(c x)^2 \left(3 d^2 i-2 d e h+e^2 g\right)}{2 e^4}-\frac{b \sin ^{-1}(c x) \log (d+e x) \left(3 d^2 i-2 d e h+e^2 g\right)}{e^4}","-\frac{i b \left(3 d^2 i-2 d e h+e^2 g\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b \left(3 d^2 i-2 d e h+e^2 g\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^4}-\frac{\left(a+b \sin ^{-1}(c x)\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(a+b \sin ^{-1}(c x)\right) \left(3 d^2 i-2 d e h+e^2 g\right)}{e^4}+\frac{x (e h-2 d i) \left(a+b \sin ^{-1}(c x)\right)}{e^3}+\frac{i x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e^2}+\frac{b c \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right) \left(d^2 e h+d^3 (-i)-d e^2 g+e^3 f\right)}{e^4 \sqrt{c^2 d^2-e^2}}+\frac{b \sin ^{-1}(c x) \left(3 d^2 i-2 d e h+e^2 g\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b \sin ^{-1}(c x) \left(3 d^2 i-2 d e h+e^2 g\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^4}+\frac{b \sqrt{1-c^2 x^2} (e h-2 d i)}{c e^3}+\frac{b i x \sqrt{1-c^2 x^2}}{4 c e^2}-\frac{b i \sin ^{-1}(c x)}{4 c^2 e^2}-\frac{i b \sin ^{-1}(c x)^2 \left(3 d^2 i-2 d e h+e^2 g\right)}{2 e^4}-\frac{b \sin ^{-1}(c x) \log (d+e x) \left(3 d^2 i-2 d e h+e^2 g\right)}{e^4}",1,"(b*(e*h - 2*d*i)*Sqrt[1 - c^2*x^2])/(c*e^3) + (b*i*x*Sqrt[1 - c^2*x^2])/(4*c*e^2) - (b*i*ArcSin[c*x])/(4*c^2*e^2) - ((I/2)*b*(e^2*g - 2*d*e*h + 3*d^2*i)*ArcSin[c*x]^2)/e^4 + ((e*h - 2*d*i)*x*(a + b*ArcSin[c*x]))/e^3 + (i*x^2*(a + b*ArcSin[c*x]))/(2*e^2) - ((e^3*f - d*e^2*g + d^2*e*h - d^3*i)*(a + b*ArcSin[c*x]))/(e^4*(d + e*x)) + (b*c*(e^3*f - d*e^2*g + d^2*e*h - d^3*i)*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^4*Sqrt[c^2*d^2 - e^2]) + (b*(e^2*g - 2*d*e*h + 3*d^2*i)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 + (b*(e^2*g - 2*d*e*h + 3*d^2*i)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4 - (b*(e^2*g - 2*d*e*h + 3*d^2*i)*ArcSin[c*x]*Log[d + e*x])/e^4 + ((e^2*g - 2*d*e*h + 3*d^2*i)*(a + b*ArcSin[c*x])*Log[d + e*x])/e^4 - (I*b*(e^2*g - 2*d*e*h + 3*d^2*i)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 - (I*b*(e^2*g - 2*d*e*h + 3*d^2*i)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4","A",18,15,31,0.4839,1,"{1850, 4753, 12, 6742, 261, 321, 216, 725, 204, 2404, 4741, 4519, 2190, 2279, 2391}"
111,1,1016,0,2.6181799,"\int \frac{\left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^3} \, dx","Int[((f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]))/(d + e*x)^3,x]","\frac{5 b c^3 i \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^4}{2 e^4 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{5 b c i \sqrt{1-c^2 x^2} d^3}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c \left(3 d h c^2+4 e i\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^2}{2 e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c (3 e h+4 d i) \sqrt{1-c^2 x^2} d^2}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c \left(\left(4 i d^3+e^2 g d\right) c^2+4 e^2 (e h-2 d i)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d}{2 e^4 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b c \left(-4 i d^2+4 e h d+e^2 g\right) \sqrt{1-c^2 x^2} d}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{i b (e h-3 d i) \sin ^{-1}(c x)^2}{2 e^4}+\frac{i x \left(a+b \sin ^{-1}(c x)\right)}{e^3}-\frac{\left(3 i d^2-2 e h d+e^2 g\right) \left(a+b \sin ^{-1}(c x)\right)}{e^4 (d+e x)}-\frac{\left(-i d^3+e h d^2-e^2 g d+e^3 f\right) \left(a+b \sin ^{-1}(c x)\right)}{2 e^4 (d+e x)^2}-\frac{b c \left(2 g e^4-6 d^2 i e^2-c^2 \left(d e^3 f-4 d^4 i\right)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right)}{2 e^4 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b (e h-3 d i) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b (e h-3 d i) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{b (e h-3 d i) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac{(e h-3 d i) \left(a+b \sin ^{-1}(c x)\right) \log (d+e x)}{e^4}-\frac{i b (e h-3 d i) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b (e h-3 d i) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b i \sqrt{1-c^2 x^2}}{c e^3}+\frac{b c \left(2 i d^3-2 e^2 g d+e^3 f\right) \sqrt{1-c^2 x^2}}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}","\frac{5 b c^3 i \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^4}{2 e^4 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{5 b c i \sqrt{1-c^2 x^2} d^3}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{b c \left(3 d h c^2+4 e i\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^2}{2 e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c (3 e h+4 d i) \sqrt{1-c^2 x^2} d^2}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c \left(\left(4 i d^3+e^2 g d\right) c^2+4 e^2 (e h-2 d i)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d}{2 e^4 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b c \left(-4 i d^2+4 e h d+e^2 g\right) \sqrt{1-c^2 x^2} d}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{i b (e h-3 d i) \sin ^{-1}(c x)^2}{2 e^4}+\frac{i x \left(a+b \sin ^{-1}(c x)\right)}{e^3}-\frac{\left(3 i d^2-2 e h d+e^2 g\right) \left(a+b \sin ^{-1}(c x)\right)}{e^4 (d+e x)}-\frac{\left(-i d^3+e h d^2-e^2 g d+e^3 f\right) \left(a+b \sin ^{-1}(c x)\right)}{2 e^4 (d+e x)^2}-\frac{b c \left(2 g e^4-6 d^2 i e^2-c^2 \left(d e^3 f-4 d^4 i\right)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right)}{2 e^4 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b (e h-3 d i) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b (e h-3 d i) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{b (e h-3 d i) \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac{(e h-3 d i) \left(a+b \sin ^{-1}(c x)\right) \log (d+e x)}{e^4}-\frac{i b (e h-3 d i) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b (e h-3 d i) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b i \sqrt{1-c^2 x^2}}{c e^3}+\frac{b c \left(2 i d^3-2 e^2 g d+e^3 f\right) \sqrt{1-c^2 x^2}}{2 e^3 \left(c^2 d^2-e^2\right) (d+e x)}",1,"(b*i*Sqrt[1 - c^2*x^2])/(c*e^3) + (5*b*c*d^3*i*Sqrt[1 - c^2*x^2])/(2*e^3*(c^2*d^2 - e^2)*(d + e*x)) - (b*c*d^2*(3*e*h + 4*d*i)*Sqrt[1 - c^2*x^2])/(2*e^3*(c^2*d^2 - e^2)*(d + e*x)) + (b*c*d*(e^2*g + 4*d*e*h - 4*d^2*i)*Sqrt[1 - c^2*x^2])/(2*e^3*(c^2*d^2 - e^2)*(d + e*x)) + (b*c*(e^3*f - 2*d*e^2*g + 2*d^3*i)*Sqrt[1 - c^2*x^2])/(2*e^3*(c^2*d^2 - e^2)*(d + e*x)) - ((I/2)*b*(e*h - 3*d*i)*ArcSin[c*x]^2)/e^4 + (i*x*(a + b*ArcSin[c*x]))/e^3 - ((e^3*f - d*e^2*g + d^2*e*h - d^3*i)*(a + b*ArcSin[c*x]))/(2*e^4*(d + e*x)^2) - ((e^2*g - 2*d*e*h + 3*d^2*i)*(a + b*ArcSin[c*x]))/(e^4*(d + e*x)) + (5*b*c^3*d^4*i*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e^4*(c^2*d^2 - e^2)^(3/2)) - (b*c*d^2*(3*c^2*d*h + 4*e*i)*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e^3*(c^2*d^2 - e^2)^(3/2)) + (b*c*d*(4*e^2*(e*h - 2*d*i) + c^2*(d*e^2*g + 4*d^3*i))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e^4*(c^2*d^2 - e^2)^(3/2)) - (b*c*(2*e^4*g - 6*d^2*e^2*i - c^2*(d*e^3*f - 4*d^4*i))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(2*e^4*(c^2*d^2 - e^2)^(3/2)) + (b*(e*h - 3*d*i)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 + (b*(e*h - 3*d*i)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4 - (b*(e*h - 3*d*i)*ArcSin[c*x]*Log[d + e*x])/e^4 + ((e*h - 3*d*i)*(a + b*ArcSin[c*x])*Log[d + e*x])/e^4 - (I*b*(e*h - 3*d*i)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 - (I*b*(e*h - 3*d*i)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4","A",30,18,31,0.5806,1,"{1850, 4753, 12, 6742, 731, 725, 204, 807, 1651, 844, 216, 1654, 2404, 4741, 4519, 2190, 2279, 2391}"
112,1,1278,0,2.8587427,"\int \frac{\left(f+g x+h x^2+i x^3\right) \left(a+b \sin ^{-1}(c x)\right)}{(d+e x)^4} \, dx","Int[((f + g*x + h*x^2 + i*x^3)*(a + b*ArcSin[c*x]))/(d + e*x)^4,x]","-\frac{11 b c^3 i \sqrt{1-c^2 x^2} d^4}{4 e^3 \left(c^2 d^2-e^2\right)^2 (d+e x)}-\frac{11 b c^3 \left(2 c^2 d^2+e^2\right) i \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^3}{12 e^4 \left(c^2 d^2-e^2\right)^{5/2}}-\frac{11 b c i \sqrt{1-c^2 x^2} d^3}{12 e^3 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(4 c^2 h d^2+e (2 e h+81 d i)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^2}{12 e^3 \left(c^2 d^2-e^2\right)^{5/2}}+\frac{b c \left(d (2 e h+9 d i) c^2+18 e^2 i\right) \sqrt{1-c^2 x^2} d^2}{4 e^3 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c (2 e h+27 d i) \sqrt{1-c^2 x^2} d^2}{12 e^3 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c \left(2 d^2 g c^4+\left(-18 i d^2-18 e h d+e^2 g\right) c^2-36 e^2 i\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d}{12 e^2 \left(c^2 d^2-e^2\right)^{5/2}}-\frac{b c \left(4 e^2 (e h+6 d i)-c^2 d \left(6 i d^2-2 e h d+e^2 g\right)\right) \sqrt{1-c^2 x^2} d}{4 e^3 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \left(-18 i d^2-6 e h d+e^2 g\right) \sqrt{1-c^2 x^2} d}{12 e^3 \left(c^2 d^2-e^2\right) (d+e x)^2}-\frac{i b i \sin ^{-1}(c x)^2}{2 e^4}-\frac{(e h-3 d i) \left(a+b \sin ^{-1}(c x)\right)}{e^4 (d+e x)}-\frac{\left(3 i d^2-2 e h d+e^2 g\right) \left(a+b \sin ^{-1}(c x)\right)}{2 e^4 (d+e x)^2}-\frac{\left(-i d^3+e h d^2-e^2 g d+e^3 f\right) \left(a+b \sin ^{-1}(c x)\right)}{3 e^4 (d+e x)^3}+\frac{b c \left(4 d^2 f c^4+\left(6 h d^2-9 e g d+2 e^2 f\right) c^2+12 e^2 h\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right)}{12 e \left(c^2 d^2-e^2\right)^{5/2}}+\frac{b i \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b i \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{b i \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac{i \left(a+b \sin ^{-1}(c x)\right) \log (d+e x)}{e^4}-\frac{i b i \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b i \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{b c \left(2 e^2 (e g-4 d h)-c^2 d \left(-2 h d^2-e g d+2 e^2 f\right)\right) \sqrt{1-c^2 x^2}}{4 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \left(6 h d^2-3 e g d+2 e^2 f\right) \sqrt{1-c^2 x^2}}{12 e^2 \left(c^2 d^2-e^2\right) (d+e x)^2}","-\frac{11 b c^3 i \sqrt{1-c^2 x^2} d^4}{4 e^3 \left(c^2 d^2-e^2\right)^2 (d+e x)}-\frac{11 b c^3 \left(2 c^2 d^2+e^2\right) i \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^3}{12 e^4 \left(c^2 d^2-e^2\right)^{5/2}}-\frac{11 b c i \sqrt{1-c^2 x^2} d^3}{12 e^3 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(4 c^2 h d^2+e (2 e h+81 d i)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d^2}{12 e^3 \left(c^2 d^2-e^2\right)^{5/2}}+\frac{b c \left(d (2 e h+9 d i) c^2+18 e^2 i\right) \sqrt{1-c^2 x^2} d^2}{4 e^3 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c (2 e h+27 d i) \sqrt{1-c^2 x^2} d^2}{12 e^3 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c \left(2 d^2 g c^4+\left(-18 i d^2-18 e h d+e^2 g\right) c^2-36 e^2 i\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) d}{12 e^2 \left(c^2 d^2-e^2\right)^{5/2}}-\frac{b c \left(4 e^2 (e h+6 d i)-c^2 d \left(6 i d^2-2 e h d+e^2 g\right)\right) \sqrt{1-c^2 x^2} d}{4 e^3 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \left(-18 i d^2-6 e h d+e^2 g\right) \sqrt{1-c^2 x^2} d}{12 e^3 \left(c^2 d^2-e^2\right) (d+e x)^2}-\frac{i b i \sin ^{-1}(c x)^2}{2 e^4}-\frac{(e h-3 d i) \left(a+b \sin ^{-1}(c x)\right)}{e^4 (d+e x)}-\frac{\left(3 i d^2-2 e h d+e^2 g\right) \left(a+b \sin ^{-1}(c x)\right)}{2 e^4 (d+e x)^2}-\frac{\left(-i d^3+e h d^2-e^2 g d+e^3 f\right) \left(a+b \sin ^{-1}(c x)\right)}{3 e^4 (d+e x)^3}+\frac{b c \left(4 d^2 f c^4+\left(6 h d^2-9 e g d+2 e^2 f\right) c^2+12 e^2 h\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right)}{12 e \left(c^2 d^2-e^2\right)^{5/2}}+\frac{b i \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}+\frac{b i \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{b i \sin ^{-1}(c x) \log (d+e x)}{e^4}+\frac{i \left(a+b \sin ^{-1}(c x)\right) \log (d+e x)}{e^4}-\frac{i b i \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{i b i \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^4}-\frac{b c \left(2 e^2 (e g-4 d h)-c^2 d \left(-2 h d^2-e g d+2 e^2 f\right)\right) \sqrt{1-c^2 x^2}}{4 e^2 \left(c^2 d^2-e^2\right)^2 (d+e x)}+\frac{b c \left(6 h d^2-3 e g d+2 e^2 f\right) \sqrt{1-c^2 x^2}}{12 e^2 \left(c^2 d^2-e^2\right) (d+e x)^2}",1,"(b*c*(2*e^2*f - 3*d*e*g + 6*d^2*h)*Sqrt[1 - c^2*x^2])/(12*e^2*(c^2*d^2 - e^2)*(d + e*x)^2) - (11*b*c*d^3*i*Sqrt[1 - c^2*x^2])/(12*e^3*(c^2*d^2 - e^2)*(d + e*x)^2) + (b*c*d^2*(2*e*h + 27*d*i)*Sqrt[1 - c^2*x^2])/(12*e^3*(c^2*d^2 - e^2)*(d + e*x)^2) + (b*c*d*(e^2*g - 6*d*e*h - 18*d^2*i)*Sqrt[1 - c^2*x^2])/(12*e^3*(c^2*d^2 - e^2)*(d + e*x)^2) - (b*c*(2*e^2*(e*g - 4*d*h) - c^2*d*(2*e^2*f - d*e*g - 2*d^2*h))*Sqrt[1 - c^2*x^2])/(4*e^2*(c^2*d^2 - e^2)^2*(d + e*x)) - (11*b*c^3*d^4*i*Sqrt[1 - c^2*x^2])/(4*e^3*(c^2*d^2 - e^2)^2*(d + e*x)) + (b*c*d^2*(18*e^2*i + c^2*d*(2*e*h + 9*d*i))*Sqrt[1 - c^2*x^2])/(4*e^3*(c^2*d^2 - e^2)^2*(d + e*x)) - (b*c*d*(4*e^2*(e*h + 6*d*i) - c^2*d*(e^2*g - 2*d*e*h + 6*d^2*i))*Sqrt[1 - c^2*x^2])/(4*e^3*(c^2*d^2 - e^2)^2*(d + e*x)) - ((I/2)*b*i*ArcSin[c*x]^2)/e^4 - ((e^3*f - d*e^2*g + d^2*e*h - d^3*i)*(a + b*ArcSin[c*x]))/(3*e^4*(d + e*x)^3) - ((e^2*g - 2*d*e*h + 3*d^2*i)*(a + b*ArcSin[c*x]))/(2*e^4*(d + e*x)^2) - ((e*h - 3*d*i)*(a + b*ArcSin[c*x]))/(e^4*(d + e*x)) + (b*c*(4*c^4*d^2*f + 12*e^2*h + c^2*(2*e^2*f - 9*d*e*g + 6*d^2*h))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(12*e*(c^2*d^2 - e^2)^(5/2)) - (11*b*c^3*d^3*(2*c^2*d^2 + e^2)*i*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(12*e^4*(c^2*d^2 - e^2)^(5/2)) + (b*c^3*d^2*(4*c^2*d^2*h + e*(2*e*h + 81*d*i))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(12*e^3*(c^2*d^2 - e^2)^(5/2)) + (b*c*d*(2*c^4*d^2*g - 36*e^2*i + c^2*(e^2*g - 18*d*e*h - 18*d^2*i))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(12*e^2*(c^2*d^2 - e^2)^(5/2)) + (b*i*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 + (b*i*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4 - (b*i*ArcSin[c*x]*Log[d + e*x])/e^4 + (i*(a + b*ArcSin[c*x])*Log[d + e*x])/e^4 - (I*b*i*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^4 - (I*b*i*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^4","A",29,17,31,0.5484,1,"{1850, 4753, 12, 6742, 745, 807, 725, 204, 835, 1651, 216, 2404, 4741, 4519, 2190, 2279, 2391}"
113,1,935,0,2.934442,"\int \frac{(f+g x) \left(a+b \sin ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[((f + g*x)*(a + b*ArcSin[c*x])^2)/(d + e*x)^3,x]","-\frac{i b^2 d (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{i b^2 d (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 d (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b^2 d (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 (e f-d g) \log (d+e x) c^2}{e^2 \left(c^2 d^2-e^2\right)}+\frac{b^2 (e f-d g) \sqrt{1-c^2 x^2} \sin ^{-1}(c x) c}{e \left(c^2 d^2-e^2\right) (d+e x)}-\frac{a b \left(2 e^2 g-c^2 d (e f+d g)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) c}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{2 i b^2 g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 i b^2 g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{a b (e f-d g) \sqrt{1-c^2 x^2} c}{e \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b^2 g^2 \sin ^{-1}(c x)^2}{2 e^2 (e f-d g)}-\frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 (e f-d g) (d+e x)^2}+\frac{a b g^2 \sin ^{-1}(c x)}{e^2 (e f-d g)}","-\frac{i b^2 d (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{i b^2 d (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 d (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b^2 d (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 (e f-d g) \log (d+e x) c^2}{e^2 \left(c^2 d^2-e^2\right)}+\frac{b^2 (e f-d g) \sqrt{1-c^2 x^2} \sin ^{-1}(c x) c}{e \left(c^2 d^2-e^2\right) (d+e x)}-\frac{a b \left(2 e^2 g-c^2 d (e f+d g)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) c}{e^2 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{2 i b^2 g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 i b^2 g \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 g \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{a b (e f-d g) \sqrt{1-c^2 x^2} c}{e \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b^2 g^2 \sin ^{-1}(c x)^2}{2 e^2 (e f-d g)}-\frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 (e f-d g) (d+e x)^2}+\frac{a b g^2 \sin ^{-1}(c x)}{e^2 (e f-d g)}",1,"(a*b*c*(e*f - d*g)*Sqrt[1 - c^2*x^2])/(e*(c^2*d^2 - e^2)*(d + e*x)) + (a*b*g^2*ArcSin[c*x])/(e^2*(e*f - d*g)) + (b^2*c*(e*f - d*g)*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(e*(c^2*d^2 - e^2)*(d + e*x)) + (b^2*g^2*ArcSin[c*x]^2)/(2*e^2*(e*f - d*g)) - ((f + g*x)^2*(a + b*ArcSin[c*x])^2)/(2*(e*f - d*g)*(d + e*x)^2) - (a*b*c*(2*e^2*g - c^2*d*(e*f + d*g))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^2*(c^2*d^2 - e^2)^(3/2)) - ((2*I)*b^2*c*g*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) - (I*b^2*c^3*d*(e*f - d*g)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^2*(c^2*d^2 - e^2)^(3/2)) + ((2*I)*b^2*c*g*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) + (I*b^2*c^3*d*(e*f - d*g)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^2*(c^2*d^2 - e^2)^(3/2)) - (b^2*c^2*(e*f - d*g)*Log[d + e*x])/(e^2*(c^2*d^2 - e^2)) - (2*b^2*c*g*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) - (b^2*c^3*d*(e*f - d*g)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^2*(c^2*d^2 - e^2)^(3/2)) + (2*b^2*c*g*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) + (b^2*c^3*d*(e*f - d*g)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^2*(c^2*d^2 - e^2)^(3/2))","A",33,20,23,0.8696,1,"{37, 4755, 12, 1651, 844, 216, 725, 204, 4799, 4797, 4641, 4773, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
114,1,1678,0,3.7093117,"\int \frac{(f+g x)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[((f + g*x)^2*(a + b*ArcSin[c*x])^2)/(d + e*x)^3,x]","-\frac{i b^2 d (e f-d g)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{i b^2 d (e f-d g)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 d (e f-d g)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b^2 d (e f-d g)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 (e f-d g)^2 \log (d+e x) c^2}{e^3 \left(c^2 d^2-e^2\right)}+\frac{b^2 (e f-d g)^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) c}{e^2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{a b (e f-d g) \left(4 e^2 g-c^2 d (e f+3 d g)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) c}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{4 i b^2 g (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{4 i b^2 g (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}-\frac{4 b^2 g (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{4 b^2 g (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{a b (e f-d g)^2 \sqrt{1-c^2 x^2} c}{e^2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{i b^2 g^2 \sin ^{-1}(c x)^3}{3 e^3}-\frac{i a b g^2 \sin ^{-1}(c x)^2}{e^3}-\frac{2 b^2 g (e f-d g) \sin ^{-1}(c x)^2}{e^3 (d+e x)}-\frac{b^2 (e f-d g)^2 \sin ^{-1}(c x)^2}{2 e^3 (d+e x)^2}-\frac{4 a b g (e f-d g) \sin ^{-1}(c x)}{e^3 (d+e x)}-\frac{a b (e f-d g)^2 \sin ^{-1}(c x)}{e^3 (d+e x)^2}+\frac{b^2 g^2 \sin ^{-1}(c x)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 a b g^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b^2 g^2 \sin ^{-1}(c x)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 a b g^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{a^2 g^2 \log (d+e x)}{e^3}-\frac{2 i a b g^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 i b^2 g^2 \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 i a b g^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 i b^2 g^2 \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 b^2 g^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 b^2 g^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 a^2 g (e f-d g)}{e^3 (d+e x)}-\frac{a^2 (e f-d g)^2}{2 e^3 (d+e x)^2}","-\frac{i b^2 d (e f-d g)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{i b^2 d (e f-d g)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 d (e f-d g)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b^2 d (e f-d g)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c^3}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 (e f-d g)^2 \log (d+e x) c^2}{e^3 \left(c^2 d^2-e^2\right)}+\frac{b^2 (e f-d g)^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) c}{e^2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{a b (e f-d g) \left(4 e^2 g-c^2 d (e f+3 d g)\right) \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right) c}{e^3 \left(c^2 d^2-e^2\right)^{3/2}}-\frac{4 i b^2 g (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{4 i b^2 g (e f-d g) \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}-\frac{4 b^2 g (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{4 b^2 g (e f-d g) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right) c}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{a b (e f-d g)^2 \sqrt{1-c^2 x^2} c}{e^2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{i b^2 g^2 \sin ^{-1}(c x)^3}{3 e^3}-\frac{i a b g^2 \sin ^{-1}(c x)^2}{e^3}-\frac{2 b^2 g (e f-d g) \sin ^{-1}(c x)^2}{e^3 (d+e x)}-\frac{b^2 (e f-d g)^2 \sin ^{-1}(c x)^2}{2 e^3 (d+e x)^2}-\frac{4 a b g (e f-d g) \sin ^{-1}(c x)}{e^3 (d+e x)}-\frac{a b (e f-d g)^2 \sin ^{-1}(c x)}{e^3 (d+e x)^2}+\frac{b^2 g^2 \sin ^{-1}(c x)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 a b g^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{b^2 g^2 \sin ^{-1}(c x)^2 \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 a b g^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{a^2 g^2 \log (d+e x)}{e^3}-\frac{2 i a b g^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 i b^2 g^2 \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 i a b g^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 i b^2 g^2 \sin ^{-1}(c x) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 b^2 g^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3}+\frac{2 b^2 g^2 \text{PolyLog}\left(3,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3}-\frac{2 a^2 g (e f-d g)}{e^3 (d+e x)}-\frac{a^2 (e f-d g)^2}{2 e^3 (d+e x)^2}",1,"-(a^2*(e*f - d*g)^2)/(2*e^3*(d + e*x)^2) - (2*a^2*g*(e*f - d*g))/(e^3*(d + e*x)) + (a*b*c*(e*f - d*g)^2*Sqrt[1 - c^2*x^2])/(e^2*(c^2*d^2 - e^2)*(d + e*x)) - (a*b*(e*f - d*g)^2*ArcSin[c*x])/(e^3*(d + e*x)^2) - (4*a*b*g*(e*f - d*g)*ArcSin[c*x])/(e^3*(d + e*x)) + (b^2*c*(e*f - d*g)^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(e^2*(c^2*d^2 - e^2)*(d + e*x)) - (I*a*b*g^2*ArcSin[c*x]^2)/e^3 - (b^2*(e*f - d*g)^2*ArcSin[c*x]^2)/(2*e^3*(d + e*x)^2) - (2*b^2*g*(e*f - d*g)*ArcSin[c*x]^2)/(e^3*(d + e*x)) - ((I/3)*b^2*g^2*ArcSin[c*x]^3)/e^3 - (a*b*c*(e*f - d*g)*(4*e^2*g - c^2*d*(e*f + 3*d*g))*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^3*(c^2*d^2 - e^2)^(3/2)) + (2*a*b*g^2*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 - ((4*I)*b^2*c*g*(e*f - d*g)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) - (I*b^2*c^3*d*(e*f - d*g)^2*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^3*(c^2*d^2 - e^2)^(3/2)) + (b^2*g^2*ArcSin[c*x]^2*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 + (2*a*b*g^2*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 + ((4*I)*b^2*c*g*(e*f - d*g)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) + (I*b^2*c^3*d*(e*f - d*g)^2*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^3*(c^2*d^2 - e^2)^(3/2)) + (b^2*g^2*ArcSin[c*x]^2*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 + (a^2*g^2*Log[d + e*x])/e^3 - (b^2*c^2*(e*f - d*g)^2*Log[d + e*x])/(e^3*(c^2*d^2 - e^2)) - ((2*I)*a*b*g^2*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 - (4*b^2*c*g*(e*f - d*g)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) - (b^2*c^3*d*(e*f - d*g)^2*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^3*(c^2*d^2 - e^2)^(3/2)) - ((2*I)*b^2*g^2*ArcSin[c*x]*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 - ((2*I)*a*b*g^2*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 + (4*b^2*c*g*(e*f - d*g)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) + (b^2*c^3*d*(e*f - d*g)^2*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^3*(c^2*d^2 - e^2)^(3/2)) - ((2*I)*b^2*g^2*ArcSin[c*x]*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3 + (2*b^2*g^2*PolyLog[3, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/e^3 + (2*b^2*g^2*PolyLog[3, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/e^3","A",55,25,25,1.000,1,"{4759, 43, 4753, 12, 6742, 807, 725, 204, 216, 2404, 4741, 4519, 2190, 2279, 2391, 4743, 4773, 3324, 3323, 2264, 2668, 31, 2531, 2282, 6589}"
115,1,1016,0,1.5801717,"\int (g+h x)^3 \left(d+e x+f x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(g + h*x)^3*(d + e*x + f*x^2)*(a + b*ArcSin[c*x])^2,x]","-\frac{1}{108} b^2 f h^3 x^6+\frac{1}{6} f h^3 \left(a+b \sin ^{-1}(c x)\right)^2 x^6+\frac{1}{5} h^2 (3 f g+e h) \left(a+b \sin ^{-1}(c x)\right)^2 x^5-\frac{2}{125} b^2 h^2 (3 f g+e h) x^5+\frac{b f h^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{18 c}-\frac{5 b^2 f h^3 x^4}{288 c^2}+\frac{1}{4} h \left(3 f g^2+h (3 e g+d h)\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{1}{32} b^2 h \left(3 f g^2+h (3 e g+d h)\right) x^4+\frac{2 b h^2 (3 f g+e h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{25 c}+\frac{1}{3} g \left(f g^2+3 h (e g+d h)\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^3-\frac{8 b^2 h^2 (3 f g+e h) x^3}{225 c^2}-\frac{2}{27} b^2 g \left(f g^2+3 h (e g+d h)\right) x^3+\frac{5 b f h^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{72 c^3}+\frac{b h \left(3 f g^2+h (3 e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{8 c}-\frac{5 b^2 f h^3 x^2}{96 c^4}+\frac{1}{2} g^2 (e g+3 d h) \left(a+b \sin ^{-1}(c x)\right)^2 x^2-\frac{1}{4} b^2 g^2 (e g+3 d h) x^2-\frac{3 b^2 h \left(3 f g^2+h (3 e g+d h)\right) x^2}{32 c^2}+\frac{8 b h^2 (3 f g+e h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{75 c^3}+\frac{2 b g \left(f g^2+3 h (e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{9 c}-2 b^2 d g^3 x+d g^3 \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{16 b^2 h^2 (3 f g+e h) x}{75 c^4}-\frac{4 b^2 g \left(f g^2+3 h (e g+d h)\right) x}{9 c^2}+\frac{5 b f h^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x}{48 c^5}+\frac{b g^2 (e g+3 d h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x}{2 c}+\frac{3 b h \left(3 f g^2+h (3 e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x}{16 c^3}-\frac{5 f h^3 \left(a+b \sin ^{-1}(c x)\right)^2}{96 c^6}-\frac{g^2 (e g+3 d h) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}-\frac{3 h \left(3 f g^2+h (3 e g+d h)\right) \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}+\frac{2 b d g^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{16 b h^2 (3 f g+e h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^5}+\frac{4 b g \left(f g^2+3 h (e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}","-\frac{1}{108} b^2 f h^3 x^6+\frac{1}{6} f h^3 \left(a+b \sin ^{-1}(c x)\right)^2 x^6+\frac{1}{5} h^2 (3 f g+e h) \left(a+b \sin ^{-1}(c x)\right)^2 x^5-\frac{2}{125} b^2 h^2 (3 f g+e h) x^5+\frac{b f h^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^5}{18 c}-\frac{5 b^2 f h^3 x^4}{288 c^2}+\frac{1}{4} h \left(3 f g^2+h (3 e g+d h)\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^4-\frac{1}{32} b^2 h \left(3 f g^2+h (3 e g+d h)\right) x^4+\frac{2 b h^2 (3 f g+e h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^4}{25 c}+\frac{1}{3} g \left(f g^2+3 h (e g+d h)\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^3-\frac{8 b^2 h^2 (3 f g+e h) x^3}{225 c^2}-\frac{2}{27} b^2 g \left(f g^2+3 h (e g+d h)\right) x^3+\frac{5 b f h^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{72 c^3}+\frac{b h \left(3 f g^2+h (3 e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^3}{8 c}-\frac{5 b^2 f h^3 x^2}{96 c^4}+\frac{1}{2} g^2 (e g+3 d h) \left(a+b \sin ^{-1}(c x)\right)^2 x^2-\frac{1}{4} b^2 g^2 (e g+3 d h) x^2-\frac{3 b^2 h \left(3 f g^2+h (3 e g+d h)\right) x^2}{32 c^2}+\frac{8 b h^2 (3 f g+e h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{75 c^3}+\frac{2 b g \left(f g^2+3 h (e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^2}{9 c}-2 b^2 d g^3 x+d g^3 \left(a+b \sin ^{-1}(c x)\right)^2 x-\frac{16 b^2 h^2 (3 f g+e h) x}{75 c^4}-\frac{4 b^2 g \left(f g^2+3 h (e g+d h)\right) x}{9 c^2}+\frac{5 b f h^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x}{48 c^5}+\frac{b g^2 (e g+3 d h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x}{2 c}+\frac{3 b h \left(3 f g^2+h (3 e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x}{16 c^3}-\frac{5 f h^3 \left(a+b \sin ^{-1}(c x)\right)^2}{96 c^6}-\frac{g^2 (e g+3 d h) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}-\frac{3 h \left(3 f g^2+h (3 e g+d h)\right) \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}+\frac{2 b d g^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{16 b h^2 (3 f g+e h) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^5}+\frac{4 b g \left(f g^2+3 h (e g+d h)\right) \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}",1,"-2*b^2*d*g^3*x - (16*b^2*h^2*(3*f*g + e*h)*x)/(75*c^4) - (4*b^2*g*(f*g^2 + 3*h*(e*g + d*h))*x)/(9*c^2) - (5*b^2*f*h^3*x^2)/(96*c^4) - (b^2*g^2*(e*g + 3*d*h)*x^2)/4 - (3*b^2*h*(3*f*g^2 + h*(3*e*g + d*h))*x^2)/(32*c^2) - (8*b^2*h^2*(3*f*g + e*h)*x^3)/(225*c^2) - (2*b^2*g*(f*g^2 + 3*h*(e*g + d*h))*x^3)/27 - (5*b^2*f*h^3*x^4)/(288*c^2) - (b^2*h*(3*f*g^2 + h*(3*e*g + d*h))*x^4)/32 - (2*b^2*h^2*(3*f*g + e*h)*x^5)/125 - (b^2*f*h^3*x^6)/108 + (2*b*d*g^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (16*b*h^2*(3*f*g + e*h)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(75*c^5) + (4*b*g*(f*g^2 + 3*h*(e*g + d*h))*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (5*b*f*h^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(48*c^5) + (b*g^2*(e*g + 3*d*h)*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c) + (3*b*h*(3*f*g^2 + h*(3*e*g + d*h))*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(16*c^3) + (8*b*h^2*(3*f*g + e*h)*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(75*c^3) + (2*b*g*(f*g^2 + 3*h*(e*g + d*h))*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) + (5*b*f*h^3*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(72*c^3) + (b*h*(3*f*g^2 + h*(3*e*g + d*h))*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (2*b*h^2*(3*f*g + e*h)*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c) + (b*f*h^3*x^5*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(18*c) - (5*f*h^3*(a + b*ArcSin[c*x])^2)/(96*c^6) - (g^2*(e*g + 3*d*h)*(a + b*ArcSin[c*x])^2)/(4*c^2) - (3*h*(3*f*g^2 + h*(3*e*g + d*h))*(a + b*ArcSin[c*x])^2)/(32*c^4) + d*g^3*x*(a + b*ArcSin[c*x])^2 + (g^2*(e*g + 3*d*h)*x^2*(a + b*ArcSin[c*x])^2)/2 + (g*(f*g^2 + 3*h*(e*g + d*h))*x^3*(a + b*ArcSin[c*x])^2)/3 + (h*(3*f*g^2 + h*(3*e*g + d*h))*x^4*(a + b*ArcSin[c*x])^2)/4 + (h^2*(3*f*g + e*h)*x^5*(a + b*ArcSin[c*x])^2)/5 + (f*h^3*x^6*(a + b*ArcSin[c*x])^2)/6","A",35,8,28,0.2857,1,"{4751, 4619, 4677, 8, 4627, 4707, 4641, 30}"
116,1,701,0,1.1229134,"\int (g+h x)^2 \left(d+e x+f x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(g + h*x)^2*(d + e*x + f*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) \left(h (d h+2 e g)+f g^2\right)}{9 c}+\frac{4 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \left(h (d h+2 e g)+f g^2\right)}{9 c^3}+\frac{b g x \sqrt{1-c^2 x^2} (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{g (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{2 b d g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{b h x^3 \sqrt{1-c^2 x^2} (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b h x \sqrt{1-c^2 x^2} (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)}{16 c^3}-\frac{3 h (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}+\frac{2 b f h^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b f h^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^3}+\frac{16 b f h^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^5}+\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)^2 \left(h (d h+2 e g)+f g^2\right)+\frac{1}{2} g x^2 (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2+d g^2 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} h x^4 (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{5} f h^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 x \left(h (d h+2 e g)+f g^2\right)}{9 c^2}-\frac{3 b^2 h x^2 (e h+2 f g)}{32 c^2}-\frac{8 b^2 f h^2 x^3}{225 c^2}-\frac{16 b^2 f h^2 x}{75 c^4}-\frac{2}{27} b^2 x^3 \left(h (d h+2 e g)+f g^2\right)-\frac{1}{4} b^2 g x^2 (2 d h+e g)-2 b^2 d g^2 x-\frac{1}{32} b^2 h x^4 (e h+2 f g)-\frac{2}{125} b^2 f h^2 x^5","\frac{2 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \left(h (d h+2 e g)+f g^2\right)}{9 c}+\frac{4 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) \left(h (d h+2 e g)+f g^2\right)}{9 c^3}+\frac{b g x \sqrt{1-c^2 x^2} (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{g (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{2 b d g^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{b h x^3 \sqrt{1-c^2 x^2} (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b h x \sqrt{1-c^2 x^2} (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)}{16 c^3}-\frac{3 h (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}+\frac{2 b f h^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b f h^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^3}+\frac{16 b f h^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^5}+\frac{1}{3} x^3 \left(a+b \sin ^{-1}(c x)\right)^2 \left(h (d h+2 e g)+f g^2\right)+\frac{1}{2} g x^2 (2 d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2+d g^2 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} h x^4 (e h+2 f g) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{5} f h^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 x \left(h (d h+2 e g)+f g^2\right)}{9 c^2}-\frac{3 b^2 h x^2 (e h+2 f g)}{32 c^2}-\frac{8 b^2 f h^2 x^3}{225 c^2}-\frac{16 b^2 f h^2 x}{75 c^4}-\frac{2}{27} b^2 x^3 \left(h (d h+2 e g)+f g^2\right)-\frac{1}{4} b^2 g x^2 (2 d h+e g)-2 b^2 d g^2 x-\frac{1}{32} b^2 h x^4 (e h+2 f g)-\frac{2}{125} b^2 f h^2 x^5",1,"-2*b^2*d*g^2*x - (16*b^2*f*h^2*x)/(75*c^4) - (4*b^2*(f*g^2 + h*(2*e*g + d*h))*x)/(9*c^2) - (b^2*g*(e*g + 2*d*h)*x^2)/4 - (3*b^2*h*(2*f*g + e*h)*x^2)/(32*c^2) - (8*b^2*f*h^2*x^3)/(225*c^2) - (2*b^2*(f*g^2 + h*(2*e*g + d*h))*x^3)/27 - (b^2*h*(2*f*g + e*h)*x^4)/32 - (2*b^2*f*h^2*x^5)/125 + (2*b*d*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (16*b*f*h^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(75*c^5) + (4*b*(f*g^2 + h*(2*e*g + d*h))*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (b*g*(e*g + 2*d*h)*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c) + (3*b*h*(2*f*g + e*h)*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(16*c^3) + (8*b*f*h^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(75*c^3) + (2*b*(f*g^2 + h*(2*e*g + d*h))*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) + (b*h*(2*f*g + e*h)*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (2*b*f*h^2*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c) - (g*(e*g + 2*d*h)*(a + b*ArcSin[c*x])^2)/(4*c^2) - (3*h*(2*f*g + e*h)*(a + b*ArcSin[c*x])^2)/(32*c^4) + d*g^2*x*(a + b*ArcSin[c*x])^2 + (g*(e*g + 2*d*h)*x^2*(a + b*ArcSin[c*x])^2)/2 + ((f*g^2 + h*(2*e*g + d*h))*x^3*(a + b*ArcSin[c*x])^2)/3 + (h*(2*f*g + e*h)*x^4*(a + b*ArcSin[c*x])^2)/4 + (f*h^2*x^5*(a + b*ArcSin[c*x])^2)/5","A",27,8,28,0.2857,1,"{4751, 4619, 4677, 8, 4627, 4707, 4641, 30}"
117,1,425,0,0.698374,"\int (g+h x) \left(d+e x+f x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(g + h*x)*(d + e*x + f*x^2)*(a + b*ArcSin[c*x])^2,x]","\frac{b x \sqrt{1-c^2 x^2} (d h+e g) \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{(d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{2 b d g \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{2 b x^2 \sqrt{1-c^2 x^2} (e h+f g) \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b \sqrt{1-c^2 x^2} (e h+f g) \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{b f h x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b f h x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^3}-\frac{3 f h \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}+\frac{1}{2} x^2 (d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2+d g x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{3} x^3 (e h+f g) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} f h x^4 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 x (e h+f g)}{9 c^2}-\frac{3 b^2 f h x^2}{32 c^2}-\frac{1}{4} b^2 x^2 (d h+e g)-2 b^2 d g x-\frac{2}{27} b^2 x^3 (e h+f g)-\frac{1}{32} b^2 f h x^4","\frac{b x \sqrt{1-c^2 x^2} (d h+e g) \left(a+b \sin ^{-1}(c x)\right)}{2 c}-\frac{(d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{2 b d g \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{2 b x^2 \sqrt{1-c^2 x^2} (e h+f g) \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b \sqrt{1-c^2 x^2} (e h+f g) \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{b f h x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b f h x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^3}-\frac{3 f h \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^4}+\frac{1}{2} x^2 (d h+e g) \left(a+b \sin ^{-1}(c x)\right)^2+d g x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{3} x^3 (e h+f g) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} f h x^4 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 x (e h+f g)}{9 c^2}-\frac{3 b^2 f h x^2}{32 c^2}-\frac{1}{4} b^2 x^2 (d h+e g)-2 b^2 d g x-\frac{2}{27} b^2 x^3 (e h+f g)-\frac{1}{32} b^2 f h x^4",1,"-2*b^2*d*g*x - (4*b^2*(f*g + e*h)*x)/(9*c^2) - (3*b^2*f*h*x^2)/(32*c^2) - (b^2*(e*g + d*h)*x^2)/4 - (2*b^2*(f*g + e*h)*x^3)/27 - (b^2*f*h*x^4)/32 + (2*b*d*g*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (4*b*(f*g + e*h)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (3*b*f*h*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(16*c^3) + (b*(e*g + d*h)*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c) + (2*b*(f*g + e*h)*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) + (b*f*h*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) - (3*f*h*(a + b*ArcSin[c*x])^2)/(32*c^4) - ((e*g + d*h)*(a + b*ArcSin[c*x])^2)/(4*c^2) + d*g*x*(a + b*ArcSin[c*x])^2 + ((e*g + d*h)*x^2*(a + b*ArcSin[c*x])^2)/2 + ((f*g + e*h)*x^3*(a + b*ArcSin[c*x])^2)/3 + (f*h*x^4*(a + b*ArcSin[c*x])^2)/4","A",20,8,26,0.3077,1,"{4751, 4619, 4677, 8, 4627, 4707, 4641, 30}"
118,1,1067,0,1.9479612,"\int \frac{\left(d+e x+f x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{g+h x} \, dx","Int[((d + e*x + f*x^2)*(a + b*ArcSin[c*x])^2)/(g + h*x),x]","-\frac{i b^2 \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)^3}{3 h^3}+\frac{b^2 f x^2 \sin ^{-1}(c x)^2}{2 h}-\frac{i a b \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 (f g-e h) x \sin ^{-1}(c x)^2}{h^2}+\frac{b^2 \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}+\frac{b^2 \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 f \sin ^{-1}(c x)^2}{4 c^2 h}+\frac{a b f x^2 \sin ^{-1}(c x)}{h}-\frac{2 a b (f g-e h) x \sin ^{-1}(c x)}{h^2}+\frac{2 a b \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 a b \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 i b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 i b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 b^2 (f g-e h) \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c h^2}+\frac{b^2 f x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{2 c h}-\frac{a b f \sin ^{-1}(c x)}{2 c^2 h}+\frac{a^2 f x^2}{2 h}-\frac{b^2 f x^2}{4 h}-\frac{a^2 (f g-e h) x}{h^2}+\frac{2 b^2 (f g-e h) x}{h^2}+\frac{a^2 \left(f g^2-e h g+d h^2\right) \log (g+h x)}{h^3}-\frac{2 i a b \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{2 i a b \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{a b (4 (f g-e h)-f h x) \sqrt{1-c^2 x^2}}{2 c h^2}","-\frac{i b^2 \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)^3}{3 h^3}+\frac{b^2 f x^2 \sin ^{-1}(c x)^2}{2 h}-\frac{i a b \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 (f g-e h) x \sin ^{-1}(c x)^2}{h^2}+\frac{b^2 \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}+\frac{b^2 \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 f \sin ^{-1}(c x)^2}{4 c^2 h}+\frac{a b f x^2 \sin ^{-1}(c x)}{h}-\frac{2 a b (f g-e h) x \sin ^{-1}(c x)}{h^2}+\frac{2 a b \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 a b \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 i b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 i b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 b^2 (f g-e h) \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c h^2}+\frac{b^2 f x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{2 c h}-\frac{a b f \sin ^{-1}(c x)}{2 c^2 h}+\frac{a^2 f x^2}{2 h}-\frac{b^2 f x^2}{4 h}-\frac{a^2 (f g-e h) x}{h^2}+\frac{2 b^2 (f g-e h) x}{h^2}+\frac{a^2 \left(f g^2-e h g+d h^2\right) \log (g+h x)}{h^3}-\frac{2 i a b \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{2 i a b \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 b^2 \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{a b (4 (f g-e h)-f h x) \sqrt{1-c^2 x^2}}{2 c h^2}",1,"-((a^2*(f*g - e*h)*x)/h^2) + (2*b^2*(f*g - e*h)*x)/h^2 + (a^2*f*x^2)/(2*h) - (b^2*f*x^2)/(4*h) - (a*b*(4*(f*g - e*h) - f*h*x)*Sqrt[1 - c^2*x^2])/(2*c*h^2) - (a*b*f*ArcSin[c*x])/(2*c^2*h) - (2*a*b*(f*g - e*h)*x*ArcSin[c*x])/h^2 + (a*b*f*x^2*ArcSin[c*x])/h - (2*b^2*(f*g - e*h)*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*h^2) + (b^2*f*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(2*c*h) - (b^2*f*ArcSin[c*x]^2)/(4*c^2*h) - (I*a*b*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]^2)/h^3 - (b^2*(f*g - e*h)*x*ArcSin[c*x]^2)/h^2 + (b^2*f*x^2*ArcSin[c*x]^2)/(2*h) - ((I/3)*b^2*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]^3)/h^3 + (2*a*b*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 + (b^2*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 + (2*a*b*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 + (b^2*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 + (a^2*(f*g^2 - e*g*h + d*h^2)*Log[g + h*x])/h^3 - ((2*I)*a*b*(f*g^2 - e*g*h + d*h^2)*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 - ((2*I)*b^2*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 - ((2*I)*a*b*(f*g^2 - e*g*h + d*h^2)*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 - ((2*I)*b^2*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 + (2*b^2*(f*g^2 - e*g*h + d*h^2)*PolyLog[3, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 + (2*b^2*(f*g^2 - e*g*h + d*h^2)*PolyLog[3, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3","A",38,23,28,0.8214,1,"{4759, 698, 4753, 12, 6742, 780, 216, 2404, 4741, 4519, 2190, 2279, 2391, 4619, 4677, 8, 4627, 4707, 4641, 30, 2531, 2282, 6589}"
119,1,1323,0,2.4734591,"\int \frac{\left(d+e x+f x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(g+h x)^2} \, dx","Int[((d + e*x + f*x^2)*(a + b*ArcSin[c*x])^2)/(g + h*x)^2,x]","\frac{i b^2 (2 f g-e h) \sin ^{-1}(c x)^3}{3 h^3}+\frac{i a b (2 f g-e h) \sin ^{-1}(c x)^2}{h^3}+\frac{b^2 f x \sin ^{-1}(c x)^2}{h^2}-\frac{b^2 (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)^2}{h^3 (g+h x)}+\frac{2 a b f x \sin ^{-1}(c x)}{h^2}-\frac{2 a b (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 i b^2 c \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3 \sqrt{c^2 g^2-h^2}}-\frac{2 a b (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 i b^2 c \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3 \sqrt{c^2 g^2-h^2}}+\frac{2 i b^2 (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 i b^2 (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 b^2 f \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c h^2}-\frac{2 a b \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)}{h^3 (g+h x)}+\frac{a^2 f x}{h^2}-\frac{2 b^2 f x}{h^2}+\frac{2 a b c \left(f g^2-e h g+d h^2\right) \tan ^{-1}\left(\frac{g x c^2+h}{\sqrt{c^2 g^2-h^2} \sqrt{1-c^2 x^2}}\right)}{h^3 \sqrt{c^2 g^2-h^2}}-\frac{a^2 (2 f g-e h) \log (g+h x)}{h^3}+\frac{2 i a b (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{2 b^2 c \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3 \sqrt{c^2 g^2-h^2}}+\frac{2 i a b (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 b^2 c \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3 \sqrt{c^2 g^2-h^2}}-\frac{2 b^2 (2 f g-e h) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{2 b^2 (2 f g-e h) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 a b f \sqrt{1-c^2 x^2}}{c h^2}-\frac{a^2 \left(f g^2-e h g+d h^2\right)}{h^3 (g+h x)}","\frac{i b^2 (2 f g-e h) \sin ^{-1}(c x)^3}{3 h^3}+\frac{i a b (2 f g-e h) \sin ^{-1}(c x)^2}{h^3}+\frac{b^2 f x \sin ^{-1}(c x)^2}{h^2}-\frac{b^2 (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)^2}{h^3}-\frac{b^2 \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)^2}{h^3 (g+h x)}+\frac{2 a b f x \sin ^{-1}(c x)}{h^2}-\frac{2 a b (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}-\frac{2 i b^2 c \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3 \sqrt{c^2 g^2-h^2}}-\frac{2 a b (2 f g-e h) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 i b^2 c \left(f g^2-e h g+d h^2\right) \log \left(1-\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3 \sqrt{c^2 g^2-h^2}}+\frac{2 i b^2 (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 i b^2 (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right) \sin ^{-1}(c x)}{h^3}+\frac{2 b^2 f \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c h^2}-\frac{2 a b \left(f g^2-e h g+d h^2\right) \sin ^{-1}(c x)}{h^3 (g+h x)}+\frac{a^2 f x}{h^2}-\frac{2 b^2 f x}{h^2}+\frac{2 a b c \left(f g^2-e h g+d h^2\right) \tan ^{-1}\left(\frac{g x c^2+h}{\sqrt{c^2 g^2-h^2} \sqrt{1-c^2 x^2}}\right)}{h^3 \sqrt{c^2 g^2-h^2}}-\frac{a^2 (2 f g-e h) \log (g+h x)}{h^3}+\frac{2 i a b (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{2 b^2 c \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3 \sqrt{c^2 g^2-h^2}}+\frac{2 i a b (2 f g-e h) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 b^2 c \left(f g^2-e h g+d h^2\right) \text{PolyLog}\left(2,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3 \sqrt{c^2 g^2-h^2}}-\frac{2 b^2 (2 f g-e h) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g-\sqrt{c^2 g^2-h^2}}\right)}{h^3}-\frac{2 b^2 (2 f g-e h) \text{PolyLog}\left(3,\frac{i e^{i \sin ^{-1}(c x)} h}{c g+\sqrt{c^2 g^2-h^2}}\right)}{h^3}+\frac{2 a b f \sqrt{1-c^2 x^2}}{c h^2}-\frac{a^2 \left(f g^2-e h g+d h^2\right)}{h^3 (g+h x)}",1,"(a^2*f*x)/h^2 - (2*b^2*f*x)/h^2 - (a^2*(f*g^2 - e*g*h + d*h^2))/(h^3*(g + h*x)) + (2*a*b*f*Sqrt[1 - c^2*x^2])/(c*h^2) + (2*a*b*f*x*ArcSin[c*x])/h^2 - (2*a*b*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x])/(h^3*(g + h*x)) + (2*b^2*f*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*h^2) + (I*a*b*(2*f*g - e*h)*ArcSin[c*x]^2)/h^3 + (b^2*f*x*ArcSin[c*x]^2)/h^2 - (b^2*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]^2)/(h^3*(g + h*x)) + ((I/3)*b^2*(2*f*g - e*h)*ArcSin[c*x]^3)/h^3 + (2*a*b*c*(f*g^2 - e*g*h + d*h^2)*ArcTan[(h + c^2*g*x)/(Sqrt[c^2*g^2 - h^2]*Sqrt[1 - c^2*x^2])])/(h^3*Sqrt[c^2*g^2 - h^2]) - (2*a*b*(2*f*g - e*h)*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 - ((2*I)*b^2*c*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/(h^3*Sqrt[c^2*g^2 - h^2]) - (b^2*(2*f*g - e*h)*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 - (2*a*b*(2*f*g - e*h)*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 + ((2*I)*b^2*c*(f*g^2 - e*g*h + d*h^2)*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/(h^3*Sqrt[c^2*g^2 - h^2]) - (b^2*(2*f*g - e*h)*ArcSin[c*x]^2*Log[1 - (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 - (a^2*(2*f*g - e*h)*Log[g + h*x])/h^3 + ((2*I)*a*b*(2*f*g - e*h)*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 - (2*b^2*c*(f*g^2 - e*g*h + d*h^2)*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/(h^3*Sqrt[c^2*g^2 - h^2]) + ((2*I)*b^2*(2*f*g - e*h)*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 + ((2*I)*a*b*(2*f*g - e*h)*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 + (2*b^2*c*(f*g^2 - e*g*h + d*h^2)*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/(h^3*Sqrt[c^2*g^2 - h^2]) + ((2*I)*b^2*(2*f*g - e*h)*ArcSin[c*x]*PolyLog[2, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3 - (2*b^2*(2*f*g - e*h)*PolyLog[3, (I*E^(I*ArcSin[c*x])*h)/(c*g - Sqrt[c^2*g^2 - h^2])])/h^3 - (2*b^2*(2*f*g - e*h)*PolyLog[3, (I*E^(I*ArcSin[c*x])*h)/(c*g + Sqrt[c^2*g^2 - h^2])])/h^3","A",45,25,28,0.8929,1,"{4759, 698, 4753, 12, 6742, 261, 725, 204, 216, 2404, 4741, 4519, 2190, 2279, 2391, 4619, 4677, 8, 4743, 4773, 3323, 2264, 2531, 2282, 6589}"
