1,1,128,0,0.1202126,"\int x^4 \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)*(a + b*ArcSin[c*x]),x]","-\frac{1}{7} c^2 d x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d \left(1-c^2 x^2\right)^{7/2}}{49 c^5}-\frac{8 b d \left(1-c^2 x^2\right)^{5/2}}{175 c^5}+\frac{b d \left(1-c^2 x^2\right)^{3/2}}{105 c^5}+\frac{2 b d \sqrt{1-c^2 x^2}}{35 c^5}","-\frac{1}{7} c^2 d x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d \left(1-c^2 x^2\right)^{7/2}}{49 c^5}-\frac{8 b d \left(1-c^2 x^2\right)^{5/2}}{175 c^5}+\frac{b d \left(1-c^2 x^2\right)^{3/2}}{105 c^5}+\frac{2 b d \sqrt{1-c^2 x^2}}{35 c^5}",1,"(2*b*d*Sqrt[1 - c^2*x^2])/(35*c^5) + (b*d*(1 - c^2*x^2)^(3/2))/(105*c^5) - (8*b*d*(1 - c^2*x^2)^(5/2))/(175*c^5) + (b*d*(1 - c^2*x^2)^(7/2))/(49*c^5) + (d*x^5*(a + b*ArcSin[c*x]))/5 - (c^2*d*x^7*(a + b*ArcSin[c*x]))/7","A",5,5,23,0.2174,1,"{14, 4687, 12, 446, 77}"
2,1,123,0,0.0959112,"\int x^3 \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)*(a + b*ArcSin[c*x]),x]","-\frac{1}{6} c^2 d x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{36} b c d x^5 \sqrt{1-c^2 x^2}+\frac{b d x^3 \sqrt{1-c^2 x^2}}{36 c}+\frac{b d x \sqrt{1-c^2 x^2}}{24 c^3}-\frac{b d \sin ^{-1}(c x)}{24 c^4}","-\frac{1}{6} c^2 d x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{36} b c d x^5 \sqrt{1-c^2 x^2}+\frac{b d x^3 \sqrt{1-c^2 x^2}}{36 c}+\frac{b d x \sqrt{1-c^2 x^2}}{24 c^3}-\frac{b d \sin ^{-1}(c x)}{24 c^4}",1,"(b*d*x*Sqrt[1 - c^2*x^2])/(24*c^3) + (b*d*x^3*Sqrt[1 - c^2*x^2])/(36*c) - (b*c*d*x^5*Sqrt[1 - c^2*x^2])/36 - (b*d*ArcSin[c*x])/(24*c^4) + (d*x^4*(a + b*ArcSin[c*x]))/4 - (c^2*d*x^6*(a + b*ArcSin[c*x]))/6","A",6,6,23,0.2609,1,"{14, 4687, 12, 459, 321, 216}"
3,1,105,0,0.1033383,"\int x^2 \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)*(a + b*ArcSin[c*x]),x]","-\frac{1}{5} c^2 d x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b d \left(1-c^2 x^2\right)^{5/2}}{25 c^3}+\frac{b d \left(1-c^2 x^2\right)^{3/2}}{45 c^3}+\frac{2 b d \sqrt{1-c^2 x^2}}{15 c^3}","-\frac{1}{5} c^2 d x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b d \left(1-c^2 x^2\right)^{5/2}}{25 c^3}+\frac{b d \left(1-c^2 x^2\right)^{3/2}}{45 c^3}+\frac{2 b d \sqrt{1-c^2 x^2}}{15 c^3}",1,"(2*b*d*Sqrt[1 - c^2*x^2])/(15*c^3) + (b*d*(1 - c^2*x^2)^(3/2))/(45*c^3) - (b*d*(1 - c^2*x^2)^(5/2))/(25*c^3) + (d*x^3*(a + b*ArcSin[c*x]))/3 - (c^2*d*x^5*(a + b*ArcSin[c*x]))/5","A",5,5,23,0.2174,1,"{14, 4687, 12, 446, 77}"
4,1,90,0,0.041917,"\int x \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)*(a + b*ArcSin[c*x]),x]","-\frac{d \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{4 c^2}+\frac{b d x \left(1-c^2 x^2\right)^{3/2}}{16 c}+\frac{3 b d x \sqrt{1-c^2 x^2}}{32 c}+\frac{3 b d \sin ^{-1}(c x)}{32 c^2}","-\frac{d \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{4 c^2}+\frac{b d x \left(1-c^2 x^2\right)^{3/2}}{16 c}+\frac{3 b d x \sqrt{1-c^2 x^2}}{32 c}+\frac{3 b d \sin ^{-1}(c x)}{32 c^2}",1,"(3*b*d*x*Sqrt[1 - c^2*x^2])/(32*c) + (b*d*x*(1 - c^2*x^2)^(3/2))/(16*c) + (3*b*d*ArcSin[c*x])/(32*c^2) - (d*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(4*c^2)","A",4,3,21,0.1429,1,"{4677, 195, 216}"
5,1,77,0,0.0609626,"\int \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)*(a + b*ArcSin[c*x]),x]","-\frac{1}{3} c^2 d x^3 \left(a+b \sin ^{-1}(c x)\right)+d x \left(a+b \sin ^{-1}(c x)\right)+\frac{b d \left(1-c^2 x^2\right)^{3/2}}{9 c}+\frac{2 b d \sqrt{1-c^2 x^2}}{3 c}","-\frac{1}{3} c^2 d x^3 \left(a+b \sin ^{-1}(c x)\right)+d x \left(a+b \sin ^{-1}(c x)\right)+\frac{b d \left(1-c^2 x^2\right)^{3/2}}{9 c}+\frac{2 b d \sqrt{1-c^2 x^2}}{3 c}",1,"(2*b*d*Sqrt[1 - c^2*x^2])/(3*c) + (b*d*(1 - c^2*x^2)^(3/2))/(9*c) + d*x*(a + b*ArcSin[c*x]) - (c^2*d*x^3*(a + b*ArcSin[c*x]))/3","A",5,4,20,0.2000,1,"{4645, 12, 444, 43}"
6,1,121,0,0.1163768,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x]))/x,x]","-\frac{1}{2} i b d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{2} d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i d \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{4} b c d x \sqrt{1-c^2 x^2}-\frac{1}{4} b d \sin ^{-1}(c x)","-\frac{1}{2} i b d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{2} d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i d \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{4} b c d x \sqrt{1-c^2 x^2}-\frac{1}{4} b d \sin ^{-1}(c x)",1,"-(b*c*d*x*Sqrt[1 - c^2*x^2])/4 - (b*d*ArcSin[c*x])/4 + (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/2 - ((I/2)*d*(a + b*ArcSin[c*x])^2)/b + d*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] - (I/2)*b*d*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",8,8,23,0.3478,1,"{4683, 4625, 3717, 2190, 2279, 2391, 195, 216}"
7,1,69,0,0.0756378,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x]))/x^2,x]","c^2 (-d) x \left(a+b \sin ^{-1}(c x)\right)-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{x}-b c d \sqrt{1-c^2 x^2}-b c d \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","c^2 (-d) x \left(a+b \sin ^{-1}(c x)\right)-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{x}-b c d \sqrt{1-c^2 x^2}-b c d \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"-(b*c*d*Sqrt[1 - c^2*x^2]) - (d*(a + b*ArcSin[c*x]))/x - c^2*d*x*(a + b*ArcSin[c*x]) - b*c*d*ArcTanh[Sqrt[1 - c^2*x^2]]","A",6,7,23,0.3043,1,"{14, 4687, 12, 446, 80, 63, 208}"
8,1,139,0,0.1206437,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x]))/x^3,x]","\frac{1}{2} i b c^2 d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{i c^2 d \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}-c^2 d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d \sqrt{1-c^2 x^2}}{2 x}-\frac{1}{2} b c^2 d \sin ^{-1}(c x)","\frac{1}{2} i b c^2 d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{i c^2 d \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}-c^2 d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d \sqrt{1-c^2 x^2}}{2 x}-\frac{1}{2} b c^2 d \sin ^{-1}(c x)",1,"-(b*c*d*Sqrt[1 - c^2*x^2])/(2*x) - (b*c^2*d*ArcSin[c*x])/2 - (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*x^2) + ((I/2)*c^2*d*(a + b*ArcSin[c*x])^2)/b - c^2*d*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] + (I/2)*b*c^2*d*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",8,8,23,0.3478,1,"{4685, 277, 216, 4625, 3717, 2190, 2279, 2391}"
9,1,81,0,0.086358,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x]))/x^4,x]","\frac{c^2 d \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{1-c^2 x^2}}{6 x^2}+\frac{5}{6} b c^3 d \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","\frac{c^2 d \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{1-c^2 x^2}}{6 x^2}+\frac{5}{6} b c^3 d \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"-(b*c*d*Sqrt[1 - c^2*x^2])/(6*x^2) - (d*(a + b*ArcSin[c*x]))/(3*x^3) + (c^2*d*(a + b*ArcSin[c*x]))/x + (5*b*c^3*d*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",6,7,23,0.3043,1,"{14, 4687, 12, 446, 78, 63, 208}"
10,1,186,0,0.2065822,"\int x^4 \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{9} c^4 d^2 x^9 \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{7} c^2 d^2 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^2 \left(1-c^2 x^2\right)^{9/2}}{81 c^5}-\frac{10 b d^2 \left(1-c^2 x^2\right)^{7/2}}{441 c^5}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{525 c^5}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2}}{945 c^5}+\frac{8 b d^2 \sqrt{1-c^2 x^2}}{315 c^5}","\frac{1}{9} c^4 d^2 x^9 \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{7} c^2 d^2 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^2 \left(1-c^2 x^2\right)^{9/2}}{81 c^5}-\frac{10 b d^2 \left(1-c^2 x^2\right)^{7/2}}{441 c^5}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{525 c^5}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2}}{945 c^5}+\frac{8 b d^2 \sqrt{1-c^2 x^2}}{315 c^5}",1,"(8*b*d^2*Sqrt[1 - c^2*x^2])/(315*c^5) + (4*b*d^2*(1 - c^2*x^2)^(3/2))/(945*c^5) + (b*d^2*(1 - c^2*x^2)^(5/2))/(525*c^5) - (10*b*d^2*(1 - c^2*x^2)^(7/2))/(441*c^5) + (b*d^2*(1 - c^2*x^2)^(9/2))/(81*c^5) + (d^2*x^5*(a + b*ArcSin[c*x]))/5 - (2*c^2*d^2*x^7*(a + b*ArcSin[c*x]))/7 + (c^4*d^2*x^9*(a + b*ArcSin[c*x]))/9","A",6,6,25,0.2400,1,"{270, 4687, 12, 1251, 897, 1153}"
11,1,184,0,0.169913,"\int x^3 \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{8} c^4 d^2 x^8 \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{3} c^2 d^2 x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{64} b c^3 d^2 x^7 \sqrt{1-c^2 x^2}-\frac{43 b c d^2 x^5 \sqrt{1-c^2 x^2}}{1152}+\frac{73 b d^2 x^3 \sqrt{1-c^2 x^2}}{4608 c}+\frac{73 b d^2 x \sqrt{1-c^2 x^2}}{3072 c^3}-\frac{73 b d^2 \sin ^{-1}(c x)}{3072 c^4}","\frac{1}{8} c^4 d^2 x^8 \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{3} c^2 d^2 x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{64} b c^3 d^2 x^7 \sqrt{1-c^2 x^2}-\frac{43 b c d^2 x^5 \sqrt{1-c^2 x^2}}{1152}+\frac{73 b d^2 x^3 \sqrt{1-c^2 x^2}}{4608 c}+\frac{73 b d^2 x \sqrt{1-c^2 x^2}}{3072 c^3}-\frac{73 b d^2 \sin ^{-1}(c x)}{3072 c^4}",1,"(73*b*d^2*x*Sqrt[1 - c^2*x^2])/(3072*c^3) + (73*b*d^2*x^3*Sqrt[1 - c^2*x^2])/(4608*c) - (43*b*c*d^2*x^5*Sqrt[1 - c^2*x^2])/1152 + (b*c^3*d^2*x^7*Sqrt[1 - c^2*x^2])/64 - (73*b*d^2*ArcSin[c*x])/(3072*c^4) + (d^2*x^4*(a + b*ArcSin[c*x]))/4 - (c^2*d^2*x^6*(a + b*ArcSin[c*x]))/3 + (c^4*d^2*x^8*(a + b*ArcSin[c*x]))/8","A",7,8,25,0.3200,1,"{266, 43, 4687, 12, 1267, 459, 321, 216}"
12,1,161,0,0.1699658,"\int x^2 \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{7} c^4 d^2 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{5} c^2 d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b d^2 \left(1-c^2 x^2\right)^{7/2}}{49 c^3}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{175 c^3}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2}}{315 c^3}+\frac{8 b d^2 \sqrt{1-c^2 x^2}}{105 c^3}","\frac{1}{7} c^4 d^2 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{5} c^2 d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b d^2 \left(1-c^2 x^2\right)^{7/2}}{49 c^3}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{175 c^3}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2}}{315 c^3}+\frac{8 b d^2 \sqrt{1-c^2 x^2}}{105 c^3}",1,"(8*b*d^2*Sqrt[1 - c^2*x^2])/(105*c^3) + (4*b*d^2*(1 - c^2*x^2)^(3/2))/(315*c^3) + (b*d^2*(1 - c^2*x^2)^(5/2))/(175*c^3) - (b*d^2*(1 - c^2*x^2)^(7/2))/(49*c^3) + (d^2*x^3*(a + b*ArcSin[c*x]))/3 - (2*c^2*d^2*x^5*(a + b*ArcSin[c*x]))/5 + (c^4*d^2*x^7*(a + b*ArcSin[c*x]))/7","A",5,5,25,0.2000,1,"{270, 4687, 12, 1251, 771}"
13,1,124,0,0.0653594,"\int x \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]),x]","-\frac{d^2 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{6 c^2}+\frac{b d^2 x \left(1-c^2 x^2\right)^{5/2}}{36 c}+\frac{5 b d^2 x \left(1-c^2 x^2\right)^{3/2}}{144 c}+\frac{5 b d^2 x \sqrt{1-c^2 x^2}}{96 c}+\frac{5 b d^2 \sin ^{-1}(c x)}{96 c^2}","-\frac{d^2 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{6 c^2}+\frac{b d^2 x \left(1-c^2 x^2\right)^{5/2}}{36 c}+\frac{5 b d^2 x \left(1-c^2 x^2\right)^{3/2}}{144 c}+\frac{5 b d^2 x \sqrt{1-c^2 x^2}}{96 c}+\frac{5 b d^2 \sin ^{-1}(c x)}{96 c^2}",1,"(5*b*d^2*x*Sqrt[1 - c^2*x^2])/(96*c) + (5*b*d^2*x*(1 - c^2*x^2)^(3/2))/(144*c) + (b*d^2*x*(1 - c^2*x^2)^(5/2))/(36*c) + (5*b*d^2*ArcSin[c*x])/(96*c^2) - (d^2*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x]))/(6*c^2)","A",5,3,23,0.1304,1,"{4677, 195, 216}"
14,1,131,0,0.1044511,"\int \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{5} c^4 d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{3} c^2 d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+d^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{25 c}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2}}{45 c}+\frac{8 b d^2 \sqrt{1-c^2 x^2}}{15 c}","\frac{1}{5} c^4 d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{3} c^2 d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+d^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{25 c}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2}}{45 c}+\frac{8 b d^2 \sqrt{1-c^2 x^2}}{15 c}",1,"(8*b*d^2*Sqrt[1 - c^2*x^2])/(15*c) + (4*b*d^2*(1 - c^2*x^2)^(3/2))/(45*c) + (b*d^2*(1 - c^2*x^2)^(5/2))/(25*c) + d^2*x*(a + b*ArcSin[c*x]) - (2*c^2*d^2*x^3*(a + b*ArcSin[c*x]))/3 + (c^4*d^2*x^5*(a + b*ArcSin[c*x]))/5","A",5,5,22,0.2273,1,"{194, 4645, 12, 1247, 698}"
15,1,184,0,0.2016748,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]))/x,x]","-\frac{1}{2} i b d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{4} d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{16} b c d^2 x \left(1-c^2 x^2\right)^{3/2}-\frac{11}{32} b c d^2 x \sqrt{1-c^2 x^2}-\frac{11}{32} b d^2 \sin ^{-1}(c x)","-\frac{1}{2} i b d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{4} d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{16} b c d^2 x \left(1-c^2 x^2\right)^{3/2}-\frac{11}{32} b c d^2 x \sqrt{1-c^2 x^2}-\frac{11}{32} b d^2 \sin ^{-1}(c x)",1,"(-11*b*c*d^2*x*Sqrt[1 - c^2*x^2])/32 - (b*c*d^2*x*(1 - c^2*x^2)^(3/2))/16 - (11*b*d^2*ArcSin[c*x])/32 + (d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/2 + (d^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/4 - ((I/2)*d^2*(a + b*ArcSin[c*x])^2)/b + d^2*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] - (I/2)*b*d^2*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",12,8,25,0.3200,1,"{4683, 4625, 3717, 2190, 2279, 2391, 195, 216}"
16,1,123,0,0.1551401,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]))/x^2,x]","\frac{1}{3} c^4 d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)-2 c^2 d^2 x \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{1}{9} b c d^2 \left(1-c^2 x^2\right)^{3/2}-\frac{5}{3} b c d^2 \sqrt{1-c^2 x^2}-b c d^2 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","\frac{1}{3} c^4 d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)-2 c^2 d^2 x \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{1}{9} b c d^2 \left(1-c^2 x^2\right)^{3/2}-\frac{5}{3} b c d^2 \sqrt{1-c^2 x^2}-b c d^2 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"(-5*b*c*d^2*Sqrt[1 - c^2*x^2])/3 - (b*c*d^2*(1 - c^2*x^2)^(3/2))/9 - (d^2*(a + b*ArcSin[c*x]))/x - 2*c^2*d^2*x*(a + b*ArcSin[c*x]) + (c^4*d^2*x^3*(a + b*ArcSin[c*x]))/3 - b*c*d^2*ArcTanh[Sqrt[1 - c^2*x^2]]","A",7,7,25,0.2800,1,"{270, 4687, 12, 1251, 897, 1153, 208}"
17,1,201,0,0.207758,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]))/x^3,x]","i b c^2 d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{i c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{b}-2 c^2 d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{4} b c^3 d^2 x \sqrt{1-c^2 x^2}-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2}}{2 x}-\frac{1}{4} b c^2 d^2 \sin ^{-1}(c x)","i b c^2 d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{i c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{b}-2 c^2 d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{4} b c^3 d^2 x \sqrt{1-c^2 x^2}-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2}}{2 x}-\frac{1}{4} b c^2 d^2 \sin ^{-1}(c x)",1,"-(b*c^3*d^2*x*Sqrt[1 - c^2*x^2])/4 - (b*c*d^2*(1 - c^2*x^2)^(3/2))/(2*x) - (b*c^2*d^2*ArcSin[c*x])/4 - c^2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]) - (d^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(2*x^2) + (I*c^2*d^2*(a + b*ArcSin[c*x])^2)/b - 2*c^2*d^2*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] + I*b*c^2*d^2*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",12,10,25,0.4000,1,"{4685, 277, 195, 216, 4683, 4625, 3717, 2190, 2279, 2391}"
18,1,128,0,0.1617038,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]))/x^4,x]","c^4 d^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{2 c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}+b c^3 d^2 \sqrt{1-c^2 x^2}-\frac{b c d^2 \sqrt{1-c^2 x^2}}{6 x^2}+\frac{11}{6} b c^3 d^2 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","c^4 d^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{2 c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}+b c^3 d^2 \sqrt{1-c^2 x^2}-\frac{b c d^2 \sqrt{1-c^2 x^2}}{6 x^2}+\frac{11}{6} b c^3 d^2 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"b*c^3*d^2*Sqrt[1 - c^2*x^2] - (b*c*d^2*Sqrt[1 - c^2*x^2])/(6*x^2) - (d^2*(a + b*ArcSin[c*x]))/(3*x^3) + (2*c^2*d^2*(a + b*ArcSin[c*x]))/x + c^4*d^2*x*(a + b*ArcSin[c*x]) + (11*b*c^3*d^2*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",7,8,25,0.3200,1,"{270, 4687, 12, 1251, 897, 1157, 388, 208}"
19,1,232,0,0.2905599,"\int x^4 \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]),x]","-\frac{1}{11} c^6 d^3 x^{11} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} c^4 d^3 x^9 \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{7} c^2 d^3 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^3 \left(1-c^2 x^2\right)^{11/2}}{121 c^5}-\frac{4 b d^3 \left(1-c^2 x^2\right)^{9/2}}{297 c^5}+\frac{b d^3 \left(1-c^2 x^2\right)^{7/2}}{1617 c^5}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2}}{1925 c^5}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2}}{3465 c^5}+\frac{16 b d^3 \sqrt{1-c^2 x^2}}{1155 c^5}","-\frac{1}{11} c^6 d^3 x^{11} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} c^4 d^3 x^9 \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{7} c^2 d^3 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^3 \left(1-c^2 x^2\right)^{11/2}}{121 c^5}-\frac{4 b d^3 \left(1-c^2 x^2\right)^{9/2}}{297 c^5}+\frac{b d^3 \left(1-c^2 x^2\right)^{7/2}}{1617 c^5}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2}}{1925 c^5}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2}}{3465 c^5}+\frac{16 b d^3 \sqrt{1-c^2 x^2}}{1155 c^5}",1,"(16*b*d^3*Sqrt[1 - c^2*x^2])/(1155*c^5) + (8*b*d^3*(1 - c^2*x^2)^(3/2))/(3465*c^5) + (2*b*d^3*(1 - c^2*x^2)^(5/2))/(1925*c^5) + (b*d^3*(1 - c^2*x^2)^(7/2))/(1617*c^5) - (4*b*d^3*(1 - c^2*x^2)^(9/2))/(297*c^5) + (b*d^3*(1 - c^2*x^2)^(11/2))/(121*c^5) + (d^3*x^5*(a + b*ArcSin[c*x]))/5 - (3*c^2*d^3*x^7*(a + b*ArcSin[c*x]))/7 + (c^4*d^3*x^9*(a + b*ArcSin[c*x]))/3 - (c^6*d^3*x^11*(a + b*ArcSin[c*x]))/11","A",5,5,25,0.2000,1,"{270, 4687, 12, 1799, 1620}"
20,1,206,0,0.178894,"\int x^3 \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]),x]","\frac{d^3 \left(1-c^2 x^2\right)^5 \left(a+b \sin ^{-1}(c x)\right)}{10 c^4}-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 c^4}-\frac{b d^3 x \left(1-c^2 x^2\right)^{9/2}}{100 c^3}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^{7/2}}{1600 c^3}+\frac{49 b d^3 x \left(1-c^2 x^2\right)^{5/2}}{9600 c^3}+\frac{49 b d^3 x \left(1-c^2 x^2\right)^{3/2}}{7680 c^3}+\frac{49 b d^3 x \sqrt{1-c^2 x^2}}{5120 c^3}+\frac{49 b d^3 \sin ^{-1}(c x)}{5120 c^4}","\frac{d^3 \left(1-c^2 x^2\right)^5 \left(a+b \sin ^{-1}(c x)\right)}{10 c^4}-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 c^4}-\frac{b d^3 x \left(1-c^2 x^2\right)^{9/2}}{100 c^3}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^{7/2}}{1600 c^3}+\frac{49 b d^3 x \left(1-c^2 x^2\right)^{5/2}}{9600 c^3}+\frac{49 b d^3 x \left(1-c^2 x^2\right)^{3/2}}{7680 c^3}+\frac{49 b d^3 x \sqrt{1-c^2 x^2}}{5120 c^3}+\frac{49 b d^3 \sin ^{-1}(c x)}{5120 c^4}",1,"(49*b*d^3*x*Sqrt[1 - c^2*x^2])/(5120*c^3) + (49*b*d^3*x*(1 - c^2*x^2)^(3/2))/(7680*c^3) + (49*b*d^3*x*(1 - c^2*x^2)^(5/2))/(9600*c^3) + (7*b*d^3*x*(1 - c^2*x^2)^(7/2))/(1600*c^3) - (b*d^3*x*(1 - c^2*x^2)^(9/2))/(100*c^3) + (49*b*d^3*ArcSin[c*x])/(5120*c^4) - (d^3*(1 - c^2*x^2)^4*(a + b*ArcSin[c*x]))/(8*c^4) + (d^3*(1 - c^2*x^2)^5*(a + b*ArcSin[c*x]))/(10*c^4)","A",8,7,25,0.2800,1,"{266, 43, 4687, 12, 388, 195, 216}"
21,1,207,0,0.2577901,"\int x^2 \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]),x]","-\frac{1}{9} c^6 d^3 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{7} c^4 d^3 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{5} c^2 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b d^3 \left(1-c^2 x^2\right)^{9/2}}{81 c^3}+\frac{b d^3 \left(1-c^2 x^2\right)^{7/2}}{441 c^3}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2}}{525 c^3}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2}}{945 c^3}+\frac{16 b d^3 \sqrt{1-c^2 x^2}}{315 c^3}","-\frac{1}{9} c^6 d^3 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{7} c^4 d^3 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{5} c^2 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{b d^3 \left(1-c^2 x^2\right)^{9/2}}{81 c^3}+\frac{b d^3 \left(1-c^2 x^2\right)^{7/2}}{441 c^3}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2}}{525 c^3}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2}}{945 c^3}+\frac{16 b d^3 \sqrt{1-c^2 x^2}}{315 c^3}",1,"(16*b*d^3*Sqrt[1 - c^2*x^2])/(315*c^3) + (8*b*d^3*(1 - c^2*x^2)^(3/2))/(945*c^3) + (2*b*d^3*(1 - c^2*x^2)^(5/2))/(525*c^3) + (b*d^3*(1 - c^2*x^2)^(7/2))/(441*c^3) - (b*d^3*(1 - c^2*x^2)^(9/2))/(81*c^3) + (d^3*x^3*(a + b*ArcSin[c*x]))/3 - (3*c^2*d^3*x^5*(a + b*ArcSin[c*x]))/5 + (3*c^4*d^3*x^7*(a + b*ArcSin[c*x]))/7 - (c^6*d^3*x^9*(a + b*ArcSin[c*x]))/9","A",5,5,25,0.2000,1,"{270, 4687, 12, 1799, 1620}"
22,1,150,0,0.0762765,"\int x \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]),x]","-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{b d^3 x \left(1-c^2 x^2\right)^{7/2}}{64 c}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^{5/2}}{384 c}+\frac{35 b d^3 x \left(1-c^2 x^2\right)^{3/2}}{1536 c}+\frac{35 b d^3 x \sqrt{1-c^2 x^2}}{1024 c}+\frac{35 b d^3 \sin ^{-1}(c x)}{1024 c^2}","-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{b d^3 x \left(1-c^2 x^2\right)^{7/2}}{64 c}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^{5/2}}{384 c}+\frac{35 b d^3 x \left(1-c^2 x^2\right)^{3/2}}{1536 c}+\frac{35 b d^3 x \sqrt{1-c^2 x^2}}{1024 c}+\frac{35 b d^3 \sin ^{-1}(c x)}{1024 c^2}",1,"(35*b*d^3*x*Sqrt[1 - c^2*x^2])/(1024*c) + (35*b*d^3*x*(1 - c^2*x^2)^(3/2))/(1536*c) + (7*b*d^3*x*(1 - c^2*x^2)^(5/2))/(384*c) + (b*d^3*x*(1 - c^2*x^2)^(7/2))/(64*c) + (35*b*d^3*ArcSin[c*x])/(1024*c^2) - (d^3*(1 - c^2*x^2)^4*(a + b*ArcSin[c*x]))/(8*c^2)","A",6,3,23,0.1304,1,"{4677, 195, 216}"
23,1,175,0,0.1712817,"\int \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]),x]","-\frac{1}{7} c^6 d^3 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{5} c^4 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)-c^2 d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+d^3 x \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^3 \left(1-c^2 x^2\right)^{7/2}}{49 c}+\frac{6 b d^3 \left(1-c^2 x^2\right)^{5/2}}{175 c}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2}}{105 c}+\frac{16 b d^3 \sqrt{1-c^2 x^2}}{35 c}","-\frac{1}{7} c^6 d^3 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{5} c^4 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)-c^2 d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+d^3 x \left(a+b \sin ^{-1}(c x)\right)+\frac{b d^3 \left(1-c^2 x^2\right)^{7/2}}{49 c}+\frac{6 b d^3 \left(1-c^2 x^2\right)^{5/2}}{175 c}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2}}{105 c}+\frac{16 b d^3 \sqrt{1-c^2 x^2}}{35 c}",1,"(16*b*d^3*Sqrt[1 - c^2*x^2])/(35*c) + (8*b*d^3*(1 - c^2*x^2)^(3/2))/(105*c) + (6*b*d^3*(1 - c^2*x^2)^(5/2))/(175*c) + (b*d^3*(1 - c^2*x^2)^(7/2))/(49*c) + d^3*x*(a + b*ArcSin[c*x]) - c^2*d^3*x^3*(a + b*ArcSin[c*x]) + (3*c^4*d^3*x^5*(a + b*ArcSin[c*x]))/5 - (c^6*d^3*x^7*(a + b*ArcSin[c*x]))/7","A",5,5,22,0.2273,1,"{194, 4645, 12, 1799, 1850}"
24,1,235,0,0.2830252,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]))/x,x]","-\frac{1}{2} i b d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{6} d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{36} b c d^3 x \left(1-c^2 x^2\right)^{5/2}-\frac{7}{72} b c d^3 x \left(1-c^2 x^2\right)^{3/2}-\frac{19}{48} b c d^3 x \sqrt{1-c^2 x^2}-\frac{19}{48} b d^3 \sin ^{-1}(c x)","-\frac{1}{2} i b d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{6} d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{i d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}+d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{36} b c d^3 x \left(1-c^2 x^2\right)^{5/2}-\frac{7}{72} b c d^3 x \left(1-c^2 x^2\right)^{3/2}-\frac{19}{48} b c d^3 x \sqrt{1-c^2 x^2}-\frac{19}{48} b d^3 \sin ^{-1}(c x)",1,"(-19*b*c*d^3*x*Sqrt[1 - c^2*x^2])/48 - (7*b*c*d^3*x*(1 - c^2*x^2)^(3/2))/72 - (b*c*d^3*x*(1 - c^2*x^2)^(5/2))/36 - (19*b*d^3*ArcSin[c*x])/48 + (d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/2 + (d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/4 + (d^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x]))/6 - ((I/2)*d^3*(a + b*ArcSin[c*x])^2)/b + d^3*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] - (I/2)*b*d^3*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",17,8,25,0.3200,1,"{4683, 4625, 3717, 2190, 2279, 2391, 195, 216}"
25,1,164,0,0.23118,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]))/x^2,x]","-\frac{1}{5} c^6 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+c^4 d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)-3 c^2 d^3 x \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{1}{25} b c d^3 \left(1-c^2 x^2\right)^{5/2}-\frac{1}{5} b c d^3 \left(1-c^2 x^2\right)^{3/2}-\frac{11}{5} b c d^3 \sqrt{1-c^2 x^2}-b c d^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","-\frac{1}{5} c^6 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+c^4 d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)-3 c^2 d^3 x \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{1}{25} b c d^3 \left(1-c^2 x^2\right)^{5/2}-\frac{1}{5} b c d^3 \left(1-c^2 x^2\right)^{3/2}-\frac{11}{5} b c d^3 \sqrt{1-c^2 x^2}-b c d^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"(-11*b*c*d^3*Sqrt[1 - c^2*x^2])/5 - (b*c*d^3*(1 - c^2*x^2)^(3/2))/5 - (b*c*d^3*(1 - c^2*x^2)^(5/2))/25 - (d^3*(a + b*ArcSin[c*x]))/x - 3*c^2*d^3*x*(a + b*ArcSin[c*x]) + c^4*d^3*x^3*(a + b*ArcSin[c*x]) - (c^6*d^3*x^5*(a + b*ArcSin[c*x]))/5 - b*c*d^3*ArcTanh[Sqrt[1 - c^2*x^2]]","A",7,7,25,0.2800,1,"{270, 4687, 12, 1799, 1620, 63, 208}"
26,1,263,0,0.2984573,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]))/x^3,x]","\frac{3}{2} i b c^2 d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}-\frac{3}{4} c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} c^2 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{3 i c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}-3 c^2 d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^3 \left(1-c^2 x^2\right)^{5/2}}{2 x}-\frac{7}{16} b c^3 d^3 x \left(1-c^2 x^2\right)^{3/2}+\frac{3}{32} b c^3 d^3 x \sqrt{1-c^2 x^2}+\frac{3}{32} b c^2 d^3 \sin ^{-1}(c x)","\frac{3}{2} i b c^2 d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}-\frac{3}{4} c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} c^2 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{3 i c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 b}-3 c^2 d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^3 \left(1-c^2 x^2\right)^{5/2}}{2 x}-\frac{7}{16} b c^3 d^3 x \left(1-c^2 x^2\right)^{3/2}+\frac{3}{32} b c^3 d^3 x \sqrt{1-c^2 x^2}+\frac{3}{32} b c^2 d^3 \sin ^{-1}(c x)",1,"(3*b*c^3*d^3*x*Sqrt[1 - c^2*x^2])/32 - (7*b*c^3*d^3*x*(1 - c^2*x^2)^(3/2))/16 - (b*c*d^3*(1 - c^2*x^2)^(5/2))/(2*x) + (3*b*c^2*d^3*ArcSin[c*x])/32 - (3*c^2*d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/2 - (3*c^2*d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/4 - (d^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x]))/(2*x^2) + (((3*I)/2)*c^2*d^3*(a + b*ArcSin[c*x])^2)/b - 3*c^2*d^3*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])] + ((3*I)/2)*b*c^2*d^3*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",17,10,25,0.4000,1,"{4685, 277, 195, 216, 4683, 4625, 3717, 2190, 2279, 2391}"
27,1,178,0,0.2512755,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]))/x^4,x]","-\frac{1}{3} c^6 d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+3 c^4 d^3 x \left(a+b \sin ^{-1}(c x)\right)+\frac{3 c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}+\frac{1}{9} b c^3 d^3 \left(1-c^2 x^2\right)^{3/2}+\frac{8}{3} b c^3 d^3 \sqrt{1-c^2 x^2}-\frac{b c d^3 \sqrt{1-c^2 x^2}}{6 x^2}+\frac{17}{6} b c^3 d^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","-\frac{1}{3} c^6 d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+3 c^4 d^3 x \left(a+b \sin ^{-1}(c x)\right)+\frac{3 c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}+\frac{1}{9} b c^3 d^3 \left(1-c^2 x^2\right)^{3/2}+\frac{8}{3} b c^3 d^3 \sqrt{1-c^2 x^2}-\frac{b c d^3 \sqrt{1-c^2 x^2}}{6 x^2}+\frac{17}{6} b c^3 d^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"(8*b*c^3*d^3*Sqrt[1 - c^2*x^2])/3 - (b*c*d^3*Sqrt[1 - c^2*x^2])/(6*x^2) + (b*c^3*d^3*(1 - c^2*x^2)^(3/2))/9 - (d^3*(a + b*ArcSin[c*x]))/(3*x^3) + (3*c^2*d^3*(a + b*ArcSin[c*x]))/x + 3*c^4*d^3*x*(a + b*ArcSin[c*x]) - (c^6*d^3*x^3*(a + b*ArcSin[c*x]))/3 + (17*b*c^3*d^3*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",8,8,25,0.3200,1,"{270, 4687, 12, 1799, 1621, 897, 1153, 208}"
28,1,172,0,0.2379308,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}-\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{c^4 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d}+\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^5 d}-\frac{4 b \sqrt{1-c^2 x^2}}{3 c^5 d}","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}-\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{c^4 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d}+\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^5 d}-\frac{4 b \sqrt{1-c^2 x^2}}{3 c^5 d}",1,"(-4*b*Sqrt[1 - c^2*x^2])/(3*c^5*d) + (b*(1 - c^2*x^2)^(3/2))/(9*c^5*d) - (x*(a + b*ArcSin[c*x]))/(c^4*d) - (x^3*(a + b*ArcSin[c*x]))/(3*c^2*d) - ((2*I)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^5*d) + (I*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^5*d) - (I*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^5*d)","A",12,8,25,0.3200,1,"{4715, 4657, 4181, 2279, 2391, 261, 266, 43}"
29,1,144,0,0.1883842,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^4 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d}-\frac{b x \sqrt{1-c^2 x^2}}{4 c^3 d}+\frac{b \sin ^{-1}(c x)}{4 c^4 d}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^4 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d}-\frac{b x \sqrt{1-c^2 x^2}}{4 c^3 d}+\frac{b \sin ^{-1}(c x)}{4 c^4 d}",1,"-(b*x*Sqrt[1 - c^2*x^2])/(4*c^3*d) + (b*ArcSin[c*x])/(4*c^4*d) - (x^2*(a + b*ArcSin[c*x]))/(2*c^2*d) + ((I/2)*(a + b*ArcSin[c*x])^2)/(b*c^4*d) - ((a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^4*d) + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^4*d)","A",8,8,25,0.3200,1,"{4715, 4675, 3719, 2190, 2279, 2391, 321, 216}"
30,1,124,0,0.1374637,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{b \sqrt{1-c^2 x^2}}{c^3 d}","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{b \sqrt{1-c^2 x^2}}{c^3 d}",1,"-((b*Sqrt[1 - c^2*x^2])/(c^3*d)) - (x*(a + b*ArcSin[c*x]))/(c^2*d) - ((2*I)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^3*d) + (I*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^3*d) - (I*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^3*d)","A",8,6,25,0.2400,1,"{4715, 4657, 4181, 2279, 2391, 261}"
31,1,82,0,0.105294,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^2 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^2 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^2 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^2 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}",1,"((I/2)*(a + b*ArcSin[c*x])^2)/(b*c^2*d) - ((a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^2*d) + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^2*d)","A",5,5,23,0.2174,1,"{4675, 3719, 2190, 2279, 2391}"
32,1,84,0,0.0672187,"\int \frac{a+b \sin ^{-1}(c x)}{d-c^2 d x^2} \, dx","Int[(a + b*ArcSin[c*x])/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c d}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d}","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c d}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d}",1,"((-2*I)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*d) + (I*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*d) - (I*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*d)","A",6,4,22,0.1818,1,"{4657, 4181, 2279, 2391}"
33,1,71,0,0.1104866,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d - c^2*d*x^2)),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}",1,"(-2*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/d + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d","A",7,5,25,0.2000,1,"{4679, 4419, 4183, 2279, 2391}"
34,1,116,0,0.1514879,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d - c^2*d*x^2)),x]","\frac{i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{a+b \sin ^{-1}(c x)}{d x}-\frac{2 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d}","\frac{i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{a+b \sin ^{-1}(c x)}{d x}-\frac{2 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d}",1,"-((a + b*ArcSin[c*x])/(d*x)) - ((2*I)*c*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/d - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d + (I*b*c*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d - (I*b*c*PolyLog[2, I*E^(I*ArcSin[c*x])])/d","A",10,8,25,0.3200,1,"{4701, 4657, 4181, 2279, 2391, 266, 63, 208}"
35,1,124,0,0.1868906,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d - c^2*d*x^2)),x]","\frac{i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{2 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 d x}","\frac{i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{2 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 d x}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*d*x) - (a + b*ArcSin[c*x])/(2*d*x^2) - (2*c^2*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/d + ((I/2)*b*c^2*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d - ((I/2)*b*c^2*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d","A",9,7,25,0.2800,1,"{4701, 4679, 4419, 4183, 2279, 2391, 264}"
36,1,173,0,0.2436565,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*(d - c^2*d*x^2)),x]","\frac{i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)}{d x}-\frac{2 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3}-\frac{b c \sqrt{1-c^2 x^2}}{6 d x^2}-\frac{7 b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d}","\frac{i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)}{d x}-\frac{2 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3}-\frac{b c \sqrt{1-c^2 x^2}}{6 d x^2}-\frac{7 b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(6*d*x^2) - (a + b*ArcSin[c*x])/(3*d*x^3) - (c^2*(a + b*ArcSin[c*x]))/(d*x) - ((2*I)*c^3*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/d - (7*b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/(6*d) + (I*b*c^3*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d - (I*b*c^3*PolyLog[2, I*E^(I*ArcSin[c*x])])/d","A",15,9,25,0.3600,1,"{4701, 4657, 4181, 2279, 2391, 266, 63, 208, 51}"
37,1,187,0,0.2367765,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^2,x]","-\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)}{2 c^4 d^2}+\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}+\frac{b \sqrt{1-c^2 x^2}}{c^5 d^2}-\frac{b}{2 c^5 d^2 \sqrt{1-c^2 x^2}}","-\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)}{2 c^4 d^2}+\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}+\frac{b \sqrt{1-c^2 x^2}}{c^5 d^2}-\frac{b}{2 c^5 d^2 \sqrt{1-c^2 x^2}}",1,"-b/(2*c^5*d^2*Sqrt[1 - c^2*x^2]) + (b*Sqrt[1 - c^2*x^2])/(c^5*d^2) + (3*x*(a + b*ArcSin[c*x]))/(2*c^4*d^2) + (x^3*(a + b*ArcSin[c*x]))/(2*c^2*d^2*(1 - c^2*x^2)) + ((3*I)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^5*d^2) - (((3*I)/2)*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^5*d^2) + (((3*I)/2)*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^5*d^2)","A",12,9,25,0.3600,1,"{4703, 4715, 4657, 4181, 2279, 2391, 261, 266, 43}"
38,1,155,0,0.1837849,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^4 d^2}+\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d^2}-\frac{b x}{2 c^3 d^2 \sqrt{1-c^2 x^2}}+\frac{b \sin ^{-1}(c x)}{2 c^4 d^2}","-\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c^4 d^2}+\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d^2}-\frac{b x}{2 c^3 d^2 \sqrt{1-c^2 x^2}}+\frac{b \sin ^{-1}(c x)}{2 c^4 d^2}",1,"-(b*x)/(2*c^3*d^2*Sqrt[1 - c^2*x^2]) + (b*ArcSin[c*x])/(2*c^4*d^2) + (x^2*(a + b*ArcSin[c*x]))/(2*c^2*d^2*(1 - c^2*x^2)) - ((I/2)*(a + b*ArcSin[c*x])^2)/(b*c^4*d^2) + ((a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^4*d^2) - ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^4*d^2)","A",8,8,25,0.3200,1,"{4703, 4675, 3719, 2190, 2279, 2391, 288, 216}"
39,1,144,0,0.1361933,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2}-\frac{b}{2 c^3 d^2 \sqrt{1-c^2 x^2}}","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2}-\frac{b}{2 c^3 d^2 \sqrt{1-c^2 x^2}}",1,"-b/(2*c^3*d^2*Sqrt[1 - c^2*x^2]) + (x*(a + b*ArcSin[c*x]))/(2*c^2*d^2*(1 - c^2*x^2)) + (I*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^3*d^2) - ((I/2)*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^3*d^2) + ((I/2)*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^3*d^2)","A",8,6,25,0.2400,1,"{4703, 4657, 4181, 2279, 2391, 261}"
40,1,57,0,0.047586,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^2,x]","\frac{a+b \sin ^{-1}(c x)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b x}{2 c d^2 \sqrt{1-c^2 x^2}}","\frac{a+b \sin ^{-1}(c x)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b x}{2 c d^2 \sqrt{1-c^2 x^2}}",1,"-(b*x)/(2*c*d^2*Sqrt[1 - c^2*x^2]) + (a + b*ArcSin[c*x])/(2*c^2*d^2*(1 - c^2*x^2))","A",2,2,23,0.08696,1,"{4677, 191}"
41,1,141,0,0.0956248,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(d - c^2*d*x^2)^2,x]","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 c d^2}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 c d^2}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d^2}-\frac{b}{2 c d^2 \sqrt{1-c^2 x^2}}","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 c d^2}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 c d^2}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d^2}-\frac{b}{2 c d^2 \sqrt{1-c^2 x^2}}",1,"-b/(2*c*d^2*Sqrt[1 - c^2*x^2]) + (x*(a + b*ArcSin[c*x]))/(2*d^2*(1 - c^2*x^2)) - (I*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*d^2) + ((I/2)*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*d^2) - ((I/2)*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*d^2)","A",8,6,22,0.2727,1,"{4655, 4657, 4181, 2279, 2391, 261}"
42,1,122,0,0.1729839,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d - c^2*d*x^2)^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{a+b \sin ^{-1}(c x)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c x}{2 d^2 \sqrt{1-c^2 x^2}}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{a+b \sin ^{-1}(c x)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c x}{2 d^2 \sqrt{1-c^2 x^2}}",1,"-(b*c*x)/(2*d^2*Sqrt[1 - c^2*x^2]) + (a + b*ArcSin[c*x])/(2*d^2*(1 - c^2*x^2)) - (2*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^2 + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^2 - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^2","A",9,7,25,0.2800,1,"{4705, 4679, 4419, 4183, 2279, 2391, 191}"
43,1,186,0,0.1925928,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d - c^2*d*x^2)^2),x]","\frac{3 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{3 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{a+b \sin ^{-1}(c x)}{d^2 x \left(1-c^2 x^2\right)}-\frac{3 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 \sqrt{1-c^2 x^2}}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2}","\frac{3 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{3 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{a+b \sin ^{-1}(c x)}{d^2 x \left(1-c^2 x^2\right)}-\frac{3 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 \sqrt{1-c^2 x^2}}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2}",1,"-(b*c)/(2*d^2*Sqrt[1 - c^2*x^2]) - (a + b*ArcSin[c*x])/(d^2*x*(1 - c^2*x^2)) + (3*c^2*x*(a + b*ArcSin[c*x]))/(2*d^2*(1 - c^2*x^2)) - ((3*I)*c*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/d^2 - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d^2 + (((3*I)/2)*b*c*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^2 - (((3*I)/2)*b*c*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^2","A",13,11,25,0.4400,1,"{4701, 4655, 4657, 4181, 2279, 2391, 261, 266, 51, 63, 208}"
44,1,159,0,0.2640218,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d - c^2*d*x^2)^2),x]","\frac{i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d^2}-\frac{i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d^2}+\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)}{d^2 \left(1-c^2 x^2\right)}-\frac{a+b \sin ^{-1}(c x)}{2 d^2 x^2 \left(1-c^2 x^2\right)}-\frac{4 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 x \sqrt{1-c^2 x^2}}","\frac{i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d^2}-\frac{i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d^2}+\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)}{d^2 \left(1-c^2 x^2\right)}-\frac{a+b \sin ^{-1}(c x)}{2 d^2 x^2 \left(1-c^2 x^2\right)}-\frac{4 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 x \sqrt{1-c^2 x^2}}",1,"-(b*c)/(2*d^2*x*Sqrt[1 - c^2*x^2]) + (c^2*(a + b*ArcSin[c*x]))/(d^2*(1 - c^2*x^2)) - (a + b*ArcSin[c*x])/(2*d^2*x^2*(1 - c^2*x^2)) - (4*c^2*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^2 + (I*b*c^2*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^2 - (I*b*c^2*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^2","A",12,9,25,0.3600,1,"{4701, 4705, 4679, 4419, 4183, 2279, 2391, 191, 271}"
45,1,285,0,0.3077258,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*(d - c^2*d*x^2)^2),x]","\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{5 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 x \left(1-c^2 x^2\right)}-\frac{a+b \sin ^{-1}(c x)}{3 d^2 x^3 \left(1-c^2 x^2\right)}-\frac{5 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{5 b c^3}{6 d^2 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d^2 x^2}+\frac{b c}{3 d^2 x^2 \sqrt{1-c^2 x^2}}-\frac{13 b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d^2}","\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{5 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 x \left(1-c^2 x^2\right)}-\frac{a+b \sin ^{-1}(c x)}{3 d^2 x^3 \left(1-c^2 x^2\right)}-\frac{5 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b c^3}{3 d^2 \sqrt{1-c^2 x^2}}-\frac{b c}{6 d^2 x^2 \sqrt{1-c^2 x^2}}-\frac{13 b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d^2}",1,"(-5*b*c^3)/(6*d^2*Sqrt[1 - c^2*x^2]) + (b*c)/(3*d^2*x^2*Sqrt[1 - c^2*x^2]) - (b*c*Sqrt[1 - c^2*x^2])/(2*d^2*x^2) - (a + b*ArcSin[c*x])/(3*d^2*x^3*(1 - c^2*x^2)) - (5*c^2*(a + b*ArcSin[c*x]))/(3*d^2*x*(1 - c^2*x^2)) + (5*c^4*x*(a + b*ArcSin[c*x]))/(2*d^2*(1 - c^2*x^2)) - ((5*I)*c^3*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/d^2 - (13*b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/(6*d^2) + (((5*I)/2)*b*c^3*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^2 - (((5*I)/2)*b*c^3*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^2","A",19,11,25,0.4400,1,"{4701, 4655, 4657, 4181, 2279, 2391, 261, 266, 51, 63, 208}"
46,1,204,0,0.2406888,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^3,x]","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 c^5 d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 c^5 d^3}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 x \left(a+b \sin ^{-1}(c x)\right)}{8 c^4 d^3 \left(1-c^2 x^2\right)}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{5 b}{8 c^5 d^3 \sqrt{1-c^2 x^2}}-\frac{b}{12 c^5 d^3 \left(1-c^2 x^2\right)^{3/2}}","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 c^5 d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 c^5 d^3}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 x \left(a+b \sin ^{-1}(c x)\right)}{8 c^4 d^3 \left(1-c^2 x^2\right)}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{5 b}{8 c^5 d^3 \sqrt{1-c^2 x^2}}-\frac{b}{12 c^5 d^3 \left(1-c^2 x^2\right)^{3/2}}",1,"-b/(12*c^5*d^3*(1 - c^2*x^2)^(3/2)) + (5*b)/(8*c^5*d^3*Sqrt[1 - c^2*x^2]) + (x^3*(a + b*ArcSin[c*x]))/(4*c^2*d^3*(1 - c^2*x^2)^2) - (3*x*(a + b*ArcSin[c*x]))/(8*c^4*d^3*(1 - c^2*x^2)) - (((3*I)/4)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^5*d^3) + (((3*I)/8)*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^5*d^3) - (((3*I)/8)*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^5*d^3)","A",12,8,25,0.3200,1,"{4703, 4657, 4181, 2279, 2391, 261, 266, 43}"
47,1,100,0,0.0844497,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^3,x]","\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x^3}{12 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{b x}{4 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{b \sin ^{-1}(c x)}{4 c^4 d^3}","\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x^3}{12 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{b x}{4 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{b \sin ^{-1}(c x)}{4 c^4 d^3}",1,"-(b*x^3)/(12*c*d^3*(1 - c^2*x^2)^(3/2)) + (b*x)/(4*c^3*d^3*Sqrt[1 - c^2*x^2]) - (b*ArcSin[c*x])/(4*c^4*d^3) + (x^4*(a + b*ArcSin[c*x]))/(4*d^3*(1 - c^2*x^2)^2)","A",4,3,25,0.1200,1,"{4681, 288, 216}"
48,1,202,0,0.1839183,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 c^3 d^3}-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{8 c^2 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b}{8 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{b}{12 c^3 d^3 \left(1-c^2 x^2\right)^{3/2}}","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 c^3 d^3}-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{8 c^2 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b}{8 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{b}{12 c^3 d^3 \left(1-c^2 x^2\right)^{3/2}}",1,"-b/(12*c^3*d^3*(1 - c^2*x^2)^(3/2)) + b/(8*c^3*d^3*Sqrt[1 - c^2*x^2]) + (x*(a + b*ArcSin[c*x]))/(4*c^2*d^3*(1 - c^2*x^2)^2) - (x*(a + b*ArcSin[c*x]))/(8*c^2*d^3*(1 - c^2*x^2)) + ((I/4)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^3*d^3) - ((I/8)*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^3*d^3) + ((I/8)*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^3*d^3)","A",10,7,25,0.2800,1,"{4703, 4655, 4657, 4181, 2279, 2391, 261}"
49,1,83,0,0.0539175,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^3,x]","\frac{a+b \sin ^{-1}(c x)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x}{6 c d^3 \sqrt{1-c^2 x^2}}-\frac{b x}{12 c d^3 \left(1-c^2 x^2\right)^{3/2}}","\frac{a+b \sin ^{-1}(c x)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x}{6 c d^3 \sqrt{1-c^2 x^2}}-\frac{b x}{12 c d^3 \left(1-c^2 x^2\right)^{3/2}}",1,"-(b*x)/(12*c*d^3*(1 - c^2*x^2)^(3/2)) - (b*x)/(6*c*d^3*Sqrt[1 - c^2*x^2]) + (a + b*ArcSin[c*x])/(4*c^2*d^3*(1 - c^2*x^2)^2)","A",3,3,23,0.1304,1,"{4677, 192, 191}"
50,1,196,0,0.1336816,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(d - c^2*d*x^2)^3,x]","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 c d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3}-\frac{3 b}{8 c d^3 \sqrt{1-c^2 x^2}}-\frac{b}{12 c d^3 \left(1-c^2 x^2\right)^{3/2}}","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 c d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3}-\frac{3 b}{8 c d^3 \sqrt{1-c^2 x^2}}-\frac{b}{12 c d^3 \left(1-c^2 x^2\right)^{3/2}}",1,"-b/(12*c*d^3*(1 - c^2*x^2)^(3/2)) - (3*b)/(8*c*d^3*Sqrt[1 - c^2*x^2]) + (x*(a + b*ArcSin[c*x]))/(4*d^3*(1 - c^2*x^2)^2) + (3*x*(a + b*ArcSin[c*x]))/(8*d^3*(1 - c^2*x^2)) - (((3*I)/4)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*d^3) + (((3*I)/8)*b*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*d^3) - (((3*I)/8)*b*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*d^3)","A",10,6,22,0.2727,1,"{4655, 4657, 4181, 2279, 2391, 261}"
51,1,173,0,0.2518424,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d - c^2*d*x^2)^3),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{a+b \sin ^{-1}(c x)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{a+b \sin ^{-1}(c x)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{2 b c x}{3 d^3 \sqrt{1-c^2 x^2}}-\frac{b c x}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{a+b \sin ^{-1}(c x)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{a+b \sin ^{-1}(c x)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{2 b c x}{3 d^3 \sqrt{1-c^2 x^2}}-\frac{b c x}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}",1,"-(b*c*x)/(12*d^3*(1 - c^2*x^2)^(3/2)) - (2*b*c*x)/(3*d^3*Sqrt[1 - c^2*x^2]) + (a + b*ArcSin[c*x])/(4*d^3*(1 - c^2*x^2)^2) + (a + b*ArcSin[c*x])/(2*d^3*(1 - c^2*x^2)) - (2*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^3 + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^3 - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^3","A",12,8,25,0.3200,1,"{4705, 4679, 4419, 4183, 2279, 2391, 191, 192}"
52,1,242,0,0.2423801,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d - c^2*d*x^2)^3),x]","\frac{15 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}+\frac{15 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{5 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \sin ^{-1}(c x)}{d^3 x \left(1-c^2 x^2\right)^2}-\frac{15 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{7 b c}{8 d^3 \sqrt{1-c^2 x^2}}-\frac{b c}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^3}","\frac{15 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}+\frac{15 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{5 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \sin ^{-1}(c x)}{d^3 x \left(1-c^2 x^2\right)^2}-\frac{15 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{7 b c}{8 d^3 \sqrt{1-c^2 x^2}}-\frac{b c}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^3}",1,"-(b*c)/(12*d^3*(1 - c^2*x^2)^(3/2)) - (7*b*c)/(8*d^3*Sqrt[1 - c^2*x^2]) - (a + b*ArcSin[c*x])/(d^3*x*(1 - c^2*x^2)^2) + (5*c^2*x*(a + b*ArcSin[c*x]))/(4*d^3*(1 - c^2*x^2)^2) + (15*c^2*x*(a + b*ArcSin[c*x]))/(8*d^3*(1 - c^2*x^2)) - (((15*I)/4)*c*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/d^3 - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d^3 + (((15*I)/8)*b*c*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^3 - (((15*I)/8)*b*c*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^3","A",16,11,25,0.4400,1,"{4701, 4655, 4657, 4181, 2279, 2391, 261, 266, 51, 63, 208}"
53,1,248,0,0.3463338,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d - c^2*d*x^2)^3),x]","\frac{3 i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{3 i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \sin ^{-1}(c x)}{2 d^3 x^2 \left(1-c^2 x^2\right)^2}-\frac{6 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{2 b c^3 x}{3 d^3 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 x}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{b c}{2 d^3 x \left(1-c^2 x^2\right)^{3/2}}","\frac{3 i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{3 i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \sin ^{-1}(c x)}{2 d^3 x^2 \left(1-c^2 x^2\right)^2}-\frac{6 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{2 b c^3 x}{3 d^3 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 x}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{b c}{2 d^3 x \left(1-c^2 x^2\right)^{3/2}}",1,"-(b*c)/(2*d^3*x*(1 - c^2*x^2)^(3/2)) + (5*b*c^3*x)/(12*d^3*(1 - c^2*x^2)^(3/2)) - (2*b*c^3*x)/(3*d^3*Sqrt[1 - c^2*x^2]) + (3*c^2*(a + b*ArcSin[c*x]))/(4*d^3*(1 - c^2*x^2)^2) - (a + b*ArcSin[c*x])/(2*d^3*x^2*(1 - c^2*x^2)^2) + (3*c^2*(a + b*ArcSin[c*x]))/(2*d^3*(1 - c^2*x^2)) - (6*c^2*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^3 + (((3*I)/2)*b*c^2*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^3 - (((3*I)/2)*b*c^2*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^3","A",16,10,25,0.4000,1,"{4701, 4705, 4679, 4419, 4183, 2279, 2391, 191, 192, 271}"
54,1,369,0,0.3816988,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*(d - c^2*d*x^2)^3),x]","\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}-\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{12 d^3 \left(1-c^2 x^2\right)^2}-\frac{7 c^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 x \left(1-c^2 x^2\right)^2}-\frac{a+b \sin ^{-1}(c x)}{3 d^3 x^3 \left(1-c^2 x^2\right)^2}-\frac{35 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{49 b c^3}{24 d^3 \sqrt{1-c^2 x^2}}-\frac{7 b c^3}{36 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c \sqrt{1-c^2 x^2}}{6 d^3 x^2}+\frac{5 b c}{9 d^3 x^2 \sqrt{1-c^2 x^2}}+\frac{b c}{9 d^3 x^2 \left(1-c^2 x^2\right)^{3/2}}-\frac{19 b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d^3}","\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}-\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{8 d^3}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{12 d^3 \left(1-c^2 x^2\right)^2}-\frac{7 c^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 x \left(1-c^2 x^2\right)^2}-\frac{a+b \sin ^{-1}(c x)}{3 d^3 x^3 \left(1-c^2 x^2\right)^2}-\frac{35 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{29 b c^3}{24 d^3 \sqrt{1-c^2 x^2}}+\frac{b c^3}{12 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{b c}{6 d^3 x^2 \left(1-c^2 x^2\right)^{3/2}}-\frac{19 b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d^3}",1,"(-7*b*c^3)/(36*d^3*(1 - c^2*x^2)^(3/2)) + (b*c)/(9*d^3*x^2*(1 - c^2*x^2)^(3/2)) - (49*b*c^3)/(24*d^3*Sqrt[1 - c^2*x^2]) + (5*b*c)/(9*d^3*x^2*Sqrt[1 - c^2*x^2]) - (5*b*c*Sqrt[1 - c^2*x^2])/(6*d^3*x^2) - (a + b*ArcSin[c*x])/(3*d^3*x^3*(1 - c^2*x^2)^2) - (7*c^2*(a + b*ArcSin[c*x]))/(3*d^3*x*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSin[c*x]))/(12*d^3*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSin[c*x]))/(8*d^3*(1 - c^2*x^2)) - (((35*I)/4)*c^3*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/d^3 - (19*b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/(6*d^3) + (((35*I)/8)*b*c^3*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^3 - (((35*I)/8)*b*c^3*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^3","A",23,11,25,0.4400,1,"{4701, 4655, 4657, 4181, 2279, 2391, 261, 266, 51, 63, 208}"
55,1,262,0,0.2818898,"\int x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","\frac{1}{6} x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{24 c^2}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^4}+\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c^5 \sqrt{1-c^2 x^2}}-\frac{b c x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}+\frac{b x^4 \sqrt{d-c^2 d x^2}}{96 c \sqrt{1-c^2 x^2}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{32 c^3 \sqrt{1-c^2 x^2}}","\frac{1}{6} x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{24 c^2}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^4}+\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c^5 \sqrt{1-c^2 x^2}}-\frac{b c x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}+\frac{b x^4 \sqrt{d-c^2 d x^2}}{96 c \sqrt{1-c^2 x^2}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{32 c^3 \sqrt{1-c^2 x^2}}",1,"(b*x^2*Sqrt[d - c^2*d*x^2])/(32*c^3*Sqrt[1 - c^2*x^2]) + (b*x^4*Sqrt[d - c^2*d*x^2])/(96*c*Sqrt[1 - c^2*x^2]) - (b*c*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[1 - c^2*x^2]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c^4) - (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(24*c^2) + (x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/6 + (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c^5*Sqrt[1 - c^2*x^2])","A",7,4,27,0.1481,1,"{4697, 4707, 4641, 30}"
56,1,189,0,0.1911559,"\int x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","\frac{1}{4} x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{\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 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}","\frac{1}{4} x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^2}+\frac{\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 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}",1,"(b*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[1 - c^2*x^2]) - (b*c*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c^2) + (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/4 + (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c^3*Sqrt[1 - c^2*x^2])","A",5,4,27,0.1481,1,"{4697, 4707, 4641, 30}"
57,1,116,0,0.0548086,"\int \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","\frac{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{\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{b c x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}","\frac{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{\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{b c x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}",1,"-(b*c*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) + (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 + (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",3,3,24,0.1250,1,"{4647, 4641, 30}"
58,1,110,0,0.1102279,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x^2,x]","-\frac{c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}","-\frac{c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}",1,"-((Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x) - (c*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*Sqrt[1 - c^2*x^2]) + (b*c*Sqrt[d - c^2*d*x^2]*Log[x])/Sqrt[1 - c^2*x^2]","A",3,3,27,0.1111,1,"{4693, 29, 4641}"
59,1,111,0,0.0925604,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x^4,x]","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{1-c^2 x^2}}-\frac{b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{1-c^2 x^2}}-\frac{b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(6*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*d*x^3) - (b*c^3*Sqrt[d - c^2*d*x^2]*Log[x])/(3*Sqrt[1 - c^2*x^2])","A",3,2,27,0.07407,1,"{4681, 14}"
60,1,187,0,0.1341581,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x^6} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x^6,x]","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 d x^3}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{1-c^2 x^2}}-\frac{2 b c^5 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 d x^3}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{1-c^2 x^2}}-\frac{2 b c^5 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(20*x^4*Sqrt[1 - c^2*x^2]) + (b*c^3*Sqrt[d - c^2*d*x^2])/(30*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(5*d*x^5) - (2*c^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(15*d*x^3) - (2*b*c^5*Sqrt[d - c^2*d*x^2]*Log[x])/(15*Sqrt[1 - c^2*x^2])","A",6,5,27,0.1852,1,"{271, 264, 4691, 12, 14}"
61,1,263,0,0.1688159,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x^8} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x^8,x]","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{105 d x^3}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{35 d x^5}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d x^7}+\frac{2 b c^5 \sqrt{d-c^2 d x^2}}{105 x^2 \sqrt{1-c^2 x^2}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{140 x^4 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{1-c^2 x^2}}-\frac{8 b c^7 \log (x) \sqrt{d-c^2 d x^2}}{105 \sqrt{1-c^2 x^2}}","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{105 d x^3}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{35 d x^5}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d x^7}+\frac{2 b c^5 \sqrt{d-c^2 d x^2}}{105 x^2 \sqrt{1-c^2 x^2}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{140 x^4 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{1-c^2 x^2}}-\frac{8 b c^7 \log (x) \sqrt{d-c^2 d x^2}}{105 \sqrt{1-c^2 x^2}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(42*x^6*Sqrt[1 - c^2*x^2]) + (b*c^3*Sqrt[d - c^2*d*x^2])/(140*x^4*Sqrt[1 - c^2*x^2]) + (2*b*c^5*Sqrt[d - c^2*d*x^2])/(105*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(7*d*x^7) - (4*c^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(35*d*x^5) - (8*c^4*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(105*d*x^3) - (8*b*c^7*Sqrt[d - c^2*d*x^2]*Log[x])/(105*Sqrt[1 - c^2*x^2])","A",7,5,27,0.1852,1,"{271, 264, 4691, 12, 14}"
62,1,256,0,0.2079797,"\int x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^6 d}-\frac{b c x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}+\frac{b x^5 \sqrt{d-c^2 d x^2}}{175 c \sqrt{1-c^2 x^2}}+\frac{4 b x^3 \sqrt{d-c^2 d x^2}}{315 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b x \sqrt{d-c^2 d x^2}}{105 c^5 \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^6 d}-\frac{b c x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}+\frac{b x^5 \sqrt{d-c^2 d x^2}}{175 c \sqrt{1-c^2 x^2}}+\frac{4 b x^3 \sqrt{d-c^2 d x^2}}{315 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b x \sqrt{d-c^2 d x^2}}{105 c^5 \sqrt{1-c^2 x^2}}",1,"(8*b*x*Sqrt[d - c^2*d*x^2])/(105*c^5*Sqrt[1 - c^2*x^2]) + (4*b*x^3*Sqrt[d - c^2*d*x^2])/(315*c^3*Sqrt[1 - c^2*x^2]) + (b*x^5*Sqrt[d - c^2*d*x^2])/(175*c*Sqrt[1 - c^2*x^2]) - (b*c*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c^6*d) + (2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*c^6*d^2) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^6*d^3)","A",6,4,27,0.1481,1,"{266, 43, 4691, 12}"
63,1,183,0,0.1680463,"\int x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d}-\frac{b c x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{b x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{1-c^2 x^2}}+\frac{2 b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}","\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d}-\frac{b c x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{b x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{1-c^2 x^2}}+\frac{2 b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}",1,"(2*b*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[1 - c^2*x^2]) + (b*x^3*Sqrt[d - c^2*d*x^2])/(45*c*Sqrt[1 - c^2*x^2]) - (b*c*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c^4*d) + ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*c^4*d^2)","A",6,4,27,0.1481,1,"{266, 43, 4691, 12}"
64,1,110,0,0.0680963,"\int x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d}-\frac{b c x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{b x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d}-\frac{b c x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{b x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}",1,"(b*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[1 - c^2*x^2]) - (b*c*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c^2*d)","A",2,1,25,0.04000,1,"{4677}"
65,1,203,0,0.2097052,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x,x]","\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{b c x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}","\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{b c x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}",1,"-((b*c*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2]) + Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]) - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (I*b*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",8,6,27,0.2222,1,"{4697, 4709, 4183, 2279, 2391, 8}"
66,1,225,0,0.2077353,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x^3,x]","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{2 x \sqrt{1-c^2 x^2}}","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{2 x \sqrt{1-c^2 x^2}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(2*x*Sqrt[1 - c^2*x^2]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*x^2) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - ((I/2)*b*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((I/2)*b*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",8,6,27,0.2222,1,"{4693, 30, 4709, 4183, 2279, 2391}"
67,1,301,0,0.2944223,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x^5} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x^5,x]","-\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{c^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 x^2}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{4 x^4}+\frac{c^4 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 \sqrt{1-c^2 x^2}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{8 x \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{1-c^2 x^2}}","-\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{c^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 x^2}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{4 x^4}+\frac{c^4 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 \sqrt{1-c^2 x^2}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{8 x \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{1-c^2 x^2}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(12*x^3*Sqrt[1 - c^2*x^2]) + (b*c^3*Sqrt[d - c^2*d*x^2])/(8*x*Sqrt[1 - c^2*x^2]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(4*x^4) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*x^2) + (c^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(4*Sqrt[1 - c^2*x^2]) - ((I/8)*b*c^4*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((I/8)*b*c^4*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",10,7,27,0.2593,1,"{4693, 30, 4701, 4709, 4183, 2279, 2391}"
68,1,340,0,0.4053035,"\int x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{1}{8} x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{16} d x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{64 c^2}-\frac{3 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c^4}+\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{256 b c^5 \sqrt{1-c^2 x^2}}+\frac{b c^3 d x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{1-c^2 x^2}}-\frac{b c d x^6 \sqrt{d-c^2 d x^2}}{32 \sqrt{1-c^2 x^2}}+\frac{b d x^4 \sqrt{d-c^2 d x^2}}{256 c \sqrt{1-c^2 x^2}}+\frac{3 b d x^2 \sqrt{d-c^2 d x^2}}{256 c^3 \sqrt{1-c^2 x^2}}","\frac{1}{8} x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{16} d x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{64 c^2}-\frac{3 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c^4}+\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{256 b c^5 \sqrt{1-c^2 x^2}}+\frac{b c^3 d x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{1-c^2 x^2}}-\frac{b c d x^6 \sqrt{d-c^2 d x^2}}{32 \sqrt{1-c^2 x^2}}+\frac{b d x^4 \sqrt{d-c^2 d x^2}}{256 c \sqrt{1-c^2 x^2}}+\frac{3 b d x^2 \sqrt{d-c^2 d x^2}}{256 c^3 \sqrt{1-c^2 x^2}}",1,"(3*b*d*x^2*Sqrt[d - c^2*d*x^2])/(256*c^3*Sqrt[1 - c^2*x^2]) + (b*d*x^4*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[1 - c^2*x^2]) - (b*c*d*x^6*Sqrt[d - c^2*d*x^2])/(32*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[1 - c^2*x^2]) - (3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c^4) - (d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(64*c^2) + (d*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/16 + (x^5*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/8 + (3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(256*b*c^5*Sqrt[1 - c^2*x^2])","A",10,6,27,0.2222,1,"{4699, 4697, 4707, 4641, 30, 14}"
69,1,265,0,0.3198077,"\int x^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{1}{6} x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^2}+\frac{d \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 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{1-c^2 x^2}}","\frac{1}{6} x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c^2}+\frac{d \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 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{1-c^2 x^2}}",1,"(b*d*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[1 - c^2*x^2]) - (7*b*c*d*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[1 - c^2*x^2]) - (d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c^2) + (d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 + (x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/6 + (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c^3*Sqrt[1 - c^2*x^2])","A",8,6,27,0.2222,1,"{4699, 4697, 4707, 4641, 30, 14}"
70,1,188,0,0.1051556,"\int \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{1}{4} x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3 d \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{b c^3 d x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{5 b c d x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}","\frac{1}{4} x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3 d \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{b c^3 d x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{5 b c d x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}",1,"(-5*b*c*d*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 + (x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/4 + (3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2])","A",6,5,24,0.2083,1,"{4649, 4647, 4641, 30, 14}"
71,1,185,0,0.1678927,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^2,x]","-\frac{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{3 c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b \sqrt{1-c^2 x^2}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{b c^3 d x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{b c d \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}","-\frac{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{3 c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b \sqrt{1-c^2 x^2}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{b c^3 d x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{b c d \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}",1,"(b*c^3*d*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) - (3*c^2*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x - (3*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*Sqrt[1 - c^2*x^2]) + (b*c*d*Sqrt[d - c^2*d*x^2]*Log[x])/Sqrt[1 - c^2*x^2]","A",6,5,27,0.1852,1,"{4695, 4647, 4641, 30, 14}"
72,1,191,0,0.2289271,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^4,x]","\frac{c^3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \sqrt{1-c^2 x^2}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{1-c^2 x^2}}-\frac{4 b c^3 d \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}","\frac{c^3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \sqrt{1-c^2 x^2}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{1-c^2 x^2}}-\frac{4 b c^3 d \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(6*x^2*Sqrt[1 - c^2*x^2]) + (c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*x^3) + (c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*Sqrt[1 - c^2*x^2]) - (4*b*c^3*d*Sqrt[d - c^2*d*x^2]*Log[x])/(3*Sqrt[1 - c^2*x^2])","A",6,5,27,0.1852,1,"{4695, 4693, 29, 4641, 14}"
73,1,154,0,0.1139884,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^6} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^6,x]","-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{5 x^2 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{1-c^2 x^2}}+\frac{b c^5 d \log (x) \sqrt{d-c^2 d x^2}}{5 \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{5 x^2 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{1-c^2 x^2}}+\frac{b c^5 d \log (x) \sqrt{d-c^2 d x^2}}{5 \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(20*x^4*Sqrt[1 - c^2*x^2]) + (b*c^3*d*Sqrt[d - c^2*d*x^2])/(5*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*d*x^5) + (b*c^5*d*Sqrt[d - c^2*d*x^2]*Log[x])/(5*Sqrt[1 - c^2*x^2])","A",4,3,27,0.1111,1,"{4681, 266, 43}"
74,1,231,0,0.1638797,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^8} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^8,x]","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{35 d x^5}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d x^7}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{70 x^2 \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d \sqrt{d-c^2 d x^2}}{35 x^4 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{1-c^2 x^2}}+\frac{2 b c^7 d \log (x) \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{35 d x^5}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d x^7}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{70 x^2 \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d \sqrt{d-c^2 d x^2}}{35 x^4 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{1-c^2 x^2}}+\frac{2 b c^7 d \log (x) \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(42*x^6*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*Sqrt[d - c^2*d*x^2])/(35*x^4*Sqrt[1 - c^2*x^2]) - (b*c^5*d*Sqrt[d - c^2*d*x^2])/(70*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(7*d*x^7) - (2*c^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(35*d*x^5) + (2*b*c^7*d*Sqrt[d - c^2*d*x^2]*Log[x])/(35*Sqrt[1 - c^2*x^2])","A",7,6,27,0.2222,1,"{271, 264, 4691, 12, 446, 76}"
75,1,308,0,0.2130513,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^{10}} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^10,x]","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{315 d x^5}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{63 d x^7}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{9 d x^9}-\frac{2 b c^7 d \sqrt{d-c^2 d x^2}}{315 x^2 \sqrt{1-c^2 x^2}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{420 x^4 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{72 x^8 \sqrt{1-c^2 x^2}}+\frac{8 b c^9 d \log (x) \sqrt{d-c^2 d x^2}}{315 \sqrt{1-c^2 x^2}}","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{315 d x^5}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{63 d x^7}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{9 d x^9}-\frac{2 b c^7 d \sqrt{d-c^2 d x^2}}{315 x^2 \sqrt{1-c^2 x^2}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{420 x^4 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{72 x^8 \sqrt{1-c^2 x^2}}+\frac{8 b c^9 d \log (x) \sqrt{d-c^2 d x^2}}{315 \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(72*x^8*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d*Sqrt[d - c^2*d*x^2])/(189*x^6*Sqrt[1 - c^2*x^2]) - (b*c^5*d*Sqrt[d - c^2*d*x^2])/(420*x^4*Sqrt[1 - c^2*x^2]) - (2*b*c^7*d*Sqrt[d - c^2*d*x^2])/(315*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(9*d*x^9) - (4*c^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(63*d*x^7) - (8*c^4*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(315*d*x^5) + (8*b*c^9*d*Sqrt[d - c^2*d*x^2]*Log[x])/(315*Sqrt[1 - c^2*x^2])","A",8,6,27,0.2222,1,"{271, 264, 4691, 12, 1251, 893}"
76,1,385,0,0.3011329,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^{12}} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^12,x]","-\frac{16 c^6 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{1155 d x^5}-\frac{8 c^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{231 d x^7}-\frac{2 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{33 d x^9}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{11 d x^{11}}-\frac{4 b c^9 d \sqrt{d-c^2 d x^2}}{1155 x^2 \sqrt{1-c^2 x^2}}-\frac{b c^7 d \sqrt{d-c^2 d x^2}}{770 x^4 \sqrt{1-c^2 x^2}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{1386 x^6 \sqrt{1-c^2 x^2}}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{66 x^8 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{1-c^2 x^2}}+\frac{16 b c^{11} d \log (x) \sqrt{d-c^2 d x^2}}{1155 \sqrt{1-c^2 x^2}}","-\frac{16 c^6 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{1155 d x^5}-\frac{8 c^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{231 d x^7}-\frac{2 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{33 d x^9}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{11 d x^{11}}-\frac{4 b c^9 d \sqrt{d-c^2 d x^2}}{1155 x^2 \sqrt{1-c^2 x^2}}-\frac{b c^7 d \sqrt{d-c^2 d x^2}}{770 x^4 \sqrt{1-c^2 x^2}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{1386 x^6 \sqrt{1-c^2 x^2}}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{66 x^8 \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{1-c^2 x^2}}+\frac{16 b c^{11} d \log (x) \sqrt{d-c^2 d x^2}}{1155 \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(110*x^10*Sqrt[1 - c^2*x^2]) + (b*c^3*d*Sqrt[d - c^2*d*x^2])/(66*x^8*Sqrt[1 - c^2*x^2]) - (b*c^5*d*Sqrt[d - c^2*d*x^2])/(1386*x^6*Sqrt[1 - c^2*x^2]) - (b*c^7*d*Sqrt[d - c^2*d*x^2])/(770*x^4*Sqrt[1 - c^2*x^2]) - (4*b*c^9*d*Sqrt[d - c^2*d*x^2])/(1155*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(11*d*x^11) - (2*c^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(33*d*x^9) - (8*c^4*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(231*d*x^7) - (16*c^6*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(1155*d*x^5) + (16*b*c^11*d*Sqrt[d - c^2*d*x^2]*Log[x])/(1155*Sqrt[1 - c^2*x^2])","A",9,6,27,0.2222,1,"{271, 264, 4691, 12, 1799, 1620}"
77,1,375,0,0.2932621,"\int x^7 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^7*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{\left(d-c^2 d x^2\right)^{11/2} \left(a+b \sin ^{-1}(c x)\right)}{11 c^8 d^4}-\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^8 d^3}+\frac{3 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^8 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^8 d}+\frac{b c^3 d x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{1-c^2 x^2}}-\frac{4 b c d x^9 \sqrt{d-c^2 d x^2}}{297 \sqrt{1-c^2 x^2}}+\frac{b d x^7 \sqrt{d-c^2 d x^2}}{1617 c \sqrt{1-c^2 x^2}}+\frac{2 b d x^5 \sqrt{d-c^2 d x^2}}{1925 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b d x^3 \sqrt{d-c^2 d x^2}}{3465 c^5 \sqrt{1-c^2 x^2}}+\frac{16 b d x \sqrt{d-c^2 d x^2}}{1155 c^7 \sqrt{1-c^2 x^2}}","\frac{\left(d-c^2 d x^2\right)^{11/2} \left(a+b \sin ^{-1}(c x)\right)}{11 c^8 d^4}-\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^8 d^3}+\frac{3 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^8 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^8 d}+\frac{b c^3 d x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{1-c^2 x^2}}-\frac{4 b c d x^9 \sqrt{d-c^2 d x^2}}{297 \sqrt{1-c^2 x^2}}+\frac{b d x^7 \sqrt{d-c^2 d x^2}}{1617 c \sqrt{1-c^2 x^2}}+\frac{2 b d x^5 \sqrt{d-c^2 d x^2}}{1925 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b d x^3 \sqrt{d-c^2 d x^2}}{3465 c^5 \sqrt{1-c^2 x^2}}+\frac{16 b d x \sqrt{d-c^2 d x^2}}{1155 c^7 \sqrt{1-c^2 x^2}}",1,"(16*b*d*x*Sqrt[d - c^2*d*x^2])/(1155*c^7*Sqrt[1 - c^2*x^2]) + (8*b*d*x^3*Sqrt[d - c^2*d*x^2])/(3465*c^5*Sqrt[1 - c^2*x^2]) + (2*b*d*x^5*Sqrt[d - c^2*d*x^2])/(1925*c^3*Sqrt[1 - c^2*x^2]) + (b*d*x^7*Sqrt[d - c^2*d*x^2])/(1617*c*Sqrt[1 - c^2*x^2]) - (4*b*c*d*x^9*Sqrt[d - c^2*d*x^2])/(297*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^11*Sqrt[d - c^2*d*x^2])/(121*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*c^8*d) + (3*(d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^8*d^2) - ((d - c^2*d*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(3*c^8*d^3) + ((d - c^2*d*x^2)^(11/2)*(a + b*ArcSin[c*x]))/(11*c^8*d^4)","A",7,5,27,0.1852,1,"{266, 43, 4691, 12, 1810}"
78,1,301,0,0.2375262,"\int x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^5*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","-\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^6 d}+\frac{b c^3 d x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{1-c^2 x^2}}-\frac{10 b c d x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{1-c^2 x^2}}+\frac{b d x^5 \sqrt{d-c^2 d x^2}}{525 c \sqrt{1-c^2 x^2}}+\frac{4 b d x^3 \sqrt{d-c^2 d x^2}}{945 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b d x \sqrt{d-c^2 d x^2}}{315 c^5 \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^6 d}+\frac{b c^3 d x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{1-c^2 x^2}}-\frac{10 b c d x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{1-c^2 x^2}}+\frac{b d x^5 \sqrt{d-c^2 d x^2}}{525 c \sqrt{1-c^2 x^2}}+\frac{4 b d x^3 \sqrt{d-c^2 d x^2}}{945 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b d x \sqrt{d-c^2 d x^2}}{315 c^5 \sqrt{1-c^2 x^2}}",1,"(8*b*d*x*Sqrt[d - c^2*d*x^2])/(315*c^5*Sqrt[1 - c^2*x^2]) + (4*b*d*x^3*Sqrt[d - c^2*d*x^2])/(945*c^3*Sqrt[1 - c^2*x^2]) + (b*d*x^5*Sqrt[d - c^2*d*x^2])/(525*c*Sqrt[1 - c^2*x^2]) - (10*b*c*d*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*c^6*d) + (2*(d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^6*d^2) - ((d - c^2*d*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(9*c^6*d^3)","A",7,5,27,0.1852,1,"{266, 43, 4691, 12, 1153}"
79,1,227,0,0.1995038,"\int x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4 d}+\frac{b c^3 d x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}-\frac{8 b c d x^5 \sqrt{d-c^2 d x^2}}{175 \sqrt{1-c^2 x^2}}+\frac{b d x^3 \sqrt{d-c^2 d x^2}}{105 c \sqrt{1-c^2 x^2}}+\frac{2 b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{1-c^2 x^2}}","\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^4 d}+\frac{b c^3 d x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}-\frac{8 b c d x^5 \sqrt{d-c^2 d x^2}}{175 \sqrt{1-c^2 x^2}}+\frac{b d x^3 \sqrt{d-c^2 d x^2}}{105 c \sqrt{1-c^2 x^2}}+\frac{2 b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{1-c^2 x^2}}",1,"(2*b*d*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[1 - c^2*x^2]) + (b*d*x^3*Sqrt[d - c^2*d*x^2])/(105*c*Sqrt[1 - c^2*x^2]) - (8*b*c*d*x^5*Sqrt[d - c^2*d*x^2])/(175*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*c^4*d) + ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^4*d^2)","A",7,5,27,0.1852,1,"{266, 43, 4691, 12, 373}"
80,1,153,0,0.087443,"\int x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2 d}+\frac{b c^3 d x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{2 b c d x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}+\frac{b d x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2 d}+\frac{b c^3 d x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{2 b c d x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}+\frac{b d x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}",1,"(b*d*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) - (2*b*c*d*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*c^2*d)","A",3,2,25,0.08000,1,"{4677, 194}"
81,1,278,0,0.3266228,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x,x]","\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{1}{3} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{b c^3 d x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}-\frac{4 b c d x \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}","\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{1}{3} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{b c^3 d x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}-\frac{4 b c d x \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}",1,"(-4*b*c*d*x*Sqrt[d - c^2*d*x^2])/(3*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) + d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]) + ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/3 - (2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (I*b*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",10,7,27,0.2593,1,"{4699, 4697, 4709, 4183, 2279, 2391, 8}"
82,1,297,0,0.3301039,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^3,x]","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{2 x \sqrt{1-c^2 x^2}}","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{2 x \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(2*x*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] - (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(2*x^2) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (((3*I)/2)*b*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (((3*I)/2)*b*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",11,8,27,0.2963,1,"{4695, 4697, 4709, 4183, 2279, 2391, 8, 14}"
83,1,307,0,0.3240403,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x^5} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x^5,x]","\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}-\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{4 x^4}-\frac{3 c^4 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{8 x \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{1-c^2 x^2}}","\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}-\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{4 x^4}-\frac{3 c^4 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{8 x \sqrt{1-c^2 x^2}}-\frac{b c d \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{1-c^2 x^2}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(12*x^3*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d*Sqrt[d - c^2*d*x^2])/(8*x*Sqrt[1 - c^2*x^2]) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*x^2) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(4*x^4) - (3*c^4*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(4*Sqrt[1 - c^2*x^2]) + (((3*I)/8)*b*c^4*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (((3*I)/8)*b*c^4*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",11,8,27,0.2963,1,"{4695, 4693, 30, 4709, 4183, 2279, 2391, 14}"
84,1,430,0,0.5530454,"\int x^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{1}{32} d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c^2}-\frac{3 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{256 c^4}+\frac{3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{512 b c^5 \sqrt{1-c^2 x^2}}+\frac{1}{10} x^5 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{16} d x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^5 d^2 x^{10} \sqrt{d-c^2 d x^2}}{100 \sqrt{1-c^2 x^2}}+\frac{21 b c^3 d^2 x^8 \sqrt{d-c^2 d x^2}}{640 \sqrt{1-c^2 x^2}}-\frac{31 b c d^2 x^6 \sqrt{d-c^2 d x^2}}{960 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^4 \sqrt{d-c^2 d x^2}}{512 c \sqrt{1-c^2 x^2}}+\frac{3 b d^2 x^2 \sqrt{d-c^2 d x^2}}{512 c^3 \sqrt{1-c^2 x^2}}","\frac{1}{32} d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c^2}-\frac{3 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{256 c^4}+\frac{3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{512 b c^5 \sqrt{1-c^2 x^2}}+\frac{1}{10} x^5 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{16} d x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^5 d^2 x^{10} \sqrt{d-c^2 d x^2}}{100 \sqrt{1-c^2 x^2}}+\frac{21 b c^3 d^2 x^8 \sqrt{d-c^2 d x^2}}{640 \sqrt{1-c^2 x^2}}-\frac{31 b c d^2 x^6 \sqrt{d-c^2 d x^2}}{960 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^4 \sqrt{d-c^2 d x^2}}{512 c \sqrt{1-c^2 x^2}}+\frac{3 b d^2 x^2 \sqrt{d-c^2 d x^2}}{512 c^3 \sqrt{1-c^2 x^2}}",1,"(3*b*d^2*x^2*Sqrt[d - c^2*d*x^2])/(512*c^3*Sqrt[1 - c^2*x^2]) + (b*d^2*x^4*Sqrt[d - c^2*d*x^2])/(512*c*Sqrt[1 - c^2*x^2]) - (31*b*c*d^2*x^6*Sqrt[d - c^2*d*x^2])/(960*Sqrt[1 - c^2*x^2]) + (21*b*c^3*d^2*x^8*Sqrt[d - c^2*d*x^2])/(640*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^10*Sqrt[d - c^2*d*x^2])/(100*Sqrt[1 - c^2*x^2]) - (3*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(256*c^4) - (d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c^2) + (d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/32 + (d*x^5*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/16 + (x^5*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/10 + (3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(512*b*c^5*Sqrt[1 - c^2*x^2])","A",14,8,27,0.2963,1,"{4699, 4697, 4707, 4641, 30, 14, 266, 43}"
85,1,351,0,0.4727281,"\int x^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{5}{64} d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{5 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c^2}+\frac{5 d^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{1}{8} x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{48} d x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^5 d^2 x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 x^6 \sqrt{d-c^2 d x^2}}{288 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 x^4 \sqrt{d-c^2 d x^2}}{768 \sqrt{1-c^2 x^2}}+\frac{5 b d^2 x^2 \sqrt{d-c^2 d x^2}}{256 c \sqrt{1-c^2 x^2}}","\frac{5}{64} d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{5 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c^2}+\frac{5 d^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{1}{8} x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{48} d x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^5 d^2 x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 x^6 \sqrt{d-c^2 d x^2}}{288 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 x^4 \sqrt{d-c^2 d x^2}}{768 \sqrt{1-c^2 x^2}}+\frac{5 b d^2 x^2 \sqrt{d-c^2 d x^2}}{256 c \sqrt{1-c^2 x^2}}",1,"(5*b*d^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[1 - c^2*x^2]) - (59*b*c*d^2*x^4*Sqrt[d - c^2*d*x^2])/(768*Sqrt[1 - c^2*x^2]) + (17*b*c^3*d^2*x^6*Sqrt[d - c^2*d*x^2])/(288*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[1 - c^2*x^2]) - (5*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c^2) + (5*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/64 + (5*d*x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/48 + (x^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/8 + (5*d^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",12,8,27,0.2963,1,"{4699, 4697, 4707, 4641, 30, 14, 266, 43}"
86,1,265,0,0.1565048,"\int \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{5}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 d^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{1}{6} x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{24} d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 b c^3 d^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}","\frac{5}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 d^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{1}{6} x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5}{24} d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 b c^3 d^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{25 b c d^2 x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}",1,"(-25*b*c*d^2*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (b*d^2*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/16 + (5*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/24 + (x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/6 + (5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2])","A",8,6,24,0.2500,1,"{4649, 4647, 4641, 30, 14, 261}"
87,1,268,0,0.2399009,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^2,x]","-\frac{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{15 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b \sqrt{1-c^2 x^2}}-\frac{5}{4} c^2 d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{b c^5 d^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{9 b c^3 d^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b c d^2 \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}","-\frac{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{15 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b \sqrt{1-c^2 x^2}}-\frac{5}{4} c^2 d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{b c^5 d^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{9 b c^3 d^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{b c d^2 \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}",1,"(9*b*c^3*d^2*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (15*c^2*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 - (5*c^2*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/4 - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x - (15*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*Sqrt[1 - c^2*x^2]) + (b*c*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/Sqrt[1 - c^2*x^2]","A",10,8,27,0.2963,1,"{4695, 4649, 4647, 4641, 30, 14, 266, 43}"
88,1,277,0,0.3043842,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^4,x]","\frac{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b \sqrt{1-c^2 x^2}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{b c^5 d^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{1-c^2 x^2}}-\frac{7 b c^3 d^2 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}","\frac{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b \sqrt{1-c^2 x^2}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{b c^5 d^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{1-c^2 x^2}}-\frac{7 b c^3 d^2 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(6*x^2*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) + (5*c^4*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 + (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*x) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(3*x^3) + (5*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*Sqrt[1 - c^2*x^2]) - (7*b*c^3*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(3*Sqrt[1 - c^2*x^2])","A",10,7,27,0.2593,1,"{4695, 4647, 4641, 30, 14, 266, 43}"
89,1,277,0,0.3543842,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^6} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^6,x]","-\frac{c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \sqrt{1-c^2 x^2}}-\frac{c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 x^5}+\frac{11 b c^3 d^2 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{1-c^2 x^2}}+\frac{23 b c^5 d^2 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}","-\frac{c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b \sqrt{1-c^2 x^2}}-\frac{c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{5 x^5}+\frac{11 b c^3 d^2 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{1-c^2 x^2}}+\frac{23 b c^5 d^2 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(20*x^4*Sqrt[1 - c^2*x^2]) + (11*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(30*x^2*Sqrt[1 - c^2*x^2]) - (c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/x + (c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*x^3) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(5*x^5) - (c^5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*Sqrt[1 - c^2*x^2]) + (23*b*c^5*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(15*Sqrt[1 - c^2*x^2])","A",10,7,27,0.2593,1,"{4695, 4693, 29, 4641, 14, 266, 43}"
90,1,203,0,0.1254423,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^8} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^8,x]","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d x^7}-\frac{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}{14 x^2 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d^2 \sqrt{d-c^2 d x^2}}{28 x^4 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{1-c^2 x^2}}-\frac{b c^7 d^2 \log (x) \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 d x^7}-\frac{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}{14 x^2 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d^2 \sqrt{d-c^2 d x^2}}{28 x^4 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{1-c^2 x^2}}-\frac{b c^7 d^2 \log (x) \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(42*x^6*Sqrt[1 - c^2*x^2]) + (3*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(28*x^4*Sqrt[1 - c^2*x^2]) - (3*b*c^5*d^2*Sqrt[d - c^2*d*x^2])/(14*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*d*x^7) - (b*c^7*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(7*Sqrt[1 - c^2*x^2])","A",4,3,27,0.1111,1,"{4681, 266, 43}"
91,1,282,0,0.1789281,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^{10}} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^10,x]","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{63 d x^7}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{9 d x^9}-\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{21 x^2 \sqrt{1-c^2 x^2}}+\frac{b c^5 d^2 \sqrt{d-c^2 d x^2}}{42 x^4 \sqrt{1-c^2 x^2}}-\frac{b c^3 d^2 \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \left(1-c^2 x^2\right)^{7/2} \sqrt{d-c^2 d x^2}}{72 x^8}-\frac{2 b c^9 d^2 \log (x) \sqrt{d-c^2 d x^2}}{63 \sqrt{1-c^2 x^2}}","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{63 d x^7}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{9 d x^9}-\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{21 x^2 \sqrt{1-c^2 x^2}}+\frac{b c^5 d^2 \sqrt{d-c^2 d x^2}}{42 x^4 \sqrt{1-c^2 x^2}}-\frac{b c^3 d^2 \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \left(1-c^2 x^2\right)^{7/2} \sqrt{d-c^2 d x^2}}{72 x^8}-\frac{2 b c^9 d^2 \log (x) \sqrt{d-c^2 d x^2}}{63 \sqrt{1-c^2 x^2}}",1,"-(b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(189*x^6*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*Sqrt[d - c^2*d*x^2])/(42*x^4*Sqrt[1 - c^2*x^2]) - (b*c^7*d^2*Sqrt[d - c^2*d*x^2])/(21*x^2*Sqrt[1 - c^2*x^2]) - (b*c*d^2*(1 - c^2*x^2)^(7/2)*Sqrt[d - c^2*d*x^2])/(72*x^8) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(9*d*x^9) - (2*c^2*(d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(63*d*x^7) - (2*b*c^9*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(63*Sqrt[1 - c^2*x^2])","A",8,7,27,0.2593,1,"{271, 264, 4691, 12, 446, 78, 43}"
92,1,361,0,0.2228609,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^{12}} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^12,x]","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{693 d x^7}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{99 d x^9}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{11 d x^{11}}+\frac{2 b c^9 d^2 \sqrt{d-c^2 d x^2}}{693 x^2 \sqrt{1-c^2 x^2}}+\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{924 x^4 \sqrt{1-c^2 x^2}}-\frac{113 b c^5 d^2 \sqrt{d-c^2 d x^2}}{4158 x^6 \sqrt{1-c^2 x^2}}+\frac{23 b c^3 d^2 \sqrt{d-c^2 d x^2}}{792 x^8 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{1-c^2 x^2}}-\frac{8 b c^{11} d^2 \log (x) \sqrt{d-c^2 d x^2}}{693 \sqrt{1-c^2 x^2}}","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{693 d x^7}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{99 d x^9}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{11 d x^{11}}+\frac{2 b c^9 d^2 \sqrt{d-c^2 d x^2}}{693 x^2 \sqrt{1-c^2 x^2}}+\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{924 x^4 \sqrt{1-c^2 x^2}}-\frac{113 b c^5 d^2 \sqrt{d-c^2 d x^2}}{4158 x^6 \sqrt{1-c^2 x^2}}+\frac{23 b c^3 d^2 \sqrt{d-c^2 d x^2}}{792 x^8 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{1-c^2 x^2}}-\frac{8 b c^{11} d^2 \log (x) \sqrt{d-c^2 d x^2}}{693 \sqrt{1-c^2 x^2}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(110*x^10*Sqrt[1 - c^2*x^2]) + (23*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(792*x^8*Sqrt[1 - c^2*x^2]) - (113*b*c^5*d^2*Sqrt[d - c^2*d*x^2])/(4158*x^6*Sqrt[1 - c^2*x^2]) + (b*c^7*d^2*Sqrt[d - c^2*d*x^2])/(924*x^4*Sqrt[1 - c^2*x^2]) + (2*b*c^9*d^2*Sqrt[d - c^2*d*x^2])/(693*x^2*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(11*d*x^11) - (4*c^2*(d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(99*d*x^9) - (8*c^4*(d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(693*d*x^7) - (8*b*c^11*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(693*Sqrt[1 - c^2*x^2])","A",8,6,27,0.2222,1,"{271, 264, 4691, 12, 1251, 893}"
93,1,354,0,0.2462114,"\int x^5 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^5*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","-\frac{\left(d-c^2 d x^2\right)^{11/2} \left(a+b \sin ^{-1}(c x)\right)}{11 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^6 d}-\frac{b c^5 d^2 x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{1-c^2 x^2}}+\frac{23 b c^3 d^2 x^9 \sqrt{d-c^2 d x^2}}{891 \sqrt{1-c^2 x^2}}-\frac{113 b c d^2 x^7 \sqrt{d-c^2 d x^2}}{4851 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^5 \sqrt{d-c^2 d x^2}}{1155 c \sqrt{1-c^2 x^2}}+\frac{4 b d^2 x^3 \sqrt{d-c^2 d x^2}}{2079 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b d^2 x \sqrt{d-c^2 d x^2}}{693 c^5 \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{11/2} \left(a+b \sin ^{-1}(c x)\right)}{11 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^6 d}-\frac{b c^5 d^2 x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{1-c^2 x^2}}+\frac{23 b c^3 d^2 x^9 \sqrt{d-c^2 d x^2}}{891 \sqrt{1-c^2 x^2}}-\frac{113 b c d^2 x^7 \sqrt{d-c^2 d x^2}}{4851 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^5 \sqrt{d-c^2 d x^2}}{1155 c \sqrt{1-c^2 x^2}}+\frac{4 b d^2 x^3 \sqrt{d-c^2 d x^2}}{2079 c^3 \sqrt{1-c^2 x^2}}+\frac{8 b d^2 x \sqrt{d-c^2 d x^2}}{693 c^5 \sqrt{1-c^2 x^2}}",1,"(8*b*d^2*x*Sqrt[d - c^2*d*x^2])/(693*c^5*Sqrt[1 - c^2*x^2]) + (4*b*d^2*x^3*Sqrt[d - c^2*d*x^2])/(2079*c^3*Sqrt[1 - c^2*x^2]) + (b*d^2*x^5*Sqrt[d - c^2*d*x^2])/(1155*c*Sqrt[1 - c^2*x^2]) - (113*b*c*d^2*x^7*Sqrt[d - c^2*d*x^2])/(4851*Sqrt[1 - c^2*x^2]) + (23*b*c^3*d^2*x^9*Sqrt[d - c^2*d*x^2])/(891*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^11*Sqrt[d - c^2*d*x^2])/(121*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^6*d) + (2*(d - c^2*d*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(9*c^6*d^2) - ((d - c^2*d*x^2)^(11/2)*(a + b*ArcSin[c*x]))/(11*c^6*d^3)","A",7,5,27,0.1852,1,"{266, 43, 4691, 12, 1153}"
94,1,278,0,0.2034296,"\int x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4 d}-\frac{b c^5 d^2 x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{1-c^2 x^2}}+\frac{19 b c^3 d^2 x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{1-c^2 x^2}}-\frac{b c d^2 x^5 \sqrt{d-c^2 d x^2}}{21 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2}}{189 c \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2}}{63 c^3 \sqrt{1-c^2 x^2}}","\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^4 d}-\frac{b c^5 d^2 x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{1-c^2 x^2}}+\frac{19 b c^3 d^2 x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{1-c^2 x^2}}-\frac{b c d^2 x^5 \sqrt{d-c^2 d x^2}}{21 \sqrt{1-c^2 x^2}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2}}{189 c \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2}}{63 c^3 \sqrt{1-c^2 x^2}}",1,"(2*b*d^2*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[1 - c^2*x^2]) + (b*d^2*x^3*Sqrt[d - c^2*d*x^2])/(189*c*Sqrt[1 - c^2*x^2]) - (b*c*d^2*x^5*Sqrt[d - c^2*d*x^2])/(21*Sqrt[1 - c^2*x^2]) + (19*b*c^3*d^2*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^4*d) + ((d - c^2*d*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(9*c^4*d^2)","A",7,5,27,0.1852,1,"{266, 43, 4691, 12, 373}"
95,1,202,0,0.0907841,"\int x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2 d}-\frac{b c^5 d^2 x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d^2 x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}-\frac{b c d^2 x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}+\frac{b d^2 x \sqrt{d-c^2 d x^2}}{7 c \sqrt{1-c^2 x^2}}","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{7 c^2 d}-\frac{b c^5 d^2 x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}+\frac{3 b c^3 d^2 x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}-\frac{b c d^2 x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}+\frac{b d^2 x \sqrt{d-c^2 d x^2}}{7 c \sqrt{1-c^2 x^2}}",1,"(b*d^2*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) - (b*c*d^2*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) + (3*b*c^3*d^2*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(7*c^2*d)","A",3,2,25,0.08000,1,"{4677, 194}"
96,1,361,0,0.4627223,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x,x]","\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{1}{5} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^5 d^2 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{11 b c^3 d^2 x^3 \sqrt{d-c^2 d x^2}}{45 \sqrt{1-c^2 x^2}}-\frac{23 b c d^2 x \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}","\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{1}{5} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^5 d^2 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{11 b c^3 d^2 x^3 \sqrt{d-c^2 d x^2}}{45 \sqrt{1-c^2 x^2}}-\frac{23 b c d^2 x \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}",1,"(-23*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(15*Sqrt[1 - c^2*x^2]) + (11*b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2])/(45*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]) + (d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/3 + ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/5 - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (I*b*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",13,8,27,0.2963,1,"{4699, 4697, 4709, 4183, 2279, 2391, 8, 194}"
97,1,386,0,0.4584055,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^3,x]","-\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}+\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}-\frac{5}{2} c^2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 c^2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{5}{6} c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}-\frac{b c^5 d^2 x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{7 b c^3 d^2 x \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{2 x \sqrt{1-c^2 x^2}}","-\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}+\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{1-c^2 x^2}}-\frac{5}{2} c^2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 c^2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{5}{6} c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}-\frac{b c^5 d^2 x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}+\frac{7 b c^3 d^2 x \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{2 x \sqrt{1-c^2 x^2}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(2*x*Sqrt[1 - c^2*x^2]) + (7*b*c^3*d^2*x*Sqrt[d - c^2*d*x^2])/(3*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) - (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/2 - (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/6 - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(2*x^2) + (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (((5*I)/2)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (((5*I)/2)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",13,9,27,0.3333,1,"{4695, 4699, 4697, 4709, 4183, 2279, 2391, 8, 270}"
98,1,389,0,0.4551996,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x^5} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x^5,x]","\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}-\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{15}{8} c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{15 c^4 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 \sqrt{1-c^2 x^2}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 x^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{4 x^4}-\frac{b c^5 d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}+\frac{9 b c^3 d^2 \sqrt{d-c^2 d x^2}}{8 x \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{1-c^2 x^2}}","\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}-\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{8 \sqrt{1-c^2 x^2}}+\frac{15}{8} c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{15 c^4 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 \sqrt{1-c^2 x^2}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 x^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{4 x^4}-\frac{b c^5 d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}+\frac{9 b c^3 d^2 \sqrt{d-c^2 d x^2}}{8 x \sqrt{1-c^2 x^2}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{1-c^2 x^2}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(12*x^3*Sqrt[1 - c^2*x^2]) + (9*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(8*x*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] + (15*c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 + (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(8*x^2) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(4*x^4) - (15*c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(4*Sqrt[1 - c^2*x^2]) + (((15*I)/8)*b*c^4*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (((15*I)/8)*b*c^4*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",14,9,27,0.3333,1,"{4695, 4697, 4709, 4183, 2279, 2391, 8, 14, 270}"
99,1,34,0,0.0305888,"\int \sqrt{1-x^2} \sin ^{-1}(x) \, dx","Int[Sqrt[1 - x^2]*ArcSin[x],x]","-\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2","-\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \sin ^{-1}(x)+\frac{1}{4} \sin ^{-1}(x)^2",1,"-x^2/4 + (x*Sqrt[1 - x^2]*ArcSin[x])/2 + ArcSin[x]^2/4","A",3,3,14,0.2143,1,"{4647, 4641, 30}"
100,1,116,0,0.0585542,"\int \sqrt{\pi -c^2 \pi  x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[Pi - c^2*Pi*x^2]*(a + b*ArcSin[c*x]),x]","\frac{1}{2} x \sqrt{\pi -\pi  c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{\sqrt{\pi -\pi  c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{b c x^2 \sqrt{\pi -\pi  c^2 x^2}}{4 \sqrt{1-c^2 x^2}}","\frac{1}{2} x \sqrt{\pi -\pi  c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{\sqrt{\pi } \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c}-\frac{1}{4} \sqrt{\pi } b c x^2",1,"-(b*c*x^2*Sqrt[Pi - c^2*Pi*x^2])/(4*Sqrt[1 - c^2*x^2]) + (x*Sqrt[Pi - c^2*Pi*x^2]*(a + b*ArcSin[c*x]))/2 + (Sqrt[Pi - c^2*Pi*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",3,3,24,0.1250,1,"{4647, 4641, 30}"
101,1,88,0,0.1515992,"\int \frac{x^4 \sin ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcSin[a*x])/Sqrt[1 - a^2*x^2],x]","\frac{3 x^2}{16 a^3}-\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{8 a^4}+\frac{3 \sin ^{-1}(a x)^2}{16 a^5}+\frac{x^4}{16 a}","\frac{3 x^2}{16 a^3}-\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{8 a^4}+\frac{3 \sin ^{-1}(a x)^2}{16 a^5}+\frac{x^4}{16 a}",1,"(3*x^2)/(16*a^3) + x^4/(16*a) - (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(8*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(4*a^2) + (3*ArcSin[a*x]^2)/(16*a^5)","A",5,3,22,0.1364,1,"{4707, 4641, 30}"
102,1,72,0,0.1071822,"\int \frac{x^3 \sin ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcSin[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 a^4}+\frac{2 x}{3 a^3}+\frac{x^3}{9 a}","-\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{3 a^4}+\frac{2 x}{3 a^3}+\frac{x^3}{9 a}",1,"(2*x)/(3*a^3) + x^3/(9*a) - (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a^2)","A",4,4,22,0.1818,1,"{4707, 4677, 8, 30}"
103,1,50,0,0.0818071,"\int \frac{x^2 \sin ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcSin[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{2 a^2}+\frac{\sin ^{-1}(a x)^2}{4 a^3}+\frac{x^2}{4 a}","-\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{2 a^2}+\frac{\sin ^{-1}(a x)^2}{4 a^3}+\frac{x^2}{4 a}",1,"x^2/(4*a) - (x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(2*a^2) + ArcSin[a*x]^2/(4*a^3)","A",3,3,22,0.1364,1,"{4707, 4641, 30}"
104,1,29,0,0.0405081,"\int \frac{x \sin ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcSin[a*x])/Sqrt[1 - a^2*x^2],x]","\frac{x}{a}-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a^2}","\frac{x}{a}-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a^2}",1,"x/a - (Sqrt[1 - a^2*x^2]*ArcSin[a*x])/a^2","A",2,2,20,0.1000,1,"{4677, 8}"
105,1,13,0,0.0197116,"\int \frac{\sin ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]/Sqrt[1 - a^2*x^2],x]","\frac{\sin ^{-1}(a x)^2}{2 a}","\frac{\sin ^{-1}(a x)^2}{2 a}",1,"ArcSin[a*x]^2/(2*a)","A",1,1,19,0.05263,1,"{4641}"
106,1,52,0,0.0839628,"\int \frac{\sin ^{-1}(a x)}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]/(x*Sqrt[1 - a^2*x^2]),x]","i \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-i \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)","i \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-i \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)",1,"-2*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])] + I*PolyLog[2, -E^(I*ArcSin[a*x])] - I*PolyLog[2, E^(I*ArcSin[a*x])]","A",6,4,22,0.1818,1,"{4709, 4183, 2279, 2391}"
107,1,28,0,0.0611197,"\int \frac{\sin ^{-1}(a x)}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]/(x^2*Sqrt[1 - a^2*x^2]),x]","a \log (x)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{x}","a \log (x)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{x}",1,"-((Sqrt[1 - a^2*x^2]*ArcSin[a*x])/x) + a*Log[x]","A",2,2,22,0.09091,1,"{4681, 29}"
108,1,98,0,0.1467767,"\int \frac{\sin ^{-1}(a x)}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]/(x^3*Sqrt[1 - a^2*x^2]),x]","\frac{1}{2} i a^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-\frac{1}{2} i a^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{2 x^2}+a^2 \left(-\sin ^{-1}(a x)\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{a}{2 x}","\frac{1}{2} i a^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-\frac{1}{2} i a^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{2 x^2}+a^2 \left(-\sin ^{-1}(a x)\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{a}{2 x}",1,"-a/(2*x) - (Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(2*x^2) - a^2*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])] + (I/2)*a^2*PolyLog[2, -E^(I*ArcSin[a*x])] - (I/2)*a^2*PolyLog[2, E^(I*ArcSin[a*x])]","A",8,6,22,0.2727,1,"{4701, 4709, 4183, 2279, 2391, 30}"
109,1,224,0,0.2652397,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^5*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2 d}-\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 c^4 d}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 c^6 d}+\frac{b x^5 \sqrt{1-c^2 x^2}}{25 c \sqrt{d-c^2 d x^2}}+\frac{4 b x^3 \sqrt{1-c^2 x^2}}{45 c^3 \sqrt{d-c^2 d x^2}}+\frac{8 b x \sqrt{1-c^2 x^2}}{15 c^5 \sqrt{d-c^2 d x^2}}","-\frac{x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{5 c^2 d}-\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 c^4 d}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 c^6 d}+\frac{b x^5 \sqrt{1-c^2 x^2}}{25 c \sqrt{d-c^2 d x^2}}+\frac{4 b x^3 \sqrt{1-c^2 x^2}}{45 c^3 \sqrt{d-c^2 d x^2}}+\frac{8 b x \sqrt{1-c^2 x^2}}{15 c^5 \sqrt{d-c^2 d x^2}}",1,"(8*b*x*Sqrt[1 - c^2*x^2])/(15*c^5*Sqrt[d - c^2*d*x^2]) + (4*b*x^3*Sqrt[1 - c^2*x^2])/(45*c^3*Sqrt[d - c^2*d*x^2]) + (b*x^5*Sqrt[1 - c^2*x^2])/(25*c*Sqrt[d - c^2*d*x^2]) - (8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(15*c^6*d) - (4*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(15*c^4*d) - (x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c^2*d)","A",6,4,27,0.1481,1,"{4707, 4677, 8, 30}"
110,1,200,0,0.2498129,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{4 c^2 d}-\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^4 d}+\frac{3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c^5 \sqrt{d-c^2 d x^2}}+\frac{b x^4 \sqrt{1-c^2 x^2}}{16 c \sqrt{d-c^2 d x^2}}+\frac{3 b x^2 \sqrt{1-c^2 x^2}}{16 c^3 \sqrt{d-c^2 d x^2}}","-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{4 c^2 d}-\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^4 d}+\frac{3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c^5 \sqrt{d-c^2 d x^2}}+\frac{b x^4 \sqrt{1-c^2 x^2}}{16 c \sqrt{d-c^2 d x^2}}+\frac{3 b x^2 \sqrt{1-c^2 x^2}}{16 c^3 \sqrt{d-c^2 d x^2}}",1,"(3*b*x^2*Sqrt[1 - c^2*x^2])/(16*c^3*Sqrt[d - c^2*d*x^2]) + (b*x^4*Sqrt[1 - c^2*x^2])/(16*c*Sqrt[d - c^2*d*x^2]) - (3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c^4*d) - (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(4*c^2*d) + (3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(16*b*c^5*Sqrt[d - c^2*d*x^2])","A",6,4,27,0.1481,1,"{4707, 4643, 4641, 30}"
111,1,148,0,0.1594911,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d}+\frac{b x^3 \sqrt{1-c^2 x^2}}{9 c \sqrt{d-c^2 d x^2}}+\frac{2 b x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}","-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d}+\frac{b x^3 \sqrt{1-c^2 x^2}}{9 c \sqrt{d-c^2 d x^2}}+\frac{2 b x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(2*b*x*Sqrt[1 - c^2*x^2])/(3*c^3*Sqrt[d - c^2*d*x^2]) + (b*x^3*Sqrt[1 - c^2*x^2])/(9*c*Sqrt[d - c^2*d*x^2]) - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^4*d) - (x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^2*d)","A",4,4,27,0.1481,1,"{4707, 4677, 8, 30}"
112,1,124,0,0.1455092,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d}+\frac{\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{b x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}","-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^2 d}+\frac{\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{b x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}",1,"(b*x^2*Sqrt[1 - c^2*x^2])/(4*c*Sqrt[d - c^2*d*x^2]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*c^2*d) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",4,4,27,0.1481,1,"{4707, 4643, 4641, 30}"
113,1,67,0,0.0605404,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{b x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}","\frac{b x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}",1,"(b*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(c^2*d)","A",2,2,25,0.08000,1,"{4677, 8}"
114,1,49,0,0.0508182,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/Sqrt[d - c^2*d*x^2],x]","\frac{\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{\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}}",1,"(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
115,1,145,0,0.1936257,"\int \frac{a+b \sin ^{-1}(c x)}{x \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/(x*Sqrt[d - c^2*d*x^2]),x]","\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}","\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}",1,"(-2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] + (I*b*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - (I*b*Sqrt[1 - c^2*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2]","A",7,5,27,0.1852,1,"{4713, 4709, 4183, 2279, 2391}"
116,1,66,0,0.0904784,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*Sqrt[d - c^2*d*x^2]),x]","\frac{b c \sqrt{1-c^2 x^2} \log (x)}{\sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{d x}","\frac{b c \sqrt{1-c^2 x^2} \log (x)}{\sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{d x}",1,"-((Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(d*x)) + (b*c*Sqrt[1 - c^2*x^2]*Log[x])/Sqrt[d - c^2*d*x^2]","A",2,2,27,0.07407,1,"{4681, 29}"
117,1,229,0,0.2991529,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*Sqrt[d - c^2*d*x^2]),x]","\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}-\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 d x^2}-\frac{c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{2 x \sqrt{d-c^2 d x^2}}","\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}-\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 d x^2}-\frac{c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{2 x \sqrt{d-c^2 d x^2}}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*x*Sqrt[d - c^2*d*x^2]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*d*x^2) - (c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] + ((I/2)*b*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - ((I/2)*b*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2]","A",9,7,27,0.2593,1,"{4701, 4713, 4709, 4183, 2279, 2391, 30}"
118,1,147,0,0.187793,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*Sqrt[d - c^2*d*x^2]),x]","-\frac{2 c^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{1-c^2 x^2}}{6 x^2 \sqrt{d-c^2 d x^2}}+\frac{2 b c^3 \sqrt{1-c^2 x^2} \log (x)}{3 \sqrt{d-c^2 d x^2}}","-\frac{2 c^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{1-c^2 x^2}}{6 x^2 \sqrt{d-c^2 d x^2}}+\frac{2 b c^3 \sqrt{1-c^2 x^2} \log (x)}{3 \sqrt{d-c^2 d x^2}}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(6*x^2*Sqrt[d - c^2*d*x^2]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*d*x^3) - (2*c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*d*x) + (2*b*c^3*Sqrt[1 - c^2*x^2]*Log[x])/(3*Sqrt[d - c^2*d*x^2])","A",4,4,27,0.1481,1,"{4701, 4681, 29, 30}"
119,1,229,0,0.2913748,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2}+\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^6 d^2}+\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b x^3 \sqrt{1-c^2 x^2}}{9 c^3 d \sqrt{d-c^2 d x^2}}-\frac{5 b x \sqrt{1-c^2 x^2}}{3 c^5 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{c^6 d \sqrt{d-c^2 d x^2}}","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^6 d^3}+\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^6 d^2}+\frac{a+b \sin ^{-1}(c x)}{c^6 d \sqrt{d-c^2 d x^2}}-\frac{b x^3 \sqrt{d-c^2 d x^2}}{9 c^3 d^2 \sqrt{1-c^2 x^2}}-\frac{5 b x \sqrt{d-c^2 d x^2}}{3 c^5 d^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{c^6 d^2 \sqrt{1-c^2 x^2}}",1,"(-5*b*x*Sqrt[1 - c^2*x^2])/(3*c^5*d*Sqrt[d - c^2*d*x^2]) - (b*x^3*Sqrt[1 - c^2*x^2])/(9*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcSin[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^6*d^2) + (4*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^4*d^2) - (b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(c^6*d*Sqrt[d - c^2*d*x^2])","A",8,7,27,0.2593,1,"{4703, 4707, 4677, 8, 30, 302, 206}"
120,1,214,0,0.2871997,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^4 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^5 d \sqrt{d-c^2 d x^2}}-\frac{b x^2 \sqrt{1-c^2 x^2}}{4 c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{2 c^5 d \sqrt{d-c^2 d x^2}}","\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^4 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^5 d \sqrt{d-c^2 d x^2}}-\frac{b x^2 \sqrt{1-c^2 x^2}}{4 c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{2 c^5 d \sqrt{d-c^2 d x^2}}",1,"-(b*x^2*Sqrt[1 - c^2*x^2])/(4*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcSin[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*c^4*d^2) - (3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c^5*d*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(2*c^5*d*Sqrt[d - c^2*d*x^2])","A",8,7,27,0.2593,1,"{4703, 4707, 4643, 4641, 30, 266, 43}"
121,1,146,0,0.1803456,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^4 d^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{c^4 d \sqrt{d-c^2 d x^2}}","\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^4 d^2}+\frac{a+b \sin ^{-1}(c x)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{b x \sqrt{d-c^2 d x^2}}{c^3 d^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{c^4 d^2 \sqrt{1-c^2 x^2}}",1,"-((b*x*Sqrt[1 - c^2*x^2])/(c^3*d*Sqrt[d - c^2*d*x^2])) + (x^2*(a + b*ArcSin[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(c^4*d^2) - (b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(c^4*d*Sqrt[d - c^2*d*x^2])","A",5,5,27,0.1852,1,"{4703, 4677, 8, 321, 206}"
122,1,135,0,0.1592554,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","-\frac{\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{x \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} \log \left(1-c^2 x^2\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}","-\frac{\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{x \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} \log \left(1-c^2 x^2\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}",1,"(x*(a + b*ArcSin[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^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*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(2*c^3*d*Sqrt[d - c^2*d*x^2])","A",4,4,27,0.1481,1,"{4703, 4643, 4641, 260}"
123,1,73,0,0.0702272,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{a+b \sin ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}","\frac{a+b \sin ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcSin[c*x])/(c^2*d*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(c^2*d*Sqrt[d - c^2*d*x^2])","A",2,2,25,0.08000,1,"{4677, 206}"
124,1,80,0,0.0363379,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d - c^2*d*x^2)^(3/2),x]","\frac{x \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{2 c d \sqrt{d-c^2 d x^2}}","\frac{x \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{2 c d \sqrt{d-c^2 d x^2}}",1,"(x*(a + b*ArcSin[c*x]))/(d*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(2*c*d*Sqrt[d - c^2*d*x^2])","A",2,2,24,0.08333,1,"{4653, 260}"
125,1,220,0,0.3112218,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d - c^2*d*x^2)^(3/2)),x]","\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}","\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcSin[c*x])/(d*Sqrt[d - c^2*d*x^2]) - (2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(d*Sqrt[d - c^2*d*x^2]) + (I*b*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (I*b*Sqrt[1 - c^2*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",9,7,27,0.2593,1,"{4705, 4713, 4709, 4183, 2279, 2391, 206}"
126,1,150,0,0.1554751,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d - c^2*d*x^2)^(3/2)),x]","\frac{2 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{a+b \sin ^{-1}(c x)}{d x \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{1-c^2 x^2} \log (x)}{d \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{2 d \sqrt{d-c^2 d x^2}}","\frac{2 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{a+b \sin ^{-1}(c x)}{d x \sqrt{d-c^2 d x^2}}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{d^2 \sqrt{1-c^2 x^2}}+\frac{b c \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{2 d^2 \sqrt{1-c^2 x^2}}",1,"-((a + b*ArcSin[c*x])/(d*x*Sqrt[d - c^2*d*x^2])) + (2*c^2*x*(a + b*ArcSin[c*x]))/(d*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[1 - c^2*x^2]*Log[x])/(d*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(2*d*Sqrt[d - c^2*d*x^2])","A",7,7,27,0.2593,1,"{4701, 4653, 260, 266, 36, 29, 31}"
127,1,316,0,0.4413887,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d - c^2*d*x^2)^(3/2)),x]","\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}-\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2}}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2 \sqrt{d-c^2 d x^2}}-\frac{3 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d x \sqrt{d-c^2 d x^2}}-\frac{b c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}","\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}-\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2}}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2 \sqrt{d-c^2 d x^2}}-\frac{3 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d x \sqrt{d-c^2 d x^2}}-\frac{b c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*d*x*Sqrt[d - c^2*d*x^2]) + (3*c^2*(a + b*ArcSin[c*x]))/(2*d*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])/(2*d*x^2*Sqrt[d - c^2*d*x^2]) - (3*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (b*c^2*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(d*Sqrt[d - c^2*d*x^2]) + (((3*I)/2)*b*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (((3*I)/2)*b*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",12,9,27,0.3333,1,"{4701, 4705, 4713, 4709, 4183, 2279, 2391, 206, 325}"
128,1,238,0,0.2920127,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*(d - c^2*d*x^2)^(3/2)),x]","\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d x \sqrt{d-c^2 d x^2}}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3 \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{6 d x^2 \sqrt{d-c^2 d x^2}}+\frac{5 b c^3 \sqrt{1-c^2 x^2} \log (x)}{3 d \sqrt{d-c^2 d x^2}}+\frac{b c^3 \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{2 d \sqrt{d-c^2 d x^2}}","\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \sin ^{-1}(c x)\right)}{3 d x \sqrt{d-c^2 d x^2}}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3 \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{6 d^2 x^2 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 d^2 \sqrt{1-c^2 x^2}}+\frac{b c^3 \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{2 d^2 \sqrt{1-c^2 x^2}}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(6*d*x^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])/(3*d*x^3*Sqrt[d - c^2*d*x^2]) - (4*c^2*(a + b*ArcSin[c*x]))/(3*d*x*Sqrt[d - c^2*d*x^2]) + (8*c^4*x*(a + b*ArcSin[c*x]))/(3*d*Sqrt[d - c^2*d*x^2]) + (5*b*c^3*Sqrt[1 - c^2*x^2]*Log[x])/(3*d*Sqrt[d - c^2*d*x^2]) + (b*c^3*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(2*d*Sqrt[d - c^2*d*x^2])","A",11,8,27,0.2963,1,"{4701, 4653, 260, 266, 36, 29, 31, 44}"
129,1,293,0,0.4425039,"\int \frac{x^6 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","-\frac{5 x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^6 d^3}+\frac{5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^7 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^5 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b x^2 \sqrt{1-c^2 x^2}}{4 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b}{6 c^7 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{7 b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{6 c^7 d^2 \sqrt{d-c^2 d x^2}}","-\frac{5 x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^6 d^3}+\frac{5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c^7 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^5 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b x^2 \sqrt{1-c^2 x^2}}{4 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b}{6 c^7 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{7 b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{6 c^7 d^2 \sqrt{d-c^2 d x^2}}",1,"-b/(6*c^7*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (b*x^2*Sqrt[1 - c^2*x^2])/(4*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (x^5*(a + b*ArcSin[c*x]))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (5*x^3*(a + b*ArcSin[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (5*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*c^6*d^3) + (5*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c^7*d^2*Sqrt[d - c^2*d*x^2]) - (7*b*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(6*c^7*d^2*Sqrt[d - c^2*d*x^2])","A",12,7,27,0.2593,1,"{4703, 4707, 4643, 4641, 30, 266, 43}"
130,1,234,0,0.3161038,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","-\frac{4 x^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^6 d^3}+\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b x^3}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{5 b x \sqrt{1-c^2 x^2}}{6 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{11 b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 c^6 d^2 \sqrt{d-c^2 d x^2}}","-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^6 d^3}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{3 c^6 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b x \sqrt{d-c^2 d x^2}}{c^5 d^3 \sqrt{1-c^2 x^2}}-\frac{b x \sqrt{d-c^2 d x^2}}{6 c^5 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{11 b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{6 c^6 d^3 \sqrt{1-c^2 x^2}}",1,"-(b*x^3)/(6*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (5*b*x*Sqrt[1 - c^2*x^2])/(6*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcSin[c*x]))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (4*x^2*(a + b*ArcSin[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c^6*d^3) + (11*b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(6*c^6*d^2*Sqrt[d - c^2*d*x^2])","A",9,6,27,0.2222,1,"{4703, 4677, 8, 321, 206, 288}"
131,1,212,0,0.3023498,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{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}{2 b c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b}{6 c^5 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}","-\frac{x \left(a+b \sin ^{-1}(c x)\right)}{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}{2 b c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b}{6 c^5 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}",1,"-b/(6*c^5*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcSin[c*x]))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (x*(a + b*ArcSin[c*x]))/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c^5*d^2*Sqrt[d - c^2*d*x^2]) - (2*b*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2])","A",8,6,27,0.2222,1,"{4703, 4643, 4641, 260, 266, 43}"
132,1,155,0,0.1970915,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","-\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b x}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{5 b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 c^4 d^2 \sqrt{d-c^2 d x^2}}","-\frac{a+b \sin ^{-1}(c x)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{3 c^4 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b x \sqrt{d-c^2 d x^2}}{6 c^3 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{5 b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{6 c^4 d^3 \sqrt{1-c^2 x^2}}",1,"-(b*x)/(6*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x^2*(a + b*ArcSin[c*x]))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (2*(a + b*ArcSin[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (5*b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(6*c^4*d^2*Sqrt[d - c^2*d*x^2])","A",5,4,27,0.1481,1,"{4703, 4677, 206, 288}"
133,1,125,0,0.1306679,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}","\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b}{6 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}",1,"-b/(6*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcSin[c*x]))/(3*d*(d - c^2*d*x^2)^(3/2)) - (b*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(6*c^3*d^2*Sqrt[d - c^2*d*x^2])","A",4,3,27,0.1111,1,"{4681, 266, 43}"
134,1,119,0,0.080653,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{a+b \sin ^{-1}(c x)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b x}{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} \tanh ^{-1}(c x)}{6 c^2 d^2 \sqrt{d-c^2 d x^2}}","\frac{a+b \sin ^{-1}(c x)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b x}{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} \tanh ^{-1}(c x)}{6 c^2 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b*x)/(6*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (a + b*ArcSin[c*x])/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(6*c^2*d^2*Sqrt[d - c^2*d*x^2])","A",3,3,25,0.1200,1,"{4677, 199, 206}"
135,1,154,0,0.078979,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d - c^2*d*x^2)^(5/2),x]","\frac{2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b}{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} \log \left(1-c^2 x^2\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}","\frac{2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b}{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} \log \left(1-c^2 x^2\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}",1,"-b/(6*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x*(a + b*ArcSin[c*x]))/(3*d*(d - c^2*d*x^2)^(3/2)) + (2*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(3*c*d^2*Sqrt[d - c^2*d*x^2])","A",4,4,24,0.1667,1,"{4655, 4653, 260, 261}"
136,1,291,0,0.4368442,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d - c^2*d*x^2)^(5/2)),x]","\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c x}{6 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{7 b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}","\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \sin ^{-1}(c x)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c x}{6 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{7 b \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b*c*x)/(6*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (a + b*ArcSin[c*x])/(3*d*(d - c^2*d*x^2)^(3/2)) + (a + b*ArcSin[c*x])/(d^2*Sqrt[d - c^2*d*x^2]) - (2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (7*b*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(6*d^2*Sqrt[d - c^2*d*x^2]) + (I*b*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (I*b*Sqrt[1 - c^2*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2])","A",12,8,27,0.2963,1,"{4705, 4713, 4709, 4183, 2279, 2391, 206, 199}"
137,1,224,0,0.2195032,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d - c^2*d*x^2)^(5/2)),x]","\frac{8 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c}{6 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{1-c^2 x^2} \log (x)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 b c \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{6 d^2 \sqrt{d-c^2 d x^2}}","\frac{8 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c \sqrt{d-c^2 d x^2}}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{d^3 \sqrt{1-c^2 x^2}}+\frac{5 b c \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{6 d^3 \sqrt{1-c^2 x^2}}",1,"-(b*c)/(6*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])/(d*x*(d - c^2*d*x^2)^(3/2)) + (4*c^2*x*(a + b*ArcSin[c*x]))/(3*d*(d - c^2*d*x^2)^(3/2)) + (8*c^2*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[1 - c^2*x^2]*Log[x])/(d^2*Sqrt[d - c^2*d*x^2]) + (5*b*c*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(6*d^2*Sqrt[d - c^2*d*x^2])","A",8,7,27,0.2593,1,"{4701, 4655, 4653, 260, 261, 266, 44}"
138,1,433,0,0.5822064,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d - c^2*d*x^2)^(5/2)),x]","\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)}{6 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2 \left(d-c^2 d x^2\right)^{3/2}}-\frac{5 b c^3 x}{12 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{3 b c \sqrt{1-c^2 x^2}}{4 d^2 x \sqrt{d-c^2 d x^2}}+\frac{b c}{4 d^2 x \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{13 b c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}","\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)}{6 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2 \left(d-c^2 d x^2\right)^{3/2}}-\frac{5 b c^3 x}{12 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{3 b c \sqrt{1-c^2 x^2}}{4 d^2 x \sqrt{d-c^2 d x^2}}+\frac{b c}{4 d^2 x \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{13 b c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}",1,"(b*c)/(4*d^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (5*b*c^3*x)/(12*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (3*b*c*Sqrt[1 - c^2*x^2])/(4*d^2*x*Sqrt[d - c^2*d*x^2]) + (5*c^2*(a + b*ArcSin[c*x]))/(6*d*(d - c^2*d*x^2)^(3/2)) - (a + b*ArcSin[c*x])/(2*d*x^2*(d - c^2*d*x^2)^(3/2)) + (5*c^2*(a + b*ArcSin[c*x]))/(2*d^2*Sqrt[d - c^2*d*x^2]) - (5*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (13*b*c^2*Sqrt[1 - c^2*x^2]*ArcTanh[c*x])/(6*d^2*Sqrt[d - c^2*d*x^2]) + (((5*I)/2)*b*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (((5*I)/2)*b*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2])","A",16,11,27,0.4074,1,"{4701, 4705, 4713, 4709, 4183, 2279, 2391, 206, 199, 290, 325}"
139,1,310,0,0.3870392,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*(d - c^2*d*x^2)^(5/2)),x]","\frac{16 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 c^2 \left(a+b \sin ^{-1}(c x)\right)}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3 \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c^3}{6 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2}}{6 d^2 x^2 \sqrt{d-c^2 d x^2}}+\frac{8 b c^3 \sqrt{1-c^2 x^2} \log (x)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 b c^3 \sqrt{1-c^2 x^2} \log \left(1-c^2 x^2\right)}{3 d^2 \sqrt{d-c^2 d x^2}}","\frac{16 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 c^2 \left(a+b \sin ^{-1}(c x)\right)}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3 \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c^3 \sqrt{d-c^2 d x^2}}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{b c \sqrt{d-c^2 d x^2}}{6 d^3 x^2 \sqrt{1-c^2 x^2}}+\frac{8 b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 d^3 \sqrt{1-c^2 x^2}}+\frac{4 b c^3 \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{3 d^3 \sqrt{1-c^2 x^2}}",1,"-(b*c^3)/(6*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[1 - c^2*x^2])/(6*d^2*x^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])/(3*d*x^3*(d - c^2*d*x^2)^(3/2)) - (2*c^2*(a + b*ArcSin[c*x]))/(d*x*(d - c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*ArcSin[c*x]))/(3*d*(d - c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) + (8*b*c^3*Sqrt[1 - c^2*x^2]*Log[x])/(3*d^2*Sqrt[d - c^2*d*x^2]) + (4*b*c^3*Sqrt[1 - c^2*x^2]*Log[1 - c^2*x^2])/(3*d^2*Sqrt[d - c^2*d*x^2])","A",12,7,27,0.2593,1,"{4701, 4655, 4653, 260, 261, 266, 44}"
140,1,210,0,0.1153128,"\int \frac{\sin ^{-1}(a x)}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSin[a*x]/(c - a^2*c*x^2)^(7/2),x]","-\frac{2}{15 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}-\frac{1}{20 a c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{1-a^2 x^2} \log \left(1-a^2 x^2\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \sin ^{-1}(a x)}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \sin ^{-1}(a x)}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x \sin ^{-1}(a x)}{5 c \left(c-a^2 c x^2\right)^{5/2}}","-\frac{2}{15 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}-\frac{1}{20 a c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{1-a^2 x^2} \log \left(1-a^2 x^2\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \sin ^{-1}(a x)}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \sin ^{-1}(a x)}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x \sin ^{-1}(a x)}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"-1/(20*a*c^3*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]) - 2/(15*a*c^3*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x])/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*ArcSin[a*x])/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*ArcSin[a*x])/(15*c^3*Sqrt[c - a^2*c*x^2]) + (4*Sqrt[1 - a^2*x^2]*Log[1 - a^2*x^2])/(15*a*c^3*Sqrt[c - a^2*c*x^2])","A",6,4,20,0.2000,1,"{4655, 4653, 260, 261}"
141,1,79,0,0.1022761,"\int \frac{(f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((f*x)^(3/2)*(a + b*ArcSin[c*x]))/Sqrt[1 - c^2*x^2],x]","\frac{2 (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{5 f}-\frac{4 b c (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2}","\frac{2 (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{5 f}-\frac{4 b c (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2}",1,"(2*(f*x)^(5/2)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(5*f) - (4*b*c*(f*x)^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(35*f^2)","A",1,1,30,0.03333,1,"{4711}"
142,1,137,0,0.216347,"\int \frac{(f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f*x)^(3/2)*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{2 \sqrt{1-c^2 x^2} (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{5 f \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{1-c^2 x^2} (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2 \sqrt{d-c^2 d x^2}}","\frac{2 \sqrt{1-c^2 x^2} (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{5 f \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{1-c^2 x^2} (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2 \sqrt{d-c^2 d x^2}}",1,"(2*(f*x)^(5/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(5*f*Sqrt[d - c^2*d*x^2]) - (4*b*c*(f*x)^(7/2)*Sqrt[1 - c^2*x^2]*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(35*f^2*Sqrt[d - c^2*d*x^2])","A",2,2,31,0.06452,1,"{4713, 4711}"
143,1,315,0,2.1644304,"\int x^m \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^m*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x]),x]","-\frac{3 c^2 d^3 x^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{m+3}+\frac{3 c^4 d^3 x^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{m+5}-\frac{c^6 d^3 x^{m+7} \left(a+b \sin ^{-1}(c x)\right)}{m+7}+\frac{d^3 x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{m+1}-\frac{3 b c d^3 \left(35 m^3+455 m^2+1813 m+2161\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2 (m+7)^2}-\frac{b c d^3 \left(m^4+27 m^3+284 m^2+1329 m+2271\right) \sqrt{1-c^2 x^2} x^{m+2}}{(m+3)^2 (m+5)^2 (m+7)^2}+\frac{b c^3 d^3 (m+9) (2 m+13) \sqrt{1-c^2 x^2} x^{m+4}}{(m+5)^2 (m+7)^2}-\frac{b c^5 d^3 \sqrt{1-c^2 x^2} x^{m+6}}{(m+7)^2}","-\frac{3 c^2 d^3 x^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{m+3}+\frac{3 c^4 d^3 x^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{m+5}-\frac{c^6 d^3 x^{m+7} \left(a+b \sin ^{-1}(c x)\right)}{m+7}+\frac{d^3 x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{m+1}-\frac{3 b c d^3 \left(35 m^3+455 m^2+1813 m+2161\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2 (m+7)^2}-\frac{b c d^3 \left(m^4+27 m^3+284 m^2+1329 m+2271\right) \sqrt{1-c^2 x^2} x^{m+2}}{(m+3)^2 (m+5)^2 (m+7)^2}+\frac{b c^3 d^3 (m+9) (2 m+13) \sqrt{1-c^2 x^2} x^{m+4}}{(m+5)^2 (m+7)^2}-\frac{b c^5 d^3 \sqrt{1-c^2 x^2} x^{m+6}}{(m+7)^2}",1,"-((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*x^(2 + m)*Sqrt[1 - c^2*x^2])/((3 + m)^2*(5 + m)^2*(7 + m)^2)) + (b*c^3*d^3*(9 + m)*(13 + 2*m)*x^(4 + m)*Sqrt[1 - c^2*x^2])/((5 + m)^2*(7 + m)^2) - (b*c^5*d^3*x^(6 + m)*Sqrt[1 - c^2*x^2])/(7 + m)^2 + (d^3*x^(1 + m)*(a + b*ArcSin[c*x]))/(1 + m) - (3*c^2*d^3*x^(3 + m)*(a + b*ArcSin[c*x]))/(3 + m) + (3*c^4*d^3*x^(5 + m)*(a + b*ArcSin[c*x]))/(5 + m) - (c^6*d^3*x^(7 + m)*(a + b*ArcSin[c*x]))/(7 + m) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/((1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*(7 + m)^2)","A",6,7,25,0.2800,1,"{270, 4687, 12, 1809, 1267, 459, 364}"
144,1,217,0,0.3063295,"\int x^m \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^m*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x]),x]","-\frac{2 c^2 d^2 x^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{m+3}+\frac{c^4 d^2 x^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{m+5}+\frac{d^2 x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{m+1}-\frac{b c d^2 \left(15 m^2+100 m+149\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2}-\frac{b c d^2 \left(m^2+13 m+38\right) \sqrt{1-c^2 x^2} x^{m+2}}{(m+3)^2 (m+5)^2}+\frac{b c^3 d^2 \sqrt{1-c^2 x^2} x^{m+4}}{(m+5)^2}","-\frac{2 c^2 d^2 x^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{m+3}+\frac{c^4 d^2 x^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{m+5}+\frac{d^2 x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{m+1}-\frac{b c d^2 \left(15 m^2+100 m+149\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2}-\frac{b c d^2 \left(m^2+13 m+38\right) \sqrt{1-c^2 x^2} x^{m+2}}{(m+3)^2 (m+5)^2}+\frac{b c^3 d^2 \sqrt{1-c^2 x^2} x^{m+4}}{(m+5)^2}",1,"-((b*c*d^2*(38 + 13*m + m^2)*x^(2 + m)*Sqrt[1 - c^2*x^2])/((3 + m)^2*(5 + m)^2)) + (b*c^3*d^2*x^(4 + m)*Sqrt[1 - c^2*x^2])/(5 + m)^2 + (d^2*x^(1 + m)*(a + b*ArcSin[c*x]))/(1 + m) - (2*c^2*d^2*x^(3 + m)*(a + b*ArcSin[c*x]))/(3 + m) + (c^4*d^2*x^(5 + m)*(a + b*ArcSin[c*x]))/(5 + m) - (b*c*d^2*(149 + 100*m + 15*m^2)*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/((1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2)","A",5,6,25,0.2400,1,"{270, 4687, 12, 1267, 459, 364}"
145,1,129,0,0.1410781,"\int x^m \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^m*(d - c^2*d*x^2)*(a + b*ArcSin[c*x]),x]","-\frac{c^2 d x^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{m+3}+\frac{d x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{m+1}-\frac{b c d (3 m+7) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+1) (m+2) (m+3)^2}-\frac{b c d \sqrt{1-c^2 x^2} x^{m+2}}{(m+3)^2}","-\frac{c^2 d x^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{m+3}+\frac{d x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{m+1}-\frac{b c d (3 m+7) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+1) (m+2) (m+3)^2}-\frac{b c d \sqrt{1-c^2 x^2} x^{m+2}}{(m+3)^2}",1,"-((b*c*d*x^(2 + m)*Sqrt[1 - c^2*x^2])/(3 + m)^2) + (d*x^(1 + m)*(a + b*ArcSin[c*x]))/(1 + m) - (c^2*d*x^(3 + m)*(a + b*ArcSin[c*x]))/(3 + m) - (b*c*d*(7 + 3*m)*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/((1 + m)*(2 + m)*(3 + m)^2)","A",4,5,23,0.2174,1,"{14, 4687, 12, 459, 364}"
146,0,0,0,0.0644057,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2),x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2), x]","A",0,0,0,0,-1,"{}"
147,0,0,0,0.1553575,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^2,x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","\frac{(1-m) \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2},x\right)}{2 d}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{b c x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{2 d^2 (m+2)}",0,"(x^(1 + m)*(a + b*ArcSin[c*x]))/(2*d^2*(1 - c^2*x^2)) - (b*c*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(2*d^2*(2 + m)) + ((1 - m)*Defer[Int][(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2), x])/(2*d)","A",0,0,0,0,-1,"{}"
148,0,0,0,0.2484242,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^3,x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","\frac{(1-m) (3-m) \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{d-c^2 d x^2},x\right)}{8 d^2}+\frac{(3-m) x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b c (3-m) x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{8 d^3 (m+2)}-\frac{b c x^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{4 d^3 (m+2)}",0,"(x^(1 + m)*(a + b*ArcSin[c*x]))/(4*d^3*(1 - c^2*x^2)^2) + ((3 - m)*x^(1 + m)*(a + b*ArcSin[c*x]))/(8*d^3*(1 - c^2*x^2)) - (b*c*(3 - m)*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(8*d^3*(2 + m)) - (b*c*x^(2 + m)*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(4*d^3*(2 + m)) + ((1 - m)*(3 - m)*Defer[Int][(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2), x])/(8*d^2)","A",0,0,0,0,-1,"{}"
149,1,635,0,0.5585132,"\int x^m \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^m*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]),x]","-\frac{15 b c d^2 x^{m+2} \sqrt{d-c^2 d x^2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{(m+1) (m+2)^2 (m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{15 d^2 x^{m+1} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+6) \left(m^3+7 m^2+14 m+8\right) \sqrt{1-c^2 x^2}}+\frac{15 d^2 x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{(m+6) \left(m^2+6 m+8\right)}+\frac{x^{m+1} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{m+6}+\frac{5 d x^{m+1} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{(m+4) (m+6)}-\frac{5 b c d^2 x^{m+2} \sqrt{d-c^2 d x^2}}{(m+6) \left(m^2+6 m+8\right) \sqrt{1-c^2 x^2}}-\frac{b c d^2 x^{m+2} \sqrt{d-c^2 d x^2}}{\left(m^2+8 m+12\right) \sqrt{1-c^2 x^2}}-\frac{15 b c d^2 x^{m+2} \sqrt{d-c^2 d x^2}}{(m+2)^2 (m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d^2 x^{m+4} \sqrt{d-c^2 d x^2}}{(m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d^2 x^{m+4} \sqrt{d-c^2 d x^2}}{(m+4)^2 (m+6) \sqrt{1-c^2 x^2}}-\frac{b c^5 d^2 x^{m+6} \sqrt{d-c^2 d x^2}}{(m+6)^2 \sqrt{1-c^2 x^2}}","-\frac{15 b c d^2 x^{m+2} \sqrt{d-c^2 d x^2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{(m+1) (m+2)^2 (m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{15 d^2 x^{m+1} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+6) \left(m^3+7 m^2+14 m+8\right) \sqrt{1-c^2 x^2}}+\frac{15 d^2 x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{(m+6) \left(m^2+6 m+8\right)}+\frac{x^{m+1} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{m+6}+\frac{5 d x^{m+1} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{(m+4) (m+6)}-\frac{5 b c d^2 x^{m+2} \sqrt{d-c^2 d x^2}}{(m+6) \left(m^2+6 m+8\right) \sqrt{1-c^2 x^2}}-\frac{b c d^2 x^{m+2} \sqrt{d-c^2 d x^2}}{\left(m^2+8 m+12\right) \sqrt{1-c^2 x^2}}-\frac{15 b c d^2 x^{m+2} \sqrt{d-c^2 d x^2}}{(m+2)^2 (m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d^2 x^{m+4} \sqrt{d-c^2 d x^2}}{(m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{5 b c^3 d^2 x^{m+4} \sqrt{d-c^2 d x^2}}{(m+4)^2 (m+6) \sqrt{1-c^2 x^2}}-\frac{b c^5 d^2 x^{m+6} \sqrt{d-c^2 d x^2}}{(m+6)^2 \sqrt{1-c^2 x^2}}",1,"(-15*b*c*d^2*x^(2 + m)*Sqrt[d - c^2*d*x^2])/((2 + m)^2*(4 + m)*(6 + m)*Sqrt[1 - c^2*x^2]) - (5*b*c*d^2*x^(2 + m)*Sqrt[d - c^2*d*x^2])/((6 + m)*(8 + 6*m + m^2)*Sqrt[1 - c^2*x^2]) - (b*c*d^2*x^(2 + m)*Sqrt[d - c^2*d*x^2])/((12 + 8*m + m^2)*Sqrt[1 - c^2*x^2]) + (5*b*c^3*d^2*x^(4 + m)*Sqrt[d - c^2*d*x^2])/((4 + m)^2*(6 + m)*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d^2*x^(4 + m)*Sqrt[d - c^2*d*x^2])/((4 + m)*(6 + m)*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^(6 + m)*Sqrt[d - c^2*d*x^2])/((6 + m)^2*Sqrt[1 - c^2*x^2]) + (15*d^2*x^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/((6 + m)*(8 + 6*m + m^2)) + (5*d*x^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/((4 + m)*(6 + m)) + (x^(1 + m)*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(6 + m) + (15*d^2*x^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/((6 + m)*(8 + 14*m + 7*m^2 + m^3)*Sqrt[1 - c^2*x^2]) - (15*b*c*d^2*x^(2 + m)*Sqrt[d - c^2*d*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/((1 + m)*(2 + m)^2*(4 + m)*(6 + m)*Sqrt[1 - c^2*x^2])","A",9,6,27,0.2222,1,"{4699, 4697, 4711, 30, 14, 270}"
150,1,399,0,0.332184,"\int x^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^m*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]),x]","-\frac{3 b c d x^{m+2} \sqrt{d-c^2 d x^2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{(m+1) (m+2)^2 (m+4) \sqrt{1-c^2 x^2}}+\frac{3 d x^{m+1} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{\left(m^3+7 m^2+14 m+8\right) \sqrt{1-c^2 x^2}}+\frac{3 d x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{m^2+6 m+8}+\frac{x^{m+1} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{m+4}-\frac{b c d x^{m+2} \sqrt{d-c^2 d x^2}}{\left(m^2+6 m+8\right) \sqrt{1-c^2 x^2}}-\frac{3 b c d x^{m+2} \sqrt{d-c^2 d x^2}}{(m+2)^2 (m+4) \sqrt{1-c^2 x^2}}+\frac{b c^3 d x^{m+4} \sqrt{d-c^2 d x^2}}{(m+4)^2 \sqrt{1-c^2 x^2}}","-\frac{3 b c d x^{m+2} \sqrt{d-c^2 d x^2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{(m+1) (m+2)^2 (m+4) \sqrt{1-c^2 x^2}}+\frac{3 d x^{m+1} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{\left(m^3+7 m^2+14 m+8\right) \sqrt{1-c^2 x^2}}+\frac{3 d x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{m^2+6 m+8}+\frac{x^{m+1} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{m+4}-\frac{b c d x^{m+2} \sqrt{d-c^2 d x^2}}{\left(m^2+6 m+8\right) \sqrt{1-c^2 x^2}}-\frac{3 b c d x^{m+2} \sqrt{d-c^2 d x^2}}{(m+2)^2 (m+4) \sqrt{1-c^2 x^2}}+\frac{b c^3 d x^{m+4} \sqrt{d-c^2 d x^2}}{(m+4)^2 \sqrt{1-c^2 x^2}}",1,"(-3*b*c*d*x^(2 + m)*Sqrt[d - c^2*d*x^2])/((2 + m)^2*(4 + m)*Sqrt[1 - c^2*x^2]) - (b*c*d*x^(2 + m)*Sqrt[d - c^2*d*x^2])/((8 + 6*m + m^2)*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^(4 + m)*Sqrt[d - c^2*d*x^2])/((4 + m)^2*Sqrt[1 - c^2*x^2]) + (3*d*x^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8 + 6*m + m^2) + (x^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(4 + m) + (3*d*x^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/((8 + 14*m + 7*m^2 + m^3)*Sqrt[1 - c^2*x^2]) - (3*b*c*d*x^(2 + m)*Sqrt[d - c^2*d*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/((1 + m)*(2 + m)^2*(4 + m)*Sqrt[1 - c^2*x^2])","A",6,5,27,0.1852,1,"{4699, 4697, 4711, 30, 14}"
151,1,245,0,0.2021243,"\int x^m \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^m*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]),x]","-\frac{b c x^{m+2} \sqrt{d-c^2 d x^2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{(m+1) (m+2)^2 \sqrt{1-c^2 x^2}}+\frac{x^{m+1} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{\left(m^2+3 m+2\right) \sqrt{1-c^2 x^2}}+\frac{x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{m+2}-\frac{b c x^{m+2} \sqrt{d-c^2 d x^2}}{(m+2)^2 \sqrt{1-c^2 x^2}}","-\frac{b c x^{m+2} \sqrt{d-c^2 d x^2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{(m+1) (m+2)^2 \sqrt{1-c^2 x^2}}+\frac{x^{m+1} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{\left(m^2+3 m+2\right) \sqrt{1-c^2 x^2}}+\frac{x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{m+2}-\frac{b c x^{m+2} \sqrt{d-c^2 d x^2}}{(m+2)^2 \sqrt{1-c^2 x^2}}",1,"-((b*c*x^(2 + m)*Sqrt[d - c^2*d*x^2])/((2 + m)^2*Sqrt[1 - c^2*x^2])) + (x^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2 + m) + (x^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/((2 + 3*m + m^2)*Sqrt[1 - c^2*x^2]) - (b*c*x^(2 + m)*Sqrt[d - c^2*d*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/((1 + m)*(2 + m)^2*Sqrt[1 - c^2*x^2])","A",3,3,27,0.1111,1,"{4697, 4711, 30}"
152,1,163,0,0.1967264,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^m*(a + b*ArcSin[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{\sqrt{1-c^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+1) \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{\left(m^2+3 m+2\right) \sqrt{d-c^2 d x^2}}","\frac{\sqrt{1-c^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+1) \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{\left(m^2+3 m+2\right) \sqrt{d-c^2 d x^2}}",1,"(x^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/((1 + m)*Sqrt[d - c^2*d*x^2]) - (b*c*x^(2 + m)*Sqrt[1 - c^2*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/((2 + 3*m + m^2)*Sqrt[d - c^2*d*x^2])","A",2,2,27,0.07407,1,"{4713, 4711}"
153,1,272,0,0.3149286,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{b c m \sqrt{1-c^2 x^2} x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{d \left(m^2+3 m+2\right) \sqrt{d-c^2 d x^2}}-\frac{m \sqrt{1-c^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{d (m+1) \sqrt{d-c^2 d x^2}}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d (m+2) \sqrt{d-c^2 d x^2}}","\frac{b c m \sqrt{1-c^2 x^2} x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{d \left(m^2+3 m+2\right) \sqrt{d-c^2 d x^2}}-\frac{m \sqrt{1-c^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{d (m+1) \sqrt{d-c^2 d x^2}}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d (m+2) \sqrt{d-c^2 d x^2}}",1,"(x^(1 + m)*(a + b*ArcSin[c*x]))/(d*Sqrt[d - c^2*d*x^2]) - (m*x^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(d*(1 + m)*Sqrt[d - c^2*d*x^2]) - (b*c*x^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d*(2 + m)*Sqrt[d - c^2*d*x^2]) + (b*c*m*x^(2 + m)*Sqrt[1 - c^2*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(d*(2 + 3*m + m^2)*Sqrt[d - c^2*d*x^2])","A",4,4,27,0.1481,1,"{4705, 4713, 4711, 364}"
154,1,408,0,0.454834,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^m*(a + b*ArcSin[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{b c (2-m) m \sqrt{1-c^2 x^2} x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{3 d^2 \left(m^2+3 m+2\right) \sqrt{d-c^2 d x^2}}-\frac{(2-m) m \sqrt{1-c^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 (m+1) \sqrt{d-c^2 d x^2}}+\frac{(2-m) x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c (2-m) \sqrt{1-c^2 x^2} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 (m+2) \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 (m+2) \sqrt{d-c^2 d x^2}}","\frac{b c (2-m) m \sqrt{1-c^2 x^2} x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{3 d^2 \left(m^2+3 m+2\right) \sqrt{d-c^2 d x^2}}-\frac{(2-m) m \sqrt{1-c^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 (m+1) \sqrt{d-c^2 d x^2}}+\frac{(2-m) x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c (2-m) \sqrt{1-c^2 x^2} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 (m+2) \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 (m+2) \sqrt{d-c^2 d x^2}}",1,"(x^(1 + m)*(a + b*ArcSin[c*x]))/(3*d*(d - c^2*d*x^2)^(3/2)) + ((2 - m)*x^(1 + m)*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) - ((2 - m)*m*x^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(3*d^2*(1 + m)*Sqrt[d - c^2*d*x^2]) - (b*c*(2 - m)*x^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(3*d^2*(2 + m)*Sqrt[d - c^2*d*x^2]) - (b*c*x^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(3*d^2*(2 + m)*Sqrt[d - c^2*d*x^2]) + (b*c*(2 - m)*m*x^(2 + m)*Sqrt[1 - c^2*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(3*d^2*(2 + 3*m + m^2)*Sqrt[d - c^2*d*x^2])","A",6,4,27,0.1481,1,"{4705, 4713, 4711, 364}"
155,1,100,0,0.0699534,"\int \frac{x^m \sin ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^m*ArcSin[a*x])/Sqrt[1 - a^2*x^2],x]","\frac{x^{m+1} \sin ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}-\frac{a x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;a^2 x^2\right)}{m^2+3 m+2}","\frac{x^{m+1} \sin ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}-\frac{a x^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;a^2 x^2\right)}{m^2+3 m+2}",1,"(x^(1 + m)*ArcSin[a*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) - (a*x^(2 + m)*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, a^2*x^2])/(2 + 3*m + m^2)","A",1,1,22,0.04545,1,"{4711}"
156,1,290,0,0.4611448,"\int x^4 \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^4*(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2,x]","\frac{1}{7} d x^5 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4 b d x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{175 c}+\frac{16 b d x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{525 c^3}+\frac{2 b d \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{49 c^5}-\frac{4 b d \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{35 c^5}+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{21 c^5}+\frac{32 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{525 c^5}+\frac{2}{35} d x^5 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^2 d x^7-\frac{152 b^2 d x^3}{11025 c^2}-\frac{304 b^2 d x}{3675 c^4}-\frac{38 b^2 d x^5}{6125}","\frac{1}{7} d x^5 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4 b d x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{175 c}+\frac{16 b d x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{525 c^3}+\frac{2 b d \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{49 c^5}-\frac{4 b d \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{35 c^5}+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{21 c^5}+\frac{32 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{525 c^5}+\frac{2}{35} d x^5 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^2 d x^7-\frac{152 b^2 d x^3}{11025 c^2}-\frac{304 b^2 d x}{3675 c^4}-\frac{38 b^2 d x^5}{6125}",1,"(-304*b^2*d*x)/(3675*c^4) - (152*b^2*d*x^3)/(11025*c^2) - (38*b^2*d*x^5)/6125 + (2*b^2*c^2*d*x^7)/343 + (32*b*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(525*c^5) + (16*b*d*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(525*c^3) + (4*b*d*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(175*c) + (2*b*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(21*c^5) - (4*b*d*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(35*c^5) + (2*b*d*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(49*c^5) + (2*d*x^5*(a + b*ArcSin[c*x])^2)/35 + (d*x^5*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/7","A",11,10,25,0.4000,1,"{4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12}"
157,1,202,0,0.5373955,"\int x^3 \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2,x]","-\frac{1}{18} b c d x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} d x^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{b d x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{12 c^3}-\frac{d \left(a+b \sin ^{-1}(c x)\right)^2}{24 c^4}+\frac{1}{12} d x^4 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{108} b^2 c^2 d x^6-\frac{b^2 d x^2}{24 c^2}-\frac{1}{72} b^2 d x^4","-\frac{1}{18} b c d x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} d x^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{b d x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{12 c^3}-\frac{d \left(a+b \sin ^{-1}(c x)\right)^2}{24 c^4}+\frac{1}{12} d x^4 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{108} b^2 c^2 d x^6-\frac{b^2 d x^2}{24 c^2}-\frac{1}{72} b^2 d x^4",1,"-(b^2*d*x^2)/(24*c^2) - (b^2*d*x^4)/72 + (b^2*c^2*d*x^6)/108 + (b*d*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(12*c^3) + (b*d*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(18*c) - (b*c*d*x^5*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/18 - (d*(a + b*ArcSin[c*x])^2)/(24*c^4) + (d*x^4*(a + b*ArcSin[c*x])^2)/12 + (d*x^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/6","A",14,6,25,0.2400,1,"{4699, 4627, 4707, 4641, 30, 4697}"
158,1,211,0,0.3374799,"\int x^2 \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2,x]","\frac{1}{5} d x^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4 b d x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c}-\frac{2 b d \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{25 c^3}+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 c^3}+\frac{8 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c^3}+\frac{2}{15} d x^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{125} b^2 c^2 d x^5-\frac{52 b^2 d x}{225 c^2}-\frac{26}{675} b^2 d x^3","\frac{1}{5} d x^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4 b d x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c}-\frac{2 b d \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{25 c^3}+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 c^3}+\frac{8 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c^3}+\frac{2}{15} d x^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{125} b^2 c^2 d x^5-\frac{52 b^2 d x}{225 c^2}-\frac{26}{675} b^2 d x^3",1,"(-52*b^2*d*x)/(225*c^2) - (26*b^2*d*x^3)/675 + (2*b^2*c^2*d*x^5)/125 + (8*b*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(45*c^3) + (4*b*d*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(45*c) + (2*b*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(15*c^3) - (2*b*d*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(25*c^3) + (2*d*x^3*(a + b*ArcSin[c*x])^2)/15 + (d*x^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/5","A",9,10,25,0.4000,1,"{4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12}"
159,1,138,0,0.1327235,"\int x \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2,x]","\frac{b d x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b d x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c}-\frac{d \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{3 d \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^2}+\frac{1}{32} b^2 c^2 d x^4-\frac{5}{32} b^2 d x^2","\frac{b d x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{3 b d x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c}-\frac{d \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2}+\frac{3 d \left(a+b \sin ^{-1}(c x)\right)^2}{32 c^2}+\frac{1}{32} b^2 c^2 d x^4-\frac{5}{32} b^2 d x^2",1,"(-5*b^2*d*x^2)/32 + (b^2*c^2*d*x^4)/32 + (3*b*d*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(16*c) + (b*d*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(8*c) + (3*d*(a + b*ArcSin[c*x])^2)/(32*c^2) - (d*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(4*c^2)","A",7,6,23,0.2609,1,"{4677, 4649, 4647, 4641, 30, 14}"
160,1,128,0,0.1372812,"\int \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2,x]","\frac{1}{3} d x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{2}{3} d x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{27} b^2 c^2 d x^3-\frac{14}{9} b^2 d x","\frac{1}{3} d x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{2}{3} d x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{27} b^2 c^2 d x^3-\frac{14}{9} b^2 d x",1,"(-14*b^2*d*x)/9 + (2*b^2*c^2*d*x^3)/27 + (4*b*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c) + (2*b*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(9*c) + (2*d*x*(a + b*ArcSin[c*x])^2)/3 + (d*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/3","A",6,4,22,0.1818,1,"{4649, 4619, 4677, 8}"
161,1,178,0,0.2382549,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2)/x,x]","-i b d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 d \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{2} d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{2} b c d x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{i d \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{1}{4} d \left(a+b \sin ^{-1}(c x)\right)^2+d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} b^2 c^2 d x^2","-i b d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 d \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)+\frac{1}{2} d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{2} b c d x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{i d \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{1}{4} d \left(a+b \sin ^{-1}(c x)\right)^2+d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} b^2 c^2 d x^2",1,"(b^2*c^2*d*x^2)/4 - (b*c*d*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/2 - (d*(a + b*ArcSin[c*x])^2)/4 + (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/2 - ((I/3)*d*(a + b*ArcSin[c*x])^3)/b + d*(a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] - I*b*d*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] + (b^2*d*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2","A",10,10,25,0.4000,1,"{4699, 4625, 3717, 2190, 2531, 2282, 6589, 4647, 4641, 30}"
162,1,149,0,0.2979926,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2)/x^2,x]","2 i b^2 c d \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c d \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-2 b c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x}-2 c^2 d x \left(a+b \sin ^{-1}(c x)\right)^2-4 b c d \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+2 b^2 c^2 d x","2 i b^2 c d \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c d \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-2 b c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x}-2 c^2 d x \left(a+b \sin ^{-1}(c x)\right)^2-4 b c d \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+2 b^2 c^2 d x",1,"2*b^2*c^2*d*x - 2*b*c*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]) - 2*c^2*d*x*(a + b*ArcSin[c*x])^2 - (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/x - 4*b*c*d*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])] + (2*I)*b^2*c*d*PolyLog[2, -E^(I*ArcSin[c*x])] - (2*I)*b^2*c*d*PolyLog[2, E^(I*ArcSin[c*x])]","A",12,9,25,0.3600,1,"{4695, 4619, 4677, 8, 4697, 4709, 4183, 2279, 2391}"
163,1,193,0,0.2866968,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2)/x^3,x]","i b c^2 d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{2} b^2 c^2 d \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{i c^2 d \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{1}{2} c^2 d \left(a+b \sin ^{-1}(c x)\right)^2-c^2 d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+b^2 c^2 d \log (x)","i b c^2 d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{2} b^2 c^2 d \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{x}+\frac{i c^2 d \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{1}{2} c^2 d \left(a+b \sin ^{-1}(c x)\right)^2-c^2 d \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+b^2 c^2 d \log (x)",1,"-((b*c*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/x) - (c^2*d*(a + b*ArcSin[c*x])^2)/2 - (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*x^2) + ((I/3)*c^2*d*(a + b*ArcSin[c*x])^3)/b - c^2*d*(a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] + b^2*c^2*d*Log[x] + I*b*c^2*d*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] - (b^2*c^2*d*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2","A",10,10,25,0.4000,1,"{4695, 4625, 3717, 2190, 2531, 2282, 6589, 4693, 29, 4641}"
164,1,176,0,0.3767321,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2)/x^4,x]","-\frac{5}{3} i b^2 c^3 d \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)+\frac{5}{3} i b^2 c^3 d \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\frac{b c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}+\frac{2 c^2 d \left(a+b \sin ^{-1}(c x)\right)^2}{3 x}+\frac{10}{3} b c^3 d \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{b^2 c^2 d}{3 x}","-\frac{5}{3} i b^2 c^3 d \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)+\frac{5}{3} i b^2 c^3 d \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\frac{b c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}+\frac{2 c^2 d \left(a+b \sin ^{-1}(c x)\right)^2}{3 x}+\frac{10}{3} b c^3 d \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{b^2 c^2 d}{3 x}",1,"-(b^2*c^2*d)/(3*x) - (b*c*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*x^2) + (2*c^2*d*(a + b*ArcSin[c*x])^2)/(3*x) - (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*x^3) + (10*b*c^3*d*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/3 - ((5*I)/3)*b^2*c^3*d*PolyLog[2, -E^(I*ArcSin[c*x])] + ((5*I)/3)*b^2*c^3*d*PolyLog[2, E^(I*ArcSin[c*x])]","A",16,8,25,0.3200,1,"{4695, 4627, 4709, 4183, 2279, 2391, 4693, 30}"
165,1,395,0,0.7242351,"\int x^4 \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^4*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2,x]","\frac{1}{9} d^2 x^5 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4}{63} d^2 x^5 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{1575 c}+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{4725 c^3}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{81 c^5}-\frac{20 b d^2 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{441 c^5}-\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{315 c^5}+\frac{8 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{189 c^5}+\frac{128 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{4725 c^5}+\frac{8}{315} d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2104 b^2 d^2 x^3}{297675 c^2}-\frac{4208 b^2 d^2 x}{99225 c^4}-\frac{526 b^2 d^2 x^5}{165375}","\frac{1}{9} d^2 x^5 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4}{63} d^2 x^5 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{16 b d^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{1575 c}+\frac{64 b d^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{4725 c^3}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{81 c^5}-\frac{20 b d^2 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{441 c^5}-\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{315 c^5}+\frac{8 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{189 c^5}+\frac{128 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{4725 c^5}+\frac{8}{315} d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{729} b^2 c^4 d^2 x^9+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2104 b^2 d^2 x^3}{297675 c^2}-\frac{4208 b^2 d^2 x}{99225 c^4}-\frac{526 b^2 d^2 x^5}{165375}",1,"(-4208*b^2*d^2*x)/(99225*c^4) - (2104*b^2*d^2*x^3)/(297675*c^2) - (526*b^2*d^2*x^5)/165375 + (212*b^2*c^2*d^2*x^7)/27783 - (2*b^2*c^4*d^2*x^9)/729 + (128*b*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(4725*c^5) + (64*b*d^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(4725*c^3) + (16*b*d^2*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(1575*c) + (8*b*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(189*c^5) - (2*b*d^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(315*c^5) - (20*b*d^2*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(441*c^5) + (2*b*d^2*(1 - c^2*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(81*c^5) + (8*d^2*x^5*(a + b*ArcSin[c*x])^2)/315 + (4*d^2*x^5*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/63 + (d^2*x^5*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/9","A",16,11,27,0.4074,1,"{4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12, 1153}"
166,1,302,0,1.0081784,"\int x^3 \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2,x]","-\frac{1}{32} b c d^2 x^5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{25}{576} b c d^2 x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{8} d^2 x^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{12} d^2 x^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{73 b d^2 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2304 c}+\frac{73 b d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{1536 c^3}-\frac{73 d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3072 c^4}+\frac{1}{24} d^2 x^4 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{256} b^2 c^4 d^2 x^8+\frac{43 b^2 c^2 d^2 x^6}{3456}-\frac{73 b^2 d^2 x^2}{3072 c^2}-\frac{73 b^2 d^2 x^4}{9216}","-\frac{1}{32} b c d^2 x^5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{25}{576} b c d^2 x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{8} d^2 x^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{12} d^2 x^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{73 b d^2 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2304 c}+\frac{73 b d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{1536 c^3}-\frac{73 d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3072 c^4}+\frac{1}{24} d^2 x^4 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{256} b^2 c^4 d^2 x^8+\frac{43 b^2 c^2 d^2 x^6}{3456}-\frac{73 b^2 d^2 x^2}{3072 c^2}-\frac{73 b^2 d^2 x^4}{9216}",1,"(-73*b^2*d^2*x^2)/(3072*c^2) - (73*b^2*d^2*x^4)/9216 + (43*b^2*c^2*d^2*x^6)/3456 - (b^2*c^4*d^2*x^8)/256 + (73*b*d^2*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(1536*c^3) + (73*b*d^2*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2304*c) - (25*b*c*d^2*x^5*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/576 - (b*c*d^2*x^5*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/32 - (73*d^2*(a + b*ArcSin[c*x])^2)/(3072*c^4) + (d^2*x^4*(a + b*ArcSin[c*x])^2)/24 + (d^2*x^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/12 + (d^2*x^4*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/8","A",25,7,27,0.2593,1,"{4699, 4627, 4707, 4641, 30, 4697, 14}"
167,1,310,0,0.5709344,"\int x^2 \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2,x]","\frac{1}{7} d^2 x^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4}{35} d^2 x^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{16 b d^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{315 c}-\frac{2 b d^2 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{49 c^3}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{175 c^3}+\frac{8 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{105 c^3}+\frac{32 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{315 c^3}+\frac{8}{105} d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{343} b^2 c^4 d^2 x^7+\frac{136 b^2 c^2 d^2 x^5}{6125}-\frac{1636 b^2 d^2 x}{11025 c^2}-\frac{818 b^2 d^2 x^3}{33075}","\frac{1}{7} d^2 x^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4}{35} d^2 x^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{16 b d^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{315 c}-\frac{2 b d^2 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{49 c^3}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{175 c^3}+\frac{8 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{105 c^3}+\frac{32 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{315 c^3}+\frac{8}{105} d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{343} b^2 c^4 d^2 x^7+\frac{136 b^2 c^2 d^2 x^5}{6125}-\frac{1636 b^2 d^2 x}{11025 c^2}-\frac{818 b^2 d^2 x^3}{33075}",1,"(-1636*b^2*d^2*x)/(11025*c^2) - (818*b^2*d^2*x^3)/33075 + (136*b^2*c^2*d^2*x^5)/6125 - (2*b^2*c^4*d^2*x^7)/343 + (32*b*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(315*c^3) + (16*b*d^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(315*c) + (8*b*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(105*c^3) + (2*b*d^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(175*c^3) - (2*b*d^2*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(49*c^3) + (8*d^2*x^3*(a + b*ArcSin[c*x])^2)/105 + (4*d^2*x^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/35 + (d^2*x^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/7","A",14,11,27,0.4074,1,"{4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12, 373}"
168,1,209,0,0.1976785,"\int x \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2,x]","\frac{b d^2 x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{72 c}+\frac{5 b d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}-\frac{d^2 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{6 c^2}+\frac{5 d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{96 c^2}+\frac{5}{288} b^2 c^2 d^2 x^4+\frac{b^2 d^2 \left(1-c^2 x^2\right)^3}{108 c^2}-\frac{25}{288} b^2 d^2 x^2","\frac{b d^2 x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b d^2 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{72 c}+\frac{5 b d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 c}-\frac{d^2 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{6 c^2}+\frac{5 d^2 \left(a+b \sin ^{-1}(c x)\right)^2}{96 c^2}+\frac{5}{288} b^2 c^2 d^2 x^4+\frac{b^2 d^2 \left(1-c^2 x^2\right)^3}{108 c^2}-\frac{25}{288} b^2 d^2 x^2",1,"(-25*b^2*d^2*x^2)/288 + (5*b^2*c^2*d^2*x^4)/288 + (b^2*d^2*(1 - c^2*x^2)^3)/(108*c^2) + (5*b*d^2*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(48*c) + (5*b*d^2*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(72*c) + (b*d^2*x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(18*c) + (5*d^2*(a + b*ArcSin[c*x])^2)/(96*c^2) - (d^2*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/(6*c^2)","A",9,7,25,0.2800,1,"{4677, 4649, 4647, 4641, 30, 14, 261}"
169,1,219,0,0.2556068,"\int \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2,x]","\frac{1}{5} d^2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4}{15} d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{45 c}+\frac{16 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 c}+\frac{8}{15} d^2 x \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{125} b^2 c^4 d^2 x^5+\frac{76}{675} b^2 c^2 d^2 x^3-\frac{298}{225} b^2 d^2 x","\frac{1}{5} d^2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4}{15} d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{45 c}+\frac{16 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 c}+\frac{8}{15} d^2 x \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{125} b^2 c^4 d^2 x^5+\frac{76}{675} b^2 c^2 d^2 x^3-\frac{298}{225} b^2 d^2 x",1,"(-298*b^2*d^2*x)/225 + (76*b^2*c^2*d^2*x^3)/675 - (2*b^2*c^4*d^2*x^5)/125 + (16*b*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(15*c) + (8*b*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(45*c) + (2*b*d^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(25*c) + (8*d^2*x*(a + b*ArcSin[c*x])^2)/15 + (4*d^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/15 + (d^2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/5","A",10,5,24,0.2083,1,"{4649, 4619, 4677, 8, 194}"
170,1,271,0,0.4149596,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2)/x,x]","-i b d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{8} b c d^2 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{11}{16} b c d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{2} d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{i d^2 \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{11}{32} d^2 \left(a+b \sin ^{-1}(c x)\right)^2+d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^4 d^2 x^4+\frac{13}{32} b^2 c^2 d^2 x^2","-i b d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{8} b c d^2 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{11}{16} b c d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{2} d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{i d^2 \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{11}{32} d^2 \left(a+b \sin ^{-1}(c x)\right)^2+d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^4 d^2 x^4+\frac{13}{32} b^2 c^2 d^2 x^2",1,"(13*b^2*c^2*d^2*x^2)/32 - (b^2*c^4*d^2*x^4)/32 - (11*b*c*d^2*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/16 - (b*c*d^2*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/8 - (11*d^2*(a + b*ArcSin[c*x])^2)/32 + (d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/2 + (d^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/4 - ((I/3)*d^2*(a + b*ArcSin[c*x])^3)/b + d^2*(a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] - I*b*d^2*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] + (b^2*d^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2","A",17,12,27,0.4444,1,"{4699, 4625, 3717, 2190, 2531, 2282, 6589, 4647, 4641, 30, 4649, 14}"
171,1,249,0,0.4932184,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2)/x^2,x]","2 i b^2 c d^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c d^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\frac{4}{3} c^2 d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{9} b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{10}{3} b c d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{8}{3} c^2 d^2 x \left(a+b \sin ^{-1}(c x)\right)^2-4 b c d^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{27} b^2 c^4 d^2 x^3+\frac{32}{9} b^2 c^2 d^2 x","2 i b^2 c d^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c d^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\frac{4}{3} c^2 d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{9} b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{10}{3} b c d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{8}{3} c^2 d^2 x \left(a+b \sin ^{-1}(c x)\right)^2-4 b c d^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{27} b^2 c^4 d^2 x^3+\frac{32}{9} b^2 c^2 d^2 x",1,"(32*b^2*c^2*d^2*x)/9 - (2*b^2*c^4*d^2*x^3)/27 - (10*b*c*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/3 - (2*b*c*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/9 - (8*c^2*d^2*x*(a + b*ArcSin[c*x])^2)/3 - (4*c^2*d^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/3 - (d^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/x - 4*b*c*d^2*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])] + (2*I)*b^2*c*d^2*PolyLog[2, -E^(I*ArcSin[c*x])] - (2*I)*b^2*c*d^2*PolyLog[2, E^(I*ArcSin[c*x])]","A",17,11,27,0.4074,1,"{4695, 4649, 4619, 4677, 8, 4699, 4697, 4709, 4183, 2279, 2391}"