120,1,520,0,1.644632,"\int \frac{\left(e f+2 d h x+e h x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Int[((e*f + 2*d*h*x + e*h*x^2)*(a + b*ArcSin[c*x])^2)/(d + e*x)^2,x]","-\frac{2 b^2 c \left(e^2 f-d^2 h\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 c \left(e^2 f-d^2 h\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 a b c \left(e^2 f-d^2 h\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 a b h \sqrt{1-c^2 x^2}}{c e}-\frac{\left(f-\frac{d^2 h}{e^2}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d+e x}+\frac{h x \left(a+b \sin ^{-1}(c x)\right)^2}{e}-\frac{2 i b^2 c \sin ^{-1}(c x) \left(e^2 f-d^2 h\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 i b^2 c \sin ^{-1}(c x) \left(e^2 f-d^2 h\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 h \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c e}-\frac{2 b^2 h x}{e}","-\frac{2 b^2 c \left(e^2 f-d^2 h\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 c \left(e^2 f-d^2 h\right) \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 a b c \left(e^2 f-d^2 h\right) \tan ^{-1}\left(\frac{c^2 d x+e}{\sqrt{1-c^2 x^2} \sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 a b h \sqrt{1-c^2 x^2}}{c e}-\frac{\left(f-\frac{d^2 h}{e^2}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d+e x}+\frac{h x \left(a+b \sin ^{-1}(c x)\right)^2}{e}-\frac{2 i b^2 c \sin ^{-1}(c x) \left(e^2 f-d^2 h\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 i b^2 c \sin ^{-1}(c x) \left(e^2 f-d^2 h\right) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e^2 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 h \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c e}-\frac{2 b^2 h x}{e}",1,"(-2*b^2*h*x)/e + (2*a*b*h*Sqrt[1 - c^2*x^2])/(c*e) + (2*b^2*h*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*e) + (h*x*(a + b*ArcSin[c*x])^2)/e - ((f - (d^2*h)/e^2)*(a + b*ArcSin[c*x])^2)/(d + e*x) + (2*a*b*c*(e^2*f - d^2*h)*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) - ((2*I)*b^2*c*(e^2*f - d^2*h)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) + ((2*I)*b^2*c*(e^2*f - d^2*h)*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) - (2*b^2*c*(e^2*f - d^2*h)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2]) + (2*b^2*c*(e^2*f - d^2*h)*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^2*Sqrt[c^2*d^2 - e^2])","A",20,18,33,0.5455,1,"{683, 4757, 6742, 261, 725, 204, 4799, 1654, 12, 4797, 4677, 8, 4773, 3323, 2264, 2190, 2279, 2391}"
121,1,920,0,4.2439405,"\int \frac{\left(e f+2 d h x+e h x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Int[((e*f + 2*d*h*x + e*h*x^2)^2*(a + b*ArcSin[c*x])^2)/(d + e*x)^2,x]","-\frac{b^2 h^2 \sin ^{-1}(c x)^2 d^3}{3 e^3}-\frac{b^2 h^2 x^2 d}{2 e}-\frac{b^2 h^2 \sin ^{-1}(c x)^2 d}{2 c^2 e}-\frac{a b \left(2 c^2 d^2+3 e^2\right) h^2 \sin ^{-1}(c x) d}{3 c^2 e^3}+\frac{b^2 h^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x) d}{c e}+\frac{5 a b h^2 (d+e x) \sqrt{1-c^2 x^2} d}{9 c e^2}-\frac{2}{27} b^2 h^2 x^3+\frac{h^2 (d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 e^3}+\frac{2 h \left(e^2 f-d^2 h\right) x \left(a+b \sin ^{-1}(c x)\right)^2}{e^2}-\frac{\left(e^2 f-d^2 h\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{e^3 (d+e x)}-\frac{4 b^2 h^2 x}{9 c^2}-\frac{2 b^2 h \left(2 e^2 f-d^2 h\right) x}{e^2}+\frac{4 b^2 h^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{9 c^3}+\frac{2 b^2 h^2 x^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{9 c}+\frac{2 b^2 h \left(2 e^2 f-d^2 h\right) \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c e^2}+\frac{2 a b c \left(e^2 f-d^2 h\right)^2 \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}-\frac{2 i b^2 c \left(e^2 f-d^2 h\right)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{2 i b^2 c \left(e^2 f-d^2 h\right)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 c \left(e^2 f-d^2 h\right)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 c \left(e^2 f-d^2 h\right)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{2 a b h^2 (d+e x)^2 \sqrt{1-c^2 x^2}}{9 c e^2}+\frac{a b h \left(\left(36 e^2 f-25 d^2 h\right) c^2+4 e^2 h\right) \sqrt{1-c^2 x^2}}{9 c^3 e^2}","-\frac{b^2 h^2 \sin ^{-1}(c x)^2 d^3}{3 e^3}-\frac{b^2 h^2 x^2 d}{2 e}-\frac{b^2 h^2 \sin ^{-1}(c x)^2 d}{2 c^2 e}-\frac{a b \left(2 c^2 d^2+3 e^2\right) h^2 \sin ^{-1}(c x) d}{3 c^2 e^3}+\frac{b^2 h^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x) d}{c e}+\frac{5 a b h^2 (d+e x) \sqrt{1-c^2 x^2} d}{9 c e^2}-\frac{2}{27} b^2 h^2 x^3+\frac{h^2 (d+e x)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 e^3}+\frac{2 h \left(e^2 f-d^2 h\right) x \left(a+b \sin ^{-1}(c x)\right)^2}{e^2}-\frac{\left(e^2 f-d^2 h\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{e^3 (d+e x)}-\frac{4 b^2 h^2 x}{9 c^2}-\frac{2 b^2 h \left(2 e^2 f-d^2 h\right) x}{e^2}+\frac{4 b^2 h^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{9 c^3}+\frac{2 b^2 h^2 x^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{9 c}+\frac{2 b^2 h \left(2 e^2 f-d^2 h\right) \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c e^2}+\frac{2 a b c \left(e^2 f-d^2 h\right)^2 \tan ^{-1}\left(\frac{d x c^2+e}{\sqrt{c^2 d^2-e^2} \sqrt{1-c^2 x^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}-\frac{2 i b^2 c \left(e^2 f-d^2 h\right)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{2 i b^2 c \left(e^2 f-d^2 h\right)^2 \sin ^{-1}(c x) \log \left(1-\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 c \left(e^2 f-d^2 h\right)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{2 b^2 c \left(e^2 f-d^2 h\right)^2 \text{PolyLog}\left(2,\frac{i e e^{i \sin ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e^3 \sqrt{c^2 d^2-e^2}}+\frac{2 a b h^2 (d+e x)^2 \sqrt{1-c^2 x^2}}{9 c e^2}+\frac{a b h \left(\left(36 e^2 f-25 d^2 h\right) c^2+4 e^2 h\right) \sqrt{1-c^2 x^2}}{9 c^3 e^2}",1,"(-4*b^2*h^2*x)/(9*c^2) - (2*b^2*h*(2*e^2*f - d^2*h)*x)/e^2 - (b^2*d*h^2*x^2)/(2*e) - (2*b^2*h^2*x^3)/27 + (a*b*h*(4*e^2*h + c^2*(36*e^2*f - 25*d^2*h))*Sqrt[1 - c^2*x^2])/(9*c^3*e^2) + (5*a*b*d*h^2*(d + e*x)*Sqrt[1 - c^2*x^2])/(9*c*e^2) + (2*a*b*h^2*(d + e*x)^2*Sqrt[1 - c^2*x^2])/(9*c*e^2) - (a*b*d*(2*c^2*d^2 + 3*e^2)*h^2*ArcSin[c*x])/(3*c^2*e^3) + (4*b^2*h^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(9*c^3) + (2*b^2*h*(2*e^2*f - d^2*h)*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*e^2) + (b^2*d*h^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*e) + (2*b^2*h^2*x^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(9*c) - (b^2*d^3*h^2*ArcSin[c*x]^2)/(3*e^3) - (b^2*d*h^2*ArcSin[c*x]^2)/(2*c^2*e) + (2*h*(e^2*f - d^2*h)*x*(a + b*ArcSin[c*x])^2)/e^2 - ((e^2*f - d^2*h)^2*(a + b*ArcSin[c*x])^2)/(e^3*(d + e*x)) + (h^2*(d + e*x)^3*(a + b*ArcSin[c*x])^2)/(3*e^3) + (2*a*b*c*(e^2*f - d^2*h)^2*ArcTan[(e + c^2*d*x)/(Sqrt[c^2*d^2 - e^2]*Sqrt[1 - c^2*x^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) - ((2*I)*b^2*c*(e^2*f - d^2*h)^2*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) + ((2*I)*b^2*c*(e^2*f - d^2*h)^2*ArcSin[c*x]*Log[1 - (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) - (2*b^2*c*(e^2*f - d^2*h)^2*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d - Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2]) + (2*b^2*c*(e^2*f - d^2*h)^2*PolyLog[2, (I*e*E^(I*ArcSin[c*x]))/(c*d + Sqrt[c^2*d^2 - e^2])])/(e^3*Sqrt[c^2*d^2 - e^2])","A",32,25,35,0.7143,1,"{683, 4757, 12, 6742, 261, 725, 204, 743, 780, 216, 4799, 1654, 844, 4797, 4641, 4677, 8, 4707, 30, 4773, 3323, 2264, 2190, 2279, 2391}"
122,1,137,0,0.1996544,"\int x^3 \sin ^{-1}(a+b x) \, dx","Int[x^3*ArcSin[a + b*x],x]","-\frac{\left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right) \sqrt{1-(a+b x)^2}}{96 b^4}-\frac{\left(8 a^4+24 a^2+3\right) \sin ^{-1}(a+b x)}{32 b^4}-\frac{7 a x^2 \sqrt{1-(a+b x)^2}}{48 b^2}+\frac{x^3 \sqrt{1-(a+b x)^2}}{16 b}+\frac{1}{4} x^4 \sin ^{-1}(a+b x)","-\frac{\left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right) \sqrt{1-(a+b x)^2}}{96 b^4}-\frac{\left(8 a^4+24 a^2+3\right) \sin ^{-1}(a+b x)}{32 b^4}-\frac{7 a x^2 \sqrt{1-(a+b x)^2}}{48 b^2}+\frac{x^3 \sqrt{1-(a+b x)^2}}{16 b}+\frac{1}{4} x^4 \sin ^{-1}(a+b x)",1,"(-7*a*x^2*Sqrt[1 - (a + b*x)^2])/(48*b^2) + (x^3*Sqrt[1 - (a + b*x)^2])/(16*b) - ((4*a*(16 + 19*a^2) - (9 + 26*a^2)*(a + b*x))*Sqrt[1 - (a + b*x)^2])/(96*b^4) - ((3 + 24*a^2 + 8*a^4)*ArcSin[a + b*x])/(32*b^4) + (x^4*ArcSin[a + b*x])/4","A",6,6,10,0.6000,1,"{4805, 4743, 743, 833, 780, 216}"
123,1,94,0,0.1184117,"\int x^2 \sin ^{-1}(a+b x) \, dx","Int[x^2*ArcSin[a + b*x],x]","\frac{\left(11 a^2-5 a b x+4\right) \sqrt{1-(a+b x)^2}}{18 b^3}+\frac{a \left(2 a^2+3\right) \sin ^{-1}(a+b x)}{6 b^3}+\frac{x^2 \sqrt{1-(a+b x)^2}}{9 b}+\frac{1}{3} x^3 \sin ^{-1}(a+b x)","\frac{\left(11 a^2-5 a b x+4\right) \sqrt{1-(a+b x)^2}}{18 b^3}+\frac{a \left(2 a^2+3\right) \sin ^{-1}(a+b x)}{6 b^3}+\frac{x^2 \sqrt{1-(a+b x)^2}}{9 b}+\frac{1}{3} x^3 \sin ^{-1}(a+b x)",1,"(x^2*Sqrt[1 - (a + b*x)^2])/(9*b) + ((4 + 11*a^2 - 5*a*b*x)*Sqrt[1 - (a + b*x)^2])/(18*b^3) + (a*(3 + 2*a^2)*ArcSin[a + b*x])/(6*b^3) + (x^3*ArcSin[a + b*x])/3","A",5,5,10,0.5000,1,"{4805, 4743, 743, 780, 216}"
124,1,80,0,0.077375,"\int x \sin ^{-1}(a+b x) \, dx","Int[x*ArcSin[a + b*x],x]","-\frac{\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{4 b^2}-\frac{3 a \sqrt{1-(a+b x)^2}}{4 b^2}+\frac{1}{2} x^2 \sin ^{-1}(a+b x)+\frac{x \sqrt{1-(a+b x)^2}}{4 b}","-\frac{\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{4 b^2}-\frac{3 a \sqrt{1-(a+b x)^2}}{4 b^2}+\frac{1}{2} x^2 \sin ^{-1}(a+b x)+\frac{x \sqrt{1-(a+b x)^2}}{4 b}",1,"(-3*a*Sqrt[1 - (a + b*x)^2])/(4*b^2) + (x*Sqrt[1 - (a + b*x)^2])/(4*b) - ((1 + 2*a^2)*ArcSin[a + b*x])/(4*b^2) + (x^2*ArcSin[a + b*x])/2","A",5,5,8,0.6250,1,"{4805, 4743, 743, 641, 216}"
125,1,35,0,0.0155002,"\int \sin ^{-1}(a+b x) \, dx","Int[ArcSin[a + b*x],x]","\frac{\sqrt{1-(a+b x)^2}}{b}+\frac{(a+b x) \sin ^{-1}(a+b x)}{b}","\frac{\sqrt{1-(a+b x)^2}}{b}+\frac{(a+b x) \sin ^{-1}(a+b x)}{b}",1,"Sqrt[1 - (a + b*x)^2]/b + ((a + b*x)*ArcSin[a + b*x])/b","A",3,3,6,0.5000,1,"{4803, 4619, 261}"
126,1,181,0,0.2789639,"\int \frac{\sin ^{-1}(a+b x)}{x} \, dx","Int[ArcSin[a + b*x]/x,x]","-i \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)-i \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x) \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x) \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)-\frac{1}{2} i \sin ^{-1}(a+b x)^2","-i \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)-i \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x) \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x) \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)-\frac{1}{2} i \sin ^{-1}(a+b x)^2",1,"(-I/2)*ArcSin[a + b*x]^2 + ArcSin[a + b*x]*Log[1 - E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] + ArcSin[a + b*x]*Log[1 - E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])] - I*PolyLog[2, E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] - I*PolyLog[2, E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])]","A",9,6,10,0.6000,1,"{4805, 4741, 4521, 2190, 2279, 2391}"
127,1,64,0,0.0754341,"\int \frac{\sin ^{-1}(a+b x)}{x^2} \, dx","Int[ArcSin[a + b*x]/x^2,x]","-\frac{b \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{\sqrt{1-a^2}}-\frac{\sin ^{-1}(a+b x)}{x}","-\frac{b \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{\sqrt{1-a^2}}-\frac{\sin ^{-1}(a+b x)}{x}",1,"-(ArcSin[a + b*x]/x) - (b*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/Sqrt[1 - a^2]","A",4,4,10,0.4000,1,"{4805, 4743, 725, 206}"
128,1,103,0,0.1162314,"\int \frac{\sin ^{-1}(a+b x)}{x^3} \, dx","Int[ArcSin[a + b*x]/x^3,x]","-\frac{a b^2 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{2 \left(1-a^2\right)^{3/2}}-\frac{b \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right) x}-\frac{\sin ^{-1}(a+b x)}{2 x^2}","-\frac{a b^2 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{2 \left(1-a^2\right)^{3/2}}-\frac{b \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right) x}-\frac{\sin ^{-1}(a+b x)}{2 x^2}",1,"-(b*Sqrt[1 - (a + b*x)^2])/(2*(1 - a^2)*x) - ArcSin[a + b*x]/(2*x^2) - (a*b^2*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/(2*(1 - a^2)^(3/2))","A",5,5,10,0.5000,1,"{4805, 4743, 731, 725, 206}"
129,1,144,0,0.1804795,"\int \frac{\sin ^{-1}(a+b x)}{x^4} \, dx","Int[ArcSin[a + b*x]/x^4,x]","-\frac{a b^2 \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right)^2 x}-\frac{\left(2 a^2+1\right) b^3 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{6 \left(1-a^2\right)^{5/2}}-\frac{b \sqrt{1-(a+b x)^2}}{6 \left(1-a^2\right) x^2}-\frac{\sin ^{-1}(a+b x)}{3 x^3}","-\frac{a b^2 \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right)^2 x}-\frac{\left(2 a^2+1\right) b^3 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{6 \left(1-a^2\right)^{5/2}}-\frac{b \sqrt{1-(a+b x)^2}}{6 \left(1-a^2\right) x^2}-\frac{\sin ^{-1}(a+b x)}{3 x^3}",1,"-(b*Sqrt[1 - (a + b*x)^2])/(6*(1 - a^2)*x^2) - (a*b^2*Sqrt[1 - (a + b*x)^2])/(2*(1 - a^2)^2*x) - ArcSin[a + b*x]/(3*x^3) - ((1 + 2*a^2)*b^3*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/(6*(1 - a^2)^(5/2))","A",6,6,10,0.6000,1,"{4805, 4743, 745, 807, 725, 206}"
130,1,186,0,0.2743158,"\int \frac{\sin ^{-1}(a+b x)}{x^5} \, dx","Int[ArcSin[a + b*x]/x^5,x]","-\frac{5 a b^2 \sqrt{1-(a+b x)^2}}{24 \left(1-a^2\right)^2 x^2}-\frac{\left(11 a^2+4\right) b^3 \sqrt{1-(a+b x)^2}}{24 \left(1-a^2\right)^3 x}-\frac{a \left(2 a^2+3\right) b^4 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{8 \left(1-a^2\right)^{7/2}}-\frac{b \sqrt{1-(a+b x)^2}}{12 \left(1-a^2\right) x^3}-\frac{\sin ^{-1}(a+b x)}{4 x^4}","-\frac{5 a b^2 \sqrt{1-(a+b x)^2}}{24 \left(1-a^2\right)^2 x^2}-\frac{\left(11 a^2+4\right) b^3 \sqrt{1-(a+b x)^2}}{24 \left(1-a^2\right)^3 x}-\frac{a \left(2 a^2+3\right) b^4 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{8 \left(1-a^2\right)^{7/2}}-\frac{b \sqrt{1-(a+b x)^2}}{12 \left(1-a^2\right) x^3}-\frac{\sin ^{-1}(a+b x)}{4 x^4}",1,"-(b*Sqrt[1 - (a + b*x)^2])/(12*(1 - a^2)*x^3) - (5*a*b^2*Sqrt[1 - (a + b*x)^2])/(24*(1 - a^2)^2*x^2) - ((4 + 11*a^2)*b^3*Sqrt[1 - (a + b*x)^2])/(24*(1 - a^2)^3*x) - ArcSin[a + b*x]/(4*x^4) - (a*(3 + 2*a^2)*b^4*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/(8*(1 - a^2)^(7/2))","A",7,7,10,0.7000,1,"{4805, 4743, 745, 835, 807, 725, 206}"
131,1,343,0,0.5956954,"\int x^3 \sin ^{-1}(a+b x)^2 \, dx","Int[x^3*ArcSin[a + b*x]^2,x]","\frac{2 a^3 x}{b^3}-\frac{3 a^2 (a+b x)^2}{4 b^4}-\frac{a^4 \sin ^{-1}(a+b x)^2}{4 b^4}-\frac{2 a^3 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^4}-\frac{3 a^2 \sin ^{-1}(a+b x)^2}{4 b^4}+\frac{3 a^2 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{2 b^4}+\frac{2 a (a+b x)^3}{9 b^4}+\frac{4 a x}{3 b^3}-\frac{(a+b x)^4}{32 b^4}-\frac{3 (a+b x)^2}{32 b^4}-\frac{2 a (a+b x)^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{3 b^4}-\frac{4 a \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{3 b^4}-\frac{3 \sin ^{-1}(a+b x)^2}{32 b^4}+\frac{(a+b x)^3 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{8 b^4}+\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{16 b^4}+\frac{1}{4} x^4 \sin ^{-1}(a+b x)^2","\frac{2 a^3 x}{b^3}-\frac{3 a^2 (a+b x)^2}{4 b^4}-\frac{a^4 \sin ^{-1}(a+b x)^2}{4 b^4}-\frac{2 a^3 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^4}-\frac{3 a^2 \sin ^{-1}(a+b x)^2}{4 b^4}+\frac{3 a^2 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{2 b^4}+\frac{2 a (a+b x)^3}{9 b^4}+\frac{4 a x}{3 b^3}-\frac{(a+b x)^4}{32 b^4}-\frac{3 (a+b x)^2}{32 b^4}-\frac{2 a (a+b x)^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{3 b^4}-\frac{4 a \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{3 b^4}-\frac{3 \sin ^{-1}(a+b x)^2}{32 b^4}+\frac{(a+b x)^3 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{8 b^4}+\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{16 b^4}+\frac{1}{4} x^4 \sin ^{-1}(a+b x)^2",1,"(4*a*x)/(3*b^3) + (2*a^3*x)/b^3 - (3*(a + b*x)^2)/(32*b^4) - (3*a^2*(a + b*x)^2)/(4*b^4) + (2*a*(a + b*x)^3)/(9*b^4) - (a + b*x)^4/(32*b^4) - (4*a*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(3*b^4) - (2*a^3*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/b^4 + (3*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(16*b^4) + (3*a^2*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(2*b^4) - (2*a*(a + b*x)^2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(3*b^4) + ((a + b*x)^3*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(8*b^4) - (3*ArcSin[a + b*x]^2)/(32*b^4) - (3*a^2*ArcSin[a + b*x]^2)/(4*b^4) - (a^4*ArcSin[a + b*x]^2)/(4*b^4) + (x^4*ArcSin[a + b*x]^2)/4","A",19,8,12,0.6667,1,"{4805, 4743, 4763, 4641, 4677, 8, 4707, 30}"
132,1,220,0,0.39453,"\int x^2 \sin ^{-1}(a+b x)^2 \, dx","Int[x^2*ArcSin[a + b*x]^2,x]","-\frac{2 a^2 x}{b^2}+\frac{a^3 \sin ^{-1}(a+b x)^2}{3 b^3}+\frac{2 a^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^3}+\frac{a (a+b x)^2}{2 b^3}-\frac{2 (a+b x)^3}{27 b^3}+\frac{a \sin ^{-1}(a+b x)^2}{2 b^3}-\frac{a (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^3}+\frac{2 (a+b x)^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{9 b^3}+\frac{4 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{9 b^3}+\frac{1}{3} x^3 \sin ^{-1}(a+b x)^2-\frac{4 x}{9 b^2}","-\frac{2 a^2 x}{b^2}+\frac{a^3 \sin ^{-1}(a+b x)^2}{3 b^3}+\frac{2 a^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^3}+\frac{a (a+b x)^2}{2 b^3}-\frac{2 (a+b x)^3}{27 b^3}+\frac{a \sin ^{-1}(a+b x)^2}{2 b^3}-\frac{a (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^3}+\frac{2 (a+b x)^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{9 b^3}+\frac{4 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{9 b^3}+\frac{1}{3} x^3 \sin ^{-1}(a+b x)^2-\frac{4 x}{9 b^2}",1,"(-4*x)/(9*b^2) - (2*a^2*x)/b^2 + (a*(a + b*x)^2)/(2*b^3) - (2*(a + b*x)^3)/(27*b^3) + (4*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(9*b^3) + (2*a^2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/b^3 - (a*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/b^3 + (2*(a + b*x)^2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(9*b^3) + (a*ArcSin[a + b*x]^2)/(2*b^3) + (a^3*ArcSin[a + b*x]^2)/(3*b^3) + (x^3*ArcSin[a + b*x]^2)/3","A",14,8,12,0.6667,1,"{4805, 4743, 4763, 4641, 4677, 8, 4707, 30}"
133,1,130,0,0.2486994,"\int x \sin ^{-1}(a+b x)^2 \, dx","Int[x*ArcSin[a + b*x]^2,x]","-\frac{a^2 \sin ^{-1}(a+b x)^2}{2 b^2}-\frac{(a+b x)^2}{4 b^2}+\frac{\sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{2 b^2}-\frac{\sin ^{-1}(a+b x)^2}{4 b^2}-\frac{2 a \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \sin ^{-1}(a+b x)^2+\frac{2 a x}{b}","-\frac{a^2 \sin ^{-1}(a+b x)^2}{2 b^2}-\frac{(a+b x)^2}{4 b^2}+\frac{\sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{2 b^2}-\frac{\sin ^{-1}(a+b x)^2}{4 b^2}-\frac{2 a \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \sin ^{-1}(a+b x)^2+\frac{2 a x}{b}",1,"(2*a*x)/b - (a + b*x)^2/(4*b^2) - (2*a*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/b^2 + ((a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(2*b^2) - ArcSin[a + b*x]^2/(4*b^2) - (a^2*ArcSin[a + b*x]^2)/(2*b^2) + (x^2*ArcSin[a + b*x]^2)/2","A",10,8,10,0.8000,1,"{4805, 4743, 4763, 4641, 4677, 8, 4707, 30}"
134,1,47,0,0.0553923,"\int \sin ^{-1}(a+b x)^2 \, dx","Int[ArcSin[a + b*x]^2,x]","\frac{(a+b x) \sin ^{-1}(a+b x)^2}{b}+\frac{2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b}-2 x","\frac{(a+b x) \sin ^{-1}(a+b x)^2}{b}+\frac{2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{b}-2 x",1,"-2*x + (2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/b + ((a + b*x)*ArcSin[a + b*x]^2)/b","A",4,4,8,0.5000,1,"{4803, 4619, 4677, 8}"
135,1,271,0,0.4100254,"\int \frac{\sin ^{-1}(a+b x)^2}{x} \, dx","Int[ArcSin[a + b*x]^2/x,x]","-2 i \sin ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)-2 i \sin ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+2 \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+2 \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^2 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^2 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)-\frac{1}{3} i \sin ^{-1}(a+b x)^3","-2 i \sin ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)-2 i \sin ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+2 \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+2 \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^2 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^2 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)-\frac{1}{3} i \sin ^{-1}(a+b x)^3",1,"(-I/3)*ArcSin[a + b*x]^3 + ArcSin[a + b*x]^2*Log[1 - E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] + ArcSin[a + b*x]^2*Log[1 - E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])] - (2*I)*ArcSin[a + b*x]*PolyLog[2, E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] - (2*I)*ArcSin[a + b*x]*PolyLog[2, E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])] + 2*PolyLog[3, E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] + 2*PolyLog[3, E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])]","A",11,7,12,0.5833,1,"{4805, 4741, 4521, 2190, 2531, 2282, 6589}"
136,1,208,0,0.4466279,"\int \frac{\sin ^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcSin[a + b*x]^2/x^2,x]","\frac{2 b \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{2 b \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}+\frac{2 i b \sin ^{-1}(a+b x) \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{2 i b \sin ^{-1}(a+b x) \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}-\frac{\sin ^{-1}(a+b x)^2}{x}","\frac{2 i b \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)}{\sqrt{1-a^2}}-\frac{2 i b \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)}{\sqrt{1-a^2}}-\frac{2 b \sin ^{-1}(a+b x) \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)}{\sqrt{1-a^2}}+\frac{2 b \sin ^{-1}(a+b x) \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)}{\sqrt{1-a^2}}-\frac{\sin ^{-1}(a+b x)^2}{x}",1,"-(ArcSin[a + b*x]^2/x) + ((2*I)*b*ArcSin[a + b*x]*Log[1 + (I*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] - ((2*I)*b*ArcSin[a + b*x]*Log[1 + (I*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] + (2*b*PolyLog[2, ((-I)*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] - (2*b*PolyLog[2, ((-I)*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/Sqrt[-1 + a^2]","A",11,8,12,0.6667,0,"{4805, 4743, 4773, 3323, 2264, 2190, 2279, 2391}"
137,1,272,0,0.5854084,"\int \frac{\sin ^{-1}(a+b x)^2}{x^3} \, dx","Int[ArcSin[a + b*x]^2/x^3,x]","-\frac{a b^2 \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\left(a^2-1\right)^{3/2}}+\frac{a b^2 \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\left(a^2-1\right)^{3/2}}+\frac{b^2 \log (x)}{1-a^2}-\frac{i a b^2 \sin ^{-1}(a+b x) \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\left(a^2-1\right)^{3/2}}+\frac{i a b^2 \sin ^{-1}(a+b x) \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\left(a^2-1\right)^{3/2}}-\frac{b \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{\left(1-a^2\right) x}-\frac{\sin ^{-1}(a+b x)^2}{2 x^2}","-\frac{a b^2 \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\left(a^2-1\right)^{3/2}}+\frac{a b^2 \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\left(a^2-1\right)^{3/2}}+\frac{b^2 \log (x)}{1-a^2}-\frac{i a b^2 \sin ^{-1}(a+b x) \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\left(a^2-1\right)^{3/2}}+\frac{i a b^2 \sin ^{-1}(a+b x) \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\left(a^2-1\right)^{3/2}}-\frac{b \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{\left(1-a^2\right) x}-\frac{\sin ^{-1}(a+b x)^2}{2 x^2}",1,"-((b*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/((1 - a^2)*x)) - ArcSin[a + b*x]^2/(2*x^2) - (I*a*b^2*ArcSin[a + b*x]*Log[1 + (I*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/(-1 + a^2)^(3/2) + (I*a*b^2*ArcSin[a + b*x]*Log[1 + (I*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/(-1 + a^2)^(3/2) + (b^2*Log[x])/(1 - a^2) - (a*b^2*PolyLog[2, ((-I)*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/(-1 + a^2)^(3/2) + (a*b^2*PolyLog[2, ((-I)*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/(-1 + a^2)^(3/2)","A",14,11,12,0.9167,1,"{4805, 4743, 4773, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
138,1,371,0,0.4508596,"\int x^2 \sin ^{-1}(a+b x)^3 \, dx","Int[x^2*ArcSin[a + b*x]^3,x]","-\frac{6 a^2 \sqrt{1-(a+b x)^2}}{b^3}-\frac{6 a^2 (a+b x) \sin ^{-1}(a+b x)}{b^3}+\frac{a^3 \sin ^{-1}(a+b x)^3}{3 b^3}+\frac{3 a^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{b^3}+\frac{3 a \sqrt{1-(a+b x)^2} (a+b x)}{4 b^3}+\frac{2 \left(1-(a+b x)^2\right)^{3/2}}{27 b^3}-\frac{14 \sqrt{1-(a+b x)^2}}{9 b^3}-\frac{2 (a+b x)^3 \sin ^{-1}(a+b x)}{9 b^3}+\frac{\sqrt{1-(a+b x)^2} (a+b x)^2 \sin ^{-1}(a+b x)^2}{3 b^3}+\frac{3 a (a+b x)^2 \sin ^{-1}(a+b x)}{2 b^3}-\frac{3 a \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)^2}{2 b^3}-\frac{4 (a+b x) \sin ^{-1}(a+b x)}{3 b^3}+\frac{a \sin ^{-1}(a+b x)^3}{2 b^3}+\frac{2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{3 b^3}-\frac{3 a \sin ^{-1}(a+b x)}{4 b^3}+\frac{1}{3} x^3 \sin ^{-1}(a+b x)^3","-\frac{6 a^2 \sqrt{1-(a+b x)^2}}{b^3}-\frac{6 a^2 (a+b x) \sin ^{-1}(a+b x)}{b^3}+\frac{a^3 \sin ^{-1}(a+b x)^3}{3 b^3}+\frac{3 a^2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{b^3}+\frac{3 a \sqrt{1-(a+b x)^2} (a+b x)}{4 b^3}+\frac{2 \left(1-(a+b x)^2\right)^{3/2}}{27 b^3}-\frac{14 \sqrt{1-(a+b x)^2}}{9 b^3}-\frac{2 (a+b x)^3 \sin ^{-1}(a+b x)}{9 b^3}+\frac{\sqrt{1-(a+b x)^2} (a+b x)^2 \sin ^{-1}(a+b x)^2}{3 b^3}+\frac{3 a (a+b x)^2 \sin ^{-1}(a+b x)}{2 b^3}-\frac{3 a \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)^2}{2 b^3}-\frac{4 (a+b x) \sin ^{-1}(a+b x)}{3 b^3}+\frac{a \sin ^{-1}(a+b x)^3}{2 b^3}+\frac{2 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{3 b^3}-\frac{3 a \sin ^{-1}(a+b x)}{4 b^3}+\frac{1}{3} x^3 \sin ^{-1}(a+b x)^3",1,"(-14*Sqrt[1 - (a + b*x)^2])/(9*b^3) - (6*a^2*Sqrt[1 - (a + b*x)^2])/b^3 + (3*a*(a + b*x)*Sqrt[1 - (a + b*x)^2])/(4*b^3) + (2*(1 - (a + b*x)^2)^(3/2))/(27*b^3) - (3*a*ArcSin[a + b*x])/(4*b^3) - (4*(a + b*x)*ArcSin[a + b*x])/(3*b^3) - (6*a^2*(a + b*x)*ArcSin[a + b*x])/b^3 + (3*a*(a + b*x)^2*ArcSin[a + b*x])/(2*b^3) - (2*(a + b*x)^3*ArcSin[a + b*x])/(9*b^3) + (2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(3*b^3) + (3*a^2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/b^3 - (3*a*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(2*b^3) + ((a + b*x)^2*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(3*b^3) + (a*ArcSin[a + b*x]^3)/(2*b^3) + (a^3*ArcSin[a + b*x]^3)/(3*b^3) + (x^3*ArcSin[a + b*x]^3)/3","A",18,11,12,0.9167,1,"{4805, 4743, 4773, 3317, 3296, 2638, 3311, 30, 2635, 8, 2633}"
139,1,211,0,0.3088783,"\int x \sin ^{-1}(a+b x)^3 \, dx","Int[x*ArcSin[a + b*x]^3,x]","-\frac{a^2 \sin ^{-1}(a+b x)^3}{2 b^2}-\frac{3 (a+b x) \sqrt{1-(a+b x)^2}}{8 b^2}+\frac{6 a \sqrt{1-(a+b x)^2}}{b^2}-\frac{\sin ^{-1}(a+b x)^3}{4 b^2}+\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{4 b^2}-\frac{3 a \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{b^2}-\frac{3 (a+b x)^2 \sin ^{-1}(a+b x)}{4 b^2}+\frac{6 a (a+b x) \sin ^{-1}(a+b x)}{b^2}+\frac{3 \sin ^{-1}(a+b x)}{8 b^2}+\frac{1}{2} x^2 \sin ^{-1}(a+b x)^3","-\frac{a^2 \sin ^{-1}(a+b x)^3}{2 b^2}-\frac{3 (a+b x) \sqrt{1-(a+b x)^2}}{8 b^2}+\frac{6 a \sqrt{1-(a+b x)^2}}{b^2}-\frac{\sin ^{-1}(a+b x)^3}{4 b^2}+\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{4 b^2}-\frac{3 a \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{b^2}-\frac{3 (a+b x)^2 \sin ^{-1}(a+b x)}{4 b^2}+\frac{6 a (a+b x) \sin ^{-1}(a+b x)}{b^2}+\frac{3 \sin ^{-1}(a+b x)}{8 b^2}+\frac{1}{2} x^2 \sin ^{-1}(a+b x)^3",1,"(6*a*Sqrt[1 - (a + b*x)^2])/b^2 - (3*(a + b*x)*Sqrt[1 - (a + b*x)^2])/(8*b^2) + (3*ArcSin[a + b*x])/(8*b^2) + (6*a*(a + b*x)*ArcSin[a + b*x])/b^2 - (3*(a + b*x)^2*ArcSin[a + b*x])/(4*b^2) - (3*a*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/b^2 + (3*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(4*b^2) - ArcSin[a + b*x]^3/(4*b^2) - (a^2*ArcSin[a + b*x]^3)/(2*b^2) + (x^2*ArcSin[a + b*x]^3)/2","A",12,10,10,1.000,1,"{4805, 4743, 4773, 3317, 3296, 2638, 3311, 30, 2635, 8}"
140,1,82,0,0.081184,"\int \sin ^{-1}(a+b x)^3 \, dx","Int[ArcSin[a + b*x]^3,x]","-\frac{6 \sqrt{1-(a+b x)^2}}{b}+\frac{(a+b x) \sin ^{-1}(a+b x)^3}{b}+\frac{3 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{b}-\frac{6 (a+b x) \sin ^{-1}(a+b x)}{b}","-\frac{6 \sqrt{1-(a+b x)^2}}{b}+\frac{(a+b x) \sin ^{-1}(a+b x)^3}{b}+\frac{3 \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{b}-\frac{6 (a+b x) \sin ^{-1}(a+b x)}{b}",1,"(-6*Sqrt[1 - (a + b*x)^2])/b - (6*(a + b*x)*ArcSin[a + b*x])/b + (3*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/b + ((a + b*x)*ArcSin[a + b*x]^3)/b","A",5,4,8,0.5000,1,"{4803, 4619, 4677, 261}"
141,1,365,0,0.4505444,"\int \frac{\sin ^{-1}(a+b x)^3}{x} \, dx","Int[ArcSin[a + b*x]^3/x,x]","-3 i \sin ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)-3 i \sin ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+6 \sin ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+6 \sin ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+6 i \text{PolyLog}\left(4,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+6 i \text{PolyLog}\left(4,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^3 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^3 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)-\frac{1}{4} i \sin ^{-1}(a+b x)^4","-3 i \sin ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)-3 i \sin ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+6 \sin ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+6 \sin ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+6 i \text{PolyLog}\left(4,\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+6 i \text{PolyLog}\left(4,\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^3 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{-\sqrt{1-a^2}+i a}\right)+\sin ^{-1}(a+b x)^3 \log \left(1-\frac{e^{i \sin ^{-1}(a+b x)}}{\sqrt{1-a^2}+i a}\right)-\frac{1}{4} i \sin ^{-1}(a+b x)^4",1,"(-I/4)*ArcSin[a + b*x]^4 + ArcSin[a + b*x]^3*Log[1 - E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] + ArcSin[a + b*x]^3*Log[1 - E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])] - (3*I)*ArcSin[a + b*x]^2*PolyLog[2, E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] - (3*I)*ArcSin[a + b*x]^2*PolyLog[2, E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])] + 6*ArcSin[a + b*x]*PolyLog[3, E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] + 6*ArcSin[a + b*x]*PolyLog[3, E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])] + (6*I)*PolyLog[4, E^(I*ArcSin[a + b*x])/(I*a - Sqrt[1 - a^2])] + (6*I)*PolyLog[4, E^(I*ArcSin[a + b*x])/(I*a + Sqrt[1 - a^2])]","A",13,8,12,0.6667,1,"{4805, 4741, 4521, 2190, 2531, 6609, 2282, 6589}"
142,1,316,0,0.6337765,"\int \frac{\sin ^{-1}(a+b x)^3}{x^2} \, dx","Int[ArcSin[a + b*x]^3/x^2,x]","\frac{6 b \sin ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{6 b \sin ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}+\frac{6 i b \text{PolyLog}\left(3,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{6 i b \text{PolyLog}\left(3,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}+\frac{3 i b \sin ^{-1}(a+b x)^2 \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{3 i b \sin ^{-1}(a+b x)^2 \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}-\frac{\sin ^{-1}(a+b x)^3}{x}","\frac{6 b \sin ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{6 b \sin ^{-1}(a+b x) \text{PolyLog}\left(2,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}+\frac{6 i b \text{PolyLog}\left(3,-\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{6 i b \text{PolyLog}\left(3,-\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}+\frac{3 i b \sin ^{-1}(a+b x)^2 \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}-\frac{3 i b \sin ^{-1}(a+b x)^2 \log \left(1+\frac{i e^{i \sin ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)}{\sqrt{a^2-1}}-\frac{\sin ^{-1}(a+b x)^3}{x}",1,"-(ArcSin[a + b*x]^3/x) + ((3*I)*b*ArcSin[a + b*x]^2*Log[1 + (I*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] - ((3*I)*b*ArcSin[a + b*x]^2*Log[1 + (I*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] + (6*b*ArcSin[a + b*x]*PolyLog[2, ((-I)*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] - (6*b*ArcSin[a + b*x]*PolyLog[2, ((-I)*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] + ((6*I)*b*PolyLog[3, ((-I)*E^(I*ArcSin[a + b*x]))/(a - Sqrt[-1 + a^2])])/Sqrt[-1 + a^2] - ((6*I)*b*PolyLog[3, ((-I)*E^(I*ArcSin[a + b*x]))/(a + Sqrt[-1 + a^2])])/Sqrt[-1 + a^2]","A",13,9,12,0.7500,1,"{4805, 4743, 4773, 3323, 2264, 2190, 2531, 2282, 6589}"
143,1,60,0,0.611634,"\int \frac{x^2}{\sin ^{-1}(a+b x)} \, dx","Int[x^2/ArcSin[a + b*x],x]","\frac{a^2 \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{b^3}+\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{\text{CosIntegral}\left(3 \sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{a \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b^3}","\frac{a^2 \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{b^3}+\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{\text{CosIntegral}\left(3 \sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{a \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b^3}",1,"CosIntegral[ArcSin[a + b*x]]/(4*b^3) + (a^2*CosIntegral[ArcSin[a + b*x]])/b^3 - CosIntegral[3*ArcSin[a + b*x]]/(4*b^3) - (a*SinIntegral[2*ArcSin[a + b*x]])/b^3","A",14,8,12,0.6667,1,"{4805, 4747, 6741, 12, 6742, 3302, 4406, 3299}"
144,1,30,0,0.2205115,"\int \frac{x}{\sin ^{-1}(a+b x)} \, dx","Int[x/ArcSin[a + b*x],x]","\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{2 b^2}-\frac{a \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{b^2}","\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{2 b^2}-\frac{a \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{b^2}",1,"-((a*CosIntegral[ArcSin[a + b*x]])/b^2) + SinIntegral[2*ArcSin[a + b*x]]/(2*b^2)","A",10,8,10,0.8000,1,"{4805, 4747, 6741, 12, 6742, 3302, 4406, 3299}"
145,1,11,0,0.0222556,"\int \frac{1}{\sin ^{-1}(a+b x)} \, dx","Int[ArcSin[a + b*x]^(-1),x]","\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{b}","\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{b}",1,"CosIntegral[ArcSin[a + b*x]]/b","A",3,3,8,0.3750,1,"{4803, 4623, 3302}"
146,0,0,0,0.0427649,"\int \frac{1}{x \sin ^{-1}(a+b x)} \, dx","Int[1/(x*ArcSin[a + b*x]),x]","\int \frac{1}{x \sin ^{-1}(a+b x)} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a+b x)},x\right)",0,"Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSin[x]), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
147,1,161,0,0.2277172,"\int \frac{x^2}{\sin ^{-1}(a+b x)^2} \, dx","Int[x^2/ArcSin[a + b*x]^2,x]","-\frac{a^2 \text{Si}\left(\sin ^{-1}(a+b x)\right)}{b^3}-\frac{a^2 \sqrt{1-(a+b x)^2}}{b^3 \sin ^{-1}(a+b x)}-\frac{2 a \text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b^3}-\frac{\text{Si}\left(\sin ^{-1}(a+b x)\right)}{4 b^3}+\frac{3 \text{Si}\left(3 \sin ^{-1}(a+b x)\right)}{4 b^3}+\frac{2 a (a+b x) \sqrt{1-(a+b x)^2}}{b^3 \sin ^{-1}(a+b x)}-\frac{(a+b x)^2 \sqrt{1-(a+b x)^2}}{b^3 \sin ^{-1}(a+b x)}","-\frac{\left(4 a^2+1\right) \text{Si}\left(\sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{2 a \text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b^3}+\frac{3 \text{Si}\left(3 \sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{x^2 \sqrt{1-(a+b x)^2}}{b \sin ^{-1}(a+b x)}",1,"-((a^2*Sqrt[1 - (a + b*x)^2])/(b^3*ArcSin[a + b*x])) + (2*a*(a + b*x)*Sqrt[1 - (a + b*x)^2])/(b^3*ArcSin[a + b*x]) - ((a + b*x)^2*Sqrt[1 - (a + b*x)^2])/(b^3*ArcSin[a + b*x]) - (2*a*CosIntegral[2*ArcSin[a + b*x]])/b^3 - SinIntegral[ArcSin[a + b*x]]/(4*b^3) - (a^2*SinIntegral[ArcSin[a + b*x]])/b^3 + (3*SinIntegral[3*ArcSin[a + b*x]])/(4*b^3)","A",12,7,12,0.5833,1,"{4805, 4745, 4621, 4723, 3299, 4631, 3302}"
148,1,87,0,0.1400558,"\int \frac{x}{\sin ^{-1}(a+b x)^2} \, dx","Int[x/ArcSin[a + b*x]^2,x]","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b^2}+\frac{a \text{Si}\left(\sin ^{-1}(a+b x)\right)}{b^2}+\frac{a \sqrt{1-(a+b x)^2}}{b^2 \sin ^{-1}(a+b x)}-\frac{(a+b x) \sqrt{1-(a+b x)^2}}{b^2 \sin ^{-1}(a+b x)}","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b^2}+\frac{a \text{Si}\left(\sin ^{-1}(a+b x)\right)}{b^2}-\frac{x \sqrt{1-(a+b x)^2}}{b \sin ^{-1}(a+b x)}",1,"(a*Sqrt[1 - (a + b*x)^2])/(b^2*ArcSin[a + b*x]) - ((a + b*x)*Sqrt[1 - (a + b*x)^2])/(b^2*ArcSin[a + b*x]) + CosIntegral[2*ArcSin[a + b*x]]/b^2 + (a*SinIntegral[ArcSin[a + b*x]])/b^2","A",8,7,10,0.7000,1,"{4805, 4745, 4621, 4723, 3299, 4631, 3302}"
149,1,41,0,0.0789604,"\int \frac{1}{\sin ^{-1}(a+b x)^2} \, dx","Int[ArcSin[a + b*x]^(-2),x]","-\frac{\text{Si}\left(\sin ^{-1}(a+b x)\right)}{b}-\frac{\sqrt{1-(a+b x)^2}}{b \sin ^{-1}(a+b x)}","-\frac{\text{Si}\left(\sin ^{-1}(a+b x)\right)}{b}-\frac{\sqrt{1-(a+b x)^2}}{b \sin ^{-1}(a+b x)}",1,"-(Sqrt[1 - (a + b*x)^2]/(b*ArcSin[a + b*x])) - SinIntegral[ArcSin[a + b*x]]/b","A",4,4,8,0.5000,1,"{4803, 4621, 4723, 3299}"
150,0,0,0,0.0370135,"\int \frac{1}{x \sin ^{-1}(a+b x)^2} \, dx","Int[1/(x*ArcSin[a + b*x]^2),x]","\int \frac{1}{x \sin ^{-1}(a+b x)^2} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a+b x)^2},x\right)",0,"Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSin[x]^2), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
151,1,263,0,0.5065117,"\int \frac{x^2}{\sin ^{-1}(a+b x)^3} \, dx","Int[x^2/ArcSin[a + b*x]^3,x]","-\frac{a^2 \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{2 b^3}+\frac{a^2 (a+b x)}{2 b^3 \sin ^{-1}(a+b x)}-\frac{a^2 \sqrt{1-(a+b x)^2}}{2 b^3 \sin ^{-1}(a+b x)^2}-\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{8 b^3}+\frac{9 \text{CosIntegral}\left(3 \sin ^{-1}(a+b x)\right)}{8 b^3}+\frac{2 a \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b^3}+\frac{3 (a+b x)^3}{2 b^3 \sin ^{-1}(a+b x)}-\frac{2 a (a+b x)^2}{b^3 \sin ^{-1}(a+b x)}-\frac{\sqrt{1-(a+b x)^2} (a+b x)^2}{2 b^3 \sin ^{-1}(a+b x)^2}-\frac{a+b x}{b^3 \sin ^{-1}(a+b x)}+\frac{a \sqrt{1-(a+b x)^2} (a+b x)}{b^3 \sin ^{-1}(a+b x)^2}+\frac{a}{b^3 \sin ^{-1}(a+b x)}","-\frac{\left(4 a^2+1\right) \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{8 b^3}+\frac{a^2 (a+b x)}{2 b^3 \sin ^{-1}(a+b x)}+\frac{9 \text{CosIntegral}\left(3 \sin ^{-1}(a+b x)\right)}{8 b^3}+\frac{2 a \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b^3}-\frac{2 a (a+b x)^2}{b^3 \sin ^{-1}(a+b x)}-\frac{3 \sin \left(3 \sin ^{-1}(a+b x)\right)}{8 b^3 \sin ^{-1}(a+b x)}+\frac{9 a+b x}{8 b^3 \sin ^{-1}(a+b x)}-\frac{x^2 \sqrt{1-(a+b x)^2}}{2 b \sin ^{-1}(a+b x)^2}",1,"-(a^2*Sqrt[1 - (a + b*x)^2])/(2*b^3*ArcSin[a + b*x]^2) + (a*(a + b*x)*Sqrt[1 - (a + b*x)^2])/(b^3*ArcSin[a + b*x]^2) - ((a + b*x)^2*Sqrt[1 - (a + b*x)^2])/(2*b^3*ArcSin[a + b*x]^2) + a/(b^3*ArcSin[a + b*x]) - (a + b*x)/(b^3*ArcSin[a + b*x]) + (a^2*(a + b*x))/(2*b^3*ArcSin[a + b*x]) - (2*a*(a + b*x)^2)/(b^3*ArcSin[a + b*x]) + (3*(a + b*x)^3)/(2*b^3*ArcSin[a + b*x]) - CosIntegral[ArcSin[a + b*x]]/(8*b^3) - (a^2*CosIntegral[ArcSin[a + b*x]])/(2*b^3) + (9*CosIntegral[3*ArcSin[a + b*x]])/(8*b^3) + (2*a*SinIntegral[2*ArcSin[a + b*x]])/b^3","A",24,12,12,1.000,1,"{4805, 4745, 4621, 4719, 4623, 3302, 4633, 4635, 4406, 12, 3299, 4641}"
152,1,151,0,0.2694256,"\int \frac{x}{\sin ^{-1}(a+b x)^3} \, dx","Int[x/ArcSin[a + b*x]^3,x]","\frac{a \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{2 b^2}-\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b^2}+\frac{(a+b x)^2}{b^2 \sin ^{-1}(a+b x)}-\frac{a (a+b x)}{2 b^2 \sin ^{-1}(a+b x)}-\frac{\sqrt{1-(a+b x)^2} (a+b x)}{2 b^2 \sin ^{-1}(a+b x)^2}-\frac{1}{2 b^2 \sin ^{-1}(a+b x)}+\frac{a \sqrt{1-(a+b x)^2}}{2 b^2 \sin ^{-1}(a+b x)^2}","\frac{a \text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{2 b^2}-\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b^2}-\frac{a (a+b x)}{2 b^2 \sin ^{-1}(a+b x)}-\frac{1-2 (a+b x)^2}{2 b^2 \sin ^{-1}(a+b x)}-\frac{x \sqrt{1-(a+b x)^2}}{2 b \sin ^{-1}(a+b x)^2}",1,"(a*Sqrt[1 - (a + b*x)^2])/(2*b^2*ArcSin[a + b*x]^2) - ((a + b*x)*Sqrt[1 - (a + b*x)^2])/(2*b^2*ArcSin[a + b*x]^2) - 1/(2*b^2*ArcSin[a + b*x]) - (a*(a + b*x))/(2*b^2*ArcSin[a + b*x]) + (a + b*x)^2/(b^2*ArcSin[a + b*x]) + (a*CosIntegral[ArcSin[a + b*x]])/(2*b^2) - SinIntegral[2*ArcSin[a + b*x]]/b^2","A",14,12,10,1.200,1,"{4805, 4745, 4621, 4719, 4623, 3302, 4633, 4635, 4406, 12, 3299, 4641}"
153,1,65,0,0.0855354,"\int \frac{1}{\sin ^{-1}(a+b x)^3} \, dx","Int[ArcSin[a + b*x]^(-3),x]","-\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{2 b}+\frac{a+b x}{2 b \sin ^{-1}(a+b x)}-\frac{\sqrt{1-(a+b x)^2}}{2 b \sin ^{-1}(a+b x)^2}","-\frac{\text{CosIntegral}\left(\sin ^{-1}(a+b x)\right)}{2 b}+\frac{a+b x}{2 b \sin ^{-1}(a+b x)}-\frac{\sqrt{1-(a+b x)^2}}{2 b \sin ^{-1}(a+b x)^2}",1,"-Sqrt[1 - (a + b*x)^2]/(2*b*ArcSin[a + b*x]^2) + (a + b*x)/(2*b*ArcSin[a + b*x]) - CosIntegral[ArcSin[a + b*x]]/(2*b)","A",5,5,8,0.6250,1,"{4803, 4621, 4719, 4623, 3302}"
154,0,0,0,0.038641,"\int \frac{1}{x \sin ^{-1}(a+b x)^3} \, dx","Int[1/(x*ArcSin[a + b*x]^3),x]","\int \frac{1}{x \sin ^{-1}(a+b x)^3} \, dx","\text{Int}\left(\frac{1}{x \sin ^{-1}(a+b x)^3},x\right)",0,"Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSin[x]^3), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
155,1,535,0,2.2334632,"\int x^2 \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[x^2*Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^3}+\frac{c^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d^3}+\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+d x)}}{\sqrt{b}}\right)}{4 d^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+d x)}}{\sqrt{b}}\right)}{12 d^3}-\frac{\sqrt{\pi } \sqrt{b} c \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{4 d^3}-\frac{\sqrt{\pi } \sqrt{b} c \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{4 d^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+d x)}}{\sqrt{b}}\right)}{4 d^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+d x)}}{\sqrt{b}}\right)}{12 d^3}+\frac{(c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{3 d^3}+\frac{c \cos \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d^3}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^3}+\frac{c^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d^3}+\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+d x)}}{\sqrt{b}}\right)}{4 d^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+d x)}}{\sqrt{b}}\right)}{12 d^3}-\frac{\sqrt{\pi } \sqrt{b} c \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{4 d^3}-\frac{\sqrt{\pi } \sqrt{b} c \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{4 d^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+d x)}}{\sqrt{b}}\right)}{4 d^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+d x)}}{\sqrt{b}}\right)}{12 d^3}+\frac{(c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{3 d^3}+\frac{c \cos \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d^3}",1,"(c^2*(c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/d^3 + ((c + d*x)^3*Sqrt[a + b*ArcSin[c + d*x]])/(3*d^3) + (c*Sqrt[a + b*ArcSin[c + d*x]]*Cos[2*ArcSin[c + d*x]])/(2*d^3) - (Sqrt[b]*c*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(4*d^3) - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*d^3) - (Sqrt[b]*c^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/d^3 + (Sqrt[b]*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(12*d^3) + (Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(4*d^3) + (Sqrt[b]*c^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/d^3 - (Sqrt[b]*c*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(4*d^3) - (Sqrt[b]*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(12*d^3)","A",23,12,18,0.6667,1,"{4805, 4747, 6741, 6742, 3386, 3353, 3352, 3351, 3385, 3354, 3443, 3357}"