172,1,287,0,0.4749135,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2)/x^3,x]","2 i b c^2 d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-b^2 c^2 d^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{2} b c^3 d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{2 i c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{1}{4} c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)^2-2 c^2 d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{4} b^2 c^4 d^2 x^2+b^2 c^2 d^2 \log (x)","2 i b c^2 d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-b^2 c^2 d^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{2} b c^3 d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{2 i c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{1}{4} c^2 d^2 \left(a+b \sin ^{-1}(c x)\right)^2-2 c^2 d^2 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{4} b^2 c^4 d^2 x^2+b^2 c^2 d^2 \log (x)",1,"-(b^2*c^4*d^2*x^2)/4 - (b*c^3*d^2*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/2 - (b*c*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/x - (c^2*d^2*(a + b*ArcSin[c*x])^2)/4 - c^2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2 - (d^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(2*x^2) + (((2*I)/3)*c^2*d^2*(a + b*ArcSin[c*x])^3)/b - 2*c^2*d^2*(a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] + b^2*c^2*d^2*Log[x] + (2*I)*b*c^2*d^2*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] - b^2*c^2*d^2*PolyLog[3, E^((2*I)*ArcSin[c*x])]","A",17,12,27,0.4444,1,"{4695, 4699, 4625, 3717, 2190, 2531, 2282, 6589, 4647, 4641, 30, 14}"
173,1,268,0,0.6754851,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2)/x^4,x]","-\frac{11}{3} i b^2 c^3 d^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)+\frac{11}{3} i b^2 c^3 d^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)+\frac{5}{3} b c^3 d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{4 c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 x}-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}+\frac{8}{3} c^4 d^2 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{22}{3} b c^3 d^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-2 b^2 c^4 d^2 x-\frac{b^2 c^2 d^2}{3 x}","-\frac{11}{3} i b^2 c^3 d^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)+\frac{11}{3} i b^2 c^3 d^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)+\frac{5}{3} b c^3 d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{4 c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 x}-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}+\frac{8}{3} c^4 d^2 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{22}{3} b c^3 d^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-2 b^2 c^4 d^2 x-\frac{b^2 c^2 d^2}{3 x}",1,"-(b^2*c^2*d^2)/(3*x) - 2*b^2*c^4*d^2*x + (5*b*c^3*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/3 - (b*c*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*x^2) + (8*c^4*d^2*x*(a + b*ArcSin[c*x])^2)/3 + (4*c^2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*x) - (d^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(3*x^3) + (22*b*c^3*d^2*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/3 - ((11*I)/3)*b^2*c^3*d^2*PolyLog[2, -E^(I*ArcSin[c*x])] + ((11*I)/3)*b^2*c^3*d^2*PolyLog[2, E^(I*ArcSin[c*x])]","A",24,10,27,0.3704,1,"{4695, 4619, 4677, 8, 4697, 4709, 4183, 2279, 2391, 14}"
174,1,476,0,1.0176522,"\int x^4 \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^4*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2,x]","\frac{1}{11} d^3 x^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{33} d^3 x^5 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{8}{231} d^3 x^5 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{32 b d^3 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{5775 c}+\frac{128 b d^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{17325 c^3}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{11/2} \left(a+b \sin ^{-1}(c x)\right)}{121 c^5}-\frac{8 b d^3 \left(1-c^2 x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{297 c^5}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{1617 c^5}-\frac{4 b d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{1155 c^5}+\frac{16 b d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{693 c^5}+\frac{256 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{17325 c^5}+\frac{16 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)^2}{1155}+\frac{2 b^2 c^6 d^3 x^{11}}{1331}-\frac{182 b^2 c^4 d^3 x^9}{29403}+\frac{9410 b^2 c^2 d^3 x^7}{1120581}-\frac{50488 b^2 d^3 x^3}{12006225 c^2}-\frac{100976 b^2 d^3 x}{4002075 c^4}-\frac{12622 b^2 d^3 x^5}{6670125}","\frac{1}{11} d^3 x^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{33} d^3 x^5 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{8}{231} d^3 x^5 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{32 b d^3 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{5775 c}+\frac{128 b d^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{17325 c^3}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{11/2} \left(a+b \sin ^{-1}(c x)\right)}{121 c^5}-\frac{8 b d^3 \left(1-c^2 x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{297 c^5}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{1617 c^5}-\frac{4 b d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{1155 c^5}+\frac{16 b d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{693 c^5}+\frac{256 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{17325 c^5}+\frac{16 d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)^2}{1155}+\frac{2 b^2 c^6 d^3 x^{11}}{1331}-\frac{182 b^2 c^4 d^3 x^9}{29403}+\frac{9410 b^2 c^2 d^3 x^7}{1120581}-\frac{50488 b^2 d^3 x^3}{12006225 c^2}-\frac{100976 b^2 d^3 x}{4002075 c^4}-\frac{12622 b^2 d^3 x^5}{6670125}",1,"(-100976*b^2*d^3*x)/(4002075*c^4) - (50488*b^2*d^3*x^3)/(12006225*c^2) - (12622*b^2*d^3*x^5)/6670125 + (9410*b^2*c^2*d^3*x^7)/1120581 - (182*b^2*c^4*d^3*x^9)/29403 + (2*b^2*c^6*d^3*x^11)/1331 + (256*b*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(17325*c^5) + (128*b*d^3*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(17325*c^3) + (32*b*d^3*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(5775*c) + (16*b*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(693*c^5) - (4*b*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(1155*c^5) + (2*b*d^3*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(1617*c^5) - (8*b*d^3*(1 - c^2*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(297*c^5) + (2*b*d^3*(1 - c^2*x^2)^(11/2)*(a + b*ArcSin[c*x]))/(121*c^5) + (16*d^3*x^5*(a + b*ArcSin[c*x])^2)/1155 + (8*d^3*x^5*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/231 + (2*d^3*x^5*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/33 + (d^3*x^5*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/11","A",21,11,27,0.4074,1,"{4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12, 1153}"
175,1,384,0,1.5938808,"\int x^3 \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2,x]","-\frac{1}{50} b c d^3 x^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{32} b c d^3 x^5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{31}{960} b c d^3 x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{10} d^3 x^4 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{40} d^3 x^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{20} d^3 x^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{79 b d^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3840 c}+\frac{79 b d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2560 c^3}-\frac{79 d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{5120 c^4}+\frac{1}{40} d^3 x^4 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{500} b^2 c^6 d^3 x^{10}-\frac{57 b^2 c^4 d^3 x^8}{6400}+\frac{401 b^2 c^2 d^3 x^6}{28800}-\frac{79 b^2 d^3 x^2}{5120 c^2}-\frac{79 b^2 d^3 x^4}{15360}","-\frac{1}{50} b c d^3 x^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{32} b c d^3 x^5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{31}{960} b c d^3 x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{10} d^3 x^4 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{40} d^3 x^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{20} d^3 x^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{79 b d^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3840 c}+\frac{79 b d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2560 c^3}-\frac{79 d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{5120 c^4}+\frac{1}{40} d^3 x^4 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{500} b^2 c^6 d^3 x^{10}-\frac{57 b^2 c^4 d^3 x^8}{6400}+\frac{401 b^2 c^2 d^3 x^6}{28800}-\frac{79 b^2 d^3 x^2}{5120 c^2}-\frac{79 b^2 d^3 x^4}{15360}",1,"(-79*b^2*d^3*x^2)/(5120*c^2) - (79*b^2*d^3*x^4)/15360 + (401*b^2*c^2*d^3*x^6)/28800 - (57*b^2*c^4*d^3*x^8)/6400 + (b^2*c^6*d^3*x^10)/500 + (79*b*d^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2560*c^3) + (79*b*d^3*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3840*c) - (31*b*c*d^3*x^5*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/960 - (b*c*d^3*x^5*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/32 - (b*c*d^3*x^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/50 - (79*d^3*(a + b*ArcSin[c*x])^2)/(5120*c^4) + (d^3*x^4*(a + b*ArcSin[c*x])^2)/40 + (d^3*x^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/20 + (3*d^3*x^4*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/40 + (d^3*x^4*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/10","A",40,9,27,0.3333,1,"{4699, 4627, 4707, 4641, 30, 4697, 14, 266, 43}"
176,1,391,0,0.822623,"\int x^2 \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2,x]","\frac{1}{9} d^3 x^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{21} d^3 x^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{8}{105} d^3 x^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{32 b d^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{945 c}-\frac{2 b d^3 \left(1-c^2 x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{81 c^3}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{441 c^3}+\frac{4 b d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{525 c^3}+\frac{16 b d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{315 c^3}+\frac{64 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{945 c^3}+\frac{16}{315} d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{729} b^2 c^6 d^3 x^9-\frac{374 b^2 c^4 d^3 x^7}{27783}+\frac{4198 b^2 c^2 d^3 x^5}{165375}-\frac{10516 b^2 d^3 x}{99225 c^2}-\frac{5258 b^2 d^3 x^3}{297675}","\frac{1}{9} d^3 x^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{21} d^3 x^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{8}{105} d^3 x^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{32 b d^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{945 c}-\frac{2 b d^3 \left(1-c^2 x^2\right)^{9/2} \left(a+b \sin ^{-1}(c x)\right)}{81 c^3}+\frac{2 b d^3 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{441 c^3}+\frac{4 b d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{525 c^3}+\frac{16 b d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{315 c^3}+\frac{64 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{945 c^3}+\frac{16}{315} d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{729} b^2 c^6 d^3 x^9-\frac{374 b^2 c^4 d^3 x^7}{27783}+\frac{4198 b^2 c^2 d^3 x^5}{165375}-\frac{10516 b^2 d^3 x}{99225 c^2}-\frac{5258 b^2 d^3 x^3}{297675}",1,"(-10516*b^2*d^3*x)/(99225*c^2) - (5258*b^2*d^3*x^3)/297675 + (4198*b^2*c^2*d^3*x^5)/165375 - (374*b^2*c^4*d^3*x^7)/27783 + (2*b^2*c^6*d^3*x^9)/729 + (64*b*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(945*c^3) + (32*b*d^3*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(945*c) + (16*b*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(315*c^3) + (4*b*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(525*c^3) + (2*b*d^3*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(441*c^3) - (2*b*d^3*(1 - c^2*x^2)^(9/2)*(a + b*ArcSin[c*x]))/(81*c^3) + (16*d^3*x^3*(a + b*ArcSin[c*x])^2)/315 + (8*d^3*x^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/105 + (2*d^3*x^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/21 + (d^3*x^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/9","A",19,11,27,0.4074,1,"{4699, 4627, 4707, 4677, 8, 30, 266, 43, 4689, 12, 373}"
177,1,268,0,0.2466538,"\int x \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2,x]","\frac{b d^3 x \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{32 c}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{192 c}+\frac{35 b d^3 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{768 c}+\frac{35 b d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{512 c}-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{35 d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{1024 c^2}+\frac{35 b^2 c^2 d^3 x^4}{3072}+\frac{b^2 d^3 \left(1-c^2 x^2\right)^4}{256 c^2}+\frac{7 b^2 d^3 \left(1-c^2 x^2\right)^3}{1152 c^2}-\frac{175 b^2 d^3 x^2}{3072}","\frac{b d^3 x \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{32 c}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{192 c}+\frac{35 b d^3 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{768 c}+\frac{35 b d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{512 c}-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{35 d^3 \left(a+b \sin ^{-1}(c x)\right)^2}{1024 c^2}+\frac{35 b^2 c^2 d^3 x^4}{3072}+\frac{b^2 d^3 \left(1-c^2 x^2\right)^4}{256 c^2}+\frac{7 b^2 d^3 \left(1-c^2 x^2\right)^3}{1152 c^2}-\frac{175 b^2 d^3 x^2}{3072}",1,"(-175*b^2*d^3*x^2)/3072 + (35*b^2*c^2*d^3*x^4)/3072 + (7*b^2*d^3*(1 - c^2*x^2)^3)/(1152*c^2) + (b^2*d^3*(1 - c^2*x^2)^4)/(256*c^2) + (35*b*d^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(512*c) + (35*b*d^3*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(768*c) + (7*b*d^3*x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(192*c) + (b*d^3*x*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(32*c) + (35*d^3*(a + b*ArcSin[c*x])^2)/(1024*c^2) - (d^3*(1 - c^2*x^2)^4*(a + b*ArcSin[c*x])^2)/(8*c^2)","A",11,7,25,0.2800,1,"{4677, 4649, 4647, 4641, 30, 14, 261}"
178,1,298,0,0.3715814,"\int \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2,x]","\frac{1}{7} d^3 x \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{6}{35} d^3 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{8}{35} d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d^3 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{49 c}+\frac{12 b d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{175 c}+\frac{16 b d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{105 c}+\frac{32 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{35 c}+\frac{16}{35} d^3 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^6 d^3 x^7-\frac{234 b^2 c^4 d^3 x^5}{6125}+\frac{1514 b^2 c^2 d^3 x^3}{11025}-\frac{4322 b^2 d^3 x}{3675}","\frac{1}{7} d^3 x \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{6}{35} d^3 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{8}{35} d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d^3 \left(1-c^2 x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)}{49 c}+\frac{12 b d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{175 c}+\frac{16 b d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{105 c}+\frac{32 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{35 c}+\frac{16}{35} d^3 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^6 d^3 x^7-\frac{234 b^2 c^4 d^3 x^5}{6125}+\frac{1514 b^2 c^2 d^3 x^3}{11025}-\frac{4322 b^2 d^3 x}{3675}",1,"(-4322*b^2*d^3*x)/3675 + (1514*b^2*c^2*d^3*x^3)/11025 - (234*b^2*c^4*d^3*x^5)/6125 + (2*b^2*c^6*d^3*x^7)/343 + (32*b*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(35*c) + (16*b*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(105*c) + (12*b*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(175*c) + (2*b*d^3*(1 - c^2*x^2)^(7/2)*(a + b*ArcSin[c*x]))/(49*c) + (16*d^3*x*(a + b*ArcSin[c*x])^2)/35 + (8*d^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/35 + (6*d^3*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/35 + (d^3*x*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/7","A",14,5,24,0.2083,1,"{4649, 4619, 4677, 8, 194}"
179,1,354,0,0.6583734,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2)/x,x]","-i b d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{18} b c d^3 x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{7}{36} b c d^3 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{19}{24} b c d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{2} d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{i d^3 \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{19}{48} d^3 \left(a+b \sin ^{-1}(c x)\right)^2+d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{7}{144} b^2 c^4 d^3 x^4+\frac{71}{144} b^2 c^2 d^3 x^2-\frac{1}{108} b^2 d^3 \left(1-c^2 x^2\right)^3","-i b d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{1}{18} b c d^3 x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{7}{36} b c d^3 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{19}{24} b c d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{4} d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{2} d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{i d^3 \left(a+b \sin ^{-1}(c x)\right)^3}{3 b}-\frac{19}{48} d^3 \left(a+b \sin ^{-1}(c x)\right)^2+d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{7}{144} b^2 c^4 d^3 x^4+\frac{71}{144} b^2 c^2 d^3 x^2-\frac{1}{108} b^2 d^3 \left(1-c^2 x^2\right)^3",1,"(71*b^2*c^2*d^3*x^2)/144 - (7*b^2*c^4*d^3*x^4)/144 - (b^2*d^3*(1 - c^2*x^2)^3)/108 - (19*b*c*d^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/24 - (7*b*c*d^3*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/36 - (b*c*d^3*x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/18 - (19*d^3*(a + b*ArcSin[c*x])^2)/48 + (d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/2 + (d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/4 + (d^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/6 - ((I/3)*d^3*(a + b*ArcSin[c*x])^3)/b + d^3*(a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] - I*b*d^3*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] + (b^2*d^3*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2","A",26,13,27,0.4815,1,"{4699, 4625, 3717, 2190, 2531, 2282, 6589, 4647, 4641, 30, 4649, 14, 261}"
180,1,329,0,0.706098,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2)/x^2,x]","2 i b^2 c d^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c d^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\frac{6}{5} c^2 d^3 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{8}{5} c^2 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{25} b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{5} b c d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{22}{5} b c d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{16}{5} c^2 d^3 x \left(a+b \sin ^{-1}(c x)\right)^2-4 b c d^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{125} b^2 c^6 d^3 x^5-\frac{14}{75} b^2 c^4 d^3 x^3+\frac{122}{25} b^2 c^2 d^3 x","2 i b^2 c d^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)-2 i b^2 c d^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)-\frac{6}{5} c^2 d^3 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{8}{5} c^2 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{25} b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{2}{5} b c d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{22}{5} b c d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{16}{5} c^2 d^3 x \left(a+b \sin ^{-1}(c x)\right)^2-4 b c d^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{125} b^2 c^6 d^3 x^5-\frac{14}{75} b^2 c^4 d^3 x^3+\frac{122}{25} b^2 c^2 d^3 x",1,"(122*b^2*c^2*d^3*x)/25 - (14*b^2*c^4*d^3*x^3)/75 + (2*b^2*c^6*d^3*x^5)/125 - (22*b*c*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/5 - (2*b*c*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/5 - (2*b*c*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/25 - (16*c^2*d^3*x*(a + b*ArcSin[c*x])^2)/5 - (8*c^2*d^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/5 - (6*c^2*d^3*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/5 - (d^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/x - 4*b*c*d^3*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])] + (2*I)*b^2*c*d^3*PolyLog[2, -E^(I*ArcSin[c*x])] - (2*I)*b^2*c*d^3*PolyLog[2, E^(I*ArcSin[c*x])]","A",24,12,27,0.4444,1,"{4695, 4649, 4619, 4677, 8, 194, 4699, 4697, 4709, 4183, 2279, 2391}"
181,1,371,0,0.7225162,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2)/x^3,x]","3 i b c^2 d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{7}{8} b c^3 d^3 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{16} b c^3 d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{4} c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{3}{2} c^2 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{i c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)^3}{b}+\frac{3}{32} c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)^2-3 c^2 d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{32} b^2 c^6 d^3 x^4-\frac{21}{32} b^2 c^4 d^3 x^2+b^2 c^2 d^3 \log (x)","3 i b c^2 d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)-\frac{7}{8} b c^3 d^3 x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{16} b c^3 d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{3}{4} c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{3}{2} c^2 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{i c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)^3}{b}+\frac{3}{32} c^2 d^3 \left(a+b \sin ^{-1}(c x)\right)^2-3 c^2 d^3 \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{32} b^2 c^6 d^3 x^4-\frac{21}{32} b^2 c^4 d^3 x^2+b^2 c^2 d^3 \log (x)",1,"(-21*b^2*c^4*d^3*x^2)/32 + (b^2*c^6*d^3*x^4)/32 + (3*b*c^3*d^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/16 - (7*b*c^3*d^3*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/8 - (b*c*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/x + (3*c^2*d^3*(a + b*ArcSin[c*x])^2)/32 - (3*c^2*d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/2 - (3*c^2*d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/4 - (d^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/(2*x^2) + (I*c^2*d^3*(a + b*ArcSin[c*x])^3)/b - 3*c^2*d^3*(a + b*ArcSin[c*x])^2*Log[1 - E^((2*I)*ArcSin[c*x])] + b^2*c^2*d^3*Log[x] + (3*I)*b*c^2*d^3*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])] - (3*b^2*c^2*d^3*PolyLog[3, E^((2*I)*ArcSin[c*x])])/2","A",28,15,27,0.5556,1,"{4695, 4699, 4625, 3717, 2190, 2531, 2282, 6589, 4647, 4641, 30, 4649, 14, 266, 43}"
182,1,348,0,0.9812328,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2)/x^4,x]","-\frac{17}{3} i b^2 c^3 d^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)+\frac{17}{3} i b^2 c^3 d^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)+\frac{8}{3} c^4 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{9} b c^3 d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+5 b c^3 d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{2 c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}+\frac{16}{3} c^4 d^3 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{34}{3} b c^3 d^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{27} b^2 c^6 d^3 x^3-\frac{50}{9} b^2 c^4 d^3 x-\frac{b^2 c^2 d^3}{3 x}","-\frac{17}{3} i b^2 c^3 d^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)+\frac{17}{3} i b^2 c^3 d^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)+\frac{8}{3} c^4 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{9} b c^3 d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+5 b c^3 d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{2 c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}+\frac{16}{3} c^4 d^3 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{34}{3} b c^3 d^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{27} b^2 c^6 d^3 x^3-\frac{50}{9} b^2 c^4 d^3 x-\frac{b^2 c^2 d^3}{3 x}",1,"-(b^2*c^2*d^3)/(3*x) - (50*b^2*c^4*d^3*x)/9 + (2*b^2*c^6*d^3*x^3)/27 + 5*b*c^3*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]) - (b*c^3*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/9 - (b*c*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x]))/(3*x^2) + (16*c^4*d^3*x*(a + b*ArcSin[c*x])^2)/3 + (8*c^4*d^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/3 + (2*c^2*d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/x - (d^3*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/(3*x^3) + (34*b*c^3*d^3*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/3 - ((17*I)/3)*b^2*c^3*d^3*PolyLog[2, -E^(I*ArcSin[c*x])] + ((17*I)/3)*b^2*c^3*d^3*PolyLog[2, E^(I*ArcSin[c*x])]","A",31,12,27,0.4444,1,"{4695, 4649, 4619, 4677, 8, 4699, 4697, 4709, 4183, 2279, 2391, 270}"
183,1,297,0,0.549021,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","Int[(x^4*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2),x]","\frac{2 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d}-\frac{2 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d}-\frac{2 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}+\frac{2 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}-\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3 d}-\frac{22 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^5 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^5 d}+\frac{2 b^2 x^3}{27 c^2 d}+\frac{22 b^2 x}{9 c^4 d}","\frac{2 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d}-\frac{2 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d}-\frac{2 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}+\frac{2 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^5 d}-\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3 d}-\frac{22 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^5 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^5 d}+\frac{2 b^2 x^3}{27 c^2 d}+\frac{22 b^2 x}{9 c^4 d}",1,"(22*b^2*x)/(9*c^4*d) + (2*b^2*x^3)/(27*c^2*d) - (22*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^5*d) - (2*b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3*d) - (x*(a + b*ArcSin[c*x])^2)/(c^4*d) - (x^3*(a + b*ArcSin[c*x])^2)/(3*c^2*d) - ((2*I)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c^5*d) + ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^5*d) - ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^5*d) - (2*b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(c^5*d) + (2*b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(c^5*d)","A",16,10,27,0.3704,1,"{4715, 4657, 4181, 2531, 2282, 6589, 4677, 8, 4707, 30}"
184,1,210,0,0.3778702,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","Int[(x^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^3 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^4 d}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^4 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d}+\frac{b^2 x^2}{4 c^2 d}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^3 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^4 d}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^4 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d}+\frac{b^2 x^2}{4 c^2 d}",1,"(b^2*x^2)/(4*c^2*d) - (b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c^3*d) + (a + b*ArcSin[c*x])^2/(4*c^4*d) - (x^2*(a + b*ArcSin[c*x])^2)/(2*c^2*d) + ((I/3)*(a + b*ArcSin[c*x])^3)/(b*c^4*d) - ((a + b*ArcSin[c*x])^2*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^4*d) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^4*d) - (b^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*c^4*d)","A",10,10,27,0.3704,1,"{4715, 4675, 3719, 2190, 2531, 2282, 6589, 4707, 4641, 30}"
185,1,218,0,0.2869287,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2),x]","\frac{2 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{2 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{2 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}+\frac{2 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d}+\frac{2 b^2 x}{c^2 d}","\frac{2 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{2 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{2 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}+\frac{2 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^3 d}-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^3 d}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d}+\frac{2 b^2 x}{c^2 d}",1,"(2*b^2*x)/(c^2*d) - (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(c^3*d) - (x*(a + b*ArcSin[c*x])^2)/(c^2*d) - ((2*I)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c^3*d) + ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^3*d) - ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^3*d) - (2*b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(c^3*d) + (2*b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(c^3*d)","A",11,8,27,0.2963,1,"{4715, 4657, 4181, 2531, 2282, 6589, 4677, 8}"
186,1,117,0,0.1721381,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^2 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^2 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^2 d}+\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^2 d}-\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d}",1,"((I/3)*(a + b*ArcSin[c*x])^3)/(b*c^2*d) - ((a + b*ArcSin[c*x])^2*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^2*d) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^2*d) - (b^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*c^2*d)","A",6,6,25,0.2400,1,"{4675, 3719, 2190, 2531, 2282, 6589}"
187,1,156,0,0.1270722,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(d - c^2*d*x^2),x]","\frac{2 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d}-\frac{2 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d}-\frac{2 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c d}+\frac{2 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c d}","\frac{2 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d}-\frac{2 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d}-\frac{2 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c d}+\frac{2 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c d}-\frac{2 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c d}",1,"((-2*I)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c*d) + ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*d) - ((2*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*d) - (2*b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(c*d) + (2*b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(c*d)","A",8,5,24,0.2083,1,"{4657, 4181, 2531, 2282, 6589}"
188,1,131,0,0.1965942,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*(d - c^2*d*x^2)),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}",1,"(-2*(a + b*ArcSin[c*x])^2*ArcTanh[E^((2*I)*ArcSin[c*x])])/d + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d - (b^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*d) + (b^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/(2*d)","A",9,6,27,0.2222,1,"{4679, 4419, 4183, 2531, 2282, 6589}"
189,1,238,0,0.3475382,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*(d - c^2*d*x^2)),x]","\frac{2 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{2 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}+\frac{2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{2 b^2 c \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d}+\frac{2 b^2 c \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d x}-\frac{2 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}-\frac{4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}","\frac{2 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{2 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}+\frac{2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{2 b^2 c \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d}+\frac{2 b^2 c \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d x}-\frac{2 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}-\frac{4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}",1,"-((a + b*ArcSin[c*x])^2/(d*x)) - ((2*I)*c*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/d - (4*b*c*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/d + ((2*I)*b^2*c*PolyLog[2, -E^(I*ArcSin[c*x])])/d + ((2*I)*b*c*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d - ((2*I)*b*c*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/d - ((2*I)*b^2*c*PolyLog[2, E^(I*ArcSin[c*x])])/d - (2*b^2*c*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/d + (2*b^2*c*PolyLog[3, I*E^(I*ArcSin[c*x])])/d","A",15,10,27,0.3704,1,"{4701, 4657, 4181, 2531, 2282, 6589, 4709, 4183, 2279, 2391}"
190,1,210,0,0.3826643,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^3*(d - c^2*d*x^2)),x]","\frac{i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{d x}-\frac{2 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2}+\frac{b^2 c^2 \log (x)}{d}","\frac{i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{d x}-\frac{2 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2}+\frac{b^2 c^2 \log (x)}{d}",1,"-((b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(d*x)) - (a + b*ArcSin[c*x])^2/(2*d*x^2) - (2*c^2*(a + b*ArcSin[c*x])^2*ArcTanh[E^((2*I)*ArcSin[c*x])])/d + (b^2*c^2*Log[x])/d + (I*b*c^2*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d - (I*b*c^2*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d - (b^2*c^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*d) + (b^2*c^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/(2*d)","A",12,9,27,0.3333,1,"{4701, 4679, 4419, 4183, 2531, 2282, 6589, 4681, 29}"
191,1,333,0,0.6542266,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^4*(d - c^2*d*x^2)),x]","\frac{2 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{2 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}+\frac{7 i b^2 c^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{3 d}-\frac{7 i b^2 c^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{3 d}-\frac{2 b^2 c^3 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d}+\frac{2 b^2 c^3 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^2}-\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d x}-\frac{2 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}-\frac{14 b c^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3}-\frac{b^2 c^2}{3 d x}","\frac{2 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}-\frac{2 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}+\frac{7 i b^2 c^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{3 d}-\frac{7 i b^2 c^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{3 d}-\frac{2 b^2 c^3 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d}+\frac{2 b^2 c^3 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^2}-\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d x}-\frac{2 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d}-\frac{14 b c^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3}-\frac{b^2 c^2}{3 d x}",1,"-(b^2*c^2)/(3*d*x) - (b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*d*x^2) - (a + b*ArcSin[c*x])^2/(3*d*x^3) - (c^2*(a + b*ArcSin[c*x])^2)/(d*x) - ((2*I)*c^3*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/d - (14*b*c^3*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(3*d) + (((7*I)/3)*b^2*c^3*PolyLog[2, -E^(I*ArcSin[c*x])])/d + ((2*I)*b*c^3*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d - ((2*I)*b*c^3*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/d - (((7*I)/3)*b^2*c^3*PolyLog[2, E^(I*ArcSin[c*x])])/d - (2*b^2*c^3*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/d + (2*b^2*c^3*PolyLog[3, I*E^(I*ArcSin[c*x])])/d","A",24,11,27,0.4074,1,"{4701, 4657, 4181, 2531, 2282, 6589, 4709, 4183, 2279, 2391, 30}"
192,1,300,0,0.5254944,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^2,x]","-\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}+\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}+\frac{3 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^5 d^2}-\frac{3 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^5 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2 \sqrt{1-c^2 x^2}}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^5 d^2}-\frac{2 b^2 x}{c^4 d^2}+\frac{b^2 \tanh ^{-1}(c x)}{c^5 d^2}","-\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}+\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}+\frac{3 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^5 d^2}-\frac{3 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^5 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{c^5 d^2 \sqrt{1-c^2 x^2}}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^5 d^2}-\frac{2 b^2 x}{c^4 d^2}+\frac{b^2 \tanh ^{-1}(c x)}{c^5 d^2}",1,"(-2*b^2*x)/(c^4*d^2) - (b*(a + b*ArcSin[c*x]))/(c^5*d^2*Sqrt[1 - c^2*x^2]) + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(c^5*d^2) + (3*x*(a + b*ArcSin[c*x])^2)/(2*c^4*d^2) + (x^3*(a + b*ArcSin[c*x])^2)/(2*c^2*d^2*(1 - c^2*x^2)) + ((3*I)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c^5*d^2) + (b^2*ArcTanh[c*x])/(c^5*d^2) - ((3*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^5*d^2) + ((3*I)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^5*d^2) + (3*b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(c^5*d^2) - (3*b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(c^5*d^2)","A",15,14,27,0.5185,1,"{4703, 4715, 4657, 4181, 2531, 2282, 6589, 4677, 8, 266, 43, 4689, 388, 208}"
193,1,227,0,0.3949616,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d^2}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2 \sqrt{1-c^2 x^2}}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^4 d^2}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^4 d^2}","-\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^4 d^2}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2 \sqrt{1-c^2 x^2}}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^4 d^2}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{\log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^4 d^2}",1,"-((b*x*(a + b*ArcSin[c*x]))/(c^3*d^2*Sqrt[1 - c^2*x^2])) + (a + b*ArcSin[c*x])^2/(2*c^4*d^2) + (x^2*(a + b*ArcSin[c*x])^2)/(2*c^2*d^2*(1 - c^2*x^2)) - ((I/3)*(a + b*ArcSin[c*x])^3)/(b*c^4*d^2) + ((a + b*ArcSin[c*x])^2*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^4*d^2) - (b^2*Log[1 - c^2*x^2])/(2*c^4*d^2) - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^4*d^2) + (b^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*c^4*d^2)","A",10,9,27,0.3333,1,"{4703, 4675, 3719, 2190, 2531, 2282, 6589, 4641, 260}"
194,1,233,0,0.29931,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2}+\frac{b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^3 d^2}-\frac{b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^3 d^2}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2 \sqrt{1-c^2 x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{b^2 \tanh ^{-1}(c x)}{c^3 d^2}","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2}+\frac{b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c^3 d^2}-\frac{b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c^3 d^2}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{c^3 d^2 \sqrt{1-c^2 x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{b^2 \tanh ^{-1}(c x)}{c^3 d^2}",1,"-((b*(a + b*ArcSin[c*x]))/(c^3*d^2*Sqrt[1 - c^2*x^2])) + (x*(a + b*ArcSin[c*x])^2)/(2*c^2*d^2*(1 - c^2*x^2)) + (I*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c^3*d^2) + (b^2*ArcTanh[c*x])/(c^3*d^2) - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^3*d^2) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^3*d^2) + (b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(c^3*d^2) - (b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(c^3*d^2)","A",11,8,27,0.2963,1,"{4703, 4657, 4181, 2531, 2282, 6589, 4677, 206}"
195,1,89,0,0.0985197,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^2,x]","-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{c d^2 \sqrt{1-c^2 x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^2 d^2}","-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{c d^2 \sqrt{1-c^2 x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 c^2 d^2}",1,"-((b*x*(a + b*ArcSin[c*x]))/(c*d^2*Sqrt[1 - c^2*x^2])) + (a + b*ArcSin[c*x])^2/(2*c^2*d^2*(1 - c^2*x^2)) - (b^2*Log[1 - c^2*x^2])/(2*c^2*d^2)","A",3,3,25,0.1200,1,"{4677, 4651, 260}"
196,1,230,0,0.2360441,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(d - c^2*d*x^2)^2,x]","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d^2}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d^2}-\frac{b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c d^2}+\frac{b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c d^2}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{c d^2 \sqrt{1-c^2 x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c d^2}+\frac{b^2 \tanh ^{-1}(c x)}{c d^2}","\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d^2}-\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c d^2}-\frac{b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{c d^2}+\frac{b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{c d^2}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{c d^2 \sqrt{1-c^2 x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c d^2}+\frac{b^2 \tanh ^{-1}(c x)}{c d^2}",1,"-((b*(a + b*ArcSin[c*x]))/(c*d^2*Sqrt[1 - c^2*x^2])) + (x*(a + b*ArcSin[c*x])^2)/(2*d^2*(1 - c^2*x^2)) - (I*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c*d^2) + (b^2*ArcTanh[c*x])/(c*d^2) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*d^2) - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*d^2) - (b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(c*d^2) + (b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(c*d^2)","A",11,8,24,0.3333,1,"{4655, 4657, 4181, 2531, 2282, 6589, 4677, 206}"
197,1,211,0,0.365164,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*(d - c^2*d*x^2)^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{b c x \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{1-c^2 x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 d^2}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{b c x \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{1-c^2 x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 \log \left(1-c^2 x^2\right)}{2 d^2}",1,"-((b*c*x*(a + b*ArcSin[c*x]))/(d^2*Sqrt[1 - c^2*x^2])) + (a + b*ArcSin[c*x])^2/(2*d^2*(1 - c^2*x^2)) - (2*(a + b*ArcSin[c*x])^2*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^2 - (b^2*Log[1 - c^2*x^2])/(2*d^2) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^2 - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^2 - (b^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*d^2) + (b^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/(2*d^2)","A",12,9,27,0.3333,1,"{4705, 4679, 4419, 4183, 2531, 2282, 6589, 4651, 260}"
198,1,324,0,0.5632707,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*(d - c^2*d*x^2)^2),x]","\frac{3 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d^2}-\frac{2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d^2}-\frac{3 b^2 c \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d^2}+\frac{3 b^2 c \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d^2}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{1-c^2 x^2}}+\frac{3 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d^2 x \left(1-c^2 x^2\right)}-\frac{3 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{b^2 c \tanh ^{-1}(c x)}{d^2}","\frac{3 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d^2}-\frac{2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d^2}-\frac{3 b^2 c \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d^2}+\frac{3 b^2 c \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d^2}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{1-c^2 x^2}}+\frac{3 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d^2 x \left(1-c^2 x^2\right)}-\frac{3 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{b^2 c \tanh ^{-1}(c x)}{d^2}",1,"-((b*c*(a + b*ArcSin[c*x]))/(d^2*Sqrt[1 - c^2*x^2])) - (a + b*ArcSin[c*x])^2/(d^2*x*(1 - c^2*x^2)) + (3*c^2*x*(a + b*ArcSin[c*x])^2)/(2*d^2*(1 - c^2*x^2)) - ((3*I)*c*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/d^2 - (4*b*c*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/d^2 + (b^2*c*ArcTanh[c*x])/d^2 + ((2*I)*b^2*c*PolyLog[2, -E^(I*ArcSin[c*x])])/d^2 + ((3*I)*b*c*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^2 - ((3*I)*b*c*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^2 - ((2*I)*b^2*c*PolyLog[2, E^(I*ArcSin[c*x])])/d^2 - (3*b^2*c*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/d^2 + (3*b^2*c*PolyLog[3, I*E^(I*ArcSin[c*x])])/d^2","A",20,14,27,0.5185,1,"{4701, 4655, 4657, 4181, 2531, 2282, 6589, 4677, 206, 4705, 4709, 4183, 2279, 2391}"
199,1,270,0,0.5506648,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^3*(d - c^2*d*x^2)^2),x]","\frac{2 i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{2 i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{d^2}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{d^2}+\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \left(1-c^2 x^2\right)}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^2 x \sqrt{1-c^2 x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 x^2 \left(1-c^2 x^2\right)}-\frac{4 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 c^2 \log \left(1-c^2 x^2\right)}{2 d^2}+\frac{b^2 c^2 \log (x)}{d^2}","\frac{2 i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{2 i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{d^2}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{d^2}+\frac{c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \left(1-c^2 x^2\right)}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^2 x \sqrt{1-c^2 x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 x^2 \left(1-c^2 x^2\right)}-\frac{4 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 c^2 \log \left(1-c^2 x^2\right)}{2 d^2}+\frac{b^2 c^2 \log (x)}{d^2}",1,"-((b*c*(a + b*ArcSin[c*x]))/(d^2*x*Sqrt[1 - c^2*x^2])) + (c^2*(a + b*ArcSin[c*x])^2)/(d^2*(1 - c^2*x^2)) - (a + b*ArcSin[c*x])^2/(2*d^2*x^2*(1 - c^2*x^2)) - (4*c^2*(a + b*ArcSin[c*x])^2*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^2 + (b^2*c^2*Log[x])/d^2 - (b^2*c^2*Log[1 - c^2*x^2])/(2*d^2) + ((2*I)*b*c^2*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^2 - ((2*I)*b*c^2*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^2 - (b^2*c^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/d^2 + (b^2*c^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/d^2","A",17,15,27,0.5556,1,"{4701, 4705, 4679, 4419, 4183, 2531, 2282, 6589, 4651, 260, 271, 191, 4689, 446, 72}"
200,1,439,0,0.9494987,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^4*(d - c^2*d*x^2)^2),x]","\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{13 i b^2 c^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{3 d^2}-\frac{13 i b^2 c^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{3 d^2}-\frac{5 b^2 c^3 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d^2}+\frac{5 b^2 c^3 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d^2}+\frac{5 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{2 b c^3 \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2}}-\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 x \left(1-c^2 x^2\right)}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{1-c^2 x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 x^3 \left(1-c^2 x^2\right)}-\frac{5 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{26 b c^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2}-\frac{b^2 c^2}{3 d^2 x}+\frac{b^2 c^3 \tanh ^{-1}(c x)}{d^2}","\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{13 i b^2 c^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{3 d^2}-\frac{13 i b^2 c^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{3 d^2}-\frac{5 b^2 c^3 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{d^2}+\frac{5 b^2 c^3 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{d^2}+\frac{5 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{2 b c^3 \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2}}-\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 x \left(1-c^2 x^2\right)}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{1-c^2 x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 x^3 \left(1-c^2 x^2\right)}-\frac{5 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2}-\frac{26 b c^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2}-\frac{b^2 c^2}{3 d^2 x}+\frac{b^2 c^3 \tanh ^{-1}(c x)}{d^2}",1,"-(b^2*c^2)/(3*d^2*x) - (2*b*c^3*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[1 - c^2*x^2]) - (b*c*(a + b*ArcSin[c*x]))/(3*d^2*x^2*Sqrt[1 - c^2*x^2]) - (a + b*ArcSin[c*x])^2/(3*d^2*x^3*(1 - c^2*x^2)) - (5*c^2*(a + b*ArcSin[c*x])^2)/(3*d^2*x*(1 - c^2*x^2)) + (5*c^4*x*(a + b*ArcSin[c*x])^2)/(2*d^2*(1 - c^2*x^2)) - ((5*I)*c^3*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/d^2 - (26*b*c^3*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(3*d^2) + (b^2*c^3*ArcTanh[c*x])/d^2 + (((13*I)/3)*b^2*c^3*PolyLog[2, -E^(I*ArcSin[c*x])])/d^2 + ((5*I)*b*c^3*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^2 - ((5*I)*b*c^3*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^2 - (((13*I)/3)*b^2*c^3*PolyLog[2, E^(I*ArcSin[c*x])])/d^2 - (5*b^2*c^3*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/d^2 + (5*b^2*c^3*PolyLog[3, I*E^(I*ArcSin[c*x])])/d^2","A",32,15,27,0.5556,1,"{4701, 4655, 4657, 4181, 2531, 2282, 6589, 4677, 206, 4705, 4709, 4183, 2279, 2391, 325}"
201,1,343,0,0.5363638,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^3,x]","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3}-\frac{3 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 c^5 d^3}+\frac{3 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 c^5 d^3}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^4 d^3 \left(1-c^2 x^2\right)}+\frac{5 b \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3 \sqrt{1-c^2 x^2}}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{6 c^5 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^5 d^3}+\frac{b^2 x}{12 c^4 d^3 \left(1-c^2 x^2\right)}-\frac{7 b^2 \tanh ^{-1}(c x)}{6 c^5 d^3}","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3}-\frac{3 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 c^5 d^3}+\frac{3 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 c^5 d^3}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^4 d^3 \left(1-c^2 x^2\right)}+\frac{5 b \left(a+b \sin ^{-1}(c x)\right)}{4 c^5 d^3 \sqrt{1-c^2 x^2}}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{6 c^5 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^5 d^3}+\frac{b^2 x}{12 c^4 d^3 \left(1-c^2 x^2\right)}-\frac{7 b^2 \tanh ^{-1}(c x)}{6 c^5 d^3}",1,"(b^2*x)/(12*c^4*d^3*(1 - c^2*x^2)) - (b*(a + b*ArcSin[c*x]))/(6*c^5*d^3*(1 - c^2*x^2)^(3/2)) + (5*b*(a + b*ArcSin[c*x]))/(4*c^5*d^3*Sqrt[1 - c^2*x^2]) + (x^3*(a + b*ArcSin[c*x])^2)/(4*c^2*d^3*(1 - c^2*x^2)^2) - (3*x*(a + b*ArcSin[c*x])^2)/(8*c^4*d^3*(1 - c^2*x^2)) - (((3*I)/4)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c^5*d^3) - (7*b^2*ArcTanh[c*x])/(6*c^5*d^3) + (((3*I)/4)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^5*d^3) - (((3*I)/4)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^5*d^3) - (3*b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(4*c^5*d^3) + (3*b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(4*c^5*d^3)","A",16,13,27,0.4815,1,"{4703, 4657, 4181, 2531, 2282, 6589, 4677, 206, 266, 43, 4689, 12, 385}"
202,1,172,0,0.3343198,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^3,x]","\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x^3 \left(a+b \sin ^{-1}(c x)\right)}{6 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{2 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^4 d^3}+\frac{b^2}{12 c^4 d^3 \left(1-c^2 x^2\right)}+\frac{b^2 \log \left(1-c^2 x^2\right)}{3 c^4 d^3}","\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x^3 \left(a+b \sin ^{-1}(c x)\right)}{6 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{2 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^4 d^3}+\frac{b^2}{12 c^4 d^3 \left(1-c^2 x^2\right)}+\frac{b^2 \log \left(1-c^2 x^2\right)}{3 c^4 d^3}",1,"b^2/(12*c^4*d^3*(1 - c^2*x^2)) - (b*x^3*(a + b*ArcSin[c*x]))/(6*c*d^3*(1 - c^2*x^2)^(3/2)) + (b*x*(a + b*ArcSin[c*x]))/(2*c^3*d^3*Sqrt[1 - c^2*x^2]) - (a + b*ArcSin[c*x])^2/(4*c^4*d^3) + (x^4*(a + b*ArcSin[c*x])^2)/(4*d^3*(1 - c^2*x^2)^2) + (b^2*Log[1 - c^2*x^2])/(3*c^4*d^3)","A",8,6,27,0.2222,1,"{4681, 4703, 4641, 260, 266, 43}"
203,1,341,0,0.4217449,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 c^3 d^3}-\frac{b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 c^3 d^3}+\frac{b \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{6 c^3 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^3 d^3}+\frac{b^2 x}{12 c^2 d^3 \left(1-c^2 x^2\right)}-\frac{b^2 \tanh ^{-1}(c x)}{6 c^3 d^3}","-\frac{i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 c^3 d^3}-\frac{b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 c^3 d^3}+\frac{b \left(a+b \sin ^{-1}(c x)\right)}{4 c^3 d^3 \sqrt{1-c^2 x^2}}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{6 c^3 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}+\frac{i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^3 d^3}+\frac{b^2 x}{12 c^2 d^3 \left(1-c^2 x^2\right)}-\frac{b^2 \tanh ^{-1}(c x)}{6 c^3 d^3}",1,"(b^2*x)/(12*c^2*d^3*(1 - c^2*x^2)) - (b*(a + b*ArcSin[c*x]))/(6*c^3*d^3*(1 - c^2*x^2)^(3/2)) + (b*(a + b*ArcSin[c*x]))/(4*c^3*d^3*Sqrt[1 - c^2*x^2]) + (x*(a + b*ArcSin[c*x])^2)/(4*c^2*d^3*(1 - c^2*x^2)^2) - (x*(a + b*ArcSin[c*x])^2)/(8*c^2*d^3*(1 - c^2*x^2)) + ((I/4)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c^3*d^3) - (b^2*ArcTanh[c*x])/(6*c^3*d^3) - ((I/4)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^3*d^3) + ((I/4)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^3*d^3) + (b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(4*c^3*d^3) - (b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(4*c^3*d^3)","A",15,10,27,0.3704,1,"{4703, 4655, 4657, 4181, 2531, 2282, 6589, 4677, 206, 199}"
204,1,150,0,0.1370275,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^3,x]","-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{3 c d^3 \sqrt{1-c^2 x^2}}-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{6 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}+\frac{b^2}{12 c^2 d^3 \left(1-c^2 x^2\right)}-\frac{b^2 \log \left(1-c^2 x^2\right)}{6 c^2 d^3}","-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{3 c d^3 \sqrt{1-c^2 x^2}}-\frac{b x \left(a+b \sin ^{-1}(c x)\right)}{6 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}+\frac{b^2}{12 c^2 d^3 \left(1-c^2 x^2\right)}-\frac{b^2 \log \left(1-c^2 x^2\right)}{6 c^2 d^3}",1,"b^2/(12*c^2*d^3*(1 - c^2*x^2)) - (b*x*(a + b*ArcSin[c*x]))/(6*c*d^3*(1 - c^2*x^2)^(3/2)) - (b*x*(a + b*ArcSin[c*x]))/(3*c*d^3*Sqrt[1 - c^2*x^2]) + (a + b*ArcSin[c*x])^2/(4*c^2*d^3*(1 - c^2*x^2)^2) - (b^2*Log[1 - c^2*x^2])/(6*c^2*d^3)","A",5,5,25,0.2000,1,"{4677, 4655, 4651, 260, 261}"
205,1,332,0,0.3508263,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])^2/(d - c^2*d*x^2)^3,x]","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3}-\frac{3 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 c d^3}+\frac{3 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 c d^3}-\frac{3 b \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3 \sqrt{1-c^2 x^2}}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{6 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c d^3}+\frac{b^2 x}{12 d^3 \left(1-c^2 x^2\right)}+\frac{5 b^2 \tanh ^{-1}(c x)}{6 c d^3}","\frac{3 i b \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3}-\frac{3 i b \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3}-\frac{3 b^2 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 c d^3}+\frac{3 b^2 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 c d^3}-\frac{3 b \left(a+b \sin ^{-1}(c x)\right)}{4 c d^3 \sqrt{1-c^2 x^2}}-\frac{b \left(a+b \sin ^{-1}(c x)\right)}{6 c d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 i \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 c d^3}+\frac{b^2 x}{12 d^3 \left(1-c^2 x^2\right)}+\frac{5 b^2 \tanh ^{-1}(c x)}{6 c d^3}",1,"(b^2*x)/(12*d^3*(1 - c^2*x^2)) - (b*(a + b*ArcSin[c*x]))/(6*c*d^3*(1 - c^2*x^2)^(3/2)) - (3*b*(a + b*ArcSin[c*x]))/(4*c*d^3*Sqrt[1 - c^2*x^2]) + (x*(a + b*ArcSin[c*x])^2)/(4*d^3*(1 - c^2*x^2)^2) + (3*x*(a + b*ArcSin[c*x])^2)/(8*d^3*(1 - c^2*x^2)) - (((3*I)/4)*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/(c*d^3) + (5*b^2*ArcTanh[c*x])/(6*c*d^3) + (((3*I)/4)*b*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*d^3) - (((3*I)/4)*b*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*d^3) - (3*b^2*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(4*c*d^3) + (3*b^2*PolyLog[3, I*E^(I*ArcSin[c*x])])/(4*c*d^3)","A",15,9,24,0.3750,1,"{4655, 4657, 4181, 2531, 2282, 6589, 4677, 206, 199}"
206,1,296,0,0.4913397,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*(d - c^2*d*x^2)^3),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{4 b c x \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 \sqrt{1-c^2 x^2}}-\frac{b c x \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^3 \left(1-c^2 x^2\right)}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^3}+\frac{b^2}{12 d^3 \left(1-c^2 x^2\right)}-\frac{2 b^2 \log \left(1-c^2 x^2\right)}{3 d^3}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{b^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{4 b c x \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 \sqrt{1-c^2 x^2}}-\frac{b c x \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^3 \left(1-c^2 x^2\right)}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^3}+\frac{b^2}{12 d^3 \left(1-c^2 x^2\right)}-\frac{2 b^2 \log \left(1-c^2 x^2\right)}{3 d^3}",1,"b^2/(12*d^3*(1 - c^2*x^2)) - (b*c*x*(a + b*ArcSin[c*x]))/(6*d^3*(1 - c^2*x^2)^(3/2)) - (4*b*c*x*(a + b*ArcSin[c*x]))/(3*d^3*Sqrt[1 - c^2*x^2]) + (a + b*ArcSin[c*x])^2/(4*d^3*(1 - c^2*x^2)^2) + (a + b*ArcSin[c*x])^2/(2*d^3*(1 - c^2*x^2)) - (2*(a + b*ArcSin[c*x])^2*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^3 - (2*b^2*Log[1 - c^2*x^2])/(3*d^3) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^3 - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^3 - (b^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*d^3) + (b^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/(2*d^3)","A",17,11,27,0.4074,1,"{4705, 4679, 4419, 4183, 2531, 2282, 6589, 4651, 260, 4655, 261}"
207,1,429,0,0.759348,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*(d - c^2*d*x^2)^3),x]","\frac{15 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}+\frac{2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d^3}-\frac{2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d^3}-\frac{15 b^2 c \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}+\frac{15 b^2 c \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}-\frac{7 b c \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \sqrt{1-c^2 x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{15 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{5 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d^3 x \left(1-c^2 x^2\right)^2}-\frac{15 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3}-\frac{4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}+\frac{b^2 c^2 x}{12 d^3 \left(1-c^2 x^2\right)}+\frac{11 b^2 c \tanh ^{-1}(c x)}{6 d^3}","\frac{15 i b c \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}+\frac{2 i b^2 c \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{d^3}-\frac{2 i b^2 c \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{d^3}-\frac{15 b^2 c \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}+\frac{15 b^2 c \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}-\frac{7 b c \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \sqrt{1-c^2 x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{15 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{5 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d^3 x \left(1-c^2 x^2\right)^2}-\frac{15 i c \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3}-\frac{4 b c \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}+\frac{b^2 c^2 x}{12 d^3 \left(1-c^2 x^2\right)}+\frac{11 b^2 c \tanh ^{-1}(c x)}{6 d^3}",1,"(b^2*c^2*x)/(12*d^3*(1 - c^2*x^2)) - (b*c*(a + b*ArcSin[c*x]))/(6*d^3*(1 - c^2*x^2)^(3/2)) - (7*b*c*(a + b*ArcSin[c*x]))/(4*d^3*Sqrt[1 - c^2*x^2]) - (a + b*ArcSin[c*x])^2/(d^3*x*(1 - c^2*x^2)^2) + (5*c^2*x*(a + b*ArcSin[c*x])^2)/(4*d^3*(1 - c^2*x^2)^2) + (15*c^2*x*(a + b*ArcSin[c*x])^2)/(8*d^3*(1 - c^2*x^2)) - (((15*I)/4)*c*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/d^3 - (4*b*c*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/d^3 + (11*b^2*c*ArcTanh[c*x])/(6*d^3) + ((2*I)*b^2*c*PolyLog[2, -E^(I*ArcSin[c*x])])/d^3 + (((15*I)/4)*b*c*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^3 - (((15*I)/4)*b*c*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^3 - ((2*I)*b^2*c*PolyLog[2, E^(I*ArcSin[c*x])])/d^3 - (15*b^2*c*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(4*d^3) + (15*b^2*c*PolyLog[3, I*E^(I*ArcSin[c*x])])/(4*d^3)","A",27,15,27,0.5556,1,"{4701, 4655, 4657, 4181, 2531, 2282, 6589, 4677, 206, 199, 4705, 4709, 4183, 2279, 2391}"
208,1,403,0,0.7840978,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^3*(d - c^2*d*x^2)^3),x]","\frac{3 i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{3 i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{3 b^2 c^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{4 b c^3 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 x \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^3 \left(1-c^2 x^2\right)}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^3 x \left(1-c^2 x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^3 x^2 \left(1-c^2 x^2\right)^2}-\frac{6 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^3}+\frac{b^2 c^2}{12 d^3 \left(1-c^2 x^2\right)}-\frac{7 b^2 c^2 \log \left(1-c^2 x^2\right)}{6 d^3}+\frac{b^2 c^2 \log (x)}{d^3}","\frac{3 i b c^2 \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{3 i b c^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}+\frac{3 b^2 c^2 \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{4 b c^3 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 \sqrt{1-c^2 x^2}}+\frac{5 b c^3 x \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^3 \left(1-c^2 x^2\right)}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^3 x \left(1-c^2 x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d^3 x^2 \left(1-c^2 x^2\right)^2}-\frac{6 c^2 \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^3}+\frac{b^2 c^2}{12 d^3 \left(1-c^2 x^2\right)}-\frac{7 b^2 c^2 \log \left(1-c^2 x^2\right)}{6 d^3}+\frac{b^2 c^2 \log (x)}{d^3}",1,"(b^2*c^2)/(12*d^3*(1 - c^2*x^2)) - (b*c*(a + b*ArcSin[c*x]))/(d^3*x*(1 - c^2*x^2)^(3/2)) + (5*b*c^3*x*(a + b*ArcSin[c*x]))/(6*d^3*(1 - c^2*x^2)^(3/2)) - (4*b*c^3*x*(a + b*ArcSin[c*x]))/(3*d^3*Sqrt[1 - c^2*x^2]) + (3*c^2*(a + b*ArcSin[c*x])^2)/(4*d^3*(1 - c^2*x^2)^2) - (a + b*ArcSin[c*x])^2/(2*d^3*x^2*(1 - c^2*x^2)^2) + (3*c^2*(a + b*ArcSin[c*x])^2)/(2*d^3*(1 - c^2*x^2)) - (6*c^2*(a + b*ArcSin[c*x])^2*ArcTanh[E^((2*I)*ArcSin[c*x])])/d^3 + (b^2*c^2*Log[x])/d^3 - (7*b^2*c^2*Log[1 - c^2*x^2])/(6*d^3) + ((3*I)*b*c^2*(a + b*ArcSin[c*x])*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/d^3 - ((3*I)*b*c^2*(a + b*ArcSin[c*x])*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^3 - (3*b^2*c^2*PolyLog[3, -E^((2*I)*ArcSin[c*x])])/(2*d^3) + (3*b^2*c^2*PolyLog[3, E^((2*I)*ArcSin[c*x])])/(2*d^3)","A",23,19,27,0.7037,1,"{4701, 4705, 4679, 4419, 4183, 2531, 2282, 6589, 4651, 260, 4655, 261, 271, 192, 191, 4689, 12, 1251, 893}"
209,1,572,0,1.3212746,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^4*(d - c^2*d*x^2)^3),x]","\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}+\frac{19 i b^2 c^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{3 d^3}-\frac{19 i b^2 c^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{3 d^3}-\frac{35 b^2 c^3 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}+\frac{35 b^2 c^3 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{12 d^3 \left(1-c^2 x^2\right)^2}-\frac{29 b c^3 \left(a+b \sin ^{-1}(c x)\right)}{12 d^3 \sqrt{1-c^2 x^2}}+\frac{b c^3 \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{7 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^3 x \left(1-c^2 x^2\right)^2}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 x^2 \left(1-c^2 x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d^3 x^3 \left(1-c^2 x^2\right)^2}-\frac{35 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3}-\frac{38 b c^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^3}-\frac{b^2 c^4 x}{12 d^3 \left(1-c^2 x^2\right)}+\frac{b^2 c^2}{6 d^3 x \left(1-c^2 x^2\right)}-\frac{b^2 c^2}{2 d^3 x}+\frac{17 b^2 c^3 \tanh ^{-1}(c x)}{6 d^3}","\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}-\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3}+\frac{19 i b^2 c^3 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right)}{3 d^3}-\frac{19 i b^2 c^3 \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right)}{3 d^3}-\frac{35 b^2 c^3 \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}+\frac{35 b^2 c^3 \text{PolyLog}\left(3,i e^{i \sin ^{-1}(c x)}\right)}{4 d^3}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{35 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{12 d^3 \left(1-c^2 x^2\right)^2}-\frac{29 b c^3 \left(a+b \sin ^{-1}(c x)\right)}{12 d^3 \sqrt{1-c^2 x^2}}+\frac{b c^3 \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}-\frac{7 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^3 x \left(1-c^2 x^2\right)^2}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^3 x^2 \left(1-c^2 x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d^3 x^3 \left(1-c^2 x^2\right)^2}-\frac{35 i c^3 \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3}-\frac{38 b c^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^3}-\frac{b^2 c^4 x}{12 d^3 \left(1-c^2 x^2\right)}+\frac{b^2 c^2}{6 d^3 x \left(1-c^2 x^2\right)}-\frac{b^2 c^2}{2 d^3 x}+\frac{17 b^2 c^3 \tanh ^{-1}(c x)}{6 d^3}",1,"-(b^2*c^2)/(2*d^3*x) + (b^2*c^2)/(6*d^3*x*(1 - c^2*x^2)) - (b^2*c^4*x)/(12*d^3*(1 - c^2*x^2)) + (b*c^3*(a + b*ArcSin[c*x]))/(6*d^3*(1 - c^2*x^2)^(3/2)) - (b*c*(a + b*ArcSin[c*x]))/(3*d^3*x^2*(1 - c^2*x^2)^(3/2)) - (29*b*c^3*(a + b*ArcSin[c*x]))/(12*d^3*Sqrt[1 - c^2*x^2]) - (a + b*ArcSin[c*x])^2/(3*d^3*x^3*(1 - c^2*x^2)^2) - (7*c^2*(a + b*ArcSin[c*x])^2)/(3*d^3*x*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSin[c*x])^2)/(12*d^3*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSin[c*x])^2)/(8*d^3*(1 - c^2*x^2)) - (((35*I)/4)*c^3*(a + b*ArcSin[c*x])^2*ArcTan[E^(I*ArcSin[c*x])])/d^3 - (38*b*c^3*(a + b*ArcSin[c*x])*ArcTanh[E^(I*ArcSin[c*x])])/(3*d^3) + (17*b^2*c^3*ArcTanh[c*x])/(6*d^3) + (((19*I)/3)*b^2*c^3*PolyLog[2, -E^(I*ArcSin[c*x])])/d^3 + (((35*I)/4)*b*c^3*(a + b*ArcSin[c*x])*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/d^3 - (((35*I)/4)*b*c^3*(a + b*ArcSin[c*x])*PolyLog[2, I*E^(I*ArcSin[c*x])])/d^3 - (((19*I)/3)*b^2*c^3*PolyLog[2, E^(I*ArcSin[c*x])])/d^3 - (35*b^2*c^3*PolyLog[3, (-I)*E^(I*ArcSin[c*x])])/(4*d^3) + (35*b^2*c^3*PolyLog[3, I*E^(I*ArcSin[c*x])])/(4*d^3)","A",43,17,27,0.6296,1,"{4701, 4655, 4657, 4181, 2531, 2282, 6589, 4677, 206, 199, 4705, 4709, 4183, 2279, 2391, 290, 325}"
210,1,374,0,0.4704167,"\int x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","\frac{4 a b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}-\frac{2 b c 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{1}{5} x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c \sqrt{1-c^2 x^2}}-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^2}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^4}-\frac{2 b^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^4}+\frac{26 b^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{675 c^4}+\frac{52 b^2 \sqrt{d-c^2 d x^2}}{225 c^4}+\frac{4 b^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{15 c^3 \sqrt{1-c^2 x^2}}","\frac{4 a b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}-\frac{2 b c 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{1}{5} x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c \sqrt{1-c^2 x^2}}-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^2}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^4}-\frac{2 b^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^4}+\frac{26 b^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{675 c^4}+\frac{52 b^2 \sqrt{d-c^2 d x^2}}{225 c^4}+\frac{4 b^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{15 c^3 \sqrt{1-c^2 x^2}}",1,"(52*b^2*Sqrt[d - c^2*d*x^2])/(225*c^4) + (4*a*b*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[1 - c^2*x^2]) + (26*b^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(675*c^4) - (2*b^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*c^4) + (4*b^2*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(15*c^3*Sqrt[1 - c^2*x^2]) + (2*b*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(45*c*Sqrt[1 - c^2*x^2]) - (2*b*c*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*c^4) - (x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*c^2) + (x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/5","A",14,8,29,0.2759,1,"{4697, 4707, 4677, 4619, 261, 4627, 266, 43}"
211,1,303,0,0.3844345,"\int x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","-\frac{b c 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} x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b 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{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{\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}{32} b^2 x^3 \sqrt{d-c^2 d x^2}+\frac{b^2 x \sqrt{d-c^2 d x^2}}{64 c^2}-\frac{b^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}","-\frac{b c 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} x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b 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{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{\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}{32} b^2 x^3 \sqrt{d-c^2 d x^2}+\frac{b^2 x \sqrt{d-c^2 d x^2}}{64 c^2}-\frac{b^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}",1,"(b^2*x*Sqrt[d - c^2*d*x^2])/(64*c^2) - (b^2*x^3*Sqrt[d - c^2*d*x^2])/32 - (b^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c^3*Sqrt[1 - c^2*x^2]) + (b*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c*Sqrt[1 - c^2*x^2]) - (b*c*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(8*c^2) + (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/4 + (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(24*b*c^3*Sqrt[1 - c^2*x^2])","A",10,6,29,0.2069,1,"{4697, 4707, 4641, 4627, 321, 216}"
212,1,188,0,0.1593791,"\int x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c 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 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{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d}+\frac{2 b^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 c^2}+\frac{4 b^2 \sqrt{d-c^2 d x^2}}{9 c^2}","-\frac{2 b c 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 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{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d}+\frac{2 b^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{27 c^2}+\frac{4 b^2 \sqrt{d-c^2 d x^2}}{9 c^2}",1,"(4*b^2*Sqrt[d - c^2*d*x^2])/(9*c^2) + (2*b^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(27*c^2) + (2*b*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*c*Sqrt[1 - c^2*x^2]) - (2*b*c*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(3*c^2*d)","A",5,4,27,0.1481,1,"{4677, 4645, 444, 43}"
213,1,192,0,0.1146788,"\int \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","\frac{\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{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c 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}{4} b^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}","\frac{\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{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c 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}{4} b^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}",1,"-(b^2*x*Sqrt[d - c^2*d*x^2])/4 + (b^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) - (b*c*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 + (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2])","A",5,5,26,0.1923,1,"{4647, 4641, 4627, 321, 216}"
214,1,378,0,0.348865,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/x,x]","\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}+\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-2 b^2 \sqrt{d-c^2 d x^2}-\frac{2 b^2 c x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}","\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}+\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-2 b^2 \sqrt{d-c^2 d x^2}-\frac{2 b^2 c x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}",1,"-2*b^2*Sqrt[d - c^2*d*x^2] - (2*a*b*c*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] - (2*b^2*c*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] + Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2 - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((2*I)*b*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - ((2*I)*b*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (2*b^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (2*b^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",12,8,29,0.2759,1,"{4697, 4709, 4183, 2531, 2282, 6589, 4619, 261}"
215,1,227,0,0.3195084,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/x^2,x]","-\frac{i b^2 c \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b \sqrt{1-c^2 x^2}}-\frac{i c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{2 b c \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}","-\frac{i b^2 c \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b \sqrt{1-c^2 x^2}}-\frac{i c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{2 b c \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}",1,"-((Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/x) - (I*c*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - (c*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*Sqrt[1 - c^2*x^2]) + (2*b*c*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b^2*c*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",7,7,29,0.2414,1,"{4693, 4625, 3717, 2190, 2279, 2391, 4641}"
216,1,398,0,0.3819503,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/x^3,x]","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{1-c^2 x^2}}","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{b c \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{1-c^2 x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{1-c^2 x^2}}",1,"-((b*c*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(x*Sqrt[1 - c^2*x^2])) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*x^2) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (b^2*c^2*Sqrt[d - c^2*d*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/Sqrt[1 - c^2*x^2] - (I*b*c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (I*b*c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (b^2*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (b^2*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",13,10,29,0.3448,1,"{4693, 4627, 266, 63, 208, 4709, 4183, 2531, 2282, 6589}"
217,1,314,0,0.2716091,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/x^4,x]","\frac{i b^2 c^3 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{1-c^2 x^2}}+\frac{i c^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3}-\frac{2 b c^3 \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}-\frac{b^2 c^2 \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{3 \sqrt{1-c^2 x^2}}","\frac{i b^2 c^3 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{1-c^2 x^2}}+\frac{i c^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{1-c^2 x^2}}-\frac{b c \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3}-\frac{2 b c^3 \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}-\frac{b^2 c^2 \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{3 \sqrt{1-c^2 x^2}}",1,"-(b^2*c^2*Sqrt[d - c^2*d*x^2])/(3*x) - (b^2*c^3*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(3*Sqrt[1 - c^2*x^2]) - (b*c*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*x^2) + ((I/3)*c^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(3*d*x^3) - (2*b*c^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/(3*Sqrt[1 - c^2*x^2]) + ((I/3)*b^2*c^3*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",9,9,29,0.3103,1,"{4681, 4685, 277, 216, 4625, 3717, 2190, 2279, 2391}"
218,1,503,0,0.779804,"\int x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{4 a b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d x^7 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{49 \sqrt{1-c^2 x^2}}-\frac{16 b c d x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{175 \sqrt{1-c^2 x^2}}+\frac{1}{7} x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{35} d x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{105 c \sqrt{1-c^2 x^2}}-\frac{d x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{35 c^2}-\frac{2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{35 c^4}-\frac{2 b^2 d \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^4}+\frac{38 b^2 d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{6125 c^4}+\frac{304 b^2 d \sqrt{d-c^2 d x^2}}{3675 c^4}+\frac{152 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11025 c^4}+\frac{4 b^2 d x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{35 c^3 \sqrt{1-c^2 x^2}}","\frac{4 a b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d x^7 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{49 \sqrt{1-c^2 x^2}}-\frac{16 b c d x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{175 \sqrt{1-c^2 x^2}}+\frac{1}{7} x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{35} d x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{105 c \sqrt{1-c^2 x^2}}-\frac{d x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{35 c^2}-\frac{2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{35 c^4}-\frac{2 b^2 d \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^4}+\frac{38 b^2 d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{6125 c^4}+\frac{304 b^2 d \sqrt{d-c^2 d x^2}}{3675 c^4}+\frac{152 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11025 c^4}+\frac{4 b^2 d x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{35 c^3 \sqrt{1-c^2 x^2}}",1,"(304*b^2*d*Sqrt[d - c^2*d*x^2])/(3675*c^4) + (4*a*b*d*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[1 - c^2*x^2]) + (152*b^2*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(11025*c^4) + (38*b^2*d*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(6125*c^4) - (2*b^2*d*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(343*c^4) + (4*b^2*d*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(35*c^3*Sqrt[1 - c^2*x^2]) + (2*b*d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(105*c*Sqrt[1 - c^2*x^2]) - (16*b*c*d*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(175*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(49*Sqrt[1 - c^2*x^2]) - (2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(35*c^4) - (d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(35*c^2) + (3*d*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/35 + (x^4*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/7","A",20,14,29,0.4828,1,"{4699, 4697, 4707, 4677, 4619, 261, 4627, 266, 43, 14, 4687, 12, 446, 77}"
219,1,421,0,0.7095405,"\int x^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{b c^3 d x^6 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 \sqrt{1-c^2 x^2}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 \sqrt{1-c^2 x^2}}+\frac{1}{6} x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c \sqrt{1-c^2 x^2}}-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 c^2}+\frac{d \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{1}{108} b^2 c^2 d x^5 \sqrt{d-c^2 d x^2}-\frac{43 b^2 d x^3 \sqrt{d-c^2 d x^2}}{1728}-\frac{7 b^2 d x \sqrt{d-c^2 d x^2}}{1152 c^2}+\frac{7 b^2 d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c^3 \sqrt{1-c^2 x^2}}","\frac{b c^3 d x^6 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{18 \sqrt{1-c^2 x^2}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{48 \sqrt{1-c^2 x^2}}+\frac{1}{6} x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 c \sqrt{1-c^2 x^2}}-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 c^2}+\frac{d \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{1}{108} b^2 c^2 d x^5 \sqrt{d-c^2 d x^2}-\frac{43 b^2 d x^3 \sqrt{d-c^2 d x^2}}{1728}-\frac{7 b^2 d x \sqrt{d-c^2 d x^2}}{1152 c^2}+\frac{7 b^2 d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c^3 \sqrt{1-c^2 x^2}}",1,"(-7*b^2*d*x*Sqrt[d - c^2*d*x^2])/(1152*c^2) - (43*b^2*d*x^3*Sqrt[d - c^2*d*x^2])/1728 + (b^2*c^2*d*x^5*Sqrt[d - c^2*d*x^2])/108 + (7*b^2*d*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(1152*c^3*Sqrt[1 - c^2*x^2]) + (b*d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(16*c*Sqrt[1 - c^2*x^2]) - (7*b*c*d*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*Sqrt[1 - c^2*x^2]) + (b*c^3*d*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(18*Sqrt[1 - c^2*x^2]) - (d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(16*c^2) + (d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 + (x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/6 + (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(48*b*c^3*Sqrt[1 - c^2*x^2])","A",17,11,29,0.3793,1,"{4699, 4697, 4707, 4641, 4627, 321, 216, 14, 4687, 12, 459}"
220,1,279,0,0.2280636,"\int x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2 b c^3 d 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 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 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{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{2 b^2 d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{16 b^2 d \sqrt{d-c^2 d x^2}}{75 c^2}+\frac{8 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{225 c^2}","\frac{2 b c^3 d 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 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 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{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{2 b^2 d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{125 c^2}+\frac{16 b^2 d \sqrt{d-c^2 d x^2}}{75 c^2}+\frac{8 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{225 c^2}",1,"(16*b^2*d*Sqrt[d - c^2*d*x^2])/(75*c^2) + (8*b^2*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(225*c^2) + (2*b^2*d*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(125*c^2) + (2*b*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(5*c*Sqrt[1 - c^2*x^2]) - (4*b*c*d*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*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(5*c^2*d)","A",6,6,27,0.2222,1,"{4677, 194, 4645, 12, 1247, 698}"
221,1,307,0,0.2396484,"\int \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{d \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{1}{4} x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d \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{3 b c d 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{15}{64} b^2 d x \sqrt{d-c^2 d x^2}-\frac{1}{32} b^2 d x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}+\frac{9 b^2 d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}","\frac{b c^3 d 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{5 b c d 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{1}{4} x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{d \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{1}{32} b^2 c^2 d x^3 \sqrt{d-c^2 d x^2}-\frac{17}{64} b^2 d x \sqrt{d-c^2 d x^2}+\frac{17 b^2 d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}",1,"(-15*b^2*d*x*Sqrt[d - c^2*d*x^2])/64 - (b^2*d*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/32 + (9*b^2*d*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*c*Sqrt[1 - c^2*x^2]) - (3*b*c*d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (b*d*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 + (x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/4 + (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*c*Sqrt[1 - c^2*x^2])","A",10,8,26,0.3077,1,"{4649, 4647, 4641, 4627, 321, 216, 4677, 195}"
222,1,545,0,0.6035785,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/x,x]","\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c d x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}+\frac{2 b c^3 d 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 c d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{1}{3} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{22}{9} b^2 d \sqrt{d-c^2 d x^2}-\frac{2}{27} b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}-\frac{2 b^2 c d x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}","\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c d x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}+\frac{2 b c^3 d 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 c d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{1}{3} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2+d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{22}{9} b^2 d \sqrt{d-c^2 d x^2}-\frac{2}{27} b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}-\frac{2 b^2 c d x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}",1,"(-22*b^2*d*Sqrt[d - c^2*d*x^2])/9 - (2*a*b*c*d*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] - (2*b^2*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/27 - (2*b^2*c*d*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] - (2*b*c*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*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*Sqrt[1 - c^2*x^2]) + d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2 + ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/3 - (2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((2*I)*b*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - ((2*I)*b*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (2*b^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (2*b^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",17,12,29,0.4138,1,"{4699, 4697, 4709, 4183, 2531, 2282, 6589, 4619, 261, 4645, 444, 43}"
223,1,424,0,0.4042783,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/x^2,x]","-\frac{i b^2 c d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{3 b c^3 d 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{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b \sqrt{1-c^2 x^2}}-\frac{i c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+b c d \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{2 b c d \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{1}{4} b^2 c^2 d x \sqrt{d-c^2 d x^2}-\frac{5 b^2 c d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 \sqrt{1-c^2 x^2}}","-\frac{i b^2 c d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{3 b c^3 d 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{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b \sqrt{1-c^2 x^2}}-\frac{i c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+b c d \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{2 b c d \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{1}{4} b^2 c^2 d x \sqrt{d-c^2 d x^2}-\frac{5 b^2 c d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{4 \sqrt{1-c^2 x^2}}",1,"(b^2*c^2*d*x*Sqrt[d - c^2*d*x^2])/4 - (5*b^2*c*d*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(4*Sqrt[1 - c^2*x^2]) + (3*b*c^3*d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + b*c*d*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]) - (3*c^2*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 - (I*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/x - (c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(2*b*Sqrt[1 - c^2*x^2]) + (2*b*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b^2*c*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",14,13,29,0.4483,1,"{4695, 4647, 4641, 4627, 321, 216, 4683, 4625, 3717, 2190, 2279, 2391, 195}"
224,1,590,0,0.612378,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/x^3,x]","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{3 b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{3 b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{3 a b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{b c^3 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{1-c^2 x^2}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+2 b^2 c^2 d \sqrt{d-c^2 d x^2}+\frac{3 b^2 c^3 d x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{1-c^2 x^2}}","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{3 b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{3 b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{3 a b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{b c^3 d x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{1-c^2 x^2}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+2 b^2 c^2 d \sqrt{d-c^2 d x^2}+\frac{3 b^2 c^3 d x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 d \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{1-c^2 x^2}}",1,"2*b^2*c^2*d*Sqrt[d - c^2*d*x^2] + (3*a*b*c^3*d*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] + (3*b^2*c^3*d*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] - (b*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(x*Sqrt[1 - c^2*x^2]) - (b*c^3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/Sqrt[1 - c^2*x^2] - (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(2*x^2) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (b^2*c^2*d*Sqrt[d - c^2*d*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/Sqrt[1 - c^2*x^2] - ((3*I)*b*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((3*I)*b*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (3*b^2*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (3*b^2*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",18,15,29,0.5172,1,"{4695, 4697, 4709, 4183, 2531, 2282, 6589, 4619, 261, 14, 4687, 446, 80, 63, 208}"
225,1,400,0,0.5548774,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/x^4,x]","\frac{4 i b^2 c^3 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{1-c^2 x^2}}+\frac{c^3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b \sqrt{1-c^2 x^2}}+\frac{4 i c^3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{1-c^2 x^2}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{b c d \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}-\frac{8 b c^3 d \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}-\frac{b^2 c^2 d \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{3 \sqrt{1-c^2 x^2}}","\frac{4 i b^2 c^3 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{1-c^2 x^2}}+\frac{c^3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b \sqrt{1-c^2 x^2}}+\frac{4 i c^3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{1-c^2 x^2}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}-\frac{b c d \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}-\frac{8 b c^3 d \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}-\frac{b^2 c^2 d \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 d \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{3 \sqrt{1-c^2 x^2}}",1,"-(b^2*c^2*d*Sqrt[d - c^2*d*x^2])/(3*x) - (b^2*c^3*d*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(3*Sqrt[1 - c^2*x^2]) - (b*c*d*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*x^2) + (c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/x + (((4*I)/3)*c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - ((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(3*x^3) + (c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*Sqrt[1 - c^2*x^2]) - (8*b*c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/(3*Sqrt[1 - c^2*x^2]) + (((4*I)/3)*b^2*c^3*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",16,11,29,0.3793,1,"{4695, 4693, 4625, 3717, 2190, 2279, 2391, 4641, 4685, 277, 216}"
226,1,651,0,1.2455294,"\int x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","\frac{4 a b d^2 x \sqrt{d-c^2 d x^2}}{63 c^3 \sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 x^9 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{81 \sqrt{1-c^2 x^2}}+\frac{38 b c^3 d^2 x^7 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{441 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{21 \sqrt{1-c^2 x^2}}+\frac{1}{21} d^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{189 c \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}{63 c^2}-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{63 c^4}+\frac{1}{9} x^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5}{63} d x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{729 c^4}+\frac{50 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{27783 c^4}+\frac{160 b^2 d^2 \sqrt{d-c^2 d x^2}}{3969 c^4}+\frac{4 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1323 c^4}+\frac{80 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11907 c^4}+\frac{4 b^2 d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{63 c^3 \sqrt{1-c^2 x^2}}","\frac{4 a b d^2 x \sqrt{d-c^2 d x^2}}{63 c^3 \sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 x^9 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{81 \sqrt{1-c^2 x^2}}+\frac{38 b c^3 d^2 x^7 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{441 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{21 \sqrt{1-c^2 x^2}}+\frac{1}{21} d^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{189 c \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}{63 c^2}-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{63 c^4}+\frac{1}{9} x^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5}{63} d x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{729 c^4}+\frac{50 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{27783 c^4}+\frac{160 b^2 d^2 \sqrt{d-c^2 d x^2}}{3969 c^4}+\frac{4 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1323 c^4}+\frac{80 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{11907 c^4}+\frac{4 b^2 d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{63 c^3 \sqrt{1-c^2 x^2}}",1,"(160*b^2*d^2*Sqrt[d - c^2*d*x^2])/(3969*c^4) + (4*a*b*d^2*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[1 - c^2*x^2]) + (80*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(11907*c^4) + (4*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(1323*c^4) + (50*b^2*d^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(27783*c^4) - (2*b^2*d^2*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2])/(729*c^4) + (4*b^2*d^2*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(63*c^3*Sqrt[1 - c^2*x^2]) + (2*b*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(189*c*Sqrt[1 - c^2*x^2]) - (2*b*c*d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(21*Sqrt[1 - c^2*x^2]) + (38*b*c^3*d^2*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(441*Sqrt[1 - c^2*x^2]) - (2*b*c^5*d^2*x^9*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(81*Sqrt[1 - c^2*x^2]) - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(63*c^4) - (d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(63*c^2) + (d^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/21 + (5*d*x^4*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/63 + (x^4*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/9","A",27,18,29,0.6207,1,"{4699, 4697, 4707, 4677, 4619, 261, 4627, 266, 43, 14, 4687, 12, 446, 77, 270, 1251, 897, 1153}"
227,1,556,0,1.1065844,"\int x^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{b c^5 d^2 x^8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{32 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 x^6 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{144 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{384 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5 b d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c \sqrt{1-c^2 x^2}}-\frac{5 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{128 c^2}+\frac{5 d^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{1}{8} x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5}{48} d x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{256} b^2 c^4 d^2 x^7 \sqrt{d-c^2 d x^2}+\frac{209 b^2 c^2 d^2 x^5 \sqrt{d-c^2 d x^2}}{13824}-\frac{1079 b^2 d^2 x^3 \sqrt{d-c^2 d x^2}}{55296}-\frac{359 b^2 d^2 x \sqrt{d-c^2 d x^2}}{36864 c^2}+\frac{359 b^2 d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{36864 c^3 \sqrt{1-c^2 x^2}}","-\frac{b c^5 d^2 x^8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{32 \sqrt{1-c^2 x^2}}+\frac{17 b c^3 d^2 x^6 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{144 \sqrt{1-c^2 x^2}}-\frac{59 b c d^2 x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{384 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5 b d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{128 c \sqrt{1-c^2 x^2}}-\frac{5 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{128 c^2}+\frac{5 d^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{1}{8} x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5}{48} d x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{256} b^2 c^4 d^2 x^7 \sqrt{d-c^2 d x^2}+\frac{209 b^2 c^2 d^2 x^5 \sqrt{d-c^2 d x^2}}{13824}-\frac{1079 b^2 d^2 x^3 \sqrt{d-c^2 d x^2}}{55296}-\frac{359 b^2 d^2 x \sqrt{d-c^2 d x^2}}{36864 c^2}+\frac{359 b^2 d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{36864 c^3 \sqrt{1-c^2 x^2}}",1,"(-359*b^2*d^2*x*Sqrt[d - c^2*d*x^2])/(36864*c^2) - (1079*b^2*d^2*x^3*Sqrt[d - c^2*d*x^2])/55296 + (209*b^2*c^2*d^2*x^5*Sqrt[d - c^2*d*x^2])/13824 - (b^2*c^4*d^2*x^7*Sqrt[d - c^2*d*x^2])/256 + (359*b^2*d^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(36864*c^3*Sqrt[1 - c^2*x^2]) + (5*b*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(128*c*Sqrt[1 - c^2*x^2]) - (59*b*c*d^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(384*Sqrt[1 - c^2*x^2]) + (17*b*c^3*d^2*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(144*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*x^8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(32*Sqrt[1 - c^2*x^2]) - (5*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(128*c^2) + (5*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/64 + (5*d*x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/48 + (x^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/8 + (5*d^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",25,14,29,0.4828,1,"{4699, 4697, 4707, 4641, 4627, 321, 216, 14, 4687, 12, 459, 266, 43, 1267}"
228,1,382,0,0.2927482,"\int x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c^5 d^2 x^7 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{49 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{35 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c \sqrt{1-c^2 x^2}}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2 d}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{32 b^2 d^2 \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{12 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{16 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{735 c^2}","-\frac{2 b c^5 d^2 x^7 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{49 \sqrt{1-c^2 x^2}}+\frac{6 b c^3 d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{35 \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{7 c \sqrt{1-c^2 x^2}}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \sin ^{-1}(c x)\right)^2}{7 c^2 d}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{343 c^2}+\frac{32 b^2 d^2 \sqrt{d-c^2 d x^2}}{245 c^2}+\frac{12 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{1225 c^2}+\frac{16 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{735 c^2}",1,"(32*b^2*d^2*Sqrt[d - c^2*d*x^2])/(245*c^2) + (16*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(735*c^2) + (12*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(1225*c^2) + (2*b^2*d^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(343*c^2) + (2*b*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(7*c*Sqrt[1 - c^2*x^2]) - (2*b*c*d^2*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*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*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(49*Sqrt[1 - c^2*x^2]) - ((d - c^2*d*x^2)^(7/2)*(a + b*ArcSin[c*x])^2)/(7*c^2*d)","A",6,6,27,0.2222,1,"{4677, 194, 4645, 12, 1799, 1850}"
229,1,438,0,0.3870966,"\int \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","\frac{5 d^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}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d^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 \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{5 b c d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 \sqrt{1-c^2 x^2}}+\frac{1}{6} x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5}{24} d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{108} b^2 d^2 x \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}-\frac{245 b^2 d^2 x \sqrt{d-c^2 d x^2}}{1152}-\frac{65 b^2 d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{1728}+\frac{115 b^2 d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}","\frac{5 d^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}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d^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 \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{5 b c d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{16 \sqrt{1-c^2 x^2}}+\frac{1}{6} x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5}{24} d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{108} b^2 d^2 x \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}-\frac{245 b^2 d^2 x \sqrt{d-c^2 d x^2}}{1152}-\frac{65 b^2 d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{1728}+\frac{115 b^2 d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{1152 c \sqrt{1-c^2 x^2}}",1,"(-245*b^2*d^2*x*Sqrt[d - c^2*d*x^2])/1152 - (65*b^2*d^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/1728 - (b^2*d^2*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/108 + (115*b^2*d^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(1152*c*Sqrt[1 - c^2*x^2]) - (5*b*c*d^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*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(48*c) + (b*d^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*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/16 + (5*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/24 + (x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/6 + (5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(48*b*c*Sqrt[1 - c^2*x^2])","A",16,8,26,0.3077,1,"{4649, 4647, 4641, 4627, 321, 216, 4677, 195}"
230,1,687,0,0.8858074,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/x,x]","\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 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{22 b c^3 d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 \sqrt{1-c^2 x^2}}-\frac{16 b c d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 \sqrt{1-c^2 x^2}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+\frac{1}{5} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{3} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{598}{225} b^2 d^2 \sqrt{d-c^2 d x^2}-\frac{2}{125} b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}-\frac{74}{675} b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}-\frac{2 b^2 c d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}","\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 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{22 b c^3 d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 \sqrt{1-c^2 x^2}}-\frac{16 b c d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{15 \sqrt{1-c^2 x^2}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+\frac{1}{5} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{3} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{598}{225} b^2 d^2 \sqrt{d-c^2 d x^2}-\frac{2}{125} b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}-\frac{74}{675} b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}-\frac{2 b^2 c d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}",1,"(-598*b^2*d^2*Sqrt[d - c^2*d*x^2])/225 - (2*a*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] - (74*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/675 - (2*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/125 - (2*b^2*c*d^2*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] - (16*b*c*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(15*Sqrt[1 - c^2*x^2]) + (22*b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(45*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*Sqrt[1 - c^2*x^2]) + d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2 + (d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/3 + ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/5 - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((2*I)*b*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - ((2*I)*b*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (2*b^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (2*b^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",23,16,29,0.5517,1,"{4699, 4697, 4709, 4183, 2531, 2282, 6589, 4619, 261, 4645, 444, 43, 194, 12, 1247, 698}"
231,1,561,0,0.6027779,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/x^2,x]","-\frac{i b^2 c d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{15 b c^3 d^2 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{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{5 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b \sqrt{1-c^2 x^2}}-\frac{i c d^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}{8} b c d^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)+b c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{5}{4} c^2 d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{31}{64} b^2 c^2 d^2 x \sqrt{d-c^2 d x^2}+\frac{1}{32} b^2 c^2 d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}-\frac{89 b^2 c d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 \sqrt{1-c^2 x^2}}","-\frac{i b^2 c d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{15 b c^3 d^2 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{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{5 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b \sqrt{1-c^2 x^2}}-\frac{i c d^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}{8} b c d^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)+b c d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)+\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{5}{4} c^2 d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{31}{64} b^2 c^2 d^2 x \sqrt{d-c^2 d x^2}+\frac{1}{32} b^2 c^2 d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}-\frac{89 b^2 c d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{64 \sqrt{1-c^2 x^2}}",1,"(31*b^2*c^2*d^2*x*Sqrt[d - c^2*d*x^2])/64 + (b^2*c^2*d^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/32 - (89*b^2*c*d^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(64*Sqrt[1 - c^2*x^2]) + (15*b*c^3*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + b*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]) - (b*c*d^2*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/8 - (15*c^2*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/8 - (I*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - (5*c^2*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/4 - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/x - (5*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*Sqrt[1 - c^2*x^2]) + (2*b*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b^2*c*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",23,15,29,0.5172,1,"{4695, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 4683, 4625, 3717, 2190, 2279, 2391}"
232,1,740,0,0.9550575,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/x^3,x]","-\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{5 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{5 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{5 a b c^3 d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 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{b c^3 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}-\frac{5}{2} c^2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{1-c^2 x^2}}+\frac{5 c^2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{5}{6} c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{40}{9} b^2 c^2 d^2 \sqrt{d-c^2 d x^2}+\frac{2}{27} b^2 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}+\frac{5 b^2 c^3 d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{1-c^2 x^2}}","-\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}+\frac{5 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{5 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{5 a b c^3 d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{1-c^2 x^2}}-\frac{2 b c^5 d^2 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{b c^3 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}-\frac{5}{2} c^2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{1-c^2 x^2}}+\frac{5 c^2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}-\frac{5}{6} c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 x^2}+\frac{40}{9} b^2 c^2 d^2 \sqrt{d-c^2 d x^2}+\frac{2}{27} b^2 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}+\frac{5 b^2 c^3 d^2 x \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-\frac{b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{1-c^2 x^2}}",1,"(40*b^2*c^2*d^2*Sqrt[d - c^2*d*x^2])/9 + (5*a*b*c^3*d^2*x*Sqrt[d - c^2*d*x^2])/Sqrt[1 - c^2*x^2] + (2*b^2*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/27 + (5*b^2*c^3*d^2*x*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] - (b*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(x*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) - (2*b*c^5*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) - (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 - (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/6 - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(2*x^2) + (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (b^2*c^2*d^2*Sqrt[d - c^2*d*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/Sqrt[1 - c^2*x^2] - ((5*I)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((5*I)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (5*b^2*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (5*b^2*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",25,20,29,0.6897,1,"{4695, 4699, 4697, 4709, 4183, 2531, 2282, 6589, 4619, 261, 4645, 444, 43, 270, 4687, 12, 1251, 897, 1153, 208}"
233,1,591,0,0.8834941,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/x^4,x]","\frac{7 i b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{1-c^2 x^2}}-\frac{5 b c^5 d^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{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b \sqrt{1-c^2 x^2}}+\frac{7 i c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{1-c^2 x^2}}-\frac{7}{3} b c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^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)}{3 x^2}-\frac{14 b c^3 d^2 \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 x}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}-\frac{7}{12} b^2 c^4 d^2 x \sqrt{d-c^2 d x^2}-\frac{b^2 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{3 x}+\frac{23 b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{12 \sqrt{1-c^2 x^2}}","\frac{7 i b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{1-c^2 x^2}}-\frac{5 b c^5 d^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{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b \sqrt{1-c^2 x^2}}+\frac{7 i c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{1-c^2 x^2}}-\frac{7}{3} b c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^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)}{3 x^2}-\frac{14 b c^3 d^2 \sqrt{d-c^2 d x^2} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 x}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 x^3}-\frac{7}{12} b^2 c^4 d^2 x \sqrt{d-c^2 d x^2}-\frac{b^2 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{3 x}+\frac{23 b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x)}{12 \sqrt{1-c^2 x^2}}",1,"(-7*b^2*c^4*d^2*x*Sqrt[d - c^2*d*x^2])/12 - (b^2*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(3*x) + (23*b^2*c^3*d^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(12*Sqrt[1 - c^2*x^2]) - (5*b*c^5*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) - (7*b*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/3 - (b*c*d^2*(1 - c^2*x^2)^(3/2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x]))/(3*x^2) + (5*c^4*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/2 + (((7*I)/3)*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] + (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(3*x) - ((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(3*x^3) + (5*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*Sqrt[1 - c^2*x^2]) - (14*b*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/(3*Sqrt[1 - c^2*x^2]) + (((7*I)/3)*b^2*c^3*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",27,15,29,0.5172,1,"{4695, 4647, 4641, 4627, 321, 216, 4683, 4625, 3717, 2190, 2279, 2391, 195, 4685, 277}"
234,1,400,0,0.5830192,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^5*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{16 a b x \sqrt{1-c^2 x^2}}{15 c^5 \sqrt{d-c^2 d x^2}}+\frac{2 b x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c \sqrt{d-c^2 d x^2}}-\frac{x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{8 b x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c^3 \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^4 d}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^6 d}+\frac{2 b^2 \left(1-c^2 x^2\right)^3}{125 c^6 \sqrt{d-c^2 d x^2}}-\frac{76 b^2 \left(1-c^2 x^2\right)^2}{675 c^6 \sqrt{d-c^2 d x^2}}+\frac{298 b^2 \left(1-c^2 x^2\right)}{225 c^6 \sqrt{d-c^2 d x^2}}+\frac{16 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{15 c^5 \sqrt{d-c^2 d x^2}}","\frac{16 a b x \sqrt{1-c^2 x^2}}{15 c^5 \sqrt{d-c^2 d x^2}}+\frac{2 b x^5 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c \sqrt{d-c^2 d x^2}}-\frac{x^4 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{8 b x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{45 c^3 \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^4 d}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{15 c^6 d}+\frac{2 b^2 \left(1-c^2 x^2\right)^3}{125 c^6 \sqrt{d-c^2 d x^2}}-\frac{76 b^2 \left(1-c^2 x^2\right)^2}{675 c^6 \sqrt{d-c^2 d x^2}}+\frac{298 b^2 \left(1-c^2 x^2\right)}{225 c^6 \sqrt{d-c^2 d x^2}}+\frac{16 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{15 c^5 \sqrt{d-c^2 d x^2}}",1,"(16*a*b*x*Sqrt[1 - c^2*x^2])/(15*c^5*Sqrt[d - c^2*d*x^2]) + (298*b^2*(1 - c^2*x^2))/(225*c^6*Sqrt[d - c^2*d*x^2]) - (76*b^2*(1 - c^2*x^2)^2)/(675*c^6*Sqrt[d - c^2*d*x^2]) + (2*b^2*(1 - c^2*x^2)^3)/(125*c^6*Sqrt[d - c^2*d*x^2]) + (16*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(15*c^5*Sqrt[d - c^2*d*x^2]) + (8*b*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(45*c^3*Sqrt[d - c^2*d*x^2]) + (2*b*x^5*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c*Sqrt[d - c^2*d*x^2]) - (8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*c^6*d) - (4*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(15*c^4*d) - (x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(5*c^2*d)","A",14,7,29,0.2414,1,"{4707, 4677, 4619, 261, 4627, 266, 43}"
235,1,337,0,0.4842044,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^4*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{b x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c \sqrt{d-c^2 d x^2}}-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d}+\frac{3 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^3 \sqrt{d-c^2 d x^2}}-\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^4 d}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c^5 \sqrt{d-c^2 d x^2}}+\frac{b^2 x^3 \left(1-c^2 x^2\right)}{32 c^2 \sqrt{d-c^2 d x^2}}+\frac{15 b^2 x \left(1-c^2 x^2\right)}{64 c^4 \sqrt{d-c^2 d x^2}}-\frac{15 b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{64 c^5 \sqrt{d-c^2 d x^2}}","\frac{b x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c \sqrt{d-c^2 d x^2}}-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 c^2 d}+\frac{3 b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{8 c^3 \sqrt{d-c^2 d x^2}}-\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^4 d}+\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c^5 \sqrt{d-c^2 d x^2}}+\frac{b^2 x^3 \left(1-c^2 x^2\right)}{32 c^2 \sqrt{d-c^2 d x^2}}+\frac{15 b^2 x \left(1-c^2 x^2\right)}{64 c^4 \sqrt{d-c^2 d x^2}}-\frac{15 b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{64 c^5 \sqrt{d-c^2 d x^2}}",1,"(15*b^2*x*(1 - c^2*x^2))/(64*c^4*Sqrt[d - c^2*d*x^2]) + (b^2*x^3*(1 - c^2*x^2))/(32*c^2*Sqrt[d - c^2*d*x^2]) - (15*b^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(64*c^5*Sqrt[d - c^2*d*x^2]) + (3*b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c^3*Sqrt[d - c^2*d*x^2]) + (b*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c*Sqrt[d - c^2*d*x^2]) - (3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(8*c^4*d) - (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(4*c^2*d) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(8*b*c^5*Sqrt[d - c^2*d*x^2])","A",11,6,29,0.2069,1,"{4707, 4643, 4641, 4627, 321, 216}"
236,1,277,0,0.329423,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{4 a b x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}+\frac{2 b 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{x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d}-\frac{2 b^2 \left(1-c^2 x^2\right)^2}{27 c^4 \sqrt{d-c^2 d x^2}}+\frac{14 b^2 \left(1-c^2 x^2\right)}{9 c^4 \sqrt{d-c^2 d x^2}}+\frac{4 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^3 \sqrt{d-c^2 d x^2}}","\frac{4 a b x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}+\frac{2 b 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{x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d}-\frac{2 b^2 \left(1-c^2 x^2\right)^2}{27 c^4 \sqrt{d-c^2 d x^2}}+\frac{14 b^2 \left(1-c^2 x^2\right)}{9 c^4 \sqrt{d-c^2 d x^2}}+\frac{4 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(4*a*b*x*Sqrt[1 - c^2*x^2])/(3*c^3*Sqrt[d - c^2*d*x^2]) + (14*b^2*(1 - c^2*x^2))/(9*c^4*Sqrt[d - c^2*d*x^2]) - (2*b^2*(1 - c^2*x^2)^2)/(27*c^4*Sqrt[d - c^2*d*x^2]) + (4*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(3*c^3*Sqrt[d - c^2*d*x^2]) + (2*b*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c*Sqrt[d - c^2*d*x^2]) - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^4*d) - (x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^2*d)","A",9,7,29,0.2414,1,"{4707, 4677, 4619, 261, 4627, 266, 43}"
237,1,213,0,0.2689244,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{\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{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d}+\frac{b 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{b^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}","\frac{\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{x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 d}+\frac{b 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{b^2 x \sqrt{d-c^2 d x^2}}{4 c^2 d}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}",1,"(b^2*x*(1 - c^2*x^2))/(4*c^2*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c^3*Sqrt[d - c^2*d*x^2]) + (b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c*Sqrt[d - c^2*d*x^2]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*c^2*d) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c^3*Sqrt[d - c^2*d*x^2])","A",6,6,29,0.2069,1,"{4707, 4643, 4641, 4627, 321, 216}"
238,1,146,0,0.1215001,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{2 a b x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d}+\frac{2 b^2 \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c \sqrt{d-c^2 d x^2}}","\frac{2 a b x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d}+\frac{2 b^2 \left(1-c^2 x^2\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c \sqrt{d-c^2 d x^2}}",1,"(2*a*b*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) + (2*b^2*(1 - c^2*x^2))/(c^2*Sqrt[d - c^2*d*x^2]) + (2*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*Sqrt[d - c^2*d*x^2]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(c^2*d)","A",4,3,27,0.1111,1,"{4677, 4619, 261}"
239,1,49,0,0.0911194,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/Sqrt[d - c^2*d*x^2],x]","\frac{\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{\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}}",1,"(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d - c^2*d*x^2])","A",2,2,26,0.07692,1,"{4643, 4641}"
240,1,257,0,0.3406973,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*Sqrt[d - c^2*d*x^2]),x]","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}",1,"(-2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] + ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] + (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2]","A",9,6,29,0.2069,1,"{4713, 4709, 4183, 2531, 2282, 6589}"
241,1,183,0,0.2202289,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*Sqrt[d - c^2*d*x^2]),x]","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{d x}-\frac{i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}+\frac{2 b c \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)}{\sqrt{d-c^2 d x^2}}","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{d x}-\frac{i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}+\frac{2 b c \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)}{\sqrt{d-c^2 d x^2}}",1,"((-I)*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2] - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(d*x) + (2*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2]","A",6,6,29,0.2069,1,"{4681, 4625, 3717, 2190, 2279, 2391}"
242,1,402,0,0.5187017,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^3 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^3*Sqrt[d - c^2*d*x^2]),x]","\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2}-\frac{c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{d-c^2 d x^2}}","\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{x \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2}-\frac{c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{\sqrt{d-c^2 d x^2}}",1,"-((b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(x*Sqrt[d - c^2*d*x^2])) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*d*x^2) - (c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - (b^2*c^2*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/Sqrt[d - c^2*d*x^2] + (I*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - (I*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] - (b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2] + (b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2]","A",14,11,29,0.3793,1,"{4701, 4713, 4709, 4183, 2531, 2282, 6589, 4627, 266, 63, 208}"
243,1,319,0,0.3903158,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^4 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^4*Sqrt[d - c^2*d*x^2]),x]","-\frac{2 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{d-c^2 d x^2}}-\frac{2 i c^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{d-c^2 d x^2}}-\frac{2 c^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3}+\frac{4 b c^3 \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 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \left(1-c^2 x^2\right)}{3 x \sqrt{d-c^2 d x^2}}","-\frac{2 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 \sqrt{d-c^2 d x^2}}-\frac{2 i c^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{d-c^2 d x^2}}-\frac{2 c^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 x^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3}+\frac{4 b c^3 \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 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \left(1-c^2 x^2\right)}{3 x \sqrt{d-c^2 d x^2}}",1,"-(b^2*c^2*(1 - c^2*x^2))/(3*x*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*x^2*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2] - (Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*d*x^3) - (2*c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*d*x) + (4*b*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/(3*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*b^2*c^3*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[d - c^2*d*x^2]","A",9,9,29,0.3103,1,"{4701, 4681, 4625, 3717, 2190, 2279, 2391, 4627, 264}"
244,1,549,0,0.7414,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d^2}+\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^6 d^2}-\frac{16 a b x \sqrt{1-c^2 x^2}}{3 c^5 d \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{2 b x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{4 i b \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^6 d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \left(1-c^2 x^2\right)^2}{27 c^6 d \sqrt{d-c^2 d x^2}}-\frac{32 b^2 \left(1-c^2 x^2\right)}{9 c^6 d \sqrt{d-c^2 d x^2}}-\frac{16 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^5 d \sqrt{d-c^2 d x^2}}","-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d^2}+\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^6 d^2}-\frac{16 a b x \sqrt{1-c^2 x^2}}{3 c^5 d \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{2 b x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{4 i b \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^6 d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \left(1-c^2 x^2\right)^2}{27 c^6 d \sqrt{d-c^2 d x^2}}-\frac{32 b^2 \left(1-c^2 x^2\right)}{9 c^6 d \sqrt{d-c^2 d x^2}}-\frac{16 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^5 d \sqrt{d-c^2 d x^2}}",1,"(-16*a*b*x*Sqrt[1 - c^2*x^2])/(3*c^5*d*Sqrt[d - c^2*d*x^2]) - (32*b^2*(1 - c^2*x^2))/(9*c^6*d*Sqrt[d - c^2*d*x^2]) + (2*b^2*(1 - c^2*x^2)^2)/(27*c^6*d*Sqrt[d - c^2*d*x^2]) - (16*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(3*c^5*d*Sqrt[d - c^2*d*x^2]) + (2*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(c^5*d*Sqrt[d - c^2*d*x^2]) - (2*b*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^6*d^2) + (4*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^4*d^2) + ((4*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^6*d*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])])/(c^6*d*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])])/(c^6*d*Sqrt[d - c^2*d*x^2])","A",22,13,29,0.4483,1,"{4703, 4707, 4677, 4619, 261, 4627, 266, 43, 4715, 4657, 4181, 2279, 2391}"
245,1,424,0,0.6427083,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^4*(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} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c^5 d \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^5 d \sqrt{d-c^2 d x^2}}+\frac{2 b \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^5 d \sqrt{d-c^2 d x^2}}-\frac{b^2 x \left(1-c^2 x^2\right)}{4 c^4 d \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^5 d \sqrt{d-c^2 d x^2}}","-\frac{i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c^5 d \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^5 d \sqrt{d-c^2 d x^2}}+\frac{2 b \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^5 d \sqrt{d-c^2 d x^2}}-\frac{b^2 x \left(1-c^2 x^2\right)}{4 c^4 d \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^5 d \sqrt{d-c^2 d x^2}}",1,"-(b^2*x*(1 - c^2*x^2))/(4*c^4*d*Sqrt[d - c^2*d*x^2]) + (b^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c^5*d*Sqrt[d - c^2*d*x^2]) - (b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) - (I*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^5*d*Sqrt[d - c^2*d*x^2]) + (3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(2*c^4*d^2) - (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(2*b*c^5*d*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^5*d*Sqrt[d - c^2*d*x^2]) - (I*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^5*d*Sqrt[d - c^2*d*x^2])","A",15,13,29,0.4483,1,"{4703, 4707, 4643, 4641, 4627, 321, 216, 4715, 4675, 3719, 2190, 2279, 2391}"
246,1,412,0,0.4540645,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{2 i b^2 \sqrt{1-c^2 x^2} \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 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{4 a b x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b \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^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \left(1-c^2 x^2\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{4 b^2 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 \sqrt{1-c^2 x^2} \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 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{4 a b x \sqrt{1-c^2 x^2}}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{2 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b \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^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \left(1-c^2 x^2\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{4 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c^3 d \sqrt{d-c^2 d x^2}}",1,"(-4*a*b*x*Sqrt[1 - c^2*x^2])/(c^3*d*Sqrt[d - c^2*d*x^2]) - (2*b^2*(1 - c^2*x^2))/(c^4*d*Sqrt[d - c^2*d*x^2]) - (4*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c^3*d*Sqrt[d - c^2*d*x^2]) + (2*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(c^3*d*Sqrt[d - c^2*d*x^2]) + (x^2*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(c^4*d^2) + ((4*I)*b*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*I)*b^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*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^4*d*Sqrt[d - c^2*d*x^2])","A",13,9,29,0.3103,1,"{4703, 4677, 4619, 261, 4715, 4657, 4181, 2279, 2391}"
247,1,250,0,0.3571226,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(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} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{\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{x \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(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} \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{i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{\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{x \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(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} \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}}",1,"(x*(a + b*ArcSin[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) - (I*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^3*d*Sqrt[d - c^2*d*x^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]) + (2*b*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]) - (I*b^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",8,8,29,0.2759,1,"{4703, 4643, 4641, 4675, 3719, 2190, 2279, 2391}"
248,1,208,0,0.1855479,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{2 i b^2 \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 \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{\left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b \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{2 i b^2 \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 \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{\left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 i b \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,"(a + b*ArcSin[c*x])^2/(c^2*d*Sqrt[d - c^2*d*x^2]) + ((4*I)*b*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*I)*b^2*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*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^2*d*Sqrt[d - c^2*d*x^2])","A",7,5,27,0.1852,1,"{4677, 4657, 4181, 2279, 2391}"
249,1,195,0,0.1610892,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(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} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c d \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{d \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 d \sqrt{d-c^2 d x^2}}+\frac{2 b \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{i b^2 \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{x \left(a+b \sin ^{-1}(c x)\right)^2}{d \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 d \sqrt{d-c^2 d x^2}}+\frac{2 b \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}}",1,"(x*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - (I*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c*d*Sqrt[d - c^2*d*x^2]) + (2*b*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]) - (I*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*d*Sqrt[d - c^2*d*x^2])","A",6,6,26,0.2308,1,"{4653, 4675, 3719, 2190, 2279, 2391}"
250,1,467,0,0.5730211,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*(d - c^2*d*x^2)^(3/2)),x]","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{4 i b \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{4 i b \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcSin[c*x])^2/(d*Sqrt[d - c^2*d*x^2]) + ((4*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) + ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/(d*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*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*Sqrt[d - c^2*d*x^2]) - ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) + (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",16,11,29,0.3793,1,"{4705, 4713, 4709, 4183, 2531, 2282, 6589, 4657, 4181, 2279, 2391}"
251,1,333,0,0.437249,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*(d - c^2*d*x^2)^(3/2)),x]","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{2 i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d x \sqrt{d-c^2 d x^2}}+\frac{4 b c \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)}{d \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{2 i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d x \sqrt{d-c^2 d x^2}}+\frac{4 b c \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)}{d \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}",1,"-((a + b*ArcSin[c*x])^2/(d*x*Sqrt[d - c^2*d*x^2])) + (2*c^2*x*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - ((2*I)*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - (4*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) + (4*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",14,10,29,0.3448,1,"{4701, 4653, 4675, 3719, 2190, 2279, 2391, 4679, 4419, 4183}"
252,1,634,0,0.9277746,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^3*(d - c^2*d*x^2)^(3/2)),x]","\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{d x \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2 \sqrt{d-c^2 d x^2}}+\frac{4 i b c^2 \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d \sqrt{d-c^2 d x^2}}","\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{d x \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2 \sqrt{d-c^2 d x^2}}+\frac{4 i b c^2 \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d \sqrt{d-c^2 d x^2}}",1,"-((b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(d*x*Sqrt[d - c^2*d*x^2])) + (3*c^2*(a + b*ArcSin[c*x])^2)/(2*d*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])^2/(2*d*x^2*Sqrt[d - c^2*d*x^2]) + ((4*I)*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (3*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (b^2*c^2*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/(d*Sqrt[d - c^2*d*x^2]) + ((3*I)*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - ((3*I)*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (3*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) + (3*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",27,15,29,0.5172,1,"{4701, 4705, 4713, 4709, 4183, 2531, 2282, 6589, 4657, 4181, 2279, 2391, 266, 63, 208}"
253,1,483,0,0.804111,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^4*(d - c^2*d*x^2)^(3/2)),x]","-\frac{i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{5 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 d \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}-\frac{8 i c^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^2 \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3 \sqrt{d-c^2 d x^2}}+\frac{16 b c^3 \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 d \sqrt{d-c^2 d x^2}}-\frac{20 b c^3 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \left(1-c^2 x^2\right)}{3 d x \sqrt{d-c^2 d x^2}}","-\frac{i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{5 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 d \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}-\frac{8 i c^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d x \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 d x^2 \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3 \sqrt{d-c^2 d x^2}}+\frac{16 b c^3 \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 d \sqrt{d-c^2 d x^2}}-\frac{20 b c^3 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \left(1-c^2 x^2\right)}{3 d x \sqrt{d-c^2 d x^2}}",1,"-(b^2*c^2*(1 - c^2*x^2))/(3*d*x*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*d*x^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])^2/(3*d*x^3*Sqrt[d - c^2*d*x^2]) - (4*c^2*(a + b*ArcSin[c*x])^2)/(3*d*x*Sqrt[d - c^2*d*x^2]) + (8*c^4*x*(a + b*ArcSin[c*x])^2)/(3*d*Sqrt[d - c^2*d*x^2]) - (((8*I)/3)*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - (20*b*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/(3*d*Sqrt[d - c^2*d*x^2]) + (16*b*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*d*Sqrt[d - c^2*d*x^2]) - (I*b^2*c^3*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (((5*I)/3)*b^2*c^3*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",24,11,29,0.3793,1,"{4701, 4653, 4675, 3719, 2190, 2279, 2391, 4679, 4419, 4183, 264}"
254,1,546,0,0.8647163,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{11 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{11 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 a b x \sqrt{1-c^2 x^2}}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{11 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^6 d^3}-\frac{22 i b \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^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{2 b^2 \left(1-c^2 x^2\right)}{c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}","\frac{11 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{11 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 a b x \sqrt{1-c^2 x^2}}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{11 b x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^6 d^3}-\frac{22 i b \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^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{2 b^2 \left(1-c^2 x^2\right)}{c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}",1,"b^2/(3*c^6*d^2*Sqrt[d - c^2*d*x^2]) + (16*a*b*x*Sqrt[1 - c^2*x^2])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (2*b^2*(1 - c^2*x^2))/(c^6*d^2*Sqrt[d - c^2*d*x^2]) + (16*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) - (b*x^3*(a + b*ArcSin[c*x]))/(3*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (11*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcSin[c*x])^2)/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (4*x^2*(a + b*ArcSin[c*x])^2)/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (8*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2)/(3*c^6*d^3) - (((22*I)/3)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^6*d^2*Sqrt[d - c^2*d*x^2]) + (((11*I)/3)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^6*d^2*Sqrt[d - c^2*d*x^2]) - (((11*I)/3)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^6*d^2*Sqrt[d - c^2*d*x^2])","A",26,11,29,0.3793,1,"{4703, 4677, 4619, 261, 4715, 4657, 4181, 2279, 2391, 266, 43}"
255,1,421,0,0.7259948,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{4 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b x^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{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)^3}{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 b \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^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 x}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}","\frac{4 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b x^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{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)^3}{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 b \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^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 x}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}",1,"(b^2*x)/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) - (b*x^2*(a + b*ArcSin[c*x]))/(3*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcSin[c*x])^2)/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (x*(a + b*ArcSin[c*x])^2)/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (((4*I)/3)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^5*d^2*Sqrt[d - c^2*d*x^2]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c^5*d^2*Sqrt[d - c^2*d*x^2]) - (8*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (((4*I)/3)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^5*d^2*Sqrt[d - c^2*d*x^2])","A",17,10,29,0.3448,1,"{4703, 4643, 4641, 4675, 3719, 2190, 2279, 2391, 288, 216}"
256,1,332,0,0.4891466,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{5 i b^2 \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{5 i b^2 \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{b x \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{10 i b \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^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}","\frac{5 i b^2 \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{5 i b^2 \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{b x \left(a+b \sin ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}-\frac{2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{10 i b \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^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}",1,"b^2/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (b*x*(a + b*ArcSin[c*x]))/(3*c^3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x^2*(a + b*ArcSin[c*x])^2)/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (2*(a + b*ArcSin[c*x])^2)/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (((10*I)/3)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (((5*I)/3)*b^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]) - (((5*I)/3)*b^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])","A",16,7,29,0.2414,1,"{4703, 4677, 4657, 4181, 2279, 2391, 261}"
257,1,332,0,0.3523054,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{i b^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{b x^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{i \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 b \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^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 x}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}","\frac{i b^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{b x^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{i \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 b \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^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 x}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}",1,"(b^2*x)/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) - (b*x^2*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcSin[c*x])^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + ((I/3)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^3*d^2*Sqrt[d - c^2*d*x^2]) - (2*b*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]) + ((I/3)*b^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",9,9,29,0.3103,1,"{4681, 4703, 4675, 3719, 2190, 2279, 2391, 288, 216}"
258,1,294,0,0.2178606,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","-\frac{i b^2 \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 \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 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{2 i b \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{\left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2}{3 c^2 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)}{3 c^2 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)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b 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{2 i b \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{\left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}",1,"b^2/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) - (b*x*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (a + b*ArcSin[c*x])^2/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) + (((2*I)/3)*b*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]) - ((I/3)*b^2*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*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])","A",9,7,27,0.2593,1,"{4677, 4655, 4657, 4181, 2279, 2391, 261}"
259,1,311,0,0.2763246,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(d - c^2*d*x^2)^(5/2),x]","-\frac{2 i b^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{b \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 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i \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{4 b \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{x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}","-\frac{2 i b^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{b \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 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i \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{4 b \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{x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}",1,"(b^2*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b*(a + b*ArcSin[c*x]))/(3*c*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (x*(a + b*ArcSin[c*x])^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + (2*x*(a + b*ArcSin[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (((2*I)/3)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c*d^2*Sqrt[d - c^2*d*x^2]) + (4*b*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*I)/3)*b^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])","A",9,9,26,0.3462,1,"{4655, 4653, 4675, 3719, 2190, 2279, 2391, 4677, 191}"
260,1,577,0,0.8601386,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*(d - c^2*d*x^2)^(5/2)),x]","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{7 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{7 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b c x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{14 i b \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2}{3 d^2 \sqrt{d-c^2 d x^2}}","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{7 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{7 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b c x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{14 i b \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2}{3 d^2 \sqrt{d-c^2 d x^2}}",1,"b^2/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b*c*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (a + b*ArcSin[c*x])^2/(3*d*(d - c^2*d*x^2)^(3/2)) + (a + b*ArcSin[c*x])^2/(d^2*Sqrt[d - c^2*d*x^2]) + (((14*I)/3)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) + ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (((7*I)/3)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) + (((7*I)/3)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) + (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2])","A",25,13,29,0.4483,1,"{4705, 4713, 4709, 4183, 2531, 2282, 6589, 4657, 4181, 2279, 2391, 4655, 261}"
261,1,452,0,0.616969,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*(d - c^2*d*x^2)^(5/2)),x]","-\frac{5 i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{8 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 b c \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d x \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 c^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}","-\frac{5 i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{8 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 b c \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d x \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 c^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}",1,"(b^2*c^2*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b*c*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])^2/(d*x*(d - c^2*d*x^2)^(3/2)) + (4*c^2*x*(a + b*ArcSin[c*x])^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + (8*c^2*x*(a + b*ArcSin[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (((8*I)/3)*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d^2*Sqrt[d - c^2*d*x^2]) - (4*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) + (16*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (((5*I)/3)*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2])","A",19,14,29,0.4828,1,"{4701, 4655, 4653, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4705, 4679, 4419, 4183}"
262,1,752,0,1.2564324,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^3*(d - c^2*d*x^2)^(5/2)),x]","\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{13 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{13 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b c^3 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^2 x \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{26 i b c^2 \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{6 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2 \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 c^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2 \sqrt{d-c^2 d x^2}}","\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{13 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{13 i b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 b^2 c^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b c^3 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{d^2 x \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{26 i b c^2 \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{6 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{2 d x^2 \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 c^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2 \sqrt{d-c^2 d x^2}}",1,"(b^2*c^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b*c*(a + b*ArcSin[c*x]))/(d^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (2*b*c^3*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) + (5*c^2*(a + b*ArcSin[c*x])^2)/(6*d*(d - c^2*d*x^2)^(3/2)) - (a + b*ArcSin[c*x])^2/(2*d*x^2*(d - c^2*d*x^2)^(3/2)) + (5*c^2*(a + b*ArcSin[c*x])^2)/(2*d^2*Sqrt[d - c^2*d*x^2]) + (((26*I)/3)*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (5*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (b^2*c^2*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/(d^2*Sqrt[d - c^2*d*x^2]) + ((5*I)*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (((13*I)/3)*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) + (((13*I)/3)*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - ((5*I)*b*c^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (5*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) + (5*b^2*c^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2])","A",39,18,29,0.6207,1,"{4701, 4705, 4713, 4709, 4183, 2531, 2282, 6589, 4657, 4181, 2279, 2391, 4655, 261, 266, 51, 63, 208}"
263,1,538,0,1.0530335,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^4*(d - c^2*d*x^2)^(5/2)),x]","-\frac{8 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 i c^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{32 b c^3 \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{32 b c^3 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3 \left(d-c^2 d x^2\right)^{3/2}}+\frac{2 b^2 c^4 x}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2}{3 d^2 x \sqrt{d-c^2 d x^2}}","-\frac{8 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 i b^2 c^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 i c^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b c \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2}}+\frac{32 b c^3 \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 d^2 \sqrt{d-c^2 d x^2}}-\frac{32 b c^3 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \sin ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 c^2 \left(a+b \sin ^{-1}(c x)\right)^2}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{3 d x^3 \left(d-c^2 d x^2\right)^{3/2}}+\frac{2 b^2 c^4 x}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2}{3 d^2 x \sqrt{d-c^2 d x^2}}",1,"-(b^2*c^2)/(3*d^2*x*Sqrt[d - c^2*d*x^2]) + (2*b^2*c^4*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b*c*(a + b*ArcSin[c*x]))/(3*d^2*x^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]) - (a + b*ArcSin[c*x])^2/(3*d*x^3*(d - c^2*d*x^2)^(3/2)) - (2*c^2*(a + b*ArcSin[c*x])^2)/(d*x*(d - c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*ArcSin[c*x])^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*ArcSin[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (((16*I)/3)*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d^2*Sqrt[d - c^2*d*x^2]) - (32*b*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) + (32*b*c^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (((8*I)/3)*b^2*c^3*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (((8*I)/3)*b^2*c^3*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(d^2*Sqrt[d - c^2*d*x^2])","A",32,15,29,0.5172,1,"{4701, 4655, 4653, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4705, 4679, 4419, 4183, 271}"
264,1,157,0,0.270624,"\int \frac{x^4 \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2],x]","\frac{x^3 \sqrt{1-a^2 x^2}}{32 a^2}+\frac{15 x \sqrt{1-a^2 x^2}}{64 a^4}-\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{4 a^2}+\frac{3 x^2 \sin ^{-1}(a x)}{8 a^3}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{8 a^4}+\frac{\sin ^{-1}(a x)^3}{8 a^5}-\frac{15 \sin ^{-1}(a x)}{64 a^5}+\frac{x^4 \sin ^{-1}(a x)}{8 a}","\frac{x^3 \sqrt{1-a^2 x^2}}{32 a^2}+\frac{15 x \sqrt{1-a^2 x^2}}{64 a^4}-\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{4 a^2}+\frac{3 x^2 \sin ^{-1}(a x)}{8 a^3}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{8 a^4}+\frac{\sin ^{-1}(a x)^3}{8 a^5}-\frac{15 \sin ^{-1}(a x)}{64 a^5}+\frac{x^4 \sin ^{-1}(a x)}{8 a}",1,"(15*x*Sqrt[1 - a^2*x^2])/(64*a^4) + (x^3*Sqrt[1 - a^2*x^2])/(32*a^2) - (15*ArcSin[a*x])/(64*a^5) + (3*x^2*ArcSin[a*x])/(8*a^3) + (x^4*ArcSin[a*x])/(8*a) - (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(8*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(4*a^2) + ArcSin[a*x]^3/(8*a^5)","A",10,5,24,0.2083,1,"{4707, 4641, 4627, 321, 216}"
265,1,126,0,0.2021624,"\int \frac{x^3 \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{2 \left(1-a^2 x^2\right)^{3/2}}{27 a^4}+\frac{14 \sqrt{1-a^2 x^2}}{9 a^4}-\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^4}+\frac{4 x \sin ^{-1}(a x)}{3 a^3}+\frac{2 x^3 \sin ^{-1}(a x)}{9 a}","-\frac{2 \left(1-a^2 x^2\right)^{3/2}}{27 a^4}+\frac{14 \sqrt{1-a^2 x^2}}{9 a^4}-\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a^4}+\frac{4 x \sin ^{-1}(a x)}{3 a^3}+\frac{2 x^3 \sin ^{-1}(a x)}{9 a}",1,"(14*Sqrt[1 - a^2*x^2])/(9*a^4) - (2*(1 - a^2*x^2)^(3/2))/(27*a^4) + (4*x*ArcSin[a*x])/(3*a^3) + (2*x^3*ArcSin[a*x])/(9*a) - (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(3*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(3*a^2)","A",8,7,24,0.2917,1,"{4707, 4677, 4619, 261, 4627, 266, 43}"
266,1,89,0,0.1374846,"\int \frac{x^2 \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2],x]","\frac{x \sqrt{1-a^2 x^2}}{4 a^2}-\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 a^2}+\frac{\sin ^{-1}(a x)^3}{6 a^3}-\frac{\sin ^{-1}(a x)}{4 a^3}+\frac{x^2 \sin ^{-1}(a x)}{2 a}","\frac{x \sqrt{1-a^2 x^2}}{4 a^2}-\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 a^2}+\frac{\sin ^{-1}(a x)^3}{6 a^3}-\frac{\sin ^{-1}(a x)}{4 a^3}+\frac{x^2 \sin ^{-1}(a x)}{2 a}",1,"(x*Sqrt[1 - a^2*x^2])/(4*a^2) - ArcSin[a*x]/(4*a^3) + (x^2*ArcSin[a*x])/(2*a) - (x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(2*a^2) + ArcSin[a*x]^3/(6*a^3)","A",5,5,24,0.2083,1,"{4707, 4641, 4627, 321, 216}"
267,1,55,0,0.0719107,"\int \frac{x \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2],x]","\frac{2 \sqrt{1-a^2 x^2}}{a^2}-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a^2}+\frac{2 x \sin ^{-1}(a x)}{a}","\frac{2 \sqrt{1-a^2 x^2}}{a^2}-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a^2}+\frac{2 x \sin ^{-1}(a x)}{a}",1,"(2*Sqrt[1 - a^2*x^2])/a^2 + (2*x*ArcSin[a*x])/a - (Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/a^2","A",3,3,22,0.1364,1,"{4677, 4619, 261}"
268,1,13,0,0.0338384,"\int \frac{\sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^2/Sqrt[1 - a^2*x^2],x]","\frac{\sin ^{-1}(a x)^3}{3 a}","\frac{\sin ^{-1}(a x)^3}{3 a}",1,"ArcSin[a*x]^3/(3*a)","A",1,1,21,0.04762,1,"{4641}"
269,1,92,0,0.1429583,"\int \frac{\sin ^{-1}(a x)^2}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^2/(x*Sqrt[1 - a^2*x^2]),x]","2 i \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-2 i \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x)^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)","2 i \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-2 i \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x)^2 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)",1,"-2*ArcSin[a*x]^2*ArcTanh[E^(I*ArcSin[a*x])] + (2*I)*ArcSin[a*x]*PolyLog[2, -E^(I*ArcSin[a*x])] - (2*I)*ArcSin[a*x]*PolyLog[2, E^(I*ArcSin[a*x])] - 2*PolyLog[3, -E^(I*ArcSin[a*x])] + 2*PolyLog[3, E^(I*ArcSin[a*x])]","A",8,5,24,0.2083,1,"{4709, 4183, 2531, 2282, 6589}"
270,1,76,0,0.1435299,"\int \frac{\sin ^{-1}(a x)^2}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^2/(x^2*Sqrt[1 - a^2*x^2]),x]","-i a \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{x}-i a \sin ^{-1}(a x)^2+2 a \sin ^{-1}(a x) \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)","-i a \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{x}-i a \sin ^{-1}(a x)^2+2 a \sin ^{-1}(a x) \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)",1,"(-I)*a*ArcSin[a*x]^2 - (Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/x + 2*a*ArcSin[a*x]*Log[1 - E^((2*I)*ArcSin[a*x])] - I*a*PolyLog[2, E^((2*I)*ArcSin[a*x])]","A",6,6,24,0.2500,1,"{4681, 4625, 3717, 2190, 2279, 2391}"
271,1,163,0,0.2548745,"\int \frac{\sin ^{-1}(a x)^2}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^2/(x^3*Sqrt[1 - a^2*x^2]),x]","i a^2 \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-i a^2 \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x^2}-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a^2 \left(-\sin ^{-1}(a x)^2\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{a \sin ^{-1}(a x)}{x}","i a^2 \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-i a^2 \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{2 x^2}-a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a^2 \left(-\sin ^{-1}(a x)^2\right) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{a \sin ^{-1}(a x)}{x}",1,"-((a*ArcSin[a*x])/x) - (Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(2*x^2) - a^2*ArcSin[a*x]^2*ArcTanh[E^(I*ArcSin[a*x])] - a^2*ArcTanh[Sqrt[1 - a^2*x^2]] + I*a^2*ArcSin[a*x]*PolyLog[2, -E^(I*ArcSin[a*x])] - I*a^2*ArcSin[a*x]*PolyLog[2, E^(I*ArcSin[a*x])] - a^2*PolyLog[3, -E^(I*ArcSin[a*x])] + a^2*PolyLog[3, E^(I*ArcSin[a*x])]","A",13,10,24,0.4167,1,"{4701, 4709, 4183, 2531, 2282, 6589, 4627, 266, 63, 208}"
272,1,42,0,0.0678907,"\int \frac{\sin ^{-1}(a x)^2}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcSin[a*x]^2/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(3*a*Sqrt[c - a^2*c*x^2])","A",2,2,22,0.09091,1,"{4643, 4641}"
273,1,179,0,0.1287562,"\int \frac{\sin ^{-1}(a x)^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSin[a*x]^2/(c - a^2*c*x^2)^(3/2),x]","-\frac{i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^2}{c \sqrt{c-a^2 c x^2}}-\frac{i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a c \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}","-\frac{i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^2}{c \sqrt{c-a^2 c x^2}}-\frac{i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a c \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}",1,"(x*ArcSin[a*x]^2)/(c*Sqrt[c - a^2*c*x^2]) - (I*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(a*c*Sqrt[c - a^2*c*x^2]) + (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[1 + E^((2*I)*ArcSin[a*x])])/(a*c*Sqrt[c - a^2*c*x^2]) - (I*Sqrt[1 - a^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[a*x])])/(a*c*Sqrt[c - a^2*c*x^2])","A",6,6,22,0.2727,1,"{4653, 4675, 3719, 2190, 2279, 2391}"
274,1,283,0,0.2166509,"\int \frac{\sin ^{-1}(a x)^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[ArcSin[a*x]^2/(c - a^2*c*x^2)^(5/2),x]","-\frac{2 i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{x}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \sin ^{-1}(a x)^2}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{2 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a c^2 \sqrt{c-a^2 c x^2}}-\frac{\sin ^{-1}(a x)}{3 a c^2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^2}{3 c \left(c-a^2 c x^2\right)^{3/2}}","-\frac{2 i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{x}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \sin ^{-1}(a x)^2}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{2 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{3 a c^2 \sqrt{c-a^2 c x^2}}-\frac{\sin ^{-1}(a x)}{3 a c^2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^2}{3 c \left(c-a^2 c x^2\right)^{3/2}}",1,"x/(3*c^2*Sqrt[c - a^2*c*x^2]) - ArcSin[a*x]/(3*a*c^2*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x]^2)/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*ArcSin[a*x]^2)/(3*c^2*Sqrt[c - a^2*c*x^2]) - (((2*I)/3)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(a*c^2*Sqrt[c - a^2*c*x^2]) + (4*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[1 + E^((2*I)*ArcSin[a*x])])/(3*a*c^2*Sqrt[c - a^2*c*x^2]) - (((2*I)/3)*Sqrt[1 - a^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2])","A",9,9,22,0.4091,1,"{4655, 4653, 4675, 3719, 2190, 2279, 2391, 4677, 191}"
275,1,390,0,0.3286183,"\int \frac{\sin ^{-1}(a x)^2}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSin[a*x]^2/(c - a^2*c*x^2)^(7/2),x]","-\frac{8 i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x}{3 c^3 \sqrt{c-a^2 c x^2}}+\frac{x}{30 c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{8 x \sin ^{-1}(a x)^2}{15 c^3 \sqrt{c-a^2 c x^2}}-\frac{8 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \sin ^{-1}(a x)^2}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{4 \sin ^{-1}(a x)}{15 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}-\frac{\sin ^{-1}(a x)}{10 a c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2}}+\frac{16 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^2}{5 c \left(c-a^2 c x^2\right)^{5/2}}","-\frac{8 i \sqrt{1-a^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x}{3 c^3 \sqrt{c-a^2 c x^2}}+\frac{x}{30 c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{8 x \sin ^{-1}(a x)^2}{15 c^3 \sqrt{c-a^2 c x^2}}-\frac{8 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \sin ^{-1}(a x)^2}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{4 \sin ^{-1}(a x)}{15 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}-\frac{\sin ^{-1}(a x)}{10 a c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2}}+\frac{16 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^2}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"x/(3*c^3*Sqrt[c - a^2*c*x^2]) + x/(30*c^3*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) - ArcSin[a*x]/(10*a*c^3*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]) - (4*ArcSin[a*x])/(15*a*c^3*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x]^2)/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*ArcSin[a*x]^2)/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*ArcSin[a*x]^2)/(15*c^3*Sqrt[c - a^2*c*x^2]) - (((8*I)/15)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(a*c^3*Sqrt[c - a^2*c*x^2]) + (16*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[1 + E^((2*I)*ArcSin[a*x])])/(15*a*c^3*Sqrt[c - a^2*c*x^2]) - (((8*I)/15)*Sqrt[1 - a^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[a*x])])/(a*c^3*Sqrt[c - a^2*c*x^2])","A",13,10,22,0.4545,1,"{4655, 4653, 4675, 3719, 2190, 2279, 2391, 4677, 191, 192}"
276,0,0,0,0.0826601,"\int x^m \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2,x]","\int x^m \left(d-c^2 d x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{m+7}+\frac{6 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{(m+5) (m+7)}+\frac{24 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{(m+7) \left(m^2+8 m+15\right)}+\frac{48 d^3 \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{(m+5) (m+7) \left(m^2+4 m+3\right)}-\frac{2 b c d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+7)^2}-\frac{12 b c d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+5)^2 (m+7)}-\frac{10 b c d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+5) (m+7)^2}-\frac{48 b c d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+3)^2 (m+5) (m+7)}-\frac{36 b c d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+3) (m+5)^2 (m+7)}-\frac{30 b c d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+7)^2 \left(m^2+8 m+15\right)}-\frac{48 b c d^3 \left(a+b \sin ^{-1}(c x)\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) x^{m+2}}{(m+2) (m+3)^2 (m+5) (m+7)}-\frac{36 b c d^3 \left(a+b \sin ^{-1}(c x)\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) x^{m+2}}{(m+5)^2 (m+7) \left(m^2+5 m+6\right)}-\frac{30 b c d^3 \left(a+b \sin ^{-1}(c x)\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) x^{m+2}}{(m+5) (m+7)^2 \left(m^2+5 m+6\right)}-\frac{96 b c d^3 \left(a+b \sin ^{-1}(c x)\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) x^{m+2}}{(m+5) (m+7) \left(m^3+6 m^2+11 m+6\right)}+\frac{48 b^2 c^2 d^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^2 x^2\right) x^{m+3}}{(m+2) (m+3)^3 (m+5) (m+7)}+\frac{36 b^2 c^2 d^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^2 x^2\right) x^{m+3}}{(m+2) (m+3)^2 (m+5)^2 (m+7)}+\frac{96 b^2 c^2 d^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^2 x^2\right) x^{m+3}}{(m+3)^2 (m+5) (m+7) \left(m^2+3 m+2\right)}+\frac{30 b^2 c^2 d^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^2 x^2\right) x^{m+3}}{(m+2) (m+3)^2 (m+5) (m+7)^2}+\frac{48 b^2 c^2 d^3 x^{m+3}}{(m+3)^3 (m+5) (m+7)}+\frac{12 b^2 c^2 d^3 x^{m+3}}{(m+3) (m+5)^2 (m+7)}+\frac{36 b^2 c^2 d^3 x^{m+3}}{(m+3)^2 (m+5)^2 (m+7)}+\frac{10 b^2 c^2 d^3 x^{m+3}}{(m+7)^2 \left(m^2+8 m+15\right)}+\frac{2 b^2 c^2 d^3 x^{m+3}}{(m+3) (m+7)^2}+\frac{30 b^2 c^2 d^3 x^{m+3}}{(m+3)^2 (m+5) (m+7)^2}-\frac{12 b^2 c^4 d^3 x^{m+5}}{(m+5)^3 (m+7)}-\frac{4 b^2 c^4 d^3 x^{m+5}}{(m+5) (m+7)^2}-\frac{10 b^2 c^4 d^3 x^{m+5}}{(m+5)^2 (m+7)^2}+\frac{2 b^2 c^6 d^3 x^{m+7}}{(m+7)^3}",1,"Defer[Int][x^m*(d - c^2*d*x^2)^3*(a + b*ArcSin[c*x])^2, x]","F",0,0,0,0,-1,"{}"
277,0,0,0,0.0806745,"\int x^m \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2,x]","\int x^m \left(d-c^2 d x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{16 b^2 c^2 d^2 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^2 x^2\right)}{(m+3)^2 (m+5) \left(m^2+3 m+2\right)}+\frac{8 b^2 c^2 d^2 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^2 x^2\right)}{(m+2) (m+3)^3 (m+5)}+\frac{6 b^2 c^2 d^2 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^2 x^2\right)}{(m+2) (m+3)^2 (m+5)^2}-\frac{6 b c d^2 x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+5)^2 \left(m^2+5 m+6\right)}-\frac{16 b c d^2 x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+5) \left(m^3+6 m^2+11 m+6\right)}-\frac{8 b c d^2 x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+2) (m+3)^2 (m+5)}+\frac{4 d^2 \left(1-c^2 x^2\right) x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{m^2+8 m+15}+\frac{d^2 \left(1-c^2 x^2\right)^2 x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{m+5}-\frac{2 b c d^2 \left(1-c^2 x^2\right)^{3/2} x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{(m+5)^2}-\frac{8 b c d^2 \sqrt{1-c^2 x^2} x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{(m+3)^2 (m+5)}-\frac{6 b c d^2 \sqrt{1-c^2 x^2} x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{(m+3) (m+5)^2}+\frac{8 d^2 x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{(m+5) \left(m^2+4 m+3\right)}+\frac{8 b^2 c^2 d^2 x^{m+3}}{(m+3)^3 (m+5)}+\frac{2 b^2 c^2 d^2 x^{m+3}}{(m+3) (m+5)^2}+\frac{6 b^2 c^2 d^2 x^{m+3}}{(m+3)^2 (m+5)^2}-\frac{2 b^2 c^4 d^2 x^{m+5}}{(m+5)^3}",1,"Defer[Int][x^m*(d - c^2*d*x^2)^2*(a + b*ArcSin[c*x])^2, x]","F",0,0,0,0,-1,"{}"
278,0,0,0,0.0489392,"\int x^m \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2,x]","\int x^m \left(d-c^2 d x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{4 b^2 c^2 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^2 x^2\right)}{(m+3)^2 \left(m^2+3 m+2\right)}+\frac{2 b^2 c^2 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^2 x^2\right)}{(m+2) (m+3)^3}-\frac{4 b c d x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{m^3+6 m^2+11 m+6}-\frac{2 b c d x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(m+2) (m+3)^2}+\frac{d \left(1-c^2 x^2\right) x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{m+3}-\frac{2 b c d \sqrt{1-c^2 x^2} x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{(m+3)^2}+\frac{2 d x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{m^2+4 m+3}+\frac{2 b^2 c^2 d x^{m+3}}{(m+3)^3}",1,"Defer[Int][x^m*(d - c^2*d*x^2)*(a + b*ArcSin[c*x])^2, x]","F",0,0,0,0,-1,"{}"
279,0,0,0,0.0906326,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","Int[(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2),x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2), x]","A",0,0,0,0,-1,"{}"
280,0,0,0,0.4082354,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^2,x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^2} \, dx","-\frac{b^2 c^2 (m+1) 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^2 x^2\right)}{d^2 \left(m^2+5 m+6\right)}+\frac{(1-m) \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2},x\right)}{2 d}+\frac{b c (m+1) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2 (m+2)}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{2 d^2 \left(1-c^2 x^2\right)}-\frac{b c x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{d^2 \sqrt{1-c^2 x^2}}+\frac{b^2 c^2 x^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{d^2 (m+3)}",0,"-((b*c*x^(2 + m)*(a + b*ArcSin[c*x]))/(d^2*Sqrt[1 - c^2*x^2])) + (x^(1 + m)*(a + b*ArcSin[c*x])^2)/(2*d^2*(1 - c^2*x^2)) + (b*c*(1 + m)*x^(2 + m)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d^2*(2 + m)) + (b^2*c^2*x^(3 + m)*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, c^2*x^2])/(d^2*(3 + m)) - (b^2*c^2*(1 + m)*x^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, c^2*x^2])/(d^2*(6 + 5*m + m^2)) + ((1 - m)*Defer[Int][(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2), x])/(2*d)","A",0,0,0,0,-1,"{}"
281,0,0,0,0.9130295,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^3,x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^3} \, dx","-\frac{b^2 c^2 (1-m) (m+1) 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^2 x^2\right)}{6 d^3 \left(m^2+5 m+6\right)}-\frac{b^2 c^2 (3-m) (m+1) 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^2 x^2\right)}{4 d^3 \left(m^2+5 m+6\right)}+\frac{(1-m) (3-m) \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{d-c^2 d x^2},x\right)}{8 d^2}+\frac{b c (1-m) (m+1) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 (m+2)}+\frac{b c (3-m) (m+1) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 (m+2)}+\frac{(3-m) x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x^{m+1} \left(a+b \sin ^{-1}(c x)\right)^2}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{b c (1-m) x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \sqrt{1-c^2 x^2}}-\frac{b c (3-m) x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{4 d^3 \sqrt{1-c^2 x^2}}-\frac{b c x^{m+2} \left(a+b \sin ^{-1}(c x)\right)}{6 d^3 \left(1-c^2 x^2\right)^{3/2}}+\frac{b^2 c^2 (1-m) x^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{6 d^3 (m+3)}+\frac{b^2 c^2 (3-m) x^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{4 d^3 (m+3)}+\frac{b^2 c^2 x^{m+3} \, _2F_1\left(2,\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{6 d^3 (m+3)}",0,"-(b*c*x^(2 + m)*(a + b*ArcSin[c*x]))/(6*d^3*(1 - c^2*x^2)^(3/2)) - (b*c*(1 - m)*x^(2 + m)*(a + b*ArcSin[c*x]))/(6*d^3*Sqrt[1 - c^2*x^2]) - (b*c*(3 - m)*x^(2 + m)*(a + b*ArcSin[c*x]))/(4*d^3*Sqrt[1 - c^2*x^2]) + (x^(1 + m)*(a + b*ArcSin[c*x])^2)/(4*d^3*(1 - c^2*x^2)^2) + ((3 - m)*x^(1 + m)*(a + b*ArcSin[c*x])^2)/(8*d^3*(1 - c^2*x^2)) + (b*c*(1 - m)*(1 + m)*x^(2 + m)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(6*d^3*(2 + m)) + (b*c*(3 - m)*(1 + m)*x^(2 + m)*(a + b*ArcSin[c*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(4*d^3*(2 + m)) + (b^2*c^2*(1 - m)*x^(3 + m)*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, c^2*x^2])/(6*d^3*(3 + m)) + (b^2*c^2*(3 - m)*x^(3 + m)*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, c^2*x^2])/(4*d^3*(3 + m)) + (b^2*c^2*x^(3 + m)*Hypergeometric2F1[2, (3 + m)/2, (5 + m)/2, c^2*x^2])/(6*d^3*(3 + m)) - (b^2*c^2*(1 - m)*(1 + m)*x^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, c^2*x^2])/(6*d^3*(6 + 5*m + m^2)) - (b^2*c^2*(3 - m)*(1 + m)*x^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, c^2*x^2])/(4*d^3*(6 + 5*m + m^2)) + ((1 - m)*(3 - m)*Defer[Int][(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2), x])/(8*d^2)","A",0,0,0,0,-1,"{}"
282,0,0,0,0.1573331,"\int x^m \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2,x]","\int x^m \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{m+6}+\frac{5 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{(m+4) (m+6)}+\frac{15 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 x^{m+1}}{(m+6) \left(m^2+6 m+8\right)}-\frac{30 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+2)^2 (m+4) (m+6) \sqrt{1-c^2 x^2}}-\frac{10 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{(m+6) \left(m^2+6 m+8\right) \sqrt{1-c^2 x^2}}-\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+2}}{\left(m^2+8 m+12\right) \sqrt{1-c^2 x^2}}+\frac{10 b^2 c^2 d^2 (3 m+10) \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right) x^{m+3}}{(m+2) (m+3) (m+4)^3 (m+6) \sqrt{1-c^2 x^2}}+\frac{2 b^2 c^2 d^2 \left(15 m^2+130 m+264\right) \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right) x^{m+3}}{(m+2) (m+3) (m+4)^2 (m+6)^3 \sqrt{1-c^2 x^2}}+\frac{30 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right) x^{m+3}}{(m+2)^2 (m+3) (m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{2 b^2 c^2 d^2 \left(m^2+15 m+52\right) \sqrt{d-c^2 d x^2} x^{m+3}}{(m+4)^2 (m+6)^3}+\frac{10 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^{m+3}}{(m+4)^3 (m+6)}+\frac{4 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+4}}{(m+4) (m+6) \sqrt{1-c^2 x^2}}+\frac{10 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+4}}{(m+4)^2 (m+6) \sqrt{1-c^2 x^2}}-\frac{2 b^2 c^4 d^2 \sqrt{d-c^2 d x^2} x^{m+5}}{(m+6)^3}-\frac{2 b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right) x^{m+6}}{(m+6)^2 \sqrt{1-c^2 x^2}}+\frac{15 d^3 \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)}{(m+6) \left(m^2+6 m+8\right)}",0,"Defer[Int][x^m*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
283,0,0,0,0.1520276,"\int x^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\int x^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{3 d^2 \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)}{m^2+6 m+8}+\frac{3 d x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{m^2+6 m+8}-\frac{2 b c d x^{m+2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{\left(m^2+6 m+8\right) \sqrt{1-c^2 x^2}}+\frac{x^{m+1} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{m+4}-\frac{6 b c d x^{m+2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{(m+2)^2 (m+4) \sqrt{1-c^2 x^2}}+\frac{2 b c^3 d x^{m+4} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{(m+4)^2 \sqrt{1-c^2 x^2}}+\frac{2 b^2 c^2 d (3 m+10) x^{m+3} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{(m+2) (m+3) (m+4)^3 \sqrt{1-c^2 x^2}}+\frac{6 b^2 c^2 d x^{m+3} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{(m+2)^2 (m+3) (m+4) \sqrt{1-c^2 x^2}}+\frac{2 b^2 c^2 d x^{m+3} \sqrt{d-c^2 d x^2}}{(m+4)^3}",0,"Defer[Int][x^m*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
284,0,0,0,0.1386715,"\int x^m \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^m*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2,x]","\int x^m \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\frac{d \text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)}{m+2}+\frac{x^{m+1} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{m+2}-\frac{2 b c x^{m+2} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)}{(m+2)^2 \sqrt{1-c^2 x^2}}+\frac{2 b^2 c^2 x^{m+3} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{(m+2)^2 (m+3) \sqrt{1-c^2 x^2}}",0,"Defer[Int][x^m*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
285,0,0,0,0.1507547,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^m*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSin[c*x])^2)/Sqrt[d - c^2*d*x^2], x]","A",0,0,0,0,-1,"{}"
286,0,0,0,0.1659467,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
287,0,0,0,0.1660029,"\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\int \frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sin ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSin[c*x])^2)/(d - c^2*d*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
288,0,0,0,0.0953553,"\int \frac{x^m \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^m*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2],x]","\int \frac{x^m \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","\text{Int}\left(\frac{x^m \sin ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}},x\right)",0,"Defer[Int][(x^m*ArcSin[a*x]^2)/Sqrt[1 - a^2*x^2], x]","A",0,0,0,0,-1,"{}"
289,1,370,0,0.6999046,"\int \left(c-a^2 c x^2\right)^3 \sin ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^3*ArcSin[a*x]^3,x]","-\frac{6 c^3 \left(1-a^2 x^2\right)^{7/2}}{2401 a}-\frac{2664 c^3 \left(1-a^2 x^2\right)^{5/2}}{214375 a}-\frac{30256 c^3 \left(1-a^2 x^2\right)^{3/2}}{385875 a}-\frac{413312 c^3 \sqrt{1-a^2 x^2}}{128625 a}+\frac{6}{343} a^6 c^3 x^7 \sin ^{-1}(a x)-\frac{702 a^4 c^3 x^5 \sin ^{-1}(a x)}{6125}+\frac{1514 a^2 c^3 x^3 \sin ^{-1}(a x)}{3675}+\frac{1}{7} c^3 x \left(1-a^2 x^2\right)^3 \sin ^{-1}(a x)^3+\frac{6}{35} c^3 x \left(1-a^2 x^2\right)^2 \sin ^{-1}(a x)^3+\frac{8}{35} c^3 x \left(1-a^2 x^2\right) \sin ^{-1}(a x)^3+\frac{3 c^3 \left(1-a^2 x^2\right)^{7/2} \sin ^{-1}(a x)^2}{49 a}+\frac{18 c^3 \left(1-a^2 x^2\right)^{5/2} \sin ^{-1}(a x)^2}{175 a}+\frac{8 c^3 \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)^2}{35 a}+\frac{48 c^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{35 a}+\frac{16}{35} c^3 x \sin ^{-1}(a x)^3-\frac{4322 c^3 x \sin ^{-1}(a x)}{1225}","-\frac{6 c^3 \left(1-a^2 x^2\right)^{7/2}}{2401 a}-\frac{2664 c^3 \left(1-a^2 x^2\right)^{5/2}}{214375 a}-\frac{30256 c^3 \left(1-a^2 x^2\right)^{3/2}}{385875 a}-\frac{413312 c^3 \sqrt{1-a^2 x^2}}{128625 a}+\frac{6}{343} a^6 c^3 x^7 \sin ^{-1}(a x)-\frac{702 a^4 c^3 x^5 \sin ^{-1}(a x)}{6125}+\frac{1514 a^2 c^3 x^3 \sin ^{-1}(a x)}{3675}+\frac{1}{7} c^3 x \left(1-a^2 x^2\right)^3 \sin ^{-1}(a x)^3+\frac{6}{35} c^3 x \left(1-a^2 x^2\right)^2 \sin ^{-1}(a x)^3+\frac{8}{35} c^3 x \left(1-a^2 x^2\right) \sin ^{-1}(a x)^3+\frac{3 c^3 \left(1-a^2 x^2\right)^{7/2} \sin ^{-1}(a x)^2}{49 a}+\frac{18 c^3 \left(1-a^2 x^2\right)^{5/2} \sin ^{-1}(a x)^2}{175 a}+\frac{8 c^3 \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)^2}{35 a}+\frac{48 c^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{35 a}+\frac{16}{35} c^3 x \sin ^{-1}(a x)^3-\frac{4322 c^3 x \sin ^{-1}(a x)}{1225}",1,"(-413312*c^3*Sqrt[1 - a^2*x^2])/(128625*a) - (30256*c^3*(1 - a^2*x^2)^(3/2))/(385875*a) - (2664*c^3*(1 - a^2*x^2)^(5/2))/(214375*a) - (6*c^3*(1 - a^2*x^2)^(7/2))/(2401*a) - (4322*c^3*x*ArcSin[a*x])/1225 + (1514*a^2*c^3*x^3*ArcSin[a*x])/3675 - (702*a^4*c^3*x^5*ArcSin[a*x])/6125 + (6*a^6*c^3*x^7*ArcSin[a*x])/343 + (48*c^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(35*a) + (8*c^3*(1 - a^2*x^2)^(3/2)*ArcSin[a*x]^2)/(35*a) + (18*c^3*(1 - a^2*x^2)^(5/2)*ArcSin[a*x]^2)/(175*a) + (3*c^3*(1 - a^2*x^2)^(7/2)*ArcSin[a*x]^2)/(49*a) + (16*c^3*x*ArcSin[a*x]^3)/35 + (8*c^3*x*(1 - a^2*x^2)*ArcSin[a*x]^3)/35 + (6*c^3*x*(1 - a^2*x^2)^2*ArcSin[a*x]^3)/35 + (c^3*x*(1 - a^2*x^2)^3*ArcSin[a*x]^3)/7","A",24,13,20,0.6500,1,"{4649, 4619, 4677, 261, 4645, 444, 43, 194, 12, 1247, 698, 1799, 1850}"
290,1,273,0,0.4073795,"\int \left(c-a^2 c x^2\right)^2 \sin ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^2*ArcSin[a*x]^3,x]","-\frac{6 c^2 \left(1-a^2 x^2\right)^{5/2}}{625 a}-\frac{272 c^2 \left(1-a^2 x^2\right)^{3/2}}{3375 a}-\frac{4144 c^2 \sqrt{1-a^2 x^2}}{1125 a}-\frac{6}{125} a^4 c^2 x^5 \sin ^{-1}(a x)+\frac{76}{225} a^2 c^2 x^3 \sin ^{-1}(a x)+\frac{1}{5} c^2 x \left(1-a^2 x^2\right)^2 \sin ^{-1}(a x)^3+\frac{4}{15} c^2 x \left(1-a^2 x^2\right) \sin ^{-1}(a x)^3+\frac{3 c^2 \left(1-a^2 x^2\right)^{5/2} \sin ^{-1}(a x)^2}{25 a}+\frac{4 c^2 \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)^2}{15 a}+\frac{8 c^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{5 a}+\frac{8}{15} c^2 x \sin ^{-1}(a x)^3-\frac{298}{75} c^2 x \sin ^{-1}(a x)","-\frac{6 c^2 \left(1-a^2 x^2\right)^{5/2}}{625 a}-\frac{272 c^2 \left(1-a^2 x^2\right)^{3/2}}{3375 a}-\frac{4144 c^2 \sqrt{1-a^2 x^2}}{1125 a}-\frac{6}{125} a^4 c^2 x^5 \sin ^{-1}(a x)+\frac{76}{225} a^2 c^2 x^3 \sin ^{-1}(a x)+\frac{1}{5} c^2 x \left(1-a^2 x^2\right)^2 \sin ^{-1}(a x)^3+\frac{4}{15} c^2 x \left(1-a^2 x^2\right) \sin ^{-1}(a x)^3+\frac{3 c^2 \left(1-a^2 x^2\right)^{5/2} \sin ^{-1}(a x)^2}{25 a}+\frac{4 c^2 \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)^2}{15 a}+\frac{8 c^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{5 a}+\frac{8}{15} c^2 x \sin ^{-1}(a x)^3-\frac{298}{75} c^2 x \sin ^{-1}(a x)",1,"(-4144*c^2*Sqrt[1 - a^2*x^2])/(1125*a) - (272*c^2*(1 - a^2*x^2)^(3/2))/(3375*a) - (6*c^2*(1 - a^2*x^2)^(5/2))/(625*a) - (298*c^2*x*ArcSin[a*x])/75 + (76*a^2*c^2*x^3*ArcSin[a*x])/225 - (6*a^4*c^2*x^5*ArcSin[a*x])/125 + (8*c^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/(5*a) + (4*c^2*(1 - a^2*x^2)^(3/2)*ArcSin[a*x]^2)/(15*a) + (3*c^2*(1 - a^2*x^2)^(5/2)*ArcSin[a*x]^2)/(25*a) + (8*c^2*x*ArcSin[a*x]^3)/15 + (4*c^2*x*(1 - a^2*x^2)*ArcSin[a*x]^3)/15 + (c^2*x*(1 - a^2*x^2)^2*ArcSin[a*x]^3)/5","A",17,11,20,0.5500,1,"{4649, 4619, 4677, 261, 4645, 444, 43, 194, 12, 1247, 698}"
291,1,158,0,0.2109075,"\int \left(c-a^2 c x^2\right) \sin ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)*ArcSin[a*x]^3,x]","-\frac{2 c \left(1-a^2 x^2\right)^{3/2}}{27 a}-\frac{40 c \sqrt{1-a^2 x^2}}{9 a}+\frac{2}{9} a^2 c x^3 \sin ^{-1}(a x)+\frac{1}{3} c x \left(1-a^2 x^2\right) \sin ^{-1}(a x)^3+\frac{c \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)^2}{3 a}+\frac{2 c \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a}+\frac{2}{3} c x \sin ^{-1}(a x)^3-\frac{14}{3} c x \sin ^{-1}(a x)","-\frac{2 c \left(1-a^2 x^2\right)^{3/2}}{27 a}-\frac{40 c \sqrt{1-a^2 x^2}}{9 a}+\frac{2}{9} a^2 c x^3 \sin ^{-1}(a x)+\frac{1}{3} c x \left(1-a^2 x^2\right) \sin ^{-1}(a x)^3+\frac{c \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)^2}{3 a}+\frac{2 c \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2}{a}+\frac{2}{3} c x \sin ^{-1}(a x)^3-\frac{14}{3} c x \sin ^{-1}(a x)",1,"(-40*c*Sqrt[1 - a^2*x^2])/(9*a) - (2*c*(1 - a^2*x^2)^(3/2))/(27*a) - (14*c*x*ArcSin[a*x])/3 + (2*a^2*c*x^3*ArcSin[a*x])/9 + (2*c*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2)/a + (c*(1 - a^2*x^2)^(3/2)*ArcSin[a*x]^2)/(3*a) + (2*c*x*ArcSin[a*x]^3)/3 + (c*x*(1 - a^2*x^2)*ArcSin[a*x]^3)/3","A",10,7,18,0.3889,1,"{4649, 4619, 4677, 261, 4645, 444, 43}"