156,1,269,0,0.7697597,"\int x \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[x*Sqrt[a + b*ArcSin[c + d*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^2}+\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 d^2}+\frac{\sqrt{\pi } \sqrt{b} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 d^2}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^2}-\frac{c (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d^2}-\frac{\cos \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d^2}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^2}+\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 d^2}+\frac{\sqrt{\pi } \sqrt{b} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 d^2}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{d^2}-\frac{c (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d^2}-\frac{\cos \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d^2}",1,"-((c*(c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/d^2) - (Sqrt[a + b*ArcSin[c + d*x]]*Cos[2*ArcSin[c + d*x]])/(4*d^2) + (Sqrt[b]*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(8*d^2) + (Sqrt[b]*c*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/d^2 - (Sqrt[b]*c*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/d^2 + (Sqrt[b]*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(8*d^2)","A",14,10,16,0.6250,1,"{4805, 4747, 6741, 6742, 3386, 3353, 3352, 3351, 3385, 3354}"
157,1,133,0,0.295289,"\int \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[Sqrt[a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{d}-\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+d x)}}{\sqrt{b}}\right)}{d}+\frac{(c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d}","\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+d x)}}{\sqrt{b}}\right)}{d}-\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+d x)}}{\sqrt{b}}\right)}{d}+\frac{(c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d}",1,"((c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/d - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/d + (Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/d","A",8,8,14,0.5714,1,"{4803, 4619, 4723, 3306, 3305, 3351, 3304, 3352}"
158,1,343,0,1.04347,"\int x \left(a+b \sin ^{-1}(c+d x)\right)^{3/2} \, dx","Int[x*(a + b*ArcSin[c + d*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+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{32 d^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} c \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 d^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} c \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 d^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+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 d^2}+\frac{3 b \sin \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{16 d^2}-\frac{3 b c \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d^2}-\frac{c (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{d^2}-\frac{\cos \left(2 \sin ^{-1}(c+d x)\right) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d^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+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{32 d^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} c \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 d^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} c \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 d^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+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 d^2}+\frac{3 b \sin \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{16 d^2}-\frac{3 b c \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d^2}-\frac{c (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{d^2}-\frac{\cos \left(2 \sin ^{-1}(c+d x)\right) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d^2}",1,"(-3*b*c*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(2*d^2) - (c*(c + d*x)*(a + b*ArcSin[c + d*x])^(3/2))/d^2 - ((a + b*ArcSin[c + d*x])^(3/2)*Cos[2*ArcSin[c + d*x]])/(4*d^2) + (3*b^(3/2)*c*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*d^2) - (3*b^(3/2)*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(32*d^2) + (3*b^(3/2)*c*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(2*d^2) + (3*b^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(32*d^2) + (3*b*Sqrt[a + b*ArcSin[c + d*x]]*Sin[2*ArcSin[c + d*x]])/(16*d^2)","A",16,10,16,0.6250,1,"{4805, 4747, 6741, 6742, 3386, 3385, 3354, 3352, 3351, 3353}"
159,1,175,0,0.2709415,"\int \left(a+b \sin ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{2 d}-\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+d x)}}{\sqrt{b}}\right)}{2 d}+\frac{3 b \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{d}","-\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+d x)}}{\sqrt{b}}\right)}{2 d}-\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+d x)}}{\sqrt{b}}\right)}{2 d}+\frac{3 b \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{d}",1,"(3*b*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(2*d) + ((c + d*x)*(a + b*ArcSin[c + d*x])^(3/2))/d - (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*d) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(2*d)","A",9,9,14,0.6429,1,"{4803, 4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352}"
160,1,406,0,1.1702869,"\int x \left(a+b \sin ^{-1}(c+d x)\right)^{5/2} \, dx","Int[x*(a + b*ArcSin[c + d*x])^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^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+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{128 d^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+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 d^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^2}+\frac{15 b^2 c (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d^2}+\frac{15 b^2 \cos \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{64 d^2}-\frac{5 b c \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d^2}+\frac{5 b \sin \left(2 \sin ^{-1}(c+d x)\right) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{16 d^2}-\frac{c (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{d^2}-\frac{\cos \left(2 \sin ^{-1}(c+d x)\right) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{4 d^2}","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^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+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{128 d^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+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 d^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^2}+\frac{15 b^2 c (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d^2}+\frac{15 b^2 \cos \left(2 \sin ^{-1}(c+d x)\right) \sqrt{a+b \sin ^{-1}(c+d x)}}{64 d^2}-\frac{5 b c \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d^2}+\frac{5 b \sin \left(2 \sin ^{-1}(c+d x)\right) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{16 d^2}-\frac{c (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{d^2}-\frac{\cos \left(2 \sin ^{-1}(c+d x)\right) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{4 d^2}",1,"(15*b^2*c*(c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/(4*d^2) - (5*b*c*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(2*d^2) - (c*(c + d*x)*(a + b*ArcSin[c + d*x])^(5/2))/d^2 + (15*b^2*Sqrt[a + b*ArcSin[c + d*x]]*Cos[2*ArcSin[c + d*x]])/(64*d^2) - ((a + b*ArcSin[c + d*x])^(5/2)*Cos[2*ArcSin[c + d*x]])/(4*d^2) - (15*b^(5/2)*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(128*d^2) - (15*b^(5/2)*c*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*d^2) + (15*b^(5/2)*c*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(4*d^2) - (15*b^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(128*d^2) + (5*b*(a + b*ArcSin[c + d*x])^(3/2)*Sin[2*ArcSin[c + d*x]])/(16*d^2)","A",18,10,16,0.6250,1,"{4805, 4747, 6741, 6742, 3386, 3385, 3353, 3352, 3351, 3354}"
161,1,204,0,0.4217904,"\int \left(a+b \sin ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{4 d}+\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+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{15 b^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}+\frac{5 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{d}","-\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+d x)}}{\sqrt{b}}\right)}{4 d}+\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+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{15 b^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}+\frac{5 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{d}",1,"(-15*b^2*(c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/(4*d) + (5*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(2*d) + ((c + d*x)*(a + b*ArcSin[c + d*x])^(5/2))/d + (15*b^(5/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*d) - (15*b^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(4*d)","A",10,9,14,0.6429,1,"{4803, 4619, 4677, 4723, 3306, 3305, 3351, 3304, 3352}"
162,1,243,0,0.4424707,"\int \left(a+b \sin ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(a + b*ArcSin[c + d*x])^(7/2),x]","\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{105 b^3 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{8 d}-\frac{35 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}+\frac{7 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{d}","\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{105 b^3 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{8 d}-\frac{35 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}+\frac{7 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{d}",1,"(-105*b^3*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(8*d) - (35*b^2*(c + d*x)*(a + b*ArcSin[c + d*x])^(3/2))/(4*d) + (7*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(5/2))/(2*d) + ((c + d*x)*(a + b*ArcSin[c + d*x])^(7/2))/d + (105*b^(7/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(8*d) + (105*b^(7/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(8*d)","A",11,9,14,0.6429,1,"{4803, 4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352}"
163,1,440,0,1.0188075,"\int \frac{x^2}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[x^2/Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{2 \pi } c^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^3}+\frac{\sqrt{2 \pi } c^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^3}+\frac{\sqrt{\pi } c \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{\sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}-\frac{\sqrt{\pi } c \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{\sqrt{b} d^3}","\frac{\sqrt{2 \pi } c^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^3}+\frac{\sqrt{2 \pi } c^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^3}+\frac{\sqrt{\pi } c \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{\sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^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+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}-\frac{\sqrt{\pi } c \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{\sqrt{b} d^3}",1,"(Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*Sqrt[b]*d^3) + (c^2*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(Sqrt[b]*d^3) - (Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*Sqrt[b]*d^3) - (c*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(Sqrt[b]*d^3) + (Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(2*Sqrt[b]*d^3) + (c^2*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*d^3) + (c*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(Sqrt[b]*d^3) - (Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(2*Sqrt[b]*d^3)","A",20,9,18,0.5000,1,"{4805, 4747, 6741, 6742, 3354, 3352, 3351, 3353, 4574}"
164,1,211,0,0.4515445,"\int \frac{x}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[x/Sqrt[a + b*ArcSin[c + d*x]],x]","-\frac{\sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} d^2}-\frac{\sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^2}-\frac{\sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^2}+\frac{\sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} d^2}","-\frac{\sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} d^2}-\frac{\sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^2}-\frac{\sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d^2}+\frac{\sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} d^2}",1,"-((c*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(Sqrt[b]*d^2)) + (Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(2*Sqrt[b]*d^2) - (c*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*d^2) - (Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(2*Sqrt[b]*d^2)","A",12,8,16,0.5000,1,"{4805, 4747, 6741, 6742, 3354, 3352, 3351, 3353}"
165,1,105,0,0.1296501,"\int \frac{1}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"(Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(Sqrt[b]*d) + (Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*d)","A",7,7,14,0.5000,1,"{4803, 4623, 3306, 3305, 3351, 3304, 3352}"
166,1,287,0,0.6109073,"\int \frac{x}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[x/(a + b*ArcSin[c + d*x])^(3/2),x]","-\frac{2 \sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} d^2}+\frac{2 \sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 c \sqrt{1-(c+d x)^2}}{b d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 (c+d x) \sqrt{1-(c+d x)^2}}{b d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}","-\frac{2 \sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} d^2}+\frac{2 \sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 c \sqrt{1-(c+d x)^2}}{b d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 (c+d x) \sqrt{1-(c+d x)^2}}{b d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(2*c*Sqrt[1 - (c + d*x)^2])/(b*d^2*Sqrt[a + b*ArcSin[c + d*x]]) - (2*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(b*d^2*Sqrt[a + b*ArcSin[c + d*x]]) + (2*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(b^(3/2)*d^2) + (2*c*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(3/2)*d^2) - (2*c*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*d^2) + (2*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(b^(3/2)*d^2)","A",16,10,16,0.6250,1,"{4805, 4745, 4621, 4723, 3306, 3305, 3351, 3304, 3352, 4631}"
167,1,144,0,0.2790417,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d 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+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(-2*Sqrt[1 - (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSin[c + d*x]]) - (2*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (2*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*d)","A",8,8,14,0.5714,1,"{4803, 4621, 4723, 3306, 3305, 3351, 3304, 3352}"
168,1,384,0,0.8959401,"\int \frac{x}{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[x/(a + b*ArcSin[c + d*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+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} d^2}+\frac{4 \sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}+\frac{4 \sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{8 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} d^2}+\frac{8 (c+d x)^2}{3 b^2 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 c (c+d x)}{3 b^2 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4}{3 b^2 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2} (c+d x)}{3 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{2 c \sqrt{1-(c+d x)^2}}{3 b d^2 \left(a+b \sin ^{-1}(c+d 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+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} d^2}+\frac{4 \sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}+\frac{4 \sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{8 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} d^2}+\frac{8 (c+d x)^2}{3 b^2 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 c (c+d x)}{3 b^2 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4}{3 b^2 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2} (c+d x)}{3 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{2 c \sqrt{1-(c+d x)^2}}{3 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}",1,"(2*c*Sqrt[1 - (c + d*x)^2])/(3*b*d^2*(a + b*ArcSin[c + d*x])^(3/2)) - (2*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(3*b*d^2*(a + b*ArcSin[c + d*x])^(3/2)) - 4/(3*b^2*d^2*Sqrt[a + b*ArcSin[c + d*x]]) - (4*c*(c + d*x))/(3*b^2*d^2*Sqrt[a + b*ArcSin[c + d*x]]) + (8*(c + d*x)^2)/(3*b^2*d^2*Sqrt[a + b*ArcSin[c + d*x]]) + (4*c*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d^2) - (8*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(3*b^(5/2)*d^2) + (4*c*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*d^2) + (8*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(3*b^(5/2)*d^2)","A",22,15,16,0.9375,1,"{4805, 4745, 4621, 4719, 4623, 3306, 3305, 3351, 3304, 3352, 4633, 4635, 4406, 12, 4641}"
169,1,179,0,0.2793217,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{3 b d \left(a+b \sin ^{-1}(c+d 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+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^(3/2)) + (4*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) - (4*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) - (4*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*d)","A",9,9,14,0.6429,1,"{4803, 4621, 4719, 4623, 3306, 3305, 3351, 3304, 3352}"
170,1,468,0,1.0639995,"\int \frac{x}{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[x/(a + b*ArcSin[c + d*x])^(7/2),x]","\frac{8 \sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{32 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{32 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{15 b^{7/2} d^2}-\frac{8 \sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}+\frac{8 (c+d x)^2}{15 b^2 d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{32 \sqrt{1-(c+d x)^2} (c+d x)}{15 b^3 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 c (c+d x)}{15 b^2 d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{8 c \sqrt{1-(c+d x)^2}}{15 b^3 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4}{15 b^2 d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{2 \sqrt{1-(c+d x)^2} (c+d x)}{5 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}+\frac{2 c \sqrt{1-(c+d x)^2}}{5 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}","\frac{8 \sqrt{2 \pi } c \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{32 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{32 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{15 b^{7/2} d^2}-\frac{8 \sqrt{2 \pi } c \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}+\frac{8 (c+d x)^2}{15 b^2 d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{32 \sqrt{1-(c+d x)^2} (c+d x)}{15 b^3 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 c (c+d x)}{15 b^2 d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{8 c \sqrt{1-(c+d x)^2}}{15 b^3 d^2 \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4}{15 b^2 d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{2 \sqrt{1-(c+d x)^2} (c+d x)}{5 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}+\frac{2 c \sqrt{1-(c+d x)^2}}{5 b d^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}",1,"(2*c*Sqrt[1 - (c + d*x)^2])/(5*b*d^2*(a + b*ArcSin[c + d*x])^(5/2)) - (2*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(5*b*d^2*(a + b*ArcSin[c + d*x])^(5/2)) - 4/(15*b^2*d^2*(a + b*ArcSin[c + d*x])^(3/2)) - (4*c*(c + d*x))/(15*b^2*d^2*(a + b*ArcSin[c + d*x])^(3/2)) + (8*(c + d*x)^2)/(15*b^2*d^2*(a + b*ArcSin[c + d*x])^(3/2)) - (8*c*Sqrt[1 - (c + d*x)^2])/(15*b^3*d^2*Sqrt[a + b*ArcSin[c + d*x]]) + (32*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(15*b^3*d^2*Sqrt[a + b*ArcSin[c + d*x]]) - (32*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(15*b^(7/2)*d^2) - (8*c*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d^2) + (8*c*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(15*b^(7/2)*d^2) - (32*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(15*b^(7/2)*d^2)","A",21,13,16,0.8125,1,"{4805, 4745, 4621, 4719, 4723, 3306, 3305, 3351, 3304, 3352, 4633, 4631, 4641}"
171,1,218,0,0.42953,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^(-7/2),x]","-\frac{8 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 (c+d x)}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{8 \sqrt{1-(c+d x)^2}}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}","-\frac{8 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 (c+d x)}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{8 \sqrt{1-(c+d x)^2}}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*Sqrt[1 - (c + d*x)^2])/(5*b*d*(a + b*ArcSin[c + d*x])^(5/2)) + (4*(c + d*x))/(15*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) + (8*Sqrt[1 - (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) + (8*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) - (8*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(15*b^(7/2)*d)","A",10,9,14,0.6429,1,"{4803, 4621, 4719, 4723, 3306, 3305, 3351, 3304, 3352}"
172,0,0,0,0.0539602,"\int x^m \left(a+b \sin ^{-1}(c+d x)\right)^n \, dx","Int[x^m*(a + b*ArcSin[c + d*x])^n,x]","\int x^m \left(a+b \sin ^{-1}(c+d x)\right)^n \, dx","\text{Int}\left(x^m \left(a+b \sin ^{-1}(c+d x)\right)^n,x\right)",0,"Defer[Subst][Defer[Int][(-(c/d) + x/d)^m*(a + b*ArcSin[x])^n, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
173,1,611,0,1.1163766,"\int x^2 \left(a+b \sin ^{-1}(c+d x)\right)^n \, dx","Int[x^2*(a + b*ArcSin[c + d*x])^n,x]","-\frac{i c^2 e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^3}+\frac{i c^2 e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^3}-\frac{i e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}+\frac{c 2^{-n-2} e^{-\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^3}+\frac{i 3^{-n-1} e^{-\frac{3 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}+\frac{i e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}+\frac{c 2^{-n-2} e^{\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^3}-\frac{i 3^{-n-1} e^{\frac{3 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}","-\frac{i c^2 e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^3}+\frac{i c^2 e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^3}-\frac{i e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}+\frac{c 2^{-n-2} e^{-\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^3}+\frac{i 3^{-n-1} e^{-\frac{3 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}+\frac{i e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}+\frac{c 2^{-n-2} e^{\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^3}-\frac{i 3^{-n-1} e^{\frac{3 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}",1,"((-I/8)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c + d*x]))/b])/(d^3*E^((I*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) - ((I/2)*c^2*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c + d*x]))/b])/(d^3*E^((I*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) + ((I/8)*E^((I*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c + d*x]))/b])/(d^3*((I*(a + b*ArcSin[c + d*x]))/b)^n) + ((I/2)*c^2*E^((I*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c + d*x]))/b])/(d^3*((I*(a + b*ArcSin[c + d*x]))/b)^n) + (2^(-2 - n)*c*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c + d*x]))/b])/(d^3*E^(((2*I)*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) + (2^(-2 - n)*c*E^(((2*I)*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c + d*x]))/b])/(d^3*((I*(a + b*ArcSin[c + d*x]))/b)^n) + ((I/8)*3^(-1 - n)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-3*I)*(a + b*ArcSin[c + d*x]))/b])/(d^3*E^(((3*I)*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) - ((I/8)*3^(-1 - n)*E^(((3*I)*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((3*I)*(a + b*ArcSin[c + d*x]))/b])/(d^3*((I*(a + b*ArcSin[c + d*x]))/b)^n)","A",22,9,16,0.5625,1,"{4805, 4747, 6741, 12, 6742, 3307, 2181, 4406, 3308}"
174,1,301,0,0.5173488,"\int x \left(a+b \sin ^{-1}(c+d x)\right)^n \, dx","Int[x*(a + b*ArcSin[c + d*x])^n,x]","\frac{i c e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^2}-\frac{2^{-n-3} e^{-\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^2}-\frac{i c e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^2}-\frac{2^{-n-3} e^{\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^2}","\frac{i c e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^2}-\frac{2^{-n-3} e^{-\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^2}-\frac{i c e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d^2}-\frac{2^{-n-3} e^{\frac{2 i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{d^2}",1,"((I/2)*c*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c + d*x]))/b])/(d^2*E^((I*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) - ((I/2)*c*E^((I*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c + d*x]))/b])/(d^2*((I*(a + b*ArcSin[c + d*x]))/b)^n) - (2^(-3 - n)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c + d*x]))/b])/(d^2*E^(((2*I)*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) - (2^(-3 - n)*E^(((2*I)*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c + d*x]))/b])/(d^2*((I*(a + b*ArcSin[c + d*x]))/b)^n)","A",14,9,14,0.6429,1,"{4805, 4747, 6741, 12, 6742, 3307, 2181, 4406, 3308}"
175,1,147,0,0.1330236,"\int \left(a+b \sin ^{-1}(c+d x)\right)^n \, dx","Int[(a + b*ArcSin[c + d*x])^n,x]","\frac{i e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d}-\frac{i e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d}","\frac{i e^{\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d}-\frac{i e^{-\frac{i a}{b}} \left(a+b \sin ^{-1}(c+d x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 d}",1,"((-I/2)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c + d*x]))/b])/(d*E^((I*a)/b)*(((-I)*(a + b*ArcSin[c + d*x]))/b)^n) + ((I/2)*E^((I*a)/b)*(a + b*ArcSin[c + d*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c + d*x]))/b])/(d*((I*(a + b*ArcSin[c + d*x]))/b)^n)","A",5,4,12,0.3333,1,"{4803, 4623, 3307, 2181}"
176,0,0,0,0.0582569,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^n}{x} \, dx","Int[(a + b*ArcSin[c + d*x])^n/x,x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^n}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^n}{x},x\right)",0,"Defer[Subst][Defer[Int][(a + b*ArcSin[x])^n/(-(c/d) + x/d), x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
177,1,106,0,0.0926155,"\int (c e+d e x)^4 \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSin[c + d*x]),x]","\frac{e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)}{5 d}+\frac{b e^4 \left(1-(c+d x)^2\right)^{5/2}}{25 d}-\frac{2 b e^4 \left(1-(c+d x)^2\right)^{3/2}}{15 d}+\frac{b e^4 \sqrt{1-(c+d x)^2}}{5 d}","\frac{e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)}{5 d}+\frac{b e^4 \left(1-(c+d x)^2\right)^{5/2}}{25 d}-\frac{2 b e^4 \left(1-(c+d x)^2\right)^{3/2}}{15 d}+\frac{b e^4 \sqrt{1-(c+d x)^2}}{5 d}",1,"(b*e^4*Sqrt[1 - (c + d*x)^2])/(5*d) - (2*b*e^4*(1 - (c + d*x)^2)^(3/2))/(15*d) + (b*e^4*(1 - (c + d*x)^2)^(5/2))/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcSin[c + d*x]))/(5*d)","A",6,5,21,0.2381,1,"{4805, 12, 4627, 266, 43}"
178,1,109,0,0.0756311,"\int (c e+d e x)^3 \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSin[c + d*x]),x]","\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)}{4 d}+\frac{b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{16 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x)}{32 d}-\frac{3 b e^3 \sin ^{-1}(c+d x)}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)}{4 d}+\frac{b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{16 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x)}{32 d}-\frac{3 b e^3 \sin ^{-1}(c+d x)}{32 d}",1,"(3*b*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(32*d) + (b*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(16*d) - (3*b*e^3*ArcSin[c + d*x])/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x]))/(4*d)","A",6,5,21,0.2381,1,"{4805, 12, 4627, 321, 216}"
179,1,80,0,0.0713548,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x]),x]","\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \left(1-(c+d x)^2\right)^{3/2}}{9 d}+\frac{b e^2 \sqrt{1-(c+d x)^2}}{3 d}","\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \left(1-(c+d x)^2\right)^{3/2}}{9 d}+\frac{b e^2 \sqrt{1-(c+d x)^2}}{3 d}",1,"(b*e^2*Sqrt[1 - (c + d*x)^2])/(3*d) - (b*e^2*(1 - (c + d*x)^2)^(3/2))/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x]))/(3*d)","A",6,5,21,0.2381,1,"{4805, 12, 4627, 266, 43}"
180,1,70,0,0.0404498,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x]),x]","\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{2 d}+\frac{b e \sqrt{1-(c+d x)^2} (c+d x)}{4 d}-\frac{b e \sin ^{-1}(c+d x)}{4 d}","\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{2 d}+\frac{b e \sqrt{1-(c+d x)^2} (c+d x)}{4 d}-\frac{b e \sin ^{-1}(c+d x)}{4 d}",1,"(b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(4*d) - (b*e*ArcSin[c + d*x])/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x]))/(2*d)","A",5,5,19,0.2632,1,"{4805, 12, 4627, 321, 216}"
181,1,40,0,0.024191,"\int \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[a + b*ArcSin[c + d*x],x]","a x+\frac{b \sqrt{1-(c+d x)^2}}{d}+\frac{b (c+d x) \sin ^{-1}(c+d x)}{d}","a x+\frac{b \sqrt{1-(c+d x)^2}}{d}+\frac{b (c+d x) \sin ^{-1}(c+d x)}{d}",1,"a*x + (b*Sqrt[1 - (c + d*x)^2])/d + (b*(c + d*x)*ArcSin[c + d*x])/d","A",4,3,10,0.3000,1,"{4803, 4619, 261}"
182,1,89,0,0.1046286,"\int \frac{a+b \sin ^{-1}(c+d x)}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x),x]","-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e}","-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e}",1,"((-I/2)*(a + b*ArcSin[c + d*x])^2)/(b*d*e) + ((a + b*ArcSin[c + d*x])*Log[1 - E^((2*I)*ArcSin[c + d*x])])/(d*e) - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c + d*x])])/(d*e)","A",7,7,21,0.3333,1,"{4805, 12, 4625, 3717, 2190, 2279, 2391}"
183,1,51,0,0.0531497,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^2,x]","-\frac{a+b \sin ^{-1}(c+d x)}{d e^2 (c+d x)}-\frac{b \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{d e^2}","-\frac{a+b \sin ^{-1}(c+d x)}{d e^2 (c+d x)}-\frac{b \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{d e^2}",1,"-((a + b*ArcSin[c + d*x])/(d*e^2*(c + d*x))) - (b*ArcTanh[Sqrt[1 - (c + d*x)^2]])/(d*e^2)","A",6,6,21,0.2857,1,"{4805, 12, 4627, 266, 63, 206}"
184,1,61,0,0.0530201,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^3,x]","-\frac{a+b \sin ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b \sqrt{1-(c+d x)^2}}{2 d e^3 (c+d x)}","-\frac{a+b \sin ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b \sqrt{1-(c+d x)^2}}{2 d e^3 (c+d x)}",1,"-(b*Sqrt[1 - (c + d*x)^2])/(2*d*e^3*(c + d*x)) - (a + b*ArcSin[c + d*x])/(2*d*e^3*(c + d*x)^2)","A",4,4,21,0.1905,1,"{4805, 12, 4627, 264}"
185,1,88,0,0.0727574,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^4,x]","-\frac{a+b \sin ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}-\frac{b \sqrt{1-(c+d x)^2}}{6 d e^4 (c+d x)^2}-\frac{b \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{6 d e^4}","-\frac{a+b \sin ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}-\frac{b \sqrt{1-(c+d x)^2}}{6 d e^4 (c+d x)^2}-\frac{b \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{6 d e^4}",1,"-(b*Sqrt[1 - (c + d*x)^2])/(6*d*e^4*(c + d*x)^2) - (a + b*ArcSin[c + d*x])/(3*d*e^4*(c + d*x)^3) - (b*ArcTanh[Sqrt[1 - (c + d*x)^2]])/(6*d*e^4)","A",7,7,21,0.3333,1,"{4805, 12, 4627, 266, 51, 63, 206}"
186,1,94,0,0.0681326,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^5} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^5,x]","-\frac{a+b \sin ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}-\frac{b \sqrt{1-(c+d x)^2}}{6 d e^5 (c+d x)}-\frac{b \sqrt{1-(c+d x)^2}}{12 d e^5 (c+d x)^3}","-\frac{a+b \sin ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}-\frac{b \sqrt{1-(c+d x)^2}}{6 d e^5 (c+d x)}-\frac{b \sqrt{1-(c+d x)^2}}{12 d e^5 (c+d x)^3}",1,"-(b*Sqrt[1 - (c + d*x)^2])/(12*d*e^5*(c + d*x)^3) - (b*Sqrt[1 - (c + d*x)^2])/(6*d*e^5*(c + d*x)) - (a + b*ArcSin[c + d*x])/(4*d*e^5*(c + d*x)^4)","A",5,5,21,0.2381,1,"{4805, 12, 4627, 271, 264}"
187,1,121,0,0.0925666,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^6} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^6,x]","-\frac{a+b \sin ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}-\frac{3 b \sqrt{1-(c+d x)^2}}{40 d e^6 (c+d x)^2}-\frac{b \sqrt{1-(c+d x)^2}}{20 d e^6 (c+d x)^4}-\frac{3 b \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{40 d e^6}","-\frac{a+b \sin ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}-\frac{3 b \sqrt{1-(c+d x)^2}}{40 d e^6 (c+d x)^2}-\frac{b \sqrt{1-(c+d x)^2}}{20 d e^6 (c+d x)^4}-\frac{3 b \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{40 d e^6}",1,"-(b*Sqrt[1 - (c + d*x)^2])/(20*d*e^6*(c + d*x)^4) - (3*b*Sqrt[1 - (c + d*x)^2])/(40*d*e^6*(c + d*x)^2) - (a + b*ArcSin[c + d*x])/(5*d*e^6*(c + d*x)^5) - (3*b*ArcTanh[Sqrt[1 - (c + d*x)^2]])/(40*d*e^6)","A",8,7,21,0.3333,1,"{4805, 12, 4627, 266, 51, 63, 206}"
188,1,203,0,0.304755,"\int (c e+d e x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSin[c + d*x])^2,x]","\frac{e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)^2}{5 d}+\frac{2 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)}{25 d}+\frac{8 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{75 d}+\frac{16 b e^4 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{75 d}-\frac{2 b^2 e^4 (c+d x)^5}{125 d}-\frac{8 b^2 e^4 (c+d x)^3}{225 d}-\frac{16}{75} b^2 e^4 x","\frac{e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)^2}{5 d}+\frac{2 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)}{25 d}+\frac{8 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{75 d}+\frac{16 b e^4 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{75 d}-\frac{2 b^2 e^4 (c+d x)^5}{125 d}-\frac{8 b^2 e^4 (c+d x)^3}{225 d}-\frac{16}{75} b^2 e^4 x",1,"(-16*b^2*e^4*x)/75 - (8*b^2*e^4*(c + d*x)^3)/(225*d) - (2*b^2*e^4*(c + d*x)^5)/(125*d) + (16*b*e^4*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(75*d) + (8*b*e^4*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(75*d) + (2*b*e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcSin[c + d*x])^2)/(5*d)","A",9,7,23,0.3043,1,"{4805, 12, 4627, 4707, 4677, 8, 30}"
189,1,176,0,0.2588366,"\int (c e+d e x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSin[c + d*x])^2,x]","\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}+\frac{b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{8 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{32 d}-\frac{b^2 e^3 (c+d x)^4}{32 d}-\frac{3 b^2 e^3 (c+d x)^2}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}+\frac{b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{8 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{32 d}-\frac{b^2 e^3 (c+d x)^4}{32 d}-\frac{3 b^2 e^3 (c+d x)^2}{32 d}",1,"(-3*b^2*e^3*(c + d*x)^2)/(32*d) - (b^2*e^3*(c + d*x)^4)/(32*d) + (3*b*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(16*d) + (b*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(8*d) - (3*e^3*(a + b*ArcSin[c + d*x])^2)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x])^2)/(4*d)","A",8,6,23,0.2609,1,"{4805, 12, 4627, 4707, 4641, 30}"
190,1,140,0,0.2066645,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x])^2,x]","\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{2 b e^2 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{9 d}+\frac{4 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{9 d}-\frac{2 b^2 e^2 (c+d x)^3}{27 d}-\frac{4}{9} b^2 e^2 x","\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{2 b e^2 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{9 d}+\frac{4 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{9 d}-\frac{2 b^2 e^2 (c+d x)^3}{27 d}-\frac{4}{9} b^2 e^2 x",1,"(-4*b^2*e^2*x)/9 - (2*b^2*e^2*(c + d*x)^3)/(27*d) + (4*b*e^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(9*d) + (2*b*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^2)/(3*d)","A",7,7,23,0.3043,1,"{4805, 12, 4627, 4707, 4677, 8, 30}"
191,1,105,0,0.1450948,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x])^2,x]","\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d}+\frac{b e \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}-\frac{b^2 e (c+d x)^2}{4 d}","\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d}+\frac{b e \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}-\frac{b^2 e (c+d x)^2}{4 d}",1,"-(b^2*e*(c + d*x)^2)/(4*d) + (b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(2*d) - (e*(a + b*ArcSin[c + d*x])^2)/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^2)/(2*d)","A",6,6,21,0.2857,1,"{4805, 12, 4627, 4707, 4641, 30}"
192,1,59,0,0.0721905,"\int \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcSin[c + d*x])^2,x]","\frac{2 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}-2 b^2 x","\frac{2 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}-2 b^2 x",1,"-2*b^2*x + (2*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/d + ((c + d*x)*(a + b*ArcSin[c + d*x])^2)/d","A",4,4,12,0.3333,1,"{4803, 4619, 4677, 8}"
193,1,126,0,0.1833611,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x),x]","-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e}","-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e}",1,"((-I/3)*(a + b*ArcSin[c + d*x])^3)/(b*d*e) + ((a + b*ArcSin[c + d*x])^2*Log[1 - E^((2*I)*ArcSin[c + d*x])])/(d*e) - (I*b*(a + b*ArcSin[c + d*x])*PolyLog[2, E^((2*I)*ArcSin[c + d*x])])/(d*e) + (b^2*PolyLog[3, E^((2*I)*ArcSin[c + d*x])])/(2*d*e)","A",8,8,23,0.3478,1,"{4805, 12, 4625, 3717, 2190, 2531, 2282, 6589}"
194,1,116,0,0.1637362,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^2,x]","\frac{2 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{2 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}-\frac{4 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}","\frac{2 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{2 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}-\frac{4 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}",1,"-((a + b*ArcSin[c + d*x])^2/(d*e^2*(c + d*x))) - (4*b*(a + b*ArcSin[c + d*x])*ArcTanh[E^(I*ArcSin[c + d*x])])/(d*e^2) + ((2*I)*b^2*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^2) - ((2*I)*b^2*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^2)","A",9,7,23,0.3043,1,"{4805, 12, 4627, 4709, 4183, 2279, 2391}"
195,1,87,0,0.1351225,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^3,x]","-\frac{b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d e^3}","-\frac{b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d e^3}",1,"-((b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(d*e^3*(c + d*x))) - (a + b*ArcSin[c + d*x])^2/(2*d*e^3*(c + d*x)^2) + (b^2*Log[c + d*x])/(d*e^3)","A",5,5,23,0.2174,1,"{4805, 12, 4627, 4681, 29}"
196,1,187,0,0.2458361,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^4,x]","\frac{i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}-\frac{2 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}","\frac{i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}-\frac{2 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}",1,"-b^2/(3*d*e^4*(c + d*x)) - (b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(3*d*e^4*(c + d*x)^2) - (a + b*ArcSin[c + d*x])^2/(3*d*e^4*(c + d*x)^3) - (2*b*(a + b*ArcSin[c + d*x])*ArcTanh[E^(I*ArcSin[c + d*x])])/(3*d*e^4) + ((I/3)*b^2*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^4) - ((I/3)*b^2*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^4)","A",11,9,23,0.3913,1,"{4805, 12, 4627, 4701, 4709, 4183, 2279, 2391, 30}"
197,1,338,0,0.4935817,"\int (c e+d e x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSin[c + d*x])^3,x]","-\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)}{125 d}-\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{75 d}-\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)^3}{5 d}+\frac{3 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2}{25 d}+\frac{4 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{25 d}+\frac{8 b e^4 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \left(1-(c+d x)^2\right)^{5/2}}{625 d}+\frac{76 b^3 e^4 \left(1-(c+d x)^2\right)^{3/2}}{1125 d}-\frac{298 b^3 e^4 \sqrt{1-(c+d x)^2}}{375 d}-\frac{16 b^3 e^4 (c+d x) \sin ^{-1}(c+d x)}{25 d}","-\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)}{125 d}-\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{75 d}-\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \sin ^{-1}(c+d x)\right)^3}{5 d}+\frac{3 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2}{25 d}+\frac{4 b e^4 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{25 d}+\frac{8 b e^4 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \left(1-(c+d x)^2\right)^{5/2}}{625 d}+\frac{76 b^3 e^4 \left(1-(c+d x)^2\right)^{3/2}}{1125 d}-\frac{298 b^3 e^4 \sqrt{1-(c+d x)^2}}{375 d}-\frac{16 b^3 e^4 (c+d x) \sin ^{-1}(c+d x)}{25 d}",1,"(-16*a*b^2*e^4*x)/25 - (298*b^3*e^4*Sqrt[1 - (c + d*x)^2])/(375*d) + (76*b^3*e^4*(1 - (c + d*x)^2)^(3/2))/(1125*d) - (6*b^3*e^4*(1 - (c + d*x)^2)^(5/2))/(625*d) - (16*b^3*e^4*(c + d*x)*ArcSin[c + d*x])/(25*d) - (8*b^2*e^4*(c + d*x)^3*(a + b*ArcSin[c + d*x]))/(75*d) - (6*b^2*e^4*(c + d*x)^5*(a + b*ArcSin[c + d*x]))/(125*d) + (8*b*e^4*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(25*d) + (4*b*e^4*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(25*d) + (3*b*e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcSin[c + d*x])^3)/(5*d)","A",17,9,23,0.3913,1,"{4805, 12, 4627, 4707, 4677, 4619, 261, 266, 43}"
198,1,287,0,0.4003938,"\int (c e+d e x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSin[c + d*x])^3,x]","-\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)}{32 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^3}{4 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{16 d}+\frac{9 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{128 d}-\frac{45 b^3 e^3 \sqrt{1-(c+d x)^2} (c+d x)}{256 d}+\frac{45 b^3 e^3 \sin ^{-1}(c+d x)}{256 d}","-\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)}{32 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^3}{4 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{16 d}+\frac{9 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{128 d}-\frac{45 b^3 e^3 \sqrt{1-(c+d x)^2} (c+d x)}{256 d}+\frac{45 b^3 e^3 \sin ^{-1}(c+d x)}{256 d}",1,"(-45*b^3*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(256*d) - (3*b^3*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(128*d) + (45*b^3*e^3*ArcSin[c + d*x])/(256*d) - (9*b^2*e^3*(c + d*x)^2*(a + b*ArcSin[c + d*x]))/(32*d) - (3*b^2*e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x]))/(32*d) + (9*b*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(32*d) + (3*b*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(16*d) - (3*e^3*(a + b*ArcSin[c + d*x])^3)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x])^3)/(4*d)","A",13,7,23,0.3043,1,"{4805, 12, 4627, 4707, 4641, 321, 216}"
199,1,235,0,0.3221737,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x])^3,x]","-\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{9 d}-\frac{4}{3} a b^2 e^2 x+\frac{2 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{b e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d}+\frac{2 b^3 e^2 \left(1-(c+d x)^2\right)^{3/2}}{27 d}-\frac{14 b^3 e^2 \sqrt{1-(c+d x)^2}}{9 d}-\frac{4 b^3 e^2 (c+d x) \sin ^{-1}(c+d x)}{3 d}","-\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)}{9 d}-\frac{4}{3} a b^2 e^2 x+\frac{2 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{b e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d}+\frac{2 b^3 e^2 \left(1-(c+d x)^2\right)^{3/2}}{27 d}-\frac{14 b^3 e^2 \sqrt{1-(c+d x)^2}}{9 d}-\frac{4 b^3 e^2 (c+d x) \sin ^{-1}(c+d x)}{3 d}",1,"(-4*a*b^2*e^2*x)/3 - (14*b^3*e^2*Sqrt[1 - (c + d*x)^2])/(9*d) + (2*b^3*e^2*(1 - (c + d*x)^2)^(3/2))/(27*d) - (4*b^3*e^2*(c + d*x)*ArcSin[c + d*x])/(3*d) - (2*b^2*e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x]))/(9*d) + (2*b*e^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(3*d) + (b*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^3)/(3*d)","A",12,9,23,0.3913,1,"{4805, 12, 4627, 4707, 4677, 4619, 261, 266, 43}"
200,1,165,0,0.2094099,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x])^3,x]","-\frac{3 b^2 e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{4 d}+\frac{3 b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e (c+d x) \sqrt{1-(c+d x)^2}}{8 d}+\frac{3 b^3 e \sin ^{-1}(c+d x)}{8 d}","-\frac{3 b^2 e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)}{4 d}+\frac{3 b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e (c+d x) \sqrt{1-(c+d x)^2}}{8 d}+\frac{3 b^3 e \sin ^{-1}(c+d x)}{8 d}",1,"(-3*b^3*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(8*d) + (3*b^3*e*ArcSin[c + d*x])/(8*d) - (3*b^2*e*(c + d*x)^2*(a + b*ArcSin[c + d*x]))/(4*d) + (3*b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(4*d) - (e*(a + b*ArcSin[c + d*x])^3)/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^3)/(2*d)","A",8,7,21,0.3333,1,"{4805, 12, 4627, 4707, 4641, 321, 216}"
201,1,104,0,0.1140042,"\int \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[(a + b*ArcSin[c + d*x])^3,x]","-6 a b^2 x+\frac{3 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{1-(c+d x)^2}}{d}-\frac{6 b^3 (c+d x) \sin ^{-1}(c+d x)}{d}","-6 a b^2 x+\frac{3 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{1-(c+d x)^2}}{d}-\frac{6 b^3 (c+d x) \sin ^{-1}(c+d x)}{d}",1,"-6*a*b^2*x - (6*b^3*Sqrt[1 - (c + d*x)^2])/d - (6*b^3*(c + d*x)*ArcSin[c + d*x])/d + (3*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/d + ((c + d*x)*(a + b*ArcSin[c + d*x])^3)/d","A",6,4,12,0.3333,1,"{4803, 4619, 4677, 261}"
202,1,169,0,0.2036226,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])^3/(c*e + d*e*x),x]","\frac{3 b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{2 d e}-\frac{3 i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(c+d x)}\right)}{4 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e}","\frac{3 b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{2 d e}-\frac{3 i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(c+d x)}\right)}{4 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e}",1,"((-I/4)*(a + b*ArcSin[c + d*x])^4)/(b*d*e) + ((a + b*ArcSin[c + d*x])^3*Log[1 - E^((2*I)*ArcSin[c + d*x])])/(d*e) - (((3*I)/2)*b*(a + b*ArcSin[c + d*x])^2*PolyLog[2, E^((2*I)*ArcSin[c + d*x])])/(d*e) + (3*b^2*(a + b*ArcSin[c + d*x])*PolyLog[3, E^((2*I)*ArcSin[c + d*x])])/(2*d*e) + (((3*I)/4)*b^3*PolyLog[4, E^((2*I)*ArcSin[c + d*x])])/(d*e)","A",9,9,23,0.3913,1,"{4805, 12, 4625, 3717, 2190, 2531, 6609, 2282, 6589}"