292,1,200,0,0.1337502,"\int \frac{\sin ^{-1}(a x)^3}{c-a^2 c x^2} \, dx","Int[ArcSin[a*x]^3/(c - a^2*c*x^2),x]","\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{6 \sin ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(a x)}\right)}{a c}+\frac{6 \sin ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{6 i \text{PolyLog}\left(4,-i e^{i \sin ^{-1}(a x)}\right)}{a c}+\frac{6 i \text{PolyLog}\left(4,i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{2 i \sin ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c}","\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{6 \sin ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(a x)}\right)}{a c}+\frac{6 \sin ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{6 i \text{PolyLog}\left(4,-i e^{i \sin ^{-1}(a x)}\right)}{a c}+\frac{6 i \text{PolyLog}\left(4,i e^{i \sin ^{-1}(a x)}\right)}{a c}-\frac{2 i \sin ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c}",1,"((-2*I)*ArcSin[a*x]^3*ArcTan[E^(I*ArcSin[a*x])])/(a*c) + ((3*I)*ArcSin[a*x]^2*PolyLog[2, (-I)*E^(I*ArcSin[a*x])])/(a*c) - ((3*I)*ArcSin[a*x]^2*PolyLog[2, I*E^(I*ArcSin[a*x])])/(a*c) - (6*ArcSin[a*x]*PolyLog[3, (-I)*E^(I*ArcSin[a*x])])/(a*c) + (6*ArcSin[a*x]*PolyLog[3, I*E^(I*ArcSin[a*x])])/(a*c) - ((6*I)*PolyLog[4, (-I)*E^(I*ArcSin[a*x])])/(a*c) + ((6*I)*PolyLog[4, I*E^(I*ArcSin[a*x])])/(a*c)","A",10,6,20,0.3000,1,"{4657, 4181, 2531, 6609, 2282, 6589}"
293,1,337,0,0.2962226,"\int \frac{\sin ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^2} \, dx","Int[ArcSin[a*x]^3/(c - a^2*c*x^2)^2,x]","\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 \sin ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{3 \sin ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(4,-i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(4,i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{x \sin ^{-1}(a x)^3}{2 c^2 \left(1-a^2 x^2\right)}-\frac{3 \sin ^{-1}(a x)^2}{2 a c^2 \sqrt{1-a^2 x^2}}-\frac{i \sin ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c^2}-\frac{6 i \sin ^{-1}(a x) \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c^2}","\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 \sin ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{3 \sin ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(4,-i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(4,i e^{i \sin ^{-1}(a x)}\right)}{a c^2}+\frac{x \sin ^{-1}(a x)^3}{2 c^2 \left(1-a^2 x^2\right)}-\frac{3 \sin ^{-1}(a x)^2}{2 a c^2 \sqrt{1-a^2 x^2}}-\frac{i \sin ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c^2}-\frac{6 i \sin ^{-1}(a x) \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c^2}",1,"(-3*ArcSin[a*x]^2)/(2*a*c^2*Sqrt[1 - a^2*x^2]) + (x*ArcSin[a*x]^3)/(2*c^2*(1 - a^2*x^2)) - ((6*I)*ArcSin[a*x]*ArcTan[E^(I*ArcSin[a*x])])/(a*c^2) - (I*ArcSin[a*x]^3*ArcTan[E^(I*ArcSin[a*x])])/(a*c^2) + ((3*I)*PolyLog[2, (-I)*E^(I*ArcSin[a*x])])/(a*c^2) + (((3*I)/2)*ArcSin[a*x]^2*PolyLog[2, (-I)*E^(I*ArcSin[a*x])])/(a*c^2) - ((3*I)*PolyLog[2, I*E^(I*ArcSin[a*x])])/(a*c^2) - (((3*I)/2)*ArcSin[a*x]^2*PolyLog[2, I*E^(I*ArcSin[a*x])])/(a*c^2) - (3*ArcSin[a*x]*PolyLog[3, (-I)*E^(I*ArcSin[a*x])])/(a*c^2) + (3*ArcSin[a*x]*PolyLog[3, I*E^(I*ArcSin[a*x])])/(a*c^2) - ((3*I)*PolyLog[4, (-I)*E^(I*ArcSin[a*x])])/(a*c^2) + ((3*I)*PolyLog[4, I*E^(I*ArcSin[a*x])])/(a*c^2)","A",18,10,20,0.5000,1,"{4655, 4657, 4181, 2531, 6609, 2282, 6589, 4677, 2279, 2391}"
294,1,455,0,0.5071239,"\int \frac{\sin ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^3} \, dx","Int[ArcSin[a*x]^3/(c - a^2*c*x^2)^3,x]","\frac{9 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 \sin ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 \sin ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}+\frac{5 i \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{2 a c^3}-\frac{5 i \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{2 a c^3}-\frac{9 i \text{PolyLog}\left(4,-i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 i \text{PolyLog}\left(4,i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}-\frac{1}{4 a c^3 \sqrt{1-a^2 x^2}}+\frac{3 x \sin ^{-1}(a x)^3}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \sin ^{-1}(a x)^3}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)^2}{4 a c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \sin ^{-1}(a x)}{4 c^3 \left(1-a^2 x^2\right)}-\frac{3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 i \sin ^{-1}(a x) \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c^3}","\frac{9 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 \sin ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 \sin ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}+\frac{5 i \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(a x)}\right)}{2 a c^3}-\frac{5 i \text{PolyLog}\left(2,i e^{i \sin ^{-1}(a x)}\right)}{2 a c^3}-\frac{9 i \text{PolyLog}\left(4,-i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 i \text{PolyLog}\left(4,i e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}-\frac{1}{4 a c^3 \sqrt{1-a^2 x^2}}+\frac{3 x \sin ^{-1}(a x)^3}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \sin ^{-1}(a x)^3}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{9 \sin ^{-1}(a x)^2}{8 a c^3 \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)^2}{4 a c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{x \sin ^{-1}(a x)}{4 c^3 \left(1-a^2 x^2\right)}-\frac{3 i \sin ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 i \sin ^{-1}(a x) \tan ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{a c^3}",1,"-1/(4*a*c^3*Sqrt[1 - a^2*x^2]) + (x*ArcSin[a*x])/(4*c^3*(1 - a^2*x^2)) - ArcSin[a*x]^2/(4*a*c^3*(1 - a^2*x^2)^(3/2)) - (9*ArcSin[a*x]^2)/(8*a*c^3*Sqrt[1 - a^2*x^2]) + (x*ArcSin[a*x]^3)/(4*c^3*(1 - a^2*x^2)^2) + (3*x*ArcSin[a*x]^3)/(8*c^3*(1 - a^2*x^2)) - ((5*I)*ArcSin[a*x]*ArcTan[E^(I*ArcSin[a*x])])/(a*c^3) - (((3*I)/4)*ArcSin[a*x]^3*ArcTan[E^(I*ArcSin[a*x])])/(a*c^3) + (((5*I)/2)*PolyLog[2, (-I)*E^(I*ArcSin[a*x])])/(a*c^3) + (((9*I)/8)*ArcSin[a*x]^2*PolyLog[2, (-I)*E^(I*ArcSin[a*x])])/(a*c^3) - (((5*I)/2)*PolyLog[2, I*E^(I*ArcSin[a*x])])/(a*c^3) - (((9*I)/8)*ArcSin[a*x]^2*PolyLog[2, I*E^(I*ArcSin[a*x])])/(a*c^3) - (9*ArcSin[a*x]*PolyLog[3, (-I)*E^(I*ArcSin[a*x])])/(4*a*c^3) + (9*ArcSin[a*x]*PolyLog[3, I*E^(I*ArcSin[a*x])])/(4*a*c^3) - (((9*I)/4)*PolyLog[4, (-I)*E^(I*ArcSin[a*x])])/(a*c^3) + (((9*I)/4)*PolyLog[4, I*E^(I*ArcSin[a*x])])/(a*c^3)","A",28,11,20,0.5500,1,"{4655, 4657, 4181, 2531, 6609, 2282, 6589, 4677, 2279, 2391, 261}"
295,1,533,0,0.5471629,"\int \left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^(5/2)*ArcSin[a*x]^3,x]","-\frac{65 a^3 c^2 x^4 \sqrt{c-a^2 c x^2}}{2304 \sqrt{1-a^2 x^2}}+\frac{865 a c^2 x^2 \sqrt{c-a^2 c x^2}}{2304 \sqrt{1-a^2 x^2}}-\frac{c^2 \left(1-a^2 x^2\right)^{5/2} \sqrt{c-a^2 c x^2}}{216 a}-\frac{15 a c^2 x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{32 \sqrt{1-a^2 x^2}}+\frac{5}{16} c^2 x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3-\frac{245}{384} c^2 x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)-\frac{1}{36} c^2 x \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)-\frac{65}{576} c^2 x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)+\frac{5 c^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^4}{64 a \sqrt{1-a^2 x^2}}+\frac{c^2 \left(1-a^2 x^2\right)^{5/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{12 a}+\frac{5 c^2 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{32 a}+\frac{115 c^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{768 a \sqrt{1-a^2 x^2}}+\frac{1}{6} x \left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^3+\frac{5}{24} c x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^3","-\frac{65 a^3 c^2 x^4 \sqrt{c-a^2 c x^2}}{2304 \sqrt{1-a^2 x^2}}+\frac{865 a c^2 x^2 \sqrt{c-a^2 c x^2}}{2304 \sqrt{1-a^2 x^2}}-\frac{c^2 \left(1-a^2 x^2\right)^{5/2} \sqrt{c-a^2 c x^2}}{216 a}-\frac{15 a c^2 x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{32 \sqrt{1-a^2 x^2}}+\frac{5}{16} c^2 x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3-\frac{245}{384} c^2 x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)-\frac{1}{36} c^2 x \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)-\frac{65}{576} c^2 x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)+\frac{5 c^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^4}{64 a \sqrt{1-a^2 x^2}}+\frac{c^2 \left(1-a^2 x^2\right)^{5/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{12 a}+\frac{5 c^2 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{32 a}+\frac{115 c^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{768 a \sqrt{1-a^2 x^2}}+\frac{1}{6} x \left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^3+\frac{5}{24} c x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^3",1,"(865*a*c^2*x^2*Sqrt[c - a^2*c*x^2])/(2304*Sqrt[1 - a^2*x^2]) - (65*a^3*c^2*x^4*Sqrt[c - a^2*c*x^2])/(2304*Sqrt[1 - a^2*x^2]) - (c^2*(1 - a^2*x^2)^(5/2)*Sqrt[c - a^2*c*x^2])/(216*a) - (245*c^2*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x])/384 - (65*c^2*x*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]*ArcSin[a*x])/576 - (c^2*x*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x])/36 + (115*c^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(768*a*Sqrt[1 - a^2*x^2]) - (15*a*c^2*x^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(32*Sqrt[1 - a^2*x^2]) + (5*c^2*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(32*a) + (c^2*(1 - a^2*x^2)^(5/2)*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(12*a) + (5*c^2*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^3)/16 + (5*c*x*(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^3)/24 + (x*(c - a^2*c*x^2)^(5/2)*ArcSin[a*x]^3)/6 + (5*c^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^4)/(64*a*Sqrt[1 - a^2*x^2])","A",24,9,22,0.4091,1,"{4649, 4647, 4641, 4627, 4707, 30, 4677, 14, 261}"
296,1,365,0,0.322146,"\int \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^3,x]","-\frac{3 a^3 c x^4 \sqrt{c-a^2 c x^2}}{128 \sqrt{1-a^2 x^2}}+\frac{51 a c x^2 \sqrt{c-a^2 c x^2}}{128 \sqrt{1-a^2 x^2}}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{16 \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^3+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3-\frac{45}{64} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)-\frac{3}{32} c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)+\frac{3 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^4}{32 a \sqrt{1-a^2 x^2}}+\frac{3 c \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{16 a}+\frac{27 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{128 a \sqrt{1-a^2 x^2}}","-\frac{3 a^3 c x^4 \sqrt{c-a^2 c x^2}}{128 \sqrt{1-a^2 x^2}}+\frac{51 a c x^2 \sqrt{c-a^2 c x^2}}{128 \sqrt{1-a^2 x^2}}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{16 \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^3+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3-\frac{45}{64} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)-\frac{3}{32} c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)+\frac{3 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^4}{32 a \sqrt{1-a^2 x^2}}+\frac{3 c \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{16 a}+\frac{27 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{128 a \sqrt{1-a^2 x^2}}",1,"(51*a*c*x^2*Sqrt[c - a^2*c*x^2])/(128*Sqrt[1 - a^2*x^2]) - (3*a^3*c*x^4*Sqrt[c - a^2*c*x^2])/(128*Sqrt[1 - a^2*x^2]) - (45*c*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x])/64 - (3*c*x*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]*ArcSin[a*x])/32 + (27*c*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(128*a*Sqrt[1 - a^2*x^2]) - (9*a*c*x^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(16*Sqrt[1 - a^2*x^2]) + (3*c*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(16*a) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^3)/8 + (x*(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^3)/4 + (3*c*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^4)/(32*a*Sqrt[1 - a^2*x^2])","A",14,8,22,0.3636,1,"{4649, 4647, 4641, 4627, 4707, 30, 4677, 14}"
297,1,215,0,0.1648416,"\int \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3 \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^3,x]","\frac{3 a x^2 \sqrt{c-a^2 c x^2}}{8 \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^4}{8 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{4 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{8 a \sqrt{1-a^2 x^2}}-\frac{3}{4} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)","\frac{3 a x^2 \sqrt{c-a^2 c x^2}}{8 \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^4}{8 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^3-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{4 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^2}{8 a \sqrt{1-a^2 x^2}}-\frac{3}{4} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)",1,"(3*a*x^2*Sqrt[c - a^2*c*x^2])/(8*Sqrt[1 - a^2*x^2]) - (3*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x])/4 + (3*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(8*a*Sqrt[1 - a^2*x^2]) - (3*a*x^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^2)/(4*Sqrt[1 - a^2*x^2]) + (x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^3)/2 + (Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^4)/(8*a*Sqrt[1 - a^2*x^2])","A",6,5,22,0.2273,1,"{4647, 4641, 4627, 4707, 30}"
298,1,42,0,0.0687473,"\int \frac{\sin ^{-1}(a x)^3}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcSin[a*x]^3/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^4}{4 a \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^4}{4 a \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*ArcSin[a*x]^4)/(4*a*Sqrt[c - a^2*c*x^2])","A",2,2,22,0.09091,1,"{4643, 4641}"
299,1,238,0,0.1748754,"\int \frac{\sin ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSin[a*x]^3/(c - a^2*c*x^2)^(3/2),x]","-\frac{3 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a x)}\right)}{2 a c \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^3}{c \sqrt{c-a^2 c x^2}}-\frac{i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a c \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2 \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}","-\frac{3 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a x)}\right)}{2 a c \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^3}{c \sqrt{c-a^2 c x^2}}-\frac{i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a c \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2 \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}",1,"(x*ArcSin[a*x]^3)/(c*Sqrt[c - a^2*c*x^2]) - (I*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(a*c*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2*Log[1 + E^((2*I)*ArcSin[a*x])])/(a*c*Sqrt[c - a^2*c*x^2]) - ((3*I)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*PolyLog[2, -E^((2*I)*ArcSin[a*x])])/(a*c*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*PolyLog[3, -E^((2*I)*ArcSin[a*x])])/(2*a*c*Sqrt[c - a^2*c*x^2])","A",7,7,22,0.3182,1,"{4653, 4675, 3719, 2190, 2531, 2282, 6589}"
300,1,388,0,0.3055634,"\int \frac{\sin ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[ArcSin[a*x]^3/(c - a^2*c*x^2)^(5/2),x]","-\frac{2 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log \left(1-a^2 x^2\right)}{2 a c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \sin ^{-1}(a x)^3}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{2 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a c^2 \sqrt{c-a^2 c x^2}}-\frac{\sin ^{-1}(a x)^2}{2 a c^2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)}{c^2 \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2 \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^3}{3 c \left(c-a^2 c x^2\right)^{3/2}}","-\frac{2 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log \left(1-a^2 x^2\right)}{2 a c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \sin ^{-1}(a x)^3}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{2 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a c^2 \sqrt{c-a^2 c x^2}}-\frac{\sin ^{-1}(a x)^2}{2 a c^2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)}{c^2 \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2 \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^3}{3 c \left(c-a^2 c x^2\right)^{3/2}}",1,"(x*ArcSin[a*x])/(c^2*Sqrt[c - a^2*c*x^2]) - ArcSin[a*x]^2/(2*a*c^2*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x]^3)/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*ArcSin[a*x]^3)/(3*c^2*Sqrt[c - a^2*c*x^2]) - (((2*I)/3)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(a*c^2*Sqrt[c - a^2*c*x^2]) + (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2*Log[1 + E^((2*I)*ArcSin[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 - a^2*x^2])/(2*a*c^2*Sqrt[c - a^2*c*x^2]) - ((2*I)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*PolyLog[2, -E^((2*I)*ArcSin[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*PolyLog[3, -E^((2*I)*ArcSin[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2])","A",11,11,22,0.5000,1,"{4655, 4653, 4675, 3719, 2190, 2531, 2282, 6589, 4677, 4651, 260}"
301,1,547,0,0.4810702,"\int \frac{\sin ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSin[a*x]^3/(c - a^2*c*x^2)^(7/2),x]","-\frac{8 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{1-a^2 x^2} \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}-\frac{1}{20 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log \left(1-a^2 x^2\right)}{2 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \sin ^{-1}(a x)^3}{15 c^3 \sqrt{c-a^2 c x^2}}-\frac{8 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \sin ^{-1}(a x)^3}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 \sin ^{-1}(a x)^2}{5 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}-\frac{3 \sin ^{-1}(a x)^2}{20 a c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)}{c^3 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)}{10 c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2 \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^3}{5 c \left(c-a^2 c x^2\right)^{5/2}}","-\frac{8 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{1-a^2 x^2} \text{PolyLog}\left(3,-e^{2 i \sin ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}-\frac{1}{20 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log \left(1-a^2 x^2\right)}{2 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \sin ^{-1}(a x)^3}{15 c^3 \sqrt{c-a^2 c x^2}}-\frac{8 i \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \sin ^{-1}(a x)^3}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 \sin ^{-1}(a x)^2}{5 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}-\frac{3 \sin ^{-1}(a x)^2}{20 a c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)}{c^3 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)}{10 c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{8 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^2 \log \left(1+e^{2 i \sin ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x \sin ^{-1}(a x)^3}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"-1/(20*a*c^3*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x])/(c^3*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x])/(10*c^3*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) - (3*ArcSin[a*x]^2)/(20*a*c^3*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]) - (2*ArcSin[a*x]^2)/(5*a*c^3*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2]) + (x*ArcSin[a*x]^3)/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*ArcSin[a*x]^3)/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*ArcSin[a*x]^3)/(15*c^3*Sqrt[c - a^2*c*x^2]) - (((8*I)/15)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(a*c^3*Sqrt[c - a^2*c*x^2]) + (8*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^2*Log[1 + E^((2*I)*ArcSin[a*x])])/(5*a*c^3*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 - a^2*x^2])/(2*a*c^3*Sqrt[c - a^2*c*x^2]) - (((8*I)/5)*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*PolyLog[2, -E^((2*I)*ArcSin[a*x])])/(a*c^3*Sqrt[c - a^2*c*x^2]) + (4*Sqrt[1 - a^2*x^2]*PolyLog[3, -E^((2*I)*ArcSin[a*x])])/(5*a*c^3*Sqrt[c - a^2*c*x^2])","A",17,12,22,0.5455,1,"{4655, 4653, 4675, 3719, 2190, 2531, 2282, 6589, 4677, 4651, 260, 261}"
302,0,0,0,0.0831826,"\int \frac{x^m \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^m*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2],x]","\int \frac{x^m \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","\text{Int}\left(\frac{x^m \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}},x\right)",0,"Defer[Int][(x^m*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2], x]","A",0,0,0,0,-1,"{}"
303,1,191,0,0.4678904,"\int \frac{x^4 \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{45 x^2}{128 a^3}-\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{4 a^2}+\frac{3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{32 a^2}+\frac{9 x^2 \sin ^{-1}(a x)^2}{16 a^3}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{8 a^4}+\frac{45 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{64 a^4}+\frac{3 \sin ^{-1}(a x)^4}{32 a^5}-\frac{45 \sin ^{-1}(a x)^2}{128 a^5}-\frac{3 x^4}{128 a}+\frac{3 x^4 \sin ^{-1}(a x)^2}{16 a}","-\frac{45 x^2}{128 a^3}-\frac{x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{4 a^2}+\frac{3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{32 a^2}+\frac{9 x^2 \sin ^{-1}(a x)^2}{16 a^3}-\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{8 a^4}+\frac{45 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{64 a^4}+\frac{3 \sin ^{-1}(a x)^4}{32 a^5}-\frac{45 \sin ^{-1}(a x)^2}{128 a^5}-\frac{3 x^4}{128 a}+\frac{3 x^4 \sin ^{-1}(a x)^2}{16 a}",1,"(-45*x^2)/(128*a^3) - (3*x^4)/(128*a) + (45*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(64*a^4) + (3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(32*a^2) - (45*ArcSin[a*x]^2)/(128*a^5) + (9*x^2*ArcSin[a*x]^2)/(16*a^3) + (3*x^4*ArcSin[a*x]^2)/(16*a) - (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(8*a^4) - (x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(4*a^2) + (3*ArcSin[a*x]^4)/(32*a^5)","A",13,4,24,0.1667,1,"{4707, 4641, 4627, 30}"
304,1,157,0,0.3207147,"\int \frac{x^3 \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a^2}+\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^2}-\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a^4}+\frac{40 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^4}-\frac{40 x}{9 a^3}+\frac{2 x \sin ^{-1}(a x)^2}{a^3}-\frac{2 x^3}{27 a}+\frac{x^3 \sin ^{-1}(a x)^2}{3 a}","-\frac{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a^2}+\frac{2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^2}-\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{3 a^4}+\frac{40 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{9 a^4}-\frac{40 x}{9 a^3}+\frac{2 x \sin ^{-1}(a x)^2}{a^3}-\frac{2 x^3}{27 a}+\frac{x^3 \sin ^{-1}(a x)^2}{3 a}",1,"(-40*x)/(9*a^3) - (2*x^3)/(27*a) + (40*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(9*a^4) + (2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(9*a^2) + (2*x*ArcSin[a*x]^2)/a^3 + (x^3*ArcSin[a*x]^2)/(3*a) - (2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(3*a^4) - (x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(3*a^2)","A",10,6,24,0.2500,1,"{4707, 4677, 4619, 8, 4627, 30}"
305,1,107,0,0.2071799,"\int \frac{x^2 \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{2 a^2}+\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{4 a^2}+\frac{\sin ^{-1}(a x)^4}{8 a^3}-\frac{3 \sin ^{-1}(a x)^2}{8 a^3}-\frac{3 x^2}{8 a}+\frac{3 x^2 \sin ^{-1}(a x)^2}{4 a}","-\frac{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{2 a^2}+\frac{3 x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{4 a^2}+\frac{\sin ^{-1}(a x)^4}{8 a^3}-\frac{3 \sin ^{-1}(a x)^2}{8 a^3}-\frac{3 x^2}{8 a}+\frac{3 x^2 \sin ^{-1}(a x)^2}{4 a}",1,"(-3*x^2)/(8*a) + (3*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(4*a^2) - (3*ArcSin[a*x]^2)/(8*a^3) + (3*x^2*ArcSin[a*x]^2)/(4*a) - (x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(2*a^2) + ArcSin[a*x]^4/(8*a^3)","A",6,4,24,0.1667,1,"{4707, 4641, 4627, 30}"
306,1,67,0,0.1051923,"\int \frac{x \sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcSin[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a^2}+\frac{6 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a^2}-\frac{6 x}{a}+\frac{3 x \sin ^{-1}(a x)^2}{a}","-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{a^2}+\frac{6 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a^2}-\frac{6 x}{a}+\frac{3 x \sin ^{-1}(a x)^2}{a}",1,"(-6*x)/a + (6*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/a^2 + (3*x*ArcSin[a*x]^2)/a - (Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/a^2","A",4,3,22,0.1364,1,"{4677, 4619, 8}"
307,1,13,0,0.0295044,"\int \frac{\sin ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^3/Sqrt[1 - a^2*x^2],x]","\frac{\sin ^{-1}(a x)^4}{4 a}","\frac{\sin ^{-1}(a x)^4}{4 a}",1,"ArcSin[a*x]^4/(4*a)","A",1,1,21,0.04762,1,"{4641}"
308,1,138,0,0.1601086,"\int \frac{\sin ^{-1}(a x)^3}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^3/(x*Sqrt[1 - a^2*x^2]),x]","3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-6 \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+6 \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-6 i \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+6 i \text{PolyLog}\left(4,e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x)^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)","3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-3 i \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-6 \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+6 \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)-6 i \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+6 i \text{PolyLog}\left(4,e^{i \sin ^{-1}(a x)}\right)-2 \sin ^{-1}(a x)^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)",1,"-2*ArcSin[a*x]^3*ArcTanh[E^(I*ArcSin[a*x])] + (3*I)*ArcSin[a*x]^2*PolyLog[2, -E^(I*ArcSin[a*x])] - (3*I)*ArcSin[a*x]^2*PolyLog[2, E^(I*ArcSin[a*x])] - 6*ArcSin[a*x]*PolyLog[3, -E^(I*ArcSin[a*x])] + 6*ArcSin[a*x]*PolyLog[3, E^(I*ArcSin[a*x])] - (6*I)*PolyLog[4, -E^(I*ArcSin[a*x])] + (6*I)*PolyLog[4, E^(I*ArcSin[a*x])]","A",10,6,24,0.2500,1,"{4709, 4183, 2531, 6609, 2282, 6589}"
309,1,99,0,0.1816079,"\int \frac{\sin ^{-1}(a x)^3}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^3/(x^2*Sqrt[1 - a^2*x^2]),x]","-3 i a \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{2} a \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{x}-i a \sin ^{-1}(a x)^3+3 a \sin ^{-1}(a x)^2 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)","-3 i a \sin ^{-1}(a x) \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(a x)}\right)+\frac{3}{2} a \text{PolyLog}\left(3,e^{2 i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{x}-i a \sin ^{-1}(a x)^3+3 a \sin ^{-1}(a x)^2 \log \left(1-e^{2 i \sin ^{-1}(a x)}\right)",1,"(-I)*a*ArcSin[a*x]^3 - (Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/x + 3*a*ArcSin[a*x]^2*Log[1 - E^((2*I)*ArcSin[a*x])] - (3*I)*a*ArcSin[a*x]*PolyLog[2, E^((2*I)*ArcSin[a*x])] + (3*a*PolyLog[3, E^((2*I)*ArcSin[a*x])])/2","A",7,7,24,0.2917,1,"{4681, 4625, 3717, 2190, 2531, 2282, 6589}"
310,1,264,0,0.3572544,"\int \frac{\sin ^{-1}(a x)^3}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^3/(x^3*Sqrt[1 - a^2*x^2]),x]","\frac{3}{2} i a^2 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-\frac{3}{2} i a^2 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-3 a^2 \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+3 a^2 \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)+3 i a^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-3 i a^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-3 i a^2 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+3 i a^2 \text{PolyLog}\left(4,e^{i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{2 x^2}-a^2 \sin ^{-1}(a x)^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-6 a^2 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{3 a \sin ^{-1}(a x)^2}{2 x}","\frac{3}{2} i a^2 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-\frac{3}{2} i a^2 \sin ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-3 a^2 \sin ^{-1}(a x) \text{PolyLog}\left(3,-e^{i \sin ^{-1}(a x)}\right)+3 a^2 \sin ^{-1}(a x) \text{PolyLog}\left(3,e^{i \sin ^{-1}(a x)}\right)+3 i a^2 \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)-3 i a^2 \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)-3 i a^2 \text{PolyLog}\left(4,-e^{i \sin ^{-1}(a x)}\right)+3 i a^2 \text{PolyLog}\left(4,e^{i \sin ^{-1}(a x)}\right)-\frac{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3}{2 x^2}-a^2 \sin ^{-1}(a x)^3 \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-6 a^2 \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)-\frac{3 a \sin ^{-1}(a x)^2}{2 x}",1,"(-3*a*ArcSin[a*x]^2)/(2*x) - (Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3)/(2*x^2) - 6*a^2*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])] - a^2*ArcSin[a*x]^3*ArcTanh[E^(I*ArcSin[a*x])] + (3*I)*a^2*PolyLog[2, -E^(I*ArcSin[a*x])] + ((3*I)/2)*a^2*ArcSin[a*x]^2*PolyLog[2, -E^(I*ArcSin[a*x])] - (3*I)*a^2*PolyLog[2, E^(I*ArcSin[a*x])] - ((3*I)/2)*a^2*ArcSin[a*x]^2*PolyLog[2, E^(I*ArcSin[a*x])] - 3*a^2*ArcSin[a*x]*PolyLog[3, -E^(I*ArcSin[a*x])] + 3*a^2*ArcSin[a*x]*PolyLog[3, E^(I*ArcSin[a*x])] - (3*I)*a^2*PolyLog[4, -E^(I*ArcSin[a*x])] + (3*I)*a^2*PolyLog[4, E^(I*ArcSin[a*x])]","A",18,10,24,0.4167,1,"{4701, 4709, 4183, 2531, 6609, 2282, 6589, 4627, 2279, 2391}"
311,1,67,0,0.1053045,"\int \frac{\left(c-a^2 c x^2\right)^3}{\sin ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)^3/ArcSin[a*x],x]","\frac{35 c^3 \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{64 a}+\frac{21 c^3 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{64 a}+\frac{c^3 \text{CosIntegral}\left(7 \sin ^{-1}(a x)\right)}{64 a}","\frac{35 c^3 \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{64 a}+\frac{21 c^3 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{64 a}+\frac{c^3 \text{CosIntegral}\left(7 \sin ^{-1}(a x)\right)}{64 a}",1,"(35*c^3*CosIntegral[ArcSin[a*x]])/(64*a) + (21*c^3*CosIntegral[3*ArcSin[a*x]])/(64*a) + (7*c^3*CosIntegral[5*ArcSin[a*x]])/(64*a) + (c^3*CosIntegral[7*ArcSin[a*x]])/(64*a)","A",7,3,20,0.1500,1,"{4661, 3312, 3302}"
312,1,50,0,0.0901502,"\int \frac{\left(c-a^2 c x^2\right)^2}{\sin ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)^2/ArcSin[a*x],x]","\frac{5 c^2 \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{8 a}+\frac{5 c^2 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{16 a}+\frac{c^2 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{16 a}","\frac{5 c^2 \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{8 a}+\frac{5 c^2 \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{16 a}+\frac{c^2 \text{CosIntegral}\left(5 \sin ^{-1}(a x)\right)}{16 a}",1,"(5*c^2*CosIntegral[ArcSin[a*x]])/(8*a) + (5*c^2*CosIntegral[3*ArcSin[a*x]])/(16*a) + (c^2*CosIntegral[5*ArcSin[a*x]])/(16*a)","A",6,3,20,0.1500,1,"{4661, 3312, 3302}"
313,1,29,0,0.0639881,"\int \frac{c-a^2 c x^2}{\sin ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)/ArcSin[a*x],x]","\frac{3 c \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{4 a}+\frac{c \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{4 a}","\frac{3 c \text{CosIntegral}\left(\sin ^{-1}(a x)\right)}{4 a}+\frac{c \text{CosIntegral}\left(3 \sin ^{-1}(a x)\right)}{4 a}",1,"(3*c*CosIntegral[ArcSin[a*x]])/(4*a) + (c*CosIntegral[3*ArcSin[a*x]])/(4*a)","A",5,3,18,0.1667,1,"{4661, 3312, 3302}"
314,0,0,0,0.0241084,"\int \frac{1}{\left(c-a^2 c x^2\right) \sin ^{-1}(a x)} \, dx","Int[1/((c - a^2*c*x^2)*ArcSin[a*x]),x]","\int \frac{1}{\left(c-a^2 c x^2\right) \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right) \sin ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c - a^2*c*x^2)*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
315,0,0,0,0.0236022,"\int \frac{1}{\left(c-a^2 c x^2\right)^2 \sin ^{-1}(a x)} \, dx","Int[1/((c - a^2*c*x^2)^2*ArcSin[a*x]),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^2 \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right)^2 \sin ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c - a^2*c*x^2)^2*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
316,1,206,0,0.4601277,"\int \frac{x^4 \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^4*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]),x]","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c^5}-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{16 b c^5}+\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c^5}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c^5}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{16 b c^5}+\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c^5}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{16 b c^5}","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^5}-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^5}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^5}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^5}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{16 b c^5}",1,"-(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c^5) - (Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(16*b*c^5) + (Cos[(6*a)/b]*CosIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c^5) + Log[a + b*ArcSin[c*x]]/(16*b*c^5) - (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c^5) - (Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(16*b*c^5) + (Sin[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c^5)","A",12,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
317,1,179,0,0.4304183,"\int \frac{x^3 \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^3*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]),x]","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^4}-\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^4}+\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^4}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^4}+\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^4}-\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^4}","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^4}-\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^4}+\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^4}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^4}+\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^4}-\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^4}",1,"-(CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(8*b*c^4) - (CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(16*b*c^4) + (CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(16*b*c^4) + (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b*c^4) + (Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b*c^4) - (Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b*c^4)","A",12,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
318,1,82,0,0.2506875,"\int \frac{x^2 \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^2*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]),x]","-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^3}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{8 b c^3}","-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b c^3}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{8 b c^3}",1,"-(Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c^3) + Log[a + b*ArcSin[c*x]]/(8*b*c^3) - (Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c^3)","A",6,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
319,1,117,0,0.2621203,"\int \frac{x \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]),x]","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^2}-\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b c^2}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^2}+\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b c^2}","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^2}-\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^2}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^2}+\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^2}",1,"-(CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(4*b*c^2) - (CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(4*b*c^2) + (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b*c^2) + (Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^2)","A",9,5,26,0.1923,1,"{4723, 4406, 3303, 3299, 3302}"
320,1,82,0,0.1662445,"\int \frac{\sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[Sqrt[1 - c^2*x^2]/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{2 b c}","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{2 b c}",1,"(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c) + Log[a + b*ArcSin[c*x]]/(2*b*c) + (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c)","A",6,5,25,0.2000,1,"{4661, 3312, 3303, 3299, 3302}"
321,0,0,0,0.3988592,"\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x*(a + b*ArcSin[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)+\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b}",0,"(CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/b - (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/b + Defer[Int][1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
322,0,0,0,0.2977007,"\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^2*(a + b*ArcSin[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)-\frac{c \log \left(a+b \sin ^{-1}(c x)\right)}{b}",0,"-((c*Log[a + b*ArcSin[c*x]])/b) + Defer[Int][1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
323,0,0,0,0.1205257,"\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^3*(a + b*ArcSin[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Sqrt[1 - c^2*x^2]/(x^3*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
324,0,0,0,0.1198727,"\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^4*(a + b*ArcSin[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Sqrt[1 - c^2*x^2]/(x^4*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
325,1,241,0,0.4990664,"\int \frac{x^3 \left(1-c^2 x^2\right)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^3*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x]),x]","-\frac{3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b c^4}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b c^4}+\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b c^4}+\frac{\sin \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b c^4}+\frac{3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b c^4}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b c^4}-\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b c^4}-\frac{\cos \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b c^4}","-\frac{3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b c^4}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^4}+\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^4}+\frac{\sin \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^4}+\frac{3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b c^4}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^4}-\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^4}-\frac{\cos \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^4}",1,"(-3*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(64*b*c^4) - (3*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(64*b*c^4) + (CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(64*b*c^4) + (CosIntegral[(7*a)/b + 7*ArcSin[c*x]]*Sin[(7*a)/b])/(64*b*c^4) + (3*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(64*b*c^4) + (3*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(64*b*c^4) - (Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(64*b*c^4) - (Cos[(7*a)/b]*SinIntegral[(7*a)/b + 7*ArcSin[c*x]])/(64*b*c^4)","A",15,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
326,1,206,0,0.4232486,"\int \frac{x^2 \left(1-c^2 x^2\right)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^2*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{16 b c^3}-\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c^3}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{16 b c^3}-\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c^3}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{16 b c^3}","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^3}-\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^3}-\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{16 b c^3}",1,"(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c^3) - (Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(16*b*c^3) - (Cos[(6*a)/b]*CosIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c^3) + Log[a + b*ArcSin[c*x]]/(16*b*c^3) + (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c^3) - (Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(16*b*c^3) - (Sin[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c^3)","A",12,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
327,1,179,0,0.3443165,"\int \frac{x \left(1-c^2 x^2\right)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x]),x]","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^2}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^2}-\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^2}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^2}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^2}+\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^2}","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^2}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^2}-\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^2}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^2}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^2}+\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^2}",1,"-(CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(8*b*c^2) - (3*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(16*b*c^2) - (CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(16*b*c^2) + (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b*c^2) + (3*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b*c^2) + (Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b*c^2)","A",12,5,26,0.1923,1,"{4723, 4406, 3303, 3299, 3302}"
328,1,144,0,0.242156,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c}+\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c}+\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c}+\frac{3 \log \left(a+b \sin ^{-1}(c x)\right)}{8 b c}","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c}+\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b c}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c}+\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b c}+\frac{3 \log \left(a+b \sin ^{-1}(c x)\right)}{8 b c}",1,"(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c) + (Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c) + (3*Log[a + b*ArcSin[c*x]])/(8*b*c) + (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c) + (Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c)","A",9,5,25,0.2000,1,"{4661, 3312, 3303, 3299, 3302}"
329,0,0,0,0.752415,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)+\frac{5 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b}+\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b}-\frac{5 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b}-\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b}",0,"(5*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(4*b) + (CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(4*b) - (5*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b) - (Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b) + Defer[Int][1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
330,0,0,0,0.5764308,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^2*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)-\frac{c \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b}-\frac{c \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b}-\frac{3 c \log \left(a+b \sin ^{-1}(c x)\right)}{2 b}",0,"-(c*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b) - (3*c*Log[a + b*ArcSin[c*x]])/(2*b) - (c*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b) + Defer[Int][1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
331,0,0,0,0.1389699,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^3*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(3/2)/(x^3*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
332,0,0,0,0.1398742,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^4*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(3/2)/(x^4*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
333,1,241,0,0.5116815,"\int \frac{x^3 \left(1-c^2 x^2\right)^{5/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^3*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x]),x]","-\frac{3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{128 b c^4}-\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{32 b c^4}+\frac{3 \sin \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{256 b c^4}+\frac{\sin \left(\frac{9 a}{b}\right) \text{CosIntegral}\left(\frac{9 a}{b}+9 \sin ^{-1}(c x)\right)}{256 b c^4}+\frac{3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{128 b c^4}+\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{32 b c^4}-\frac{3 \cos \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{256 b c^4}-\frac{\cos \left(\frac{9 a}{b}\right) \text{Si}\left(\frac{9 a}{b}+9 \sin ^{-1}(c x)\right)}{256 b c^4}","-\frac{3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{128 b c^4}-\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^4}+\frac{3 \sin \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b c^4}+\frac{\sin \left(\frac{9 a}{b}\right) \text{CosIntegral}\left(\frac{9 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b c^4}+\frac{3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{128 b c^4}+\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^4}-\frac{3 \cos \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b c^4}-\frac{\cos \left(\frac{9 a}{b}\right) \text{Si}\left(\frac{9 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b c^4}",1,"(-3*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(128*b*c^4) - (CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(32*b*c^4) + (3*CosIntegral[(7*a)/b + 7*ArcSin[c*x]]*Sin[(7*a)/b])/(256*b*c^4) + (CosIntegral[(9*a)/b + 9*ArcSin[c*x]]*Sin[(9*a)/b])/(256*b*c^4) + (3*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(128*b*c^4) + (Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(32*b*c^4) - (3*Cos[(7*a)/b]*SinIntegral[(7*a)/b + 7*ArcSin[c*x]])/(256*b*c^4) - (Cos[(9*a)/b]*SinIntegral[(9*a)/b + 9*ArcSin[c*x]])/(256*b*c^4)","A",15,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
334,1,268,0,0.5295878,"\int \frac{x^2 \left(1-c^2 x^2\right)^{5/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^2*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x]),x]","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\cos \left(\frac{8 a}{b}\right) \text{CosIntegral}\left(\frac{8 a}{b}+8 \sin ^{-1}(c x)\right)}{128 b c^3}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c^3}-\frac{\sin \left(\frac{8 a}{b}\right) \text{Si}\left(\frac{8 a}{b}+8 \sin ^{-1}(c x)\right)}{128 b c^3}+\frac{5 \log \left(a+b \sin ^{-1}(c x)\right)}{128 b c^3}","\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\cos \left(\frac{8 a}{b}\right) \text{CosIntegral}\left(\frac{8 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 b c^3}+\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sin \left(\frac{8 a}{b}\right) \text{Si}\left(\frac{8 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 b c^3}+\frac{5 \log \left(a+b \sin ^{-1}(c x)\right)}{128 b c^3}",1,"(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c^3) - (Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(32*b*c^3) - (Cos[(6*a)/b]*CosIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c^3) - (Cos[(8*a)/b]*CosIntegral[(8*a)/b + 8*ArcSin[c*x]])/(128*b*c^3) + (5*Log[a + b*ArcSin[c*x]])/(128*b*c^3) + (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c^3) - (Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(32*b*c^3) - (Sin[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c^3) - (Sin[(8*a)/b]*SinIntegral[(8*a)/b + 8*ArcSin[c*x]])/(128*b*c^3)","A",15,5,28,0.1786,1,"{4723, 4406, 3303, 3299, 3302}"
335,1,241,0,0.4470023,"\int \frac{x \left(1-c^2 x^2\right)^{5/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x]),x]","-\frac{5 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b c^2}-\frac{9 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b c^2}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b c^2}-\frac{\sin \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b c^2}+\frac{5 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b c^2}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b c^2}+\frac{5 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b c^2}+\frac{\cos \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b c^2}","-\frac{5 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b c^2}-\frac{9 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^2}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^2}-\frac{\sin \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^2}+\frac{5 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b c^2}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^2}+\frac{5 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^2}+\frac{\cos \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b c^2}",1,"(-5*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(64*b*c^2) - (9*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(64*b*c^2) - (5*CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(64*b*c^2) - (CosIntegral[(7*a)/b + 7*ArcSin[c*x]]*Sin[(7*a)/b])/(64*b*c^2) + (5*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(64*b*c^2) + (9*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(64*b*c^2) + (5*Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(64*b*c^2) + (Cos[(7*a)/b]*SinIntegral[(7*a)/b + 7*ArcSin[c*x]])/(64*b*c^2)","A",15,5,26,0.1923,1,"{4723, 4406, 3303, 3299, 3302}"
336,1,206,0,0.3205513,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(a + b*ArcSin[c*x]),x]","\frac{15 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c}+\frac{3 \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{16 b c}+\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c}+\frac{15 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{32 b c}+\frac{3 \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{16 b c}+\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{32 b c}+\frac{5 \log \left(a+b \sin ^{-1}(c x)\right)}{16 b c}","\frac{15 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c}+\frac{3 \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c}+\frac{\cos \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c}+\frac{15 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c}+\frac{3 \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c}+\frac{\sin \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b c}+\frac{5 \log \left(a+b \sin ^{-1}(c x)\right)}{16 b c}",1,"(15*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c) + (3*Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(16*b*c) + (Cos[(6*a)/b]*CosIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c) + (5*Log[a + b*ArcSin[c*x]])/(16*b*c) + (15*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(32*b*c) + (3*Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(16*b*c) + (Sin[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(32*b*c)","A",12,5,25,0.2000,1,"{4661, 3312, 3303, 3299, 3302}"
337,0,0,0,1.1450686,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)+\frac{11 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b}+\frac{7 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b}+\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b}-\frac{11 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b}-\frac{7 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b}-\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b}",0,"(11*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(8*b) + (7*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(16*b) + (CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(16*b) - (11*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b) - (7*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b) - (Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b) + Defer[Int][1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
338,0,0,0,0.9325339,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^2*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)-\frac{c \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b}-\frac{c \cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b}-\frac{c \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b}-\frac{c \sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b}-\frac{15 c \log \left(a+b \sin ^{-1}(c x)\right)}{8 b}",0,"-((c*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/b) - (c*Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b) - (15*c*Log[a + b*ArcSin[c*x]])/(8*b) - (c*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/b - (c*Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b) + Defer[Int][1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
339,0,0,0,0.1426376,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^3*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(5/2)/(x^3*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
340,0,0,0,0.1447906,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^4*(a + b*ArcSin[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(5/2)/(x^4*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
341,1,41,0,0.1589488,"\int \frac{x^4}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[x^4/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^5}+\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{8 a^5}+\frac{3 \log \left(\sin ^{-1}(a x)\right)}{8 a^5}","-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^5}+\frac{\text{CosIntegral}\left(4 \sin ^{-1}(a x)\right)}{8 a^5}+\frac{3 \log \left(\sin ^{-1}(a x)\right)}{8 a^5}",1,"-CosIntegral[2*ArcSin[a*x]]/(2*a^5) + CosIntegral[4*ArcSin[a*x]]/(8*a^5) + (3*Log[ArcSin[a*x]])/(8*a^5)","A",5,3,24,0.1250,1,"{4723, 3312, 3302}"
342,1,27,0,0.1453941,"\int \frac{x^3}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[x^3/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\frac{3 \text{Si}\left(\sin ^{-1}(a x)\right)}{4 a^4}-\frac{\text{Si}\left(3 \sin ^{-1}(a x)\right)}{4 a^4}","\frac{3 \text{Si}\left(\sin ^{-1}(a x)\right)}{4 a^4}-\frac{\text{Si}\left(3 \sin ^{-1}(a x)\right)}{4 a^4}",1,"(3*SinIntegral[ArcSin[a*x]])/(4*a^4) - SinIntegral[3*ArcSin[a*x]]/(4*a^4)","A",5,3,24,0.1250,1,"{4723, 3312, 3299}"
343,1,27,0,0.1362858,"\int \frac{x^2}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[x^2/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\frac{\log \left(\sin ^{-1}(a x)\right)}{2 a^3}-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^3}","\frac{\log \left(\sin ^{-1}(a x)\right)}{2 a^3}-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^3}",1,"-CosIntegral[2*ArcSin[a*x]]/(2*a^3) + Log[ArcSin[a*x]]/(2*a^3)","A",4,3,24,0.1250,1,"{4723, 3312, 3302}"
344,1,27,0,0.1346129,"\int \frac{x^2}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[x^2/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\frac{\log \left(\sin ^{-1}(a x)\right)}{2 a^3}-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^3}","\frac{\log \left(\sin ^{-1}(a x)\right)}{2 a^3}-\frac{\text{CosIntegral}\left(2 \sin ^{-1}(a x)\right)}{2 a^3}",1,"-CosIntegral[2*ArcSin[a*x]]/(2*a^3) + Log[ArcSin[a*x]]/(2*a^3)","A",4,3,24,0.1250,1,"{4723, 3312, 3302}"
345,1,9,0,0.0750753,"\int \frac{x}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[x/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{a^2}","\frac{\text{Si}\left(\sin ^{-1}(a x)\right)}{a^2}",1,"SinIntegral[ArcSin[a*x]]/a^2","A",2,2,22,0.09091,1,"{4723, 3299}"
346,1,9,0,0.032975,"\int \frac{1}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\frac{\log \left(\sin ^{-1}(a x)\right)}{a}","\frac{\log \left(\sin ^{-1}(a x)\right)}{a}",1,"Log[ArcSin[a*x]]/a","A",1,1,21,0.04762,1,"{4639}"
347,0,0,0,0.0888625,"\int \frac{1}{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[1/(x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\int \frac{1}{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*Sqrt[1 - a^2*x^2]*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
348,0,0,0,0.0923622,"\int \frac{1}{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[1/(x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\int \frac{1}{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
349,1,179,0,0.3727902,"\int \frac{x^5}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^5/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","-\frac{5 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^6}+\frac{5 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^6}-\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^6}+\frac{5 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^6}-\frac{5 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^6}+\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^6}","-\frac{5 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^6}+\frac{5 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^6}-\frac{\sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^6}+\frac{5 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^6}-\frac{5 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^6}+\frac{\cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^6}",1,"(-5*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(8*b*c^6) + (5*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(16*b*c^6) - (CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(16*b*c^6) + (5*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b*c^6) - (5*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b*c^6) + (Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b*c^6)","A",12,5,28,0.1786,1,"{4723, 3312, 3303, 3299, 3302}"
350,1,144,0,0.330929,"\int \frac{x^4}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^4/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c^5}+\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^5}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c^5}+\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b c^5}+\frac{3 \log \left(a+b \sin ^{-1}(c x)\right)}{8 b c^5}","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^5}+\frac{\cos \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b c^5}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^5}+\frac{\sin \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b c^5}+\frac{3 \log \left(a+b \sin ^{-1}(c x)\right)}{8 b c^5}",1,"-(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^5) + (Cos[(4*a)/b]*CosIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c^5) + (3*Log[a + b*ArcSin[c*x]])/(8*b*c^5) - (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^5) + (Sin[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b*c^5)","A",9,5,28,0.1786,1,"{4723, 3312, 3303, 3299, 3302}"
351,1,117,0,0.3097327,"\int \frac{x^3}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^3/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","-\frac{3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^4}+\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b c^4}+\frac{3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^4}-\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b c^4}","-\frac{3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^4}+\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^4}+\frac{3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^4}-\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^4}",1,"(-3*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(4*b*c^4) + (CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(4*b*c^4) + (3*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b*c^4) - (Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^4)","A",9,5,28,0.1786,1,"{4723, 3312, 3303, 3299, 3302}"
352,1,82,0,0.250137,"\int \frac{x^2}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^2/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c^3}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{2 b c^3}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{2 b c^3}","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^3}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^3}+\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{2 b c^3}",1,"-(Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^3) + Log[a + b*ArcSin[c*x]]/(2*b*c^3) - (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(2*b*c^3)","A",6,5,28,0.1786,1,"{4723, 3312, 3303, 3299, 3302}"
353,1,50,0,0.1539134,"\int \frac{x}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c^2}-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{b c^2}","\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c^2}-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c^2}",1,"-((CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(b*c^2)) + (Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b*c^2)","A",4,4,26,0.1538,1,"{4723, 3303, 3299, 3302}"
354,1,16,0,0.0480692,"\int \frac{1}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{b c}","\frac{\log \left(a+b \sin ^{-1}(c x)\right)}{b c}",1,"Log[a + b*ArcSin[c*x]]/(b*c)","A",1,1,25,0.04000,1,"{4639}"
355,0,0,0,0.1243287,"\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
356,0,0,0,0.1277698,"\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
357,0,0,0,0.1421572,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^2/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^2/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
358,0,0,0,0.1007764,"\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
359,0,0,0,0.0469016,"\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
360,0,0,0,0.1338314,"\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
361,0,0,0,0.1362761,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
362,0,0,0,0.1397926,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^2/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^2/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
363,0,0,0,0.0918417,"\int \frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
364,0,0,0,0.0470863,"\int \frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
365,0,0,0,0.1352566,"\int \frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
366,0,0,0,0.1360248,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
367,0,0,0,0.1279805,"\int \frac{x^m \left(1-c^2 x^2\right)^{5/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^m*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x]),x]","\int \frac{x^m \left(1-c^2 x^2\right)^{5/2}}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2} x^m}{a+b \sin ^{-1}(c x)},x\right)",0,"Defer[Int][(x^m*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
368,0,0,0,0.1268174,"\int \frac{x^m \left(1-c^2 x^2\right)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^m*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x]),x]","\int \frac{x^m \left(1-c^2 x^2\right)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2} x^m}{a+b \sin ^{-1}(c x)},x\right)",0,"Defer[Int][(x^m*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
369,0,0,0,0.1133257,"\int \frac{x^m \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[(x^m*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]),x]","\int \frac{x^m \sqrt{1-c^2 x^2}}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2} x^m}{a+b \sin ^{-1}(c x)},x\right)",0,"Defer[Int][(x^m*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
370,0,0,0,0.1199735,"\int \frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^m/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])),x]","\int \frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^m/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
371,0,0,0,0.1396766,"\int \frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^m/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^m/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
372,0,0,0,0.1322323,"\int \frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[x^m/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^m/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
373,0,0,0,0.0897566,"\int \frac{x^m}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","Int[x^m/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]),x]","\int \frac{x^m}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^m}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)},x\right)",0,"Defer[Int][x^m/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]), x]","A",0,0,0,0,-1,"{}"
374,1,95,0,0.1741395,"\int \frac{\left(c-a^2 c x^2\right)^3}{\sin ^{-1}(a x)^2} \, dx","Int[(c - a^2*c*x^2)^3/ArcSin[a*x]^2,x]","-\frac{c^3 \left(1-a^2 x^2\right)^{7/2}}{a \sin ^{-1}(a x)}-\frac{35 c^3 \text{Si}\left(\sin ^{-1}(a x)\right)}{64 a}-\frac{63 c^3 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{64 a}-\frac{35 c^3 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{64 a}-\frac{7 c^3 \text{Si}\left(7 \sin ^{-1}(a x)\right)}{64 a}","-\frac{c^3 \left(1-a^2 x^2\right)^{7/2}}{a \sin ^{-1}(a x)}-\frac{35 c^3 \text{Si}\left(\sin ^{-1}(a x)\right)}{64 a}-\frac{63 c^3 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{64 a}-\frac{35 c^3 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{64 a}-\frac{7 c^3 \text{Si}\left(7 \sin ^{-1}(a x)\right)}{64 a}",1,"-((c^3*(1 - a^2*x^2)^(7/2))/(a*ArcSin[a*x])) - (35*c^3*SinIntegral[ArcSin[a*x]])/(64*a) - (63*c^3*SinIntegral[3*ArcSin[a*x]])/(64*a) - (35*c^3*SinIntegral[5*ArcSin[a*x]])/(64*a) - (7*c^3*SinIntegral[7*ArcSin[a*x]])/(64*a)","A",8,4,20,0.2000,1,"{4659, 4723, 4406, 3299}"
375,1,78,0,0.1613961,"\int \frac{\left(c-a^2 c x^2\right)^2}{\sin ^{-1}(a x)^2} \, dx","Int[(c - a^2*c*x^2)^2/ArcSin[a*x]^2,x]","-\frac{c^2 \left(1-a^2 x^2\right)^{5/2}}{a \sin ^{-1}(a x)}-\frac{5 c^2 \text{Si}\left(\sin ^{-1}(a x)\right)}{8 a}-\frac{15 c^2 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{16 a}-\frac{5 c^2 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{16 a}","-\frac{c^2 \left(1-a^2 x^2\right)^{5/2}}{a \sin ^{-1}(a x)}-\frac{5 c^2 \text{Si}\left(\sin ^{-1}(a x)\right)}{8 a}-\frac{15 c^2 \text{Si}\left(3 \sin ^{-1}(a x)\right)}{16 a}-\frac{5 c^2 \text{Si}\left(5 \sin ^{-1}(a x)\right)}{16 a}",1,"-((c^2*(1 - a^2*x^2)^(5/2))/(a*ArcSin[a*x])) - (5*c^2*SinIntegral[ArcSin[a*x]])/(8*a) - (15*c^2*SinIntegral[3*ArcSin[a*x]])/(16*a) - (5*c^2*SinIntegral[5*ArcSin[a*x]])/(16*a)","A",7,4,20,0.2000,1,"{4659, 4723, 4406, 3299}"
376,1,55,0,0.1176506,"\int \frac{c-a^2 c x^2}{\sin ^{-1}(a x)^2} \, dx","Int[(c - a^2*c*x^2)/ArcSin[a*x]^2,x]","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{a \sin ^{-1}(a x)}-\frac{3 c \text{Si}\left(\sin ^{-1}(a x)\right)}{4 a}-\frac{3 c \text{Si}\left(3 \sin ^{-1}(a x)\right)}{4 a}","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{a \sin ^{-1}(a x)}-\frac{3 c \text{Si}\left(\sin ^{-1}(a x)\right)}{4 a}-\frac{3 c \text{Si}\left(3 \sin ^{-1}(a x)\right)}{4 a}",1,"-((c*(1 - a^2*x^2)^(3/2))/(a*ArcSin[a*x])) - (3*c*SinIntegral[ArcSin[a*x]])/(4*a) - (3*c*SinIntegral[3*ArcSin[a*x]])/(4*a)","A",6,4,18,0.2222,1,"{4659, 4723, 4406, 3299}"
377,0,0,0,0.0956909,"\int \frac{1}{\left(c-a^2 c x^2\right) \sin ^{-1}(a x)^2} \, dx","Int[1/((c - a^2*c*x^2)*ArcSin[a*x]^2),x]","\int \frac{1}{\left(c-a^2 c x^2\right) \sin ^{-1}(a x)^2} \, dx","\frac{a \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)},x\right)}{c}-\frac{1}{a c \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}",0,"-(1/(a*c*Sqrt[1 - a^2*x^2]*ArcSin[a*x])) + (a*Defer[Int][x/((1 - a^2*x^2)^(3/2)*ArcSin[a*x]), x])/c","A",0,0,0,0,-1,"{}"
378,0,0,0,0.0974797,"\int \frac{1}{\left(c-a^2 c x^2\right)^2 \sin ^{-1}(a x)^2} \, dx","Int[1/((c - a^2*c*x^2)^2*ArcSin[a*x]^2),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^2 \sin ^{-1}(a x)^2} \, dx","\frac{3 a \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^{5/2} \sin ^{-1}(a x)},x\right)}{c^2}-\frac{1}{a c^2 \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)}",0,"-(1/(a*c^2*(1 - a^2*x^2)^(3/2)*ArcSin[a*x])) + (3*a*Defer[Int][x/((1 - a^2*x^2)^(5/2)*ArcSin[a*x]), x])/c^2","A",0,0,0,0,-1,"{}"
379,1,17,0,0.1250404,"\int \left(\frac{1}{\left(1-x^2\right) \sin ^{-1}(x)^2}-\frac{x}{\left(1-x^2\right)^{3/2} \sin ^{-1}(x)}\right) \, dx","Int[1/((1 - x^2)*ArcSin[x]^2) - x/((1 - x^2)^(3/2)*ArcSin[x]),x]","-\frac{1}{\sqrt{1-x^2} \sin ^{-1}(x)}","-\frac{1}{\sqrt{1-x^2} \sin ^{-1}(x)}",1,"-(1/(Sqrt[1 - x^2]*ArcSin[x]))","A",2,1,33,0.03030,1,"{4659}"
380,0,0,0,0.1136871,"\int \frac{x^m \sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^m*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])^2,x]","\int \frac{x^m \sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2} x^m}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(x^m*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
381,1,210,0,0.6331164,"\int \frac{x^3 \sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^3*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])^2,x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^4}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^4}-\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^4}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^4}+\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^4}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^4}-\frac{x^3 \left(1-c^2 x^2\right)}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^4}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}-\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^4}+\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}-\frac{x^3 \left(1-c^2 x^2\right)}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x^3*(1 - c^2*x^2))/(b*c*(a + b*ArcSin[c*x]))) + (Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^4) + (3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^4) - (5*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^4) + (Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^4) + (3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^4) - (5*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^4)","A",22,6,28,0.2143,1,"{4721, 4635, 4406, 3303, 3299, 3302}"
382,1,94,0,0.4681219,"\int \frac{x^2 \sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^2*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])^2,x]","-\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{x^2 \left(1-c^2 x^2\right)}{b c \left(a+b \sin ^{-1}(c x)\right)}","-\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}+\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}-\frac{x^2 \left(1-c^2 x^2\right)}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x^2*(1 - c^2*x^2))/(b*c*(a + b*ArcSin[c*x]))) - (CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(2*b^2*c^3) + (Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(2*b^2*c^3)","A",16,7,28,0.2500,1,"{4721, 4635, 4406, 12, 3303, 3299, 3302}"
383,1,198,0,0.3701958,"\int \frac{x \sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x*Sqrt[1 - c^2*x^2])/(a + b*ArcSin[c*x])^2,x]","-\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^2}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b^2 c^2}+\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^2}+\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b^2 c^2}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{x \left(1-c^2 x^2\right)}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2 c^2}+\frac{3 \cos \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^2}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2 c^2}+\frac{3 \sin \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^2}-\frac{x \left(1-c^2 x^2\right)}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x*(1 - c^2*x^2))/(b*c*(a + b*ArcSin[c*x]))) - (3*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^2) + (3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^2) + (Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/(b^2*c^2) - (3*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^2) + (3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^2) + (Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(b^2*c^2)","A",14,7,26,0.2692,1,"{4721, 4623, 3303, 3299, 3302, 4635, 4406}"
384,1,86,0,0.1624825,"\int \frac{\sqrt{1-c^2 x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(a + b*ArcSin[c*x])^2,x]","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c}-\frac{1-c^2 x^2}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c}-\frac{1-c^2 x^2}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((1 - c^2*x^2)/(b*c*(a + b*ArcSin[c*x]))) + (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(b^2*c) - (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c)","A",7,7,25,0.2800,1,"{4659, 4635, 4406, 12, 3303, 3299, 3302}"
385,0,0,0,0.2036708,"\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x*(a + b*ArcSin[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2}-\frac{1-c^2 x^2}{b c x \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)/(b*c*x*(a + b*ArcSin[c*x]))) - (Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/b^2 - (Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/b^2 - Defer[Int][1/(x^2*(a + b*ArcSin[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
386,0,0,0,0.1490652,"\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^2*(a + b*ArcSin[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{1}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{1-c^2 x^2}{b c x^2 \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)/(b*c*x^2*(a + b*ArcSin[c*x]))) - (2*Defer[Int][1/(x^3*(a + b*ArcSin[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
387,0,0,0,0.1214982,"\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^3*(a + b*ArcSin[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[1 - c^2*x^2]/(x^3*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
388,0,0,0,0.1208723,"\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^4*(a + b*ArcSin[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[1 - c^2*x^2]/(x^4*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
389,0,0,0,0.1348227,"\int \frac{x^m \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^m*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x])^2,x]","\int \frac{x^m \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2} x^m}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(x^m*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
390,1,274,0,0.889903,"\int \frac{x^3 \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^3*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x])^2,x]","\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{7 \cos \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{7 \sin \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{x^3 \left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b^2 c^4}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{7 \cos \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}+\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b^2 c^4}+\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{7 \sin \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{x^3 \left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x^3*(1 - c^2*x^2)^2)/(b*c*(a + b*ArcSin[c*x]))) + (3*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(64*b^2*c^4) + (9*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(64*b^2*c^4) - (5*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(64*b^2*c^4) - (7*Cos[(7*a)/b]*CosIntegral[(7*a)/b + 7*ArcSin[c*x]])/(64*b^2*c^4) + (3*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(64*b^2*c^4) + (9*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(64*b^2*c^4) - (5*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(64*b^2*c^4) - (7*Sin[(7*a)/b]*SinIntegral[(7*a)/b + 7*ArcSin[c*x]])/(64*b^2*c^4)","A",28,6,28,0.2143,1,"{4721, 4723, 4406, 3303, 3299, 3302}"
391,1,220,0,0.636239,"\int \frac{x^2 \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^2*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x])^2,x]","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 \sin \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{16 b^2 c^3}+\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{3 \cos \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{x^2 \left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{3 \sin \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}+\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}+\frac{3 \cos \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{x^2 \left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x^2*(1 - c^2*x^2)^2)/(b*c*(a + b*ArcSin[c*x]))) + (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(16*b^2*c^3) - (CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(4*b^2*c^3) - (3*CosIntegral[(6*a)/b + 6*ArcSin[c*x]]*Sin[(6*a)/b])/(16*b^2*c^3) - (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(16*b^2*c^3) + (Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(4*b^2*c^3) + (3*Cos[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(16*b^2*c^3)","A",19,6,28,0.2143,1,"{4721, 4723, 4406, 3303, 3299, 3302}"
392,1,210,0,0.666335,"\int \frac{x \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x*(1 - c^2*x^2)^(3/2))/(a + b*ArcSin[c*x])^2,x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^2}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^2}+\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^2}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^2}+\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^2}+\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^2}-\frac{x \left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^2}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}+\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^2}+\frac{9 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}+\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}-\frac{x \left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x*(1 - c^2*x^2)^2)/(b*c*(a + b*ArcSin[c*x]))) + (Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^2) + (9*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^2) + (5*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^2) + (Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^2) + (9*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^2) + (5*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^2)","A",22,8,26,0.3077,1,"{4721, 4661, 3312, 3303, 3299, 3302, 4723, 4406}"
393,1,150,0,0.2729357,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(a + b*ArcSin[c*x])^2,x]","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c}+\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{2 b^2 c}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c}-\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{2 b^2 c}-\frac{\left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c}+\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c}-\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c}-\frac{\left(1-c^2 x^2\right)^2}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((1 - c^2*x^2)^2/(b*c*(a + b*ArcSin[c*x]))) + (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(b^2*c) + (CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(2*b^2*c) - (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c) - (Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(2*b^2*c)","A",10,6,25,0.2400,1,"{4659, 4723, 4406, 3303, 3299, 3302}"
394,0,0,0,0.4037176,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{1-c^2 x^2}{x^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{9 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2}-\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2}-\frac{9 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2}-\frac{\left(1-c^2 x^2\right)^2}{b c x \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)^2/(b*c*x*(a + b*ArcSin[c*x]))) - (9*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(4*b^2) - (3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2) - (9*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b^2) - (3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2) - Defer[Int][(1 - c^2*x^2)/(x^2*(a + b*ArcSin[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
395,0,0,0,0.24623,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^2*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{1-c^2 x^2}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{2 c \text{Int}\left(\frac{1-c^2 x^2}{x \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b}-\frac{\left(1-c^2 x^2\right)^2}{b c x^2 \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)^2/(b*c*x^2*(a + b*ArcSin[c*x]))) - (2*Defer[Int][(1 - c^2*x^2)/(x^3*(a + b*ArcSin[c*x])), x])/(b*c) - (2*c*Defer[Int][(1 - c^2*x^2)/(x*(a + b*ArcSin[c*x])), x])/b","A",0,0,0,0,-1,"{}"
396,0,0,0,0.1404761,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^3*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(3/2)/(x^3*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
397,0,0,0,0.1974667,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^4*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{4 \text{Int}\left(\frac{1-c^2 x^2}{x^5 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{\left(1-c^2 x^2\right)^2}{b c x^4 \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)^2/(b*c*x^4*(a + b*ArcSin[c*x]))) - (4*Defer[Int][(1 - c^2*x^2)/(x^5*(a + b*ArcSin[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
398,0,0,0,0.1368721,"\int \frac{x^m \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^m*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x])^2,x]","\int \frac{x^m \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2} x^m}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(x^m*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
399,1,274,0,1.1549902,"\int \frac{x^3 \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^3*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x])^2,x]","\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{128 b^2 c^4}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{32 b^2 c^4}-\frac{21 \cos \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{256 b^2 c^4}-\frac{9 \cos \left(\frac{9 a}{b}\right) \text{CosIntegral}\left(\frac{9 a}{b}+9 \sin ^{-1}(c x)\right)}{256 b^2 c^4}+\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{128 b^2 c^4}+\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{32 b^2 c^4}-\frac{21 \sin \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{256 b^2 c^4}-\frac{9 \sin \left(\frac{9 a}{b}\right) \text{Si}\left(\frac{9 a}{b}+9 \sin ^{-1}(c x)\right)}{256 b^2 c^4}-\frac{x^3 \left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{128 b^2 c^4}+\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b^2 c^4}-\frac{21 \cos \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}-\frac{9 \cos \left(\frac{9 a}{b}\right) \text{CosIntegral}\left(\frac{9 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}+\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{128 b^2 c^4}+\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 b^2 c^4}-\frac{21 \sin \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}-\frac{9 \sin \left(\frac{9 a}{b}\right) \text{Si}\left(\frac{9 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}-\frac{x^3 \left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x^3*(1 - c^2*x^2)^3)/(b*c*(a + b*ArcSin[c*x]))) + (3*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(128*b^2*c^4) + (3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(32*b^2*c^4) - (21*Cos[(7*a)/b]*CosIntegral[(7*a)/b + 7*ArcSin[c*x]])/(256*b^2*c^4) - (9*Cos[(9*a)/b]*CosIntegral[(9*a)/b + 9*ArcSin[c*x]])/(256*b^2*c^4) + (3*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(128*b^2*c^4) + (3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(32*b^2*c^4) - (21*Sin[(7*a)/b]*SinIntegral[(7*a)/b + 7*ArcSin[c*x]])/(256*b^2*c^4) - (9*Sin[(9*a)/b]*SinIntegral[(9*a)/b + 9*ArcSin[c*x]])/(256*b^2*c^4)","A",34,6,28,0.2143,1,"{4721, 4723, 4406, 3303, 3299, 3302}"
400,1,282,0,0.9333669,"\int \frac{x^2 \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x^2*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x])^2,x]","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b^2 c^3}-\frac{3 \sin \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\sin \left(\frac{8 a}{b}\right) \text{CosIntegral}\left(\frac{8 a}{b}+8 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{16 b^2 c^3}+\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{8 b^2 c^3}+\frac{3 \cos \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{16 b^2 c^3}+\frac{\cos \left(\frac{8 a}{b}\right) \text{Si}\left(\frac{8 a}{b}+8 \sin ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{x^2 \left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b^2 c^3}-\frac{3 \sin \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\sin \left(\frac{8 a}{b}\right) \text{CosIntegral}\left(\frac{8 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}+\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 b^2 c^3}+\frac{3 \cos \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}+\frac{\cos \left(\frac{8 a}{b}\right) \text{Si}\left(\frac{8 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{x^2 \left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x^2*(1 - c^2*x^2)^3)/(b*c*(a + b*ArcSin[c*x]))) + (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(16*b^2*c^3) - (CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(8*b^2*c^3) - (3*CosIntegral[(6*a)/b + 6*ArcSin[c*x]]*Sin[(6*a)/b])/(16*b^2*c^3) - (CosIntegral[(8*a)/b + 8*ArcSin[c*x]]*Sin[(8*a)/b])/(16*b^2*c^3) - (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(16*b^2*c^3) + (Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(8*b^2*c^3) + (3*Cos[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(16*b^2*c^3) + (Cos[(8*a)/b]*SinIntegral[(8*a)/b + 8*ArcSin[c*x]])/(16*b^2*c^3)","A",28,6,28,0.2143,1,"{4721, 4723, 4406, 3303, 3299, 3302}"
401,1,272,0,0.8721723,"\int \frac{x \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(x*(1 - c^2*x^2)^(5/2))/(a + b*ArcSin[c*x])^2,x]","\frac{5 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{27 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{25 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{7 \cos \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{5 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{27 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{25 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{7 \sin \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 a}{b}+7 \sin ^{-1}(c x)\right)}{64 b^2 c^2}-\frac{x \left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{5 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b^2 c^2}+\frac{27 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{25 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{7 \cos \left(\frac{7 a}{b}\right) \text{CosIntegral}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{5 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{64 b^2 c^2}+\frac{27 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{25 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{7 \sin \left(\frac{7 a}{b}\right) \text{Si}\left(\frac{7 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}-\frac{x \left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((x*(1 - c^2*x^2)^3)/(b*c*(a + b*ArcSin[c*x]))) + (5*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(64*b^2*c^2) + (27*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(64*b^2*c^2) + (25*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(64*b^2*c^2) + (7*Cos[(7*a)/b]*CosIntegral[(7*a)/b + 7*ArcSin[c*x]])/(64*b^2*c^2) + (5*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(64*b^2*c^2) + (27*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(64*b^2*c^2) + (25*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(64*b^2*c^2) + (7*Sin[(7*a)/b]*SinIntegral[(7*a)/b + 7*ArcSin[c*x]])/(64*b^2*c^2)","A",28,8,26,0.3077,1,"{4721, 4661, 3312, 3303, 3299, 3302, 4723, 4406}"
402,1,217,0,0.3997167,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(a + b*ArcSin[c*x])^2,x]","\frac{15 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{16 b^2 c}+\frac{3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{4 b^2 c}+\frac{3 \sin \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{16 b^2 c}-\frac{15 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{16 b^2 c}-\frac{3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{4 b^2 c}-\frac{3 \cos \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 a}{b}+6 \sin ^{-1}(c x)\right)}{16 b^2 c}-\frac{\left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{15 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}+\frac{3 \sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2 c}+\frac{3 \sin \left(\frac{6 a}{b}\right) \text{CosIntegral}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}-\frac{15 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}-\frac{3 \cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b^2 c}-\frac{3 \cos \left(\frac{6 a}{b}\right) \text{Si}\left(\frac{6 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}-\frac{\left(1-c^2 x^2\right)^3}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-((1 - c^2*x^2)^3/(b*c*(a + b*ArcSin[c*x]))) + (15*CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(16*b^2*c) + (3*CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(4*b^2*c) + (3*CosIntegral[(6*a)/b + 6*ArcSin[c*x]]*Sin[(6*a)/b])/(16*b^2*c) - (15*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(16*b^2*c) - (3*Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(4*b^2*c) - (3*Cos[(6*a)/b]*SinIntegral[(6*a)/b + 6*ArcSin[c*x]])/(16*b^2*c)","A",13,6,25,0.2400,1,"{4659, 4723, 4406, 3303, 3299, 3302}"
403,0,0,0,0.5343497,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{\left(1-c^2 x^2\right)^2}{x^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{25 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2}-\frac{25 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{25 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2}-\frac{25 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{\left(1-c^2 x^2\right)^3}{b c x \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)^3/(b*c*x*(a + b*ArcSin[c*x]))) - (25*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(8*b^2) - (25*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2) - (5*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2) - (25*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b^2) - (25*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2) - (5*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2) - Defer[Int][(1 - c^2*x^2)^2/(x^2*(a + b*ArcSin[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
404,0,0,0,0.3116259,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^2*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{\left(1-c^2 x^2\right)^2}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{4 c \text{Int}\left(\frac{\left(1-c^2 x^2\right)^2}{x \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b}-\frac{\left(1-c^2 x^2\right)^3}{b c x^2 \left(a+b \sin ^{-1}(c x)\right)}",0,"-((1 - c^2*x^2)^3/(b*c*x^2*(a + b*ArcSin[c*x]))) - (2*Defer[Int][(1 - c^2*x^2)^2/(x^3*(a + b*ArcSin[c*x])), x])/(b*c) - (4*c*Defer[Int][(1 - c^2*x^2)^2/(x*(a + b*ArcSin[c*x])), x])/b","A",0,0,0,0,-1,"{}"
405,0,0,0,0.1399292,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^3*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(5/2)/(x^3*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