203,1,190,0,0.2475607,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSin[c + d*x])^3/(c*e + d*e*x)^2,x]","\frac{6 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}-\frac{6 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}-\frac{6 b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}+\frac{6 b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}-\frac{6 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2}","\frac{6 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}-\frac{6 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}-\frac{6 b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}+\frac{6 b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}-\frac{6 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2}",1,"-((a + b*ArcSin[c + d*x])^3/(d*e^2*(c + d*x))) - (6*b*(a + b*ArcSin[c + d*x])^2*ArcTanh[E^(I*ArcSin[c + d*x])])/(d*e^2) + ((6*I)*b^2*(a + b*ArcSin[c + d*x])*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^2) - ((6*I)*b^2*(a + b*ArcSin[c + d*x])*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^2) - (6*b^3*PolyLog[3, -E^(I*ArcSin[c + d*x])])/(d*e^2) + (6*b^3*PolyLog[3, E^(I*ArcSin[c + d*x])])/(d*e^2)","A",11,8,23,0.3478,1,"{4805, 12, 4627, 4709, 4183, 2531, 2282, 6589}"
204,1,167,0,0.2505533,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSin[c + d*x])^3/(c*e + d*e*x)^3,x]","-\frac{3 i b^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e^3}+\frac{3 b^2 \log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 i b \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}","-\frac{3 i b^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e^3}+\frac{3 b^2 \log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 i b \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}",1,"(((-3*I)/2)*b*(a + b*ArcSin[c + d*x])^2)/(d*e^3) - (3*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(2*d*e^3*(c + d*x)) - (a + b*ArcSin[c + d*x])^3/(2*d*e^3*(c + d*x)^2) + (3*b^2*(a + b*ArcSin[c + d*x])*Log[1 - E^((2*I)*ArcSin[c + d*x])])/(d*e^3) - (((3*I)/2)*b^3*PolyLog[2, E^((2*I)*ArcSin[c + d*x])])/(d*e^3)","A",9,9,23,0.3913,1,"{4805, 12, 4627, 4681, 4625, 3717, 2190, 2279, 2391}"
205,1,291,0,0.3941303,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSin[c + d*x])^3/(c*e + d*e*x)^4,x]","\frac{i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}-\frac{i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}+\frac{b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{b^2 \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}-\frac{b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4}-\frac{b^3 \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{d e^4}","\frac{i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}-\frac{i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}+\frac{b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{b^2 \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}-\frac{b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4}-\frac{b^3 \tanh ^{-1}\left(\sqrt{1-(c+d x)^2}\right)}{d e^4}",1,"-((b^2*(a + b*ArcSin[c + d*x]))/(d*e^4*(c + d*x))) - (b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/(2*d*e^4*(c + d*x)^2) - (a + b*ArcSin[c + d*x])^3/(3*d*e^4*(c + d*x)^3) - (b*(a + b*ArcSin[c + d*x])^2*ArcTanh[E^(I*ArcSin[c + d*x])])/(d*e^4) - (b^3*ArcTanh[Sqrt[1 - (c + d*x)^2]])/(d*e^4) + (I*b^2*(a + b*ArcSin[c + d*x])*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^4) - (I*b^2*(a + b*ArcSin[c + d*x])*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^4) - (b^3*PolyLog[3, -E^(I*ArcSin[c + d*x])])/(d*e^4) + (b^3*PolyLog[3, E^(I*ArcSin[c + d*x])])/(d*e^4)","A",16,12,23,0.5217,1,"{4805, 12, 4627, 4701, 4709, 4183, 2531, 2282, 6589, 266, 63, 206}"
206,1,357,0,0.6401424,"\int (c e+d e x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSin[c + d*x])^4,x]","-\frac{3 b^3 e^3 (c+d x)^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{32 d}-\frac{45 b^3 e^3 (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{64 d}-\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2}{16 d}+\frac{45 b^2 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{128 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{16 d}+\frac{b e^3 (c+d x)^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{4 d}+\frac{3 b e^3 (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}+\frac{45 b^4 e^3 (c+d x)^2}{128 d}","-\frac{3 b^3 e^3 (c+d x)^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{32 d}-\frac{45 b^3 e^3 (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{64 d}-\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^2}{16 d}+\frac{45 b^2 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{128 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{16 d}+\frac{b e^3 (c+d x)^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{4 d}+\frac{3 b e^3 (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}+\frac{45 b^4 e^3 (c+d x)^2}{128 d}",1,"(45*b^4*e^3*(c + d*x)^2)/(128*d) + (3*b^4*e^3*(c + d*x)^4)/(128*d) - (45*b^3*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(64*d) - (3*b^3*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(32*d) + (45*b^2*e^3*(a + b*ArcSin[c + d*x])^2)/(128*d) - (9*b^2*e^3*(c + d*x)^2*(a + b*ArcSin[c + d*x])^2)/(16*d) - (3*b^2*e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x])^2)/(16*d) + (3*b*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/(8*d) + (b*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/(4*d) - (3*e^3*(a + b*ArcSin[c + d*x])^4)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x])^4)/(4*d)","A",16,6,23,0.2609,1,"{4805, 12, 4627, 4707, 4641, 30}"
207,1,289,0,0.4819047,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x])^4,x]","-\frac{160 b^3 e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{27 d}-\frac{8 b^3 e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{27 d}-\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{9 d}-\frac{8 b^2 e^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{8 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{9 d}+\frac{4 b e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}+\frac{160}{27} b^4 e^2 x","-\frac{160 b^3 e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{27 d}-\frac{8 b^3 e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{27 d}-\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^2}{9 d}-\frac{8 b^2 e^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d}+\frac{8 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{9 d}+\frac{4 b e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}+\frac{160}{27} b^4 e^2 x",1,"(160*b^4*e^2*x)/27 + (8*b^4*e^2*(c + d*x)^3)/(81*d) - (160*b^3*e^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(27*d) - (8*b^3*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(27*d) - (8*b^2*e^2*(c + d*x)*(a + b*ArcSin[c + d*x])^2)/(3*d) - (4*b^2*e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^2)/(9*d) + (8*b*e^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/(9*d) + (4*b*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^4)/(3*d)","A",13,8,23,0.3478,1,"{4805, 12, 4627, 4707, 4677, 4619, 8, 30}"
208,1,198,0,0.305862,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x])^4,x]","-\frac{3 b^3 e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{2 d}-\frac{3 b^2 e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d}+\frac{3 b^2 e \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}+\frac{b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^4}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}","-\frac{3 b^3 e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{2 d}-\frac{3 b^2 e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{2 d}+\frac{3 b^2 e \left(a+b \sin ^{-1}(c+d x)\right)^2}{4 d}+\frac{b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^4}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}",1,"(3*b^4*e*(c + d*x)^2)/(4*d) - (3*b^3*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/(2*d) + (3*b^2*e*(a + b*ArcSin[c + d*x])^2)/(4*d) - (3*b^2*e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^2)/(2*d) + (b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/d - (e*(a + b*ArcSin[c + d*x])^4)/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^4)/(2*d)","A",9,6,21,0.2857,1,"{4805, 12, 4627, 4707, 4641, 30}"
209,1,119,0,0.1586828,"\int \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","Int[(a + b*ArcSin[c + d*x])^4,x]","-\frac{24 b^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{d}-\frac{12 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}+\frac{4 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^4}{d}+24 b^4 x","-\frac{24 b^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)}{d}-\frac{12 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}+\frac{4 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^4}{d}+24 b^4 x",1,"24*b^4*x - (24*b^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x]))/d - (12*b^2*(c + d*x)*(a + b*ArcSin[c + d*x])^2)/d + (4*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/d + ((c + d*x)*(a + b*ArcSin[c + d*x])^4)/d","A",6,4,12,0.3333,1,"{4803, 4619, 4677, 8}"
210,1,202,0,0.2341065,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])^4/(c*e + d*e*x),x]","\frac{3 b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e}+\frac{3 i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e}-\frac{2 i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^4 \text{PolyLog}\left(5,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^4}{d e}","\frac{3 b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e}+\frac{3 i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e}-\frac{2 i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^4 \text{PolyLog}\left(5,e^{2 i \sin ^{-1}(c+d x)}\right)}{2 d e}-\frac{i \left(a+b \sin ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^4}{d e}",1,"((-I/5)*(a + b*ArcSin[c + d*x])^5)/(b*d*e) + ((a + b*ArcSin[c + d*x])^4*Log[1 - E^((2*I)*ArcSin[c + d*x])])/(d*e) - ((2*I)*b*(a + b*ArcSin[c + d*x])^3*PolyLog[2, E^((2*I)*ArcSin[c + d*x])])/(d*e) + (3*b^2*(a + b*ArcSin[c + d*x])^2*PolyLog[3, E^((2*I)*ArcSin[c + d*x])])/(d*e) + ((3*I)*b^3*(a + b*ArcSin[c + d*x])*PolyLog[4, E^((2*I)*ArcSin[c + d*x])])/(d*e) - (3*b^4*PolyLog[5, E^((2*I)*ArcSin[c + d*x])])/(2*d*e)","A",10,9,23,0.3913,1,"{4805, 12, 4625, 3717, 2190, 2531, 6609, 2282, 6589}"
211,1,270,0,0.312955,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSin[c + d*x])^4/(c*e + d*e*x)^2,x]","-\frac{24 b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}+\frac{24 b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}+\frac{12 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2}-\frac{12 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2}-\frac{24 i b^4 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 i b^4 \text{PolyLog}\left(4,e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}-\frac{8 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^2}","-\frac{24 b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}+\frac{24 b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}+\frac{12 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2}-\frac{12 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^2}-\frac{24 i b^4 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 i b^4 \text{PolyLog}\left(4,e^{i \sin ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}-\frac{8 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^2}",1,"-((a + b*ArcSin[c + d*x])^4/(d*e^2*(c + d*x))) - (8*b*(a + b*ArcSin[c + d*x])^3*ArcTanh[E^(I*ArcSin[c + d*x])])/(d*e^2) + ((12*I)*b^2*(a + b*ArcSin[c + d*x])^2*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^2) - ((12*I)*b^2*(a + b*ArcSin[c + d*x])^2*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^2) - (24*b^3*(a + b*ArcSin[c + d*x])*PolyLog[3, -E^(I*ArcSin[c + d*x])])/(d*e^2) + (24*b^3*(a + b*ArcSin[c + d*x])*PolyLog[3, E^(I*ArcSin[c + d*x])])/(d*e^2) - ((24*I)*b^4*PolyLog[4, -E^(I*ArcSin[c + d*x])])/(d*e^2) + ((24*I)*b^4*PolyLog[4, E^(I*ArcSin[c + d*x])])/(d*e^2)","A",13,9,23,0.3913,1,"{4805, 12, 4627, 4709, 4183, 2531, 6609, 2282, 6589}"
212,1,198,0,0.319608,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSin[c + d*x])^4/(c*e + d*e*x)^3,x]","-\frac{6 i b^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b^4 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right)}{d e^3}+\frac{6 b^2 \log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^3}-\frac{2 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}-\frac{2 i b \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}","-\frac{6 i b^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b^4 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c+d x)}\right)}{d e^3}+\frac{6 b^2 \log \left(1-e^{2 i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^3}-\frac{2 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}-\frac{2 i b \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}",1,"((-2*I)*b*(a + b*ArcSin[c + d*x])^3)/(d*e^3) - (2*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/(d*e^3*(c + d*x)) - (a + b*ArcSin[c + d*x])^4/(2*d*e^3*(c + d*x)^2) + (6*b^2*(a + b*ArcSin[c + d*x])^2*Log[1 - E^((2*I)*ArcSin[c + d*x])])/(d*e^3) - ((6*I)*b^3*(a + b*ArcSin[c + d*x])*PolyLog[2, E^((2*I)*ArcSin[c + d*x])])/(d*e^3) + (3*b^4*PolyLog[3, E^((2*I)*ArcSin[c + d*x])])/(d*e^3)","A",10,10,23,0.4348,1,"{4805, 12, 4627, 4681, 4625, 3717, 2190, 2531, 2282, 6589}"
213,1,439,0,0.5760848,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSin[c + d*x])^4/(c*e + d*e*x)^4,x]","-\frac{4 b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}+\frac{4 b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}+\frac{2 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4}-\frac{2 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(4,e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{2 b^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}-\frac{8 b^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}-\frac{2 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}-\frac{4 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e^4}","-\frac{4 b^3 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}+\frac{4 b^3 \text{PolyLog}\left(3,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}+\frac{2 i b^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4}-\frac{2 i b^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(4,e^{i \sin ^{-1}(c+d x)}\right)}{d e^4}-\frac{2 b^2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}-\frac{8 b^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^4}-\frac{2 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}-\frac{4 b \tanh ^{-1}\left(e^{i \sin ^{-1}(c+d x)}\right) \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e^4}",1,"(-2*b^2*(a + b*ArcSin[c + d*x])^2)/(d*e^4*(c + d*x)) - (2*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^3)/(3*d*e^4*(c + d*x)^2) - (a + b*ArcSin[c + d*x])^4/(3*d*e^4*(c + d*x)^3) - (8*b^3*(a + b*ArcSin[c + d*x])*ArcTanh[E^(I*ArcSin[c + d*x])])/(d*e^4) - (4*b*(a + b*ArcSin[c + d*x])^3*ArcTanh[E^(I*ArcSin[c + d*x])])/(3*d*e^4) + ((4*I)*b^4*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^4) + ((2*I)*b^2*(a + b*ArcSin[c + d*x])^2*PolyLog[2, -E^(I*ArcSin[c + d*x])])/(d*e^4) - ((4*I)*b^4*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^4) - ((2*I)*b^2*(a + b*ArcSin[c + d*x])^2*PolyLog[2, E^(I*ArcSin[c + d*x])])/(d*e^4) - (4*b^3*(a + b*ArcSin[c + d*x])*PolyLog[3, -E^(I*ArcSin[c + d*x])])/(d*e^4) + (4*b^3*(a + b*ArcSin[c + d*x])*PolyLog[3, E^(I*ArcSin[c + d*x])])/(d*e^4) - ((4*I)*b^4*PolyLog[4, -E^(I*ArcSin[c + d*x])])/(d*e^4) + ((4*I)*b^4*PolyLog[4, E^(I*ArcSin[c + d*x])])/(d*e^4)","A",21,12,23,0.5217,1,"{4805, 12, 4627, 4701, 4709, 4183, 2531, 6609, 2282, 6589, 2279, 2391}"
214,1,164,0,0.2087576,"\int \left(a+b \sin ^{-1}(c+d x)\right)^5 \, dx","Int[(a + b*ArcSin[c + d*x])^5,x]","-\frac{60 b^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}-\frac{20 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}+120 a b^4 x+\frac{5 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^4}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^5}{d}+\frac{120 b^5 \sqrt{1-(c+d x)^2}}{d}+\frac{120 b^5 (c+d x) \sin ^{-1}(c+d x)}{d}","-\frac{60 b^3 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d}-\frac{20 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^3}{d}+120 a b^4 x+\frac{5 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^4}{d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^5}{d}+\frac{120 b^5 \sqrt{1-(c+d x)^2}}{d}+\frac{120 b^5 (c+d x) \sin ^{-1}(c+d x)}{d}",1,"120*a*b^4*x + (120*b^5*Sqrt[1 - (c + d*x)^2])/d + (120*b^5*(c + d*x)*ArcSin[c + d*x])/d - (60*b^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^2)/d - (20*b^2*(c + d*x)*(a + b*ArcSin[c + d*x])^3)/d + (5*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^4)/d + ((c + d*x)*(a + b*ArcSin[c + d*x])^5)/d","A",8,4,12,0.3333,1,"{4803, 4619, 4677, 261}"
215,1,209,0,0.4084383,"\int \frac{(c e+d e x)^4}{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSin[c + d*x]),x]","\frac{e^4 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{8 b d}-\frac{3 e^4 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{16 b d}+\frac{e^4 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{16 b d}+\frac{e^4 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{8 b d}-\frac{3 e^4 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{16 b d}+\frac{e^4 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{16 b d}","\frac{e^4 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{8 b d}-\frac{3 e^4 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{8 b d}-\frac{3 e^4 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b d}",1,"(e^4*Cos[a/b]*CosIntegral[a/b + ArcSin[c + d*x]])/(8*b*d) - (3*e^4*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(16*b*d) + (e^4*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c + d*x]])/(16*b*d) + (e^4*Sin[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(8*b*d) - (3*e^4*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(16*b*d) + (e^4*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c + d*x]])/(16*b*d)","A",14,7,23,0.3043,1,"{4805, 12, 4635, 4406, 3303, 3299, 3302}"
216,1,145,0,0.3141283,"\int \frac{(c e+d e x)^3}{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x]),x]","-\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{4 b d}+\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{8 b d}+\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{4 b d}-\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{8 b d}","-\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 b d}+\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{4 b d}-\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 b d}",1,"-(e^3*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]]*Sin[(2*a)/b])/(4*b*d) + (e^3*CosIntegral[(4*a)/b + 4*ArcSin[c + d*x]]*Sin[(4*a)/b])/(8*b*d) + (e^3*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(4*b*d) - (e^3*Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c + d*x]])/(8*b*d)","A",11,7,23,0.3043,1,"{4805, 12, 4635, 4406, 3303, 3299, 3302}"
217,1,137,0,0.2775193,"\int \frac{(c e+d e x)^2}{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x]),x]","\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{4 b d}-\frac{e^2 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{4 b d}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{4 b d}-\frac{e^2 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{4 b d}","\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{4 b d}-\frac{e^2 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{4 b d}-\frac{e^2 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{4 b d}",1,"(e^2*Cos[a/b]*CosIntegral[a/b + ArcSin[c + d*x]])/(4*b*d) - (e^2*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(4*b*d) + (e^2*Sin[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(4*b*d) - (e^2*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(4*b*d)","A",11,7,23,0.3043,1,"{4805, 12, 4635, 4406, 3303, 3299, 3302}"
218,1,69,0,0.1452132,"\int \frac{c e+d e x}{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x]),x]","\frac{e \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{2 b d}-\frac{e \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{2 b d}","\frac{e \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b d}-\frac{e \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b d}",1,"-(e*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]]*Sin[(2*a)/b])/(2*b*d) + (e*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(2*b*d)","A",8,7,21,0.3333,1,"{4805, 12, 4635, 4406, 3303, 3299, 3302}"
219,1,57,0,0.0839661,"\int \frac{1}{a+b \sin ^{-1}(c+d x)} \, dx","Int[(a + b*ArcSin[c + d*x])^(-1),x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b d}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b d}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b d}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b d}",1,"(Cos[a/b]*CosIntegral[(a + b*ArcSin[c + d*x])/b])/(b*d) + (Sin[a/b]*SinIntegral[(a + b*ArcSin[c + d*x])/b])/(b*d)","A",5,5,12,0.4167,1,"{4803, 4623, 3303, 3299, 3302}"
220,0,0,0,0.0638499,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
221,1,254,0,0.3676858,"\int \frac{(c e+d e x)^4}{\left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSin[c + d*x])^2,x]","\frac{e^4 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{8 b^2 d}-\frac{9 e^4 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{16 b^2 d}+\frac{5 e^4 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{e^4 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{8 b^2 d}+\frac{9 e^4 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{5 e^4 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{e^4 (c+d x)^4 \sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}","\frac{e^4 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{8 b^2 d}-\frac{9 e^4 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}+\frac{5 e^4 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{8 b^2 d}+\frac{9 e^4 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{5 e^4 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 (c+d x)^4 \sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}",1,"-((e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2])/(b*d*(a + b*ArcSin[c + d*x]))) + (e^4*CosIntegral[a/b + ArcSin[c + d*x]]*Sin[a/b])/(8*b^2*d) - (9*e^4*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]]*Sin[(3*a)/b])/(16*b^2*d) + (5*e^4*CosIntegral[(5*a)/b + 5*ArcSin[c + d*x]]*Sin[(5*a)/b])/(16*b^2*d) - (e^4*Cos[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(8*b^2*d) + (9*e^4*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(16*b^2*d) - (5*e^4*Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c + d*x]])/(16*b^2*d)","A",13,6,23,0.2609,1,"{4805, 12, 4631, 3303, 3299, 3302}"
222,1,190,0,0.2947962,"\int \frac{(c e+d e x)^3}{\left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x])^2,x]","\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{2 b^2 d}+\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 (c+d x)^3 \sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}","\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}+\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 (c+d x)^3 \sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}",1,"-((e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(b*d*(a + b*ArcSin[c + d*x]))) + (e^3*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(2*b^2*d) - (e^3*Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c + d*x]])/(2*b^2*d) + (e^3*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(2*b^2*d) - (e^3*Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c + d*x]])/(2*b^2*d)","A",10,6,23,0.2609,1,"{4805, 12, 4631, 3303, 3299, 3302}"
223,1,182,0,0.264746,"\int \frac{(c e+d e x)^2}{\left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x])^2,x]","\frac{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{3 e^2 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{4 b^2 d}+\frac{3 e^2 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{e^2 (c+d x)^2 \sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}","\frac{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{4 b^2 d}-\frac{3 e^2 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{4 b^2 d}+\frac{3 e^2 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 (c+d x)^2 \sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}",1,"-((e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(b*d*(a + b*ArcSin[c + d*x]))) + (e^2*CosIntegral[a/b + ArcSin[c + d*x]]*Sin[a/b])/(4*b^2*d) - (3*e^2*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]]*Sin[(3*a)/b])/(4*b^2*d) - (e^2*Cos[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(4*b^2*d) + (3*e^2*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(4*b^2*d)","A",10,6,23,0.2609,1,"{4805, 12, 4631, 3303, 3299, 3302}"
224,1,104,0,0.1410799,"\int \frac{c e+d e x}{\left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x])^2,x]","\frac{e \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{b^2 d}+\frac{e \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{b^2 d}-\frac{e \sqrt{1-(c+d x)^2} (c+d x)}{b d \left(a+b \sin ^{-1}(c+d x)\right)}","\frac{e \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}+\frac{e \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sqrt{1-(c+d x)^2} (c+d x)}{b d \left(a+b \sin ^{-1}(c+d x)\right)}",1,"-((e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(b*d*(a + b*ArcSin[c + d*x]))) + (e*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(b^2*d) + (e*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(b^2*d)","A",6,6,21,0.2857,1,"{4805, 12, 4631, 3303, 3299, 3302}"
225,1,89,0,0.1715621,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","Int[(a + b*ArcSin[c + d*x])^(-2),x]","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{b^2 d}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{b^2 d}-\frac{\sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\sqrt{1-(c+d x)^2}}{b d \left(a+b \sin ^{-1}(c+d x)\right)}",1,"-(Sqrt[1 - (c + d*x)^2]/(b*d*(a + b*ArcSin[c + d*x]))) + (CosIntegral[a/b + ArcSin[c + d*x]]*Sin[a/b])/(b^2*d) - (Cos[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(b^2*d)","A",6,6,12,0.5000,1,"{4803, 4621, 4723, 3303, 3299, 3302}"
226,0,0,0,0.0592427,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])^2),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^2} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^2},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])^2), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
227,1,318,0,0.8623837,"\int \frac{(c e+d e x)^4}{\left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSin[c + d*x])^3,x]","-\frac{e^4 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{16 b^3 d}+\frac{27 e^4 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{25 e^4 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{e^4 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{16 b^3 d}+\frac{27 e^4 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{25 e^4 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{32 b^3 d}+\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{1-(c+d x)^2} (c+d x)^4}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}","-\frac{e^4 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{16 b^3 d}+\frac{27 e^4 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{25 e^4 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{e^4 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{16 b^3 d}+\frac{27 e^4 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{25 e^4 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}+\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{1-(c+d x)^2} (c+d x)^4}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}",1,"-(e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2])/(2*b*d*(a + b*ArcSin[c + d*x])^2) - (2*e^4*(c + d*x)^3)/(b^2*d*(a + b*ArcSin[c + d*x])) + (5*e^4*(c + d*x)^5)/(2*b^2*d*(a + b*ArcSin[c + d*x])) - (e^4*Cos[a/b]*CosIntegral[a/b + ArcSin[c + d*x]])/(16*b^3*d) + (27*e^4*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(32*b^3*d) - (25*e^4*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c + d*x]])/(32*b^3*d) - (e^4*Sin[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(16*b^3*d) + (27*e^4*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(32*b^3*d) - (25*e^4*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c + d*x]])/(32*b^3*d)","A",26,9,23,0.3913,1,"{4805, 12, 4633, 4719, 4635, 4406, 3303, 3299, 3302}"
228,1,249,0,0.6599387,"\int \frac{(c e+d e x)^3}{\left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x])^3,x]","\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{2 b^3 d}-\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{b^3 d}-\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{2 b^3 d}+\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{b^3 d}+\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}","\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}-\frac{e^3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}+\frac{e^3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}",1,"-(e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(2*b*d*(a + b*ArcSin[c + d*x])^2) - (3*e^3*(c + d*x)^2)/(2*b^2*d*(a + b*ArcSin[c + d*x])) + (2*e^3*(c + d*x)^4)/(b^2*d*(a + b*ArcSin[c + d*x])) + (e^3*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]]*Sin[(2*a)/b])/(2*b^3*d) - (e^3*CosIntegral[(4*a)/b + 4*ArcSin[c + d*x]]*Sin[(4*a)/b])/(b^3*d) - (e^3*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(2*b^3*d) + (e^3*Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c + d*x]])/(b^3*d)","A",20,9,23,0.3913,1,"{4805, 12, 4633, 4719, 4635, 4406, 3303, 3299, 3302}"
229,1,306,0,0.5778715,"\int \frac{(c e+d e x)^2}{\left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x])^3,x]","-\frac{9 e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{9 e^2 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b^3 d}-\frac{9 e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{9 e^2 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{b^3 d}+\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}","-\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{8 b^3 d}+\frac{9 e^2 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}-\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{8 b^3 d}+\frac{9 e^2 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}+\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}",1,"-(e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(2*b*d*(a + b*ArcSin[c + d*x])^2) - (e^2*(c + d*x))/(b^2*d*(a + b*ArcSin[c + d*x])) + (3*e^2*(c + d*x)^3)/(2*b^2*d*(a + b*ArcSin[c + d*x])) - (9*e^2*Cos[a/b]*CosIntegral[a/b + ArcSin[c + d*x]])/(8*b^3*d) + (9*e^2*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(8*b^3*d) + (e^2*Cos[a/b]*CosIntegral[(a + b*ArcSin[c + d*x])/b])/(b^3*d) - (9*e^2*Sin[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(8*b^3*d) + (9*e^2*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(8*b^3*d) + (e^2*Sin[a/b]*SinIntegral[(a + b*ArcSin[c + d*x])/b])/(b^3*d)","A",18,10,23,0.4348,1,"{4805, 12, 4633, 4719, 4635, 4406, 3303, 3299, 3302, 4623}"
230,1,157,0,0.3296731,"\int \frac{c e+d e x}{\left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x])^3,x]","\frac{e \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{b^3 d}-\frac{e \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{b^3 d}+\frac{e (c+d x)^2}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e \sqrt{1-(c+d x)^2} (c+d x)}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}","\frac{e \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{e \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{e (c+d x)^2}{b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e \sqrt{1-(c+d x)^2} (c+d x)}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}",1,"-(e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(2*b*d*(a + b*ArcSin[c + d*x])^2) - e/(2*b^2*d*(a + b*ArcSin[c + d*x])) + (e*(c + d*x)^2)/(b^2*d*(a + b*ArcSin[c + d*x])) + (e*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]]*Sin[(2*a)/b])/(b^3*d) - (e*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(b^3*d)","A",11,10,21,0.4762,1,"{4805, 12, 4633, 4719, 4635, 4406, 3303, 3299, 3302, 4641}"
231,1,127,0,0.1721132,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","Int[(a + b*ArcSin[c + d*x])^(-3),x]","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{2 b^3 d}+\frac{c+d x}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{\sqrt{1-(c+d x)^2}}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{2 b^3 d}+\frac{c+d x}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{\sqrt{1-(c+d x)^2}}{2 b d \left(a+b \sin ^{-1}(c+d x)\right)^2}",1,"-Sqrt[1 - (c + d*x)^2]/(2*b*d*(a + b*ArcSin[c + d*x])^2) + (c + d*x)/(2*b^2*d*(a + b*ArcSin[c + d*x])) - (Cos[a/b]*CosIntegral[(a + b*ArcSin[c + d*x])/b])/(2*b^3*d) - (Sin[a/b]*SinIntegral[(a + b*ArcSin[c + d*x])/b])/(2*b^3*d)","A",7,7,12,0.5833,1,"{4803, 4621, 4719, 4623, 3303, 3299, 3302}"
232,0,0,0,0.0578594,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])^3),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^3} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^3},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])^3), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
233,1,412,0,0.8634945,"\int \frac{(c e+d e x)^4}{\left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSin[c + d*x])^4,x]","-\frac{e^4 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{48 b^4 d}+\frac{27 e^4 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{32 b^4 d}-\frac{125 e^4 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{96 b^4 d}+\frac{e^4 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{48 b^4 d}-\frac{27 e^4 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{32 b^4 d}+\frac{125 e^4 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c+d x)\right)}{96 b^4 d}+\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{25 e^4 \sqrt{1-(c+d x)^2} (c+d x)^4}{6 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{2 e^4 \sqrt{1-(c+d x)^2} (c+d x)^2}{b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{1-(c+d x)^2} (c+d x)^4}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}","-\frac{e^4 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{48 b^4 d}+\frac{27 e^4 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}-\frac{125 e^4 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}+\frac{e^4 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{48 b^4 d}-\frac{27 e^4 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}+\frac{125 e^4 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}+\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{25 e^4 \sqrt{1-(c+d x)^2} (c+d x)^4}{6 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{2 e^4 \sqrt{1-(c+d x)^2} (c+d x)^2}{b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{1-(c+d x)^2} (c+d x)^4}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}",1,"-(e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^3) - (2*e^4*(c + d*x)^3)/(3*b^2*d*(a + b*ArcSin[c + d*x])^2) + (5*e^4*(c + d*x)^5)/(6*b^2*d*(a + b*ArcSin[c + d*x])^2) - (2*e^4*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(b^3*d*(a + b*ArcSin[c + d*x])) + (25*e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2])/(6*b^3*d*(a + b*ArcSin[c + d*x])) - (e^4*CosIntegral[a/b + ArcSin[c + d*x]]*Sin[a/b])/(48*b^4*d) + (27*e^4*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]]*Sin[(3*a)/b])/(32*b^4*d) - (125*e^4*CosIntegral[(5*a)/b + 5*ArcSin[c + d*x]]*Sin[(5*a)/b])/(96*b^4*d) + (e^4*Cos[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(48*b^4*d) - (27*e^4*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(32*b^4*d) + (125*e^4*Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c + d*x]])/(96*b^4*d)","A",24,8,23,0.3478,1,"{4805, 12, 4633, 4719, 4631, 3303, 3299, 3302}"
234,1,346,0,0.6813972,"\int \frac{(c e+d e x)^3}{\left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x])^4,x]","-\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{4 e^3 \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{4 e^3 \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{8 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{3 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{e^3 \sqrt{1-(c+d x)^2} (c+d x)}{b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}","-\frac{e^3 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{4 e^3 \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{e^3 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{4 e^3 \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{8 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{3 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{e^3 \sqrt{1-(c+d x)^2} (c+d x)}{b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}",1,"-(e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^3) - (e^3*(c + d*x)^2)/(2*b^2*d*(a + b*ArcSin[c + d*x])^2) + (2*e^3*(c + d*x)^4)/(3*b^2*d*(a + b*ArcSin[c + d*x])^2) - (e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(b^3*d*(a + b*ArcSin[c + d*x])) + (8*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(3*b^3*d*(a + b*ArcSin[c + d*x])) - (e^3*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(3*b^4*d) + (4*e^3*Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c + d*x]])/(3*b^4*d) - (e^3*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(3*b^4*d) + (4*e^3*Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c + d*x]])/(3*b^4*d)","A",17,8,23,0.3478,1,"{4805, 12, 4633, 4719, 4631, 3303, 3299, 3302}"
235,1,333,0,0.6698892,"\int \frac{(c e+d e x)^2}{\left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x])^4,x]","-\frac{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{24 b^4 d}+\frac{9 e^2 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{8 b^4 d}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{24 b^4 d}-\frac{9 e^2 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c+d x)\right)}{8 b^4 d}+\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{3 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{2 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{e^2 \sqrt{1-(c+d x)^2}}{3 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}","-\frac{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{24 b^4 d}+\frac{9 e^2 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{24 b^4 d}-\frac{9 e^2 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}+\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{3 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{2 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{e^2 \sqrt{1-(c+d x)^2}}{3 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}",1,"-(e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^3) - (e^2*(c + d*x))/(3*b^2*d*(a + b*ArcSin[c + d*x])^2) + (e^2*(c + d*x)^3)/(2*b^2*d*(a + b*ArcSin[c + d*x])^2) - (e^2*Sqrt[1 - (c + d*x)^2])/(3*b^3*d*(a + b*ArcSin[c + d*x])) + (3*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(2*b^3*d*(a + b*ArcSin[c + d*x])) - (e^2*CosIntegral[a/b + ArcSin[c + d*x]]*Sin[a/b])/(24*b^4*d) + (9*e^2*CosIntegral[(3*a)/b + 3*ArcSin[c + d*x]]*Sin[(3*a)/b])/(8*b^4*d) + (e^2*Cos[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(24*b^4*d) - (9*e^2*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c + d*x]])/(8*b^4*d)","A",18,10,23,0.4348,1,"{4805, 12, 4633, 4719, 4631, 3303, 3299, 3302, 4621, 4723}"
236,1,208,0,0.330869,"\int \frac{c e+d e x}{\left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x])^4,x]","-\frac{2 e \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{2 e \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{e (c+d x)^2}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{3 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e}{6 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{1-(c+d x)^2} (c+d x)}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}","-\frac{2 e \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{e (c+d x)^2}{3 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{3 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{e}{6 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{1-(c+d x)^2} (c+d x)}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}",1,"-(e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^3) - e/(6*b^2*d*(a + b*ArcSin[c + d*x])^2) + (e*(c + d*x)^2)/(3*b^2*d*(a + b*ArcSin[c + d*x])^2) + (2*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(3*b^3*d*(a + b*ArcSin[c + d*x])) - (2*e*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(3*b^4*d) - (2*e*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c + d*x]])/(3*b^4*d)","A",9,9,21,0.4286,1,"{4805, 12, 4633, 4719, 4631, 3303, 3299, 3302, 4641}"
237,1,160,0,0.2684089,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","Int[(a + b*ArcSin[c + d*x])^(-4),x]","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{6 b^4 d}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c+d x)\right)}{6 b^4 d}+\frac{c+d x}{6 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{\sqrt{1-(c+d x)^2}}{6 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{\sqrt{1-(c+d x)^2}}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{6 b^4 d}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{6 b^4 d}+\frac{c+d x}{6 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^2}+\frac{\sqrt{1-(c+d x)^2}}{6 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)}-\frac{\sqrt{1-(c+d x)^2}}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^3}",1,"-Sqrt[1 - (c + d*x)^2]/(3*b*d*(a + b*ArcSin[c + d*x])^3) + (c + d*x)/(6*b^2*d*(a + b*ArcSin[c + d*x])^2) + Sqrt[1 - (c + d*x)^2]/(6*b^3*d*(a + b*ArcSin[c + d*x])) - (CosIntegral[a/b + ArcSin[c + d*x]]*Sin[a/b])/(6*b^4*d) + (Cos[a/b]*SinIntegral[a/b + ArcSin[c + d*x]])/(6*b^4*d)","A",8,7,12,0.5833,1,"{4803, 4621, 4719, 4723, 3303, 3299, 3302}"
238,0,0,0,0.0592177,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])^4),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^4} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^4},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])^4), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
239,1,191,0,0.2819966,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^5} \, dx","Int[(a + b*ArcSin[c + d*x])^(-5),x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{24 b^5 d}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{24 b^5 d}-\frac{c+d x}{24 b^4 d \left(a+b \sin ^{-1}(c+d x)\right)}+\frac{c+d x}{12 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^3}+\frac{\sqrt{1-(c+d x)^2}}{24 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{\sqrt{1-(c+d x)^2}}{4 b d \left(a+b \sin ^{-1}(c+d x)\right)^4}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{24 b^5 d}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c+d x)}{b}\right)}{24 b^5 d}-\frac{c+d x}{24 b^4 d \left(a+b \sin ^{-1}(c+d x)\right)}+\frac{c+d x}{12 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^3}+\frac{\sqrt{1-(c+d x)^2}}{24 b^3 d \left(a+b \sin ^{-1}(c+d x)\right)^2}-\frac{\sqrt{1-(c+d x)^2}}{4 b d \left(a+b \sin ^{-1}(c+d x)\right)^4}",1,"-Sqrt[1 - (c + d*x)^2]/(4*b*d*(a + b*ArcSin[c + d*x])^4) + (c + d*x)/(12*b^2*d*(a + b*ArcSin[c + d*x])^3) + Sqrt[1 - (c + d*x)^2]/(24*b^3*d*(a + b*ArcSin[c + d*x])^2) - (c + d*x)/(24*b^4*d*(a + b*ArcSin[c + d*x])) + (Cos[a/b]*CosIntegral[(a + b*ArcSin[c + d*x])/b])/(24*b^5*d) + (Sin[a/b]*SinIntegral[(a + b*ArcSin[c + d*x])/b])/(24*b^5*d)","A",9,7,12,0.5833,1,"{4803, 4621, 4719, 4623, 3303, 3299, 3302}"
240,1,288,0,0.7235366,"\int (c e+d e x)^3 \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^3*Sqrt[a + b*ArcSin[c + d*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{\sqrt{\pi } \sqrt{b} e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{16 d}+\frac{\sqrt{\pi } \sqrt{b} e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{32 d}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{\sqrt{\pi } \sqrt{b} e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{16 d}+\frac{\sqrt{\pi } \sqrt{b} e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{32 d}",1,"(-3*e^3*Sqrt[a + b*ArcSin[c + d*x]])/(32*d) + (e^3*(c + d*x)^4*Sqrt[a + b*ArcSin[c + d*x]])/(4*d) - (Sqrt[b]*e^3*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(64*d) + (Sqrt[b]*e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(16*d) + (Sqrt[b]*e^3*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(16*d) - (Sqrt[b]*e^3*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(64*d)","A",16,10,25,0.4000,1,"{4805, 12, 4629, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
241,1,274,0,0.7481316,"\int (c e+d e x)^2 \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^2*Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{3 d}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{3 d}",1,"(e^2*(c + d*x)^3*Sqrt[a + b*ArcSin[c + d*x]])/(3*d) - (Sqrt[b]*e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*d) + (Sqrt[b]*e^2*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(12*d) + (Sqrt[b]*e^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(4*d) - (Sqrt[b]*e^2*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(12*d)","A",16,10,25,0.4000,1,"{4805, 12, 4629, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
242,1,156,0,0.4243983,"\int (c e+d e x) \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)*Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{\pi } \sqrt{b} e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 d}+\frac{\sqrt{\pi } \sqrt{b} e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 d}+\frac{e (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d}-\frac{e \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}","\frac{\sqrt{\pi } \sqrt{b} e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 d}+\frac{\sqrt{\pi } \sqrt{b} e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 d}+\frac{e (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d}-\frac{e \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}",1,"-(e*Sqrt[a + b*ArcSin[c + d*x]])/(4*d) + (e*(c + d*x)^2*Sqrt[a + b*ArcSin[c + d*x]])/(2*d) + (Sqrt[b]*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(8*d) + (Sqrt[b]*e*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(8*d)","A",11,10,23,0.4348,1,"{4805, 12, 4629, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