406,0,0,0,0.1384334,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^4*(a + b*ArcSin[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(1 - c^2*x^2)^(5/2)/(x^4*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
407,0,0,0,0.1624995,"\int \frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^m/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\frac{m \text{Int}\left(\frac{x^{m-1}}{a+b \sin ^{-1}(c x)},x\right)}{b c}-\frac{x^m}{b c \left(a+b \sin ^{-1}(c x)\right)}",0,"-(x^m/(b*c*(a + b*ArcSin[c*x]))) + (m*Defer[Int][x^(-1 + m)/(a + b*ArcSin[c*x]), x])/(b*c)","A",0,0,0,0,-1,"{}"
408,1,200,0,0.440519,"\int \frac{x^5}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^5/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","\frac{5 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^6}-\frac{15 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^6}+\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^6}+\frac{5 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^6}-\frac{15 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^6}+\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^6}-\frac{x^5}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{5 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^6}-\frac{15 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}+\frac{5 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}+\frac{5 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^6}-\frac{15 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}+\frac{5 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}-\frac{x^5}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-(x^5/(b*c*(a + b*ArcSin[c*x]))) + (5*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^6) - (15*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^6) + (5*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^6) + (5*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^6) - (15*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^6) + (5*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^6)","A",13,6,28,0.2143,1,"{4719, 4635, 4406, 3303, 3299, 3302}"
409,1,141,0,0.3586003,"\int \frac{x^4}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^4/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c^5}+\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{2 b^2 c^5}+\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c^5}-\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 a}{b}+4 \sin ^{-1}(c x)\right)}{2 b^2 c^5}-\frac{x^4}{b c \left(a+b \sin ^{-1}(c x)\right)}","-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c^5}+\frac{\sin \left(\frac{4 a}{b}\right) \text{CosIntegral}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^5}+\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c^5}-\frac{\cos \left(\frac{4 a}{b}\right) \text{Si}\left(\frac{4 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^5}-\frac{x^4}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-(x^4/(b*c*(a + b*ArcSin[c*x]))) - (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(b^2*c^5) + (CosIntegral[(4*a)/b + 4*ArcSin[c*x]]*Sin[(4*a)/b])/(2*b^2*c^5) + (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^5) - (Cos[(4*a)/b]*SinIntegral[(4*a)/b + 4*ArcSin[c*x]])/(2*b^2*c^5)","A",10,6,28,0.2143,1,"{4719, 4635, 4406, 3303, 3299, 3302}"
410,1,138,0,0.3404511,"\int \frac{x^3}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^3/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^4}-\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b^2 c^4}+\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b^2 c^4}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{4 b^2 c^4}-\frac{x^3}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2 c^4}-\frac{3 \cos \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^4}+\frac{3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b^2 c^4}-\frac{3 \sin \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^4}-\frac{x^3}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-(x^3/(b*c*(a + b*ArcSin[c*x]))) + (3*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^4) - (3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^4) + (3*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^4) - (3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^4)","A",10,6,28,0.2143,1,"{4719, 4635, 4406, 3303, 3299, 3302}"
411,1,79,0,0.2443077,"\int \frac{x^2}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^2/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c^3}+\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sin ^{-1}(c x)\right)}{b^2 c^3}-\frac{x^2}{b c \left(a+b \sin ^{-1}(c x)\right)}","-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c^3}+\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{b^2 c^3}-\frac{x^2}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-(x^2/(b*c*(a + b*ArcSin[c*x]))) - (CosIntegral[(2*a)/b + 2*ArcSin[c*x]]*Sin[(2*a)/b])/(b^2*c^3) + (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSin[c*x]])/(b^2*c^3)","A",7,7,28,0.2500,1,"{4719, 4635, 4406, 12, 3303, 3299, 3302}"
412,1,72,0,0.1498461,"\int \frac{x}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c^2}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{x}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c^2}+\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{x}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-(x/(b*c*(a + b*ArcSin[c*x]))) + (Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/(b^2*c^2) + (Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(b^2*c^2)","A",5,5,26,0.1923,1,"{4719, 4623, 3303, 3299, 3302}"
413,1,18,0,0.0437099,"\int \frac{1}{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","-\frac{1}{b c \left(a+b \sin ^{-1}(c x)\right)}","-\frac{1}{b c \left(a+b \sin ^{-1}(c x)\right)}",1,"-(1/(b*c*(a + b*ArcSin[c*x])))","A",1,1,25,0.04000,1,"{4641}"
414,0,0,0,0.1523268,"\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{1}{b c x \left(a+b \sin ^{-1}(c x)\right)}",0,"-(1/(b*c*x*(a + b*ArcSin[c*x]))) - Defer[Int][1/(x^2*(a + b*ArcSin[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
415,0,0,0,0.1493,"\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{1}{x^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{1}{b c x^2 \left(a+b \sin ^{-1}(c x)\right)}",0,"-(1/(b*c*x^2*(a + b*ArcSin[c*x]))) - (2*Defer[Int][1/(x^3*(a + b*ArcSin[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
416,0,0,0,0.136483,"\int \frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^m/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^m/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
417,0,0,0,0.1407233,"\int \frac{x^3}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^3/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^3}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^3}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^3/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
418,0,0,0,0.2012538,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^2/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\frac{2 \text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b c}-\frac{x^2}{b c \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}",0,"-(x^2/(b*c*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))) + (2*Defer[Int][x/((1 - c^2*x^2)^2*(a + b*ArcSin[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
419,0,0,0,0.0929563,"\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
420,0,0,0,0.1077052,"\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\frac{2 c \text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b}-\frac{1}{b c \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}",0,"-(1/(b*c*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))) + (2*c*Defer[Int][x/((1 - c^2*x^2)^2*(a + b*ArcSin[c*x])), x])/b","A",0,0,0,0,-1,"{}"
421,0,0,0,0.1315106,"\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
422,0,0,0,0.1321169,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
423,0,0,0,0.1331071,"\int \frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^m/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^m/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
424,0,0,0,0.1342319,"\int \frac{x^3}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^3/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^3}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^3}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^3/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
425,0,0,0,0.1361835,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x^2/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^2/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
426,0,0,0,0.0935245,"\int \frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[x/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
427,0,0,0,0.109742,"\int \frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\frac{4 c \text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)},x\right)}{b}-\frac{1}{b c \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}",0,"-(1/(b*c*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))) + (4*c*Defer[Int][x/((1 - c^2*x^2)^3*(a + b*ArcSin[c*x])), x])/b","A",0,0,0,0,-1,"{}"
428,0,0,0,0.1314774,"\int \frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
429,0,0,0,0.1316317,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
430,1,13,0,0.0309994,"\int \frac{1}{\sqrt{1-a^2 x^2} \sin ^{-1}(a x)^3} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcSin[a*x]^3),x]","-\frac{1}{2 a \sin ^{-1}(a x)^2}","-\frac{1}{2 a \sin ^{-1}(a x)^2}",1,"-1/(2*a*ArcSin[a*x]^2)","A",1,1,21,0.04762,1,"{4641}"
431,1,251,0,1.4444096,"\int \frac{x^3 \left(d-c^2 d x^2\right)}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^3*(d - c^2*d*x^2))/(a + b*ArcSin[c*x])^(3/2),x]","-\frac{\sqrt{3 \pi } d \cos \left(\frac{6 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 b^{3/2} c^4}-\frac{\sqrt{3 \pi } d \sin \left(\frac{6 a}{b}\right) S\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}-\frac{2 d x^3 \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","-\frac{\sqrt{3 \pi } d \cos \left(\frac{6 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 b^{3/2} c^4}-\frac{\sqrt{3 \pi } d \sin \left(\frac{6 a}{b}\right) S\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}-\frac{2 d x^3 \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d*x^3*(1 - c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (d*Sqrt[3*Pi]*Cos[(6*a)/b]*FresnelC[(2*Sqrt[3/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*b^(3/2)*c^4) + (3*d*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(8*b^(3/2)*c^4) + (3*d*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(8*b^(3/2)*c^4) - (d*Sqrt[3*Pi]*FresnelS[(2*Sqrt[3/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(6*a)/b])/(8*b^(3/2)*c^4)","A",27,8,27,0.2963,1,"{4721, 4723, 4406, 3306, 3305, 3351, 3304, 3352}"
432,1,591,0,1.6682197,"\int \frac{x^2 \left(d-c^2 d x^2\right)}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^2*(d - c^2*d*x^2))/(a + b*ArcSin[c*x])^(3/2),x]","-\frac{\sqrt{2 \pi } d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{5 \sqrt{\frac{\pi }{2}} d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^3}-\frac{\sqrt{\frac{2 \pi }{3}} d \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{5 \sqrt{\frac{\pi }{6}} d \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{\sqrt{\frac{5 \pi }{2}} d \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{2 \pi } d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{5 \sqrt{\frac{\pi }{2}} d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^3}+\frac{\sqrt{\frac{2 \pi }{3}} d \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{5 \sqrt{\frac{\pi }{6}} d \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{\frac{5 \pi }{2}} d \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{2 d x^2 \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","-\frac{\sqrt{2 \pi } d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{5 \sqrt{\frac{\pi }{2}} d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^3}-\frac{\sqrt{\frac{2 \pi }{3}} d \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{5 \sqrt{\frac{\pi }{6}} d \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{\sqrt{\frac{5 \pi }{2}} d \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{2 \pi } d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{5 \sqrt{\frac{\pi }{2}} d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^3}+\frac{\sqrt{\frac{2 \pi }{3}} d \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{5 \sqrt{\frac{\pi }{6}} d \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{\frac{5 \pi }{2}} d \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{2 d x^2 \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d*x^2*(1 - c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (5*d*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*b^(3/2)*c^3) + (d*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) - (5*d*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3) + (d*Sqrt[(2*Pi)/3]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) + (d*Sqrt[(5*Pi)/2]*Cos[(5*a)/b]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3) + (5*d*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*b^(3/2)*c^3) - (d*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c^3) + (5*d*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(4*b^(3/2)*c^3) - (d*Sqrt[(2*Pi)/3]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(3/2)*c^3) - (d*Sqrt[(5*Pi)/2]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(5*a)/b])/(4*b^(3/2)*c^3)","A",32,8,27,0.2963,1,"{4721, 4723, 4406, 3306, 3305, 3351, 3304, 3352}"
433,1,241,0,0.7865327,"\int \frac{x \left(d-c^2 d x^2\right)}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x*(d - c^2*d*x^2))/(a + b*ArcSin[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} d \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{\pi } d \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{\pi } d \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 d x \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} d \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{\pi } d \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{\pi } d \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 d x \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d*x*(1 - c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) + (d*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^2) + (d*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(b^(3/2)*c^2) + (d*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(b^(3/2)*c^2) + (d*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(4*a)/b])/(b^(3/2)*c^2)","A",17,10,25,0.4000,1,"{4721, 4661, 3312, 3306, 3305, 3351, 3304, 3352, 4723, 4406}"
434,1,253,0,0.5918688,"\int \frac{d-c^2 d x^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)/(a + b*ArcSin[c*x])^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\frac{3 \pi }{2}} d \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{3 \sqrt{\frac{\pi }{2}} d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{\sqrt{\frac{3 \pi }{2}} d \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{3 \sqrt{\frac{\pi }{2}} d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\frac{3 \pi }{2}} d \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{3 \sqrt{\frac{\pi }{2}} d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{\sqrt{\frac{3 \pi }{2}} d \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \left(1-c^2 x^2\right)^{3/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d*(1 - c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (3*d*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c) - (d*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c) + (3*d*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c) + (d*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(3/2)*c)","A",14,8,24,0.3333,1,"{4659, 4723, 4406, 3306, 3305, 3351, 3304, 3352}"
435,0,0,0,0.7786964,"\int \frac{d-c^2 d x^2}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)/(x*(a + b*ArcSin[c*x])^(3/2)),x]","\int \frac{d-c^2 d x^2}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","-\frac{2 d \text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}},x\right)}{b c}-\frac{2 \sqrt{\pi } d \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2}}-\frac{2 \sqrt{\pi } d \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2}}-\frac{2 d \left(1-c^2 x^2\right)^{3/2}}{b c x \sqrt{a+b \sin ^{-1}(c x)}}",0,"(-2*d*(1 - c^2*x^2)^(3/2))/(b*c*x*Sqrt[a + b*ArcSin[c*x]]) - (2*d*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/b^(3/2) - (2*d*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/b^(3/2) - (2*d*Defer[Int][1/(x^2*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]]), x])/(b*c)","A",0,0,0,0,-1,"{}"
436,1,485,0,1.6620509,"\int \frac{x^3 \left(d-c^2 d x^2\right)^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^3*(d - c^2*d*x^2)^2)/(a + b*ArcSin[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}-\frac{\sqrt{3 \pi } d^2 \cos \left(\frac{6 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d^2 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\pi } d^2 \cos \left(\frac{8 a}{b}\right) \text{FresnelC}\left(\frac{4 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d^2 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{16 b^{3/2} c^4}+\frac{\sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}-\frac{\sqrt{3 \pi } d^2 \sin \left(\frac{6 a}{b}\right) S\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\pi } d^2 \sin \left(\frac{8 a}{b}\right) S\left(\frac{4 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{16 b^{3/2} c^4}-\frac{2 d^2 x^3 \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}-\frac{\sqrt{3 \pi } d^2 \cos \left(\frac{6 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d^2 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\pi } d^2 \cos \left(\frac{8 a}{b}\right) \text{FresnelC}\left(\frac{4 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{3 \sqrt{\pi } d^2 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{16 b^{3/2} c^4}+\frac{\sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^4}-\frac{\sqrt{3 \pi } d^2 \sin \left(\frac{6 a}{b}\right) S\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\pi } d^2 \sin \left(\frac{8 a}{b}\right) S\left(\frac{4 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{16 b^{3/2} c^4}-\frac{2 d^2 x^3 \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d^2*x^3*(1 - c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) + (d^2*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*b^(3/2)*c^4) - (d^2*Sqrt[3*Pi]*Cos[(6*a)/b]*FresnelC[(2*Sqrt[3/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4) + (3*d^2*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(16*b^(3/2)*c^4) - (d^2*Sqrt[Pi]*Cos[(8*a)/b]*FresnelC[(4*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(16*b^(3/2)*c^4) + (3*d^2*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(16*b^(3/2)*c^4) + (d^2*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(4*a)/b])/(8*b^(3/2)*c^4) - (d^2*Sqrt[3*Pi]*FresnelS[(2*Sqrt[3/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(6*a)/b])/(16*b^(3/2)*c^4) - (d^2*Sqrt[Pi]*FresnelS[(4*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(8*a)/b])/(16*b^(3/2)*c^4)","A",32,8,29,0.2759,1,"{4721, 4723, 4406, 3306, 3305, 3351, 3304, 3352}"
437,1,511,0,2.1235638,"\int \frac{x^2 \left(d-c^2 d x^2\right)^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^2*(d - c^2*d*x^2)^2)/(a + b*ArcSin[c*x])^(3/2),x]","\frac{5 \sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} d^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{3 \sqrt{\frac{5 \pi }{2}} d^2 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{\frac{7 \pi }{2}} d^2 \sin \left(\frac{7 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{14}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{5 \sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{\sqrt{\frac{3 \pi }{2}} d^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{3 \sqrt{\frac{5 \pi }{2}} d^2 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{\sqrt{\frac{7 \pi }{2}} d^2 \cos \left(\frac{7 a}{b}\right) S\left(\frac{\sqrt{\frac{14}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{2 d^2 x^2 \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{5 \sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} d^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{3 \sqrt{\frac{5 \pi }{2}} d^2 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{\frac{7 \pi }{2}} d^2 \sin \left(\frac{7 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{14}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{5 \sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{\sqrt{\frac{3 \pi }{2}} d^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{3 \sqrt{\frac{5 \pi }{2}} d^2 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{\sqrt{\frac{7 \pi }{2}} d^2 \cos \left(\frac{7 a}{b}\right) S\left(\frac{\sqrt{\frac{14}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{2 d^2 x^2 \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d^2*x^2*(1 - c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (5*d^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) + (d^2*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) + (3*d^2*Sqrt[(5*Pi)/2]*Cos[(5*a)/b]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) + (d^2*Sqrt[(7*Pi)/2]*Cos[(7*a)/b]*FresnelS[(Sqrt[14/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) + (5*d^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(16*b^(3/2)*c^3) - (d^2*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(16*b^(3/2)*c^3) - (3*d^2*Sqrt[(5*Pi)/2]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(5*a)/b])/(16*b^(3/2)*c^3) - (d^2*Sqrt[(7*Pi)/2]*FresnelC[(Sqrt[14/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(7*a)/b])/(16*b^(3/2)*c^3)","A",42,8,29,0.2759,1,"{4721, 4723, 4406, 3306, 3305, 3351, 3304, 3352}"
438,1,373,0,1.4008683,"\int \frac{x \left(d-c^2 d x^2\right)^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x*(d - c^2*d*x^2)^2)/(a + b*ArcSin[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{3 \pi } d^2 \cos \left(\frac{6 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^2}+\frac{5 \sqrt{\pi } d^2 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 b^{3/2} c^2}+\frac{5 \sqrt{\pi } d^2 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{3 \pi } d^2 \sin \left(\frac{6 a}{b}\right) S\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^2}-\frac{2 d^2 x \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{3 \pi } d^2 \cos \left(\frac{6 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^2}+\frac{5 \sqrt{\pi } d^2 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 b^{3/2} c^2}+\frac{5 \sqrt{\pi } d^2 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{3 \pi } d^2 \sin \left(\frac{6 a}{b}\right) S\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^2}-\frac{2 d^2 x \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d^2*x*(1 - c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) + (d^2*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^2) + (d^2*Sqrt[3*Pi]*Cos[(6*a)/b]*FresnelC[(2*Sqrt[3/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*b^(3/2)*c^2) + (5*d^2*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(8*b^(3/2)*c^2) + (5*d^2*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(8*b^(3/2)*c^2) + (d^2*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(4*a)/b])/(b^(3/2)*c^2) + (d^2*Sqrt[3*Pi]*FresnelS[(2*Sqrt[3/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(6*a)/b])/(8*b^(3/2)*c^2)","A",32,10,27,0.3704,1,"{4721, 4661, 3312, 3306, 3305, 3351, 3304, 3352, 4723, 4406}"
439,1,390,0,0.8163957,"\int \frac{\left(d-c^2 d x^2\right)^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)^2/(a + b*ArcSin[c*x])^(3/2),x]","\frac{5 \sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c}+\frac{5 \sqrt{\frac{3 \pi }{2}} d^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}+\frac{\sqrt{\frac{5 \pi }{2}} d^2 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{5 \sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c}-\frac{5 \sqrt{\frac{3 \pi }{2}} d^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{\sqrt{\frac{5 \pi }{2}} d^2 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{2 d^2 \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{5 \sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c}+\frac{5 \sqrt{\frac{3 \pi }{2}} d^2 \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}+\frac{\sqrt{\frac{5 \pi }{2}} d^2 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{5 \sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c}-\frac{5 \sqrt{\frac{3 \pi }{2}} d^2 \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{\sqrt{\frac{5 \pi }{2}} d^2 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{2 d^2 \left(1-c^2 x^2\right)^{5/2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d^2*(1 - c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (5*d^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*b^(3/2)*c) - (5*d^2*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*b^(3/2)*c) - (d^2*Sqrt[(5*Pi)/2]*Cos[(5*a)/b]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*b^(3/2)*c) + (5*d^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*b^(3/2)*c) + (5*d^2*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(4*b^(3/2)*c) + (d^2*Sqrt[(5*Pi)/2]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(5*a)/b])/(4*b^(3/2)*c)","A",19,8,26,0.3077,1,"{4659, 4723, 4406, 3306, 3305, 3351, 3304, 3352}"
440,0,0,0,1.4632037,"\int \frac{\left(d-c^2 d x^2\right)^2}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)^2/(x*(a + b*ArcSin[c*x])^(3/2)),x]","\int \frac{\left(d-c^2 d x^2\right)^2}{x \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","-\frac{2 d^2 \text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}},x\right)}{b c}-\frac{\sqrt{\frac{\pi }{2}} d^2 \cos \left(\frac{4 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{3 \sqrt{\pi } d^2 \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2}}-\frac{3 \sqrt{\pi } d^2 \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} d^2 \sin \left(\frac{4 a}{b}\right) S\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{2 d^2 \left(1-c^2 x^2\right)^{5/2}}{b c x \sqrt{a+b \sin ^{-1}(c x)}}",0,"(-2*d^2*(1 - c^2*x^2)^(5/2))/(b*c*x*Sqrt[a + b*ArcSin[c*x]]) - (d^2*Sqrt[Pi/2]*Cos[(4*a)/b]*FresnelC[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/b^(3/2) - (3*d^2*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])])/b^(3/2) - (3*d^2*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcSin[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/b^(3/2) - (d^2*Sqrt[Pi/2]*FresnelS[(2*Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(4*a)/b])/b^(3/2) - (2*d^2*Defer[Int][1/(x^2*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]]), x])/(b*c)","A",0,0,0,0,-1,"{}"
441,1,42,0,0.1505345,"\int \left(-\frac{3 x}{8 \left(1-x^2\right) \sqrt{\sin ^{-1}(x)}}+\frac{x \sin ^{-1}(x)^{3/2}}{\left(1-x^2\right)^2}\right) \, dx","Int[(-3*x)/(8*(1 - x^2)*Sqrt[ArcSin[x]]) + (x*ArcSin[x]^(3/2))/(1 - x^2)^2,x]","\frac{\sin ^{-1}(x)^{3/2}}{2 \left(1-x^2\right)}-\frac{3 x \sqrt{\sin ^{-1}(x)}}{4 \sqrt{1-x^2}}","\frac{\sin ^{-1}(x)^{3/2}}{2 \left(1-x^2\right)}-\frac{3 x \sqrt{\sin ^{-1}(x)}}{4 \sqrt{1-x^2}}",1,"(-3*x*Sqrt[ArcSin[x]])/(4*Sqrt[1 - x^2]) + ArcSin[x]^(3/2)/(2*(1 - x^2))","A",3,2,38,0.05263,1,"{4677, 4651}"
442,1,227,0,0.2829973,"\int \left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)^(3/2)*Sqrt[ArcSin[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{64 a \sqrt{1-a^2 x^2}}-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)}+\frac{c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{4 a \sqrt{1-a^2 x^2}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}","-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{64 a \sqrt{1-a^2 x^2}}-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)}+\frac{c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{4 a \sqrt{1-a^2 x^2}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}",1,"(3*c*x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/8 + (x*(c - a^2*c*x^2)^(3/2)*Sqrt[ArcSin[a*x]])/4 + (c*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(4*a*Sqrt[1 - a^2*x^2]) - (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(64*a*Sqrt[1 - a^2*x^2]) - (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(8*a*Sqrt[1 - a^2*x^2])","A",15,9,24,0.3750,1,"{4649, 4647, 4641, 4635, 4406, 12, 3305, 3351, 4723}"
443,1,130,0,0.1176245,"\int \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)} \, dx","Int[Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]],x]","-\frac{\sqrt{\pi } \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{3 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}","-\frac{\sqrt{\pi } \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{3 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}",1,"(x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/2 + (Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(3*a*Sqrt[1 - a^2*x^2]) - (Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(8*a*Sqrt[1 - a^2*x^2])","A",7,7,24,0.2917,1,"{4647, 4641, 4635, 4406, 12, 3305, 3351}"
444,1,44,0,0.0752011,"\int \frac{\sqrt{\sin ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[Sqrt[ArcSin[a*x]]/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{3 a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{3/2}}{3 a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(3/2))/(3*a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
445,0,0,0,0.0949667,"\int \frac{\sqrt{\sin ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[Sqrt[ArcSin[a*x]]/(c - a^2*c*x^2)^(3/2),x]","\int \frac{\sqrt{\sin ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","\frac{x \sqrt{\sin ^{-1}(a x)}}{c \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right) \sqrt{\sin ^{-1}(a x)}},x\right)}{2 c \sqrt{c-a^2 c x^2}}",0,"(x*Sqrt[ArcSin[a*x]])/(c*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)*Sqrt[ArcSin[a*x]]), x])/(2*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
446,0,0,0,0.1885716,"\int \frac{\sqrt{\sin ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[Sqrt[ArcSin[a*x]]/(c - a^2*c*x^2)^(5/2),x]","\int \frac{\sqrt{\sin ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","-\frac{a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^2 \sqrt{\sin ^{-1}(a x)}},x\right)}{6 c^2 \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right) \sqrt{\sin ^{-1}(a x)}},x\right)}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \sqrt{\sin ^{-1}(a x)}}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{\sin ^{-1}(a x)}}{3 c \left(c-a^2 c x^2\right)^{3/2}}",0,"(x*Sqrt[ArcSin[a*x]])/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*Sqrt[ArcSin[a*x]])/(3*c^2*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)^2*Sqrt[ArcSin[a*x]]), x])/(6*c^2*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)*Sqrt[ArcSin[a*x]]), x])/(3*c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
447,1,363,0,0.433735,"\int \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{3/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{512 a \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{3 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}}{20 a \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{3/2}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}+\frac{3 c \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{32 a}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{32 \sqrt{1-a^2 x^2}}+\frac{27 c \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{256 a \sqrt{1-a^2 x^2}}","-\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{512 a \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{3 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}}{20 a \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{3/2}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}+\frac{3 c \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{32 a}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{32 \sqrt{1-a^2 x^2}}+\frac{27 c \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{256 a \sqrt{1-a^2 x^2}}",1,"(27*c*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(256*a*Sqrt[1 - a^2*x^2]) - (9*a*c*x^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(32*Sqrt[1 - a^2*x^2]) + (3*c*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(32*a) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/8 + (x*(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(3/2))/4 + (3*c*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(5/2))/(20*a*Sqrt[1 - a^2*x^2]) - (3*c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(512*a*Sqrt[1 - a^2*x^2]) - (3*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(32*a*Sqrt[1 - a^2*x^2])","A",17,10,24,0.4167,1,"{4649, 4647, 4641, 4629, 4723, 3312, 3304, 3352, 4677, 4661}"
448,1,219,0,0.2249872,"\int \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2} \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}}{5 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{8 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{16 a \sqrt{1-a^2 x^2}}","-\frac{3 \sqrt{\pi } \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}}{5 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{8 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{16 a \sqrt{1-a^2 x^2}}",1,"(3*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(16*a*Sqrt[1 - a^2*x^2]) - (3*a*x^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(8*Sqrt[1 - a^2*x^2]) + (x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/2 + (Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(5/2))/(5*a*Sqrt[1 - a^2*x^2]) - (3*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(32*a*Sqrt[1 - a^2*x^2])","A",8,7,24,0.2917,1,"{4647, 4641, 4629, 4723, 3312, 3304, 3352}"
449,1,44,0,0.0724626,"\int \frac{\sin ^{-1}(a x)^{3/2}}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcSin[a*x]^(3/2)/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{5/2}}{5 a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{5/2}}{5 a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(5/2))/(5*a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
450,0,0,0,0.0880517,"\int \frac{\sin ^{-1}(a x)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSin[a*x]^(3/2)/(c - a^2*c*x^2)^(3/2),x]","\int \frac{\sin ^{-1}(a x)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","\frac{x \sin ^{-1}(a x)^{3/2}}{c \sqrt{c-a^2 c x^2}}-\frac{3 a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x \sqrt{\sin ^{-1}(a x)}}{1-a^2 x^2},x\right)}{2 c \sqrt{c-a^2 c x^2}}",0,"(x*ArcSin[a*x]^(3/2))/(c*Sqrt[c - a^2*c*x^2]) - (3*a*Sqrt[1 - a^2*x^2]*Defer[Int][(x*Sqrt[ArcSin[a*x]])/(1 - a^2*x^2), x])/(2*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
451,1,431,0,0.5778381,"\int \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{5/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4096 a \sqrt{1-a^2 x^2}}+\frac{15 \sqrt{\pi } c \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a \sqrt{1-a^2 x^2}}+\frac{3 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{7/2}}{28 a \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{5/2}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}+\frac{5 c \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{32 a}-\frac{15 a c x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{32 \sqrt{1-a^2 x^2}}+\frac{45 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{256 a \sqrt{1-a^2 x^2}}-\frac{225}{512} c x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}-\frac{15}{256} c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{4096 a \sqrt{1-a^2 x^2}}+\frac{15 \sqrt{\pi } c \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a \sqrt{1-a^2 x^2}}+\frac{3 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{7/2}}{28 a \sqrt{1-a^2 x^2}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{5/2}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}+\frac{5 c \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{32 a}-\frac{15 a c x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{32 \sqrt{1-a^2 x^2}}+\frac{45 c \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{256 a \sqrt{1-a^2 x^2}}-\frac{225}{512} c x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}-\frac{15}{256} c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}",1,"(-225*c*x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/512 - (15*c*x*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/256 + (45*c*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(256*a*Sqrt[1 - a^2*x^2]) - (15*a*c*x^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(32*Sqrt[1 - a^2*x^2]) + (5*c*(1 - a^2*x^2)^(3/2)*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(32*a) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(5/2))/8 + (x*(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(5/2))/4 + (3*c*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(7/2))/(28*a*Sqrt[1 - a^2*x^2]) + (15*c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4096*a*Sqrt[1 - a^2*x^2]) + (15*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(128*a*Sqrt[1 - a^2*x^2])","A",27,12,24,0.5000,1,"{4649, 4647, 4641, 4629, 4707, 4635, 4406, 12, 3305, 3351, 4677, 4723}"
452,1,247,0,0.2493612,"\int \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2} \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(5/2),x]","\frac{15 \sqrt{\pi } \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{7/2}}{7 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}-\frac{5 a x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{8 \sqrt{1-a^2 x^2}}+\frac{5 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{16 a \sqrt{1-a^2 x^2}}-\frac{15}{32} x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}","\frac{15 \sqrt{\pi } \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{7/2}}{7 a \sqrt{1-a^2 x^2}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}-\frac{5 a x^2 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{8 \sqrt{1-a^2 x^2}}+\frac{5 \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}{16 a \sqrt{1-a^2 x^2}}-\frac{15}{32} x \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}",1,"(-15*x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/32 + (5*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(16*a*Sqrt[1 - a^2*x^2]) - (5*a*x^2*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))/(8*Sqrt[1 - a^2*x^2]) + (x*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(5/2))/2 + (Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(7/2))/(7*a*Sqrt[1 - a^2*x^2]) + (15*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(128*a*Sqrt[1 - a^2*x^2])","A",10,9,24,0.3750,1,"{4647, 4641, 4629, 4707, 4635, 4406, 12, 3305, 3351}"
453,1,44,0,0.0693307,"\int \frac{\sin ^{-1}(a x)^{5/2}}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcSin[a*x]^(5/2)/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{7/2}}{7 a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)^{7/2}}{7 a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]^(7/2))/(7*a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
454,0,0,0,0.0851827,"\int \frac{\sin ^{-1}(a x)^{5/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSin[a*x]^(5/2)/(c - a^2*c*x^2)^(3/2),x]","\int \frac{\sin ^{-1}(a x)^{5/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","\frac{x \sin ^{-1}(a x)^{5/2}}{c \sqrt{c-a^2 c x^2}}-\frac{5 a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x \sin ^{-1}(a x)^{3/2}}{1-a^2 x^2},x\right)}{2 c \sqrt{c-a^2 c x^2}}",0,"(x*ArcSin[a*x]^(5/2))/(c*Sqrt[c - a^2*c*x^2]) - (5*a*Sqrt[1 - a^2*x^2]*Defer[Int][(x*ArcSin[a*x]^(3/2))/(1 - a^2*x^2), x])/(2*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
455,1,226,0,0.2366832,"\int \left(a^2-x^2\right)^{3/2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)} \, dx","Int[(a^2 - x^2)^(3/2)*Sqrt[ArcSin[x/a]],x]","-\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{1-\frac{x^2}{a^2}}}-\frac{\sqrt{\pi } a^3 \sqrt{a^2-x^2} S\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{8 \sqrt{1-\frac{x^2}{a^2}}}+\frac{a^3 \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{4 \sqrt{1-\frac{x^2}{a^2}}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}+\frac{1}{4} x \left(a^2-x^2\right)^{3/2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}","-\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{1-\frac{x^2}{a^2}}}-\frac{\sqrt{\pi } a^3 \sqrt{a^2-x^2} S\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{8 \sqrt{1-\frac{x^2}{a^2}}}+\frac{a^3 \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{4 \sqrt{1-\frac{x^2}{a^2}}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}+\frac{1}{4} x \left(a^2-x^2\right)^{3/2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}",1,"(3*a^2*x*Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]])/8 + (x*(a^2 - x^2)^(3/2)*Sqrt[ArcSin[x/a]])/4 + (a^3*Sqrt[a^2 - x^2]*ArcSin[x/a]^(3/2))/(4*Sqrt[1 - x^2/a^2]) - (a^3*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[x/a]]])/(64*Sqrt[1 - x^2/a^2]) - (a^3*Sqrt[Pi]*Sqrt[a^2 - x^2]*FresnelS[(2*Sqrt[ArcSin[x/a]])/Sqrt[Pi]])/(8*Sqrt[1 - x^2/a^2])","A",15,9,24,0.3750,1,"{4649, 4647, 4641, 4635, 4406, 12, 3305, 3351, 4723}"
456,1,126,0,0.1057086,"\int \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)} \, dx","Int[Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]],x]","-\frac{\sqrt{\pi } a \sqrt{a^2-x^2} S\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{8 \sqrt{1-\frac{x^2}{a^2}}}+\frac{a \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{1-\frac{x^2}{a^2}}}+\frac{1}{2} x \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}","-\frac{\sqrt{\pi } a \sqrt{a^2-x^2} S\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{8 \sqrt{1-\frac{x^2}{a^2}}}+\frac{a \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{1-\frac{x^2}{a^2}}}+\frac{1}{2} x \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}",1,"(x*Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]])/2 + (a*Sqrt[a^2 - x^2]*ArcSin[x/a]^(3/2))/(3*Sqrt[1 - x^2/a^2]) - (a*Sqrt[Pi]*Sqrt[a^2 - x^2]*FresnelS[(2*Sqrt[ArcSin[x/a]])/Sqrt[Pi]])/(8*Sqrt[1 - x^2/a^2])","A",7,7,24,0.2917,1,"{4647, 4641, 4635, 4406, 12, 3305, 3351}"
457,1,42,0,0.0613725,"\int \frac{\sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{a^2-x^2}} \, dx","Int[Sqrt[ArcSin[x/a]]/Sqrt[a^2 - x^2],x]","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{a^2-x^2}}","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{a^2-x^2}}",1,"(2*a*Sqrt[1 - x^2/a^2]*ArcSin[x/a]^(3/2))/(3*Sqrt[a^2 - x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
458,0,0,0,0.0754712,"\int \frac{\sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{3/2}} \, dx","Int[Sqrt[ArcSin[x/a]]/(a^2 - x^2)^(3/2),x]","\int \frac{\sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{3/2}} \, dx","\frac{x \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{a^2 \sqrt{a^2-x^2}}-\frac{\sqrt{1-\frac{x^2}{a^2}} \text{Int}\left(\frac{x}{\left(1-\frac{x^2}{a^2}\right) \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}},x\right)}{2 a^3 \sqrt{a^2-x^2}}",0,"(x*Sqrt[ArcSin[x/a]])/(a^2*Sqrt[a^2 - x^2]) - (Sqrt[1 - x^2/a^2]*Defer[Int][x/((1 - x^2/a^2)*Sqrt[ArcSin[x/a]]), x])/(2*a^3*Sqrt[a^2 - x^2])","A",0,0,0,0,-1,"{}"
459,0,0,0,0.1559564,"\int \frac{\sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{5/2}} \, dx","Int[Sqrt[ArcSin[x/a]]/(a^2 - x^2)^(5/2),x]","\int \frac{\sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{5/2}} \, dx","-\frac{\sqrt{1-\frac{x^2}{a^2}} \text{Int}\left(\frac{x}{\left(1-\frac{x^2}{a^2}\right)^2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}},x\right)}{6 a^5 \sqrt{a^2-x^2}}-\frac{\sqrt{1-\frac{x^2}{a^2}} \text{Int}\left(\frac{x}{\left(1-\frac{x^2}{a^2}\right) \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}},x\right)}{3 a^5 \sqrt{a^2-x^2}}+\frac{2 x \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{3 a^4 \sqrt{a^2-x^2}}+\frac{x \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{3 a^2 \left(a^2-x^2\right)^{3/2}}",0,"(x*Sqrt[ArcSin[x/a]])/(3*a^2*(a^2 - x^2)^(3/2)) + (2*x*Sqrt[ArcSin[x/a]])/(3*a^4*Sqrt[a^2 - x^2]) - (Sqrt[1 - x^2/a^2]*Defer[Int][x/((1 - x^2/a^2)^2*Sqrt[ArcSin[x/a]]), x])/(6*a^5*Sqrt[a^2 - x^2]) - (Sqrt[1 - x^2/a^2]*Defer[Int][x/((1 - x^2/a^2)*Sqrt[ArcSin[x/a]]), x])/(3*a^5*Sqrt[a^2 - x^2])","A",0,0,0,0,-1,"{}"
460,1,359,0,0.4210753,"\int \left(a^2-x^2\right)^{3/2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2} \, dx","Int[(a^2 - x^2)^(3/2)*ArcSin[x/a]^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}\right)}{512 \sqrt{1-\frac{x^2}{a^2}}}-\frac{3 \sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{32 \sqrt{1-\frac{x^2}{a^2}}}+\frac{3 a^3 \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{20 \sqrt{1-\frac{x^2}{a^2}}}+\frac{27 a^3 \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{256 \sqrt{1-\frac{x^2}{a^2}}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{9 a x^2 \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{32 \sqrt{1-\frac{x^2}{a^2}}}+\frac{1}{4} x \left(a^2-x^2\right)^{3/2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}+\frac{3 \left(a^2-x^2\right)^{5/2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{32 a \sqrt{1-\frac{x^2}{a^2}}}","-\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}\right)}{512 \sqrt{1-\frac{x^2}{a^2}}}-\frac{3 \sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{32 \sqrt{1-\frac{x^2}{a^2}}}+\frac{3 a^3 \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{20 \sqrt{1-\frac{x^2}{a^2}}}+\frac{27 a^3 \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{256 \sqrt{1-\frac{x^2}{a^2}}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{9 a x^2 \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{32 \sqrt{1-\frac{x^2}{a^2}}}+\frac{1}{4} x \left(a^2-x^2\right)^{3/2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}+\frac{3 \left(a^2-x^2\right)^{5/2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{32 a \sqrt{1-\frac{x^2}{a^2}}}",1,"(27*a^3*Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]])/(256*Sqrt[1 - x^2/a^2]) - (9*a*x^2*Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]])/(32*Sqrt[1 - x^2/a^2]) + (3*(a^2 - x^2)^(5/2)*Sqrt[ArcSin[x/a]])/(32*a*Sqrt[1 - x^2/a^2]) + (3*a^2*x*Sqrt[a^2 - x^2]*ArcSin[x/a]^(3/2))/8 + (x*(a^2 - x^2)^(3/2)*ArcSin[x/a]^(3/2))/4 + (3*a^3*Sqrt[a^2 - x^2]*ArcSin[x/a]^(5/2))/(20*Sqrt[1 - x^2/a^2]) - (3*a^3*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[x/a]]])/(512*Sqrt[1 - x^2/a^2]) - (3*a^3*Sqrt[Pi]*Sqrt[a^2 - x^2]*FresnelC[(2*Sqrt[ArcSin[x/a]])/Sqrt[Pi]])/(32*Sqrt[1 - x^2/a^2])","A",17,10,24,0.4167,1,"{4649, 4647, 4641, 4629, 4723, 3312, 3304, 3352, 4677, 4661}"
461,1,215,0,0.2317745,"\int \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2} \, dx","Int[Sqrt[a^2 - x^2]*ArcSin[x/a]^(3/2),x]","-\frac{3 \sqrt{\pi } a \sqrt{a^2-x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{32 \sqrt{1-\frac{x^2}{a^2}}}+\frac{a \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{1-\frac{x^2}{a^2}}}+\frac{1}{2} x \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 x^2 \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{8 a \sqrt{1-\frac{x^2}{a^2}}}+\frac{3 a \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{16 \sqrt{1-\frac{x^2}{a^2}}}","-\frac{3 \sqrt{\pi } a \sqrt{a^2-x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{\pi }}\right)}{32 \sqrt{1-\frac{x^2}{a^2}}}+\frac{a \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{1-\frac{x^2}{a^2}}}+\frac{1}{2} x \sqrt{a^2-x^2} \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 x^2 \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{8 a \sqrt{1-\frac{x^2}{a^2}}}+\frac{3 a \sqrt{a^2-x^2} \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{16 \sqrt{1-\frac{x^2}{a^2}}}",1,"(3*a*Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]])/(16*Sqrt[1 - x^2/a^2]) - (3*x^2*Sqrt[a^2 - x^2]*Sqrt[ArcSin[x/a]])/(8*a*Sqrt[1 - x^2/a^2]) + (x*Sqrt[a^2 - x^2]*ArcSin[x/a]^(3/2))/2 + (a*Sqrt[a^2 - x^2]*ArcSin[x/a]^(5/2))/(5*Sqrt[1 - x^2/a^2]) - (3*a*Sqrt[Pi]*Sqrt[a^2 - x^2]*FresnelC[(2*Sqrt[ArcSin[x/a]])/Sqrt[Pi]])/(32*Sqrt[1 - x^2/a^2])","A",8,7,24,0.2917,1,"{4647, 4641, 4629, 4723, 3312, 3304, 3352}"
462,1,42,0,0.0646827,"\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2-x^2}} \, dx","Int[ArcSin[x/a]^(3/2)/Sqrt[a^2 - x^2],x]","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}","\frac{2 a \sqrt{1-\frac{x^2}{a^2}} \sin ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}",1,"(2*a*Sqrt[1 - x^2/a^2]*ArcSin[x/a]^(5/2))/(5*Sqrt[a^2 - x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
463,0,0,0,0.0749571,"\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\left(a^2-x^2\right)^{3/2}} \, dx","Int[ArcSin[x/a]^(3/2)/(a^2 - x^2)^(3/2),x]","\int \frac{\sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\left(a^2-x^2\right)^{3/2}} \, dx","\frac{x \sin ^{-1}\left(\frac{x}{a}\right)^{3/2}}{a^2 \sqrt{a^2-x^2}}-\frac{3 \sqrt{1-\frac{x^2}{a^2}} \text{Int}\left(\frac{x \sqrt{\sin ^{-1}\left(\frac{x}{a}\right)}}{1-\frac{x^2}{a^2}},x\right)}{2 a^3 \sqrt{a^2-x^2}}",0,"(x*ArcSin[x/a]^(3/2))/(a^2*Sqrt[a^2 - x^2]) - (3*Sqrt[1 - x^2/a^2]*Defer[Int][(x*Sqrt[ArcSin[x/a]])/(1 - x^2/a^2), x])/(2*a^3*Sqrt[a^2 - x^2])","A",0,0,0,0,-1,"{}"
464,1,25,0,0.0607728,"\int \frac{x}{\sqrt{1-x^2} \sqrt{\sin ^{-1}(x)}} \, dx","Int[x/(Sqrt[1 - x^2]*Sqrt[ArcSin[x]]),x]","\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(x)}\right)","\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(x)}\right)",1,"Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[x]]]","A",3,3,19,0.1579,1,"{4723, 3305, 3351}"
465,1,244,0,0.1933423,"\int \frac{\left(c-a^2 c x^2\right)^{5/2}}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[(c - a^2*c*x^2)^(5/2)/Sqrt[ArcSin[a*x]],x]","\frac{3 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{\frac{\pi }{3}} c^2 \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{15 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{5 c^2 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{8 a \sqrt{1-a^2 x^2}}","\frac{3 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{16 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{\frac{\pi }{3}} c^2 \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{15 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a \sqrt{1-a^2 x^2}}+\frac{5 c^2 \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{8 a \sqrt{1-a^2 x^2}}",1,"(5*c^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(8*a*Sqrt[1 - a^2*x^2]) + (3*c^2*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(16*a*Sqrt[1 - a^2*x^2]) + (c^2*Sqrt[Pi/3]*Sqrt[c - a^2*c*x^2]*FresnelC[2*Sqrt[3/Pi]*Sqrt[ArcSin[a*x]]])/(32*a*Sqrt[1 - a^2*x^2]) + (15*c^2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(32*a*Sqrt[1 - a^2*x^2])","A",10,5,24,0.2083,1,"{4663, 4661, 3312, 3304, 3352}"
466,1,170,0,0.1544731,"\int \frac{\left(c-a^2 c x^2\right)^{3/2}}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[(c - a^2*c*x^2)^(3/2)/Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a \sqrt{1-a^2 x^2}}+\frac{3 c \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{4 a \sqrt{1-a^2 x^2}}","\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a \sqrt{1-a^2 x^2}}+\frac{3 c \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{4 a \sqrt{1-a^2 x^2}}",1,"(3*c*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(4*a*Sqrt[1 - a^2*x^2]) + (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a*Sqrt[1 - a^2*x^2]) + (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a*Sqrt[1 - a^2*x^2])","A",8,5,24,0.2083,1,"{4663, 4661, 3312, 3304, 3352}"
467,1,99,0,0.121941,"\int \frac{\sqrt{c-a^2 c x^2}}{\sqrt{\sin ^{-1}(a x)}} \, dx","Int[Sqrt[c - a^2*c*x^2]/Sqrt[ArcSin[a*x]],x]","\frac{\sqrt{\pi } \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{a \sqrt{1-a^2 x^2}}","\frac{\sqrt{\pi } \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}{a \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])/(a*Sqrt[1 - a^2*x^2]) + (Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a*Sqrt[1 - a^2*x^2])","A",6,5,24,0.2083,1,"{4663, 4661, 3312, 3304, 3352}"
468,1,42,0,0.0699013,"\int \frac{1}{\sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}} \, dx","Int[1/(Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]]),x]","\frac{2 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2} \sqrt{\sin ^{-1}(a x)}}{a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - a^2*x^2]*Sqrt[ArcSin[a*x]])/(a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{4643, 4641}"
469,0,0,0,0.0405698,"\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)}} \, dx","Int[1/((c - a^2*c*x^2)^(3/2)*Sqrt[ArcSin[a*x]]),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)}},x\right)",0,"Defer[Int][1/((c - a^2*c*x^2)^(3/2)*Sqrt[ArcSin[a*x]]), x]","A",0,0,0,0,-1,"{}"
470,0,0,0,0.0403315,"\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sqrt{\sin ^{-1}(a x)}} \, dx","Int[1/((c - a^2*c*x^2)^(5/2)*Sqrt[ArcSin[a*x]]),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sqrt{\sin ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sqrt{\sin ^{-1}(a x)}},x\right)",0,"Defer[Int][1/((c - a^2*c*x^2)^(5/2)*Sqrt[ArcSin[a*x]]), x]","A",0,0,0,0,-1,"{}"
471,1,237,0,0.1860187,"\int \frac{\left(c-a^2 c x^2\right)^{5/2}}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[(c - a^2*c*x^2)^(5/2)/ArcSin[a*x]^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a \sqrt{1-a^2 x^2}}-\frac{\sqrt{3 \pi } c^2 \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a \sqrt{1-a^2 x^2}}-\frac{15 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^{5/2}}{a \sqrt{\sin ^{-1}(a x)}}","-\frac{3 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{2 a \sqrt{1-a^2 x^2}}-\frac{\sqrt{3 \pi } c^2 \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{8 a \sqrt{1-a^2 x^2}}-\frac{15 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^{5/2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"(-2*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^(5/2))/(a*Sqrt[ArcSin[a*x]]) - (3*c^2*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a*Sqrt[1 - a^2*x^2]) - (c^2*Sqrt[3*Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[2*Sqrt[3/Pi]*Sqrt[ArcSin[a*x]]])/(8*a*Sqrt[1 - a^2*x^2]) - (15*c^2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(8*a*Sqrt[1 - a^2*x^2])","A",10,5,24,0.2083,1,"{4659, 4723, 4406, 3305, 3351}"
472,1,163,0,0.1338589,"\int \frac{\left(c-a^2 c x^2\right)^{3/2}}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[(c - a^2*c*x^2)^(3/2)/ArcSin[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{\pi } c \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^{3/2}}{a \sqrt{\sin ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{\pi } c \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^{3/2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"(-2*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^(3/2))/(a*Sqrt[ArcSin[a*x]]) - (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(a*Sqrt[1 - a^2*x^2]) - (2*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(a*Sqrt[1 - a^2*x^2])","A",8,5,24,0.2083,1,"{4659, 4723, 4406, 3305, 3351}"
473,1,98,0,0.0799091,"\int \frac{\sqrt{c-a^2 c x^2}}{\sin ^{-1}(a x)^{3/2}} \, dx","Int[Sqrt[c - a^2*c*x^2]/ArcSin[a*x]^(3/2),x]","-\frac{2 \sqrt{\pi } \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}{a \sqrt{\sin ^{-1}(a x)}}","-\frac{2 \sqrt{\pi } \sqrt{c-a^2 c x^2} S\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}{a \sqrt{\sin ^{-1}(a x)}}",1,"(-2*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2])/(a*Sqrt[ArcSin[a*x]]) - (2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(a*Sqrt[1 - a^2*x^2])","A",6,6,24,0.2500,1,"{4659, 4635, 4406, 12, 3305, 3351}"
474,1,42,0,0.0695152,"\int \frac{1}{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}} \, dx","Int[1/(Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2)),x]","-\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}","-\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{c-a^2 c x^2} \sqrt{\sin ^{-1}(a x)}}",1,"(-2*Sqrt[1 - a^2*x^2])/(a*Sqrt[c - a^2*c*x^2]*Sqrt[ArcSin[a*x]])","A",2,2,24,0.08333,1,"{4643, 4641}"
475,0,0,0,0.0917123,"\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{3/2}} \, dx","Int[1/((c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(3/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{3/2}} \, dx","\frac{4 a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^2 \sqrt{\sin ^{-1}(a x)}},x\right)}{c \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{1-a^2 x^2}}{a \left(c-a^2 c x^2\right)^{3/2} \sqrt{\sin ^{-1}(a x)}}",0,"(-2*Sqrt[1 - a^2*x^2])/(a*(c - a^2*c*x^2)^(3/2)*Sqrt[ArcSin[a*x]]) + (4*a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)^2*Sqrt[ArcSin[a*x]]), x])/(c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
476,0,0,0,0.0938901,"\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^{3/2}} \, dx","Int[1/((c - a^2*c*x^2)^(5/2)*ArcSin[a*x]^(3/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^{3/2}} \, dx","\frac{8 a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^3 \sqrt{\sin ^{-1}(a x)}},x\right)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{1-a^2 x^2}}{a \left(c-a^2 c x^2\right)^{5/2} \sqrt{\sin ^{-1}(a x)}}",0,"(-2*Sqrt[1 - a^2*x^2])/(a*(c - a^2*c*x^2)^(5/2)*Sqrt[ArcSin[a*x]]) + (8*a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)^3*Sqrt[ArcSin[a*x]]), x])/(c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
477,1,206,0,0.29656,"\int \frac{\left(c-a^2 c x^2\right)^{3/2}}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[(c - a^2*c*x^2)^(3/2)/ArcSin[a*x]^(5/2),x]","-\frac{4 \sqrt{2 \pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^{3/2}}{3 a \sin ^{-1}(a x)^{3/2}}+\frac{16 c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}{3 \sqrt{\sin ^{-1}(a x)}}","-\frac{4 \sqrt{2 \pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\sin ^{-1}(a x)}\right)}{3 a \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^{3/2}}{3 a \sin ^{-1}(a x)^{3/2}}+\frac{16 c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}{3 \sqrt{\sin ^{-1}(a x)}}",1,"(-2*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^(3/2))/(3*a*ArcSin[a*x]^(3/2)) + (16*c*x*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2])/(3*Sqrt[ArcSin[a*x]]) - (4*c*Sqrt[2*Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a*Sqrt[1 - a^2*x^2]) - (8*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(3*a*Sqrt[1 - a^2*x^2])","A",12,8,24,0.3333,1,"{4659, 4721, 4661, 3312, 3304, 3352, 4723, 4406}"
478,1,130,0,0.0733973,"\int \frac{\sqrt{c-a^2 c x^2}}{\sin ^{-1}(a x)^{5/2}} \, dx","Int[Sqrt[c - a^2*c*x^2]/ArcSin[a*x]^(5/2),x]","-\frac{8 \sqrt{\pi } \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a \sqrt{1-a^2 x^2}}+\frac{8 x \sqrt{c-a^2 c x^2}}{3 \sqrt{\sin ^{-1}(a x)}}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}{3 a \sin ^{-1}(a x)^{3/2}}","-\frac{8 \sqrt{\pi } \sqrt{c-a^2 c x^2} \text{FresnelC}\left(\frac{2 \sqrt{\sin ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a \sqrt{1-a^2 x^2}}+\frac{8 x \sqrt{c-a^2 c x^2}}{3 \sqrt{\sin ^{-1}(a x)}}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}{3 a \sin ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2])/(3*a*ArcSin[a*x]^(3/2)) + (8*x*Sqrt[c - a^2*c*x^2])/(3*Sqrt[ArcSin[a*x]]) - (8*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*FresnelC[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(3*a*Sqrt[1 - a^2*x^2])","A",4,4,24,0.1667,1,"{4659, 4631, 3304, 3352}"
479,1,44,0,0.0690032,"\int \frac{1}{\sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{5/2}} \, dx","Int[1/(Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(5/2)),x]","-\frac{2 \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a^2 c x^2} \sin ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[c - a^2*c*x^2]*ArcSin[a*x]^(3/2))","A",2,2,24,0.08333,1,"{4643, 4641}"
480,0,0,0,0.0870418,"\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{5/2}} \, dx","Int[1/((c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(5/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{5/2}} \, dx","\frac{4 a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^2 \sin ^{-1}(a x)^{3/2}},x\right)}{3 c \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{1-a^2 x^2}}{3 a \left(c-a^2 c x^2\right)^{3/2} \sin ^{-1}(a x)^{3/2}}",0,"(-2*Sqrt[1 - a^2*x^2])/(3*a*(c - a^2*c*x^2)^(3/2)*ArcSin[a*x]^(3/2)) + (4*a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)^2*ArcSin[a*x]^(3/2)), x])/(3*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
481,0,0,0,0.0889734,"\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^{5/2}} \, dx","Int[1/((c - a^2*c*x^2)^(5/2)*ArcSin[a*x]^(5/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^{5/2}} \, dx","\frac{8 a \sqrt{1-a^2 x^2} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right)^3 \sin ^{-1}(a x)^{3/2}},x\right)}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{1-a^2 x^2}}{3 a \left(c-a^2 c x^2\right)^{5/2} \sin ^{-1}(a x)^{3/2}}",0,"(-2*Sqrt[1 - a^2*x^2])/(3*a*(c - a^2*c*x^2)^(5/2)*ArcSin[a*x]^(3/2)) + (8*a*Sqrt[1 - a^2*x^2]*Defer[Int][x/((1 - a^2*x^2)^3*ArcSin[a*x]^(3/2)), x])/(3*c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
482,1,259,0,0.4556656,"\int x^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n,x]","\frac{i 2^{-2 (n+3)} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-2 (n+3)} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{8 b c^3 (n+1) \sqrt{1-c^2 x^2}}","\frac{i 2^{-2 (n+3)} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-2 (n+3)} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{8 b c^3 (n+1) \sqrt{1-c^2 x^2}}",1,"(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^(1 + n))/(8*b*c^3*(1 + n)*Sqrt[1 - c^2*x^2]) + (I*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-4*I)*(a + b*ArcSin[c*x]))/b])/(2^(2*(3 + n))*c^3*E^(((4*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (I*E^(((4*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((4*I)*(a + b*ArcSin[c*x]))/b])/(2^(2*(3 + n))*c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",7,5,29,0.1724,1,"{4725, 4723, 4406, 3307, 2181}"
483,1,391,0,0.4402358,"\int x \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[x*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n,x]","-\frac{e^{-\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{-n-1} e^{-\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}-\frac{e^{\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{-n-1} e^{\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}","-\frac{e^{-\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{-n-1} e^{-\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}-\frac{e^{\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{-n-1} e^{\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{1-c^2 x^2}}",1,"-(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c*x]))/b])/(8*c^2*E^((I*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (E^((I*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c*x]))/b])/(8*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (3^(-1 - n)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-3*I)*(a + b*ArcSin[c*x]))/b])/(8*c^2*E^(((3*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (3^(-1 - n)*E^(((3*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((3*I)*(a + b*ArcSin[c*x]))/b])/(8*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",10,5,27,0.1852,1,"{4725, 4723, 4406, 3308, 2181}"
484,1,259,0,0.292758,"\int \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n,x]","-\frac{i 2^{-n-3} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i 2^{-n-3} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{2 b c (n+1) \sqrt{1-c^2 x^2}}","-\frac{i 2^{-n-3} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i 2^{-n-3} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{2 b c (n+1) \sqrt{1-c^2 x^2}}",1,"(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^(1 + n))/(2*b*c*(1 + n)*Sqrt[1 - c^2*x^2]) - (I*2^(-3 - n)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c*x]))/b])/(c*E^(((2*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-3 - n)*E^(((2*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c*x]))/b])/(c*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",7,5,26,0.1923,1,"{4663, 4661, 3312, 3307, 2181}"
485,0,0,0,0.1382969,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n}{x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n)/x,x]","\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n}{x} \, dx","d \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)+\frac{d e^{-\frac{i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 \sqrt{d-c^2 d x^2}}+\frac{d e^{\frac{i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 \sqrt{d-c^2 d x^2}}",0,"Defer[Int][(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n)/x, x]","A",0,0,0,0,-1,"{}"
486,0,0,0,0.1418651,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n}{x^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n)/x^2,x]","\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n}{x^2} \, dx","d \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)-\frac{c d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{b (n+1) \sqrt{d-c^2 d x^2}}",0,"Defer[Int][(Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n)/x^2, x]","A",0,0,0,0,-1,"{}"
487,1,684,0,0.8102447,"\int x^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[x^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n,x]","-\frac{i d 2^{-n-7} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{i d 2^{-2 n-7} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{i d 2^{-n-7} 3^{-n-1} e^{-\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{i d 2^{-n-7} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i d 2^{-2 n-7} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i d 2^{-n-7} 3^{-n-1} e^{\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{16 b c^3 (n+1) \sqrt{1-c^2 x^2}}","-\frac{i d 2^{-n-7} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{i d 2^{-2 n-7} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{i d 2^{-n-7} 3^{-n-1} e^{-\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{i d 2^{-n-7} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i d 2^{-2 n-7} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i d 2^{-n-7} 3^{-n-1} e^{\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{16 b c^3 (n+1) \sqrt{1-c^2 x^2}}",1,"(d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^(1 + n))/(16*b*c^3*(1 + n)*Sqrt[1 - c^2*x^2]) - (I*2^(-7 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c*x]))/b])/(c^3*E^(((2*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-7 - n)*d*E^(((2*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-7 - 2*n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-4*I)*(a + b*ArcSin[c*x]))/b])/(c^3*E^(((4*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (I*2^(-7 - 2*n)*d*E^(((4*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((4*I)*(a + b*ArcSin[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-7 - n)*3^(-1 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-6*I)*(a + b*ArcSin[c*x]))/b])/(c^3*E^(((6*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (I*2^(-7 - n)*3^(-1 - n)*d*E^(((6*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((6*I)*(a + b*ArcSin[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",13,5,29,0.1724,1,"{4725, 4723, 4406, 3307, 2181}"
488,1,595,0,0.5860506,"\int x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n,x]","-\frac{d e^{-\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 c^2 \sqrt{1-c^2 x^2}}-\frac{d 3^{-n} e^{-\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}-\frac{d 5^{-n-1} e^{-\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}-\frac{d e^{\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 c^2 \sqrt{1-c^2 x^2}}-\frac{d 3^{-n} e^{\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}-\frac{d 5^{-n-1} e^{\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}","-\frac{d e^{-\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 c^2 \sqrt{1-c^2 x^2}}-\frac{d 3^{-n} e^{-\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}-\frac{d 5^{-n-1} e^{-\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}-\frac{d e^{\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 c^2 \sqrt{1-c^2 x^2}}-\frac{d 3^{-n} e^{\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}-\frac{d 5^{-n-1} e^{\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{1-c^2 x^2}}",1,"-(d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c*x]))/b])/(16*c^2*E^((I*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (d*E^((I*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c*x]))/b])/(16*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-3*I)*(a + b*ArcSin[c*x]))/b])/(32*3^n*c^2*E^(((3*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (d*E^(((3*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((3*I)*(a + b*ArcSin[c*x]))/b])/(32*3^n*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (5^(-1 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-5*I)*(a + b*ArcSin[c*x]))/b])/(32*c^2*E^(((5*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (5^(-1 - n)*d*E^(((5*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((5*I)*(a + b*ArcSin[c*x]))/b])/(32*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",13,5,27,0.1852,1,"{4725, 4723, 4406, 3308, 2181}"
489,1,466,0,0.4069261,"\int \left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[(d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n,x]","-\frac{i d 2^{-n-3} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}-\frac{i d 2^{-2 (n+3)} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i d 2^{-n-3} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i d 2^{-2 (n+3)} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{8 b c (n+1) \sqrt{1-c^2 x^2}}","-\frac{i d 2^{-n-3} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}-\frac{i d 2^{-2 (n+3)} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i d 2^{-n-3} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i d 2^{-2 (n+3)} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{8 b c (n+1) \sqrt{1-c^2 x^2}}",1,"(3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^(1 + n))/(8*b*c*(1 + n)*Sqrt[1 - c^2*x^2]) - (I*2^(-3 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c*x]))/b])/(c*E^(((2*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-3 - n)*d*E^(((2*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c*x]))/b])/(c*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (I*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-4*I)*(a + b*ArcSin[c*x]))/b])/(2^(2*(3 + n))*c*E^(((4*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + (I*d*E^(((4*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((4*I)*(a + b*ArcSin[c*x]))/b])/(2^(2*(3 + n))*c*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",10,5,26,0.1923,1,"{4663, 4661, 3312, 3307, 2181}"
490,0,0,0,0.1588244,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n)/x,x]","\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x} \, dx","d^2 \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)+\frac{5 d^2 e^{-\frac{i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}+\frac{d^2 3^{-n-1} e^{-\frac{3 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}+\frac{5 d^2 e^{\frac{i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}+\frac{d^2 3^{-n-1} e^{\frac{3 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}",0,"Defer[Int][((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n)/x, x]","A",0,0,0,0,-1,"{}"
491,0,0,0,0.1583006,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x^2} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n)/x^2,x]","\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x^2} \, dx","d^2 \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)+\frac{i c d^2 2^{-n-3} e^{-\frac{2 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i c d^2 2^{-n-3} e^{\frac{2 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{3 c d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{2 b (n+1) \sqrt{d-c^2 d x^2}}",0,"Defer[Int][((d - c^2*d*x^2)^(3/2)*(a + b*ArcSin[c*x])^n)/x^2, x]","A",0,0,0,0,-1,"{}"
492,1,906,0,0.9596157,"\int x^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[x^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n,x]","-\frac{i 2^{-n-7} d^2 e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{i 2^{-2 (n+4)} d^2 e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{i 2^{-n-7} 3^{-n-1} d^2 e^{-\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{i 2^{-3 n-11} d^2 e^{-\frac{8 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{8 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{128 b c^3 (n+1) \sqrt{1-c^2 x^2}}+\frac{i 2^{-n-7} d^2 e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-2 (n+4)} d^2 e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-n-7} 3^{-n-1} d^2 e^{\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-3 n-11} d^2 e^{\frac{8 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{8 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}","-\frac{i 2^{-n-7} d^2 e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{i 2^{-2 (n+4)} d^2 e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{i 2^{-n-7} 3^{-n-1} d^2 e^{-\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{i 2^{-3 n-11} d^2 e^{-\frac{8 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{8 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{c^3 \sqrt{1-c^2 x^2}}+\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{128 b c^3 (n+1) \sqrt{1-c^2 x^2}}+\frac{i 2^{-n-7} d^2 e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-2 (n+4)} d^2 e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-n-7} 3^{-n-1} d^2 e^{\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{i 2^{-3 n-11} d^2 e^{\frac{8 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{8 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}",1,"(5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^(1 + n))/(128*b*c^3*(1 + n)*Sqrt[1 - c^2*x^2]) - (I*2^(-7 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c*x]))/b])/(c^3*E^(((2*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-7 - n)*d^2*E^(((2*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) + (I*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-4*I)*(a + b*ArcSin[c*x]))/b])/(2^(2*(4 + n))*c^3*E^(((4*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (I*d^2*E^(((4*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((4*I)*(a + b*ArcSin[c*x]))/b])/(2^(2*(4 + n))*c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-7 - n)*3^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-6*I)*(a + b*ArcSin[c*x]))/b])/(c^3*E^(((6*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (I*2^(-7 - n)*3^(-1 - n)*d^2*E^(((6*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((6*I)*(a + b*ArcSin[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-11 - 3*n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-8*I)*(a + b*ArcSin[c*x]))/b])/(c^3*E^(((8*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (I*2^(-11 - 3*n)*d^2*E^(((8*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((8*I)*(a + b*ArcSin[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",16,5,29,0.1724,1,"{4725, 4723, 4406, 3307, 2181}"
493,1,815,0,0.7346518,"\int x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n,x]","-\frac{5 d^2 e^{-\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{1-n} d^2 e^{-\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{5^{-n} d^2 e^{-\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{7^{-n-1} d^2 e^{-\frac{7 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{7 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{5 d^2 e^{\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{1-n} d^2 e^{\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{5^{-n} d^2 e^{\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{7^{-n-1} d^2 e^{\frac{7 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{7 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}","-\frac{5 d^2 e^{-\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{1-n} d^2 e^{-\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{5^{-n} d^2 e^{-\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{7^{-n-1} d^2 e^{-\frac{7 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{7 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{5 d^2 e^{\frac{i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{3^{1-n} d^2 e^{\frac{3 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{5^{-n} d^2 e^{\frac{5 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}-\frac{7^{-n-1} d^2 e^{\frac{7 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{7 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{1-c^2 x^2}}",1,"(-5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-I)*(a + b*ArcSin[c*x]))/b])/(128*c^2*E^((I*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (5*d^2*E^((I*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, (I*(a + b*ArcSin[c*x]))/b])/(128*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (3^(1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-3*I)*(a + b*ArcSin[c*x]))/b])/(128*c^2*E^(((3*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (3^(1 - n)*d^2*E^(((3*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((3*I)*(a + b*ArcSin[c*x]))/b])/(128*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-5*I)*(a + b*ArcSin[c*x]))/b])/(128*5^n*c^2*E^(((5*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (d^2*E^(((5*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((5*I)*(a + b*ArcSin[c*x]))/b])/(128*5^n*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (7^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-7*I)*(a + b*ArcSin[c*x]))/b])/(128*c^2*E^(((7*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) - (7^(-1 - n)*d^2*E^(((7*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((7*I)*(a + b*ArcSin[c*x]))/b])/(128*c^2*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",16,5,27,0.1852,1,"{4725, 4723, 4406, 3308, 2181}"
494,1,698,0,0.5769218,"\int \left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n \, dx","Int[(d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n,x]","-\frac{15 i d^2 2^{-n-7} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}-\frac{3 i d^2 2^{-2 n-7} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}-\frac{i d^2 2^{-n-7} 3^{-n-1} e^{-\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{15 i d^2 2^{-n-7} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{3 i d^2 2^{-2 n-7} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i d^2 2^{-n-7} 3^{-n-1} e^{\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{16 b c (n+1) \sqrt{1-c^2 x^2}}","-\frac{15 i d^2 2^{-n-7} e^{-\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}-\frac{3 i d^2 2^{-2 n-7} e^{-\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}-\frac{i d^2 2^{-n-7} 3^{-n-1} e^{-\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{15 i d^2 2^{-n-7} e^{\frac{2 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{3 i d^2 2^{-2 n-7} e^{\frac{4 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{i d^2 2^{-n-7} 3^{-n-1} e^{\frac{6 i a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{c \sqrt{1-c^2 x^2}}+\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{16 b c (n+1) \sqrt{1-c^2 x^2}}",1,"(5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^(1 + n))/(16*b*c*(1 + n)*Sqrt[1 - c^2*x^2]) - ((15*I)*2^(-7 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-2*I)*(a + b*ArcSin[c*x]))/b])/(c*E^(((2*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + ((15*I)*2^(-7 - n)*d^2*E^(((2*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((2*I)*(a + b*ArcSin[c*x]))/b])/(c*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - ((3*I)*2^(-7 - 2*n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-4*I)*(a + b*ArcSin[c*x]))/b])/(c*E^(((4*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + ((3*I)*2^(-7 - 2*n)*d^2*E^(((4*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((4*I)*(a + b*ArcSin[c*x]))/b])/(c*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n) - (I*2^(-7 - n)*3^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((-6*I)*(a + b*ArcSin[c*x]))/b])/(c*E^(((6*I)*a)/b)*Sqrt[1 - c^2*x^2]*(((-I)*(a + b*ArcSin[c*x]))/b)^n) + (I*2^(-7 - n)*3^(-1 - n)*d^2*E^(((6*I)*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcSin[c*x])^n*Gamma[1 + n, ((6*I)*(a + b*ArcSin[c*x]))/b])/(c*Sqrt[1 - c^2*x^2]*((I*(a + b*ArcSin[c*x]))/b)^n)","A",13,5,26,0.1923,1,"{4663, 4661, 3312, 3307, 2181}"
495,0,0,0,0.1545424,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n)/x,x]","\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x} \, dx","\frac{11 d^3 e^{-\frac{i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{16 \sqrt{d-c^2 d x^2}}-\frac{5\ 3^{-n-1} d^3 e^{-\frac{3 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{32 \sqrt{d-c^2 d x^2}}+\frac{3^{-n} d^3 e^{-\frac{3 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{8 \sqrt{d-c^2 d x^2}}+\frac{5^{-n-1} d^3 e^{-\frac{5 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right) \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n}}{32 \sqrt{d-c^2 d x^2}}+\frac{11 d^3 e^{\frac{i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 \sqrt{d-c^2 d x^2}}-\frac{5\ 3^{-n-1} d^3 e^{\frac{3 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{d-c^2 d x^2}}+\frac{3^{-n} d^3 e^{\frac{3 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}+\frac{5^{-n-1} d^3 e^{\frac{5 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{d-c^2 d x^2}}+d^3 \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)",0,"Defer[Int][((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n)/x, x]","A",0,0,0,0,-1,"{}"
496,0,0,0,0.1595832,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x^2} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n)/x^2,x]","\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^n}{x^2} \, dx","d^3 \text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)+\frac{i c d^3 2^{-n-2} e^{-\frac{2 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}+\frac{i c d^3 2^{-2 (n+3)} e^{-\frac{4 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(-\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i c d^3 2^{-n-2} e^{\frac{2 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i c d^3 2^{-2 (n+3)} e^{\frac{4 i a}{b}} \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^n \left(\frac{i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 i \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{15 c d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^{n+1}}{8 b (n+1) \sqrt{d-c^2 d x^2}}",0,"Defer[Int][((d - c^2*d*x^2)^(5/2)*(a + b*ArcSin[c*x])^n)/x^2, x]","A",0,0,0,0,-1,"{}"
497,0,0,0,0.1018028,"\int \frac{x^m \sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^m*ArcSin[a*x]^n)/Sqrt[1 - a^2*x^2],x]","\int \frac{x^m \sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}} \, dx","\text{Int}\left(\frac{x^m \sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}},x\right)",0,"Defer[Int][(x^m*ArcSin[a*x]^n)/Sqrt[1 - a^2*x^2], x]","A",0,0,0,0,-1,"{}"
498,1,163,0,0.2463961,"\int \frac{x^3 \sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcSin[a*x]^n)/Sqrt[1 - a^2*x^2],x]","-\frac{3 \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \sin ^{-1}(a x)\right)}{8 a^4}+\frac{3^{-n-1} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 i \sin ^{-1}(a x)\right)}{8 a^4}-\frac{3 \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,i \sin ^{-1}(a x)\right)}{8 a^4}+\frac{3^{-n-1} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,3 i \sin ^{-1}(a x)\right)}{8 a^4}","-\frac{3 \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \sin ^{-1}(a x)\right)}{8 a^4}+\frac{3^{-n-1} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 i \sin ^{-1}(a x)\right)}{8 a^4}-\frac{3 \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,i \sin ^{-1}(a x)\right)}{8 a^4}+\frac{3^{-n-1} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,3 i \sin ^{-1}(a x)\right)}{8 a^4}",1,"(-3*ArcSin[a*x]^n*Gamma[1 + n, (-I)*ArcSin[a*x]])/(8*a^4*((-I)*ArcSin[a*x])^n) - (3*ArcSin[a*x]^n*Gamma[1 + n, I*ArcSin[a*x]])/(8*a^4*(I*ArcSin[a*x])^n) + (3^(-1 - n)*ArcSin[a*x]^n*Gamma[1 + n, (-3*I)*ArcSin[a*x]])/(8*a^4*((-I)*ArcSin[a*x])^n) + (3^(-1 - n)*ArcSin[a*x]^n*Gamma[1 + n, (3*I)*ArcSin[a*x]])/(8*a^4*(I*ArcSin[a*x])^n)","A",9,4,24,0.1667,1,"{4723, 3312, 3308, 2181}"
499,1,109,0,0.2073302,"\int \frac{x^2 \sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcSin[a*x]^n)/Sqrt[1 - a^2*x^2],x]","\frac{i 2^{-n-3} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 i \sin ^{-1}(a x)\right)}{a^3}-\frac{i 2^{-n-3} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,2 i \sin ^{-1}(a x)\right)}{a^3}+\frac{\sin ^{-1}(a x)^{n+1}}{2 a^3 (n+1)}","\frac{i 2^{-n-3} \sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 i \sin ^{-1}(a x)\right)}{a^3}-\frac{i 2^{-n-3} \left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,2 i \sin ^{-1}(a x)\right)}{a^3}+\frac{\sin ^{-1}(a x)^{n+1}}{2 a^3 (n+1)}",1,"ArcSin[a*x]^(1 + n)/(2*a^3*(1 + n)) + (I*2^(-3 - n)*ArcSin[a*x]^n*Gamma[1 + n, (-2*I)*ArcSin[a*x]])/(a^3*((-I)*ArcSin[a*x])^n) - (I*2^(-3 - n)*ArcSin[a*x]^n*Gamma[1 + n, (2*I)*ArcSin[a*x]])/(a^3*(I*ArcSin[a*x])^n)","A",6,4,24,0.1667,1,"{4723, 3312, 3307, 2181}"
500,1,75,0,0.1159137,"\int \frac{x \sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcSin[a*x]^n)/Sqrt[1 - a^2*x^2],x]","-\frac{\sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \sin ^{-1}(a x)\right)}{2 a^2}-\frac{\left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,i \sin ^{-1}(a x)\right)}{2 a^2}","-\frac{\sin ^{-1}(a x)^n \left(-i \sin ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \sin ^{-1}(a x)\right)}{2 a^2}-\frac{\left(i \sin ^{-1}(a x)\right)^{-n} \sin ^{-1}(a x)^n \text{Gamma}\left(n+1,i \sin ^{-1}(a x)\right)}{2 a^2}",1,"-(ArcSin[a*x]^n*Gamma[1 + n, (-I)*ArcSin[a*x]])/(2*a^2*((-I)*ArcSin[a*x])^n) - (ArcSin[a*x]^n*Gamma[1 + n, I*ArcSin[a*x]])/(2*a^2*(I*ArcSin[a*x])^n)","A",4,3,22,0.1364,1,"{4723, 3308, 2181}"
501,1,17,0,0.0363865,"\int \frac{\sin ^{-1}(a x)^n}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^n/Sqrt[1 - a^2*x^2],x]","\frac{\sin ^{-1}(a x)^{n+1}}{a (n+1)}","\frac{\sin ^{-1}(a x)^{n+1}}{a (n+1)}",1,"ArcSin[a*x]^(1 + n)/(a*(1 + n))","A",1,1,21,0.04762,1,"{4641}"
502,0,0,0,0.1020105,"\int \frac{\sin ^{-1}(a x)^n}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^n/(x*Sqrt[1 - a^2*x^2]),x]","\int \frac{\sin ^{-1}(a x)^n}{x \sqrt{1-a^2 x^2}} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^n}{x \sqrt{1-a^2 x^2}},x\right)",0,"Defer[Int][ArcSin[a*x]^n/(x*Sqrt[1 - a^2*x^2]), x]","A",0,0,0,0,-1,"{}"
503,0,0,0,0.1016143,"\int \frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcSin[a*x]^n/(x^2*Sqrt[1 - a^2*x^2]),x]","\int \frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}} \, dx","\text{Int}\left(\frac{\sin ^{-1}(a x)^n}{x^2 \sqrt{1-a^2 x^2}},x\right)",0,"Defer[Int][ArcSin[a*x]^n/(x^2*Sqrt[1 - a^2*x^2]), x]","A",0,0,0,0,-1,"{}"
504,1,376,0,0.5369657,"\int (d+c d x)^{5/2} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^(5/2)*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]),x]","\frac{1}{4} c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 d^2 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{2 d^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{3}{8} d^2 x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^3 d^2 x^4 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}-\frac{2 b c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c d^2 x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}","\frac{1}{4} c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 d^2 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{2 d^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{3}{8} d^2 x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^3 d^2 x^4 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}-\frac{2 b c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c d^2 x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}+\frac{2 b d^2 x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}",1,"(2*b*d^2*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(3*Sqrt[1 - c^2*x^2]) - (3*b*c*d^2*x^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(16*Sqrt[1 - c^2*x^2]) - (2*b*c^2*d^2*x^3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(9*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*x^4*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(16*Sqrt[1 - c^2*x^2]) + (3*d^2*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/8 + (c^2*d^2*x^3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/4 - (2*d^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c) + (5*d^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2])","A",13,8,30,0.2667,1,"{4673, 4763, 4647, 4641, 30, 4677, 4697, 4707}"
505,1,273,0,0.2966945,"\int (d+c d x)^{3/2} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^(3/2)*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]),x]","\frac{d \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{d \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{1}{2} d x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^2 d x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{b c d x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{4 \sqrt{1-c^2 x^2}}+\frac{b d x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}","\frac{d \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{d \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{1}{2} d x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^2 d x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{b c d x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{4 \sqrt{1-c^2 x^2}}+\frac{b d x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}",1,"(b*d*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(3*Sqrt[1 - c^2*x^2]) - (b*c*d*x^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(4*Sqrt[1 - c^2*x^2]) - (b*c^2*d*x^3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(9*Sqrt[1 - c^2*x^2]) + (d*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/2 - (d*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c) + (d*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",8,6,30,0.2000,1,"{4673, 4763, 4647, 4641, 30, 4677}"
506,1,134,0,0.1652604,"\int \sqrt{d+c d x} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]),x]","\frac{\sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{1}{2} x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{4 \sqrt{1-c^2 x^2}}","\frac{\sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{1}{2} x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{4 \sqrt{1-c^2 x^2}}",1,"-(b*c*x^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(4*Sqrt[1 - c^2*x^2]) + (x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/2 + (Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",4,4,30,0.1333,1,"{4673, 4647, 4641, 30}"
507,1,141,0,0.2639364,"\int \frac{\sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d+c d x}} \, dx","Int[(Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/Sqrt[d + c*d*x],x]","\frac{f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{f \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{b f x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}","\frac{f \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{f \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{b f x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}",1,"-((b*f*x*Sqrt[1 - c^2*x^2])/(Sqrt[d + c*d*x]*Sqrt[f - c*f*x])) + (f*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (f*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",6,5,30,0.1667,1,"{4673, 4763, 4641, 4677, 8}"
508,1,162,0,0.3604232,"\int \frac{\sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{(d+c d x)^{3/2}} \, dx","Int[(Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/(d + c*d*x)^(3/2),x]","-\frac{f^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{2 f^2 (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 b f^2 \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}","-\frac{f^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{2 f^2 (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 b f^2 \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(-2*f^2*(1 - c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (f^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(2*b*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (2*b*f^2*(1 - c^2*x^2)^(3/2)*Log[1 + c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",8,8,30,0.2667,1,"{4673, 4775, 637, 4761, 12, 627, 31, 4641}"
509,1,163,0,0.2691343,"\int \frac{\sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{(d+c d x)^{5/2}} \, dx","Int[(Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/(d + c*d*x)^(5/2),x]","-\frac{f^3 (1-c x)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 b f^3 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^3 \left(1-c^2 x^2\right)^{5/2} \log (c x+1)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","-\frac{f^3 (1-c x)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 b f^3 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^3 \left(1-c^2 x^2\right)^{5/2} \log (c x+1)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"(-2*b*f^3*(1 - c^2*x^2)^(5/2))/(3*c*(1 + c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (f^3*(1 - c*x)^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (b*f^3*(1 - c^2*x^2)^(5/2)*Log[1 + c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",6,6,30,0.2000,1,"{4673, 651, 4761, 12, 627, 43}"
510,1,414,0,0.3897283,"\int (d+c d x)^{5/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^(5/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{3 d x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)}+\frac{3 d (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \left(1-c^2 x^2\right)^{3/2}}-\frac{d \left(1-c^2 x^2\right) (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c}+\frac{1}{4} d x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{b c^4 d x^5 (c d x+d)^{3/2} (f-c f x)^{3/2}}{25 \left(1-c^2 x^2\right)^{3/2}}+\frac{b c^3 d x^4 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}-\frac{2 b c^2 d x^3 (c d x+d)^{3/2} (f-c f x)^{3/2}}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c d x^2 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}+\frac{b d x (c d x+d)^{3/2} (f-c f x)^{3/2}}{5 \left(1-c^2 x^2\right)^{3/2}}","\frac{3 d x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)}+\frac{3 d (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \left(1-c^2 x^2\right)^{3/2}}-\frac{d \left(1-c^2 x^2\right) (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c}+\frac{1}{4} d x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{b c^4 d x^5 (c d x+d)^{3/2} (f-c f x)^{3/2}}{25 \left(1-c^2 x^2\right)^{3/2}}+\frac{b c^3 d x^4 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}-\frac{2 b c^2 d x^3 (c d x+d)^{3/2} (f-c f x)^{3/2}}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c d x^2 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}+\frac{b d x (c d x+d)^{3/2} (f-c f x)^{3/2}}{5 \left(1-c^2 x^2\right)^{3/2}}",1,"(b*d*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(5*(1 - c^2*x^2)^(3/2)) - (5*b*c*d*x^2*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(16*(1 - c^2*x^2)^(3/2)) - (2*b*c^2*d*x^3*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(15*(1 - c^2*x^2)^(3/2)) + (b*c^3*d*x^4*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(16*(1 - c^2*x^2)^(3/2)) + (b*c^4*d*x^5*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(25*(1 - c^2*x^2)^(3/2)) + (d*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/4 + (3*d*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)) - (d*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(5*c) + (3*d*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(16*b*c*(1 - c^2*x^2)^(3/2))","A",12,9,30,0.3000,1,"{4673, 4763, 4649, 4647, 4641, 30, 14, 4677, 194}"
511,1,226,0,0.2238221,"\int (d+c d x)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{3 x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)}+\frac{3 (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{1}{4} x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{b c^3 x^4 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c x^2 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}","\frac{3 x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)}+\frac{3 (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{1}{4} x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{b c^3 x^4 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c x^2 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}",1,"(-5*b*c*x^2*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(16*(1 - c^2*x^2)^(3/2)) + (b*c^3*x^4*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(16*(1 - c^2*x^2)^(3/2)) + (x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/4 + (3*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)) + (3*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(16*b*c*(1 - c^2*x^2)^(3/2))","A",7,6,30,0.2000,1,"{4673, 4649, 4647, 4641, 30, 14}"
512,1,273,0,0.3117578,"\int \sqrt{d+c d x} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[d + c*d*x]*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]),x]","\frac{f \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{f \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{1}{2} f x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)+\frac{b c^2 f x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{b c f x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{4 \sqrt{1-c^2 x^2}}-\frac{b f x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}","\frac{f \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{f \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{1}{2} f x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)+\frac{b c^2 f x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{b c f x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{4 \sqrt{1-c^2 x^2}}-\frac{b f x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}",1,"-(b*f*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(3*Sqrt[1 - c^2*x^2]) - (b*c*f*x^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(4*Sqrt[1 - c^2*x^2]) + (b*c^2*f*x^3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(9*Sqrt[1 - c^2*x^2]) + (f*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/2 + (f*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c) + (f*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",8,6,30,0.2000,1,"{4673, 4763, 4647, 4641, 30, 4677}"
513,1,242,0,0.4252925,"\int \frac{(f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d+c d x}} \, dx","Int[((f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/Sqrt[d + c*d*x],x]","\frac{3 f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{f^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{2 f^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b c f^2 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{2 b f^2 x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}","\frac{3 f^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{f^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{2 f^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b c f^2 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{2 b f^2 x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}",1,"(-2*b*f^2*x*Sqrt[1 - c^2*x^2])/(Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (b*c*f^2*x^2*Sqrt[1 - c^2*x^2])/(4*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (2*f^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (f^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (3*f^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",9,7,30,0.2333,1,"{4673, 4763, 4641, 4677, 8, 4707, 30}"
514,1,252,0,0.4364662,"\int \frac{(f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{(d+c d x)^{3/2}} \, dx","Int[((f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/(d + c*d*x)^(3/2),x]","-\frac{3 f^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{f^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{4 f^3 (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b f^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{4 b f^3 \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}","-\frac{3 f^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{f^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{4 f^3 (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b f^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{4 b f^3 \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(b*f^3*x*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (4*f^3*(1 - c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (f^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (3*f^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(2*b*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (4*b*f^3*(1 - c^2*x^2)^(3/2)*Log[1 + c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",10,10,30,0.3333,1,"{4673, 4775, 637, 4761, 12, 627, 31, 4641, 4677, 8}"
515,1,324,0,0.3531519,"\int \frac{(f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{(d+c d x)^{5/2}} \, dx","Int[((f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/(d + c*d*x)^(5/2),x]","\frac{2 f^4 (1-c x) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 f^4 (1-c x)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{f^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{4 b f^4 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b f^4 \left(1-c^2 x^2\right)^{5/2} \log (c x+1)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{2 f^4 (1-c x) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 f^4 (1-c x)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{f^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{4 b f^4 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b f^4 \left(1-c^2 x^2\right)^{5/2} \log (c x+1)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"(-4*b*f^4*(1 - c^2*x^2)^(5/2))/(3*c*(1 + c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (b*f^4*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]^2)/(2*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (2*f^4*(1 - c*x)^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*f^4*(1 - c*x)*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (f^4*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (8*b*f^4*(1 - c^2*x^2)^(5/2)*Log[1 + c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",9,9,30,0.3000,1,"{4673, 669, 653, 216, 4761, 627, 43, 31, 4641}"
516,1,315,0,0.265264,"\int (d+c d x)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{5 x (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{24 \left(1-c^2 x^2\right)}+\frac{5 x (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{16 \left(1-c^2 x^2\right)^2}+\frac{5 (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \left(1-c^2 x^2\right)^{5/2}}+\frac{1}{6} x (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 b c^3 x^4 (c d x+d)^{5/2} (f-c f x)^{5/2}}{96 \left(1-c^2 x^2\right)^{5/2}}-\frac{25 b c x^2 (c d x+d)^{5/2} (f-c f x)^{5/2}}{96 \left(1-c^2 x^2\right)^{5/2}}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{5/2} (f-c f x)^{5/2}}{36 c}","\frac{5 x (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{24 \left(1-c^2 x^2\right)}+\frac{5 x (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{16 \left(1-c^2 x^2\right)^2}+\frac{5 (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{32 b c \left(1-c^2 x^2\right)^{5/2}}+\frac{1}{6} x (c d x+d)^{5/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 b c^3 x^4 (c d x+d)^{5/2} (f-c f x)^{5/2}}{96 \left(1-c^2 x^2\right)^{5/2}}-\frac{25 b c x^2 (c d x+d)^{5/2} (f-c f x)^{5/2}}{96 \left(1-c^2 x^2\right)^{5/2}}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{5/2} (f-c f x)^{5/2}}{36 c}",1,"(-25*b*c*x^2*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))/(96*(1 - c^2*x^2)^(5/2)) + (5*b*c^3*x^4*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))/(96*(1 - c^2*x^2)^(5/2)) + (b*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)*Sqrt[1 - c^2*x^2])/(36*c) + (x*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]))/6 + (5*x*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]))/(16*(1 - c^2*x^2)^2) + (5*x*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]))/(24*(1 - c^2*x^2)) + (5*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(32*b*c*(1 - c^2*x^2)^(5/2))","A",9,7,30,0.2333,1,"{4673, 4649, 4647, 4641, 30, 14, 261}"
517,1,414,0,0.3823198,"\int (d+c d x)^{3/2} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + c*d*x)^(3/2)*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{3 f x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)}+\frac{3 f (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{f \left(1-c^2 x^2\right) (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c}+\frac{1}{4} f x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^4 f x^5 (c d x+d)^{3/2} (f-c f x)^{3/2}}{25 \left(1-c^2 x^2\right)^{3/2}}+\frac{b c^3 f x^4 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}+\frac{2 b c^2 f x^3 (c d x+d)^{3/2} (f-c f x)^{3/2}}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c f x^2 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}-\frac{b f x (c d x+d)^{3/2} (f-c f x)^{3/2}}{5 \left(1-c^2 x^2\right)^{3/2}}","\frac{3 f x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)}+\frac{3 f (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{f \left(1-c^2 x^2\right) (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 c}+\frac{1}{4} f x (c d x+d)^{3/2} (f-c f x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^4 f x^5 (c d x+d)^{3/2} (f-c f x)^{3/2}}{25 \left(1-c^2 x^2\right)^{3/2}}+\frac{b c^3 f x^4 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}+\frac{2 b c^2 f x^3 (c d x+d)^{3/2} (f-c f x)^{3/2}}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{5 b c f x^2 (c d x+d)^{3/2} (f-c f x)^{3/2}}{16 \left(1-c^2 x^2\right)^{3/2}}-\frac{b f x (c d x+d)^{3/2} (f-c f x)^{3/2}}{5 \left(1-c^2 x^2\right)^{3/2}}",1,"-(b*f*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(5*(1 - c^2*x^2)^(3/2)) - (5*b*c*f*x^2*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(16*(1 - c^2*x^2)^(3/2)) + (2*b*c^2*f*x^3*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(15*(1 - c^2*x^2)^(3/2)) + (b*c^3*f*x^4*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(16*(1 - c^2*x^2)^(3/2)) - (b*c^4*f*x^5*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))/(25*(1 - c^2*x^2)^(3/2)) + (f*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/4 + (3*f*x*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)) + (f*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(5*c) + (3*f*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(16*b*c*(1 - c^2*x^2)^(3/2))","A",12,9,30,0.3000,1,"{4673, 4763, 4649, 4647, 4641, 30, 14, 4677, 194}"
518,1,376,0,0.5391144,"\int \sqrt{d+c d x} (f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[d + c*d*x]*(f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]),x]","\frac{1}{4} c^2 f^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 f^2 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}+\frac{2 f^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{3}{8} f^2 x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^3 f^2 x^4 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}+\frac{2 b c^2 f^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c f^2 x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}-\frac{2 b f^2 x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}","\frac{1}{4} c^2 f^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)+\frac{5 f^2 \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}+\frac{2 f^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{3}{8} f^2 x \sqrt{c d x+d} \sqrt{f-c f x} \left(a+b \sin ^{-1}(c x)\right)-\frac{b c^3 f^2 x^4 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}+\frac{2 b c^2 f^2 x^3 \sqrt{c d x+d} \sqrt{f-c f x}}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c f^2 x^2 \sqrt{c d x+d} \sqrt{f-c f x}}{16 \sqrt{1-c^2 x^2}}-\frac{2 b f^2 x \sqrt{c d x+d} \sqrt{f-c f x}}{3 \sqrt{1-c^2 x^2}}",1,"(-2*b*f^2*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(3*Sqrt[1 - c^2*x^2]) - (3*b*c*f^2*x^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(16*Sqrt[1 - c^2*x^2]) + (2*b*c^2*f^2*x^3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(9*Sqrt[1 - c^2*x^2]) - (b*c^3*f^2*x^4*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])/(16*Sqrt[1 - c^2*x^2]) + (3*f^2*x*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/8 + (c^2*f^2*x^3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x]))/4 + (2*f^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c) + (5*f^2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]*(a + b*ArcSin[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2])","A",13,8,30,0.2667,1,"{4673, 4763, 4647, 4641, 30, 4677, 4697, 4707}"
519,1,345,0,0.5919493,"\int \frac{(f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{d+c d x}} \, dx","Int[((f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]))/Sqrt[d + c*d*x],x]","\frac{5 f^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{c f^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{3 f^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{11 f^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{b c^2 f^3 x^3 \sqrt{1-c^2 x^2}}{9 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{3 b c f^3 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{11 b f^3 x \sqrt{1-c^2 x^2}}{3 \sqrt{c d x+d} \sqrt{f-c f x}}","\frac{5 f^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{c f^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{3 f^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{11 f^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{b c^2 f^3 x^3 \sqrt{1-c^2 x^2}}{9 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{3 b c f^3 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{11 b f^3 x \sqrt{1-c^2 x^2}}{3 \sqrt{c d x+d} \sqrt{f-c f x}}",1,"(-11*b*f^3*x*Sqrt[1 - c^2*x^2])/(3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (3*b*c*f^3*x^2*Sqrt[1 - c^2*x^2])/(4*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (b*c^2*f^3*x^3*Sqrt[1 - c^2*x^2])/(9*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (11*f^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (3*f^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (c*f^3*x^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (5*f^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",13,7,30,0.2333,1,"{4673, 4763, 4641, 4677, 8, 4707, 30}"
520,1,465,0,0.3750027,"\int \frac{(f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{(d+c d x)^{3/2}} \, dx","Int[((f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]))/(d + c*d*x)^(3/2),x]","-\frac{5 f^4 (1-c x) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{15 f^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{2 f^4 (1-c x)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{15 f^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b c f^4 x^2 \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{5 b f^4 (1-c x)^2 \left(1-c^2 x^2\right)^{3/2}}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{3 b f^4 x \left(1-c^2 x^2\right)^{3/2}}{2 (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{8 b f^4 \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{15 b f^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)^2}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}","-\frac{5 f^4 (1-c x) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{15 f^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{2 f^4 (1-c x)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{15 f^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b c f^4 x^2 \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{5 b f^4 (1-c x)^2 \left(1-c^2 x^2\right)^{3/2}}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{3 b f^4 x \left(1-c^2 x^2\right)^{3/2}}{2 (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{8 b f^4 \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{15 b f^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)^2}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(3*b*f^4*x*(1 - c^2*x^2)^(3/2))/(2*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (b*c*f^4*x^2*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (5*b*f^4*(1 - c*x)^2*(1 - c^2*x^2)^(3/2))/(4*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (15*b*f^4*(1 - c^2*x^2)^(3/2)*ArcSin[c*x]^2)/(4*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (2*f^4*(1 - c*x)^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (15*f^4*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (5*f^4*(1 - c*x)*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (15*f^4*(1 - c^2*x^2)^(3/2)*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (8*b*f^4*(1 - c^2*x^2)^(3/2)*Log[1 + c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",7,9,30,0.3000,1,"{4673, 669, 671, 641, 216, 4761, 627, 43, 4641}"
521,1,420,0,0.3940308,"\int \frac{(f-c f x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{(d+c d x)^{5/2}} \, dx","Int[((f - c*f*x)^(5/2)*(a + b*ArcSin[c*x]))/(d + c*d*x)^(5/2),x]","\frac{5 f^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{10 f^5 (1-c x)^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 f^5 (1-c x)^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{5 f^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b f^5 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{28 b f^5 \left(1-c^2 x^2\right)^{5/2} \log (c x+1)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{5 b f^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{5 f^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{10 f^5 (1-c x)^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 f^5 (1-c x)^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{5 f^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b f^5 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{28 b f^5 \left(1-c^2 x^2\right)^{5/2} \log (c x+1)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{5 b f^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"-((b*f^5*x*(1 - c^2*x^2)^(5/2))/((d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))) - (8*b*f^5*(1 - c^2*x^2)^(5/2))/(3*c*(1 + c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (5*b*f^5*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]^2)/(2*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (2*f^5*(1 - c*x)^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (10*f^5*(1 - c*x)^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (5*f^5*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (5*f^5*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (28*b*f^5*(1 - c^2*x^2)^(5/2)*Log[1 + c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",10,8,30,0.2667,1,"{4673, 669, 641, 216, 4761, 627, 43, 4641}"
522,1,345,0,0.5865569,"\int \frac{(d+c d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{f-c f x}} \, dx","Int[((d + c*d*x)^(5/2)*(a + b*ArcSin[c*x]))/Sqrt[f - c*f*x],x]","\frac{5 d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{c d^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{3 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{11 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b c^2 d^3 x^3 \sqrt{1-c^2 x^2}}{9 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{3 b c d^3 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{11 b d^3 x \sqrt{1-c^2 x^2}}{3 \sqrt{c d x+d} \sqrt{f-c f x}}","\frac{5 d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{c d^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{3 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{11 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b c^2 d^3 x^3 \sqrt{1-c^2 x^2}}{9 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{3 b c d^3 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{11 b d^3 x \sqrt{1-c^2 x^2}}{3 \sqrt{c d x+d} \sqrt{f-c f x}}",1,"(11*b*d^3*x*Sqrt[1 - c^2*x^2])/(3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (3*b*c*d^3*x^2*Sqrt[1 - c^2*x^2])/(4*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (b*c^2*d^3*x^3*Sqrt[1 - c^2*x^2])/(9*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (11*d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (3*d^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (c*d^3*x^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (5*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",13,7,30,0.2333,1,"{4673, 4763, 4641, 4677, 8, 4707, 30}"
523,1,242,0,0.4196266,"\int \frac{(d+c d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{f-c f x}} \, dx","Int[((d + c*d*x)^(3/2)*(a + b*ArcSin[c*x]))/Sqrt[f - c*f*x],x]","\frac{3 d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b c d^2 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{2 b d^2 x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}","\frac{3 d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{4 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b c d^2 x^2 \sqrt{1-c^2 x^2}}{4 \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{2 b d^2 x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}",1,"(2*b*d^2*x*Sqrt[1 - c^2*x^2])/(Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (b*c*d^2*x^2*Sqrt[1 - c^2*x^2])/(4*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (d^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (3*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(4*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",9,7,30,0.2333,1,"{4673, 4763, 4641, 4677, 8, 4707, 30}"
524,1,141,0,0.2575827,"\int \frac{\sqrt{d+c d x} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{f-c f x}} \, dx","Int[(Sqrt[d + c*d*x]*(a + b*ArcSin[c*x]))/Sqrt[f - c*f*x],x]","\frac{d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b d x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}","\frac{d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{c d x+d} \sqrt{f-c f x}}-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c \sqrt{c d x+d} \sqrt{f-c f x}}+\frac{b d x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{f-c f x}}",1,"(b*d*x*Sqrt[1 - c^2*x^2])/(Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) - (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x]) + (d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",6,5,30,0.1667,1,"{4673, 4763, 4641, 4677, 8}"
525,1,55,0,0.1440876,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d+c d x} \sqrt{f-c f x}} \, dx","Int[(a + b*ArcSin[c*x])/(Sqrt[d + c*d*x]*Sqrt[f - c*f*x]),x]","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{c d x+d} \sqrt{f-c f x}}","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c \sqrt{c d x+d} \sqrt{f-c f x}}",1,"(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(2*b*c*Sqrt[d + c*d*x]*Sqrt[f - c*f*x])","A",2,2,30,0.06667,1,"{4673, 4641}"
526,1,99,0,0.2133557,"\int \frac{a+b \sin ^{-1}(c x)}{(d+c d x)^{3/2} \sqrt{f-c f x}} \, dx","Int[(a + b*ArcSin[c*x])/((d + c*d*x)^(3/2)*Sqrt[f - c*f*x]),x]","\frac{b f \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{f (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}","\frac{b f \left(1-c^2 x^2\right)^{3/2} \log (c x+1)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{f (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"-((f*(1 - c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))) + (b*f*(1 - c^2*x^2)^(3/2)*Log[1 + c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",5,6,30,0.2000,1,"{4673, 637, 4761, 12, 627, 31}"
527,1,265,0,0.2999607,"\int \frac{a+b \sin ^{-1}(c x)}{(d+c d x)^{5/2} \sqrt{f-c f x}} \, dx","Int[(a + b*ArcSin[c*x])/((d + c*d*x)^(5/2)*Sqrt[f - c*f*x]),x]","\frac{f^2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 f^2 (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^2 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f^2 \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f^2 \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{f^2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 f^2 (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f^2 \left(1-c^2 x^2\right)^{5/2}}{3 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f^2 \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f^2 \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"-(b*f^2*(1 - c^2*x^2)^(5/2))/(3*c*(1 + c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (2*f^2*(1 - c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (f^2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*f^2*(1 - c^2*x^2)^(5/2)*ArcTanh[c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*f^2*(1 - c^2*x^2)^(5/2)*Log[1 - c^2*x^2])/(6*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",8,8,30,0.2667,1,"{4673, 653, 191, 4761, 627, 44, 207, 260}"
528,1,463,0,0.370384,"\int \frac{(d+c d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{(f-c f x)^{3/2}} \, dx","Int[((d + c*d*x)^(5/2)*(a + b*ArcSin[c*x]))/(f - c*f*x)^(3/2),x]","\frac{5 d^4 (c x+1) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{15 d^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 d^4 (c x+1)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{15 d^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b c d^4 x^2 \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{5 b d^4 (c x+1)^2 \left(1-c^2 x^2\right)^{3/2}}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{3 b d^4 x \left(1-c^2 x^2\right)^{3/2}}{2 (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{8 b d^4 \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{15 b d^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)^2}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}","\frac{5 d^4 (c x+1) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{15 d^4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 d^4 (c x+1)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{15 d^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b c d^4 x^2 \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{5 b d^4 (c x+1)^2 \left(1-c^2 x^2\right)^{3/2}}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{3 b d^4 x \left(1-c^2 x^2\right)^{3/2}}{2 (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{8 b d^4 \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{15 b d^4 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)^2}{4 c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(-3*b*d^4*x*(1 - c^2*x^2)^(3/2))/(2*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (b*c*d^4*x^2*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (5*b*d^4*(1 + c*x)^2*(1 - c^2*x^2)^(3/2))/(4*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (15*b*d^4*(1 - c^2*x^2)^(3/2)*ArcSin[c*x]^2)/(4*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (2*d^4*(1 + c*x)^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (15*d^4*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (5*d^4*(1 + c*x)*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (15*d^4*(1 - c^2*x^2)^(3/2)*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (8*b*d^4*(1 - c^2*x^2)^(3/2)*Log[1 - c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",7,9,30,0.3000,1,"{4673, 669, 671, 641, 216, 4761, 627, 43, 4641}"
529,1,252,0,0.4219525,"\int \frac{(d+c d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{(f-c f x)^{3/2}} \, dx","Int[((d + c*d*x)^(3/2)*(a + b*ArcSin[c*x]))/(f - c*f*x)^(3/2),x]","-\frac{3 d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{4 d^3 (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{b d^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{4 b d^3 \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}","-\frac{3 d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{4 d^3 (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}-\frac{b d^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{4 b d^3 \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"-((b*d^3*x*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))) + (4*d^3*(1 + c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (3*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(2*b*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (4*b*d^3*(1 - c^2*x^2)^(3/2)*Log[1 - c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",10,10,30,0.3333,1,"{4673, 4775, 637, 4761, 12, 627, 31, 4641, 4677, 8}"
530,1,162,0,0.3468512,"\int \frac{\sqrt{d+c d x} \left(a+b \sin ^{-1}(c x)\right)}{(f-c f x)^{3/2}} \, dx","Int[(Sqrt[d + c*d*x]*(a + b*ArcSin[c*x]))/(f - c*f*x)^(3/2),x]","-\frac{d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 d^2 (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}","-\frac{d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{2 b c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 d^2 (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(2*d^2*(1 + c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) - (d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(2*b*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (2*b*d^2*(1 - c^2*x^2)^(3/2)*Log[1 - c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",8,8,30,0.2667,1,"{4673, 4775, 637, 4761, 12, 627, 31, 4641}"
531,1,98,0,0.210481,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d+c d x} (f-c f x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(Sqrt[d + c*d*x]*(f - c*f*x)^(3/2)),x]","\frac{d (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b d \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}","\frac{d (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b d \left(1-c^2 x^2\right)^{3/2} \log (1-c x)}{c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(d*(1 + c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (b*d*(1 - c^2*x^2)^(3/2)*Log[1 - c*x])/(c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",5,6,30,0.2000,1,"{4673, 637, 4761, 12, 627, 31}"
532,1,96,0,0.1747144,"\int \frac{a+b \sin ^{-1}(c x)}{(d+c d x)^{3/2} (f-c f x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/((d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)),x]","\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b \left(1-c^2 x^2\right)^{3/2} \log \left(1-c^2 x^2\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}","\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{(c d x+d)^{3/2} (f-c f x)^{3/2}}+\frac{b \left(1-c^2 x^2\right)^{3/2} \log \left(1-c^2 x^2\right)}{2 c (c d x+d)^{3/2} (f-c f x)^{3/2}}",1,"(x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/((d + c*d*x)^(3/2)*(f - c*f*x)^(3/2)) + (b*(1 - c^2*x^2)^(3/2)*Log[1 - c^2*x^2])/(2*c*(d + c*d*x)^(3/2)*(f - c*f*x)^(3/2))","A",3,3,30,0.1000,1,"{4673, 4651, 260}"
533,1,255,0,0.2617789,"\int \frac{a+b \sin ^{-1}(c x)}{(d+c d x)^{5/2} (f-c f x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/((d + c*d*x)^(5/2)*(f - c*f*x)^(3/2)),x]","\frac{2 f x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{f (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f \left(1-c^2 x^2\right)^{5/2}}{6 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{2 f x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{f (1-c x) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b f \left(1-c^2 x^2\right)^{5/2}}{6 c (c x+1) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b f \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"-(b*f*(1 - c^2*x^2)^(5/2))/(6*c*(1 + c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (f*(1 - c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*f*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*f*(1 - c^2*x^2)^(5/2)*ArcTanh[c*x])/(6*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*f*(1 - c^2*x^2)^(5/2)*Log[1 - c^2*x^2])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",8,8,30,0.2667,1,"{4673, 639, 191, 4761, 627, 44, 207, 260}"
534,1,419,0,0.3798246,"\int \frac{(d+c d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{(f-c f x)^{5/2}} \, dx","Int[((d + c*d*x)^(5/2)*(a + b*ArcSin[c*x]))/(f - c*f*x)^(5/2),x]","-\frac{5 d^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{10 d^5 (c x+1)^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{2 d^5 (c x+1)^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{5 d^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b d^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b d^5 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{28 b d^5 \left(1-c^2 x^2\right)^{5/2} \log (1-c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{5 b d^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","-\frac{5 d^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{10 d^5 (c x+1)^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{2 d^5 (c x+1)^4 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{5 d^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b d^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b d^5 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{28 b d^5 \left(1-c^2 x^2\right)^{5/2} \log (1-c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{5 b d^5 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"(b*d^5*x*(1 - c^2*x^2)^(5/2))/((d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (8*b*d^5*(1 - c^2*x^2)^(5/2))/(3*c*(1 - c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (5*b*d^5*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]^2)/(2*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*d^5*(1 + c*x)^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (10*d^5*(1 + c*x)^2*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (5*d^5*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (5*d^5*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (28*b*d^5*(1 - c^2*x^2)^(5/2)*Log[1 - c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",10,8,30,0.2667,1,"{4673, 669, 641, 216, 4761, 627, 43, 4641}"
535,1,324,0,0.3410363,"\int \frac{(d+c d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{(f-c f x)^{5/2}} \, dx","Int[((d + c*d*x)^(3/2)*(a + b*ArcSin[c*x]))/(f - c*f*x)^(5/2),x]","-\frac{2 d^4 (c x+1) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{2 d^4 (c x+1)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{d^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{4 b d^4 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b d^4 \left(1-c^2 x^2\right)^{5/2} \log (1-c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","-\frac{2 d^4 (c x+1) \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{2 d^4 (c x+1)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{d^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{4 b d^4 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{8 b d^4 \left(1-c^2 x^2\right)^{5/2} \log (1-c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^4 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)^2}{2 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"(-4*b*d^4*(1 - c^2*x^2)^(5/2))/(3*c*(1 - c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (b*d^4*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]^2)/(2*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*d^4*(1 + c*x)^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (2*d^4*(1 + c*x)*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (d^4*(1 - c^2*x^2)^(5/2)*ArcSin[c*x]*(a + b*ArcSin[c*x]))/(c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (8*b*d^4*(1 - c^2*x^2)^(5/2)*Log[1 - c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",9,9,30,0.3000,1,"{4673, 669, 653, 216, 4761, 627, 43, 31, 4641}"
536,1,164,0,0.2560985,"\int \frac{\sqrt{d+c d x} \left(a+b \sin ^{-1}(c x)\right)}{(f-c f x)^{5/2}} \, dx","Int[(Sqrt[d + c*d*x]*(a + b*ArcSin[c*x]))/(f - c*f*x)^(5/2),x]","\frac{d^3 (c x+1)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^3 \left(1-c^2 x^2\right)^{5/2} \log (1-c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{d^3 (c x+1)^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^3 \left(1-c^2 x^2\right)^{5/2} \log (1-c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"(-2*b*d^3*(1 - c^2*x^2)^(5/2))/(3*c*(1 - c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (d^3*(1 + c*x)^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (b*d^3*(1 - c^2*x^2)^(5/2)*Log[1 - c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",6,6,30,0.2000,1,"{4673, 651, 4761, 12, 627, 43}"
537,1,265,0,0.2864077,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d+c d x} (f-c f x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(Sqrt[d + c*d*x]*(f - c*f*x)^(5/2)),x]","\frac{d^2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{2 d^2 (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^2 \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{d^2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{2 d^2 (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^2 \left(1-c^2 x^2\right)^{5/2}}{3 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b d^2 \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d^2 \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"-(b*d^2*(1 - c^2*x^2)^(5/2))/(3*c*(1 - c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*d^2*(1 + c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (d^2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (b*d^2*(1 - c^2*x^2)^(5/2)*ArcTanh[c*x])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*d^2*(1 - c^2*x^2)^(5/2)*Log[1 - c^2*x^2])/(6*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",8,8,30,0.2667,1,"{4673, 653, 191, 4761, 627, 44, 207, 260}"
538,1,255,0,0.2521464,"\int \frac{a+b \sin ^{-1}(c x)}{(d+c d x)^{3/2} (f-c f x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/((d + c*d*x)^(3/2)*(f - c*f*x)^(5/2)),x]","\frac{2 d x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{d (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d \left(1-c^2 x^2\right)^{5/2}}{6 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b d \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{2 d x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{d (c x+1) \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d \left(1-c^2 x^2\right)^{5/2}}{6 c (1-c x) (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b d \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b d \left(1-c^2 x^2\right)^{5/2} \tanh ^{-1}(c x)}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"-(b*d*(1 - c^2*x^2)^(5/2))/(6*c*(1 - c*x)*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (d*(1 + c*x)*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*d*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) - (b*d*(1 - c^2*x^2)^(5/2)*ArcTanh[c*x])/(6*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*d*(1 - c^2*x^2)^(5/2)*Log[1 - c^2*x^2])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",8,8,30,0.2667,1,"{4673, 639, 191, 4761, 627, 44, 207, 260}"
539,1,188,0,0.2020066,"\int \frac{a+b \sin ^{-1}(c x)}{(d+c d x)^{5/2} (f-c f x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/((d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)),x]","\frac{2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b \left(1-c^2 x^2\right)^{3/2}}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}","\frac{2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (f-c f x)^{5/2}}-\frac{b \left(1-c^2 x^2\right)^{3/2}}{6 c (c d x+d)^{5/2} (f-c f x)^{5/2}}+\frac{b \left(1-c^2 x^2\right)^{5/2} \log \left(1-c^2 x^2\right)}{3 c (c d x+d)^{5/2} (f-c f x)^{5/2}}",1,"-(b*(1 - c^2*x^2)^(3/2))/(6*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (x*(1 - c^2*x^2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2)) + (b*(1 - c^2*x^2)^(5/2)*Log[1 - c^2*x^2])/(3*c*(d + c*d*x)^(5/2)*(f - c*f*x)^(5/2))","A",5,5,30,0.1667,1,"{4673, 4655, 4651, 260, 261}"
540,1,613,0,1.0099747,"\int (d+c d x)^{5/2} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(5/2)*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2,x]","-\frac{b c^3 d^2 x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{1}{4} c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c d^2 x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{4 b d^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{5 d^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c \sqrt{1-c^2 x^2}}-\frac{2 d^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} d^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x}+\frac{4 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{15 b^2 d^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 d^2 x \sqrt{c d x+d} \sqrt{e-c e x}+\frac{8 b^2 d^2 \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}","-\frac{b c^3 d^2 x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{1}{4} c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c d^2 x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{4 b d^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{5 d^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c \sqrt{1-c^2 x^2}}-\frac{2 d^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} d^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 d^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x}+\frac{4 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{15 b^2 d^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 d^2 x \sqrt{c d x+d} \sqrt{e-c e x}+\frac{8 b^2 d^2 \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}",1,"(8*b^2*d^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(9*c) - (15*b^2*d^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/64 - (b^2*c^2*d^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/32 + (4*b^2*d^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/(27*c) + (15*b^2*d^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(64*c*Sqrt[1 - c^2*x^2]) + (4*b*d^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) - (3*b*c*d^2*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) - (4*b*c^2*d^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*x^4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (3*d^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/8 + (c^2*d^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/4 - (2*d^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c) + (5*d^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(24*b*c*Sqrt[1 - c^2*x^2])","A",23,13,32,0.4062,1,"{4673, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43, 4697, 4707}"
541,1,455,0,0.5710389,"\int (d+c d x)^{3/2} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(3/2)*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c^2 d x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{b c d x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{2 b d x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{d \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{d \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} d x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b^2 d \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{b^2 d \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 d x \sqrt{c d x+d} \sqrt{e-c e x}+\frac{4 b^2 d \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}","-\frac{2 b c^2 d x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{b c d x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{2 b d x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{d \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{d \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} d x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2 b^2 d \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{b^2 d \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 d x \sqrt{c d x+d} \sqrt{e-c e x}+\frac{4 b^2 d \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}",1,"(4*b^2*d*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(9*c) - (b^2*d*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/4 + (2*b^2*d*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/(27*c) + (b^2*d*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) + (2*b*d*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) - (b*c*d*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) - (2*b*c^2*d*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) + (d*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/2 - (d*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c) + (d*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2])","A",13,11,32,0.3438,1,"{4673, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43}"
542,1,222,0,0.2988647,"\int \sqrt{d+c d x} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2,x]","\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{b c x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 x \sqrt{c d x+d} \sqrt{e-c e x}","\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{b c x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 x \sqrt{c d x+d} \sqrt{e-c e x}",1,"-(b^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/4 + (b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) - (b*c*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + (x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/2 + (Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2])","A",6,6,32,0.1875,1,"{4673, 4647, 4641, 4627, 321, 216}"
543,1,230,0,0.4410297,"\int \frac{\sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x}} \, dx","Int[(Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/Sqrt[d + c*d*x],x]","-\frac{2 a b e x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{e \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 e \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 e x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{\sqrt{c d x+d} \sqrt{e-c e x}}","-\frac{2 a b e x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{e \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 e \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 e x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{\sqrt{c d x+d} \sqrt{e-c e x}}",1,"(-2*a*b*e*x*Sqrt[1 - c^2*x^2])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*b^2*e*(1 - c^2*x^2))/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*b^2*e*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (e*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (e*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",8,6,32,0.1875,1,"{4673, 4763, 4641, 4677, 4619, 261}"
544,1,530,0,0.9475747,"\int \frac{\sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2}} \, dx","Int[(Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/(d + c*d*x)^(3/2),x]","\frac{4 i b^2 e^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b^2 e^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i b^2 e^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 e^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 b e^2 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b e^2 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}","\frac{4 i b^2 e^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b^2 e^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i b^2 e^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 e^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 b e^2 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b e^2 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(-2*e^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*e^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((2*I)*e^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (e^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^3)/(3*b*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*b*e^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (4*b*e^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((4*I)*b^2*e^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*b^2*e^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((2*I)*b^2*e^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",19,13,32,0.4062,1,"{4673, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641}"
545,1,486,0,1.1189183,"\int \frac{\sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{5/2}} \, dx","Int[(Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/(d + c*d*x)^(5/2),x]","\frac{4 i b^2 e^3 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{i e^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b e^3 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^3 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b e^3 \left(1-c^2 x^2\right)^{5/2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{e^3 \left(1-c^2 x^2\right)^{5/2} \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) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b^2 e^3 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}","\frac{4 i b^2 e^3 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{i e^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b e^3 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^3 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b e^3 \left(1-c^2 x^2\right)^{5/2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{e^3 \left(1-c^2 x^2\right)^{5/2} \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) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b^2 e^3 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"((I/3)*e^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (4*b^2*e^3*(1 - c^2*x^2)^(5/2)*Cot[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (e^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*b*e^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (e^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2]*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (4*b*e^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 - I*E^(I*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((4*I)/3)*b^2*e^3*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",20,12,32,0.3750,1,"{4673, 4775, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
546,1,697,0,0.8004339,"\int (d+c d x)^{5/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(5/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2 b c^4 d x^5 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{25 \left(1-c^2 x^2\right)^{3/2}}-\frac{4 b c^2 d x^3 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{3 b c d x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 d x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}+\frac{2 b d x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 \left(1-c^2 x^2\right)^{3/2}}+\frac{d (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}-\frac{d \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c}+\frac{b d \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{1}{4} d x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 d x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}+\frac{2 b^2 d \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2}}{125 c}+\frac{16 b^2 d (c d x+d)^{3/2} (e-c e x)^{3/2}}{75 c \left(1-c^2 x^2\right)}+\frac{9 b^2 d (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 d x (c d x+d)^{3/2} (e-c e x)^{3/2}+\frac{8 b^2 d (c d x+d)^{3/2} (e-c e x)^{3/2}}{225 c}","\frac{2 b c^4 d x^5 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{25 \left(1-c^2 x^2\right)^{3/2}}-\frac{4 b c^2 d x^3 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{3 b c d x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 d x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}+\frac{2 b d x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 \left(1-c^2 x^2\right)^{3/2}}+\frac{d (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}-\frac{d \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c}+\frac{b d \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{1}{4} d x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 d x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}+\frac{2 b^2 d \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2}}{125 c}+\frac{16 b^2 d (c d x+d)^{3/2} (e-c e x)^{3/2}}{75 c \left(1-c^2 x^2\right)}+\frac{9 b^2 d (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 d x (c d x+d)^{3/2} (e-c e x)^{3/2}+\frac{8 b^2 d (c d x+d)^{3/2} (e-c e x)^{3/2}}{225 c}",1,"(8*b^2*d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(225*c) - (b^2*d*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/32 + (16*b^2*d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(75*c*(1 - c^2*x^2)) - (15*b^2*d*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(64*(1 - c^2*x^2)) + (2*b^2*d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(1 - c^2*x^2))/(125*c) + (9*b^2*d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*ArcSin[c*x])/(64*c*(1 - c^2*x^2)^(3/2)) + (2*b*d*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(5*(1 - c^2*x^2)^(3/2)) - (3*b*c*d*x^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)^(3/2)) - (4*b*c^2*d*x^3*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(15*(1 - c^2*x^2)^(3/2)) + (2*b*c^4*d*x^5*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(25*(1 - c^2*x^2)^(3/2)) + (b*d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (d*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/4 + (3*d*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(8*(1 - c^2*x^2)) - (d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(5*c) + (d*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^3)/(8*b*c*(1 - c^2*x^2)^(3/2))","A",19,15,32,0.4688,1,"{4673, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1247, 698}"
547,1,362,0,0.4308855,"\int (d+c d x)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{(c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{3 x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}-\frac{3 b c x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{1}{4} x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}+\frac{9 b^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}","\frac{(c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{3 x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}-\frac{3 b c x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{1}{4} x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}+\frac{9 b^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}",1,"-(b^2*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/32 - (15*b^2*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(64*(1 - c^2*x^2)) + (9*b^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*ArcSin[c*x])/(64*c*(1 - c^2*x^2)^(3/2)) - (3*b*c*x^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)^(3/2)) + (b*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/4 + (3*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(8*(1 - c^2*x^2)) + ((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^3)/(8*b*c*(1 - c^2*x^2)^(3/2))","A",11,9,32,0.2812,1,"{4673, 4649, 4647, 4641, 4627, 321, 216, 4677, 195}"
548,1,455,0,0.5918052,"\int \sqrt{d+c d x} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + c*d*x]*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2 b c^2 e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{b c e x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}-\frac{2 b e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}+\frac{e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b^2 e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{b^2 e \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 e x \sqrt{c d x+d} \sqrt{e-c e x}-\frac{4 b^2 e \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}","\frac{2 b c^2 e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{b c e x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}-\frac{2 b e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}+\frac{e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b^2 e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{b^2 e \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 e x \sqrt{c d x+d} \sqrt{e-c e x}-\frac{4 b^2 e \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}",1,"(-4*b^2*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(9*c) - (b^2*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/4 - (2*b^2*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/(27*c) + (b^2*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) - (2*b*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) - (b*c*e*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + (2*b*c^2*e*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) + (e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/2 + (e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c) + (e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2])","A",13,11,32,0.3438,1,"{4673, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43}"
549,1,398,0,0.5775014,"\int \frac{(e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x}} \, dx","Int[((e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/Sqrt[d + c*d*x],x]","\frac{e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{e^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b c e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{4 b e^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{4 b^2 e^2 \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b^2 e^2 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{b^2 e^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{e^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b c e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{4 b e^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{4 b^2 e^2 \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b^2 e^2 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{b^2 e^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(-4*b^2*e^2*(1 - c^2*x^2))/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (b^2*e^2*x*(1 - c^2*x^2))/(4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (b^2*e^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (4*b*e^2*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (b*c*e^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*e^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (e^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (e^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(2*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",11,9,32,0.2812,1,"{4673, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8}"
550,1,714,0,1.0848483,"\int \frac{(e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2}} \, dx","Int[((e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(d + c*d*x)^(3/2),x]","\frac{8 i b^2 e^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b^2 e^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b^2 e^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 a b e^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{b c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i e^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 e^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 e^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b e^3 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{16 i b e^3 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b^2 e^3 \left(1-c^2 x^2\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b^2 e^3 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)}{(c d x+d)^{3/2} (e-c e x)^{3/2}}","\frac{8 i b^2 e^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b^2 e^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b^2 e^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 a b e^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{b c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i e^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 e^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 e^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b e^3 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{16 i b e^3 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b^2 e^3 \left(1-c^2 x^2\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b^2 e^3 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)}{(c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(2*a*b*e^3*x*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*b^2*e^3*(1 - c^2*x^2)^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*b^2*e^3*x*(1 - c^2*x^2)^(3/2)*ArcSin[c*x])/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (4*e^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (4*e^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*e^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (e^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (e^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^3)/(b*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((16*I)*b*e^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*b*e^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((8*I)*b^2*e^3*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*b^2*e^3*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*b^2*e^3*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",23,15,32,0.4688,1,"{4673, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641, 4619, 261}"
551,1,544,0,1.1542614,"\int \frac{(e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{5/2}} \, dx","Int[((e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(d + c*d*x)^(5/2),x]","\frac{32 i b^2 e^4 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{8 i e^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{32 b e^4 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{8 e^4 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b e^4 \left(1-c^2 x^2\right)^{5/2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 e^4 \left(1-c^2 x^2\right)^{5/2} \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) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 b^2 e^4 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}","\frac{32 i b^2 e^4 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{8 i e^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{32 b e^4 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{8 e^4 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b e^4 \left(1-c^2 x^2\right)^{5/2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 e^4 \left(1-c^2 x^2\right)^{5/2} \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) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 b^2 e^4 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"(((8*I)/3)*e^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (e^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^3)/(3*b*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (8*b^2*e^4*(1 - c^2*x^2)^(5/2)*Cot[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (8*e^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (4*b*e^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*e^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2]*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (32*b*e^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 - I*E^(I*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((32*I)/3)*b^2*e^4*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",21,13,32,0.4062,1,"{4673, 4775, 4641, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
552,1,502,0,0.5678988,"\int (d+c d x)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2,x]","\frac{5 (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \left(1-c^2 x^2\right)^{5/2}}+\frac{5 x (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{24 \left(1-c^2 x^2\right)}+\frac{5 x (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 \left(1-c^2 x^2\right)^2}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{48 c \sqrt{1-c^2 x^2}}-\frac{5 b c x^2 (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{16 \left(1-c^2 x^2\right)^{5/2}}+\frac{1}{6} x (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{65 b^2 x (c d x+d)^{5/2} (e-c e x)^{5/2}}{1728 \left(1-c^2 x^2\right)}-\frac{245 b^2 x (c d x+d)^{5/2} (e-c e x)^{5/2}}{1152 \left(1-c^2 x^2\right)^2}+\frac{115 b^2 (c d x+d)^{5/2} (e-c e x)^{5/2} \sin ^{-1}(c x)}{1152 c \left(1-c^2 x^2\right)^{5/2}}-\frac{1}{108} b^2 x (c d x+d)^{5/2} (e-c e x)^{5/2}","\frac{5 (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c \left(1-c^2 x^2\right)^{5/2}}+\frac{5 x (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{24 \left(1-c^2 x^2\right)}+\frac{5 x (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{16 \left(1-c^2 x^2\right)^2}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{18 c}+\frac{5 b (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{48 c \sqrt{1-c^2 x^2}}-\frac{5 b c x^2 (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)}{16 \left(1-c^2 x^2\right)^{5/2}}+\frac{1}{6} x (c d x+d)^{5/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{65 b^2 x (c d x+d)^{5/2} (e-c e x)^{5/2}}{1728 \left(1-c^2 x^2\right)}-\frac{245 b^2 x (c d x+d)^{5/2} (e-c e x)^{5/2}}{1152 \left(1-c^2 x^2\right)^2}+\frac{115 b^2 (c d x+d)^{5/2} (e-c e x)^{5/2} \sin ^{-1}(c x)}{1152 c \left(1-c^2 x^2\right)^{5/2}}-\frac{1}{108} b^2 x (c d x+d)^{5/2} (e-c e x)^{5/2}",1,"-(b^2*x*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))/108 - (245*b^2*x*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))/(1152*(1 - c^2*x^2)^2) - (65*b^2*x*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))/(1728*(1 - c^2*x^2)) + (115*b^2*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*ArcSin[c*x])/(1152*c*(1 - c^2*x^2)^(5/2)) - (5*b*c*x^2*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x]))/(16*(1 - c^2*x^2)^(5/2)) + (5*b*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x]))/(48*c*Sqrt[1 - c^2*x^2]) + (b*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(18*c) + (x*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2)/6 + (5*x*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(16*(1 - c^2*x^2)^2) + (5*x*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(24*(1 - c^2*x^2)) + (5*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^3)/(48*b*c*(1 - c^2*x^2)^(5/2))","A",17,9,32,0.2812,1,"{4673, 4649, 4647, 4641, 4627, 321, 216, 4677, 195}"
553,1,697,0,0.7936761,"\int (d+c d x)^{3/2} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(3/2)*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c^4 e x^5 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{25 \left(1-c^2 x^2\right)^{3/2}}+\frac{4 b c^2 e x^3 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{3 b c e x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 e x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}-\frac{2 b e x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 \left(1-c^2 x^2\right)^{3/2}}+\frac{e (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{e \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c}+\frac{b e \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{1}{4} e x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 e x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}-\frac{2 b^2 e \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2}}{125 c}-\frac{16 b^2 e (c d x+d)^{3/2} (e-c e x)^{3/2}}{75 c \left(1-c^2 x^2\right)}+\frac{9 b^2 e (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 e x (c d x+d)^{3/2} (e-c e x)^{3/2}-\frac{8 b^2 e (c d x+d)^{3/2} (e-c e x)^{3/2}}{225 c}","-\frac{2 b c^4 e x^5 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{25 \left(1-c^2 x^2\right)^{3/2}}+\frac{4 b c^2 e x^3 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{15 \left(1-c^2 x^2\right)^{3/2}}-\frac{3 b c e x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{3 e x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}-\frac{2 b e x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{5 \left(1-c^2 x^2\right)^{3/2}}+\frac{e (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{e \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c}+\frac{b e \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}+\frac{1}{4} e x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 e x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}-\frac{2 b^2 e \left(1-c^2 x^2\right) (c d x+d)^{3/2} (e-c e x)^{3/2}}{125 c}-\frac{16 b^2 e (c d x+d)^{3/2} (e-c e x)^{3/2}}{75 c \left(1-c^2 x^2\right)}+\frac{9 b^2 e (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 e x (c d x+d)^{3/2} (e-c e x)^{3/2}-\frac{8 b^2 e (c d x+d)^{3/2} (e-c e x)^{3/2}}{225 c}",1,"(-8*b^2*e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(225*c) - (b^2*e*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/32 - (16*b^2*e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(75*c*(1 - c^2*x^2)) - (15*b^2*e*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(64*(1 - c^2*x^2)) - (2*b^2*e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(1 - c^2*x^2))/(125*c) + (9*b^2*e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*ArcSin[c*x])/(64*c*(1 - c^2*x^2)^(3/2)) - (2*b*e*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(5*(1 - c^2*x^2)^(3/2)) - (3*b*c*e*x^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)^(3/2)) + (4*b*c^2*e*x^3*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(15*(1 - c^2*x^2)^(3/2)) - (2*b*c^4*e*x^5*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(25*(1 - c^2*x^2)^(3/2)) + (b*e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (e*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/4 + (3*e*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(8*(1 - c^2*x^2)) + (e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(5*c) + (e*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^3)/(8*b*c*(1 - c^2*x^2)^(3/2))","A",19,15,32,0.4688,1,"{4673, 4763, 4649, 4647, 4641, 4627, 321, 216, 4677, 195, 194, 4645, 12, 1247, 698}"
554,1,613,0,1.0034491,"\int \sqrt{d+c d x} (e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + c*d*x]*(e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2,x]","-\frac{b c^3 e^2 x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{1}{4} c^2 e^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4 b c^2 e^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c e^2 x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}-\frac{4 b e^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{5 e^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c \sqrt{1-c^2 x^2}}+\frac{2 e^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} e^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 e^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x}-\frac{4 b^2 e^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{15 b^2 e^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 e^2 x \sqrt{c d x+d} \sqrt{e-c e x}-\frac{8 b^2 e^2 \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}","-\frac{b c^3 e^2 x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{1}{4} c^2 e^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{4 b c^2 e^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{3 b c e^2 x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}-\frac{4 b e^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{5 e^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c \sqrt{1-c^2 x^2}}+\frac{2 e^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} e^2 x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 e^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x}-\frac{4 b^2 e^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c}+\frac{15 b^2 e^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{64 c \sqrt{1-c^2 x^2}}-\frac{15}{64} b^2 e^2 x \sqrt{c d x+d} \sqrt{e-c e x}-\frac{8 b^2 e^2 \sqrt{c d x+d} \sqrt{e-c e x}}{9 c}",1,"(-8*b^2*e^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(9*c) - (15*b^2*e^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/64 - (b^2*c^2*e^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/32 - (4*b^2*e^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/(27*c) + (15*b^2*e^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(64*c*Sqrt[1 - c^2*x^2]) - (4*b*e^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) - (3*b*c*e^2*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (4*b*c^2*e^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) - (b*c^3*e^2*x^4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) + (3*e^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/8 + (c^2*e^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/4 + (2*e^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c) + (5*e^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(24*b*c*Sqrt[1 - c^2*x^2])","A",23,13,32,0.4062,1,"{4673, 4763, 4647, 4641, 4627, 321, 216, 4677, 4645, 444, 43, 4697, 4707}"
555,1,559,0,0.6875534,"\int \frac{(e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x}} \, dx","Int[((e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2)/Sqrt[d + c*d*x],x]","\frac{5 e^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{c e^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 e^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{11 e^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b c^2 e^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b c e^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{22 b e^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 e^3 \left(1-c^2 x^2\right)^2}{27 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b^2 e^3 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{68 b^2 e^3 \left(1-c^2 x^2\right)}{9 c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 b^2 e^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{5 e^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{c e^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 e^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{11 e^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b c^2 e^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b c e^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{22 b e^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 e^3 \left(1-c^2 x^2\right)^2}{27 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b^2 e^3 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{68 b^2 e^3 \left(1-c^2 x^2\right)}{9 c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 b^2 e^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(-68*b^2*e^3*(1 - c^2*x^2))/(9*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (3*b^2*e^3*x*(1 - c^2*x^2))/(4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*e^3*(1 - c^2*x^2)^2)/(27*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (3*b^2*e^3*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (22*b*e^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (3*b*c*e^3*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*b*c^2*e^3*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (11*e^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (3*e^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (c*e^3*x^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (5*e^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",17,10,32,0.3125,1,"{4673, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8, 2633}"
556,1,918,0,1.2725664,"\int \frac{(e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2}} \, dx","Int[((e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(d + c*d*x)^(3/2),x]","-\frac{5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 e^4}{2 b c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b^2 x \left(1-c^2 x^2\right)^2 e^4}{4 (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b^2 \left(1-c^2 x^2\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 a b x \left(1-c^2 x^2\right)^{3/2} e^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b^2 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) e^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{b^2 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) e^4}{4 c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b c x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) e^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{32 i b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}","-\frac{5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 e^4}{2 b c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b^2 x \left(1-c^2 x^2\right)^2 e^4}{4 (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b^2 \left(1-c^2 x^2\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 a b x \left(1-c^2 x^2\right)^{3/2} e^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b^2 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) e^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{b^2 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) e^4}{4 c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b c x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) e^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{32 i b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) e^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}",1,"(8*a*b*e^4*x*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*b^2*e^4*(1 - c^2*x^2)^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (b^2*e^4*x*(1 - c^2*x^2)^2)/(4*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (b^2*e^4*(1 - c^2*x^2)^(3/2)*ArcSin[c*x])/(4*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*b^2*e^4*x*(1 - c^2*x^2)^(3/2)*ArcSin[c*x])/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (b*c*e^4*x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (8*e^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*e^4*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*e^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (4*e^4*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (e^4*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (5*e^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^3)/(2*b*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((32*I)*b*e^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (16*b*e^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((16*I)*b^2*e^4*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((16*I)*b^2*e^4*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*b^2*e^4*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",28,19,32,0.5938,1,"{4673, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641, 4619, 261, 4707, 4627, 321, 216}"
557,1,729,0,1.3032133,"\int \frac{(e-c e x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{5/2}} \, dx","Int[((e - c*e*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(d + c*d*x)^(5/2),x]","\frac{112 i b^2 e^5 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 a b e^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{5 e^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{28 i e^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{112 b e^5 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{28 e^5 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 b e^5 \left(1-c^2 x^2\right)^{5/2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 e^5 \left(1-c^2 x^2\right)^{5/2} \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) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b^2 e^5 \left(1-c^2 x^2\right)^3}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b^2 e^5 x \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{(c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{16 b^2 e^5 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}","\frac{112 i b^2 e^5 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 a b e^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{5 e^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{28 i e^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{112 b e^5 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{28 e^5 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 b e^5 \left(1-c^2 x^2\right)^{5/2} \csc ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 e^5 \left(1-c^2 x^2\right)^{5/2} \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) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b^2 e^5 \left(1-c^2 x^2\right)^3}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b^2 e^5 x \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{(c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{16 b^2 e^5 \left(1-c^2 x^2\right)^{5/2} \cot \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"(-2*a*b*e^5*x*(1 - c^2*x^2)^(5/2))/((d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*b^2*e^5*(1 - c^2*x^2)^3)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*b^2*e^5*x*(1 - c^2*x^2)^(5/2)*ArcSin[c*x])/((d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((28*I)/3)*e^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (e^5*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (5*e^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^3)/(3*b*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (16*b^2*e^5*(1 - c^2*x^2)^(5/2)*Cot[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (28*e^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (8*b*e^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (4*e^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Cot[Pi/4 + ArcSin[c*x]/2]*Csc[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (112*b*e^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 - I*E^(I*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((112*I)/3)*b^2*e^5*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",25,16,32,0.5000,1,"{4673, 4775, 4641, 4677, 4619, 261, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
558,1,559,0,0.659786,"\int \frac{(d+c d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{e-c e x}} \, dx","Int[((d + c*d*x)^(5/2)*(a + b*ArcSin[c*x])^2)/Sqrt[e - c*e*x],x]","\frac{5 d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{c d^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{11 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b c^2 d^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b c d^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{22 b d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 d^3 \left(1-c^2 x^2\right)^2}{27 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b^2 d^3 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{68 b^2 d^3 \left(1-c^2 x^2\right)}{9 c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 b^2 d^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{5 d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{c d^3 x^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{11 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b c^2 d^3 x^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b c d^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{22 b d^3 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 d^3 \left(1-c^2 x^2\right)^2}{27 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{3 b^2 d^3 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{68 b^2 d^3 \left(1-c^2 x^2\right)}{9 c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{3 b^2 d^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(68*b^2*d^3*(1 - c^2*x^2))/(9*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (3*b^2*d^3*x*(1 - c^2*x^2))/(4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*b^2*d^3*(1 - c^2*x^2)^2)/(27*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (3*b^2*d^3*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (22*b*d^3*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (3*b*c*d^3*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b*c^2*d^3*x^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (11*d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (3*d^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (c*d^3*x^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (5*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",17,10,32,0.3125,1,"{4673, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8, 2633}"
559,1,398,0,0.5620528,"\int \frac{(d+c d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{e-c e x}} \, dx","Int[((d + c*d*x)^(3/2)*(a + b*ArcSin[c*x])^2)/Sqrt[e - c*e*x],x]","\frac{d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b c d^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 b d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 b^2 d^2 \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b^2 d^2 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{b^2 d^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b c d^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 b d^2 x \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 b^2 d^2 \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b^2 d^2 x \left(1-c^2 x^2\right)}{4 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{b^2 d^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(4*b^2*d^2*(1 - c^2*x^2))/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (b^2*d^2*x*(1 - c^2*x^2))/(4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (b^2*d^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (4*b*d^2*x*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (b*c*d^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (d^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(2*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",11,9,32,0.2812,1,"{4673, 4773, 3317, 3296, 2638, 3311, 32, 2635, 8}"
560,1,231,0,0.4416453,"\int \frac{\sqrt{d+c d x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{e-c e x}} \, dx","Int[(Sqrt[d + c*d*x]*(a + b*ArcSin[c*x])^2)/Sqrt[e - c*e*x],x]","\frac{2 a b d x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 d \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 d x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{\sqrt{c d x+d} \sqrt{e-c e x}}","\frac{2 a b d x \sqrt{1-c^2 x^2}}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 d \left(1-c^2 x^2\right)}{c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 d x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{\sqrt{c d x+d} \sqrt{e-c e x}}",1,"(2*a*b*d*x*Sqrt[1 - c^2*x^2])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*d*(1 - c^2*x^2))/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*d*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",8,6,32,0.1875,1,"{4673, 4763, 4641, 4677, 4619, 261}"
561,1,55,0,0.2375056,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x} \sqrt{e-c e x}} \, dx","Int[(a + b*ArcSin[c*x])^2/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]),x]","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",2,2,32,0.06250,1,"{4673, 4641}"
562,1,455,0,0.6718819,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2} \sqrt{e-c e x}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(3/2)*Sqrt[e - c*e*x]),x]","\frac{2 i b^2 e \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i b^2 e \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i b^2 e \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i e \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{e x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b e \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b e \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}","\frac{2 i b^2 e \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i b^2 e \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i b^2 e \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i e \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{e \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{e x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b e \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b e \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"-((e*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))) + (e*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*e*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*b*e*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*b*e*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((2*I)*b^2*e*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((2*I)*b^2*e*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*b^2*e*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",16,11,32,0.3438,1,"{4673, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181}"