243,1,133,0,0.2725951,"\int \sqrt{a+b \sin ^{-1}(c+d x)} \, dx","Int[Sqrt[a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{d}-\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+d x)}}{\sqrt{b}}\right)}{d}+\frac{(c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d}","\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+d x)}}{\sqrt{b}}\right)}{d}-\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+d x)}}{\sqrt{b}}\right)}{d}+\frac{(c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{d}",1,"((c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/d - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/d + (Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/d","A",8,8,14,0.5714,1,"{4803, 4619, 4723, 3306, 3305, 3351, 3304, 3352}"
244,0,0,0,0.0825867,"\int \frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx","Int[Sqrt[a + b*ArcSin[c + d*x]]/(c*e + d*e*x),x]","\int \frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][Sqrt[a + b*ArcSin[x]]/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
245,1,380,0,1.1244298,"\int (c e+d e x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSin[c + d*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e^3 \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{64 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 \sin \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 \cos \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{3 \sqrt{\pi } b^{3/2} e^3 \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{64 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{32 d}+\frac{9 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{32 d}","\frac{3 \sqrt{\pi } b^{3/2} e^3 \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{64 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 \sin \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 \cos \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{3 \sqrt{\pi } b^{3/2} e^3 \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{64 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}+\frac{3 b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{32 d}+\frac{9 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{32 d}",1,"(9*b*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(64*d) + (3*b*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(32*d) - (3*e^3*(a + b*ArcSin[c + d*x])^(3/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x])^(3/2))/(4*d) + (3*b^(3/2)*e^3*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(512*d) - (3*b^(3/2)*e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(64*d) + (3*b^(3/2)*e^3*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(64*d) - (3*b^(3/2)*e^3*Sqrt[Pi/2]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(512*d)","A",27,12,25,0.4800,1,"{4805, 12, 4629, 4707, 4641, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
246,1,361,0,1.0326324,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{3 d}+\frac{b e^2 \sqrt{1-(c+d x)^2} (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{6 d}+\frac{b e^2 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{3 d}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{3 d}+\frac{b e^2 \sqrt{1-(c+d x)^2} (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{6 d}+\frac{b e^2 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{3 d}",1,"(b*e^2*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(3*d) + (b*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(6*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^(3/2))/(3*d) - (3*b^(3/2)*e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(8*d) + (b^(3/2)*e^2*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(24*d) - (3*b^(3/2)*e^2*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(8*d) + (b^(3/2)*e^2*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(24*d)","A",24,13,25,0.5200,1,"{4805, 12, 4629, 4707, 4677, 4623, 3306, 3305, 3351, 3304, 3352, 4635, 4406}"
247,1,199,0,0.4930798,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{32 d}-\frac{3 \sqrt{\pi } b^{3/2} e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{3 b e \sqrt{1-(c+d x)^2} (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{8 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}","\frac{3 \sqrt{\pi } b^{3/2} e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{32 d}-\frac{3 \sqrt{\pi } b^{3/2} e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{3 b e \sqrt{1-(c+d x)^2} (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{8 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}",1,"(3*b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(8*d) - (e*(a + b*ArcSin[c + d*x])^(3/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^(3/2))/(2*d) - (3*b^(3/2)*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(32*d) + (3*b^(3/2)*e*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(32*d)","A",13,12,23,0.5217,1,"{4805, 12, 4629, 4707, 4641, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
248,1,175,0,0.2634164,"\int \left(a+b \sin ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{2 d}-\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+d x)}}{\sqrt{b}}\right)}{2 d}+\frac{3 b \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{d}","-\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+d x)}}{\sqrt{b}}\right)}{2 d}-\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+d x)}}{\sqrt{b}}\right)}{2 d}+\frac{3 b \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{d}",1,"(3*b*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(2*d) + ((c + d*x)*(a + b*ArcSin[c + d*x])^(3/2))/d - (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*d) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(2*d)","A",9,9,14,0.6429,1,"{4803, 4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352}"
249,0,0,0,0.0967922,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])^(3/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcSin[x])^(3/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
250,1,475,0,1.600052,"\int (c e+d e x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSin[c + d*x])^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4096 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{256 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4096 d}-\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \sin ^{-1}(c+d x)}}{256 d}-\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{256 d}+\frac{225 b^2 e^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{4 d}+\frac{5 b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{15 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{32 d}","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4096 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{256 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4096 d}-\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \sin ^{-1}(c+d x)}}{256 d}-\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{256 d}+\frac{225 b^2 e^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{4 d}+\frac{5 b e^3 \sqrt{1-(c+d x)^2} (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{15 b e^3 \sqrt{1-(c+d x)^2} (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{32 d}",1,"(225*b^2*e^3*Sqrt[a + b*ArcSin[c + d*x]])/(2048*d) - (45*b^2*e^3*(c + d*x)^2*Sqrt[a + b*ArcSin[c + d*x]])/(256*d) - (15*b^2*e^3*(c + d*x)^4*Sqrt[a + b*ArcSin[c + d*x]])/(256*d) + (15*b*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(64*d) + (5*b*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(32*d) - (3*e^3*(a + b*ArcSin[c + d*x])^(5/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSin[c + d*x])^(5/2))/(4*d) + (15*b^(5/2)*e^3*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4096*d) - (15*b^(5/2)*e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(256*d) - (15*b^(5/2)*e^3*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(256*d) + (15*b^(5/2)*e^3*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(4096*d)","A",29,12,25,0.4800,1,"{4805, 12, 4629, 4707, 4641, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
251,1,427,0,1.32544,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{144 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{144 d}-\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{36 d}-\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{3 d}+\frac{5 b e^2 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{5 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{9 d}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{144 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{144 d}-\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \sin ^{-1}(c+d x)}}{36 d}-\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{3 d}+\frac{5 b e^2 \sqrt{1-(c+d x)^2} (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{5 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{9 d}",1,"(-5*b^2*e^2*(c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/(6*d) - (5*b^2*e^2*(c + d*x)^3*Sqrt[a + b*ArcSin[c + d*x]])/(36*d) + (5*b*e^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(9*d) + (5*b*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^(5/2))/(3*d) + (15*b^(5/2)*e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(16*d) - (5*b^(5/2)*e^2*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(144*d) - (15*b^(5/2)*e^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(16*d) + (5*b^(5/2)*e^2*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(144*d)","A",26,13,25,0.5200,1,"{4805, 12, 4629, 4707, 4677, 4619, 4723, 3306, 3305, 3351, 3304, 3352, 3312}"
252,1,256,0,0.7194081,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{128 d}-\frac{15 \sqrt{\pi } b^{5/2} e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 d}-\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{32 d}+\frac{15 b^2 e \sqrt{a+b \sin ^{-1}(c+d x)}}{64 d}+\frac{5 b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{4 d}","-\frac{15 \sqrt{\pi } b^{5/2} e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{128 d}-\frac{15 \sqrt{\pi } b^{5/2} e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 d}-\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \sin ^{-1}(c+d x)}}{32 d}+\frac{15 b^2 e \sqrt{a+b \sin ^{-1}(c+d x)}}{64 d}+\frac{5 b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{4 d}",1,"(15*b^2*e*Sqrt[a + b*ArcSin[c + d*x]])/(64*d) - (15*b^2*e*(c + d*x)^2*Sqrt[a + b*ArcSin[c + d*x]])/(32*d) + (5*b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(8*d) - (e*(a + b*ArcSin[c + d*x])^(5/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^(5/2))/(2*d) - (15*b^(5/2)*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(128*d) - (15*b^(5/2)*e*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(128*d)","A",14,12,23,0.5217,1,"{4805, 12, 4629, 4707, 4641, 4723, 3312, 3306, 3305, 3351, 3304, 3352}"
253,1,204,0,0.4158171,"\int \left(a+b \sin ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{4 d}+\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+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{15 b^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}+\frac{5 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{d}","-\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+d x)}}{\sqrt{b}}\right)}{4 d}+\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+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{15 b^2 (c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}}{4 d}+\frac{5 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{d}",1,"(-15*b^2*(c + d*x)*Sqrt[a + b*ArcSin[c + d*x]])/(4*d) + (5*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(3/2))/(2*d) + ((c + d*x)*(a + b*ArcSin[c + d*x])^(5/2))/d + (15*b^(5/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*d) - (15*b^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(4*d)","A",10,9,14,0.6429,1,"{4803, 4619, 4677, 4723, 3306, 3305, 3351, 3304, 3352}"
254,0,0,0,0.0940867,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])^(5/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcSin[x])^(5/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
255,1,518,0,1.6146567,"\int (c e+d e x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSin[c + d*x])^(7/2),x]","\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{35 \sqrt{\frac{\pi }{6}} b^{7/2} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{864 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{35 \sqrt{\frac{\pi }{6}} b^{7/2} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{864 d}-\frac{175 b^3 e^2 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{54 d}-\frac{35 b^3 e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{216 d}-\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{108 d}-\frac{35 b^2 e^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{7 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{9 d}+\frac{7 b e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{18 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{3 d}","\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{35 \sqrt{\frac{\pi }{6}} b^{7/2} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{864 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{35 \sqrt{\frac{\pi }{6}} b^{7/2} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{864 d}-\frac{175 b^3 e^2 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{54 d}-\frac{35 b^3 e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{216 d}-\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{108 d}-\frac{35 b^2 e^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{7 b e^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{9 d}+\frac{7 b e^2 (c+d x)^2 \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{18 d}+\frac{e^2 (c+d x)^3 \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{3 d}",1,"(-175*b^3*e^2*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(54*d) - (35*b^3*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(216*d) - (35*b^2*e^2*(c + d*x)*(a + b*ArcSin[c + d*x])^(3/2))/(18*d) - (35*b^2*e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^(3/2))/(108*d) + (7*b*e^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(5/2))/(9*d) + (7*b*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(5/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*ArcSin[c + d*x])^(7/2))/(3*d) + (105*b^(7/2)*e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(32*d) - (35*b^(7/2)*e^2*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(864*d) + (105*b^(7/2)*e^2*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(32*d) - (35*b^(7/2)*e^2*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(864*d)","A",35,14,25,0.5600,1,"{4805, 12, 4629, 4707, 4677, 4619, 4623, 3306, 3305, 3351, 3304, 3352, 4635, 4406}"
256,1,301,0,0.762957,"\int (c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcSin[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\pi } b^{7/2} e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{512 d}+\frac{105 \sqrt{\pi } b^{7/2} e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{512 d}-\frac{105 b^3 e (c+d x) \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{128 d}-\frac{35 b^2 e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{35 b^2 e \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{64 d}+\frac{7 b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{4 d}","-\frac{105 \sqrt{\pi } b^{7/2} e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{512 d}+\frac{105 \sqrt{\pi } b^{7/2} e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{512 d}-\frac{105 b^3 e (c+d x) \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{128 d}-\frac{35 b^2 e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{35 b^2 e \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{64 d}+\frac{7 b e (c+d x) \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{2 d}-\frac{e \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{4 d}",1,"(-105*b^3*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(128*d) + (35*b^2*e*(a + b*ArcSin[c + d*x])^(3/2))/(64*d) - (35*b^2*e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^(3/2))/(32*d) + (7*b*e*(c + d*x)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(5/2))/(8*d) - (e*(a + b*ArcSin[c + d*x])^(7/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcSin[c + d*x])^(7/2))/(2*d) + (105*b^(7/2)*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(512*d) - (105*b^(7/2)*e*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(512*d)","A",16,12,23,0.5217,1,"{4805, 12, 4629, 4707, 4641, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
257,1,243,0,0.4103706,"\int \left(a+b \sin ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(a + b*ArcSin[c + d*x])^(7/2),x]","\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{105 b^3 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{8 d}-\frac{35 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}+\frac{7 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{d}","\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{105 b^3 \sqrt{1-(c+d x)^2} \sqrt{a+b \sin ^{-1}(c+d x)}}{8 d}-\frac{35 b^2 (c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}{4 d}+\frac{7 b \sqrt{1-(c+d x)^2} \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{d}",1,"(-105*b^3*Sqrt[1 - (c + d*x)^2]*Sqrt[a + b*ArcSin[c + d*x]])/(8*d) - (35*b^2*(c + d*x)*(a + b*ArcSin[c + d*x])^(3/2))/(4*d) + (7*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcSin[c + d*x])^(5/2))/(2*d) + ((c + d*x)*(a + b*ArcSin[c + d*x])^(7/2))/d + (105*b^(7/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(8*d) + (105*b^(7/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(8*d)","A",11,9,14,0.6429,1,"{4803, 4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352}"
258,0,0,0,0.0946881,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","Int[(a + b*ArcSin[c + d*x])^(7/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcSin[x])^(7/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
259,1,365,0,0.9163378,"\int \frac{(c e+d e x)^4}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^4/Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e^4 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{3 \pi }{2}} e^4 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{10}} e^4 \cos \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^4 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{3 \pi }{2}} e^4 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{10}} e^4 \sin \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}","\frac{\sqrt{\frac{\pi }{2}} e^4 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{3 \pi }{2}} e^4 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{10}} e^4 \cos \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^4 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{3 \pi }{2}} e^4 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{10}} e^4 \sin \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"(e^4*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d) - (e^4*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) + (e^4*Sqrt[Pi/10]*Cos[(5*a)/b]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) + (e^4*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(4*Sqrt[b]*d) - (e^4*Sqrt[(3*Pi)/2]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(8*Sqrt[b]*d) + (e^4*Sqrt[Pi/10]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(5*a)/b])/(8*Sqrt[b]*d)","A",20,9,25,0.3600,1,"{4805, 12, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
260,1,233,0,0.5170304,"\int \frac{(c e+d e x)^3}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^3/Sqrt[a + b*ArcSin[c + d*x]],x]","-\frac{\sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{4 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 \sin \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 \cos \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{4 \sqrt{b} d}","-\frac{\sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{4 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 \sin \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 \cos \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{4 \sqrt{b} d}",1,"-(e^3*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) + (e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(4*Sqrt[b]*d) - (e^3*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(4*Sqrt[b]*d) + (e^3*Sqrt[Pi/2]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(8*Sqrt[b]*d)","A",15,9,25,0.3600,1,"{4805, 12, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
261,1,243,0,0.5669759,"\int \frac{(c e+d e x)^2}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^2/Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{6}} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{6}} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\frac{\pi }{2}} e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{6}} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{6}} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*Sqrt[b]*d) - (e^2*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*Sqrt[b]*d) + (e^2*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(2*Sqrt[b]*d) - (e^2*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(2*Sqrt[b]*d)","A",15,9,25,0.3600,1,"{4805, 12, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
262,1,105,0,0.2349415,"\int \frac{c e+d e x}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)/Sqrt[a + b*ArcSin[c + d*x]],x]","\frac{\sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(2*Sqrt[b]*d) - (e*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(2*Sqrt[b]*d)","A",10,9,23,0.3913,1,"{4805, 12, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
263,1,105,0,0.1277525,"\int \frac{1}{\sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"(Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(Sqrt[b]*d) + (Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*d)","A",7,7,14,0.5000,1,"{4803, 4623, 3306, 3305, 3351, 3304, 3352}"
264,0,0,0,0.0907175,"\int \frac{1}{(c e+d e x) \sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","Int[1/((c*e + d*e*x)*Sqrt[a + b*ArcSin[c + d*x]]),x]","\int \frac{1}{(c e+d e x) \sqrt{a+b \sin ^{-1}(c+d x)}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \sqrt{a+b \sin ^{-1}(c+d x)}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*Sqrt[a + b*ArcSin[x]]), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
265,1,412,0,0.8660429,"\int \frac{(c e+d e x)^4}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSin[c + d*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e^4 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{3 \sqrt{\frac{3 \pi }{2}} e^4 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{5 \pi }{2}} e^4 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^4 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{3 \sqrt{\frac{3 \pi }{2}} e^4 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{5 \pi }{2}} e^4 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^4 (c+d x)^4 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}","\frac{\sqrt{\frac{\pi }{2}} e^4 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{3 \sqrt{\frac{3 \pi }{2}} e^4 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{5 \pi }{2}} e^4 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^4 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{3 \sqrt{\frac{3 \pi }{2}} e^4 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{5 \pi }{2}} e^4 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^4 (c+d x)^4 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(-2*e^4*(c + d*x)^4*Sqrt[1 - (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSin[c + d*x]]) - (e^4*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(2*b^(3/2)*d) + (3*e^4*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d) - (e^4*Sqrt[(5*Pi)/2]*Cos[(5*a)/b]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d) + (e^4*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(2*b^(3/2)*d) - (3*e^4*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(4*b^(3/2)*d) + (e^4*Sqrt[(5*Pi)/2]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(5*a)/b])/(4*b^(3/2)*d)","A",19,8,25,0.3200,1,"{4805, 12, 4631, 3306, 3305, 3351, 3304, 3352}"
266,1,270,0,0.5160209,"\int \frac{(c e+d e x)^3}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x])^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e^3 (c+d x)^3 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}","-\frac{\sqrt{\frac{\pi }{2}} e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e^3 (c+d x)^3 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(-2*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSin[c + d*x]]) - (e^3*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(b^(3/2)*d) + (e^3*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(b^(3/2)*d) - (e^3*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(b^(3/2)*d)","A",14,8,25,0.3200,1,"{4805, 12, 4631, 3306, 3305, 3351, 3304, 3352}"
267,1,280,0,0.5491658,"\int \frac{(c e+d e x)^2}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{\sqrt{\frac{3 \pi }{2}} e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{3 \pi }{2}} e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e^2 (c+d x)^2 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}","\frac{\sqrt{\frac{\pi }{2}} e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{\sqrt{\frac{3 \pi }{2}} e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{3 \pi }{2}} e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e^2 (c+d x)^2 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(-2*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSin[c + d*x]]) - (e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (e^2*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (e^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*d) - (e^2*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(3/2)*d)","A",14,8,25,0.3200,1,"{4805, 12, 4631, 3306, 3305, 3351, 3304, 3352}"
268,1,144,0,0.2309922,"\int \frac{c e+d e x}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x])^(3/2),x]","\frac{2 \sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} d}+\frac{2 \sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} d}-\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}","\frac{2 \sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} d}+\frac{2 \sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} d}-\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(-2*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSin[c + d*x]]) + (2*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(b^(3/2)*d) + (2*e*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(b^(3/2)*d)","A",8,8,23,0.3478,1,"{4805, 12, 4631, 3306, 3305, 3351, 3304, 3352}"
269,1,144,0,0.286833,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d 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+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{1-(c+d x)^2}}{b d \sqrt{a+b \sin ^{-1}(c+d x)}}",1,"(-2*Sqrt[1 - (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSin[c + d*x]]) - (2*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (2*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*d)","A",8,8,14,0.5714,1,"{4803, 4621, 4723, 3306, 3305, 3351, 3304, 3352}"
270,0,0,0,0.1053671,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])^(3/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])^(3/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
271,1,344,0,1.1726376,"\int \frac{(c e+d e x)^3}{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x])^(5/2),x]","\frac{4 \sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{2 \pi } e^3 \sin \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{4 \sqrt{2 \pi } e^3 \cos \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} d}+\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}","\frac{4 \sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{2 \pi } e^3 \sin \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{4 \sqrt{2 \pi } e^3 \cos \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} d}+\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^(3/2)) - (4*e^3*(c + d*x)^2)/(b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) + (16*e^3*(c + d*x)^4)/(3*b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) + (4*e^3*Sqrt[2*Pi]*Cos[(4*a)/b]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) - (4*e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(3*b^(5/2)*d) + (4*e^3*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(3*b^(5/2)*d) - (4*e^3*Sqrt[2*Pi]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(3*b^(5/2)*d)","A",26,11,25,0.4400,1,"{4805, 12, 4633, 4719, 4635, 4406, 3306, 3305, 3351, 3304, 3352}"
272,1,342,0,1.0540792,"\int \frac{(c e+d e x)^2}{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x])^(5/2),x]","-\frac{\sqrt{2 \pi } e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{6 \pi } e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}-\frac{\sqrt{2 \pi } e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{6 \pi } e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}+\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}","-\frac{\sqrt{2 \pi } e^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{6 \pi } e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}-\frac{\sqrt{2 \pi } e^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{6 \pi } e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}+\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^(3/2)) - (8*e^2*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) + (4*e^2*(c + d*x)^3)/(b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) - (e^2*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) + (e^2*Sqrt[6*Pi]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(b^(5/2)*d) - (e^2*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*d) + (e^2*Sqrt[6*Pi]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(5/2)*d)","A",24,12,25,0.4800,1,"{4805, 12, 4633, 4719, 4635, 4406, 3306, 3305, 3351, 3304, 3352, 4623}"
273,1,207,0,0.5358867,"\int \frac{c e+d e x}{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x])^(5/2),x]","\frac{8 \sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 \sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} d}+\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}","\frac{8 \sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 \sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} d}+\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^(3/2)) - (4*e)/(3*b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) + (8*e*(c + d*x)^2)/(3*b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) - (8*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(3*b^(5/2)*d) + (8*e*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(3*b^(5/2)*d)","A",13,12,23,0.5217,1,"{4805, 12, 4633, 4719, 4635, 4406, 3306, 3305, 3351, 3304, 3352, 4641}"
274,1,179,0,0.280521,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c + d*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+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{3 b d \left(a+b \sin ^{-1}(c+d 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+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{3 b d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*Sqrt[1 - (c + d*x)^2])/(3*b*d*(a + b*ArcSin[c + d*x])^(3/2)) + (4*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcSin[c + d*x]]) - (4*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) - (4*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*d)","A",9,9,14,0.6429,1,"{4803, 4621, 4719, 4623, 3306, 3305, 3351, 3304, 3352}"
275,0,0,0,0.1017622,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])^(5/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])^(5/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
276,1,442,0,1.1372628,"\int \frac{(c e+d e x)^3}{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSin[c + d*x])^(7/2),x]","\frac{32 \sqrt{2 \pi } e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 \sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 \sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{15 b^{7/2} d}+\frac{32 \sqrt{2 \pi } e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{128 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^3 \sqrt{1-(c+d x)^2} (c+d x)}{5 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}","\frac{32 \sqrt{2 \pi } e^3 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 \sqrt{\pi } e^3 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 \sqrt{\pi } e^3 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{15 b^{7/2} d}+\frac{32 \sqrt{2 \pi } e^3 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{128 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^3 \sqrt{1-(c+d x)^2} (c+d x)}{5 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{1-(c+d x)^2} (c+d x)^3}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(5*b*d*(a + b*ArcSin[c + d*x])^(5/2)) - (4*e^3*(c + d*x)^2)/(5*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) + (16*e^3*(c + d*x)^4)/(15*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) - (16*e^3*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(5*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) + (128*e^3*(c + d*x)^3*Sqrt[1 - (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) + (32*e^3*Sqrt[2*Pi]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) - (16*e^3*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(15*b^(7/2)*d) - (16*e^3*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(15*b^(7/2)*d) + (32*e^3*Sqrt[2*Pi]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(4*a)/b])/(15*b^(7/2)*d)","A",23,10,25,0.4000,1,"{4805, 12, 4633, 4719, 4631, 3306, 3305, 3351, 3304, 3352}"
277,1,441,0,1.1978572,"\int \frac{(c e+d e x)^2}{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSin[c + d*x])^(7/2),x]","-\frac{2 \sqrt{2 \pi } e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{6 \sqrt{6 \pi } e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{2 \sqrt{2 \pi } e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{6 \sqrt{6 \pi } e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{24 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{5 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^2 \sqrt{1-(c+d x)^2}}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}","-\frac{2 \sqrt{2 \pi } e^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{6 \sqrt{6 \pi } e^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{2 \sqrt{2 \pi } e^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{6 \sqrt{6 \pi } e^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{24 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{5 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^2 \sqrt{1-(c+d x)^2}}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{1-(c+d x)^2} (c+d x)^2}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(5*b*d*(a + b*ArcSin[c + d*x])^(5/2)) - (8*e^2*(c + d*x))/(15*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) + (4*e^2*(c + d*x)^3)/(5*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) - (16*e^2*Sqrt[1 - (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) + (24*e^2*(c + d*x)^2*Sqrt[1 - (c + d*x)^2])/(5*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) + (2*e^2*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) - (6*e^2*Sqrt[6*Pi]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(5*b^(7/2)*d) - (2*e^2*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(15*b^(7/2)*d) + (6*e^2*Sqrt[6*Pi]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[(3*a)/b])/(5*b^(7/2)*d)","A",24,12,25,0.4800,1,"{4805, 12, 4633, 4719, 4631, 3306, 3305, 3351, 3304, 3352, 4621, 4723}"
278,1,252,0,0.5412536,"\int \frac{c e+d e x}{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSin[c + d*x])^(7/2),x]","-\frac{32 \sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{15 b^{7/2} d}-\frac{32 \sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{15 b^{7/2} d}+\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{32 e \sqrt{1-(c+d x)^2} (c+d x)}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}","-\frac{32 \sqrt{\pi } e \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{\pi } \sqrt{b}}\right)}{15 b^{7/2} d}-\frac{32 \sqrt{\pi } e \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b} \sqrt{\pi }}\right)}{15 b^{7/2} d}+\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{32 e \sqrt{1-(c+d x)^2} (c+d x)}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{4 e}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{1-(c+d x)^2} (c+d x)}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(5*b*d*(a + b*ArcSin[c + d*x])^(5/2)) - (4*e)/(15*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) + (8*e*(c + d*x)^2)/(15*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) + (32*e*(c + d*x)*Sqrt[1 - (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) - (32*e*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])])/(15*b^(7/2)*d) - (32*e*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c + d*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(15*b^(7/2)*d)","A",11,11,23,0.4783,1,"{4805, 12, 4633, 4719, 4631, 3306, 3305, 3351, 3304, 3352, 4641}"
279,1,218,0,0.4516154,"\int \frac{1}{\left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^(-7/2),x]","-\frac{8 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 (c+d x)}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{8 \sqrt{1-(c+d x)^2}}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}","-\frac{8 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 (c+d x)}{15 b^2 d \left(a+b \sin ^{-1}(c+d x)\right)^{3/2}}+\frac{8 \sqrt{1-(c+d x)^2}}{15 b^3 d \sqrt{a+b \sin ^{-1}(c+d x)}}-\frac{2 \sqrt{1-(c+d x)^2}}{5 b d \left(a+b \sin ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*Sqrt[1 - (c + d*x)^2])/(5*b*d*(a + b*ArcSin[c + d*x])^(5/2)) + (4*(c + d*x))/(15*b^2*d*(a + b*ArcSin[c + d*x])^(3/2)) + (8*Sqrt[1 - (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSin[c + d*x]]) + (8*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) - (8*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c + d*x]])/Sqrt[b]]*Sin[a/b])/(15*b^(7/2)*d)","A",10,9,14,0.6429,1,"{4803, 4621, 4719, 4723, 3306, 3305, 3351, 3304, 3352}"
280,0,0,0,0.1021085,"\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSin[c + d*x])^(7/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sin ^{-1}(c+d x)\right)^{7/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSin[x])^(7/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
281,1,156,0,0.1240936,"\int (c e+d e x)^{7/2} \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcSin[c + d*x]),x]","\frac{2 (e (c+d x))^{9/2} \left(a+b \sin ^{-1}(c+d x)\right)}{9 d e}+\frac{28 b e^2 \sqrt{1-(c+d x)^2} (e (c+d x))^{3/2}}{405 d}+\frac{28 b e^3 \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{135 d \sqrt{c+d x}}+\frac{4 b \sqrt{1-(c+d x)^2} (e (c+d x))^{7/2}}{81 d}","\frac{2 (e (c+d x))^{9/2} \left(a+b \sin ^{-1}(c+d x)\right)}{9 d e}+\frac{28 b e^2 \sqrt{1-(c+d x)^2} (e (c+d x))^{3/2}}{405 d}+\frac{28 b e^3 \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{135 d \sqrt{c+d x}}+\frac{4 b \sqrt{1-(c+d x)^2} (e (c+d x))^{7/2}}{81 d}",1,"(28*b*e^2*(e*(c + d*x))^(3/2)*Sqrt[1 - (c + d*x)^2])/(405*d) + (4*b*(e*(c + d*x))^(7/2)*Sqrt[1 - (c + d*x)^2])/(81*d) + (2*(e*(c + d*x))^(9/2)*(a + b*ArcSin[c + d*x]))/(9*d*e) + (28*b*e^3*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 - c - d*x]/Sqrt[2]], 2])/(135*d*Sqrt[c + d*x])","A",7,6,23,0.2609,1,"{4805, 4627, 321, 320, 318, 424}"
282,1,136,0,0.1133452,"\int (c e+d e x)^{5/2} \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcSin[c + d*x]),x]","\frac{2 (e (c+d x))^{7/2} \left(a+b \sin ^{-1}(c+d x)\right)}{7 d e}+\frac{20 b e^2 \sqrt{1-(c+d x)^2} \sqrt{e (c+d x)}}{147 d}-\frac{20 b e^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{147 d}+\frac{4 b \sqrt{1-(c+d x)^2} (e (c+d x))^{5/2}}{49 d}","\frac{2 (e (c+d x))^{7/2} \left(a+b \sin ^{-1}(c+d x)\right)}{7 d e}+\frac{20 b e^2 \sqrt{1-(c+d x)^2} \sqrt{e (c+d x)}}{147 d}-\frac{20 b e^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{147 d}+\frac{4 b \sqrt{1-(c+d x)^2} (e (c+d x))^{5/2}}{49 d}",1,"(20*b*e^2*Sqrt[e*(c + d*x)]*Sqrt[1 - (c + d*x)^2])/(147*d) + (4*b*(e*(c + d*x))^(5/2)*Sqrt[1 - (c + d*x)^2])/(49*d) + (2*(e*(c + d*x))^(7/2)*(a + b*ArcSin[c + d*x]))/(7*d*e) - (20*b*e^(5/2)*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(147*d)","A",6,5,23,0.2174,1,"{4805, 4627, 321, 329, 221}"
283,1,117,0,0.0974955,"\int (c e+d e x)^{3/2} \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcSin[c + d*x]),x]","\frac{2 (e (c+d x))^{5/2} \left(a+b \sin ^{-1}(c+d x)\right)}{5 d e}+\frac{4 b \sqrt{1-(c+d x)^2} (e (c+d x))^{3/2}}{25 d}+\frac{12 b e \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{25 d \sqrt{c+d x}}","\frac{2 (e (c+d x))^{5/2} \left(a+b \sin ^{-1}(c+d x)\right)}{5 d e}+\frac{4 b \sqrt{1-(c+d x)^2} (e (c+d x))^{3/2}}{25 d}+\frac{12 b e \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{25 d \sqrt{c+d x}}",1,"(4*b*(e*(c + d*x))^(3/2)*Sqrt[1 - (c + d*x)^2])/(25*d) + (2*(e*(c + d*x))^(5/2)*(a + b*ArcSin[c + d*x]))/(5*d*e) + (12*b*e*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 - c - d*x]/Sqrt[2]], 2])/(25*d*Sqrt[c + d*x])","A",6,6,23,0.2609,1,"{4805, 4627, 321, 320, 318, 424}"
284,1,99,0,0.0809253,"\int \sqrt{c e+d e x} \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSin[c + d*x]),x]","\frac{2 (e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e}+\frac{4 b \sqrt{1-(c+d x)^2} \sqrt{e (c+d x)}}{9 d}-\frac{4 b \sqrt{e} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{9 d}","\frac{2 (e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e}+\frac{4 b \sqrt{1-(c+d x)^2} \sqrt{e (c+d x)}}{9 d}-\frac{4 b \sqrt{e} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{9 d}",1,"(4*b*Sqrt[e*(c + d*x)]*Sqrt[1 - (c + d*x)^2])/(9*d) + (2*(e*(c + d*x))^(3/2)*(a + b*ArcSin[c + d*x]))/(3*d*e) - (4*b*Sqrt[e]*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(9*d)","A",5,5,23,0.2174,1,"{4805, 4627, 321, 329, 221}"
285,1,81,0,0.0759981,"\int \frac{a+b \sin ^{-1}(c+d x)}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSin[c + d*x])/Sqrt[c*e + d*e*x],x]","\frac{2 \sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)}{d e}+\frac{4 b \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{d e \sqrt{c+d x}}","\frac{2 \sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)}{d e}+\frac{4 b \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{d e \sqrt{c+d x}}",1,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSin[c + d*x]))/(d*e) + (4*b*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 - c - d*x]/Sqrt[2]], 2])/(d*e*Sqrt[c + d*x])","A",5,5,23,0.2174,1,"{4805, 4627, 320, 318, 424}"
286,1,61,0,0.0680877,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^(3/2),x]","\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}","\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}",1,"(-2*(a + b*ArcSin[c + d*x]))/(d*e*Sqrt[e*(c + d*x)]) + (4*b*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(d*e^(3/2))","A",4,4,23,0.1739,1,"{4805, 4627, 329, 221}"
287,1,122,0,0.1049806,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^(5/2),x]","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}-\frac{4 b \sqrt{1-(c+d x)^2}}{3 d e^2 \sqrt{e (c+d x)}}+\frac{4 b \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{3 d e^3 \sqrt{c+d x}}","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}-\frac{4 b \sqrt{1-(c+d x)^2}}{3 d e^2 \sqrt{e (c+d x)}}+\frac{4 b \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{3 d e^3 \sqrt{c+d x}}",1,"(-4*b*Sqrt[1 - (c + d*x)^2])/(3*d*e^2*Sqrt[e*(c + d*x)]) - (2*(a + b*ArcSin[c + d*x]))/(3*d*e*(e*(c + d*x))^(3/2)) + (4*b*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 - c - d*x]/Sqrt[2]], 2])/(3*d*e^3*Sqrt[c + d*x])","A",6,6,23,0.2609,1,"{4805, 4627, 325, 320, 318, 424}"
288,1,102,0,0.0905582,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^(7/2),x]","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}-\frac{4 b \sqrt{1-(c+d x)^2}}{15 d e^2 (e (c+d x))^{3/2}}+\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{15 d e^{7/2}}","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}-\frac{4 b \sqrt{1-(c+d x)^2}}{15 d e^2 (e (c+d x))^{3/2}}+\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{15 d e^{7/2}}",1,"(-4*b*Sqrt[1 - (c + d*x)^2])/(15*d*e^2*(e*(c + d*x))^(3/2)) - (2*(a + b*ArcSin[c + d*x]))/(5*d*e*(e*(c + d*x))^(5/2)) + (4*b*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(15*d*e^(7/2))","A",5,5,23,0.2174,1,"{4805, 4627, 325, 329, 221}"
289,1,159,0,0.1275134,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^{9/2}} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^(9/2),x]","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{7 d e (e (c+d x))^{7/2}}-\frac{12 b \sqrt{1-(c+d x)^2}}{35 d e^4 \sqrt{e (c+d x)}}-\frac{4 b \sqrt{1-(c+d x)^2}}{35 d e^2 (e (c+d x))^{5/2}}+\frac{12 b \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{35 d e^5 \sqrt{c+d x}}","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{7 d e (e (c+d x))^{7/2}}-\frac{12 b \sqrt{1-(c+d x)^2}}{35 d e^4 \sqrt{e (c+d x)}}-\frac{4 b \sqrt{1-(c+d x)^2}}{35 d e^2 (e (c+d x))^{5/2}}+\frac{12 b \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{-c-d x+1}}{\sqrt{2}}\right)\right|2\right)}{35 d e^5 \sqrt{c+d x}}",1,"(-4*b*Sqrt[1 - (c + d*x)^2])/(35*d*e^2*(e*(c + d*x))^(5/2)) - (12*b*Sqrt[1 - (c + d*x)^2])/(35*d*e^4*Sqrt[e*(c + d*x)]) - (2*(a + b*ArcSin[c + d*x]))/(7*d*e*(e*(c + d*x))^(7/2)) + (12*b*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 - c - d*x]/Sqrt[2]], 2])/(35*d*e^5*Sqrt[c + d*x])","A",7,6,23,0.2609,1,"{4805, 4627, 325, 320, 318, 424}"
290,1,139,0,0.1138512,"\int \frac{a+b \sin ^{-1}(c+d x)}{(c e+d e x)^{11/2}} \, dx","Int[(a + b*ArcSin[c + d*x])/(c*e + d*e*x)^(11/2),x]","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{9 d e (e (c+d x))^{9/2}}-\frac{20 b \sqrt{1-(c+d x)^2}}{189 d e^4 (e (c+d x))^{3/2}}-\frac{4 b \sqrt{1-(c+d x)^2}}{63 d e^2 (e (c+d x))^{7/2}}+\frac{20 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{189 d e^{11/2}}","-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)}{9 d e (e (c+d x))^{9/2}}-\frac{20 b \sqrt{1-(c+d x)^2}}{189 d e^4 (e (c+d x))^{3/2}}-\frac{4 b \sqrt{1-(c+d x)^2}}{63 d e^2 (e (c+d x))^{7/2}}+\frac{20 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{189 d e^{11/2}}",1,"(-4*b*Sqrt[1 - (c + d*x)^2])/(63*d*e^2*(e*(c + d*x))^(7/2)) - (20*b*Sqrt[1 - (c + d*x)^2])/(189*d*e^4*(e*(c + d*x))^(3/2)) - (2*(a + b*ArcSin[c + d*x]))/(9*d*e*(e*(c + d*x))^(9/2)) + (20*b*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(189*d*e^(11/2))","A",6,5,23,0.2174,1,"{4805, 4627, 325, 329, 221}"
291,1,130,0,0.2050764,"\int (c e+d e x)^{7/2} \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcSin[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};(c+d x)^2\right)}{1287 d e^3}-\frac{8 b (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{99 d e^2}+\frac{2 (e (c+d x))^{9/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{9 d e}","\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};(c+d x)^2\right)}{1287 d e^3}-\frac{8 b (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{99 d e^2}+\frac{2 (e (c+d x))^{9/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{9 d e}",1,"(2*(e*(c + d*x))^(9/2)*(a + b*ArcSin[c + d*x])^2)/(9*d*e) - (8*b*(e*(c + d*x))^(11/2)*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/2, 11/4, 15/4, (c + d*x)^2])/(99*d*e^2) + (16*b^2*(e*(c + d*x))^(13/2)*HypergeometricPFQ[{1, 13/4, 13/4}, {15/4, 17/4}, (c + d*x)^2])/(1287*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
292,1,130,0,0.206382,"\int (c e+d e x)^{5/2} \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcSin[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};(c+d x)^2\right)}{693 d e^3}-\frac{8 b (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{63 d e^2}+\frac{2 (e (c+d x))^{7/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{7 d e}","\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};(c+d x)^2\right)}{693 d e^3}-\frac{8 b (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{63 d e^2}+\frac{2 (e (c+d x))^{7/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{7 d e}",1,"(2*(e*(c + d*x))^(7/2)*(a + b*ArcSin[c + d*x])^2)/(7*d*e) - (8*b*(e*(c + d*x))^(9/2)*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/2, 9/4, 13/4, (c + d*x)^2])/(63*d*e^2) + (16*b^2*(e*(c + d*x))^(11/2)*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, (c + d*x)^2])/(693*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
293,1,130,0,0.2057957,"\int (c e+d e x)^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcSin[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};(c+d x)^2\right)}{315 d e^3}-\frac{8 b (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{35 d e^2}+\frac{2 (e (c+d x))^{5/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{5 d e}","\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};(c+d x)^2\right)}{315 d e^3}-\frac{8 b (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{35 d e^2}+\frac{2 (e (c+d x))^{5/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{5 d e}",1,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcSin[c + d*x])^2)/(5*d*e) - (8*b*(e*(c + d*x))^(7/2)*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/2, 7/4, 11/4, (c + d*x)^2])/(35*d*e^2) + (16*b^2*(e*(c + d*x))^(9/2)*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, (c + d*x)^2])/(315*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
294,1,130,0,0.1967167,"\int \sqrt{c e+d e x} \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSin[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};(c+d x)^2\right)}{105 d e^3}-\frac{8 b (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{15 d e^2}+\frac{2 (e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d e}","\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};(c+d x)^2\right)}{105 d e^3}-\frac{8 b (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{15 d e^2}+\frac{2 (e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d e}",1,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcSin[c + d*x])^2)/(3*d*e) - (8*b*(e*(c + d*x))^(5/2)*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/2, 5/4, 9/4, (c + d*x)^2])/(15*d*e^2) + (16*b^2*(e*(c + d*x))^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, (c + d*x)^2])/(105*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
295,1,128,0,0.1931973,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSin[c + d*x])^2/Sqrt[c*e + d*e*x],x]","\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};(c+d x)^2\right)}{15 d e^3}-\frac{8 b (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^2}+\frac{2 \sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e}","\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};(c+d x)^2\right)}{15 d e^3}-\frac{8 b (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^2}+\frac{2 \sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e}",1,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSin[c + d*x])^2)/(d*e) - (8*b*(e*(c + d*x))^(3/2)*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/2, 3/4, 7/4, (c + d*x)^2])/(3*d*e^2) + (16*b^2*(e*(c + d*x))^(5/2)*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, (c + d*x)^2])/(15*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
296,1,126,0,0.2012112,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^(3/2),x]","-\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}","-\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}",1,"(-2*(a + b*ArcSin[c + d*x])^2)/(d*e*Sqrt[e*(c + d*x)]) + (8*b*Sqrt[e*(c + d*x)]*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/4, 1/2, 5/4, (c + d*x)^2])/(d*e^2) - (16*b^2*(e*(c + d*x))^(3/2)*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, (c + d*x)^2])/(3*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
297,1,130,0,0.2128589,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^(5/2),x]","\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};(c+d x)^2\right)}{3 d e^3}-\frac{8 b \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{e (c+d x)}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}","\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};(c+d x)^2\right)}{3 d e^3}-\frac{8 b \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{e (c+d x)}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}",1,"(-2*(a + b*ArcSin[c + d*x])^2)/(3*d*e*(e*(c + d*x))^(3/2)) - (8*b*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[-1/4, 1/2, 3/4, (c + d*x)^2])/(3*d*e^2*Sqrt[e*(c + d*x)]) + (16*b^2*Sqrt[e*(c + d*x)]*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, (c + d*x)^2])/(3*d*e^3)","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
298,1,130,0,0.2168703,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^(7/2),x]","-\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{15 d e^2 (e (c+d x))^{3/2}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}","-\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{15 d e^2 (e (c+d x))^{3/2}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}",1,"(-2*(a + b*ArcSin[c + d*x])^2)/(5*d*e*(e*(c + d*x))^(5/2)) - (8*b*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[-3/4, 1/2, 1/4, (c + d*x)^2])/(15*d*e^2*(e*(c + d*x))^(3/2)) - (16*b^2*HypergeometricPFQ[{-1/4, -1/4, 1}, {1/4, 3/4}, (c + d*x)^2])/(15*d*e^3*Sqrt[e*(c + d*x)])","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
299,1,130,0,0.2158168,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{(c e+d e x)^{9/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^2/(c*e + d*e*x)^(9/2),x]","-\frac{16 b^2 \, _3F_2\left(-\frac{3}{4},-\frac{3}{4},1;-\frac{1}{4},\frac{1}{4};(c+d x)^2\right)}{105 d e^3 (e (c+d x))^{3/2}}-\frac{8 b \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{35 d e^2 (e (c+d x))^{5/2}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{7 d e (e (c+d x))^{7/2}}","-\frac{16 b^2 \, _3F_2\left(-\frac{3}{4},-\frac{3}{4},1;-\frac{1}{4},\frac{1}{4};(c+d x)^2\right)}{105 d e^3 (e (c+d x))^{3/2}}-\frac{8 b \, _2F_1\left(-\frac{5}{4},\frac{1}{2};-\frac{1}{4};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{35 d e^2 (e (c+d x))^{5/2}}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^2}{7 d e (e (c+d x))^{7/2}}",1,"(-2*(a + b*ArcSin[c + d*x])^2)/(7*d*e*(e*(c + d*x))^(7/2)) - (8*b*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[-5/4, 1/2, -1/4, (c + d*x)^2])/(35*d*e^2*(e*(c + d*x))^(5/2)) - (16*b^2*HypergeometricPFQ[{-3/4, -3/4, 1}, {-1/4, 1/4}, (c + d*x)^2])/(105*d*e^3*(e*(c + d*x))^(3/2))","A",3,3,25,0.1200,1,"{4805, 4627, 4711}"
300,0,0,0,0.1971866,"\int \sqrt{c e+d e x} \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSin[c + d*x])^3,x]","\int \sqrt{c e+d e x} \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e}-\frac{2 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^2}{\sqrt{1-(c+d x)^2}},x\right)}{e}",0,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcSin[c + d*x])^3)/(3*d*e) - (2*b*Defer[Subst][Defer[Int][((e*x)^(3/2)*(a + b*ArcSin[x])^2)/Sqrt[1 - x^2], x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
301,0,0,0,0.1837668,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSin[c + d*x])^3/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e}-\frac{6 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)^2}{\sqrt{1-(c+d x)^2}},x\right)}{e}",0,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSin[c + d*x])^3)/(d*e) - (6*b*Defer[Subst][Defer[Int][(Sqrt[e*x]*(a + b*ArcSin[x])^2)/Sqrt[1 - x^2], x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
302,0,0,0,0.1916049,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^3/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{\sqrt{1-(c+d x)^2} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e \sqrt{e (c+d x)}}",0,"(-2*(a + b*ArcSin[c + d*x])^3)/(d*e*Sqrt[e*(c + d*x)]) + (6*b*Defer[Subst][Defer[Int][(a + b*ArcSin[x])^2/(Sqrt[e*x]*Sqrt[1 - x^2]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
303,0,0,0,0.2062285,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^3/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","\frac{2 b \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^2}{\sqrt{1-(c+d x)^2} (e (c+d x))^{3/2}},x\right)}{e}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^3}{3 d e (e (c+d x))^{3/2}}",0,"(-2*(a + b*ArcSin[c + d*x])^3)/(3*d*e*(e*(c + d*x))^(3/2)) + (2*b*Defer[Subst][Defer[Int][(a + b*ArcSin[x])^2/((e*x)^(3/2)*Sqrt[1 - x^2]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
304,0,0,0,0.1935708,"\int \sqrt{c e+d e x} \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSin[c + d*x])^4,x]","\int \sqrt{c e+d e x} \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^4}{3 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{1-(c+d x)^2}},x\right)}{3 e}",0,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcSin[c + d*x])^4)/(3*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(3/2)*(a + b*ArcSin[x])^3)/Sqrt[1 - x^2], x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
305,0,0,0,0.1789858,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSin[c + d*x])^4/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)^4}{d e}-\frac{8 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{1-(c+d x)^2}},x\right)}{e}",0,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSin[c + d*x])^4)/(d*e) - (8*b*Defer[Subst][Defer[Int][(Sqrt[e*x]*(a + b*ArcSin[x])^3)/Sqrt[1 - x^2], x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
306,0,0,0,0.1891414,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^4/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{1-(c+d x)^2} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^4}{d e \sqrt{e (c+d x)}}",0,"(-2*(a + b*ArcSin[c + d*x])^4)/(d*e*Sqrt[e*(c + d*x)]) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcSin[x])^3/(Sqrt[e*x]*Sqrt[1 - x^2]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
307,0,0,0,0.2061582,"\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c + d*x])^4/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \sin ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{1-(c+d x)^2} (e (c+d x))^{3/2}},x\right)}{3 e}-\frac{2 \left(a+b \sin ^{-1}(c+d x)\right)^4}{3 d e (e (c+d x))^{3/2}}",0,"(-2*(a + b*ArcSin[c + d*x])^4)/(3*d*e*(e*(c + d*x))^(3/2)) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcSin[x])^3/((e*x)^(3/2)*Sqrt[1 - x^2]), x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
308,0,0,0,0.1868207,"\int (c e+d e x)^m \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSin[c + d*x])^4,x]","\int (c e+d e x)^m \left(a+b \sin ^{-1}(c+d x)\right)^4 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)^4}{d e (m+1)}-\frac{4 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)^3}{\sqrt{1-(c+d x)^2}},x\right)}{e (m+1)}",0,"((e*(c + d*x))^(1 + m)*(a + b*ArcSin[c + d*x])^4)/(d*e*(1 + m)) - (4*b*Defer[Subst][Defer[Int][((e*x)^(1 + m)*(a + b*ArcSin[x])^3)/Sqrt[1 - x^2], x], x, c + d*x])/(d*e*(1 + m))","A",0,0,0,0,-1,"{}"
309,0,0,0,0.1787893,"\int (c e+d e x)^m \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSin[c + d*x])^3,x]","\int (c e+d e x)^m \left(a+b \sin ^{-1}(c+d x)\right)^3 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)^3}{d e (m+1)}-\frac{3 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)^2}{\sqrt{1-(c+d x)^2}},x\right)}{e (m+1)}",0,"((e*(c + d*x))^(1 + m)*(a + b*ArcSin[c + d*x])^3)/(d*e*(1 + m)) - (3*b*Defer[Subst][Defer[Int][((e*x)^(1 + m)*(a + b*ArcSin[x])^2)/Sqrt[1 - x^2], x], x, c + d*x])/(d*e*(1 + m))","A",0,0,0,0,-1,"{}"
310,1,183,0,0.1988483,"\int (c e+d e x)^m \left(a+b \sin ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSin[c + d*x])^2,x]","\frac{2 b^2 (e (c+d 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};(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2)}+\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e (m+1)}","\frac{2 b^2 (e (c+d 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};(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right) \left(a+b \sin ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2)}+\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)^2}{d e (m+1)}",1,"((e*(c + d*x))^(1 + m)*(a + b*ArcSin[c + d*x])^2)/(d*e*(1 + m)) - (2*b*(e*(c + d*x))^(2 + m)*(a + b*ArcSin[c + d*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2])/(d*e^2*(1 + m)*(2 + m)) + (2*b^2*(e*(c + d*x))^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, (c + d*x)^2])/(d*e^3*(1 + m)*(2 + m)*(3 + m))","A",3,3,23,0.1304,1,"{4805, 4627, 4711}"
311,1,89,0,0.0621221,"\int (c e+d e x)^m \left(a+b \sin ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSin[c + d*x]),x]","\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right)}{d e^2 (m+1) (m+2)}","\frac{(e (c+d x))^{m+1} \left(a+b \sin ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right)}{d e^2 (m+1) (m+2)}",1,"((e*(c + d*x))^(1 + m)*(a + b*ArcSin[c + d*x]))/(d*e*(1 + m)) - (b*(e*(c + d*x))^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2])/(d*e^2*(1 + m)*(2 + m))","A",3,3,21,0.1429,1,"{4805, 4627, 364}"
312,0,0,0,0.0579832,"\int \frac{(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^m/(a + b*ArcSin[c + d*x]),x]","\int \frac{(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx","\text{Int}\left(\frac{(e (c+d x))^m}{a+b \sin ^{-1}(c+d x)},x\right)",0,"Defer[Subst][Defer[Int][(e*x)^m/(a + b*ArcSin[x]), x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
313,1,135,0,0.1934013,"\int \sqrt{1-a^2-2 a b x-b^2 x^2} \sin ^{-1}(a+b x)^3 \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSin[a + b*x]^3,x]","\frac{3 (a+b x)^2}{8 b}+\frac{\sin ^{-1}(a+b x)^4}{8 b}+\frac{(a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^3}{2 b}-\frac{3 (a+b x)^2 \sin ^{-1}(a+b x)^2}{4 b}+\frac{3 \sin ^{-1}(a+b x)^2}{8 b}-\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{4 b}","\frac{3 (a+b x)^2}{8 b}+\frac{\sin ^{-1}(a+b x)^4}{8 b}+\frac{(a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^3}{2 b}-\frac{3 (a+b x)^2 \sin ^{-1}(a+b x)^2}{4 b}+\frac{3 \sin ^{-1}(a+b x)^2}{8 b}-\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)}{4 b}",1,"(3*(a + b*x)^2)/(8*b) - (3*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(4*b) + (3*ArcSin[a + b*x]^2)/(8*b) - (3*(a + b*x)^2*ArcSin[a + b*x]^2)/(4*b) + ((a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^3)/(2*b) + ArcSin[a + b*x]^4/(8*b)","A",7,6,33,0.1818,1,"{4807, 4647, 4641, 4627, 4707, 30}"
314,1,111,0,0.1272104,"\int \sqrt{1-a^2-2 a b x-b^2 x^2} \sin ^{-1}(a+b x)^2 \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSin[a + b*x]^2,x]","-\frac{(a+b x) \sqrt{1-(a+b x)^2}}{4 b}+\frac{\sin ^{-1}(a+b x)^3}{6 b}+\frac{(a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{2 b}-\frac{(a+b x)^2 \sin ^{-1}(a+b x)}{2 b}+\frac{\sin ^{-1}(a+b x)}{4 b}","-\frac{(a+b x) \sqrt{1-(a+b x)^2}}{4 b}+\frac{\sin ^{-1}(a+b x)^3}{6 b}+\frac{(a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{2 b}-\frac{(a+b x)^2 \sin ^{-1}(a+b x)}{2 b}+\frac{\sin ^{-1}(a+b x)}{4 b}",1,"-((a + b*x)*Sqrt[1 - (a + b*x)^2])/(4*b) + ArcSin[a + b*x]/(4*b) - ((a + b*x)^2*ArcSin[a + b*x])/(2*b) + ((a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(2*b) + ArcSin[a + b*x]^3/(6*b)","A",6,6,33,0.1818,1,"{4807, 4647, 4641, 4627, 321, 216}"
315,1,63,0,0.070168,"\int \sqrt{1-a^2-2 a b x-b^2 x^2} \sin ^{-1}(a+b x) \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSin[a + b*x],x]","-\frac{(a+b x)^2}{4 b}+\frac{\sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{2 b}+\frac{\sin ^{-1}(a+b x)^2}{4 b}","-\frac{(a+b x)^2}{4 b}+\frac{\sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{2 b}+\frac{\sin ^{-1}(a+b x)^2}{4 b}",1,"-(a + b*x)^2/(4*b) + ((a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(2*b) + ArcSin[a + b*x]^2/(4*b)","A",4,4,31,0.1290,1,"{4807, 4647, 4641, 30}"
316,1,31,0,0.1218918,"\int \frac{\sqrt{1-a^2-2 a b x-b^2 x^2}}{\sin ^{-1}(a+b x)} \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]/ArcSin[a + b*x],x]","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{2 b}+\frac{\log \left(\sin ^{-1}(a+b x)\right)}{2 b}","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{2 b}+\frac{\log \left(\sin ^{-1}(a+b x)\right)}{2 b}",1,"CosIntegral[2*ArcSin[a + b*x]]/(2*b) + Log[ArcSin[a + b*x]]/(2*b)","A",5,4,33,0.1212,1,"{4807, 4661, 3312, 3302}"
317,1,39,0,0.1144535,"\int \frac{\sqrt{1-a^2-2 a b x-b^2 x^2}}{\sin ^{-1}(a+b x)^2} \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]/ArcSin[a + b*x]^2,x]","-\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b}-\frac{1-(a+b x)^2}{b \sin ^{-1}(a+b x)}","-\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b}-\frac{1-(a+b x)^2}{b \sin ^{-1}(a+b x)}",1,"-((1 - (a + b*x)^2)/(b*ArcSin[a + b*x])) - SinIntegral[2*ArcSin[a + b*x]]/b","A",6,6,33,0.1818,1,"{4807, 4659, 4635, 4406, 12, 3299}"
318,1,73,0,0.1127506,"\int \frac{\sqrt{1-a^2-2 a b x-b^2 x^2}}{\sin ^{-1}(a+b x)^3} \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]/ArcSin[a + b*x]^3,x]","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b}+\frac{\sqrt{1-(a+b x)^2} (a+b x)}{b \sin ^{-1}(a+b x)}-\frac{1-(a+b x)^2}{2 b \sin ^{-1}(a+b x)^2}","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b}+\frac{\sqrt{1-(a+b x)^2} (a+b x)}{b \sin ^{-1}(a+b x)}-\frac{1-(a+b x)^2}{2 b \sin ^{-1}(a+b x)^2}",1,"-(1 - (a + b*x)^2)/(2*b*ArcSin[a + b*x]^2) + ((a + b*x)*Sqrt[1 - (a + b*x)^2])/(b*ArcSin[a + b*x]) - CosIntegral[2*ArcSin[a + b*x]]/b","A",4,4,33,0.1212,1,"{4807, 4659, 4631, 3302}"
319,1,115,0,0.2240369,"\int \frac{\sqrt{1-a^2-2 a b x-b^2 x^2}}{\sin ^{-1}(a+b x)^4} \, dx","Int[Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]/ArcSin[a + b*x]^4,x]","\frac{2 \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{3 b}-\frac{2 (a+b x)^2}{3 b \sin ^{-1}(a+b x)}+\frac{\sqrt{1-(a+b x)^2} (a+b x)}{3 b \sin ^{-1}(a+b x)^2}+\frac{1}{3 b \sin ^{-1}(a+b x)}-\frac{1-(a+b x)^2}{3 b \sin ^{-1}(a+b x)^3}","\frac{2 \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{3 b}-\frac{2 (a+b x)^2}{3 b \sin ^{-1}(a+b x)}+\frac{\sqrt{1-(a+b x)^2} (a+b x)}{3 b \sin ^{-1}(a+b x)^2}+\frac{1}{3 b \sin ^{-1}(a+b x)}-\frac{1-(a+b x)^2}{3 b \sin ^{-1}(a+b x)^3}",1,"-(1 - (a + b*x)^2)/(3*b*ArcSin[a + b*x]^3) + ((a + b*x)*Sqrt[1 - (a + b*x)^2])/(3*b*ArcSin[a + b*x]^2) + 1/(3*b*ArcSin[a + b*x]) - (2*(a + b*x)^2)/(3*b*ArcSin[a + b*x]) + (2*SinIntegral[2*ArcSin[a + b*x]])/(3*b)","A",9,9,33,0.2727,1,"{4807, 4659, 4633, 4719, 4635, 4406, 12, 3299, 4641}"
320,1,245,0,0.3247461,"\int \left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x)^3 \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)*ArcSin[a + b*x]^3,x]","-\frac{3 (a+b x)^4}{128 b}+\frac{51 (a+b x)^2}{128 b}-\frac{9 (a+b x)^2 \sin ^{-1}(a+b x)^2}{16 b}+\frac{\left(1-(a+b x)^2\right)^{3/2} (a+b x) \sin ^{-1}(a+b x)^3}{4 b}+\frac{3 \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)^3}{8 b}-\frac{3 \left(1-(a+b x)^2\right)^{3/2} (a+b x) \sin ^{-1}(a+b x)}{32 b}-\frac{45 \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{64 b}+\frac{3 \sin ^{-1}(a+b x)^4}{32 b}+\frac{3 \left(1-(a+b x)^2\right)^2 \sin ^{-1}(a+b x)^2}{16 b}+\frac{27 \sin ^{-1}(a+b x)^2}{128 b}","-\frac{3 (a+b x)^4}{128 b}+\frac{51 (a+b x)^2}{128 b}-\frac{9 (a+b x)^2 \sin ^{-1}(a+b x)^2}{16 b}+\frac{\left(1-(a+b x)^2\right)^{3/2} (a+b x) \sin ^{-1}(a+b x)^3}{4 b}+\frac{3 \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)^3}{8 b}-\frac{3 \left(1-(a+b x)^2\right)^{3/2} (a+b x) \sin ^{-1}(a+b x)}{32 b}-\frac{45 \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{64 b}+\frac{3 \sin ^{-1}(a+b x)^4}{32 b}+\frac{3 \left(1-(a+b x)^2\right)^2 \sin ^{-1}(a+b x)^2}{16 b}+\frac{27 \sin ^{-1}(a+b x)^2}{128 b}",1,"(51*(a + b*x)^2)/(128*b) - (3*(a + b*x)^4)/(128*b) - (45*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(64*b) - (3*(a + b*x)*(1 - (a + b*x)^2)^(3/2)*ArcSin[a + b*x])/(32*b) + (27*ArcSin[a + b*x]^2)/(128*b) - (9*(a + b*x)^2*ArcSin[a + b*x]^2)/(16*b) + (3*(1 - (a + b*x)^2)^2*ArcSin[a + b*x]^2)/(16*b) + (3*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^3)/(8*b) + ((a + b*x)*(1 - (a + b*x)^2)^(3/2)*ArcSin[a + b*x]^3)/(4*b) + (3*ArcSin[a + b*x]^4)/(32*b)","A",15,9,33,0.2727,1,"{4807, 4649, 4647, 4641, 4627, 4707, 30, 4677, 14}"
321,1,199,0,0.204458,"\int \left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x)^2 \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)*ArcSin[a + b*x]^2,x]","-\frac{(a+b x) \left(1-(a+b x)^2\right)^{3/2}}{32 b}-\frac{15 (a+b x) \sqrt{1-(a+b x)^2}}{64 b}+\frac{\sin ^{-1}(a+b x)^3}{8 b}+\frac{(a+b x) \left(1-(a+b x)^2\right)^{3/2} \sin ^{-1}(a+b x)^2}{4 b}+\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{8 b}-\frac{3 (a+b x)^2 \sin ^{-1}(a+b x)}{8 b}+\frac{\left(1-(a+b x)^2\right)^2 \sin ^{-1}(a+b x)}{8 b}+\frac{9 \sin ^{-1}(a+b x)}{64 b}","-\frac{(a+b x) \left(1-(a+b x)^2\right)^{3/2}}{32 b}-\frac{15 (a+b x) \sqrt{1-(a+b x)^2}}{64 b}+\frac{\sin ^{-1}(a+b x)^3}{8 b}+\frac{(a+b x) \left(1-(a+b x)^2\right)^{3/2} \sin ^{-1}(a+b x)^2}{4 b}+\frac{3 (a+b x) \sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{8 b}-\frac{3 (a+b x)^2 \sin ^{-1}(a+b x)}{8 b}+\frac{\left(1-(a+b x)^2\right)^2 \sin ^{-1}(a+b x)}{8 b}+\frac{9 \sin ^{-1}(a+b x)}{64 b}",1,"(-15*(a + b*x)*Sqrt[1 - (a + b*x)^2])/(64*b) - ((a + b*x)*(1 - (a + b*x)^2)^(3/2))/(32*b) + (9*ArcSin[a + b*x])/(64*b) - (3*(a + b*x)^2*ArcSin[a + b*x])/(8*b) + ((1 - (a + b*x)^2)^2*ArcSin[a + b*x])/(8*b) + (3*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(8*b) + ((a + b*x)*(1 - (a + b*x)^2)^(3/2)*ArcSin[a + b*x]^2)/(4*b) + ArcSin[a + b*x]^3/(8*b)","A",11,9,33,0.2727,1,"{4807, 4649, 4647, 4641, 4627, 321, 216, 4677, 195}"
322,1,110,0,0.1057564,"\int \left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x) \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)*ArcSin[a + b*x],x]","\frac{(a+b x)^4}{16 b}-\frac{5 (a+b x)^2}{16 b}+\frac{\left(1-(a+b x)^2\right)^{3/2} (a+b x) \sin ^{-1}(a+b x)}{4 b}+\frac{3 \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{8 b}+\frac{3 \sin ^{-1}(a+b x)^2}{16 b}","\frac{(a+b x)^4}{16 b}-\frac{5 (a+b x)^2}{16 b}+\frac{\left(1-(a+b x)^2\right)^{3/2} (a+b x) \sin ^{-1}(a+b x)}{4 b}+\frac{3 \sqrt{1-(a+b x)^2} (a+b x) \sin ^{-1}(a+b x)}{8 b}+\frac{3 \sin ^{-1}(a+b x)^2}{16 b}",1,"(-5*(a + b*x)^2)/(16*b) + (a + b*x)^4/(16*b) + (3*(a + b*x)*Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x])/(8*b) + ((a + b*x)*(1 - (a + b*x)^2)^(3/2)*ArcSin[a + b*x])/(4*b) + (3*ArcSin[a + b*x]^2)/(16*b)","A",7,6,31,0.1935,1,"{4807, 4649, 4647, 4641, 30, 14}"
323,1,47,0,0.1381568,"\int \frac{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}}{\sin ^{-1}(a+b x)} \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)/ArcSin[a + b*x],x]","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{2 b}+\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a+b x)\right)}{8 b}+\frac{3 \log \left(\sin ^{-1}(a+b x)\right)}{8 b}","\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{2 b}+\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a+b x)\right)}{8 b}+\frac{3 \log \left(\sin ^{-1}(a+b x)\right)}{8 b}",1,"CosIntegral[2*ArcSin[a + b*x]]/(2*b) + CosIntegral[4*ArcSin[a + b*x]]/(8*b) + (3*Log[ArcSin[a + b*x]])/(8*b)","A",6,4,33,0.1212,1,"{4807, 4661, 3312, 3302}"
324,1,57,0,0.1520605,"\int \frac{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}}{\sin ^{-1}(a+b x)^2} \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)/ArcSin[a + b*x]^2,x]","-\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b}-\frac{\text{Si}\left(4 \sin ^{-1}(a+b x)\right)}{2 b}-\frac{\left(1-(a+b x)^2\right)^2}{b \sin ^{-1}(a+b x)}","-\frac{\text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{b}-\frac{\text{Si}\left(4 \sin ^{-1}(a+b x)\right)}{2 b}-\frac{\left(1-(a+b x)^2\right)^2}{b \sin ^{-1}(a+b x)}",1,"-((1 - (a + b*x)^2)^2/(b*ArcSin[a + b*x])) - SinIntegral[2*ArcSin[a + b*x]]/b - SinIntegral[4*ArcSin[a + b*x]]/(2*b)","A",7,5,33,0.1515,1,"{4807, 4659, 4723, 4406, 3299}"
325,1,90,0,0.2835457,"\int \frac{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}}{\sin ^{-1}(a+b x)^3} \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)/ArcSin[a + b*x]^3,x]","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b}-\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a+b x)\right)}{b}-\frac{\left(1-(a+b x)^2\right)^2}{2 b \sin ^{-1}(a+b x)^2}+\frac{2 (a+b x) \left(1-(a+b x)^2\right)^{3/2}}{b \sin ^{-1}(a+b x)}","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a+b x)\right)}{b}-\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a+b x)\right)}{b}-\frac{\left(1-(a+b x)^2\right)^2}{2 b \sin ^{-1}(a+b x)^2}+\frac{2 (a+b x) \left(1-(a+b x)^2\right)^{3/2}}{b \sin ^{-1}(a+b x)}",1,"-(1 - (a + b*x)^2)^2/(2*b*ArcSin[a + b*x]^2) + (2*(a + b*x)*(1 - (a + b*x)^2)^(3/2))/(b*ArcSin[a + b*x]) - CosIntegral[2*ArcSin[a + b*x]]/b - CosIntegral[4*ArcSin[a + b*x]]/b","A",11,8,33,0.2424,1,"{4807, 4659, 4721, 4661, 3312, 3302, 4723, 4406}"
326,1,155,0,0.3452099,"\int \frac{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}}{\sin ^{-1}(a+b x)^4} \, dx","Int[(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)/ArcSin[a + b*x]^4,x]","\frac{2 \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{3 b}+\frac{4 \text{Si}\left(4 \sin ^{-1}(a+b x)\right)}{3 b}-\frac{8 \left(1-(a+b x)^2\right) (a+b x)^2}{3 b \sin ^{-1}(a+b x)}+\frac{2 \left(1-(a+b x)^2\right)^{3/2} (a+b x)}{3 b \sin ^{-1}(a+b x)^2}+\frac{2 \left(1-(a+b x)^2\right)}{3 b \sin ^{-1}(a+b x)}-\frac{\left(1-(a+b x)^2\right)^2}{3 b \sin ^{-1}(a+b x)^3}","\frac{2 \text{Si}\left(2 \sin ^{-1}(a+b x)\right)}{3 b}+\frac{4 \text{Si}\left(4 \sin ^{-1}(a+b x)\right)}{3 b}-\frac{8 \left(1-(a+b x)^2\right) (a+b x)^2}{3 b \sin ^{-1}(a+b x)}+\frac{2 \left(1-(a+b x)^2\right)^{3/2} (a+b x)}{3 b \sin ^{-1}(a+b x)^2}+\frac{2 \left(1-(a+b x)^2\right)}{3 b \sin ^{-1}(a+b x)}-\frac{\left(1-(a+b x)^2\right)^2}{3 b \sin ^{-1}(a+b x)^3}",1,"-(1 - (a + b*x)^2)^2/(3*b*ArcSin[a + b*x]^3) + (2*(a + b*x)*(1 - (a + b*x)^2)^(3/2))/(3*b*ArcSin[a + b*x]^2) + (2*(1 - (a + b*x)^2))/(3*b*ArcSin[a + b*x]) - (8*(a + b*x)^2*(1 - (a + b*x)^2))/(3*b*ArcSin[a + b*x]) + (2*SinIntegral[2*ArcSin[a + b*x]])/(3*b) + (4*SinIntegral[4*ArcSin[a + b*x]])/(3*b)","A",18,7,33,0.2121,1,"{4807, 4659, 4721, 4635, 4406, 12, 3299}"
327,1,19,0,0.0749411,"\int \frac{\sin ^{-1}(a+b x)^n}{\sqrt{1-a^2-2 a b x-b^2 x^2}} \, dx","Int[ArcSin[a + b*x]^n/Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2],x]","\frac{\sin ^{-1}(a+b x)^{n+1}}{b (n+1)}","\frac{\sin ^{-1}(a+b x)^{n+1}}{b (n+1)}",1,"ArcSin[a + b*x]^(1 + n)/(b*(1 + n))","A",2,2,33,0.06061,1,"{4807, 4641}"
328,1,15,0,0.0712881,"\int \frac{\sin ^{-1}(a+b x)^2}{\sqrt{1-a^2-2 a b x-b^2 x^2}} \, dx","Int[ArcSin[a + b*x]^2/Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2],x]","\frac{\sin ^{-1}(a+b x)^3}{3 b}","\frac{\sin ^{-1}(a+b x)^3}{3 b}",1,"ArcSin[a + b*x]^3/(3*b)","A",2,2,33,0.06061,1,"{4807, 4641}"
329,1,15,0,0.0406008,"\int \frac{\sin ^{-1}(a+b x)}{\sqrt{1-a^2-2 a b x-b^2 x^2}} \, dx","Int[ArcSin[a + b*x]/Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2],x]","\frac{\sin ^{-1}(a+b x)^2}{2 b}","\frac{\sin ^{-1}(a+b x)^2}{2 b}",1,"ArcSin[a + b*x]^2/(2*b)","A",2,2,31,0.06452,1,"{4807, 4641}"
330,1,11,0,0.0761958,"\int \frac{1}{\sqrt{1-a^2-2 a b x-b^2 x^2} \sin ^{-1}(a+b x)} \, dx","Int[1/(Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSin[a + b*x]),x]","\frac{\log \left(\sin ^{-1}(a+b x)\right)}{b}","\frac{\log \left(\sin ^{-1}(a+b x)\right)}{b}",1,"Log[ArcSin[a + b*x]]/b","A",2,2,33,0.06061,1,"{4807, 4639}"
331,1,13,0,0.0752961,"\int \frac{1}{\sqrt{1-a^2-2 a b x-b^2 x^2} \sin ^{-1}(a+b x)^2} \, dx","Int[1/(Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSin[a + b*x]^2),x]","-\frac{1}{b \sin ^{-1}(a+b x)}","-\frac{1}{b \sin ^{-1}(a+b x)}",1,"-(1/(b*ArcSin[a + b*x]))","A",2,2,33,0.06061,1,"{4807, 4641}"
332,1,15,0,0.0703002,"\int \frac{1}{\sqrt{1-a^2-2 a b x-b^2 x^2} \sin ^{-1}(a+b x)^3} \, dx","Int[1/(Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSin[a + b*x]^3),x]","-\frac{1}{2 b \sin ^{-1}(a+b x)^2}","-\frac{1}{2 b \sin ^{-1}(a+b x)^2}",1,"-1/(2*b*ArcSin[a + b*x]^2)","A",2,2,33,0.06061,1,"{4807, 4641}"
333,1,128,0,0.2065061,"\int \frac{\sin ^{-1}(a+b x)^3}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}} \, dx","Int[ArcSin[a + b*x]^3/(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2),x]","-\frac{3 i \sin ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a+b x)}\right)}{b}+\frac{3 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a+b x)}\right)}{2 b}+\frac{(a+b x) \sin ^{-1}(a+b x)^3}{b \sqrt{1-(a+b x)^2}}-\frac{i \sin ^{-1}(a+b x)^3}{b}+\frac{3 \sin ^{-1}(a+b x)^2 \log \left(1+e^{2 i \sin ^{-1}(a+b x)}\right)}{b}","-\frac{3 i \sin ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a+b x)}\right)}{b}+\frac{3 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a+b x)}\right)}{2 b}+\frac{(a+b x) \sin ^{-1}(a+b x)^3}{b \sqrt{1-(a+b x)^2}}-\frac{i \sin ^{-1}(a+b x)^3}{b}+\frac{3 \sin ^{-1}(a+b x)^2 \log \left(1+e^{2 i \sin ^{-1}(a+b x)}\right)}{b}",1,"((-I)*ArcSin[a + b*x]^3)/b + ((a + b*x)*ArcSin[a + b*x]^3)/(b*Sqrt[1 - (a + b*x)^2]) + (3*ArcSin[a + b*x]^2*Log[1 + E^((2*I)*ArcSin[a + b*x])])/b - ((3*I)*ArcSin[a + b*x]*PolyLog[2, -E^((2*I)*ArcSin[a + b*x])])/b + (3*PolyLog[3, -E^((2*I)*ArcSin[a + b*x])])/(2*b)","A",8,8,33,0.2424,1,"{4807, 4651, 4675, 3719, 2190, 2531, 2282, 6589}"
334,1,97,0,0.1634309,"\int \frac{\sin ^{-1}(a+b x)^2}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}} \, dx","Int[ArcSin[a + b*x]^2/(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2),x]","-\frac{i \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sin ^{-1}(a+b x)^2}{b \sqrt{1-(a+b x)^2}}-\frac{i \sin ^{-1}(a+b x)^2}{b}+\frac{2 \sin ^{-1}(a+b x) \log \left(1+e^{2 i \sin ^{-1}(a+b x)}\right)}{b}","-\frac{i \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sin ^{-1}(a+b x)^2}{b \sqrt{1-(a+b x)^2}}-\frac{i \sin ^{-1}(a+b x)^2}{b}+\frac{2 \sin ^{-1}(a+b x) \log \left(1+e^{2 i \sin ^{-1}(a+b x)}\right)}{b}",1,"((-I)*ArcSin[a + b*x]^2)/b + ((a + b*x)*ArcSin[a + b*x]^2)/(b*Sqrt[1 - (a + b*x)^2]) + (2*ArcSin[a + b*x]*Log[1 + E^((2*I)*ArcSin[a + b*x])])/b - (I*PolyLog[2, -E^((2*I)*ArcSin[a + b*x])])/b","A",7,7,33,0.2121,1,"{4807, 4651, 4675, 3719, 2190, 2279, 2391}"
335,1,50,0,0.0597169,"\int \frac{\sin ^{-1}(a+b x)}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2}} \, dx","Int[ArcSin[a + b*x]/(1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2),x]","\frac{\log \left(1-(a+b x)^2\right)}{2 b}+\frac{(a+b x) \sin ^{-1}(a+b x)}{b \sqrt{1-(a+b x)^2}}","\frac{\log \left(1-(a+b x)^2\right)}{2 b}+\frac{(a+b x) \sin ^{-1}(a+b x)}{b \sqrt{1-(a+b x)^2}}",1,"((a + b*x)*ArcSin[a + b*x])/(b*Sqrt[1 - (a + b*x)^2]) + Log[1 - (a + b*x)^2]/(2*b)","A",3,3,31,0.09677,1,"{4807, 4651, 260}"
336,0,0,0,0.0815288,"\int \frac{1}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x)} \, dx","Int[1/((1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)*ArcSin[a + b*x]),x]","\int \frac{1}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x)} \, dx","\text{Int}\left(\frac{1}{\left(1-(a+b x)^2\right)^{3/2} \sin ^{-1}(a+b x)},x\right)",0,"Defer[Subst][Defer[Int][1/((1 - x^2)^(3/2)*ArcSin[x]), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
337,0,0,0,0.1248732,"\int \frac{1}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x)^2} \, dx","Int[1/((1 - a^2 - 2*a*b*x - b^2*x^2)^(3/2)*ArcSin[a + b*x]^2),x]","\int \frac{1}{\left(1-a^2-2 a b x-b^2 x^2\right)^{3/2} \sin ^{-1}(a+b x)^2} \, dx","2 \text{Int}\left(\frac{a+b x}{\left(1-(a+b x)^2\right)^2 \sin ^{-1}(a+b x)},x\right)-\frac{1}{b \left(1-(a+b x)^2\right) \sin ^{-1}(a+b x)}",0,"-(1/(b*(1 - (a + b*x)^2)*ArcSin[a + b*x])) + (2*Defer[Subst][Defer[Int][x/((1 - x^2)^2*ArcSin[x]), x], x, a + b*x])/b","A",0,0,0,0,-1,"{}"
338,1,46,0,0.1582313,"\int \frac{\sin ^{-1}(a+b x)}{\sqrt{c-c (a+b x)^2}} \, dx","Int[ArcSin[a + b*x]/Sqrt[c - c*(a + b*x)^2],x]","\frac{\sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{2 b \sqrt{c-c (a+b x)^2}}","\frac{\sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{2 b \sqrt{c-c (a+b x)^2}}",1,"(Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(2*b*Sqrt[c - c*(a + b*x)^2])","A",3,5,23,0.2174,1,"{247, 217, 203, 4643, 4641}"
339,1,46,0,0.0843548,"\int \frac{\sin ^{-1}(a+b x)}{\sqrt{\left(1-a^2\right) c-2 a b c x-b^2 c x^2}} \, dx","Int[ArcSin[a + b*x]/Sqrt[(1 - a^2)*c - 2*a*b*c*x - b^2*c*x^2],x]","\frac{\sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{2 b \sqrt{c-c (a+b x)^2}}","\frac{\sqrt{1-(a+b x)^2} \sin ^{-1}(a+b x)^2}{2 b \sqrt{c-c (a+b x)^2}}",1,"(Sqrt[1 - (a + b*x)^2]*ArcSin[a + b*x]^2)/(2*b*Sqrt[c - c*(a + b*x)^2])","A",3,3,36,0.08333,1,"{4807, 4643, 4641}"
340,1,84,0,0.064852,"\int x^9 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^9*(a + b*ArcSin[c*x^2]),x]","\frac{1}{10} x^{10} \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{b \left(1-c^2 x^4\right)^{5/2}}{50 c^5}-\frac{b \left(1-c^2 x^4\right)^{3/2}}{15 c^5}+\frac{b \sqrt{1-c^2 x^4}}{10 c^5}","\frac{1}{10} x^{10} \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{b \left(1-c^2 x^4\right)^{5/2}}{50 c^5}-\frac{b \left(1-c^2 x^4\right)^{3/2}}{15 c^5}+\frac{b \sqrt{1-c^2 x^4}}{10 c^5}",1,"(b*Sqrt[1 - c^2*x^4])/(10*c^5) - (b*(1 - c^2*x^4)^(3/2))/(15*c^5) + (b*(1 - c^2*x^4)^(5/2))/(50*c^5) + (x^10*(a + b*ArcSin[c*x^2]))/10","A",5,4,14,0.2857,1,"{4842, 12, 266, 43}"
341,1,82,0,0.0609173,"\int x^7 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^7*(a + b*ArcSin[c*x^2]),x]","\frac{1}{8} x^8 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{b x^6 \sqrt{1-c^2 x^4}}{32 c}+\frac{3 b x^2 \sqrt{1-c^2 x^4}}{64 c^3}-\frac{3 b \sin ^{-1}\left(c x^2\right)}{64 c^4}","\frac{1}{8} x^8 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{b x^6 \sqrt{1-c^2 x^4}}{32 c}+\frac{3 b x^2 \sqrt{1-c^2 x^4}}{64 c^3}-\frac{3 b \sin ^{-1}\left(c x^2\right)}{64 c^4}",1,"(3*b*x^2*Sqrt[1 - c^2*x^4])/(64*c^3) + (b*x^6*Sqrt[1 - c^2*x^4])/(32*c) - (3*b*ArcSin[c*x^2])/(64*c^4) + (x^8*(a + b*ArcSin[c*x^2]))/8","A",6,5,14,0.3571,1,"{4842, 12, 275, 321, 216}"
342,1,62,0,0.0479316,"\int x^5 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^5*(a + b*ArcSin[c*x^2]),x]","\frac{1}{6} x^6 \left(a+b \sin ^{-1}\left(c x^2\right)\right)-\frac{b \left(1-c^2 x^4\right)^{3/2}}{18 c^3}+\frac{b \sqrt{1-c^2 x^4}}{6 c^3}","\frac{1}{6} x^6 \left(a+b \sin ^{-1}\left(c x^2\right)\right)-\frac{b \left(1-c^2 x^4\right)^{3/2}}{18 c^3}+\frac{b \sqrt{1-c^2 x^4}}{6 c^3}",1,"(b*Sqrt[1 - c^2*x^4])/(6*c^3) - (b*(1 - c^2*x^4)^(3/2))/(18*c^3) + (x^6*(a + b*ArcSin[c*x^2]))/6","A",5,4,14,0.2857,1,"{4842, 12, 266, 43}"
343,1,57,0,0.0435031,"\int x^3 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^3*(a + b*ArcSin[c*x^2]),x]","\frac{1}{4} x^4 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{b x^2 \sqrt{1-c^2 x^4}}{8 c}-\frac{b \sin ^{-1}\left(c x^2\right)}{8 c^2}","\frac{1}{4} x^4 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{b x^2 \sqrt{1-c^2 x^4}}{8 c}-\frac{b \sin ^{-1}\left(c x^2\right)}{8 c^2}",1,"(b*x^2*Sqrt[1 - c^2*x^4])/(8*c) - (b*ArcSin[c*x^2])/(8*c^2) + (x^4*(a + b*ArcSin[c*x^2]))/4","A",5,5,14,0.3571,1,"{4842, 12, 275, 321, 216}"
344,1,45,0,0.0388268,"\int x \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x*(a + b*ArcSin[c*x^2]),x]","\frac{a x^2}{2}+\frac{b \sqrt{1-c^2 x^4}}{2 c}+\frac{1}{2} b x^2 \sin ^{-1}\left(c x^2\right)","\frac{a x^2}{2}+\frac{b \sqrt{1-c^2 x^4}}{2 c}+\frac{1}{2} b x^2 \sin ^{-1}\left(c x^2\right)",1,"(a*x^2)/2 + (b*Sqrt[1 - c^2*x^4])/(2*c) + (b*x^2*ArcSin[c*x^2])/2","A",4,3,12,0.2500,1,"{6715, 4619, 261}"
345,1,69,0,0.0979946,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x} \, dx","Int[(a + b*ArcSin[c*x^2])/x,x]","-\frac{1}{4} i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(c x^2\right)}\right)+a \log (x)-\frac{1}{4} i b \sin ^{-1}\left(c x^2\right)^2+\frac{1}{2} b \sin ^{-1}\left(c x^2\right) \log \left(1-e^{2 i \sin ^{-1}\left(c x^2\right)}\right)","-\frac{1}{4} i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(c x^2\right)}\right)+a \log (x)-\frac{1}{4} i b \sin ^{-1}\left(c x^2\right)^2+\frac{1}{2} b \sin ^{-1}\left(c x^2\right) \log \left(1-e^{2 i \sin ^{-1}\left(c x^2\right)}\right)",1,"(-I/4)*b*ArcSin[c*x^2]^2 + (b*ArcSin[c*x^2]*Log[1 - E^((2*I)*ArcSin[c*x^2])])/2 + a*Log[x] - (I/4)*b*PolyLog[2, E^((2*I)*ArcSin[c*x^2])]","A",7,6,14,0.4286,1,"{6742, 4830, 3717, 2190, 2279, 2391}"
346,1,39,0,0.0331595,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^3} \, dx","Int[(a + b*ArcSin[c*x^2])/x^3,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{2 x^2}-\frac{1}{2} b c \tanh ^{-1}\left(\sqrt{1-c^2 x^4}\right)","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{2 x^2}-\frac{1}{2} b c \tanh ^{-1}\left(\sqrt{1-c^2 x^4}\right)",1,"-(a + b*ArcSin[c*x^2])/(2*x^2) - (b*c*ArcTanh[Sqrt[1 - c^2*x^4]])/2","A",5,5,14,0.3571,1,"{4842, 12, 266, 63, 208}"
347,1,41,0,0.026372,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^5} \, dx","Int[(a + b*ArcSin[c*x^2])/x^5,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{4 x^4}-\frac{b c \sqrt{1-c^2 x^4}}{4 x^2}","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{4 x^4}-\frac{b c \sqrt{1-c^2 x^4}}{4 x^2}",1,"-(b*c*Sqrt[1 - c^2*x^4])/(4*x^2) - (a + b*ArcSin[c*x^2])/(4*x^4)","A",3,3,14,0.2143,1,"{4842, 12, 264}"
348,1,64,0,0.0473027,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^7} \, dx","Int[(a + b*ArcSin[c*x^2])/x^7,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{6 x^6}-\frac{b c \sqrt{1-c^2 x^4}}{12 x^4}-\frac{1}{12} b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^4}\right)","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{6 x^6}-\frac{b c \sqrt{1-c^2 x^4}}{12 x^4}-\frac{1}{12} b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^4}\right)",1,"-(b*c*Sqrt[1 - c^2*x^4])/(12*x^4) - (a + b*ArcSin[c*x^2])/(6*x^6) - (b*c^3*ArcTanh[Sqrt[1 - c^2*x^4]])/12","A",6,6,14,0.4286,1,"{4842, 12, 266, 51, 63, 208}"
349,1,66,0,0.0372158,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^9} \, dx","Int[(a + b*ArcSin[c*x^2])/x^9,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{8 x^8}-\frac{b c^3 \sqrt{1-c^2 x^4}}{12 x^2}-\frac{b c \sqrt{1-c^2 x^4}}{24 x^6}","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{8 x^8}-\frac{b c^3 \sqrt{1-c^2 x^4}}{12 x^2}-\frac{b c \sqrt{1-c^2 x^4}}{24 x^6}",1,"-(b*c*Sqrt[1 - c^2*x^4])/(24*x^6) - (b*c^3*Sqrt[1 - c^2*x^4])/(12*x^2) - (a + b*ArcSin[c*x^2])/(8*x^8)","A",4,4,14,0.2857,1,"{4842, 12, 271, 264}"
350,1,89,0,0.0632384,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^{11}} \, dx","Int[(a + b*ArcSin[c*x^2])/x^11,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{10 x^{10}}-\frac{3 b c^3 \sqrt{1-c^2 x^4}}{80 x^4}-\frac{b c \sqrt{1-c^2 x^4}}{40 x^8}-\frac{3}{80} b c^5 \tanh ^{-1}\left(\sqrt{1-c^2 x^4}\right)","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{10 x^{10}}-\frac{3 b c^3 \sqrt{1-c^2 x^4}}{80 x^4}-\frac{b c \sqrt{1-c^2 x^4}}{40 x^8}-\frac{3}{80} b c^5 \tanh ^{-1}\left(\sqrt{1-c^2 x^4}\right)",1,"-(b*c*Sqrt[1 - c^2*x^4])/(40*x^8) - (3*b*c^3*Sqrt[1 - c^2*x^4])/(80*x^4) - (a + b*ArcSin[c*x^2])/(10*x^10) - (3*b*c^5*ArcTanh[Sqrt[1 - c^2*x^4]])/80","A",7,6,14,0.4286,1,"{4842, 12, 266, 51, 63, 208}"
351,1,91,0,0.0464586,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^{13}} \, dx","Int[(a + b*ArcSin[c*x^2])/x^13,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{12 x^{12}}-\frac{2 b c^5 \sqrt{1-c^2 x^4}}{45 x^2}-\frac{b c^3 \sqrt{1-c^2 x^4}}{45 x^6}-\frac{b c \sqrt{1-c^2 x^4}}{60 x^{10}}","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{12 x^{12}}-\frac{2 b c^5 \sqrt{1-c^2 x^4}}{45 x^2}-\frac{b c^3 \sqrt{1-c^2 x^4}}{45 x^6}-\frac{b c \sqrt{1-c^2 x^4}}{60 x^{10}}",1,"-(b*c*Sqrt[1 - c^2*x^4])/(60*x^10) - (b*c^3*Sqrt[1 - c^2*x^4])/(45*x^6) - (2*b*c^5*Sqrt[1 - c^2*x^4])/(45*x^2) - (a + b*ArcSin[c*x^2])/(12*x^12)","A",5,4,14,0.2857,1,"{4842, 12, 271, 264}"
352,1,86,0,0.0496963,"\int x^6 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^6*(a + b*ArcSin[c*x^2]),x]","\frac{1}{7} x^7 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{2 b x^5 \sqrt{1-c^2 x^4}}{49 c}+\frac{10 b x \sqrt{1-c^2 x^4}}{147 c^3}-\frac{10 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{147 c^{7/2}}","\frac{1}{7} x^7 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{2 b x^5 \sqrt{1-c^2 x^4}}{49 c}+\frac{10 b x \sqrt{1-c^2 x^4}}{147 c^3}-\frac{10 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{147 c^{7/2}}",1,"(10*b*x*Sqrt[1 - c^2*x^4])/(147*c^3) + (2*b*x^5*Sqrt[1 - c^2*x^4])/(49*c) + (x^7*(a + b*ArcSin[c*x^2]))/7 - (10*b*EllipticF[ArcSin[Sqrt[c]*x], -1])/(147*c^(7/2))","A",5,4,14,0.2857,1,"{4842, 12, 321, 221}"
353,1,83,0,0.0609729,"\int x^4 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^4*(a + b*ArcSin[c*x^2]),x]","\frac{1}{5} x^5 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{2 b x^3 \sqrt{1-c^2 x^4}}{25 c}+\frac{6 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{25 c^{5/2}}-\frac{6 b E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{25 c^{5/2}}","\frac{1}{5} x^5 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{2 b x^3 \sqrt{1-c^2 x^4}}{25 c}+\frac{6 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{25 c^{5/2}}-\frac{6 b E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{25 c^{5/2}}",1,"(2*b*x^3*Sqrt[1 - c^2*x^4])/(25*c) + (x^5*(a + b*ArcSin[c*x^2]))/5 - (6*b*EllipticE[ArcSin[Sqrt[c]*x], -1])/(25*c^(5/2)) + (6*b*EllipticF[ArcSin[Sqrt[c]*x], -1])/(25*c^(5/2))","A",7,7,14,0.5000,1,"{4842, 12, 321, 307, 221, 1199, 424}"
354,1,61,0,0.0345188,"\int x^2 \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[x^2*(a + b*ArcSin[c*x^2]),x]","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{2 b x \sqrt{1-c^2 x^4}}{9 c}-\frac{2 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{9 c^{3/2}}","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(c x^2\right)\right)+\frac{2 b x \sqrt{1-c^2 x^4}}{9 c}-\frac{2 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{9 c^{3/2}}",1,"(2*b*x*Sqrt[1 - c^2*x^4])/(9*c) + (x^3*(a + b*ArcSin[c*x^2]))/3 - (2*b*EllipticF[ArcSin[Sqrt[c]*x], -1])/(9*c^(3/2))","A",4,4,14,0.2857,1,"{4842, 12, 321, 221}"
355,1,49,0,0.0426012,"\int \left(a+b \sin ^{-1}\left(c x^2\right)\right) \, dx","Int[a + b*ArcSin[c*x^2],x]","a x+b x \sin ^{-1}\left(c x^2\right)+\frac{2 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{\sqrt{c}}-\frac{2 b E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{\sqrt{c}}","a x+b x \sin ^{-1}\left(c x^2\right)+\frac{2 b F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{\sqrt{c}}-\frac{2 b E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)}{\sqrt{c}}",1,"a*x + b*x*ArcSin[c*x^2] - (2*b*EllipticE[ArcSin[Sqrt[c]*x], -1])/Sqrt[c] + (2*b*EllipticF[ArcSin[Sqrt[c]*x], -1])/Sqrt[c]","A",7,6,10,0.6000,1,"{4840, 12, 307, 221, 1199, 424}"
356,1,34,0,0.0224676,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^2} \, dx","Int[(a + b*ArcSin[c*x^2])/x^2,x]","2 b \sqrt{c} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)-\frac{a+b \sin ^{-1}\left(c x^2\right)}{x}","2 b \sqrt{c} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)-\frac{a+b \sin ^{-1}\left(c x^2\right)}{x}",1,"-((a + b*ArcSin[c*x^2])/x) + 2*b*Sqrt[c]*EllipticF[ArcSin[Sqrt[c]*x], -1]","A",3,3,14,0.2143,1,"{4842, 12, 221}"
357,1,81,0,0.0575011,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^4} \, dx","Int[(a + b*ArcSin[c*x^2])/x^4,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{3 x^3}-\frac{2 b c \sqrt{1-c^2 x^4}}{3 x}+\frac{2}{3} b c^{3/2} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)-\frac{2}{3} b c^{3/2} E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{3 x^3}-\frac{2 b c \sqrt{1-c^2 x^4}}{3 x}+\frac{2}{3} b c^{3/2} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)-\frac{2}{3} b c^{3/2} E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)",1,"(-2*b*c*Sqrt[1 - c^2*x^4])/(3*x) - (a + b*ArcSin[c*x^2])/(3*x^3) - (2*b*c^(3/2)*EllipticE[ArcSin[Sqrt[c]*x], -1])/3 + (2*b*c^(3/2)*EllipticF[ArcSin[Sqrt[c]*x], -1])/3","A",7,7,14,0.5000,1,"{4842, 12, 325, 307, 221, 1199, 424}"
358,1,61,0,0.0338484,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^6} \, dx","Int[(a + b*ArcSin[c*x^2])/x^6,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{5 x^5}-\frac{2 b c \sqrt{1-c^2 x^4}}{15 x^3}+\frac{2}{15} b c^{5/2} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{5 x^5}-\frac{2 b c \sqrt{1-c^2 x^4}}{15 x^3}+\frac{2}{15} b c^{5/2} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)",1,"(-2*b*c*Sqrt[1 - c^2*x^4])/(15*x^3) - (a + b*ArcSin[c*x^2])/(5*x^5) + (2*b*c^(5/2)*EllipticF[ArcSin[Sqrt[c]*x], -1])/15","A",4,4,14,0.2857,1,"{4842, 12, 325, 221}"
359,1,106,0,0.0742363,"\int \frac{a+b \sin ^{-1}\left(c x^2\right)}{x^8} \, dx","Int[(a + b*ArcSin[c*x^2])/x^8,x]","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{7 x^7}-\frac{6 b c^3 \sqrt{1-c^2 x^4}}{35 x}-\frac{2 b c \sqrt{1-c^2 x^4}}{35 x^5}+\frac{6}{35} b c^{7/2} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)-\frac{6}{35} b c^{7/2} E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)","-\frac{a+b \sin ^{-1}\left(c x^2\right)}{7 x^7}-\frac{6 b c^3 \sqrt{1-c^2 x^4}}{35 x}-\frac{2 b c \sqrt{1-c^2 x^4}}{35 x^5}+\frac{6}{35} b c^{7/2} F\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)-\frac{6}{35} b c^{7/2} E\left(\left.\sin ^{-1}\left(\sqrt{c} x\right)\right|-1\right)",1,"(-2*b*c*Sqrt[1 - c^2*x^4])/(35*x^5) - (6*b*c^3*Sqrt[1 - c^2*x^4])/(35*x) - (a + b*ArcSin[c*x^2])/(7*x^7) - (6*b*c^(7/2)*EllipticE[ArcSin[Sqrt[c]*x], -1])/35 + (6*b*c^(7/2)*EllipticF[ArcSin[Sqrt[c]*x], -1])/35","A",8,7,14,0.5000,1,"{4842, 12, 325, 307, 221, 1199, 424}"
360,1,62,0,0.0633814,"\int \frac{\sin ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcSin[a*x^5]/x,x]","-\frac{1}{10} i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} i \sin ^{-1}\left(a x^5\right)^2+\frac{1}{5} \sin ^{-1}\left(a x^5\right) \log \left(1-e^{2 i \sin ^{-1}\left(a x^5\right)}\right)","-\frac{1}{10} i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} i \sin ^{-1}\left(a x^5\right)^2+\frac{1}{5} \sin ^{-1}\left(a x^5\right) \log \left(1-e^{2 i \sin ^{-1}\left(a x^5\right)}\right)",1,"(-I/10)*ArcSin[a*x^5]^2 + (ArcSin[a*x^5]*Log[1 - E^((2*I)*ArcSin[a*x^5])])/5 - (I/10)*PolyLog[2, E^((2*I)*ArcSin[a*x^5])]","A",5,5,10,0.5000,1,"{4830, 3717, 2190, 2279, 2391}"
361,1,78,0,0.0302778,"\int x^2 \sin ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcSin[Sqrt[x]],x]","\frac{1}{18} \sqrt{1-x} x^{5/2}+\frac{5}{72} \sqrt{1-x} x^{3/2}+\frac{1}{3} x^3 \sin ^{-1}\left(\sqrt{x}\right)+\frac{5}{48} \sqrt{1-x} \sqrt{x}+\frac{5}{96} \sin ^{-1}(1-2 x)","\frac{1}{18} \sqrt{1-x} x^{5/2}+\frac{5}{72} \sqrt{1-x} x^{3/2}+\frac{1}{3} x^3 \sin ^{-1}\left(\sqrt{x}\right)+\frac{5}{48} \sqrt{1-x} \sqrt{x}+\frac{5}{96} \sin ^{-1}(1-2 x)",1,"(5*Sqrt[1 - x]*Sqrt[x])/48 + (5*Sqrt[1 - x]*x^(3/2))/72 + (Sqrt[1 - x]*x^(5/2))/18 + (5*ArcSin[1 - 2*x])/96 + (x^3*ArcSin[Sqrt[x]])/3","A",8,6,10,0.6000,1,"{4842, 12, 50, 53, 619, 216}"
362,1,60,0,0.0208128,"\int x \sin ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcSin[Sqrt[x]],x]","\frac{1}{8} \sqrt{1-x} x^{3/2}+\frac{1}{2} x^2 \sin ^{-1}\left(\sqrt{x}\right)+\frac{3}{16} \sqrt{1-x} \sqrt{x}+\frac{3}{32} \sin ^{-1}(1-2 x)","\frac{1}{8} \sqrt{1-x} x^{3/2}+\frac{1}{2} x^2 \sin ^{-1}\left(\sqrt{x}\right)+\frac{3}{16} \sqrt{1-x} \sqrt{x}+\frac{3}{32} \sin ^{-1}(1-2 x)",1,"(3*Sqrt[1 - x]*Sqrt[x])/16 + (Sqrt[1 - x]*x^(3/2))/8 + (3*ArcSin[1 - 2*x])/32 + (x^2*ArcSin[Sqrt[x]])/2","A",7,6,8,0.7500,1,"{4842, 12, 50, 53, 619, 216}"
363,1,37,0,0.011631,"\int \sin ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcSin[Sqrt[x]],x]","\frac{1}{2} \sqrt{1-x} \sqrt{x}+\frac{1}{4} \sin ^{-1}(1-2 x)+x \sin ^{-1}\left(\sqrt{x}\right)","\frac{1}{2} \sqrt{1-x} \sqrt{x}+\frac{1}{4} \sin ^{-1}(1-2 x)+x \sin ^{-1}\left(\sqrt{x}\right)",1,"(Sqrt[1 - x]*Sqrt[x])/2 + ArcSin[1 - 2*x]/4 + x*ArcSin[Sqrt[x]]","A",6,6,6,1.000,1,"{4840, 12, 50, 53, 619, 216}"
364,1,56,0,0.0610309,"\int \frac{\sin ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcSin[Sqrt[x]]/x,x]","-i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\sqrt{x}\right)}\right)-i \sin ^{-1}\left(\sqrt{x}\right)^2+2 \sin ^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\sqrt{x}\right)}\right)","-i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\sqrt{x}\right)}\right)-i \sin ^{-1}\left(\sqrt{x}\right)^2+2 \sin ^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\sqrt{x}\right)}\right)",1,"(-I)*ArcSin[Sqrt[x]]^2 + 2*ArcSin[Sqrt[x]]*Log[1 - E^((2*I)*ArcSin[Sqrt[x]])] - I*PolyLog[2, E^((2*I)*ArcSin[Sqrt[x]])]","A",5,5,10,0.5000,1,"{4830, 3717, 2190, 2279, 2391}"
365,1,28,0,0.0132777,"\int \frac{\sin ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcSin[Sqrt[x]]/x^2,x]","-\frac{\sqrt{1-x}}{\sqrt{x}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{x}","-\frac{\sqrt{1-x}}{\sqrt{x}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{x}",1,"-(Sqrt[1 - x]/Sqrt[x]) - ArcSin[Sqrt[x]]/x","A",3,3,10,0.3000,1,"{4842, 12, 37}"
366,1,50,0,0.017673,"\int \frac{\sin ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcSin[Sqrt[x]]/x^3,x]","-\frac{\sqrt{1-x}}{6 x^{3/2}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{\sqrt{1-x}}{3 \sqrt{x}}","-\frac{\sqrt{1-x}}{6 x^{3/2}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{\sqrt{1-x}}{3 \sqrt{x}}",1,"-Sqrt[1 - x]/(6*x^(3/2)) - Sqrt[1 - x]/(3*Sqrt[x]) - ArcSin[Sqrt[x]]/(2*x^2)","A",4,4,10,0.4000,1,"{4842, 12, 45, 37}"
367,1,68,0,0.0223059,"\int \frac{\sin ^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Int[ArcSin[Sqrt[x]]/x^4,x]","-\frac{4 \sqrt{1-x}}{45 x^{3/2}}-\frac{\sqrt{1-x}}{15 x^{5/2}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{3 x^3}-\frac{8 \sqrt{1-x}}{45 \sqrt{x}}","-\frac{4 \sqrt{1-x}}{45 x^{3/2}}-\frac{\sqrt{1-x}}{15 x^{5/2}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{3 x^3}-\frac{8 \sqrt{1-x}}{45 \sqrt{x}}",1,"-Sqrt[1 - x]/(15*x^(5/2)) - (4*Sqrt[1 - x])/(45*x^(3/2)) - (8*Sqrt[1 - x])/(45*Sqrt[x]) - ArcSin[Sqrt[x]]/(3*x^3)","A",5,4,10,0.4000,1,"{4842, 12, 45, 37}"
368,1,86,0,0.0290164,"\int \frac{\sin ^{-1}\left(\sqrt{x}\right)}{x^5} \, dx","Int[ArcSin[Sqrt[x]]/x^5,x]","-\frac{2 \sqrt{1-x}}{35 x^{3/2}}-\frac{3 \sqrt{1-x}}{70 x^{5/2}}-\frac{\sqrt{1-x}}{28 x^{7/2}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{4 x^4}-\frac{4 \sqrt{1-x}}{35 \sqrt{x}}","-\frac{2 \sqrt{1-x}}{35 x^{3/2}}-\frac{3 \sqrt{1-x}}{70 x^{5/2}}-\frac{\sqrt{1-x}}{28 x^{7/2}}-\frac{\sin ^{-1}\left(\sqrt{x}\right)}{4 x^4}-\frac{4 \sqrt{1-x}}{35 \sqrt{x}}",1,"-Sqrt[1 - x]/(28*x^(7/2)) - (3*Sqrt[1 - x])/(70*x^(5/2)) - (2*Sqrt[1 - x])/(35*x^(3/2)) - (4*Sqrt[1 - x])/(35*Sqrt[x]) - ArcSin[Sqrt[x]]/(4*x^4)","A",6,4,10,0.4000,1,"{4842, 12, 45, 37}"
369,1,89,0,0.0587458,"\int x^4 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^4*(a + b*ArcSin[c/x]),x]","\frac{1}{5} x^5 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{3}{40} b c^3 x^2 \sqrt{1-\frac{c^2}{x^2}}+\frac{1}{20} b c x^4 \sqrt{1-\frac{c^2}{x^2}}+\frac{3}{40} b c^5 \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{x^2}}\right)","\frac{1}{5} x^5 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{3}{40} b c^3 x^2 \sqrt{1-\frac{c^2}{x^2}}+\frac{1}{20} b c x^4 \sqrt{1-\frac{c^2}{x^2}}+\frac{3}{40} b c^5 \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{x^2}}\right)",1,"(3*b*c^3*Sqrt[1 - c^2/x^2]*x^2)/40 + (b*c*Sqrt[1 - c^2/x^2]*x^4)/20 + (x^5*(a + b*ArcSin[c/x]))/5 + (3*b*c^5*ArcTanh[Sqrt[1 - c^2/x^2]])/40","A",7,6,14,0.4286,1,"{4842, 12, 266, 51, 63, 208}"
370,1,64,0,0.0380079,"\int x^3 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^3*(a + b*ArcSin[c/x]),x]","\frac{1}{4} x^4 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{12} b c x^3 \sqrt{1-\frac{c^2}{x^2}}+\frac{1}{6} b c^3 x \sqrt{1-\frac{c^2}{x^2}}","\frac{1}{4} x^4 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{12} b c x^3 \sqrt{1-\frac{c^2}{x^2}}+\frac{1}{6} b c^3 x \sqrt{1-\frac{c^2}{x^2}}",1,"(b*c^3*Sqrt[1 - c^2/x^2]*x)/6 + (b*c*Sqrt[1 - c^2/x^2]*x^3)/12 + (x^4*(a + b*ArcSin[c/x]))/4","A",4,4,14,0.2857,1,"{4842, 12, 271, 191}"
371,1,64,0,0.0426628,"\int x^2 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^2*(a + b*ArcSin[c/x]),x]","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{6} b c x^2 \sqrt{1-\frac{c^2}{x^2}}+\frac{1}{6} b c^3 \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{x^2}}\right)","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{6} b c x^2 \sqrt{1-\frac{c^2}{x^2}}+\frac{1}{6} b c^3 \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{x^2}}\right)",1,"(b*c*Sqrt[1 - c^2/x^2]*x^2)/6 + (x^3*(a + b*ArcSin[c/x]))/3 + (b*c^3*ArcTanh[Sqrt[1 - c^2/x^2]])/6","A",6,6,14,0.4286,1,"{4842, 12, 266, 51, 63, 208}"
372,1,39,0,0.0174758,"\int x \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x*(a + b*ArcSin[c/x]),x]","\frac{1}{2} x^2 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{2} b c x \sqrt{1-\frac{c^2}{x^2}}","\frac{1}{2} x^2 \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right)+\frac{1}{2} b c x \sqrt{1-\frac{c^2}{x^2}}",1,"(b*c*Sqrt[1 - c^2/x^2]*x)/2 + (x^2*(a + b*ArcSin[c/x]))/2","A",3,3,12,0.2500,1,"{4842, 12, 191}"
373,1,31,0,0.0218781,"\int \left(a+b \sin ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[a + b*ArcSin[c/x],x]","a x+b c \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{x^2}}\right)+b x \csc ^{-1}\left(\frac{x}{c}\right)","a x+b c \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{x^2}}\right)+b x \csc ^{-1}\left(\frac{x}{c}\right)",1,"a*x + b*x*ArcCsc[x/c] + b*c*ArcTanh[Sqrt[1 - c^2/x^2]]","A",6,5,10,0.5000,1,"{4832, 5215, 266, 63, 208}"
374,1,67,0,0.0923537,"\int \frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{x} \, dx","Int[(a + b*ArcSin[c/x])/x,x]","\frac{1}{2} i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{c}{x}\right)}\right)+a \log (x)+\frac{1}{2} i b \sin ^{-1}\left(\frac{c}{x}\right)^2-b \sin ^{-1}\left(\frac{c}{x}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\frac{c}{x}\right)}\right)","\frac{1}{2} i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{c}{x}\right)}\right)+a \log (x)+\frac{1}{2} i b \sin ^{-1}\left(\frac{c}{x}\right)^2-b \sin ^{-1}\left(\frac{c}{x}\right) \log \left(1-e^{2 i \sin ^{-1}\left(\frac{c}{x}\right)}\right)",1,"(I/2)*b*ArcSin[c/x]^2 - b*ArcSin[c/x]*Log[1 - E^((2*I)*ArcSin[c/x])] + a*Log[x] + (I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c/x])]","A",7,6,14,0.4286,1,"{6742, 4830, 3717, 2190, 2279, 2391}"
375,1,39,0,0.0359881,"\int \frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{x^2} \, dx","Int[(a + b*ArcSin[c/x])/x^2,x]","-\frac{a}{x}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{c}-\frac{b \csc ^{-1}\left(\frac{x}{c}\right)}{x}","-\frac{a}{x}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{c}-\frac{b \csc ^{-1}\left(\frac{x}{c}\right)}{x}",1,"-((b*Sqrt[1 - c^2/x^2])/c) - a/x - (b*ArcCsc[x/c])/x","A",4,3,14,0.2143,1,"{6715, 4619, 261}"
376,1,57,0,0.0425392,"\int \frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{x^3} \, dx","Int[(a + b*ArcSin[c/x])/x^3,x]","-\frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{2 x^2}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{4 c x}+\frac{b \csc ^{-1}\left(\frac{x}{c}\right)}{4 c^2}","-\frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{2 x^2}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{4 c x}+\frac{b \csc ^{-1}\left(\frac{x}{c}\right)}{4 c^2}",1,"-(b*Sqrt[1 - c^2/x^2])/(4*c*x) + (b*ArcCsc[x/c])/(4*c^2) - (a + b*ArcSin[c/x])/(2*x^2)","A",5,5,14,0.3571,1,"{4842, 12, 335, 321, 216}"
377,1,62,0,0.0474299,"\int \frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{x^4} \, dx","Int[(a + b*ArcSin[c/x])/x^4,x]","-\frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{3 x^3}+\frac{b \left(1-\frac{c^2}{x^2}\right)^{3/2}}{9 c^3}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{3 c^3}","-\frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{3 x^3}+\frac{b \left(1-\frac{c^2}{x^2}\right)^{3/2}}{9 c^3}-\frac{b \sqrt{1-\frac{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) - (a + b*ArcSin[c/x])/(3*x^3)","A",5,4,14,0.2857,1,"{4842, 12, 266, 43}"
378,1,82,0,0.0546526,"\int \frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{x^5} \, dx","Int[(a + b*ArcSin[c/x])/x^5,x]","-\frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{4 x^4}-\frac{3 b \sqrt{1-\frac{c^2}{x^2}}}{32 c^3 x}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{16 c x^3}+\frac{3 b \csc ^{-1}\left(\frac{x}{c}\right)}{32 c^4}","-\frac{a+b \sin ^{-1}\left(\frac{c}{x}\right)}{4 x^4}-\frac{3 b \sqrt{1-\frac{c^2}{x^2}}}{32 c^3 x}-\frac{b \sqrt{1-\frac{c^2}{x^2}}}{16 c x^3}+\frac{3 b \csc ^{-1}\left(\frac{x}{c}\right)}{32 c^4}",1,"-(b*Sqrt[1 - c^2/x^2])/(16*c*x^3) - (3*b*Sqrt[1 - c^2/x^2])/(32*c^3*x) + (3*b*ArcCsc[x/c])/(32*c^4) - (a + b*ArcSin[c/x])/(4*x^4)","A",6,5,14,0.3571,1,"{4842, 12, 335, 321, 216}"
379,1,81,0,0.0513925,"\int x^m \left(a+b \sin ^{-1}\left(c x^n\right)\right) \, dx","Int[x^m*(a + b*ArcSin[c*x^n]),x]","\frac{x^{m+1} \left(a+b \sin ^{-1}\left(c x^n\right)\right)}{m+1}-\frac{b c n x^{m+n+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{2 n};\frac{m+3 n+1}{2 n};c^2 x^{2 n}\right)}{(m+1) (m+n+1)}","\frac{x^{m+1} \left(a+b \sin ^{-1}\left(c x^n\right)\right)}{m+1}-\frac{b c n x^{m+n+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{2 n};\frac{m+3 n+1}{2 n};c^2 x^{2 n}\right)}{(m+1) (m+n+1)}",1,"(x^(1 + m)*(a + b*ArcSin[c*x^n]))/(1 + m) - (b*c*n*x^(1 + m + n)*Hypergeometric2F1[1/2, (1 + m + n)/(2*n), (1 + m + 3*n)/(2*n), c^2*x^(2*n)])/((1 + m)*(1 + m + n))","A",3,3,14,0.2143,1,"{4842, 12, 364}"
380,1,68,0,0.0409463,"\int x^2 \left(a+b \sin ^{-1}\left(c x^n\right)\right) \, dx","Int[x^2*(a + b*ArcSin[c*x^n]),x]","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2 n};\frac{3 (n+1)}{2 n};c^2 x^{2 n}\right)}{3 (n+3)}","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2 n};\frac{3 (n+1)}{2 n};c^2 x^{2 n}\right)}{3 (n+3)}",1,"(x^3*(a + b*ArcSin[c*x^n]))/3 - (b*c*n*x^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/(2*n), (3*(1 + n))/(2*n), c^2*x^(2*n)])/(3*(3 + n))","A",3,3,14,0.2143,1,"{4842, 12, 364}"
381,1,69,0,0.0333579,"\int x \left(a+b \sin ^{-1}\left(c x^n\right)\right) \, dx","Int[x*(a + b*ArcSin[c*x^n]),x]","\frac{1}{2} x^2 \left(a+b \sin ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2 n};\frac{1}{2} \left(3+\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (n+2)}","\frac{1}{2} x^2 \left(a+b \sin ^{-1}\left(c x^n\right)\right)-\frac{b c n x^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2 n};\frac{1}{2} \left(3+\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (n+2)}",1,"(x^2*(a + b*ArcSin[c*x^n]))/2 - (b*c*n*x^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/(2*n), (3 + 2/n)/2, c^2*x^(2*n)])/(2*(2 + n))","A",3,3,12,0.2500,1,"{4842, 12, 364}"
382,1,60,0,0.0349295,"\int \left(a+b \sin ^{-1}\left(c x^n\right)\right) \, dx","Int[a + b*ArcSin[c*x^n],x]","a x-\frac{b c n x^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2 n};\frac{1}{2} \left(3+\frac{1}{n}\right);c^2 x^{2 n}\right)}{n+1}+b x \sin ^{-1}\left(c x^n\right)","a x-\frac{b c n x^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2 n};\frac{1}{2} \left(3+\frac{1}{n}\right);c^2 x^{2 n}\right)}{n+1}+b x \sin ^{-1}\left(c x^n\right)",1,"a*x + b*x*ArcSin[c*x^n] - (b*c*n*x^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/(2*n), (3 + n^(-1))/2, c^2*x^(2*n)])/(1 + n)","A",4,3,10,0.3000,1,"{4840, 12, 364}"
383,1,75,0,0.1040859,"\int \frac{a+b \sin ^{-1}\left(c x^n\right)}{x} \, dx","Int[(a + b*ArcSin[c*x^n])/x,x]","-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(c x^n\right)}\right)}{2 n}+a \log (x)-\frac{i b \sin ^{-1}\left(c x^n\right)^2}{2 n}+\frac{b \sin ^{-1}\left(c x^n\right) \log \left(1-e^{2 i \sin ^{-1}\left(c x^n\right)}\right)}{n}","-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(c x^n\right)}\right)}{2 n}+a \log (x)-\frac{i b \sin ^{-1}\left(c x^n\right)^2}{2 n}+\frac{b \sin ^{-1}\left(c x^n\right) \log \left(1-e^{2 i \sin ^{-1}\left(c x^n\right)}\right)}{n}",1,"((-I/2)*b*ArcSin[c*x^n]^2)/n + (b*ArcSin[c*x^n]*Log[1 - E^((2*I)*ArcSin[c*x^n])])/n + a*Log[x] - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x^n])])/n","A",7,6,14,0.4286,1,"{6742, 4830, 3717, 2190, 2279, 2391}"
384,1,69,0,0.0431259,"\int \frac{a+b \sin ^{-1}\left(c x^n\right)}{x^2} \, dx","Int[(a + b*ArcSin[c*x^n])/x^2,x]","-\frac{a+b \sin ^{-1}\left(c x^n\right)}{x}-\frac{b c n x^{n-1} \, _2F_1\left(\frac{1}{2},-\frac{1-n}{2 n};\frac{1}{2} \left(3-\frac{1}{n}\right);c^2 x^{2 n}\right)}{1-n}","-\frac{a+b \sin ^{-1}\left(c x^n\right)}{x}-\frac{b c n x^{n-1} \, _2F_1\left(\frac{1}{2},-\frac{1-n}{2 n};\frac{1}{2} \left(3-\frac{1}{n}\right);c^2 x^{2 n}\right)}{1-n}",1,"-((a + b*ArcSin[c*x^n])/x) - (b*c*n*x^(-1 + n)*Hypergeometric2F1[1/2, -(1 - n)/(2*n), (3 - n^(-1))/2, c^2*x^(2*n)])/(1 - n)","A",3,3,14,0.2143,1,"{4842, 12, 364}"
385,1,72,0,0.0453786,"\int \frac{a+b \sin ^{-1}\left(c x^n\right)}{x^3} \, dx","Int[(a + b*ArcSin[c*x^n])/x^3,x]","-\frac{a+b \sin ^{-1}\left(c x^n\right)}{2 x^2}-\frac{b c n x^{n-2} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1-\frac{2}{n}\right);\frac{1}{2} \left(3-\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (2-n)}","-\frac{a+b \sin ^{-1}\left(c x^n\right)}{2 x^2}-\frac{b c n x^{n-2} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1-\frac{2}{n}\right);\frac{1}{2} \left(3-\frac{2}{n}\right);c^2 x^{2 n}\right)}{2 (2-n)}",1,"-(a + b*ArcSin[c*x^n])/(2*x^2) - (b*c*n*x^(-2 + n)*Hypergeometric2F1[1/2, (1 - 2/n)/2, (3 - 2/n)/2, c^2*x^(2*n)])/(2*(2 - n))","A",3,3,14,0.2143,1,"{4842, 12, 364}"
386,1,129,0,0.1553575,"\int x^5 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right) \, dx","Int[x^5*(a + b*ArcSin[c + d*x^2]),x]","\frac{1}{6} x^6 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{b x^4 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{18 d}+\frac{b \left(11 c^2-5 c d x^2+4\right) \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{36 d^3}+\frac{b c \left(2 c^2+3\right) \sin ^{-1}\left(c+d x^2\right)}{12 d^3}","\frac{1}{6} x^6 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{b x^4 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{18 d}+\frac{b \left(11 c^2-5 c d x^2+4\right) \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{36 d^3}+\frac{b c \left(2 c^2+3\right) \sin ^{-1}\left(c+d x^2\right)}{12 d^3}",1,"(b*x^4*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(18*d) + (b*(4 + 11*c^2 - 5*c*d*x^2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(36*d^3) + (b*c*(3 + 2*c^2)*ArcSin[c + d*x^2])/(12*d^3) + (x^6*(a + b*ArcSin[c + d*x^2]))/6","A",7,7,16,0.4375,1,"{4842, 12, 1114, 742, 779, 619, 216}"
387,1,115,0,0.1301904,"\int x^3 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right) \, dx","Int[x^3*(a + b*ArcSin[c + d*x^2]),x]","\frac{1}{4} x^4 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{b x^2 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{8 d}-\frac{3 b c \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{8 d^2}-\frac{b \left(2 c^2+1\right) \sin ^{-1}\left(c+d x^2\right)}{8 d^2}","\frac{1}{4} x^4 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{b x^2 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{8 d}-\frac{3 b c \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{8 d^2}-\frac{b \left(2 c^2+1\right) \sin ^{-1}\left(c+d x^2\right)}{8 d^2}",1,"(-3*b*c*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(8*d^2) + (b*x^2*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(8*d) - (b*(1 + 2*c^2)*ArcSin[c + d*x^2])/(8*d^2) + (x^4*(a + b*ArcSin[c + d*x^2]))/4","A",7,7,16,0.4375,1,"{4842, 12, 1114, 742, 640, 619, 216}"
388,1,57,0,0.0609813,"\int x \left(a+b \sin ^{-1}\left(c+d x^2\right)\right) \, dx","Int[x*(a + b*ArcSin[c + d*x^2]),x]","\frac{a x^2}{2}+\frac{b \sqrt{1-\left(c+d x^2\right)^2}}{2 d}+\frac{b \left(c+d x^2\right) \sin ^{-1}\left(c+d x^2\right)}{2 d}","\frac{a x^2}{2}+\frac{b \sqrt{1-\left(c+d x^2\right)^2}}{2 d}+\frac{b \left(c+d x^2\right) \sin ^{-1}\left(c+d x^2\right)}{2 d}",1,"(a*x^2)/2 + (b*Sqrt[1 - (c + d*x^2)^2])/(2*d) + (b*(c + d*x^2)*ArcSin[c + d*x^2])/(2*d)","A",5,4,14,0.2857,1,"{6715, 4803, 4619, 261}"
389,1,214,0,0.3756034,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x,x]","-\frac{1}{2} i b \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{-\sqrt{1-c^2}+i c}\right)-\frac{1}{2} i b \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{\sqrt{1-c^2}+i c}\right)+a \log (x)+\frac{1}{2} b \sin ^{-1}\left(c+d x^2\right) \log \left(1-\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{-\sqrt{1-c^2}+i c}\right)+\frac{1}{2} b \sin ^{-1}\left(c+d x^2\right) \log \left(1-\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{\sqrt{1-c^2}+i c}\right)-\frac{1}{4} i b \sin ^{-1}\left(c+d x^2\right)^2","-\frac{1}{2} i b \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{-\sqrt{1-c^2}+i c}\right)-\frac{1}{2} i b \text{PolyLog}\left(2,\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{\sqrt{1-c^2}+i c}\right)+a \log (x)+\frac{1}{2} b \sin ^{-1}\left(c+d x^2\right) \log \left(1-\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{-\sqrt{1-c^2}+i c}\right)+\frac{1}{2} b \sin ^{-1}\left(c+d x^2\right) \log \left(1-\frac{e^{i \sin ^{-1}\left(c+d x^2\right)}}{\sqrt{1-c^2}+i c}\right)-\frac{1}{4} i b \sin ^{-1}\left(c+d x^2\right)^2",1,"(-I/4)*b*ArcSin[c + d*x^2]^2 + (b*ArcSin[c + d*x^2]*Log[1 - E^(I*ArcSin[c + d*x^2])/(I*c - Sqrt[1 - c^2])])/2 + (b*ArcSin[c + d*x^2]*Log[1 - E^(I*ArcSin[c + d*x^2])/(I*c + Sqrt[1 - c^2])])/2 + a*Log[x] - (I/2)*b*PolyLog[2, E^(I*ArcSin[c + d*x^2])/(I*c - Sqrt[1 - c^2])] - (I/2)*b*PolyLog[2, E^(I*ArcSin[c + d*x^2])/(I*c + Sqrt[1 - c^2])]","A",12,7,16,0.4375,1,"{6742, 4805, 4741, 4521, 2190, 2279, 2391}"
390,1,90,0,0.0924383,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x^3} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x^3,x]","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{2 x^2}-\frac{b d \tanh ^{-1}\left(\frac{-c^2-c d x^2+1}{\sqrt{1-c^2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}\right)}{2 \sqrt{1-c^2}}","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{2 x^2}-\frac{b d \tanh ^{-1}\left(\frac{-c^2-c d x^2+1}{\sqrt{1-c^2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}\right)}{2 \sqrt{1-c^2}}",1,"-(a + b*ArcSin[c + d*x^2])/(2*x^2) - (b*d*ArcTanh[(1 - c^2 - c*d*x^2)/(Sqrt[1 - c^2]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])])/(2*Sqrt[1 - c^2])","A",5,5,16,0.3125,1,"{4842, 12, 1114, 724, 206}"
391,1,137,0,0.1347732,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x^5} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x^5,x]","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{4 x^4}-\frac{b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{4 \left(1-c^2\right) x^2}-\frac{b c d^2 \tanh ^{-1}\left(\frac{-c^2-c d x^2+1}{\sqrt{1-c^2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}\right)}{4 \left(1-c^2\right)^{3/2}}","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{4 x^4}-\frac{b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{4 \left(1-c^2\right) x^2}-\frac{b c d^2 \tanh ^{-1}\left(\frac{-c^2-c d x^2+1}{\sqrt{1-c^2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}\right)}{4 \left(1-c^2\right)^{3/2}}",1,"-(b*d*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(4*(1 - c^2)*x^2) - (a + b*ArcSin[c + d*x^2])/(4*x^4) - (b*c*d^2*ArcTanh[(1 - c^2 - c*d*x^2)/(Sqrt[1 - c^2]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])])/(4*(1 - c^2)^(3/2))","A",6,6,16,0.3750,1,"{4842, 12, 1114, 730, 724, 206}"
392,1,190,0,0.2249497,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x^7} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x^7,x]","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{6 x^6}-\frac{b c d^2 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{4 \left(1-c^2\right)^2 x^2}-\frac{b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{12 \left(1-c^2\right) x^4}-\frac{b \left(2 c^2+1\right) d^3 \tanh ^{-1}\left(\frac{-c^2-c d x^2+1}{\sqrt{1-c^2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}\right)}{12 \left(1-c^2\right)^{5/2}}","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{6 x^6}-\frac{b c d^2 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{4 \left(1-c^2\right)^2 x^2}-\frac{b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{12 \left(1-c^2\right) x^4}-\frac{b \left(2 c^2+1\right) d^3 \tanh ^{-1}\left(\frac{-c^2-c d x^2+1}{\sqrt{1-c^2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}\right)}{12 \left(1-c^2\right)^{5/2}}",1,"-(b*d*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(12*(1 - c^2)*x^4) - (b*c*d^2*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(4*(1 - c^2)^2*x^2) - (a + b*ArcSin[c + d*x^2])/(6*x^6) - (b*(1 + 2*c^2)*d^3*ArcTanh[(1 - c^2 - c*d*x^2)/(Sqrt[1 - c^2]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])])/(12*(1 - c^2)^(5/2))","A",7,7,16,0.4375,1,"{4842, 12, 1114, 744, 806, 724, 206}"
393,1,336,0,0.4175221,"\int x^4 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right) \, dx","Int[x^4*(a + b*ArcSin[c + d*x^2]),x]","\frac{1}{5} x^5 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{2 b x^3 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{25 d}-\frac{16 b c x \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{75 d^2}+\frac{2 b \sqrt{1-c} (c+1) \left(15 c^2+8 c+9\right) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{75 d^{5/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{2 b \sqrt{1-c} (c+1) \left(23 c^2+9\right) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{75 d^{5/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}","\frac{1}{5} x^5 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{2 b x^3 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{25 d}-\frac{16 b c x \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{75 d^2}+\frac{2 b \sqrt{1-c} (c+1) \left(15 c^2+8 c+9\right) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{75 d^{5/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{2 b \sqrt{1-c} (c+1) \left(23 c^2+9\right) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{75 d^{5/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}",1,"(-16*b*c*x*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(75*d^2) + (2*b*x^3*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(25*d) + (x^5*(a + b*ArcSin[c + d*x^2]))/5 - (2*b*Sqrt[1 - c]*(1 + c)*(9 + 23*c^2)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticE[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(75*d^(5/2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4]) + (2*b*Sqrt[1 - c]*(1 + c)*(9 + 8*c + 15*c^2)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticF[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(75*d^(5/2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])","A",8,8,16,0.5000,1,"{4842, 12, 1122, 1279, 1202, 524, 424, 419}"
394,1,287,0,0.2881007,"\int x^2 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right) \, dx","Int[x^2*(a + b*ArcSin[c + d*x^2]),x]","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{2 b x \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{9 d}-\frac{2 b \sqrt{1-c} (c+1) (3 c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{9 d^{3/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}+\frac{8 b \sqrt{1-c} c (c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{9 d^{3/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}","\frac{1}{3} x^3 \left(a+b \sin ^{-1}\left(c+d x^2\right)\right)+\frac{2 b x \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{9 d}-\frac{2 b \sqrt{1-c} (c+1) (3 c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{9 d^{3/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}+\frac{8 b \sqrt{1-c} c (c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{9 d^{3/2} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}",1,"(2*b*x*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(9*d) + (x^3*(a + b*ArcSin[c + d*x^2]))/3 + (8*b*Sqrt[1 - c]*c*(1 + c)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticE[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(9*d^(3/2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4]) - (2*b*Sqrt[1 - c]*(1 + c)*(1 + 3*c)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticF[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(9*d^(3/2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])","A",7,7,16,0.4375,1,"{4842, 12, 1122, 1202, 524, 424, 419}"
395,1,237,0,0.2231651,"\int \left(a+b \sin ^{-1}\left(c+d x^2\right)\right) \, dx","Int[a + b*ArcSin[c + d*x^2],x]","a x+\frac{2 b \sqrt{1-c} (c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{\sqrt{d} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{2 b \sqrt{1-c} (c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{\sqrt{d} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}+b x \sin ^{-1}\left(c+d x^2\right)","a x+\frac{2 b \sqrt{1-c} (c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{\sqrt{d} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{2 b \sqrt{1-c} (c+1) \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{\sqrt{d} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}+b x \sin ^{-1}\left(c+d x^2\right)",1,"a*x + b*x*ArcSin[c + d*x^2] - (2*b*Sqrt[1 - c]*(1 + c)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticE[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(Sqrt[d]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4]) + (2*b*Sqrt[1 - c]*(1 + c)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticF[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(Sqrt[d]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])","A",7,6,12,0.5000,1,"{4840, 12, 1140, 493, 424, 419}"
396,1,126,0,0.0764169,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x^2} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x^2,x]","\frac{2 b \sqrt{1-c} \sqrt{d} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{\sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x}","\frac{2 b \sqrt{1-c} \sqrt{d} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{\sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x}",1,"-((a + b*ArcSin[c + d*x^2])/x) + (2*b*Sqrt[1 - c]*Sqrt[d]*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticF[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4]","A",4,4,16,0.2500,1,"{4842, 12, 1104, 419}"
397,1,284,0,0.2534675,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x^4} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x^4,x]","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{3 x^3}-\frac{2 b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{3 \left(1-c^2\right) x}+\frac{2 b d^{3/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{3 \sqrt{1-c} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{2 b d^{3/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{3 \sqrt{1-c} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{3 x^3}-\frac{2 b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{3 \left(1-c^2\right) x}+\frac{2 b d^{3/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{3 \sqrt{1-c} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{2 b d^{3/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{3 \sqrt{1-c} \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}",1,"(-2*b*d*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(3*(1 - c^2)*x) - (a + b*ArcSin[c + d*x^2])/(3*x^3) - (2*b*d^(3/2)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticE[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(3*Sqrt[1 - c]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4]) + (2*b*d^(3/2)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticF[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(3*Sqrt[1 - c]*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])","A",8,7,16,0.4375,1,"{4842, 12, 1123, 1140, 493, 424, 419}"
398,1,355,0,0.3560873,"\int \frac{a+b \sin ^{-1}\left(c+d x^2\right)}{x^6} \, dx","Int[(a + b*ArcSin[c + d*x^2])/x^6,x]","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{5 x^5}-\frac{8 b c d^2 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{15 \left(1-c^2\right)^2 x}-\frac{2 b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{15 \left(1-c^2\right) x^3}+\frac{2 b (3 c+1) d^{5/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{15 \sqrt{1-c} \left(1-c^2\right) \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{8 b c d^{5/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{15 \sqrt{1-c} \left(1-c^2\right) \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}","-\frac{a+b \sin ^{-1}\left(c+d x^2\right)}{5 x^5}-\frac{8 b c d^2 \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{15 \left(1-c^2\right)^2 x}-\frac{2 b d \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}{15 \left(1-c^2\right) x^3}+\frac{2 b (3 c+1) d^{5/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{15 \sqrt{1-c} \left(1-c^2\right) \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}-\frac{8 b c d^{5/2} \sqrt{1-\frac{d x^2}{1-c}} \sqrt{\frac{d x^2}{c+1}+1} E\left(\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{1-c}}\right)|-\frac{1-c}{c+1}\right)}{15 \sqrt{1-c} \left(1-c^2\right) \sqrt{-c^2-2 c d x^2-d^2 x^4+1}}",1,"(-2*b*d*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(15*(1 - c^2)*x^3) - (8*b*c*d^2*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])/(15*(1 - c^2)^2*x) - (a + b*ArcSin[c + d*x^2])/(5*x^5) - (8*b*c*d^(5/2)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticE[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(15*Sqrt[1 - c]*(1 - c^2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4]) + (2*b*(1 + 3*c)*d^(5/2)*Sqrt[1 - (d*x^2)/(1 - c)]*Sqrt[1 + (d*x^2)/(1 + c)]*EllipticF[ArcSin[(Sqrt[d]*x)/Sqrt[1 - c]], -((1 - c)/(1 + c))])/(15*Sqrt[1 - c]*(1 - c^2)*Sqrt[1 - c^2 - 2*c*d*x^2 - d^2*x^4])","A",8,8,16,0.5000,1,"{4842, 12, 1123, 1281, 1202, 524, 424, 419}"
399,1,47,0,0.0577193,"\int x^3 \sin ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcSin[a + b*x^4],x]","\frac{\sqrt{1-\left(a+b x^4\right)^2}}{4 b}+\frac{\left(a+b x^4\right) \sin ^{-1}\left(a+b x^4\right)}{4 b}","\frac{\sqrt{1-\left(a+b x^4\right)^2}}{4 b}+\frac{\left(a+b x^4\right) \sin ^{-1}\left(a+b x^4\right)}{4 b}",1,"Sqrt[1 - (a + b*x^4)^2]/(4*b) + ((a + b*x^4)*ArcSin[a + b*x^4])/(4*b)","A",4,4,12,0.3333,1,"{6715, 4803, 4619, 261}"
400,1,47,0,0.0534496,"\int x^{-1+n} \sin ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcSin[a + b*x^n],x]","\frac{\sqrt{1-\left(a+b x^n\right)^2}}{b n}+\frac{\left(a+b x^n\right) \sin ^{-1}\left(a+b x^n\right)}{b n}","\frac{\sqrt{1-\left(a+b x^n\right)^2}}{b n}+\frac{\left(a+b x^n\right) \sin ^{-1}\left(a+b x^n\right)}{b n}",1,"Sqrt[1 - (a + b*x^n)^2]/(b*n) + ((a + b*x^n)*ArcSin[a + b*x^n])/(b*n)","A",4,4,14,0.2857,1,"{6715, 4803, 4619, 261}"
401,1,127,0,0.0311803,"\int \left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^4 \, dx","Int[(a + b*ArcSin[1 + d*x^2])^4,x]","-\frac{192 b^3 \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}{d x}-48 b^2 x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2+\frac{8 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^3}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^4+384 b^4 x","-\frac{192 b^3 \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}{d x}-48 b^2 x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2+\frac{8 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^3}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^4+384 b^4 x",1,"384*b^4*x - (192*b^3*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcSin[1 + d*x^2]))/(d*x) - 48*b^2*x*(a + b*ArcSin[1 + d*x^2])^2 + (8*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcSin[1 + d*x^2])^3)/(d*x) + x*(a + b*ArcSin[1 + d*x^2])^4","A",3,2,14,0.1429,1,"{4814, 8}"
402,1,110,0,0.0576415,"\int \left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^3 \, dx","Int[(a + b*ArcSin[1 + d*x^2])^3,x]","-24 a b^2 x+\frac{6 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^3-\frac{48 b^3 \sqrt{-d^2 x^4-2 d x^2}}{d x}-24 b^3 x \sin ^{-1}\left(d x^2+1\right)","-24 a b^2 x+\frac{6 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^3-\frac{48 b^3 \sqrt{-d^2 x^4-2 d x^2}}{d x}-24 b^3 x \sin ^{-1}\left(d x^2+1\right)",1,"-24*a*b^2*x - (48*b^3*Sqrt[-2*d*x^2 - d^2*x^4])/(d*x) - 24*b^3*x*ArcSin[1 + d*x^2] + (6*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcSin[1 + d*x^2])^2)/(d*x) + x*(a + b*ArcSin[1 + d*x^2])^3","A",5,4,14,0.2857,1,"{4814, 4840, 12, 1588}"
403,1,63,0,0.0123104,"\int \left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^2 \, dx","Int[(a + b*ArcSin[1 + d*x^2])^2,x]","\frac{4 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2-8 b^2 x","\frac{4 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2-8 b^2 x",1,"-8*b^2*x + (4*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcSin[1 + d*x^2]))/(d*x) + x*(a + b*ArcSin[1 + d*x^2])^2","A",2,2,14,0.1429,1,"{4814, 8}"
404,1,43,0,0.0381969,"\int \left(a+b \sin ^{-1}\left(1+d x^2\right)\right) \, dx","Int[a + b*ArcSin[1 + d*x^2],x]","a x+\frac{2 b \sqrt{-d^2 x^4-2 d x^2}}{d x}+b x \sin ^{-1}\left(d x^2+1\right)","a x+\frac{2 b \sqrt{-d^2 x^4-2 d x^2}}{d x}+b x \sin ^{-1}\left(d x^2+1\right)",1,"a*x + (2*b*Sqrt[-2*d*x^2 - d^2*x^4])/(d*x) + b*x*ArcSin[1 + d*x^2]","A",4,3,12,0.2500,1,"{4840, 12, 1588}"
405,1,159,0,0.0416802,"\int \frac{1}{a+b \sin ^{-1}\left(1+d x^2\right)} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(-1),x]","-\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}","-\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}",1,"-(x*CosIntegral[(a + b*ArcSin[1 + d*x^2])/(2*b)]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(2*b*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) - (x*(Cos[a/(2*b)] + Sin[a/(2*b)])*SinIntegral[(a + b*ArcSin[1 + d*x^2])/(2*b)])/(2*b*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",1,1,14,0.07143,1,"{4816}"
406,1,205,0,0.0257812,"\int \frac{1}{\left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^2} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(-2),x]","-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{2 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}","-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{2 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}",1,"-Sqrt[-2*d*x^2 - d^2*x^4]/(2*b*d*x*(a + b*ArcSin[1 + d*x^2])) - (x*CosIntegral[(a + b*ArcSin[1 + d*x^2])/(2*b)]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(4*b^2*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) + (x*(Cos[a/(2*b)] - Sin[a/(2*b)])*SinIntegral[(a + b*ArcSin[1 + d*x^2])/(2*b)])/(4*b^2*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",1,1,14,0.07143,1,"{4825}"
407,1,227,0,0.0483044,"\int \frac{1}{\left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^3} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(-3),x]","\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x}{8 b^2 \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{4 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2}","\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a+b \sin ^{-1}\left(d x^2+1\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x}{8 b^2 \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{4 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^2}",1,"-Sqrt[-2*d*x^2 - d^2*x^4]/(4*b*d*x*(a + b*ArcSin[1 + d*x^2])^2) + x/(8*b^2*(a + b*ArcSin[1 + d*x^2])) + (x*CosIntegral[(a + b*ArcSin[1 + d*x^2])/(2*b)]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(16*b^3*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) + (x*(Cos[a/(2*b)] + Sin[a/(2*b)])*SinIntegral[(a + b*ArcSin[1 + d*x^2])/(2*b)])/(16*b^3*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",2,2,14,0.1429,1,"{4828, 4816}"
408,1,135,0,0.0309465,"\int \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^4 \, dx","Int[(a - b*ArcSin[1 - d*x^2])^4,x]","-\frac{192 b^3 \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}{d x}-48 b^2 x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2+\frac{8 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^3}{d x}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^4+384 b^4 x","-\frac{192 b^3 \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}{d x}-48 b^2 x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2+\frac{8 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^3}{d x}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^4+384 b^4 x",1,"384*b^4*x - (192*b^3*Sqrt[2*d*x^2 - d^2*x^4]*(a - b*ArcSin[1 - d*x^2]))/(d*x) - 48*b^2*x*(a - b*ArcSin[1 - d*x^2])^2 + (8*b*Sqrt[2*d*x^2 - d^2*x^4]*(a - b*ArcSin[1 - d*x^2])^3)/(d*x) + x*(a - b*ArcSin[1 - d*x^2])^4","A",3,2,16,0.1250,1,"{4814, 8}"
409,1,115,0,0.0607515,"\int \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^3 \, dx","Int[(a - b*ArcSin[1 - d*x^2])^3,x]","-24 a b^2 x+\frac{6 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2}{d x}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^3-\frac{48 b^3 \sqrt{2 d x^2-d^2 x^4}}{d x}+24 b^3 x \sin ^{-1}\left(1-d x^2\right)","-24 a b^2 x+\frac{6 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2}{d x}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^3-\frac{48 b^3 \sqrt{2 d x^2-d^2 x^4}}{d x}+24 b^3 x \sin ^{-1}\left(1-d x^2\right)",1,"-24*a*b^2*x - (48*b^3*Sqrt[2*d*x^2 - d^2*x^4])/(d*x) + 24*b^3*x*ArcSin[1 - d*x^2] + (6*b*Sqrt[2*d*x^2 - d^2*x^4]*(a - b*ArcSin[1 - d*x^2])^2)/(d*x) + x*(a - b*ArcSin[1 - d*x^2])^3","A",5,4,16,0.2500,1,"{4814, 4840, 12, 1588}"
410,1,67,0,0.0124719,"\int \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2 \, dx","Int[(a - b*ArcSin[1 - d*x^2])^2,x]","\frac{4 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}{d x}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2-8 b^2 x","\frac{4 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}{d x}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2-8 b^2 x",1,"-8*b^2*x + (4*b*Sqrt[2*d*x^2 - d^2*x^4]*(a - b*ArcSin[1 - d*x^2]))/(d*x) + x*(a - b*ArcSin[1 - d*x^2])^2","A",2,2,16,0.1250,1,"{4814, 8}"
411,1,45,0,0.0392835,"\int \left(a-b \sin ^{-1}\left(1-d x^2\right)\right) \, dx","Int[a - b*ArcSin[1 - d*x^2],x]","a x+\frac{2 b \sqrt{2 d x^2-d^2 x^4}}{d x}+b (-x) \sin ^{-1}\left(1-d x^2\right)","a x+\frac{2 b \sqrt{2 d x^2-d^2 x^4}}{d x}+b (-x) \sin ^{-1}\left(1-d x^2\right)",1,"a*x + (2*b*Sqrt[2*d*x^2 - d^2*x^4])/(d*x) - b*x*ArcSin[1 - d*x^2]","A",4,3,14,0.2143,1,"{4840, 12, 1588}"
412,1,168,0,0.0228204,"\int \frac{1}{a-b \sin ^{-1}\left(1-d x^2\right)} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(-1),x]","\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{a-b \sin ^{-1}\left(1-d x^2\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}","\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{a-b \sin ^{-1}\left(1-d x^2\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}",1,"(x*CosIntegral[-(a - b*ArcSin[1 - d*x^2])/(2*b)]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(2*b*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) - (x*(Cos[a/(2*b)] - Sin[a/(2*b)])*SinIntegral[a/(2*b) - ArcSin[1 - d*x^2]/2])/(2*b*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",1,1,16,0.06250,1,"{4816}"
413,1,216,0,0.024594,"\int \frac{1}{\left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(-2),x]","-\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{a-b \sin ^{-1}\left(1-d x^2\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{\sqrt{2 d x^2-d^2 x^4}}{2 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}","-\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{a-b \sin ^{-1}\left(1-d x^2\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{\sqrt{2 d x^2-d^2 x^4}}{2 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}",1,"-Sqrt[2*d*x^2 - d^2*x^4]/(2*b*d*x*(a - b*ArcSin[1 - d*x^2])) - (x*CosIntegral[-(a - b*ArcSin[1 - d*x^2])/(2*b)]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(4*b^2*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) - (x*(Cos[a/(2*b)] + Sin[a/(2*b)])*SinIntegral[a/(2*b) - ArcSin[1 - d*x^2]/2])/(4*b^2*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",1,1,16,0.06250,1,"{4825}"
414,1,240,0,0.0470692,"\int \frac{1}{\left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^3} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(-3),x]","-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{a-b \sin ^{-1}\left(1-d x^2\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{x}{8 b^2 \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}-\frac{\sqrt{2 d x^2-d^2 x^4}}{4 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2}","-\frac{x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{a-b \sin ^{-1}\left(1-d x^2\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{x}{8 b^2 \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)}-\frac{\sqrt{2 d x^2-d^2 x^4}}{4 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^2}",1,"-Sqrt[2*d*x^2 - d^2*x^4]/(4*b*d*x*(a - b*ArcSin[1 - d*x^2])^2) + x/(8*b^2*(a - b*ArcSin[1 - d*x^2])) - (x*CosIntegral[-(a - b*ArcSin[1 - d*x^2])/(2*b)]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(16*b^3*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) + (x*(Cos[a/(2*b)] - Sin[a/(2*b)])*SinIntegral[a/(2*b) - ArcSin[1 - d*x^2]/2])/(16*b^3*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",2,2,16,0.1250,1,"{4828, 4816}"
415,1,40,0,0.0062437,"\int \sin ^{-1}\left(1+x^2\right)^2 \, dx","Int[ArcSin[1 + x^2]^2,x]","x \sin ^{-1}\left(x^2+1\right)^2+\frac{4 \sqrt{-x^4-2 x^2} \sin ^{-1}\left(x^2+1\right)}{x}-8 x","x \sin ^{-1}\left(x^2+1\right)^2+\frac{4 \sqrt{-x^4-2 x^2} \sin ^{-1}\left(x^2+1\right)}{x}-8 x",1,"-8*x + (4*Sqrt[-2*x^2 - x^4]*ArcSin[1 + x^2])/x + x*ArcSin[1 + x^2]^2","A",2,2,8,0.2500,1,"{4814, 8}"
416,1,44,0,0.0071933,"\int \sin ^{-1}\left(1-x^2\right)^2 \, dx","Int[ArcSin[1 - x^2]^2,x]","x \sin ^{-1}\left(1-x^2\right)^2-\frac{4 \sqrt{2 x^2-x^4} \sin ^{-1}\left(1-x^2\right)}{x}-8 x","x \sin ^{-1}\left(1-x^2\right)^2-\frac{4 \sqrt{2 x^2-x^4} \sin ^{-1}\left(1-x^2\right)}{x}-8 x",1,"-8*x - (4*Sqrt[2*x^2 - x^4]*ArcSin[1 - x^2])/x + x*ArcSin[1 - x^2]^2","A",2,2,10,0.2000,1,"{4814, 8}"
417,1,277,0,0.1044516,"\int \left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^{5/2} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(5/2),x]","-15 b^2 x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}+\frac{5 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}}{d x}+\frac{15 \sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{15 \sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{5/2}","-15 b^2 x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}+\frac{5 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}}{d x}+\frac{15 \sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{15 \sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{5/2}",1,"-15*b^2*x*Sqrt[a + b*ArcSin[1 + d*x^2]] + (5*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcSin[1 + d*x^2])^(3/2))/(d*x) + x*(a + b*ArcSin[1 + d*x^2])^(5/2) - (15*Sqrt[Pi]*x*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/((b^(-1))^(5/2)*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) + (15*Sqrt[Pi]*x*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/((b^(-1))^(5/2)*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",2,2,16,0.1250,1,"{4814, 4811}"
418,1,247,0,0.0757509,"\int \left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^{3/2} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi } \sqrt{b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}+\frac{3 \sqrt{\pi } b^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{b} \sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}+\frac{3 b \sqrt{-d^2 x^4-2 d x^2} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}","\frac{3 \sqrt{\pi } b^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi } \sqrt{b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}+\frac{3 \sqrt{\pi } b^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{b} \sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}+\frac{3 b \sqrt{-d^2 x^4-2 d x^2} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{d x}+x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}",1,"(3*b*Sqrt[-2*d*x^2 - d^2*x^4]*Sqrt[a + b*ArcSin[1 + d*x^2]])/(d*x) + x*(a + b*ArcSin[1 + d*x^2])^(3/2) + (3*b^(3/2)*Sqrt[Pi]*x*FresnelC[Sqrt[a + b*ArcSin[1 + d*x^2]]/(Sqrt[b]*Sqrt[Pi])]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]) + (3*b^(3/2)*Sqrt[Pi]*x*FresnelS[Sqrt[a + b*ArcSin[1 + d*x^2]]/(Sqrt[b]*Sqrt[Pi])]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])","A",2,2,16,0.1250,1,"{4814, 4819}"
419,1,210,0,0.0242479,"\int \sqrt{a+b \sin ^{-1}\left(1+d x^2\right)} \, dx","Int[Sqrt[a + b*ArcSin[1 + d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}","-\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}",1,"x*Sqrt[a + b*ArcSin[1 + d*x^2]] + (Sqrt[Pi]*x*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Sqrt[b^(-1)]*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) - (Sqrt[Pi]*x*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Sqrt[b^(-1)]*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",1,1,16,0.06250,1,"{4811}"
420,1,185,0,0.0268245,"\int \frac{1}{\sqrt{a+b \sin ^{-1}\left(1+d x^2\right)}} \, dx","Int[1/Sqrt[a + b*ArcSin[1 + d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi } \sqrt{b}}\right)}{\sqrt{b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{b} \sqrt{\pi }}\right)}{\sqrt{b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}","-\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi } \sqrt{b}}\right)}{\sqrt{b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{b} \sqrt{\pi }}\right)}{\sqrt{b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}",1,"-((Sqrt[Pi]*x*FresnelC[Sqrt[a + b*ArcSin[1 + d*x^2]]/(Sqrt[b]*Sqrt[Pi])]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Sqrt[b]*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))) - (Sqrt[Pi]*x*FresnelS[Sqrt[a + b*ArcSin[1 + d*x^2]]/(Sqrt[b]*Sqrt[Pi])]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Sqrt[b]*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",1,1,16,0.06250,1,"{4819}"
421,1,238,0,0.0358891,"\int \frac{1}{\left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^{3/2}} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(-3/2),x]","-\frac{\sqrt{-d^2 x^4-2 d x^2}}{b d x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}-\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}+\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}","-\frac{\sqrt{-d^2 x^4-2 d x^2}}{b d x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}-\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}+\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)}",1,"-(Sqrt[-2*d*x^2 - d^2*x^4]/(b*d*x*Sqrt[a + b*ArcSin[1 + d*x^2]])) + ((b^(-1))^(3/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]) - ((b^(-1))^(3/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])","A",1,1,16,0.06250,1,"{4822}"
422,1,261,0,0.0657306,"\int \frac{1}{\left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^{5/2}} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(-5/2),x]","\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x}{3 b^2 \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{3 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}}","\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}+\frac{x}{3 b^2 \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{3 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}}",1,"-Sqrt[-2*d*x^2 - d^2*x^4]/(3*b*d*x*(a + b*ArcSin[1 + d*x^2])^(3/2)) + x/(3*b^2*Sqrt[a + b*ArcSin[1 + d*x^2]]) + (Sqrt[Pi]*x*FresnelC[Sqrt[a + b*ArcSin[1 + d*x^2]]/(Sqrt[b]*Sqrt[Pi])]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(3*b^(5/2)*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) + (Sqrt[Pi]*x*FresnelS[Sqrt[a + b*ArcSin[1 + d*x^2]]/(Sqrt[b]*Sqrt[Pi])]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(3*b^(5/2)*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",2,2,16,0.1250,1,"{4828, 4819}"
423,1,317,0,0.0648529,"\int \frac{1}{\left(a+b \sin ^{-1}\left(1+d x^2\right)\right)^{7/2}} \, dx","Int[(a + b*ArcSin[1 + d*x^2])^(-7/2),x]","\frac{\sqrt{-d^2 x^4-2 d x^2}}{15 b^3 d x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}+\frac{x}{15 b^2 \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{5 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{5/2}}+\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}","\frac{\sqrt{-d^2 x^4-2 d x^2}}{15 b^3 d x \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}+\frac{x}{15 b^2 \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{3/2}}-\frac{\sqrt{-d^2 x^4-2 d x^2}}{5 b d x \left(a+b \sin ^{-1}\left(d x^2+1\right)\right)^{5/2}}+\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}-\frac{\sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \sin ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(d x^2+1\right)\right)\right)}",1,"-Sqrt[-2*d*x^2 - d^2*x^4]/(5*b*d*x*(a + b*ArcSin[1 + d*x^2])^(5/2)) + x/(15*b^2*(a + b*ArcSin[1 + d*x^2])^(3/2)) + Sqrt[-2*d*x^2 - d^2*x^4]/(15*b^3*d*x*Sqrt[a + b*ArcSin[1 + d*x^2]]) - ((b^(-1))^(7/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(15*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2])) + ((b^(-1))^(7/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcSin[1 + d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(15*(Cos[ArcSin[1 + d*x^2]/2] - Sin[ArcSin[1 + d*x^2]/2]))","A",2,2,16,0.1250,1,"{4828, 4822}"
424,1,299,0,0.1323518,"\int \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{5/2} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(5/2),x]","-15 b^2 x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}+\frac{5 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}}{d x}+\frac{15 \sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\left(-\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{15 \sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\left(-\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{5/2}","-15 b^2 x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}+\frac{5 b \sqrt{2 d x^2-d^2 x^4} \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}}{d x}+\frac{15 \sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\left(-\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{15 \sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\left(-\frac{1}{b}\right)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{5/2}",1,"-15*b^2*x*Sqrt[a - b*ArcSin[1 - d*x^2]] + (5*b*Sqrt[2*d*x^2 - d^2*x^4]*(a - b*ArcSin[1 - d*x^2])^(3/2))/(d*x) + x*(a - b*ArcSin[1 - d*x^2])^(5/2) + (15*Sqrt[Pi]*x*FresnelC[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/((-b^(-1))^(5/2)*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) - (15*Sqrt[Pi]*x*FresnelS[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/((-b^(-1))^(5/2)*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",2,2,18,0.1111,1,"{4814, 4811}"
425,1,267,0,0.0976497,"\int \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(3/2),x]","\frac{3 b \sqrt{2 d x^2-d^2 x^4} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{d x}+\frac{3 \sqrt{\pi } (-b)^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi } \sqrt{-b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}+\frac{3 \sqrt{\pi } (-b)^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{-b} \sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}","\frac{3 b \sqrt{2 d x^2-d^2 x^4} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{d x}+\frac{3 \sqrt{\pi } (-b)^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi } \sqrt{-b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}+\frac{3 \sqrt{\pi } (-b)^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{-b} \sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}+x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}",1,"(3*b*Sqrt[2*d*x^2 - d^2*x^4]*Sqrt[a - b*ArcSin[1 - d*x^2]])/(d*x) + x*(a - b*ArcSin[1 - d*x^2])^(3/2) + (3*(-b)^(3/2)*Sqrt[Pi]*x*FresnelS[Sqrt[a - b*ArcSin[1 - d*x^2]]/(Sqrt[-b]*Sqrt[Pi])]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]) + (3*(-b)^(3/2)*Sqrt[Pi]*x*FresnelC[Sqrt[a - b*ArcSin[1 - d*x^2]]/(Sqrt[-b]*Sqrt[Pi])]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])","A",2,2,18,0.1111,1,"{4814, 4819}"
426,1,228,0,0.0371218,"\int \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)} \, dx","Int[Sqrt[a - b*ArcSin[1 - d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}","-\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{1}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}",1,"x*Sqrt[a - b*ArcSin[1 - d*x^2]] - (Sqrt[Pi]*x*FresnelC[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Sqrt[-b^(-1)]*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) + (Sqrt[Pi]*x*FresnelS[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Sqrt[-b^(-1)]*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",1,1,18,0.05556,1,"{4811}"
427,1,201,0,0.0296038,"\int \frac{1}{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}} \, dx","Int[1/Sqrt[a - b*ArcSin[1 - d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi } \sqrt{-b}}\right)}{\sqrt{-b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{-b} \sqrt{\pi }}\right)}{\sqrt{-b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}","-\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi } \sqrt{-b}}\right)}{\sqrt{-b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{-b} \sqrt{\pi }}\right)}{\sqrt{-b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}",1,"-((Sqrt[Pi]*x*FresnelS[Sqrt[a - b*ArcSin[1 - d*x^2]]/(Sqrt[-b]*Sqrt[Pi])]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Sqrt[-b]*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))) - (Sqrt[Pi]*x*FresnelC[Sqrt[a - b*ArcSin[1 - d*x^2]]/(Sqrt[-b]*Sqrt[Pi])]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Sqrt[-b]*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",1,1,18,0.05556,1,"{4819}"
428,1,256,0,0.05705,"\int \frac{1}{\left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(-3/2),x]","-\frac{\sqrt{2 d x^2-d^2 x^4}}{b d x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}-\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}+\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}","-\frac{\sqrt{2 d x^2-d^2 x^4}}{b d x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}-\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{3/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}+\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{3/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)}",1,"-(Sqrt[2*d*x^2 - d^2*x^4]/(b*d*x*Sqrt[a - b*ArcSin[1 - d*x^2]])) - ((-b^(-1))^(3/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]) + ((-b^(-1))^(3/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])","A",1,1,18,0.05556,1,"{4822}"
429,1,281,0,0.0750609,"\int \frac{1}{\left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{5/2}} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(-5/2),x]","\frac{x}{3 b^2 \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}-\frac{\sqrt{2 d x^2-d^2 x^4}}{3 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}}+\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi } \sqrt{-b}}\right)}{3 (-b)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{-b} \sqrt{\pi }}\right)}{3 (-b)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}","\frac{x}{3 b^2 \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}-\frac{\sqrt{2 d x^2-d^2 x^4}}{3 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}}+\frac{\sqrt{\pi } x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi } \sqrt{-b}}\right)}{3 (-b)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{-b} \sqrt{\pi }}\right)}{3 (-b)^{5/2} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}",1,"-Sqrt[2*d*x^2 - d^2*x^4]/(3*b*d*x*(a - b*ArcSin[1 - d*x^2])^(3/2)) + x/(3*b^2*Sqrt[a - b*ArcSin[1 - d*x^2]]) + (Sqrt[Pi]*x*FresnelS[Sqrt[a - b*ArcSin[1 - d*x^2]]/(Sqrt[-b]*Sqrt[Pi])]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(3*(-b)^(5/2)*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) + (Sqrt[Pi]*x*FresnelC[Sqrt[a - b*ArcSin[1 - d*x^2]]/(Sqrt[-b]*Sqrt[Pi])]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(3*(-b)^(5/2)*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",2,2,18,0.1111,1,"{4828, 4819}"
430,1,339,0,0.0984169,"\int \frac{1}{\left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{7/2}} \, dx","Int[(a - b*ArcSin[1 - d*x^2])^(-7/2),x]","\frac{\sqrt{2 d x^2-d^2 x^4}}{15 b^3 d x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}+\frac{x}{15 b^2 \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}}-\frac{\sqrt{2 d x^2-d^2 x^4}}{5 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{5/2}}+\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{7/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{7/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}","\frac{\sqrt{2 d x^2-d^2 x^4}}{15 b^3 d x \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}+\frac{x}{15 b^2 \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{3/2}}-\frac{\sqrt{2 d x^2-d^2 x^4}}{5 b d x \left(a-b \sin ^{-1}\left(1-d x^2\right)\right)^{5/2}}+\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{7/2} x \left(\cos \left(\frac{a}{2 b}\right)-\sin \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}-\frac{\sqrt{\pi } \left(-\frac{1}{b}\right)^{7/2} x \left(\sin \left(\frac{a}{2 b}\right)+\cos \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{1}{b}} \sqrt{a-b \sin ^{-1}\left(1-d x^2\right)}}{\sqrt{\pi }}\right)}{15 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-d x^2\right)\right)\right)}",1,"-Sqrt[2*d*x^2 - d^2*x^4]/(5*b*d*x*(a - b*ArcSin[1 - d*x^2])^(5/2)) + x/(15*b^2*(a - b*ArcSin[1 - d*x^2])^(3/2)) + Sqrt[2*d*x^2 - d^2*x^4]/(15*b^3*d*x*Sqrt[a - b*ArcSin[1 - d*x^2]]) + ((-b^(-1))^(7/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] - Sin[a/(2*b)]))/(15*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2])) - ((-b^(-1))^(7/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[-b^(-1)]*Sqrt[a - b*ArcSin[1 - d*x^2]])/Sqrt[Pi]]*(Cos[a/(2*b)] + Sin[a/(2*b)]))/(15*(Cos[ArcSin[1 - d*x^2]/2] - Sin[ArcSin[1 - d*x^2]/2]))","A",2,2,18,0.1111,1,"{4828, 4822}"
431,0,0,0,0.0465118,"\int \frac{\left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Defer[Int][(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
432,1,275,0,0.223743,"\int \frac{\left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","-\frac{3 b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}+\frac{i \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(1-e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}","-\frac{3 b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b^3 \text{PolyLog}\left(4,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}+\frac{i \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(1-e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"((I/4)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^4)/(b*c) - ((a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*Log[1 - E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + (((3*I)/2)*b*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (3*b^2*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c) - (((3*I)/4)*b^3*PolyLog[4, E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c","A",8,8,40,0.2000,1,"{6681, 4625, 3717, 2190, 2531, 6609, 2282, 6589}"
433,1,205,0,0.1816834,"\int \frac{\left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(1-e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(1-e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"((I/3)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3)/(b*c) - ((a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*Log[1 - E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + (I*b*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (b^2*PolyLog[3, E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c)","A",7,7,40,0.1750,1,"{6681, 4625, 3717, 2190, 2531, 2282, 6589}"
434,1,141,0,0.1114458,"\int \frac{a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(1-e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}","\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(1-e^{2 i \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}",1,"((I/2)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2)/(b*c) - ((a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*Log[1 - E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c","A",6,7,38,0.1842,1,"{206, 6681, 4625, 3717, 2190, 2279, 2391}"
435,0,0,0,0.0427648,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
436,0,0,0,0.0431535,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcSin[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
437,1,22,0,0.038355,"\int e^x \sin ^{-1}\left(e^x\right) \, dx","Int[E^x*ArcSin[E^x],x]","\sqrt{1-e^{2 x}}+e^x \sin ^{-1}\left(e^x\right)","\sqrt{1-e^{2 x}}+e^x \sin ^{-1}\left(e^x\right)",1,"Sqrt[1 - E^(2*x)] + E^x*ArcSin[E^x]","A",3,4,8,0.5000,1,"{2194, 4844, 2246, 32}"
438,1,84,0,0.0707198,"\int \sin ^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcSin[c*E^(a + b*x)],x]","-\frac{i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{i \sin ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\sin ^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 i \sin ^{-1}\left(c e^{a+b x}\right)}\right)}{b}","-\frac{i \text{PolyLog}\left(2,e^{2 i \sin ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{i \sin ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\sin ^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 i \sin ^{-1}\left(c e^{a+b x}\right)}\right)}{b}",1,"((-I/2)*ArcSin[c*E^(a + b*x)]^2)/b + (ArcSin[c*E^(a + b*x)]*Log[1 - E^((2*I)*ArcSin[c*E^(a + b*x)])])/b - ((I/2)*PolyLog[2, E^((2*I)*ArcSin[c*E^(a + b*x)])])/b","A",6,6,10,0.6000,1,"{2282, 4625, 3717, 2190, 2279, 2391}"
439,1,81,0,0.0656336,"\int e^{\sin ^{-1}(a x)} x^3 \, dx","Int[E^ArcSin[a*x]*x^3,x]","\frac{e^{\sin ^{-1}(a x)} \sin \left(2 \sin ^{-1}(a x)\right)}{20 a^4}-\frac{e^{\sin ^{-1}(a x)} \sin \left(4 \sin ^{-1}(a x)\right)}{136 a^4}-\frac{e^{\sin ^{-1}(a x)} \cos \left(2 \sin ^{-1}(a x)\right)}{10 a^4}+\frac{e^{\sin ^{-1}(a x)} \cos \left(4 \sin ^{-1}(a x)\right)}{34 a^4}","\frac{e^{\sin ^{-1}(a x)} \sin \left(2 \sin ^{-1}(a x)\right)}{20 a^4}-\frac{e^{\sin ^{-1}(a x)} \sin \left(4 \sin ^{-1}(a x)\right)}{136 a^4}-\frac{e^{\sin ^{-1}(a x)} \cos \left(2 \sin ^{-1}(a x)\right)}{10 a^4}+\frac{e^{\sin ^{-1}(a x)} \cos \left(4 \sin ^{-1}(a x)\right)}{34 a^4}",1,"-(E^ArcSin[a*x]*Cos[2*ArcSin[a*x]])/(10*a^4) + (E^ArcSin[a*x]*Cos[4*ArcSin[a*x]])/(34*a^4) + (E^ArcSin[a*x]*Sin[2*ArcSin[a*x]])/(20*a^4) - (E^ArcSin[a*x]*Sin[4*ArcSin[a*x]])/(136*a^4)","A",6,4,10,0.4000,1,"{4836, 12, 4469, 4432}"
440,1,82,0,0.062202,"\int e^{\sin ^{-1}(a x)} x^2 \, dx","Int[E^ArcSin[a*x]*x^2,x]","\frac{\sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}}{8 a^3}+\frac{x e^{\sin ^{-1}(a x)}}{8 a^2}-\frac{3 e^{\sin ^{-1}(a x)} \sin \left(3 \sin ^{-1}(a x)\right)}{40 a^3}-\frac{e^{\sin ^{-1}(a x)} \cos \left(3 \sin ^{-1}(a x)\right)}{40 a^3}","\frac{\sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}}{8 a^3}+\frac{x e^{\sin ^{-1}(a x)}}{8 a^2}-\frac{3 e^{\sin ^{-1}(a x)} \sin \left(3 \sin ^{-1}(a x)\right)}{40 a^3}-\frac{e^{\sin ^{-1}(a x)} \cos \left(3 \sin ^{-1}(a x)\right)}{40 a^3}",1,"(E^ArcSin[a*x]*x)/(8*a^2) + (E^ArcSin[a*x]*Sqrt[1 - a^2*x^2])/(8*a^3) - (E^ArcSin[a*x]*Cos[3*ArcSin[a*x]])/(40*a^3) - (3*E^ArcSin[a*x]*Sin[3*ArcSin[a*x]])/(40*a^3)","A",6,4,10,0.4000,1,"{4836, 12, 4469, 4433}"
441,1,41,0,0.0338236,"\int e^{\sin ^{-1}(a x)} x \, dx","Int[E^ArcSin[a*x]*x,x]","\frac{e^{\sin ^{-1}(a x)} \sin \left(2 \sin ^{-1}(a x)\right)}{10 a^2}-\frac{e^{\sin ^{-1}(a x)} \cos \left(2 \sin ^{-1}(a x)\right)}{5 a^2}","\frac{e^{\sin ^{-1}(a x)} \sin \left(2 \sin ^{-1}(a x)\right)}{10 a^2}-\frac{e^{\sin ^{-1}(a x)} \cos \left(2 \sin ^{-1}(a x)\right)}{5 a^2}",1,"-(E^ArcSin[a*x]*Cos[2*ArcSin[a*x]])/(5*a^2) + (E^ArcSin[a*x]*Sin[2*ArcSin[a*x]])/(10*a^2)","A",5,4,8,0.5000,1,"{4836, 12, 4469, 4432}"
442,1,39,0,0.0143872,"\int e^{\sin ^{-1}(a x)} \, dx","Int[E^ArcSin[a*x],x]","\frac{\sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}}{2 a}+\frac{1}{2} x e^{\sin ^{-1}(a x)}","\frac{\sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}}{2 a}+\frac{1}{2} x e^{\sin ^{-1}(a x)}",1,"(E^ArcSin[a*x]*x)/2 + (E^ArcSin[a*x]*Sqrt[1 - a^2*x^2])/(2*a)","A",2,2,6,0.3333,1,"{4836, 4433}"
443,1,43,0,0.0569787,"\int \frac{e^{\sin ^{-1}(a x)}}{x} \, dx","Int[E^ArcSin[a*x]/x,x]","i e^{\sin ^{-1}(a x)}-2 i e^{\sin ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};e^{2 i \sin ^{-1}(a x)}\right)","i e^{\sin ^{-1}(a x)}-2 i e^{\sin ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};e^{2 i \sin ^{-1}(a x)}\right)",1,"I*E^ArcSin[a*x] - (2*I)*E^ArcSin[a*x]*Hypergeometric2F1[-I/2, 1, 1 - I/2, E^((2*I)*ArcSin[a*x])]","A",6,5,10,0.5000,1,"{4836, 12, 4443, 2194, 2251}"
444,1,83,0,0.1069181,"\int \frac{e^{\sin ^{-1}(a x)}}{x^2} \, dx","Int[E^ArcSin[a*x]/x^2,x]","(1-i) a e^{(1+i) \sin ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};e^{2 i \sin ^{-1}(a x)}\right)-(2-2 i) a e^{(1+i) \sin ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};e^{2 i \sin ^{-1}(a x)}\right)","(1-i) a e^{(1+i) \sin ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};e^{2 i \sin ^{-1}(a x)}\right)-(2-2 i) a e^{(1+i) \sin ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};e^{2 i \sin ^{-1}(a x)}\right)",1,"(1 - I)*a*E^((1 + I)*ArcSin[a*x])*Hypergeometric2F1[1/2 - I/2, 1, 3/2 - I/2, E^((2*I)*ArcSin[a*x])] - (2 - 2*I)*a*E^((1 + I)*ArcSin[a*x])*Hypergeometric2F1[1/2 - I/2, 2, 3/2 - I/2, E^((2*I)*ArcSin[a*x])]","A",6,4,10,0.4000,1,"{4836, 12, 4471, 2251}"
445,1,101,0,0.1234161,"\int e^{\sin ^{-1}(a x)^2} x^3 \, dx","Int[E^ArcSin[a*x]^2*x^3,x]","\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a x)\right)}{16 a^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2-i \sin ^{-1}(a x)\right)}{32 a^4}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a x)\right)}{16 a^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2+i \sin ^{-1}(a x)\right)}{32 a^4}","\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a x)\right)}{16 a^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2-i \sin ^{-1}(a x)\right)}{32 a^4}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a x)\right)}{16 a^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2+i \sin ^{-1}(a x)\right)}{32 a^4}",1,"(E*Sqrt[Pi]*Erf[1 - I*ArcSin[a*x]])/(16*a^4) - (E^4*Sqrt[Pi]*Erf[2 - I*ArcSin[a*x]])/(32*a^4) + (E*Sqrt[Pi]*Erf[1 + I*ArcSin[a*x]])/(16*a^4) - (E^4*Sqrt[Pi]*Erf[2 + I*ArcSin[a*x]])/(32*a^4)","A",12,5,12,0.4167,1,"{4836, 12, 4474, 2234, 2204}"
446,1,129,0,0.1292406,"\int e^{\sin ^{-1}(a x)^2} x^2 \, dx","Int[E^ArcSin[a*x]^2*x^2,x]","\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)-i\right)\right)}{16 a^3}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)+i\right)\right)}{16 a^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)-3 i\right)\right)}{16 a^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)+3 i\right)\right)}{16 a^3}","\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)-i\right)\right)}{16 a^3}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)+i\right)\right)}{16 a^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)-3 i\right)\right)}{16 a^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)+3 i\right)\right)}{16 a^3}",1,"(E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a*x])/2])/(16*a^3) + (E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a*x])/2])/(16*a^3) - (E^(9/4)*Sqrt[Pi]*Erfi[(-3*I + 2*ArcSin[a*x])/2])/(16*a^3) - (E^(9/4)*Sqrt[Pi]*Erfi[(3*I + 2*ArcSin[a*x])/2])/(16*a^3)","A",12,5,12,0.4167,1,"{4836, 12, 4474, 2234, 2204}"
447,1,49,0,0.06189,"\int e^{\sin ^{-1}(a x)^2} x \, dx","Int[E^ArcSin[a*x]^2*x,x]","\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a x)\right)}{8 a^2}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a x)\right)}{8 a^2}","\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a x)\right)}{8 a^2}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a x)\right)}{8 a^2}",1,"(E*Sqrt[Pi]*Erf[1 - I*ArcSin[a*x]])/(8*a^2) + (E*Sqrt[Pi]*Erf[1 + I*ArcSin[a*x]])/(8*a^2)","A",8,5,10,0.5000,1,"{4836, 12, 4474, 2234, 2204}"
448,1,65,0,0.0502309,"\int e^{\sin ^{-1}(a x)^2} \, dx","Int[E^ArcSin[a*x]^2,x]","\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)-i\right)\right)}{4 a}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)+i\right)\right)}{4 a}","\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)-i\right)\right)}{4 a}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a x)+i\right)\right)}{4 a}",1,"(E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a*x])/2])/(4*a) + (E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a*x])/2])/(4*a)","A",7,4,8,0.5000,1,"{4836, 4473, 2234, 2204}"
449,0,0,0,0.0377262,"\int \frac{e^{\sin ^{-1}(a x)^2}}{x} \, dx","Int[E^ArcSin[a*x]^2/x,x]","\int \frac{e^{\sin ^{-1}(a x)^2}}{x} \, dx","a \text{Int}\left(\frac{e^{\sin ^{-1}(a x)^2}}{a x},x\right)",0,"Defer[Subst][Defer[Int][E^x^2*Cot[x], x], x, ArcSin[a*x]]","A",0,0,0,0,-1,"{}"
450,0,0,0,0.07802,"\int \frac{e^{\sin ^{-1}(a x)^2}}{x^2} \, dx","Int[E^ArcSin[a*x]^2/x^2,x]","\int \frac{e^{\sin ^{-1}(a x)^2}}{x^2} \, dx","a^2 \text{Int}\left(\frac{e^{\sin ^{-1}(a x)^2}}{a^2 x^2},x\right)",0,"a*Defer[Subst][Defer[Int][E^x^2*Cot[x]*Csc[x], x], x, ArcSin[a*x]]","A",0,0,0,0,-1,"{}"
451,1,309,0,0.5274352,"\int e^{\sin ^{-1}(a+b x)} x^3 \, dx","Int[E^ArcSin[a + b*x]*x^3,x]","-\frac{a^3 (a+b x) e^{\sin ^{-1}(a+b x)}}{2 b^4}-\frac{a^3 \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b^4}+\frac{3 a^2 e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{10 b^4}-\frac{3 a^2 e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{5 b^4}-\frac{3 a (a+b x) e^{\sin ^{-1}(a+b x)}}{8 b^4}+\frac{9 a e^{\sin ^{-1}(a+b x)} \sin \left(3 \sin ^{-1}(a+b x)\right)}{40 b^4}-\frac{3 a \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{8 b^4}+\frac{e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{20 b^4}-\frac{e^{\sin ^{-1}(a+b x)} \sin \left(4 \sin ^{-1}(a+b x)\right)}{136 b^4}+\frac{3 a e^{\sin ^{-1}(a+b x)} \cos \left(3 \sin ^{-1}(a+b x)\right)}{40 b^4}-\frac{e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{10 b^4}+\frac{e^{\sin ^{-1}(a+b x)} \cos \left(4 \sin ^{-1}(a+b x)\right)}{34 b^4}","-\frac{a^3 (a+b x) e^{\sin ^{-1}(a+b x)}}{2 b^4}-\frac{a^3 \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b^4}+\frac{3 a^2 e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{10 b^4}-\frac{3 a^2 e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{5 b^4}-\frac{3 a (a+b x) e^{\sin ^{-1}(a+b x)}}{8 b^4}+\frac{9 a e^{\sin ^{-1}(a+b x)} \sin \left(3 \sin ^{-1}(a+b x)\right)}{40 b^4}-\frac{3 a \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{8 b^4}+\frac{e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{20 b^4}-\frac{e^{\sin ^{-1}(a+b x)} \sin \left(4 \sin ^{-1}(a+b x)\right)}{136 b^4}+\frac{3 a e^{\sin ^{-1}(a+b x)} \cos \left(3 \sin ^{-1}(a+b x)\right)}{40 b^4}-\frac{e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{10 b^4}+\frac{e^{\sin ^{-1}(a+b x)} \cos \left(4 \sin ^{-1}(a+b x)\right)}{34 b^4}",1,"(-3*a*E^ArcSin[a + b*x]*(a + b*x))/(8*b^4) - (a^3*E^ArcSin[a + b*x]*(a + b*x))/(2*b^4) - (3*a*E^ArcSin[a + b*x]*Sqrt[1 - (a + b*x)^2])/(8*b^4) - (a^3*E^ArcSin[a + b*x]*Sqrt[1 - (a + b*x)^2])/(2*b^4) - (E^ArcSin[a + b*x]*Cos[2*ArcSin[a + b*x]])/(10*b^4) - (3*a^2*E^ArcSin[a + b*x]*Cos[2*ArcSin[a + b*x]])/(5*b^4) + (3*a*E^ArcSin[a + b*x]*Cos[3*ArcSin[a + b*x]])/(40*b^4) + (E^ArcSin[a + b*x]*Cos[4*ArcSin[a + b*x]])/(34*b^4) + (E^ArcSin[a + b*x]*Sin[2*ArcSin[a + b*x]])/(20*b^4) + (3*a^2*E^ArcSin[a + b*x]*Sin[2*ArcSin[a + b*x]])/(10*b^4) + (9*a*E^ArcSin[a + b*x]*Sin[3*ArcSin[a + b*x]])/(40*b^4) - (E^ArcSin[a + b*x]*Sin[4*ArcSin[a + b*x]])/(136*b^4)","A",17,7,12,0.5833,1,"{4836, 6741, 12, 6742, 4433, 4469, 4432}"
452,1,205,0,0.3641482,"\int e^{\sin ^{-1}(a+b x)} x^2 \, dx","Int[E^ArcSin[a + b*x]*x^2,x]","\frac{a^2 (a+b x) e^{\sin ^{-1}(a+b x)}}{2 b^3}+\frac{a^2 \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{5 b^3}+\frac{(a+b x) e^{\sin ^{-1}(a+b x)}}{8 b^3}-\frac{3 e^{\sin ^{-1}(a+b x)} \sin \left(3 \sin ^{-1}(a+b x)\right)}{40 b^3}+\frac{\sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{8 b^3}+\frac{2 a e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{5 b^3}-\frac{e^{\sin ^{-1}(a+b x)} \cos \left(3 \sin ^{-1}(a+b x)\right)}{40 b^3}","\frac{a^2 (a+b x) e^{\sin ^{-1}(a+b x)}}{2 b^3}+\frac{a^2 \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{5 b^3}+\frac{(a+b x) e^{\sin ^{-1}(a+b x)}}{8 b^3}-\frac{3 e^{\sin ^{-1}(a+b x)} \sin \left(3 \sin ^{-1}(a+b x)\right)}{40 b^3}+\frac{\sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{8 b^3}+\frac{2 a e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{5 b^3}-\frac{e^{\sin ^{-1}(a+b x)} \cos \left(3 \sin ^{-1}(a+b x)\right)}{40 b^3}",1,"(E^ArcSin[a + b*x]*(a + b*x))/(8*b^3) + (a^2*E^ArcSin[a + b*x]*(a + b*x))/(2*b^3) + (E^ArcSin[a + b*x]*Sqrt[1 - (a + b*x)^2])/(8*b^3) + (a^2*E^ArcSin[a + b*x]*Sqrt[1 - (a + b*x)^2])/(2*b^3) + (2*a*E^ArcSin[a + b*x]*Cos[2*ArcSin[a + b*x]])/(5*b^3) - (E^ArcSin[a + b*x]*Cos[3*ArcSin[a + b*x]])/(40*b^3) - (a*E^ArcSin[a + b*x]*Sin[2*ArcSin[a + b*x]])/(5*b^3) - (3*E^ArcSin[a + b*x]*Sin[3*ArcSin[a + b*x]])/(40*b^3)","A",13,7,12,0.5833,1,"{4836, 6741, 12, 6742, 4433, 4469, 4432}"
453,1,101,0,0.1838471,"\int e^{\sin ^{-1}(a+b x)} x \, dx","Int[E^ArcSin[a + b*x]*x,x]","-\frac{a (a+b x) e^{\sin ^{-1}(a+b x)}}{2 b^2}-\frac{a \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b^2}+\frac{e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{10 b^2}-\frac{e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{5 b^2}","-\frac{a (a+b x) e^{\sin ^{-1}(a+b x)}}{2 b^2}-\frac{a \sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b^2}+\frac{e^{\sin ^{-1}(a+b x)} \sin \left(2 \sin ^{-1}(a+b x)\right)}{10 b^2}-\frac{e^{\sin ^{-1}(a+b x)} \cos \left(2 \sin ^{-1}(a+b x)\right)}{5 b^2}",1,"-(a*E^ArcSin[a + b*x]*(a + b*x))/(2*b^2) - (a*E^ArcSin[a + b*x]*Sqrt[1 - (a + b*x)^2])/(2*b^2) - (E^ArcSin[a + b*x]*Cos[2*ArcSin[a + b*x]])/(5*b^2) + (E^ArcSin[a + b*x]*Sin[2*ArcSin[a + b*x]])/(10*b^2)","A",9,7,10,0.7000,1,"{4836, 6741, 12, 6742, 4433, 4469, 4432}"
454,1,51,0,0.0195506,"\int e^{\sin ^{-1}(a+b x)} \, dx","Int[E^ArcSin[a + b*x],x]","\frac{(a+b x) e^{\sin ^{-1}(a+b x)}}{2 b}+\frac{\sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b}","\frac{(a+b x) e^{\sin ^{-1}(a+b x)}}{2 b}+\frac{\sqrt{1-(a+b x)^2} e^{\sin ^{-1}(a+b x)}}{2 b}",1,"(E^ArcSin[a + b*x]*(a + b*x))/(2*b) + (E^ArcSin[a + b*x]*Sqrt[1 - (a + b*x)^2])/(2*b)","A",2,2,8,0.2500,1,"{4836, 4433}"
455,0,0,0,0.1994838,"\int \frac{e^{\sin ^{-1}(a+b x)}}{x} \, dx","Int[E^ArcSin[a + b*x]/x,x]","\int \frac{e^{\sin ^{-1}(a+b x)}}{x} \, dx","b \text{Int}\left(\frac{e^{\sin ^{-1}(a+b x)}}{b x},x\right)",0,"Defer[Subst][Defer[Int][(E^x*Cos[x])/(-a + Sin[x]), x], x, ArcSin[a + b*x]]","A",0,0,0,0,-1,"{}"
456,0,0,0,0.2636807,"\int \frac{e^{\sin ^{-1}(a+b x)}}{x^2} \, dx","Int[E^ArcSin[a + b*x]/x^2,x]","\int \frac{e^{\sin ^{-1}(a+b x)}}{x^2} \, dx","b^2 \text{Int}\left(\frac{e^{\sin ^{-1}(a+b x)}}{b^2 x^2},x\right)",0,"b*Defer[Subst][Defer[Int][(E^x*Cos[x])/(a - Sin[x])^2, x], x, ArcSin[a + b*x]]","A",0,0,0,0,-1,"{}"
457,1,381,0,0.673329,"\int e^{\sin ^{-1}(a+b x)^2} x^3 \, dx","Int[E^ArcSin[a + b*x]^2*x^3,x]","\frac{3 e \sqrt{\pi } a^2 \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{8 b^4}+\frac{3 e \sqrt{\pi } a^2 \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{8 b^4}-\frac{\sqrt[4]{e} \sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b^4}-\frac{\sqrt[4]{e} \sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b^4}+\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{16 b^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2-i \sin ^{-1}(a+b x)\right)}{32 b^4}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{16 b^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2+i \sin ^{-1}(a+b x)\right)}{32 b^4}-\frac{3 \sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{16 b^4}-\frac{3 \sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{16 b^4}+\frac{3 e^{9/4} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-3 i\right)\right)}{16 b^4}+\frac{3 e^{9/4} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+3 i\right)\right)}{16 b^4}","\frac{3 e \sqrt{\pi } a^2 \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{8 b^4}+\frac{3 e \sqrt{\pi } a^2 \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{8 b^4}-\frac{\sqrt[4]{e} \sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b^4}-\frac{\sqrt[4]{e} \sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b^4}+\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{16 b^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2-i \sin ^{-1}(a+b x)\right)}{32 b^4}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{16 b^4}-\frac{e^4 \sqrt{\pi } \text{Erf}\left(2+i \sin ^{-1}(a+b x)\right)}{32 b^4}-\frac{3 \sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{16 b^4}-\frac{3 \sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{16 b^4}+\frac{3 e^{9/4} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-3 i\right)\right)}{16 b^4}+\frac{3 e^{9/4} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+3 i\right)\right)}{16 b^4}",1,"(E*Sqrt[Pi]*Erf[1 - I*ArcSin[a + b*x]])/(16*b^4) + (3*a^2*E*Sqrt[Pi]*Erf[1 - I*ArcSin[a + b*x]])/(8*b^4) - (E^4*Sqrt[Pi]*Erf[2 - I*ArcSin[a + b*x]])/(32*b^4) + (E*Sqrt[Pi]*Erf[1 + I*ArcSin[a + b*x]])/(16*b^4) + (3*a^2*E*Sqrt[Pi]*Erf[1 + I*ArcSin[a + b*x]])/(8*b^4) - (E^4*Sqrt[Pi]*Erf[2 + I*ArcSin[a + b*x]])/(32*b^4) - (3*a*E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a + b*x])/2])/(16*b^4) - (a^3*E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a + b*x])/2])/(4*b^4) - (3*a*E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a + b*x])/2])/(16*b^4) - (a^3*E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a + b*x])/2])/(4*b^4) + (3*a*E^(9/4)*Sqrt[Pi]*Erfi[(-3*I + 2*ArcSin[a + b*x])/2])/(16*b^4) + (3*a*E^(9/4)*Sqrt[Pi]*Erfi[(3*I + 2*ArcSin[a + b*x])/2])/(16*b^4)","A",37,8,14,0.5714,1,"{4836, 6741, 12, 6742, 4473, 2234, 2204, 4474}"
458,1,265,0,0.4741037,"\int e^{\sin ^{-1}(a+b x)^2} x^2 \, dx","Int[E^ArcSin[a + b*x]^2*x^2,x]","\frac{\sqrt[4]{e} \sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b^3}+\frac{\sqrt[4]{e} \sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b^3}-\frac{e \sqrt{\pi } a \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{e \sqrt{\pi } a \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{4 b^3}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{16 b^3}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{16 b^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-3 i\right)\right)}{16 b^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+3 i\right)\right)}{16 b^3}","\frac{\sqrt[4]{e} \sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b^3}+\frac{\sqrt[4]{e} \sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b^3}-\frac{e \sqrt{\pi } a \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{4 b^3}-\frac{e \sqrt{\pi } a \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{4 b^3}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{16 b^3}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{16 b^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-3 i\right)\right)}{16 b^3}-\frac{e^{9/4} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+3 i\right)\right)}{16 b^3}",1,"-(a*E*Sqrt[Pi]*Erf[1 - I*ArcSin[a + b*x]])/(4*b^3) - (a*E*Sqrt[Pi]*Erf[1 + I*ArcSin[a + b*x]])/(4*b^3) + (E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a + b*x])/2])/(16*b^3) + (a^2*E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a + b*x])/2])/(4*b^3) + (E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a + b*x])/2])/(16*b^3) + (a^2*E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a + b*x])/2])/(4*b^3) - (E^(9/4)*Sqrt[Pi]*Erfi[(-3*I + 2*ArcSin[a + b*x])/2])/(16*b^3) - (E^(9/4)*Sqrt[Pi]*Erfi[(3*I + 2*ArcSin[a + b*x])/2])/(16*b^3)","A",27,8,14,0.5714,1,"{4836, 6741, 12, 6742, 4473, 2234, 2204, 4474}"
459,1,123,0,0.2728308,"\int e^{\sin ^{-1}(a+b x)^2} x \, dx","Int[E^ArcSin[a + b*x]^2*x,x]","\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{8 b^2}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{8 b^2}-\frac{\sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b^2}-\frac{\sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b^2}","\frac{e \sqrt{\pi } \text{Erf}\left(1-i \sin ^{-1}(a+b x)\right)}{8 b^2}+\frac{e \sqrt{\pi } \text{Erf}\left(1+i \sin ^{-1}(a+b x)\right)}{8 b^2}-\frac{\sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b^2}-\frac{\sqrt[4]{e} \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b^2}",1,"(E*Sqrt[Pi]*Erf[1 - I*ArcSin[a + b*x]])/(8*b^2) + (E*Sqrt[Pi]*Erf[1 + I*ArcSin[a + b*x]])/(8*b^2) - (a*E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a + b*x])/2])/(4*b^2) - (a*E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a + b*x])/2])/(4*b^2)","A",17,8,12,0.6667,1,"{4836, 6741, 12, 6742, 4473, 2234, 2204, 4474}"
460,1,69,0,0.0518688,"\int e^{\sin ^{-1}(a+b x)^2} \, dx","Int[E^ArcSin[a + b*x]^2,x]","\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b}","\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)-i\right)\right)}{4 b}+\frac{\sqrt[4]{e} \sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sin ^{-1}(a+b x)+i\right)\right)}{4 b}",1,"(E^(1/4)*Sqrt[Pi]*Erfi[(-I + 2*ArcSin[a + b*x])/2])/(4*b) + (E^(1/4)*Sqrt[Pi]*Erfi[(I + 2*ArcSin[a + b*x])/2])/(4*b)","A",7,4,10,0.4000,1,"{4836, 4473, 2234, 2204}"
461,0,0,0,0.1969997,"\int \frac{e^{\sin ^{-1}(a+b x)^2}}{x} \, dx","Int[E^ArcSin[a + b*x]^2/x,x]","\int \frac{e^{\sin ^{-1}(a+b x)^2}}{x} \, dx","b \text{Int}\left(\frac{e^{\sin ^{-1}(a+b x)^2}}{b x},x\right)",0,"Defer[Subst][Defer[Int][(E^x^2*Cos[x])/(-a + Sin[x]), x], x, ArcSin[a + b*x]]","A",0,0,0,0,-1,"{}"
462,0,0,0,0.2639459,"\int \frac{e^{\sin ^{-1}(a+b x)^2}}{x^2} \, dx","Int[E^ArcSin[a + b*x]^2/x^2,x]","\int \frac{e^{\sin ^{-1}(a+b x)^2}}{x^2} \, dx","b^2 \text{Int}\left(\frac{e^{\sin ^{-1}(a+b x)^2}}{b^2 x^2},x\right)",0,"b*Defer[Subst][Defer[Int][(E^x^2*Cos[x])/(a - Sin[x])^2, x], x, ArcSin[a + b*x]]","A",0,0,0,0,-1,"{}"
463,1,162,0,0.4304219,"\int e^{\sin ^{-1}(a x)} \left(1-a^2 x^2\right)^{5/2} \, dx","Int[E^ArcSin[a*x]*(1 - a^2*x^2)^(5/2),x]","\frac{\left(1-a^2 x^2\right)^3 e^{\sin ^{-1}(a x)}}{37 a}+\frac{6}{37} x \left(1-a^2 x^2\right)^{5/2} e^{\sin ^{-1}(a x)}+\frac{30 \left(1-a^2 x^2\right)^2 e^{\sin ^{-1}(a x)}}{629 a}+\frac{120}{629} x \left(1-a^2 x^2\right)^{3/2} e^{\sin ^{-1}(a x)}+\frac{72 \left(1-a^2 x^2\right) e^{\sin ^{-1}(a x)}}{629 a}+\frac{144}{629} x \sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}+\frac{144 e^{\sin ^{-1}(a x)}}{629 a}","\frac{\left(1-a^2 x^2\right)^3 e^{\sin ^{-1}(a x)}}{37 a}+\frac{6}{37} x \left(1-a^2 x^2\right)^{5/2} e^{\sin ^{-1}(a x)}+\frac{30 \left(1-a^2 x^2\right)^2 e^{\sin ^{-1}(a x)}}{629 a}+\frac{120}{629} x \left(1-a^2 x^2\right)^{3/2} e^{\sin ^{-1}(a x)}+\frac{72 \left(1-a^2 x^2\right) e^{\sin ^{-1}(a x)}}{629 a}+\frac{144}{629} x \sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}+\frac{144 e^{\sin ^{-1}(a x)}}{629 a}",1,"(144*E^ArcSin[a*x])/(629*a) + (144*E^ArcSin[a*x]*x*Sqrt[1 - a^2*x^2])/629 + (72*E^ArcSin[a*x]*(1 - a^2*x^2))/(629*a) + (120*E^ArcSin[a*x]*x*(1 - a^2*x^2)^(3/2))/629 + (30*E^ArcSin[a*x]*(1 - a^2*x^2)^2)/(629*a) + (6*E^ArcSin[a*x]*x*(1 - a^2*x^2)^(5/2))/37 + (E^ArcSin[a*x]*(1 - a^2*x^2)^3)/(37*a)","A",7,5,21,0.2381,1,"{4836, 6688, 6720, 4435, 2194}"
464,1,112,0,0.3034618,"\int e^{\sin ^{-1}(a x)} \left(1-a^2 x^2\right)^{3/2} \, dx","Int[E^ArcSin[a*x]*(1 - a^2*x^2)^(3/2),x]","\frac{\left(1-a^2 x^2\right)^2 e^{\sin ^{-1}(a x)}}{17 a}+\frac{4}{17} x \left(1-a^2 x^2\right)^{3/2} e^{\sin ^{-1}(a x)}+\frac{12 \left(1-a^2 x^2\right) e^{\sin ^{-1}(a x)}}{85 a}+\frac{24}{85} x \sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}+\frac{24 e^{\sin ^{-1}(a x)}}{85 a}","\frac{\left(1-a^2 x^2\right)^2 e^{\sin ^{-1}(a x)}}{17 a}+\frac{4}{17} x \left(1-a^2 x^2\right)^{3/2} e^{\sin ^{-1}(a x)}+\frac{12 \left(1-a^2 x^2\right) e^{\sin ^{-1}(a x)}}{85 a}+\frac{24}{85} x \sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}+\frac{24 e^{\sin ^{-1}(a x)}}{85 a}",1,"(24*E^ArcSin[a*x])/(85*a) + (24*E^ArcSin[a*x]*x*Sqrt[1 - a^2*x^2])/85 + (12*E^ArcSin[a*x]*(1 - a^2*x^2))/(85*a) + (4*E^ArcSin[a*x]*x*(1 - a^2*x^2)^(3/2))/17 + (E^ArcSin[a*x]*(1 - a^2*x^2)^2)/(17*a)","A",6,5,21,0.2381,1,"{4836, 6688, 6720, 4435, 2194}"
465,1,62,0,0.2066799,"\int e^{\sin ^{-1}(a x)} \sqrt{1-a^2 x^2} \, dx","Int[E^ArcSin[a*x]*Sqrt[1 - a^2*x^2],x]","\frac{2}{5} x \sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}+\frac{\left(1-a^2 x^2\right) e^{\sin ^{-1}(a x)}}{5 a}+\frac{2 e^{\sin ^{-1}(a x)}}{5 a}","\frac{2}{5} x \sqrt{1-a^2 x^2} e^{\sin ^{-1}(a x)}+\frac{\left(1-a^2 x^2\right) e^{\sin ^{-1}(a x)}}{5 a}+\frac{2 e^{\sin ^{-1}(a x)}}{5 a}",1,"(2*E^ArcSin[a*x])/(5*a) + (2*E^ArcSin[a*x]*x*Sqrt[1 - a^2*x^2])/5 + (E^ArcSin[a*x]*(1 - a^2*x^2))/(5*a)","A",5,5,21,0.2381,1,"{4836, 6688, 6720, 4435, 2194}"
466,1,10,0,0.2143406,"\int \frac{e^{\sin ^{-1}(a x)}}{\sqrt{1-a^2 x^2}} \, dx","Int[E^ArcSin[a*x]/Sqrt[1 - a^2*x^2],x]","\frac{e^{\sin ^{-1}(a x)}}{a}","\frac{e^{\sin ^{-1}(a x)}}{a}",1,"E^ArcSin[a*x]/a","A",4,4,21,0.1905,1,"{4836, 6688, 6720, 2194}"
467,1,45,0,0.2580815,"\int \frac{e^{\sin ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[E^ArcSin[a*x]/(1 - a^2*x^2)^(3/2),x]","\frac{\left(\frac{4}{5}-\frac{8 i}{5}\right) e^{(1+2 i) \sin ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};-e^{2 i \sin ^{-1}(a x)}\right)}{a}","\frac{\left(\frac{4}{5}-\frac{8 i}{5}\right) e^{(1+2 i) \sin ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};-e^{2 i \sin ^{-1}(a x)}\right)}{a}",1,"((4/5 - (8*I)/5)*E^((1 + 2*I)*ArcSin[a*x])*Hypergeometric2F1[1 - I/2, 2, 2 - I/2, -E^((2*I)*ArcSin[a*x])])/a","A",4,4,21,0.1905,1,"{4836, 6688, 6720, 4451}"
468,1,96,0,0.2891811,"\int \frac{e^{\sin ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^ArcSin[a*x]/(1 - a^2*x^2)^(5/2),x]","\frac{x e^{\sin ^{-1}(a x)}}{3 \left(1-a^2 x^2\right)^{3/2}}-\frac{e^{\sin ^{-1}(a x)}}{6 a \left(1-a^2 x^2\right)}+\frac{\left(\frac{2}{3}-\frac{4 i}{3}\right) e^{(1+2 i) \sin ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};-e^{2 i \sin ^{-1}(a x)}\right)}{a}","\frac{x e^{\sin ^{-1}(a x)}}{3 \left(1-a^2 x^2\right)^{3/2}}-\frac{e^{\sin ^{-1}(a x)}}{6 a \left(1-a^2 x^2\right)}+\frac{\left(\frac{2}{3}-\frac{4 i}{3}\right) e^{(1+2 i) \sin ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};-e^{2 i \sin ^{-1}(a x)}\right)}{a}",1,"(E^ArcSin[a*x]*x)/(3*(1 - a^2*x^2)^(3/2)) - E^ArcSin[a*x]/(6*a*(1 - a^2*x^2)) + ((2/3 - (4*I)/3)*E^((1 + 2*I)*ArcSin[a*x])*Hypergeometric2F1[1 - I/2, 2, 2 - I/2, -E^((2*I)*ArcSin[a*x])])/a","A",5,5,21,0.2381,1,"{4836, 6688, 6720, 4448, 4451}"
469,1,47,0,0.032551,"\int \sin ^{-1}\left(\frac{c}{a+b x}\right) \, dx","Int[ArcSin[c/(a + b*x)],x]","\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{(a+b x)^2}}\right)}{b}+\frac{(a+b x) \csc ^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}","\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{(a+b x)^2}}\right)}{b}+\frac{(a+b x) \csc ^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}",1,"((a + b*x)*ArcCsc[a/c + (b*x)/c])/b + (c*ArcTanh[Sqrt[1 - c^2/(a + b*x)^2]])/b","A",6,6,10,0.6000,1,"{4832, 5251, 372, 266, 63, 206}"
470,0,0,0,0.0387074,"\int \frac{x}{\sin ^{-1}(\sin (x))} \, dx","Int[x/ArcSin[Sin[x]],x]","\int \frac{x}{\sin ^{-1}(\sin (x))} \, dx","\sin ^{-1}(\sin (x))+\log \left(\sin ^{-1}(\sin (x))\right) \left(x \sqrt{\cos ^2(x)} \sec (x)-\sin ^{-1}(\sin (x))\right)",1,"Defer[Int][x/ArcSin[Sin[x]], x]","F",0,0,0,0,-1,"{}"
471,1,38,0,0.067233,"\int \frac{\sin ^{-1}\left(\sqrt{1+b x^2}\right)^n}{\sqrt{1+b x^2}} \, dx","Int[ArcSin[Sqrt[1 + b*x^2]]^n/Sqrt[1 + b*x^2],x]","\frac{\sqrt{-b x^2} \sin ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}","\frac{\sqrt{-b x^2} \sin ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}",1,"(Sqrt[-(b*x^2)]*ArcSin[Sqrt[1 + b*x^2]]^(1 + n))/(b*(1 + n)*x)","A",2,2,26,0.07692,1,"{4834, 4641}"
472,1,30,0,0.0605774,"\int \frac{1}{\sqrt{1+b x^2} \sin ^{-1}\left(\sqrt{1+b x^2}\right)} \, dx","Int[1/(Sqrt[1 + b*x^2]*ArcSin[Sqrt[1 + b*x^2]]),x]","\frac{\sqrt{-b x^2} \log \left(\sin ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}","\frac{\sqrt{-b x^2} \log \left(\sin ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}",1,"(Sqrt[-(b*x^2)]*Log[ArcSin[Sqrt[1 + b*x^2]]])/(b*x)","A",2,2,26,0.07692,1,"{4834, 4639}"
473,1,16,0,0.0282553,"\int \left(\frac{x}{1-x^2}+\frac{1}{\sqrt{1-x^2} \sin ^{-1}(x)}\right) \, dx","Int[x/(1 - x^2) + 1/(Sqrt[1 - x^2]*ArcSin[x]),x]","\log \left(\sin ^{-1}(x)\right)-\frac{1}{2} \log \left(1-x^2\right)","\log \left(\sin ^{-1}(x)\right)-\frac{1}{2} \log \left(1-x^2\right)",1,"-Log[1 - x^2]/2 + Log[ArcSin[x]]","A",3,2,28,0.07143,1,"{260, 4639}"
474,0,0,0,0.1566405,"\int \frac{\sqrt{1-x^2}+x \sin ^{-1}(x)}{\sin ^{-1}(x)-x^2 \sin ^{-1}(x)} \, dx","Int[(Sqrt[1 - x^2] + x*ArcSin[x])/(ArcSin[x] - x^2*ArcSin[x]),x]","\int \frac{\sqrt{1-x^2}+x \sin ^{-1}(x)}{\sin ^{-1}(x)-x^2 \sin ^{-1}(x)} \, dx","\log \left(\sin ^{-1}(x)\right)-\frac{1}{2} \log \left(1-x^2\right)",1,"Defer[Int][(Sqrt[1 - x^2] + x*ArcSin[x])/((1 - x^2)*ArcSin[x]), x]","F",0,0,0,0,-1,"{}"