563,1,896,0,1.2392966,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{5/2} \sqrt{e-c e x}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(5/2)*Sqrt[e - c*e*x]),x]","\frac{c^2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^3}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b c e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x^2}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 e^2 \left(1-c^2 x^2\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 e^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b^2 e^2 \left(1-c^2 x^2\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i e^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 i b e^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b e^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 i b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}","\frac{c^2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^3}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b c e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x^2}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 e^2 \left(1-c^2 x^2\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 e^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b^2 e^2 \left(1-c^2 x^2\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i e^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 e^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b e^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 i b e^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b e^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 i b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i b^2 e^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}",1,"(-2*b^2*e^2*(1 - c^2*x^2)^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b^2*e^2*x*(1 - c^2*x^2)^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b^2*e^2*(1 - c^2*x^2)^(5/2)*ArcSin[c*x])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*e^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b*e^2*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*c*e^2*x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*e^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (e^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (c^2*e^2*x^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*e^2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - ((I/3)*e^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((4*I)/3)*b*e^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b*e^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((2*I)/3)*b^2*e^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*b^2*e^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - ((I/3)*b^2*e^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",30,18,32,0.5625,1,"{4673, 4763, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4657, 4181, 261, 4681, 4703, 288, 216}"
564,1,918,0,1.2751875,"\int \frac{(d+c d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(e-c e x)^{3/2}} \, dx","Int[((d + c*d*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(e - c*e*x)^(3/2),x]","-\frac{5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 d^4}{2 b c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b^2 x \left(1-c^2 x^2\right)^2 d^4}{4 (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 b^2 \left(1-c^2 x^2\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 a b x \left(1-c^2 x^2\right)^{3/2} d^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 b^2 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) d^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{b^2 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) d^4}{4 c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b c x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) d^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{32 i b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}","-\frac{5 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3 d^4}{2 b c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b^2 x \left(1-c^2 x^2\right)^2 d^4}{4 (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 b^2 \left(1-c^2 x^2\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 a b x \left(1-c^2 x^2\right)^{3/2} d^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 b^2 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) d^4}{(c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{b^2 \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x) d^4}{4 c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{b c x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) d^4}{2 (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{32 i b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}-\frac{8 i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right) d^4}{c (c x d+d)^{3/2} (e-c e x)^{3/2}}",1,"(-8*a*b*d^4*x*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (8*b^2*d^4*(1 - c^2*x^2)^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (b^2*d^4*x*(1 - c^2*x^2)^2)/(4*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (b^2*d^4*(1 - c^2*x^2)^(3/2)*ArcSin[c*x])/(4*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (8*b^2*d^4*x*(1 - c^2*x^2)^(3/2)*ArcSin[c*x])/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (b*c*d^4*x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*d^4*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*d^4*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*d^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (4*d^4*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (d^4*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (5*d^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^3)/(2*b*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((32*I)*b*d^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (16*b*d^4*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((16*I)*b^2*d^4*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((16*I)*b^2*d^4*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*b^2*d^4*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",28,19,32,0.5938,1,"{4673, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641, 4619, 261, 4707, 4627, 321, 216}"
565,1,713,0,1.0494672,"\int \frac{(d+c d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(e-c e x)^{3/2}} \, dx","Int[((d + c*d*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(e - c*e*x)^(3/2),x]","-\frac{8 i b^2 d^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 i b^2 d^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b^2 d^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 a b d^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{b c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 i b d^3 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 b^2 d^3 \left(1-c^2 x^2\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 b^2 d^3 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)}{(c d x+d)^{3/2} (e-c e x)^{3/2}}","-\frac{8 i b^2 d^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 i b^2 d^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i b^2 d^3 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 a b d^3 x \left(1-c^2 x^2\right)^{3/2}}{(c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{b c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{d^3 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{4 i d^3 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 d^3 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 d^3 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 b d^3 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{16 i b d^3 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 b^2 d^3 \left(1-c^2 x^2\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 b^2 d^3 x \left(1-c^2 x^2\right)^{3/2} \sin ^{-1}(c x)}{(c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(-2*a*b*d^3*x*(1 - c^2*x^2)^(3/2))/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (2*b^2*d^3*(1 - c^2*x^2)^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (2*b^2*d^3*x*(1 - c^2*x^2)^(3/2)*ArcSin[c*x])/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (4*d^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (4*d^3*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (d^3*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^3)/(b*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((16*I)*b*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (8*b*d^3*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((8*I)*b^2*d^3*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((8*I)*b^2*d^3*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*b^2*d^3*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",23,15,32,0.4688,1,"{4673, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641, 4619, 261}"
566,1,530,0,0.9089539,"\int \frac{\sqrt{d+c d x} \left(a+b \sin ^{-1}(c x)\right)^2}{(e-c e x)^{3/2}} \, dx","Int[(Sqrt[d + c*d*x]*(a + b*ArcSin[c*x])^2)/(e - c*e*x)^(3/2),x]","-\frac{4 i b^2 d^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 i b^2 d^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i b^2 d^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 i b d^2 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}","-\frac{4 i b^2 d^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 i b^2 d^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i b^2 d^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{2 i d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 d^2 x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 b d^2 \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{8 i b d^2 \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*d^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((2*I)*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^3)/(3*b*c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((8*I)*b*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (4*b*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((4*I)*b^2*d^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((4*I)*b^2*d^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((2*I)*b^2*d^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",19,13,32,0.4062,1,"{4673, 4775, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181, 4641}"
567,1,454,0,0.6593878,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x} (e-c e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(Sqrt[d + c*d*x]*(e - c*e*x)^(3/2)),x]","-\frac{2 i b^2 d \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 i b^2 d \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i b^2 d \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{d x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 i b d \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}","-\frac{2 i b^2 d \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 i b^2 d \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i b^2 d \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{d x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b d \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{4 i b d \left(1-c^2 x^2\right)^{3/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (d*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((4*I)*b*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*b*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - ((2*I)*b^2*d*(1 - c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + ((2*I)*b^2*d*(1 - c^2*x^2)^(3/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*b^2*d*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",16,11,32,0.3438,1,"{4673, 4763, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 4657, 4181}"
568,1,217,0,0.3772337,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2} (e-c e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)),x]","-\frac{i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}","-\frac{i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*b*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*b^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",7,7,32,0.2188,1,"{4673, 4651, 4675, 3719, 2190, 2279, 2391}"
569,1,709,0,0.8393333,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{5/2} (e-c e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(5/2)*(e - c*e*x)^(3/2)),x]","\frac{i b^2 e \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{i b^2 e \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 e \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i e \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 e x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b e \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b e x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{e \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b e \left(1-c^2 x^2\right)^{5/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b e \left(1-c^2 x^2\right)^{5/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b^2 e \left(1-c^2 x^2\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 e x \left(1-c^2 x^2\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}","\frac{i b^2 e \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{i b^2 e \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 e \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i e \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 e x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b e \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b e x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{e \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{e x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b e \left(1-c^2 x^2\right)^{5/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b e \left(1-c^2 x^2\right)^{5/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b^2 e \left(1-c^2 x^2\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 e x \left(1-c^2 x^2\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"-(b^2*e*(1 - c^2*x^2)^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (b^2*e*x*(1 - c^2*x^2)^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*e*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (b*e*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (e*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (e*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*e*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*e*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*b*e*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (4*b*e*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + ((I/3)*b^2*e*(1 - c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - ((I/3)*b^2*e*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*b^2*e*(1 - c^2*x^2)^(5/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",21,14,32,0.4375,1,"{4673, 4763, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4657, 4181, 261}"
570,1,730,0,1.2914794,"\int \frac{(d+c d x)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(e-c e x)^{5/2}} \, dx","Int[((d + c*d*x)^(5/2)*(a + b*ArcSin[c*x])^2)/(e - c*e*x)^(5/2),x]","-\frac{112 i b^2 d^5 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 a b d^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{5 d^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{d^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{28 i d^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{112 b d^5 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{28 d^5 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 b d^5 \left(1-c^2 x^2\right)^{5/2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 d^5 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^5 \left(1-c^2 x^2\right)^3}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^5 x \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{(c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{16 b^2 d^5 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}","-\frac{112 i b^2 d^5 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 a b d^5 x \left(1-c^2 x^2\right)^{5/2}}{(c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{5 d^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{d^5 \left(1-c^2 x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{28 i d^5 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{112 b d^5 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{28 d^5 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 b d^5 \left(1-c^2 x^2\right)^{5/2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 d^5 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^5 \left(1-c^2 x^2\right)^3}{c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^5 x \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{(c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{16 b^2 d^5 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"(2*a*b*d^5*x*(1 - c^2*x^2)^(5/2))/((d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b^2*d^5*(1 - c^2*x^2)^3)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b^2*d^5*x*(1 - c^2*x^2)^(5/2)*ArcSin[c*x])/((d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((28*I)/3)*d^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (d^5*(1 - c^2*x^2)^3*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (5*d^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^3)/(3*b*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (112*b*d^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 - I/E^(I*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((112*I)/3)*b^2*d^5*(1 - c^2*x^2)^(5/2)*PolyLog[2, I/E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (8*b*d^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Sec[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (16*b^2*d^5*(1 - c^2*x^2)^(5/2)*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (28*d^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (4*d^5*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Sec[Pi/4 + ArcSin[c*x]/2]^2*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",25,16,32,0.5000,1,"{4673, 4775, 4641, 4677, 4619, 261, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
571,1,544,0,1.1445552,"\int \frac{(d+c d x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{(e-c e x)^{5/2}} \, dx","Int[((d + c*d*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(e - c*e*x)^(5/2),x]","-\frac{32 i b^2 d^4 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 i d^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{32 b d^4 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 d^4 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b d^4 \left(1-c^2 x^2\right)^{5/2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d^4 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{8 b^2 d^4 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}","-\frac{32 i b^2 d^4 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 i d^4 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{32 b d^4 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{8 d^4 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b d^4 \left(1-c^2 x^2\right)^{5/2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d^4 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{8 b^2 d^4 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"(((-8*I)/3)*d^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (d^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^3)/(3*b*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (32*b*d^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 - I/E^(I*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((32*I)/3)*b^2*d^4*(1 - c^2*x^2)^(5/2)*PolyLog[2, I/E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (4*b*d^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Sec[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (8*b^2*d^4*(1 - c^2*x^2)^(5/2)*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (8*d^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*d^4*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Sec[Pi/4 + ArcSin[c*x]/2]^2*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",21,13,32,0.4062,1,"{4673, 4775, 4641, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
572,1,486,0,1.0697777,"\int \frac{\sqrt{d+c d x} \left(a+b \sin ^{-1}(c x)\right)^2}{(e-c e x)^{5/2}} \, dx","Int[(Sqrt[d + c*d*x]*(a + b*ArcSin[c*x])^2)/(e - c*e*x)^(5/2),x]","-\frac{4 i b^2 d^3 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{i d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b d^3 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{d^3 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d^3 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b^2 d^3 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}","-\frac{4 i b^2 d^3 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{-i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{i d^3 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{4 b d^3 \left(1-c^2 x^2\right)^{5/2} \log \left(1-i e^{-i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{d^3 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b d^3 \left(1-c^2 x^2\right)^{5/2} \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d^3 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \sec ^2\left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b^2 d^3 \left(1-c^2 x^2\right)^{5/2} \tan \left(\frac{1}{2} \sin ^{-1}(c x)+\frac{\pi }{4}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"((-I/3)*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (4*b*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 - I/E^(I*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((4*I)/3)*b^2*d^3*(1 - c^2*x^2)^(5/2)*PolyLog[2, I/E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*b*d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Sec[Pi/4 + ArcSin[c*x]/2]^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (4*b^2*d^3*(1 - c^2*x^2)^(5/2)*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (d^3*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2*Sec[Pi/4 + ArcSin[c*x]/2]^2*Tan[Pi/4 + ArcSin[c*x]/2])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",20,12,32,0.3750,1,"{4673, 4775, 4773, 3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
573,1,896,0,1.2307395,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x} (e-c e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(Sqrt[d + c*d*x]*(e - c*e*x)^(5/2)),x]","\frac{c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^3}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x^2}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 i b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 i b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}","\frac{c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x^3}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b c d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x^2}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d^2 \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2 x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right) x}{3 (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d^2 \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \sin ^{-1}(c x)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{b d^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 i b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 b d^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 i b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}-\frac{i b^2 d^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c x d+d)^{5/2} (e-c e x)^{5/2}}",1,"(2*b^2*d^2*(1 - c^2*x^2)^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b^2*d^2*x*(1 - c^2*x^2)^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b^2*d^2*(1 - c^2*x^2)^(5/2)*ArcSin[c*x])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*d^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (2*b*d^2*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*c*d^2*x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*d^2*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (d^2*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (c^2*d^2*x^3*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*d^2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - ((I/3)*d^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((4*I)/3)*b*d^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*b*d^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*b^2*d^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((2*I)/3)*b^2*d^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - ((I/3)*b^2*d^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",30,18,32,0.5625,1,"{4673, 4763, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4657, 4181, 261, 4681, 4703, 288, 216}"
574,1,709,0,0.8355584,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2} (e-c e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(3/2)*(e - c*e*x)^(5/2)),x]","-\frac{i b^2 d \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{i b^2 d \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 d \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i d \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b d x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b d \left(1-c^2 x^2\right)^{5/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 i b d \left(1-c^2 x^2\right)^{5/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 d \left(1-c^2 x^2\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 d x \left(1-c^2 x^2\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}","-\frac{i b^2 d \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{i b^2 d \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i b^2 d \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i d \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 d x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b d \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b d x \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{d x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b d \left(1-c^2 x^2\right)^{5/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 i b d \left(1-c^2 x^2\right)^{5/2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 d \left(1-c^2 x^2\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 d x \left(1-c^2 x^2\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"(b^2*d*(1 - c^2*x^2)^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (b^2*d*x*(1 - c^2*x^2)^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*d*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*d*x*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (d*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (d*x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*d*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*d*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (((2*I)/3)*b*d*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (4*b*d*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - ((I/3)*b^2*d*(1 - c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + ((I/3)*b^2*d*(1 - c^2*x^2)^(5/2)*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*b^2*d*(1 - c^2*x^2)^(5/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",21,14,32,0.4375,1,"{4673, 4763, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191, 4657, 4181, 261}"
575,1,366,0,0.4741407,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{5/2} (e-c e x)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)),x]","-\frac{2 i b^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b \left(1-c^2 x^2\right)^{5/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 x \left(1-c^2 x^2\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}","-\frac{2 i b^2 \left(1-c^2 x^2\right)^{5/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{2 i \left(1-c^2 x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{2 x \left(1-c^2 x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{4 b \left(1-c^2 x^2\right)^{5/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{3 c (c d x+d)^{5/2} (e-c e x)^{5/2}}+\frac{b^2 x \left(1-c^2 x^2\right)^2}{3 (c d x+d)^{5/2} (e-c e x)^{5/2}}",1,"(b^2*x*(1 - c^2*x^2)^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (b*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x]))/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (2*x*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(3*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) + (4*b*(1 - c^2*x^2)^(5/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(3*c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2)) - (((2*I)/3)*b^2*(1 - c^2*x^2)^(5/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(5/2)*(e - c*e*x)^(5/2))","A",10,10,32,0.3125,1,"{4673, 4655, 4651, 4675, 3719, 2190, 2279, 2391, 4677, 191}"
576,1,351,0,0.7049802,"\int x^2 \sqrt{d+c d x} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2,x]","-\frac{b c x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{b x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{1-c^2 x^2}}-\frac{x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{1}{4} x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}+\frac{b^2 x \sqrt{c d x+d} \sqrt{e-c e x}}{64 c^2}-\frac{1}{32} b^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x}","-\frac{b c x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 \sqrt{1-c^2 x^2}}+\frac{b x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{8 c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{1-c^2 x^2}}-\frac{x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{8 c^2}+\frac{1}{4} x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{b^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{64 c^3 \sqrt{1-c^2 x^2}}+\frac{b^2 x \sqrt{c d x+d} \sqrt{e-c e x}}{64 c^2}-\frac{1}{32} b^2 x^3 \sqrt{c d x+d} \sqrt{e-c e x}",1,"(b^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(64*c^2) - (b^2*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/32 - (b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(64*c^3*Sqrt[1 - c^2*x^2]) + (b*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(8*c*Sqrt[1 - c^2*x^2]) - (b*c*x^4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(8*Sqrt[1 - c^2*x^2]) - (x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/(8*c^2) + (x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/4 + (Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(24*b*c^3*Sqrt[1 - c^2*x^2])","A",11,7,35,0.2000,1,"{4739, 4697, 4707, 4641, 4627, 321, 216}"
577,1,225,0,0.3949563,"\int x \sqrt{d+c d x} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2,x]","-\frac{2 b c x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}+\frac{2 b x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{1-c^2 x^2}}-\frac{\left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2}+\frac{2 b^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c^2}+\frac{4 b^2 \sqrt{c d x+d} \sqrt{e-c e x}}{9 c^2}","-\frac{2 b c x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}+\frac{2 b x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 c \sqrt{1-c^2 x^2}}-\frac{\left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{3 c^2}+\frac{2 b^2 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{27 c^2}+\frac{4 b^2 \sqrt{c d x+d} \sqrt{e-c e x}}{9 c^2}",1,"(4*b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(9*c^2) + (2*b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/(27*c^2) + (2*b*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(3*c*Sqrt[1 - c^2*x^2]) - (2*b*c*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) - (Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(3*c^2)","A",6,5,33,0.1515,1,"{4739, 4677, 4645, 444, 43}"
578,1,222,0,0.2904949,"\int \sqrt{d+c d x} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2,x]","\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{b c x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 x \sqrt{c d x+d} \sqrt{e-c e x}","\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c \sqrt{1-c^2 x^2}}-\frac{b c x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}+\frac{1}{2} x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b^2 \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 c \sqrt{1-c^2 x^2}}-\frac{1}{4} b^2 x \sqrt{c d x+d} \sqrt{e-c e x}",1,"-(b^2*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/4 + (b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(4*c*Sqrt[1 - c^2*x^2]) - (b*c*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + (x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/2 + (Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(6*b*c*Sqrt[1 - c^2*x^2])","A",6,6,32,0.1875,1,"{4673, 4647, 4641, 4627, 321, 216}"
579,1,432,0,0.6808997,"\int \frac{\sqrt{d+c d x} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/x,x]","\frac{2 i b \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c x \sqrt{c d x+d} \sqrt{e-c e x}}{\sqrt{1-c^2 x^2}}-\frac{2 \sqrt{c d x+d} \sqrt{e-c e x} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b^2 c x \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-2 b^2 \sqrt{c d x+d} \sqrt{e-c e x}","\frac{2 i b \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c x \sqrt{c d x+d} \sqrt{e-c e x}}{\sqrt{1-c^2 x^2}}-\frac{2 \sqrt{c d x+d} \sqrt{e-c e x} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 b^2 c x \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-2 b^2 \sqrt{c d x+d} \sqrt{e-c e x}",1,"-2*b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x] - (2*a*b*c*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/Sqrt[1 - c^2*x^2] - (2*b^2*c*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] + Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2 - (2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((2*I)*b*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - ((2*I)*b*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (2*b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (2*b^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",13,9,35,0.2571,1,"{4739, 4697, 4709, 4183, 2531, 2282, 6589, 4619, 261}"
580,1,257,0,0.5944168,"\int \frac{\sqrt{d+c d x} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/x^2,x]","-\frac{i b^2 c \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{c \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b \sqrt{1-c^2 x^2}}-\frac{i c \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+\frac{2 b c \sqrt{c d x+d} \sqrt{e-c e x} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{x}","-\frac{i b^2 c \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{c \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b \sqrt{1-c^2 x^2}}-\frac{i c \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+\frac{2 b c \sqrt{c d x+d} \sqrt{e-c e x} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{\sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{x}",1,"-((Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/x) - (I*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - (c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(3*b*Sqrt[1 - c^2*x^2]) + (2*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b^2*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",8,8,35,0.2286,1,"{4739, 4693, 4625, 3717, 2190, 2279, 2391, 4641}"
581,1,509,0,1.0256536,"\int x^2 (d+c d x)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{b c^3 d e x^6 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{18 \sqrt{1-c^2 x^2}}-\frac{7 b c d e x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{48 \sqrt{1-c^2 x^2}}+\frac{1}{6} d e x^3 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d e x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{16 c \sqrt{1-c^2 x^2}}+\frac{d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{1-c^2 x^2}}-\frac{d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{16 c^2}+\frac{1}{8} d e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{108} b^2 c^2 d e x^5 \sqrt{c d x+d} \sqrt{e-c e x}+\frac{7 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{1152 c^3 \sqrt{1-c^2 x^2}}-\frac{7 b^2 d e x \sqrt{c d x+d} \sqrt{e-c e x}}{1152 c^2}-\frac{43 b^2 d e x^3 \sqrt{c d x+d} \sqrt{e-c e x}}{1728}","\frac{b c^3 d e x^6 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{18 \sqrt{1-c^2 x^2}}-\frac{7 b c d e x^4 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{48 \sqrt{1-c^2 x^2}}+\frac{1}{6} d e x^3 \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{b d e x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{16 c \sqrt{1-c^2 x^2}}+\frac{d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{1-c^2 x^2}}-\frac{d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{16 c^2}+\frac{1}{8} d e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{108} b^2 c^2 d e x^5 \sqrt{c d x+d} \sqrt{e-c e x}+\frac{7 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{1152 c^3 \sqrt{1-c^2 x^2}}-\frac{7 b^2 d e x \sqrt{c d x+d} \sqrt{e-c e x}}{1152 c^2}-\frac{43 b^2 d e x^3 \sqrt{c d x+d} \sqrt{e-c e x}}{1728}",1,"(-7*b^2*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(1152*c^2) - (43*b^2*d*e*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/1728 + (b^2*c^2*d*e*x^5*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/108 + (7*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(1152*c^3*Sqrt[1 - c^2*x^2]) + (b*d*e*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(16*c*Sqrt[1 - c^2*x^2]) - (7*b*c*d*e*x^4*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(48*Sqrt[1 - c^2*x^2]) + (b*c^3*d*e*x^6*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(18*Sqrt[1 - c^2*x^2]) - (d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/(16*c^2) + (d*e*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/8 + (d*e*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/6 + (d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(48*b*c^3*Sqrt[1 - c^2*x^2])","A",18,12,35,0.3429,1,"{4739, 4699, 4697, 4707, 4641, 4627, 321, 216, 14, 4687, 12, 459}"
582,1,338,0,0.5069422,"\int x (d+c d x)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{2 b c^3 d e x^5 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{25 \sqrt{1-c^2 x^2}}-\frac{4 b c d e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{15 \sqrt{1-c^2 x^2}}+\frac{2 b d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{5 c \sqrt{1-c^2 x^2}}-\frac{d e \left(1-c^2 x^2\right)^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}+\frac{2 b^2 d e \left(1-c^2 x^2\right)^2 \sqrt{c d x+d} \sqrt{e-c e x}}{125 c^2}+\frac{8 b^2 d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{225 c^2}+\frac{16 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}{75 c^2}","\frac{2 b c^3 d e x^5 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{25 \sqrt{1-c^2 x^2}}-\frac{4 b c d e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{15 \sqrt{1-c^2 x^2}}+\frac{2 b d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{5 c \sqrt{1-c^2 x^2}}-\frac{d e \left(1-c^2 x^2\right)^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{5 c^2}+\frac{2 b^2 d e \left(1-c^2 x^2\right)^2 \sqrt{c d x+d} \sqrt{e-c e x}}{125 c^2}+\frac{8 b^2 d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}}{225 c^2}+\frac{16 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}{75 c^2}",1,"(16*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/(75*c^2) + (8*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/(225*c^2) + (2*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)^2)/(125*c^2) + (2*b*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(5*c*Sqrt[1 - c^2*x^2]) - (4*b*c*d*e*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(15*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*e*x^5*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(25*Sqrt[1 - c^2*x^2]) - (d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)^2*(a + b*ArcSin[c*x])^2)/(5*c^2)","A",7,7,33,0.2121,1,"{4739, 4677, 194, 4645, 12, 1247, 698}"
583,1,362,0,0.4222203,"\int (d+c d x)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2,x]","\frac{(c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{3 x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}-\frac{3 b c x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{1}{4} x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}+\frac{9 b^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}","\frac{(c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^3}{8 b c \left(1-c^2 x^2\right)^{3/2}}+\frac{3 x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{8 \left(1-c^2 x^2\right)}+\frac{b \sqrt{1-c^2 x^2} (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 c}-\frac{3 b c x^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)}{8 \left(1-c^2 x^2\right)^{3/2}}+\frac{1}{4} x (c d x+d)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{15 b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}}{64 \left(1-c^2 x^2\right)}+\frac{9 b^2 (c d x+d)^{3/2} (e-c e x)^{3/2} \sin ^{-1}(c x)}{64 c \left(1-c^2 x^2\right)^{3/2}}-\frac{1}{32} b^2 x (c d x+d)^{3/2} (e-c e x)^{3/2}",1,"-(b^2*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/32 - (15*b^2*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))/(64*(1 - c^2*x^2)) + (9*b^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*ArcSin[c*x])/(64*c*(1 - c^2*x^2)^(3/2)) - (3*b*c*x^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x]))/(8*(1 - c^2*x^2)^(3/2)) + (b*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(8*c) + (x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/4 + (3*x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/(8*(1 - c^2*x^2)) + ((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^3)/(8*b*c*(1 - c^2*x^2)^(3/2))","A",11,9,32,0.2812,1,"{4673, 4649, 4647, 4641, 4627, 321, 216, 4677, 195}"
584,1,647,0,0.9411184,"\int \frac{(d+c d x)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/x,x]","\frac{2 i b d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c d e x \sqrt{c d x+d} \sqrt{e-c e x}}{\sqrt{1-c^2 x^2}}+\frac{2 b c^3 d e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{2 b c d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{1}{3} d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 d e \sqrt{c d x+d} \sqrt{e-c e x} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{27} b^2 d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}-\frac{2 b^2 c d e x \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-\frac{22}{9} b^2 d e \sqrt{c d x+d} \sqrt{e-c e x}","\frac{2 i b d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 i b d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{2 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{2 b^2 d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}-\frac{2 a b c d e x \sqrt{c d x+d} \sqrt{e-c e x}}{\sqrt{1-c^2 x^2}}+\frac{2 b c^3 d e x^3 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{9 \sqrt{1-c^2 x^2}}-\frac{2 b c d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{3 \sqrt{1-c^2 x^2}}+\frac{1}{3} d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2 d e \sqrt{c d x+d} \sqrt{e-c e x} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{2}{27} b^2 d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x}-\frac{2 b^2 c d e x \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{\sqrt{1-c^2 x^2}}-\frac{22}{9} b^2 d e \sqrt{c d x+d} \sqrt{e-c e x}",1,"(-22*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/9 - (2*a*b*c*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/Sqrt[1 - c^2*x^2] - (2*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2))/27 - (2*b^2*c*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/Sqrt[1 - c^2*x^2] - (2*b*c*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(3*Sqrt[1 - c^2*x^2]) + (2*b*c^3*d*e*x^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(9*Sqrt[1 - c^2*x^2]) + d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2 + (d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/3 - (2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + ((2*I)*b*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - ((2*I)*b*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (2*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*PolyLog[3, -E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] + (2*b^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*PolyLog[3, E^(I*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",18,13,35,0.3714,1,"{4739, 4699, 4697, 4709, 4183, 2531, 2282, 6589, 4619, 261, 4645, 444, 43}"
585,1,505,0,0.8074296,"\int \frac{(d+c d x)^{3/2} (e-c e x)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)*(a + b*ArcSin[c*x])^2)/x^2,x]","-\frac{i b^2 c d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{3 b c^3 d e x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}-\frac{c d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b \sqrt{1-c^2 x^2}}-\frac{i c d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+b c d e \sqrt{1-c^2 x^2} \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)-\frac{d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{2 b c d e \sqrt{c d x+d} \sqrt{e-c e x} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{3}{2} c^2 d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{5 b^2 c d e \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 \sqrt{1-c^2 x^2}}+\frac{1}{4} b^2 c^2 d e x \sqrt{c d x+d} \sqrt{e-c e x}","-\frac{i b^2 c d e \sqrt{c d x+d} \sqrt{e-c e x} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{1-c^2 x^2}}+\frac{3 b c^3 d e x^2 \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)}{2 \sqrt{1-c^2 x^2}}-\frac{c d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^3}{2 b \sqrt{1-c^2 x^2}}-\frac{i c d e \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}}+b c d e \sqrt{1-c^2 x^2} \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)-\frac{d e \left(1-c^2 x^2\right) \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2}{x}+\frac{2 b c d e \sqrt{c d x+d} \sqrt{e-c e x} \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}}-\frac{3}{2} c^2 d e x \sqrt{c d x+d} \sqrt{e-c e x} \left(a+b \sin ^{-1}(c x)\right)^2-\frac{5 b^2 c d e \sqrt{c d x+d} \sqrt{e-c e x} \sin ^{-1}(c x)}{4 \sqrt{1-c^2 x^2}}+\frac{1}{4} b^2 c^2 d e x \sqrt{c d x+d} \sqrt{e-c e x}",1,"(b^2*c^2*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])/4 - (5*b^2*c*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*ArcSin[c*x])/(4*Sqrt[1 - c^2*x^2]) + (3*b*c^3*d*e*x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x]))/(2*Sqrt[1 - c^2*x^2]) + b*c*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]) - (3*c^2*d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/2 - (I*c*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^2)/Sqrt[1 - c^2*x^2] - (d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/x - (c*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])^3)/(2*b*Sqrt[1 - c^2*x^2]) + (2*b*c*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2] - (I*b^2*c*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/Sqrt[1 - c^2*x^2]","A",15,14,35,0.4000,1,"{4739, 4695, 4647, 4641, 4627, 321, 216, 4683, 4625, 3717, 2190, 2279, 2391, 195}"
586,1,250,0,0.5823368,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x} \sqrt{e-c e x}} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]),x]","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{2 c^2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{2 c \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{b^2 x \left(1-c^2 x^2\right)}{4 c^2 \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{b^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 c^3 \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(b^2*x*(1 - c^2*x^2))/(4*c^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (b^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(4*c^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(2*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(2*c^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(6*b*c^3*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",6,6,35,0.1714,1,"{4739, 4707, 4641, 4627, 321, 216}"
587,1,177,0,0.3766485,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x} \sqrt{e-c e x}} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]),x]","\frac{2 a b x \sqrt{1-c^2 x^2}}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 \left(1-c^2 x^2\right)}{c^2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{2 a b x \sqrt{1-c^2 x^2}}{c \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 \left(1-c^2 x^2\right)}{c^2 \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 x \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(2*a*b*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*(1 - c^2*x^2))/(c^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*x*Sqrt[1 - c^2*x^2]*ArcSin[c*x])/(c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(c^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",5,4,33,0.1212,1,"{4739, 4677, 4619, 261}"
588,1,55,0,0.2323889,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+c d x} \sqrt{e-c e x}} \, dx","Int[(a + b*ArcSin[c*x])^2/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]),x]","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",2,2,32,0.06250,1,"{4673, 4641}"
589,1,287,0,0.5796078,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x \sqrt{d+c d x} \sqrt{e-c e x}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]),x]","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{c d x+d} \sqrt{e-c e x}}","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{c d x+d} \sqrt{e-c e x}}",1,"(-2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",9,6,35,0.1714,1,"{4739, 4709, 4183, 2531, 2282, 6589}"
590,1,214,0,0.584327,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 \sqrt{d+c d x} \sqrt{e-c e x}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]),x]","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b c \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)}{\sqrt{c d x+d} \sqrt{e-c e x}}","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{x \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b c \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)}{\sqrt{c d x+d} \sqrt{e-c e x}}",1,"((-I)*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/(x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",7,7,35,0.2000,1,"{4739, 4681, 4625, 3717, 2190, 2279, 2391}"
591,1,295,0,0.7425096,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2} (e-c e x)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)),x]","-\frac{i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b \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^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}","-\frac{i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^3}{3 b c^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{c^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b \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^3 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(x*(a + b*ArcSin[c*x])^2)/(c^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (I*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(c^3*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^3)/(3*b*c^3*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c^3*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (I*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c^3*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",8,8,35,0.2286,1,"{4739, 4703, 4641, 4675, 3719, 2190, 2279, 2391}"
592,1,244,0,0.4881999,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2} (e-c e x)^{3/2}} \, dx","Int[(x*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)),x]","-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 i b \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 e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}","-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 i b \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 e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{c^2 d e \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(a + b*ArcSin[c*x])^2/(c^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + ((4*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(c^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(c^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(c^2*d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",8,6,33,0.1818,1,"{4739, 4677, 4657, 4181, 2279, 2391}"
593,1,217,0,0.3825202,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{(d+c d x)^{3/2} (e-c e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)),x]","-\frac{i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}","-\frac{i b^2 \left(1-c^2 x^2\right)^{3/2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}-\frac{i \left(1-c^2 x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{x \left(1-c^2 x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2}{(c d x+d)^{3/2} (e-c e x)^{3/2}}+\frac{2 b \left(1-c^2 x^2\right)^{3/2} \log \left(1+e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{c (c d x+d)^{3/2} (e-c e x)^{3/2}}",1,"(x*(1 - c^2*x^2)*(a + b*ArcSin[c*x])^2)/((d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])^2)/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) + (2*b*(1 - c^2*x^2)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)) - (I*b^2*(1 - c^2*x^2)^(3/2)*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(c*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2))","A",7,7,32,0.2188,1,"{4673, 4651, 4675, 3719, 2190, 2279, 2391}"
594,1,548,0,0.8534291,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x (d+c d x)^{3/2} (e-c e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)),x]","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 i b \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}","\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-i e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 i b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,i e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,-e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 b^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(3,e^{i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 i b \sqrt{1-c^2 x^2} \tan ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}",1,"(a + b*ArcSin[c*x])^2/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + ((4*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTan[E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2*ArcTanh[E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, -E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, (-I)*E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + ((2*I)*b^2*Sqrt[1 - c^2*x^2]*PolyLog[2, I*E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((2*I)*b*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*PolyLog[2, E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, -E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (2*b^2*Sqrt[1 - c^2*x^2]*PolyLog[3, E^(I*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",16,11,35,0.3143,1,"{4739, 4705, 4709, 4183, 2531, 2282, 6589, 4657, 4181, 2279, 2391}"
595,1,396,0,0.8575306,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{x^2 (d+c d x)^{3/2} (e-c e x)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(x^2*(d + c*d*x)^(3/2)*(e - c*e*x)^(3/2)),x]","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 b c \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)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{4 b c \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d e x \sqrt{c d x+d} \sqrt{e-c e x}}","-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-e^{2 i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{i b^2 c \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{2 i c \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{4 b c \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)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{4 b c \sqrt{1-c^2 x^2} \tanh ^{-1}\left(e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d e \sqrt{c d x+d} \sqrt{e-c e x}}+\frac{2 c^2 x \left(a+b \sin ^{-1}(c x)\right)^2}{d e \sqrt{c d x+d} \sqrt{e-c e x}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{d e x \sqrt{c d x+d} \sqrt{e-c e x}}",1,"-((a + b*ArcSin[c*x])^2/(d*e*x*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])) + (2*c^2*x*(a + b*ArcSin[c*x])^2)/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - ((2*I)*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])^2)/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (4*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*ArcTanh[E^((2*I)*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) + (4*b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x])*Log[1 + E^((2*I)*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, -E^((2*I)*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x]) - (I*b^2*c*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(d*e*Sqrt[d + c*d*x]*Sqrt[e - c*e*x])","A",15,11,35,0.3143,1,"{4739, 4701, 4651, 4675, 3719, 2190, 2279, 2391, 4679, 4419, 4183}"
596,1,152,0,0.1503824,"\int x^4 \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*ArcSin[c*x]),x]","\frac{1}{5} d x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^{5/2} \left(7 c^2 d+15 e\right)}{175 c^7}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(14 c^2 d+15 e\right)}{105 c^7}+\frac{b \sqrt{1-c^2 x^2} \left(7 c^2 d+5 e\right)}{35 c^7}-\frac{b e \left(1-c^2 x^2\right)^{7/2}}{49 c^7}","\frac{1}{5} d x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^{5/2} \left(7 c^2 d+15 e\right)}{175 c^7}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(14 c^2 d+15 e\right)}{105 c^7}+\frac{b \sqrt{1-c^2 x^2} \left(7 c^2 d+5 e\right)}{35 c^7}-\frac{b e \left(1-c^2 x^2\right)^{7/2}}{49 c^7}",1,"(b*(7*c^2*d + 5*e)*Sqrt[1 - c^2*x^2])/(35*c^7) - (b*(14*c^2*d + 15*e)*(1 - c^2*x^2)^(3/2))/(105*c^7) + (b*(7*c^2*d + 15*e)*(1 - c^2*x^2)^(5/2))/(175*c^7) - (b*e*(1 - c^2*x^2)^(7/2))/(49*c^7) + (d*x^5*(a + b*ArcSin[c*x]))/5 + (e*x^7*(a + b*ArcSin[c*x]))/7","A",5,5,19,0.2632,1,"{14, 4731, 12, 446, 77}"
597,1,149,0,0.1170262,"\int x^3 \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*ArcSin[c*x]),x]","\frac{1}{4} d x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-c^2 x^2} \left(9 c^2 d+5 e\right)}{144 c^3}+\frac{b x \sqrt{1-c^2 x^2} \left(9 c^2 d+5 e\right)}{96 c^5}-\frac{b \left(9 c^2 d+5 e\right) \sin ^{-1}(c x)}{96 c^6}+\frac{b e x^5 \sqrt{1-c^2 x^2}}{36 c}","\frac{1}{4} d x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-c^2 x^2} \left(9 c^2 d+5 e\right)}{144 c^3}+\frac{b x \sqrt{1-c^2 x^2} \left(9 c^2 d+5 e\right)}{96 c^5}-\frac{b \left(9 c^2 d+5 e\right) \sin ^{-1}(c x)}{96 c^6}+\frac{b e x^5 \sqrt{1-c^2 x^2}}{36 c}",1,"(b*(9*c^2*d + 5*e)*x*Sqrt[1 - c^2*x^2])/(96*c^5) + (b*(9*c^2*d + 5*e)*x^3*Sqrt[1 - c^2*x^2])/(144*c^3) + (b*e*x^5*Sqrt[1 - c^2*x^2])/(36*c) - (b*(9*c^2*d + 5*e)*ArcSin[c*x])/(96*c^6) + (d*x^4*(a + b*ArcSin[c*x]))/4 + (e*x^6*(a + b*ArcSin[c*x]))/6","A",6,6,19,0.3158,1,"{14, 4731, 12, 459, 321, 216}"
598,1,120,0,0.1271088,"\int x^2 \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*ArcSin[c*x]),x]","\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \sin ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(5 c^2 d+6 e\right)}{45 c^5}+\frac{b \sqrt{1-c^2 x^2} \left(5 c^2 d+3 e\right)}{15 c^5}+\frac{b e \left(1-c^2 x^2\right)^{5/2}}{25 c^5}","\frac{1}{3} d x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \sin ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(5 c^2 d+6 e\right)}{45 c^5}+\frac{b \sqrt{1-c^2 x^2} \left(5 c^2 d+3 e\right)}{15 c^5}+\frac{b e \left(1-c^2 x^2\right)^{5/2}}{25 c^5}",1,"(b*(5*c^2*d + 3*e)*Sqrt[1 - c^2*x^2])/(15*c^5) - (b*(5*c^2*d + 6*e)*(1 - c^2*x^2)^(3/2))/(45*c^5) + (b*e*(1 - c^2*x^2)^(5/2))/(25*c^5) + (d*x^3*(a + b*ArcSin[c*x]))/3 + (e*x^5*(a + b*ArcSin[c*x]))/5","A",5,5,19,0.2632,1,"{14, 4731, 12, 446, 77}"
599,1,122,0,0.0877116,"\int x \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)*(a + b*ArcSin[c*x]),x]","\frac{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{4 e}-\frac{b \left(8 c^4 d^2+8 c^2 d e+3 e^2\right) \sin ^{-1}(c x)}{32 c^4 e}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)}{16 c}+\frac{3 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right)}{32 c^3}","\frac{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{4 e}-\frac{b \left(8 c^4 d^2+8 c^2 d e+3 e^2\right) \sin ^{-1}(c x)}{32 c^4 e}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)}{16 c}+\frac{3 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right)}{32 c^3}",1,"(3*b*(2*c^2*d + e)*x*Sqrt[1 - c^2*x^2])/(32*c^3) + (b*x*Sqrt[1 - c^2*x^2]*(d + e*x^2))/(16*c) - (b*(8*c^4*d^2 + 8*c^2*d*e + 3*e^2)*ArcSin[c*x])/(32*c^4*e) + ((d + e*x^2)^2*(a + b*ArcSin[c*x]))/(4*e)","A",4,4,17,0.2353,1,"{4729, 416, 388, 216}"
600,1,81,0,0.0650839,"\int \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcSin[c*x]),x]","d x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(3 c^2 d+e\right)}{3 c^3}-\frac{b e \left(1-c^2 x^2\right)^{3/2}}{9 c^3}","d x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(3 c^2 d+e\right)}{3 c^3}-\frac{b e \left(1-c^2 x^2\right)^{3/2}}{9 c^3}",1,"(b*(3*c^2*d + e)*Sqrt[1 - c^2*x^2])/(3*c^3) - (b*e*(1 - c^2*x^2)^(3/2))/(9*c^3) + d*x*(a + b*ArcSin[c*x]) + (e*x^3*(a + b*ArcSin[c*x]))/3","A",4,3,16,0.1875,1,"{4665, 444, 43}"
601,1,132,0,0.2387652,"\int \frac{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*ArcSin[c*x]))/x,x]","-\frac{1}{2} i b d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+d \log (x) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e x \sqrt{1-c^2 x^2}}{4 c}-\frac{b e \sin ^{-1}(c x)}{4 c^2}-\frac{1}{2} i b d \sin ^{-1}(c x)^2+b d \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b d \log (x) \sin ^{-1}(c x)","-\frac{1}{2} i b d \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+d \log (x) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e x \sqrt{1-c^2 x^2}}{4 c}-\frac{b e \sin ^{-1}(c x)}{4 c^2}-\frac{1}{2} i b d \sin ^{-1}(c x)^2+b d \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b d \log (x) \sin ^{-1}(c x)",1,"(b*e*x*Sqrt[1 - c^2*x^2])/(4*c) - (b*e*ArcSin[c*x])/(4*c^2) - (I/2)*b*d*ArcSin[c*x]^2 + (e*x^2*(a + b*ArcSin[c*x]))/2 + b*d*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - b*d*ArcSin[c*x]*Log[x] + d*(a + b*ArcSin[c*x])*Log[x] - (I/2)*b*d*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",12,12,19,0.6316,1,"{14, 4731, 12, 6742, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
602,1,66,0,0.0773946,"\int \frac{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*ArcSin[c*x]))/x^2,x]","-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{x}+e x \left(a+b \sin ^{-1}(c x)\right)-b c d \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\frac{b e \sqrt{1-c^2 x^2}}{c}","-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{x}+e x \left(a+b \sin ^{-1}(c x)\right)-b c d \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\frac{b e \sqrt{1-c^2 x^2}}{c}",1,"(b*e*Sqrt[1 - c^2*x^2])/c - (d*(a + b*ArcSin[c*x]))/x + e*x*(a + b*ArcSin[c*x]) - b*c*d*ArcTanh[Sqrt[1 - c^2*x^2]]","A",5,6,19,0.3158,1,"{14, 4731, 446, 80, 63, 208}"
603,1,119,0,0.2231199,"\int \frac{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*ArcSin[c*x]))/x^3,x]","-\frac{1}{2} i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+e \log (x) \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d \sqrt{1-c^2 x^2}}{2 x}-\frac{1}{2} i b e \sin ^{-1}(c x)^2+b e \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b e \log (x) \sin ^{-1}(c x)","-\frac{1}{2} i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+e \log (x) \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d \sqrt{1-c^2 x^2}}{2 x}-\frac{1}{2} i b e \sin ^{-1}(c x)^2+b e \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b e \log (x) \sin ^{-1}(c x)",1,"-(b*c*d*Sqrt[1 - c^2*x^2])/(2*x) - (I/2)*b*e*ArcSin[c*x]^2 - (d*(a + b*ArcSin[c*x]))/(2*x^2) + b*e*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - b*e*ArcSin[c*x]*Log[x] + e*(a + b*ArcSin[c*x])*Log[x] - (I/2)*b*e*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",10,10,19,0.5263,1,"{14, 4731, 6742, 264, 2326, 4625, 3717, 2190, 2279, 2391}"
604,1,85,0,0.0865374,"\int \frac{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*ArcSin[c*x]))/x^4,x]","-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{1}{6} b c \left(c^2 d+6 e\right) \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b c d \sqrt{1-c^2 x^2}}{6 x^2}","-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{1}{6} b c \left(c^2 d+6 e\right) \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b c d \sqrt{1-c^2 x^2}}{6 x^2}",1,"-(b*c*d*Sqrt[1 - c^2*x^2])/(6*x^2) - (d*(a + b*ArcSin[c*x]))/(3*x^3) - (e*(a + b*ArcSin[c*x]))/x - (b*c*(c^2*d + 6*e)*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",6,7,19,0.3684,1,"{14, 4731, 12, 446, 78, 63, 208}"
605,1,241,0,0.3175488,"\int x^4 \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{5} d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{7} d e x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{9} e^2 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^{5/2} \left(21 c^4 d^2+90 c^2 d e+70 e^2\right)}{525 c^9}-\frac{2 b \left(1-c^2 x^2\right)^{3/2} \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{945 c^9}+\frac{b \sqrt{1-c^2 x^2} \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{315 c^9}-\frac{2 b e \left(1-c^2 x^2\right)^{7/2} \left(9 c^2 d+14 e\right)}{441 c^9}+\frac{b e^2 \left(1-c^2 x^2\right)^{9/2}}{81 c^9}","\frac{1}{5} d^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{7} d e x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{9} e^2 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^{5/2} \left(21 c^4 d^2+90 c^2 d e+70 e^2\right)}{525 c^9}-\frac{2 b \left(1-c^2 x^2\right)^{3/2} \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{945 c^9}+\frac{b \sqrt{1-c^2 x^2} \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{315 c^9}-\frac{2 b e \left(1-c^2 x^2\right)^{7/2} \left(9 c^2 d+14 e\right)}{441 c^9}+\frac{b e^2 \left(1-c^2 x^2\right)^{9/2}}{81 c^9}",1,"(b*(63*c^4*d^2 + 90*c^2*d*e + 35*e^2)*Sqrt[1 - c^2*x^2])/(315*c^9) - (2*b*(63*c^4*d^2 + 135*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^(3/2))/(945*c^9) + (b*(21*c^4*d^2 + 90*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^(5/2))/(525*c^9) - (2*b*e*(9*c^2*d + 14*e)*(1 - c^2*x^2)^(7/2))/(441*c^9) + (b*e^2*(1 - c^2*x^2)^(9/2))/(81*c^9) + (d^2*x^5*(a + b*ArcSin[c*x]))/5 + (2*d*e*x^7*(a + b*ArcSin[c*x]))/7 + (e^2*x^9*(a + b*ArcSin[c*x]))/9","A",6,6,21,0.2857,1,"{270, 4731, 12, 1251, 897, 1153}"
606,1,241,0,0.2505708,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{4} d^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-c^2 x^2} \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{4608 c^5}+\frac{b x \sqrt{1-c^2 x^2} \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{3072 c^7}-\frac{b \left(288 c^4 d^2+320 c^2 d e+105 e^2\right) \sin ^{-1}(c x)}{3072 c^8}+\frac{b e x^5 \sqrt{1-c^2 x^2} \left(64 c^2 d+21 e\right)}{1152 c^3}+\frac{b e^2 x^7 \sqrt{1-c^2 x^2}}{64 c}","\frac{1}{4} d^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \sin ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-c^2 x^2} \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{4608 c^5}+\frac{b x \sqrt{1-c^2 x^2} \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{3072 c^7}-\frac{b \left(288 c^4 d^2+320 c^2 d e+105 e^2\right) \sin ^{-1}(c x)}{3072 c^8}+\frac{b e x^5 \sqrt{1-c^2 x^2} \left(64 c^2 d+21 e\right)}{1152 c^3}+\frac{b e^2 x^7 \sqrt{1-c^2 x^2}}{64 c}",1,"(b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*x*Sqrt[1 - c^2*x^2])/(3072*c^7) + (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*x^3*Sqrt[1 - c^2*x^2])/(4608*c^5) + (b*e*(64*c^2*d + 21*e)*x^5*Sqrt[1 - c^2*x^2])/(1152*c^3) + (b*e^2*x^7*Sqrt[1 - c^2*x^2])/(64*c) - (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*ArcSin[c*x])/(3072*c^8) + (d^2*x^4*(a + b*ArcSin[c*x]))/4 + (d*e*x^6*(a + b*ArcSin[c*x]))/3 + (e^2*x^8*(a + b*ArcSin[c*x]))/8","A",7,8,21,0.3810,1,"{266, 43, 4731, 12, 1267, 459, 321, 216}"
607,1,198,0,0.2214658,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{1}{3} d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(35 c^4 d^2+84 c^2 d e+45 e^2\right)}{315 c^7}+\frac{b \sqrt{1-c^2 x^2} \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7}+\frac{b e \left(1-c^2 x^2\right)^{5/2} \left(14 c^2 d+15 e\right)}{175 c^7}-\frac{b e^2 \left(1-c^2 x^2\right)^{7/2}}{49 c^7}","\frac{1}{3} d^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(35 c^4 d^2+84 c^2 d e+45 e^2\right)}{315 c^7}+\frac{b \sqrt{1-c^2 x^2} \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7}+\frac{b e \left(1-c^2 x^2\right)^{5/2} \left(14 c^2 d+15 e\right)}{175 c^7}-\frac{b e^2 \left(1-c^2 x^2\right)^{7/2}}{49 c^7}",1,"(b*(35*c^4*d^2 + 42*c^2*d*e + 15*e^2)*Sqrt[1 - c^2*x^2])/(105*c^7) - (b*(35*c^4*d^2 + 84*c^2*d*e + 45*e^2)*(1 - c^2*x^2)^(3/2))/(315*c^7) + (b*e*(14*c^2*d + 15*e)*(1 - c^2*x^2)^(5/2))/(175*c^7) - (b*e^2*(1 - c^2*x^2)^(7/2))/(49*c^7) + (d^2*x^3*(a + b*ArcSin[c*x]))/3 + (2*d*e*x^5*(a + b*ArcSin[c*x]))/5 + (e^2*x^7*(a + b*ArcSin[c*x]))/7","A",5,5,21,0.2381,1,"{270, 4731, 12, 1251, 771}"
608,1,183,0,0.1758344,"\int x \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{\left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{6 e}+\frac{b x \sqrt{1-c^2 x^2} \left(44 c^4 d^2+44 c^2 d e+15 e^2\right)}{288 c^5}-\frac{b \left(2 c^2 d+e\right) \left(8 c^4 d^2+8 c^2 d e+5 e^2\right) \sin ^{-1}(c x)}{96 c^6 e}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)^2}{36 c}+\frac{5 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right) \left(d+e x^2\right)}{144 c^3}","\frac{\left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{6 e}+\frac{b x \sqrt{1-c^2 x^2} \left(44 c^4 d^2+44 c^2 d e+15 e^2\right)}{288 c^5}-\frac{b \left(2 c^2 d+e\right) \left(8 c^4 d^2+8 c^2 d e+5 e^2\right) \sin ^{-1}(c x)}{96 c^6 e}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)^2}{36 c}+\frac{5 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right) \left(d+e x^2\right)}{144 c^3}",1,"(b*(44*c^4*d^2 + 44*c^2*d*e + 15*e^2)*x*Sqrt[1 - c^2*x^2])/(288*c^5) + (5*b*(2*c^2*d + e)*x*Sqrt[1 - c^2*x^2]*(d + e*x^2))/(144*c^3) + (b*x*Sqrt[1 - c^2*x^2]*(d + e*x^2)^2)/(36*c) - (b*(2*c^2*d + e)*(8*c^4*d^2 + 8*c^2*d*e + 5*e^2)*ArcSin[c*x])/(96*c^6*e) + ((d + e*x^2)^3*(a + b*ArcSin[c*x]))/(6*e)","A",5,5,19,0.2632,1,"{4729, 416, 528, 388, 216}"
609,1,150,0,0.1361569,"\int \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcSin[c*x]),x]","d^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(15 c^4 d^2+10 c^2 d e+3 e^2\right)}{15 c^5}-\frac{2 b e \left(1-c^2 x^2\right)^{3/2} \left(5 c^2 d+3 e\right)}{45 c^5}+\frac{b e^2 \left(1-c^2 x^2\right)^{5/2}}{25 c^5}","d^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b \sqrt{1-c^2 x^2} \left(15 c^4 d^2+10 c^2 d e+3 e^2\right)}{15 c^5}-\frac{2 b e \left(1-c^2 x^2\right)^{3/2} \left(5 c^2 d+3 e\right)}{45 c^5}+\frac{b e^2 \left(1-c^2 x^2\right)^{5/2}}{25 c^5}",1,"(b*(15*c^4*d^2 + 10*c^2*d*e + 3*e^2)*Sqrt[1 - c^2*x^2])/(15*c^5) - (2*b*e*(5*c^2*d + 3*e)*(1 - c^2*x^2)^(3/2))/(45*c^5) + (b*e^2*(1 - c^2*x^2)^(5/2))/(25*c^5) + d^2*x*(a + b*ArcSin[c*x]) + (2*d*e*x^3*(a + b*ArcSin[c*x]))/3 + (e^2*x^5*(a + b*ArcSin[c*x]))/5","A",5,5,18,0.2778,1,"{194, 4665, 12, 1247, 698}"
610,1,229,0,0.3347524,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSin[c*x]))/x,x]","-\frac{1}{2} i b d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+d^2 \log (x) \left(a+b \sin ^{-1}(c x)\right)+d e x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d e x \sqrt{1-c^2 x^2}}{2 c}-\frac{b d e \sin ^{-1}(c x)}{2 c^2}+\frac{b e^2 x^3 \sqrt{1-c^2 x^2}}{16 c}+\frac{3 b e^2 x \sqrt{1-c^2 x^2}}{32 c^3}-\frac{3 b e^2 \sin ^{-1}(c x)}{32 c^4}-\frac{1}{2} i b d^2 \sin ^{-1}(c x)^2+b d^2 \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b d^2 \log (x) \sin ^{-1}(c x)","-\frac{1}{2} i b d^2 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+d^2 \log (x) \left(a+b \sin ^{-1}(c x)\right)+d e x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{b d e x \sqrt{1-c^2 x^2}}{2 c}-\frac{b d e \sin ^{-1}(c x)}{2 c^2}+\frac{b e^2 x^3 \sqrt{1-c^2 x^2}}{16 c}+\frac{3 b e^2 x \sqrt{1-c^2 x^2}}{32 c^3}-\frac{3 b e^2 \sin ^{-1}(c x)}{32 c^4}-\frac{1}{2} i b d^2 \sin ^{-1}(c x)^2+b d^2 \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b d^2 \log (x) \sin ^{-1}(c x)",1,"(b*d*e*x*Sqrt[1 - c^2*x^2])/(2*c) + (3*b*e^2*x*Sqrt[1 - c^2*x^2])/(32*c^3) + (b*e^2*x^3*Sqrt[1 - c^2*x^2])/(16*c) - (b*d*e*ArcSin[c*x])/(2*c^2) - (3*b*e^2*ArcSin[c*x])/(32*c^4) - (I/2)*b*d^2*ArcSin[c*x]^2 + d*e*x^2*(a + b*ArcSin[c*x]) + (e^2*x^4*(a + b*ArcSin[c*x]))/4 + b*d^2*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - b*d^2*ArcSin[c*x]*Log[x] + d^2*(a + b*ArcSin[c*x])*Log[x] - (I/2)*b*d^2*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",14,12,21,0.5714,1,"{266, 43, 4731, 6742, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
611,1,126,0,0.1836626,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSin[c*x]))/x^2,x]","-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \sin ^{-1}(c x)\right)-b c d^2 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\frac{b e \sqrt{1-c^2 x^2} \left(6 c^2 d+e\right)}{3 c^3}-\frac{b e^2 \left(1-c^2 x^2\right)^{3/2}}{9 c^3}","-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \sin ^{-1}(c x)\right)-b c d^2 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\frac{b e \sqrt{1-c^2 x^2} \left(6 c^2 d+e\right)}{3 c^3}-\frac{b e^2 \left(1-c^2 x^2\right)^{3/2}}{9 c^3}",1,"(b*e*(6*c^2*d + e)*Sqrt[1 - c^2*x^2])/(3*c^3) - (b*e^2*(1 - c^2*x^2)^(3/2))/(9*c^3) - (d^2*(a + b*ArcSin[c*x]))/x + 2*d*e*x*(a + b*ArcSin[c*x]) + (e^2*x^3*(a + b*ArcSin[c*x]))/3 - b*c*d^2*ArcTanh[Sqrt[1 - c^2*x^2]]","A",6,6,21,0.2857,1,"{270, 4731, 1251, 897, 1153, 208}"
612,1,185,0,0.3380317,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSin[c*x]))/x^3,x]","-i b d e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+2 d e \log (x) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{1-c^2 x^2}}{2 x}+\frac{b e^2 x \sqrt{1-c^2 x^2}}{4 c}-\frac{b e^2 \sin ^{-1}(c x)}{4 c^2}-i b d e \sin ^{-1}(c x)^2+2 b d e \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-2 b d e \log (x) \sin ^{-1}(c x)","-i b d e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+2 d e \log (x) \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{1-c^2 x^2}}{2 x}+\frac{b e^2 x \sqrt{1-c^2 x^2}}{4 c}-\frac{b e^2 \sin ^{-1}(c x)}{4 c^2}-i b d e \sin ^{-1}(c x)^2+2 b d e \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-2 b d e \log (x) \sin ^{-1}(c x)",1,"-(b*c*d^2*Sqrt[1 - c^2*x^2])/(2*x) + (b*e^2*x*Sqrt[1 - c^2*x^2])/(4*c) - (b*e^2*ArcSin[c*x])/(4*c^2) - I*b*d*e*ArcSin[c*x]^2 - (d^2*(a + b*ArcSin[c*x]))/(2*x^2) + (e^2*x^2*(a + b*ArcSin[c*x]))/2 + 2*b*d*e*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - 2*b*d*e*ArcSin[c*x]*Log[x] + 2*d*e*(a + b*ArcSin[c*x])*Log[x] - I*b*d*e*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",13,14,21,0.6667,1,"{266, 43, 4731, 12, 6742, 264, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
613,1,126,0,0.2012526,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSin[c*x]))/x^4,x]","-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \sin ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{1-c^2 x^2}}{6 x^2}-\frac{1}{6} b c d \left(c^2 d+12 e\right) \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\frac{b e^2 \sqrt{1-c^2 x^2}}{c}","-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \sin ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{1-c^2 x^2}}{6 x^2}-\frac{1}{6} b c d \left(c^2 d+12 e\right) \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)+\frac{b e^2 \sqrt{1-c^2 x^2}}{c}",1,"(b*e^2*Sqrt[1 - c^2*x^2])/c - (b*c*d^2*Sqrt[1 - c^2*x^2])/(6*x^2) - (d^2*(a + b*ArcSin[c*x]))/(3*x^3) - (2*d*e*(a + b*ArcSin[c*x]))/x + e^2*x*(a + b*ArcSin[c*x]) - (b*c*d*(c^2*d + 12*e)*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",6,7,21,0.3333,1,"{270, 4731, 1251, 897, 1157, 388, 208}"
614,1,341,0,0.4348353,"\int x^4 \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)^3*(a + b*ArcSin[c*x]),x]","\frac{3}{7} d^2 e x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d e^2 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{11} e^3 x^{11} \left(a+b \sin ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^{7/2} \left(99 c^4 d^2+308 c^2 d e+210 e^2\right)}{1617 c^{11}}+\frac{b \left(1-c^2 x^2\right)^{5/2} \left(495 c^4 d^2 e+77 c^6 d^3+770 c^2 d e^2+350 e^3\right)}{1925 c^{11}}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(1485 c^4 d^2 e+462 c^6 d^3+1540 c^2 d e^2+525 e^3\right)}{3465 c^{11}}+\frac{b \sqrt{1-c^2 x^2} \left(495 c^4 d^2 e+231 c^6 d^3+385 c^2 d e^2+105 e^3\right)}{1155 c^{11}}+\frac{b e^2 \left(1-c^2 x^2\right)^{9/2} \left(11 c^2 d+15 e\right)}{297 c^{11}}-\frac{b e^3 \left(1-c^2 x^2\right)^{11/2}}{121 c^{11}}","\frac{3}{7} d^2 e x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d e^2 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{11} e^3 x^{11} \left(a+b \sin ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^{7/2} \left(99 c^4 d^2+308 c^2 d e+210 e^2\right)}{1617 c^{11}}+\frac{b \left(1-c^2 x^2\right)^{5/2} \left(495 c^4 d^2 e+77 c^6 d^3+770 c^2 d e^2+350 e^3\right)}{1925 c^{11}}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(1485 c^4 d^2 e+462 c^6 d^3+1540 c^2 d e^2+525 e^3\right)}{3465 c^{11}}+\frac{b \sqrt{1-c^2 x^2} \left(495 c^4 d^2 e+231 c^6 d^3+385 c^2 d e^2+105 e^3\right)}{1155 c^{11}}+\frac{b e^2 \left(1-c^2 x^2\right)^{9/2} \left(11 c^2 d+15 e\right)}{297 c^{11}}-\frac{b e^3 \left(1-c^2 x^2\right)^{11/2}}{121 c^{11}}",1,"(b*(231*c^6*d^3 + 495*c^4*d^2*e + 385*c^2*d*e^2 + 105*e^3)*Sqrt[1 - c^2*x^2])/(1155*c^11) - (b*(462*c^6*d^3 + 1485*c^4*d^2*e + 1540*c^2*d*e^2 + 525*e^3)*(1 - c^2*x^2)^(3/2))/(3465*c^11) + (b*(77*c^6*d^3 + 495*c^4*d^2*e + 770*c^2*d*e^2 + 350*e^3)*(1 - c^2*x^2)^(5/2))/(1925*c^11) - (b*e*(99*c^4*d^2 + 308*c^2*d*e + 210*e^2)*(1 - c^2*x^2)^(7/2))/(1617*c^11) + (b*e^2*(11*c^2*d + 15*e)*(1 - c^2*x^2)^(9/2))/(297*c^11) - (b*e^3*(1 - c^2*x^2)^(11/2))/(121*c^11) + (d^3*x^5*(a + b*ArcSin[c*x]))/5 + (3*d^2*e*x^7*(a + b*ArcSin[c*x]))/7 + (d*e^2*x^9*(a + b*ArcSin[c*x]))/3 + (e^3*x^11*(a + b*ArcSin[c*x]))/11","A",5,5,21,0.2381,1,"{270, 4731, 12, 1799, 1620}"
615,1,380,0,0.5083529,"\int x^3 \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^3*(a + b*ArcSin[c*x]),x]","\frac{\left(d+e x^2\right)^5 \left(a+b \sin ^{-1}(c x)\right)}{10 e^2}-\frac{d \left(d+e x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 e^2}+\frac{b x \sqrt{1-c^2 x^2} \left(26 c^4 d^2+201 c^2 d e+126 e^2\right) \left(d+e x^2\right)^2}{9600 c^5 e}-\frac{b x \sqrt{1-c^2 x^2} \left(-1096 c^4 d^2 e+136 c^6 d^3-1617 c^2 d e^2-630 e^3\right) \left(d+e x^2\right)}{38400 c^7 e}-\frac{b x \sqrt{1-c^2 x^2} \left(-7758 c^4 d^2 e^2-2536 c^6 d^3 e+1232 c^8 d^4-6615 c^2 d e^3-1890 e^4\right)}{76800 c^9 e}+\frac{b \left(-480 c^6 d^3 e^2-800 c^4 d^2 e^3+128 c^{10} d^5-525 c^2 d e^4-126 e^5\right) \sin ^{-1}(c x)}{5120 c^{10} e^2}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)^4}{100 c e}+\frac{b x \sqrt{1-c^2 x^2} \left(11 c^2 d+18 e\right) \left(d+e x^2\right)^3}{1600 c^3 e}","\frac{\left(d+e x^2\right)^5 \left(a+b \sin ^{-1}(c x)\right)}{10 e^2}-\frac{d \left(d+e x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 e^2}+\frac{b x \sqrt{1-c^2 x^2} \left(26 c^4 d^2+201 c^2 d e+126 e^2\right) \left(d+e x^2\right)^2}{9600 c^5 e}-\frac{b x \sqrt{1-c^2 x^2} \left(-1096 c^4 d^2 e+136 c^6 d^3-1617 c^2 d e^2-630 e^3\right) \left(d+e x^2\right)}{38400 c^7 e}-\frac{b x \sqrt{1-c^2 x^2} \left(-7758 c^4 d^2 e^2-2536 c^6 d^3 e+1232 c^8 d^4-6615 c^2 d e^3-1890 e^4\right)}{76800 c^9 e}+\frac{b \left(-480 c^6 d^3 e^2-800 c^4 d^2 e^3+128 c^{10} d^5-525 c^2 d e^4-126 e^5\right) \sin ^{-1}(c x)}{5120 c^{10} e^2}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)^4}{100 c e}+\frac{b x \sqrt{1-c^2 x^2} \left(11 c^2 d+18 e\right) \left(d+e x^2\right)^3}{1600 c^3 e}",1,"-(b*(1232*c^8*d^4 - 2536*c^6*d^3*e - 7758*c^4*d^2*e^2 - 6615*c^2*d*e^3 - 1890*e^4)*x*Sqrt[1 - c^2*x^2])/(76800*c^9*e) - (b*(136*c^6*d^3 - 1096*c^4*d^2*e - 1617*c^2*d*e^2 - 630*e^3)*x*Sqrt[1 - c^2*x^2]*(d + e*x^2))/(38400*c^7*e) + (b*(26*c^4*d^2 + 201*c^2*d*e + 126*e^2)*x*Sqrt[1 - c^2*x^2]*(d + e*x^2)^2)/(9600*c^5*e) + (b*(11*c^2*d + 18*e)*x*Sqrt[1 - c^2*x^2]*(d + e*x^2)^3)/(1600*c^3*e) + (b*x*Sqrt[1 - c^2*x^2]*(d + e*x^2)^4)/(100*c*e) + (b*(128*c^10*d^5 - 480*c^6*d^3*e^2 - 800*c^4*d^2*e^3 - 525*c^2*d*e^4 - 126*e^5)*ArcSin[c*x])/(5120*c^10*e^2) - (d*(d + e*x^2)^4*(a + b*ArcSin[c*x]))/(8*e^2) + ((d + e*x^2)^5*(a + b*ArcSin[c*x]))/(10*e^2)","A",8,7,21,0.3333,1,"{266, 43, 4731, 12, 528, 388, 216}"
616,1,287,0,0.3731678,"\int x^2 \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^3*(a + b*ArcSin[c*x]),x]","\frac{3}{5} d^2 e x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{7} d e^2 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{9} e^3 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right)^{5/2} \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{525 c^9}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(378 c^4 d^2 e+105 c^6 d^3+405 c^2 d e^2+140 e^3\right)}{945 c^9}+\frac{b \sqrt{1-c^2 x^2} \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{315 c^9}-\frac{b e^2 \left(1-c^2 x^2\right)^{7/2} \left(27 c^2 d+28 e\right)}{441 c^9}+\frac{b e^3 \left(1-c^2 x^2\right)^{9/2}}{81 c^9}","\frac{3}{5} d^2 e x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{7} d e^2 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{9} e^3 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right)^{5/2} \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{525 c^9}-\frac{b \left(1-c^2 x^2\right)^{3/2} \left(378 c^4 d^2 e+105 c^6 d^3+405 c^2 d e^2+140 e^3\right)}{945 c^9}+\frac{b \sqrt{1-c^2 x^2} \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{315 c^9}-\frac{b e^2 \left(1-c^2 x^2\right)^{7/2} \left(27 c^2 d+28 e\right)}{441 c^9}+\frac{b e^3 \left(1-c^2 x^2\right)^{9/2}}{81 c^9}",1,"(b*(105*c^6*d^3 + 189*c^4*d^2*e + 135*c^2*d*e^2 + 35*e^3)*Sqrt[1 - c^2*x^2])/(315*c^9) - (b*(105*c^6*d^3 + 378*c^4*d^2*e + 405*c^2*d*e^2 + 140*e^3)*(1 - c^2*x^2)^(3/2))/(945*c^9) + (b*e*(63*c^4*d^2 + 135*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^(5/2))/(525*c^9) - (b*e^2*(27*c^2*d + 28*e)*(1 - c^2*x^2)^(7/2))/(441*c^9) + (b*e^3*(1 - c^2*x^2)^(9/2))/(81*c^9) + (d^3*x^3*(a + b*ArcSin[c*x]))/3 + (3*d^2*e*x^5*(a + b*ArcSin[c*x]))/5 + (3*d*e^2*x^7*(a + b*ArcSin[c*x]))/7 + (e^3*x^9*(a + b*ArcSin[c*x]))/9","A",5,5,21,0.2381,1,"{270, 4731, 12, 1799, 1620}"
617,1,258,0,0.2676784,"\int x \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^3*(a + b*ArcSin[c*x]),x]","\frac{\left(d+e x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 e}+\frac{b x \sqrt{1-c^2 x^2} \left(104 c^4 d^2+104 c^2 d e+35 e^2\right) \left(d+e x^2\right)}{1536 c^5}+\frac{5 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right) \left(40 c^4 d^2+40 c^2 d e+21 e^2\right)}{3072 c^7}-\frac{b \left(288 c^4 d^2 e^2+256 c^6 d^3 e+128 c^8 d^4+160 c^2 d e^3+35 e^4\right) \sin ^{-1}(c x)}{1024 c^8 e}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)^3}{64 c}+\frac{7 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right) \left(d+e x^2\right)^2}{384 c^3}","\frac{\left(d+e x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right)}{8 e}+\frac{b x \sqrt{1-c^2 x^2} \left(104 c^4 d^2+104 c^2 d e+35 e^2\right) \left(d+e x^2\right)}{1536 c^5}+\frac{5 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right) \left(40 c^4 d^2+40 c^2 d e+21 e^2\right)}{3072 c^7}-\frac{b \left(288 c^4 d^2 e^2+256 c^6 d^3 e+128 c^8 d^4+160 c^2 d e^3+35 e^4\right) \sin ^{-1}(c x)}{1024 c^8 e}+\frac{b x \sqrt{1-c^2 x^2} \left(d+e x^2\right)^3}{64 c}+\frac{7 b x \sqrt{1-c^2 x^2} \left(2 c^2 d+e\right) \left(d+e x^2\right)^2}{384 c^3}",1,"(5*b*(2*c^2*d + e)*(40*c^4*d^2 + 40*c^2*d*e + 21*e^2)*x*Sqrt[1 - c^2*x^2])/(3072*c^7) + (b*(104*c^4*d^2 + 104*c^2*d*e + 35*e^2)*x*Sqrt[1 - c^2*x^2]*(d + e*x^2))/(1536*c^5) + (7*b*(2*c^2*d + e)*x*Sqrt[1 - c^2*x^2]*(d + e*x^2)^2)/(384*c^3) + (b*x*Sqrt[1 - c^2*x^2]*(d + e*x^2)^3)/(64*c) - (b*(128*c^8*d^4 + 256*c^6*d^3*e + 288*c^4*d^2*e^2 + 160*c^2*d*e^3 + 35*e^4)*ArcSin[c*x])/(1024*c^8*e) + ((d + e*x^2)^4*(a + b*ArcSin[c*x]))/(8*e)","A",6,5,19,0.2632,1,"{4729, 416, 528, 388, 216}"
618,1,225,0,0.2506566,"\int \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^3*(a + b*ArcSin[c*x]),x]","d^2 e x^3 \left(a+b \sin ^{-1}(c x)\right)+d^3 x \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e^3 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^{3/2} \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7}+\frac{b \sqrt{1-c^2 x^2} \left(35 c^4 d^2 e+35 c^6 d^3+21 c^2 d e^2+5 e^3\right)}{35 c^7}+\frac{3 b e^2 \left(1-c^2 x^2\right)^{5/2} \left(7 c^2 d+5 e\right)}{175 c^7}-\frac{b e^3 \left(1-c^2 x^2\right)^{7/2}}{49 c^7}","d^2 e x^3 \left(a+b \sin ^{-1}(c x)\right)+d^3 x \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{7} e^3 x^7 \left(a+b \sin ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^{3/2} \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7}+\frac{b \sqrt{1-c^2 x^2} \left(35 c^4 d^2 e+35 c^6 d^3+21 c^2 d e^2+5 e^3\right)}{35 c^7}+\frac{3 b e^2 \left(1-c^2 x^2\right)^{5/2} \left(7 c^2 d+5 e\right)}{175 c^7}-\frac{b e^3 \left(1-c^2 x^2\right)^{7/2}}{49 c^7}",1,"(b*(35*c^6*d^3 + 35*c^4*d^2*e + 21*c^2*d*e^2 + 5*e^3)*Sqrt[1 - c^2*x^2])/(35*c^7) - (b*e*(35*c^4*d^2 + 42*c^2*d*e + 15*e^2)*(1 - c^2*x^2)^(3/2))/(105*c^7) + (3*b*e^2*(7*c^2*d + 5*e)*(1 - c^2*x^2)^(5/2))/(175*c^7) - (b*e^3*(1 - c^2*x^2)^(7/2))/(49*c^7) + d^3*x*(a + b*ArcSin[c*x]) + d^2*e*x^3*(a + b*ArcSin[c*x]) + (3*d*e^2*x^5*(a + b*ArcSin[c*x]))/5 + (e^3*x^7*(a + b*ArcSin[c*x]))/7","A",5,5,18,0.2778,1,"{194, 4665, 12, 1799, 1850}"
619,1,357,0,0.4756107,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^3*(a + b*ArcSin[c*x]))/x,x]","-\frac{1}{2} i b d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{3}{2} d^2 e x^2 \left(a+b \sin ^{-1}(c x)\right)+d^3 \log (x) \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{4} d e^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^3 x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{3 b d^2 e x \sqrt{1-c^2 x^2}}{4 c}-\frac{3 b d^2 e \sin ^{-1}(c x)}{4 c^2}+\frac{3 b d e^2 x^3 \sqrt{1-c^2 x^2}}{16 c}+\frac{9 b d e^2 x \sqrt{1-c^2 x^2}}{32 c^3}-\frac{9 b d e^2 \sin ^{-1}(c x)}{32 c^4}+\frac{b e^3 x^5 \sqrt{1-c^2 x^2}}{36 c}+\frac{5 b e^3 x^3 \sqrt{1-c^2 x^2}}{144 c^3}+\frac{5 b e^3 x \sqrt{1-c^2 x^2}}{96 c^5}-\frac{5 b e^3 \sin ^{-1}(c x)}{96 c^6}-\frac{1}{2} i b d^3 \sin ^{-1}(c x)^2+b d^3 \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b d^3 \log (x) \sin ^{-1}(c x)","-\frac{1}{2} i b d^3 \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+\frac{3}{2} d^2 e x^2 \left(a+b \sin ^{-1}(c x)\right)+d^3 \log (x) \left(a+b \sin ^{-1}(c x)\right)+\frac{3}{4} d e^2 x^4 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{6} e^3 x^6 \left(a+b \sin ^{-1}(c x)\right)+\frac{3 b d^2 e x \sqrt{1-c^2 x^2}}{4 c}-\frac{3 b d^2 e \sin ^{-1}(c x)}{4 c^2}+\frac{3 b d e^2 x^3 \sqrt{1-c^2 x^2}}{16 c}+\frac{9 b d e^2 x \sqrt{1-c^2 x^2}}{32 c^3}-\frac{9 b d e^2 \sin ^{-1}(c x)}{32 c^4}+\frac{b e^3 x^5 \sqrt{1-c^2 x^2}}{36 c}+\frac{5 b e^3 x^3 \sqrt{1-c^2 x^2}}{144 c^3}+\frac{5 b e^3 x \sqrt{1-c^2 x^2}}{96 c^5}-\frac{5 b e^3 \sin ^{-1}(c x)}{96 c^6}-\frac{1}{2} i b d^3 \sin ^{-1}(c x)^2+b d^3 \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-b d^3 \log (x) \sin ^{-1}(c x)",1,"(3*b*d^2*e*x*Sqrt[1 - c^2*x^2])/(4*c) + (9*b*d*e^2*x*Sqrt[1 - c^2*x^2])/(32*c^3) + (5*b*e^3*x*Sqrt[1 - c^2*x^2])/(96*c^5) + (3*b*d*e^2*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (5*b*e^3*x^3*Sqrt[1 - c^2*x^2])/(144*c^3) + (b*e^3*x^5*Sqrt[1 - c^2*x^2])/(36*c) - (3*b*d^2*e*ArcSin[c*x])/(4*c^2) - (9*b*d*e^2*ArcSin[c*x])/(32*c^4) - (5*b*e^3*ArcSin[c*x])/(96*c^6) - (I/2)*b*d^3*ArcSin[c*x]^2 + (3*d^2*e*x^2*(a + b*ArcSin[c*x]))/2 + (3*d*e^2*x^4*(a + b*ArcSin[c*x]))/4 + (e^3*x^6*(a + b*ArcSin[c*x]))/6 + b*d^3*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - b*d^3*ArcSin[c*x]*Log[x] + d^3*(a + b*ArcSin[c*x])*Log[x] - (I/2)*b*d^3*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",19,13,21,0.6190,1,"{266, 43, 4731, 12, 6742, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
620,1,190,0,0.2710359,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^3*(a + b*ArcSin[c*x]))/x^2,x]","3 d^2 e x \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{x}+d e^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e \sqrt{1-c^2 x^2} \left(15 c^4 d^2+5 c^2 d e+e^2\right)}{5 c^5}-b c d^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b e^2 \left(1-c^2 x^2\right)^{3/2} \left(5 c^2 d+2 e\right)}{15 c^5}+\frac{b e^3 \left(1-c^2 x^2\right)^{5/2}}{25 c^5}","3 d^2 e x \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{x}+d e^2 x^3 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{5} e^3 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{b e \sqrt{1-c^2 x^2} \left(15 c^4 d^2+5 c^2 d e+e^2\right)}{5 c^5}-b c d^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b e^2 \left(1-c^2 x^2\right)^{3/2} \left(5 c^2 d+2 e\right)}{15 c^5}+\frac{b e^3 \left(1-c^2 x^2\right)^{5/2}}{25 c^5}",1,"(b*e*(15*c^4*d^2 + 5*c^2*d*e + e^2)*Sqrt[1 - c^2*x^2])/(5*c^5) - (b*e^2*(5*c^2*d + 2*e)*(1 - c^2*x^2)^(3/2))/(15*c^5) + (b*e^3*(1 - c^2*x^2)^(5/2))/(25*c^5) - (d^3*(a + b*ArcSin[c*x]))/x + 3*d^2*e*x*(a + b*ArcSin[c*x]) + d*e^2*x^3*(a + b*ArcSin[c*x]) + (e^3*x^5*(a + b*ArcSin[c*x]))/5 - b*c*d^3*ArcTanh[Sqrt[1 - c^2*x^2]]","A",6,6,21,0.2857,1,"{270, 4731, 1799, 1620, 63, 208}"
621,1,262,0,0.7792307,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^3*(a + b*ArcSin[c*x]))/x^3,x]","-\frac{3}{2} i b d^2 e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+3 d^2 e \log (x) \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{3}{2} d e^2 x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^3 x^4 \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^3 \sqrt{1-c^2 x^2}}{2 x}+\frac{3 b e^2 x \sqrt{1-c^2 x^2} \left(8 c^2 d+e\right)}{32 c^3}-\frac{3 b e^2 \left(8 c^2 d+e\right) \sin ^{-1}(c x)}{32 c^4}+\frac{b e^3 x^3 \sqrt{1-c^2 x^2}}{16 c}-\frac{3}{2} i b d^2 e \sin ^{-1}(c x)^2+3 b d^2 e \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-3 b d^2 e \log (x) \sin ^{-1}(c x)","-\frac{3}{2} i b d^2 e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)+3 d^2 e \log (x) \left(a+b \sin ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{2 x^2}+\frac{3}{2} d e^2 x^2 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{4} e^3 x^4 \left(a+b \sin ^{-1}(c x)\right)-\frac{b c d^3 \sqrt{1-c^2 x^2}}{2 x}+\frac{3 b e^2 x \sqrt{1-c^2 x^2} \left(8 c^2 d+e\right)}{32 c^3}-\frac{3 b e^2 \left(8 c^2 d+e\right) \sin ^{-1}(c x)}{32 c^4}+\frac{b e^3 x^3 \sqrt{1-c^2 x^2}}{16 c}-\frac{3}{2} i b d^2 e \sin ^{-1}(c x)^2+3 b d^2 e \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)-3 b d^2 e \log (x) \sin ^{-1}(c x)",1,"-(b*c*d^3*Sqrt[1 - c^2*x^2])/(2*x) + (3*b*e^2*(8*c^2*d + e)*x*Sqrt[1 - c^2*x^2])/(32*c^3) + (b*e^3*x^3*Sqrt[1 - c^2*x^2])/(16*c) - (3*b*e^2*(8*c^2*d + e)*ArcSin[c*x])/(32*c^4) - ((3*I)/2)*b*d^2*e*ArcSin[c*x]^2 - (d^3*(a + b*ArcSin[c*x]))/(2*x^2) + (3*d*e^2*x^2*(a + b*ArcSin[c*x]))/2 + (e^3*x^4*(a + b*ArcSin[c*x]))/4 + 3*b*d^2*e*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])] - 3*b*d^2*e*ArcSin[c*x]*Log[x] + 3*d^2*e*(a + b*ArcSin[c*x])*Log[x] - ((3*I)/2)*b*d^2*e*PolyLog[2, E^((2*I)*ArcSin[c*x])]","A",15,16,21,0.7619,1,"{266, 43, 4731, 12, 6742, 1807, 1584, 459, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
622,1,186,0,0.3153914,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^3*(a + b*ArcSin[c*x]))/x^4,x]","-\frac{3 d^2 e \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}+3 d e^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e^3 x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{6} b c d^2 \left(c^2 d+18 e\right) \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b c d^3 \sqrt{1-c^2 x^2}}{6 x^2}+\frac{b e^2 \sqrt{1-c^2 x^2} \left(9 c^2 d+e\right)}{3 c^3}-\frac{b e^3 \left(1-c^2 x^2\right)^{3/2}}{9 c^3}","-\frac{3 d^2 e \left(a+b \sin ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \sin ^{-1}(c x)\right)}{3 x^3}+3 d e^2 x \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{3} e^3 x^3 \left(a+b \sin ^{-1}(c x)\right)-\frac{1}{6} b c d^2 \left(c^2 d+18 e\right) \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{b c d^3 \sqrt{1-c^2 x^2}}{6 x^2}+\frac{b e^2 \sqrt{1-c^2 x^2} \left(9 c^2 d+e\right)}{3 c^3}-\frac{b e^3 \left(1-c^2 x^2\right)^{3/2}}{9 c^3}",1,"(b*e^2*(9*c^2*d + e)*Sqrt[1 - c^2*x^2])/(3*c^3) - (b*c*d^3*Sqrt[1 - c^2*x^2])/(6*x^2) - (b*e^3*(1 - c^2*x^2)^(3/2))/(9*c^3) - (d^3*(a + b*ArcSin[c*x]))/(3*x^3) - (3*d^2*e*(a + b*ArcSin[c*x]))/x + 3*d*e^2*x*(a + b*ArcSin[c*x]) + (e^3*x^3*(a + b*ArcSin[c*x]))/3 - (b*c*d^2*(c^2*d + 18*e)*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",8,8,21,0.3810,1,"{270, 4731, 12, 1799, 1621, 897, 1153, 208}"
623,1,317,0,0.340063,"\int \left(d+e x^2\right)^4 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^4*(a + b*ArcSin[c*x]),x]","\frac{6}{5} d^2 e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{4}{3} d^3 e x^3 \left(a+b \sin ^{-1}(c x)\right)+d^4 x \left(a+b \sin ^{-1}(c x)\right)+\frac{4}{7} d e^3 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{9} e^4 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{2 b e^2 \left(1-c^2 x^2\right)^{5/2} \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{525 c^9}-\frac{4 b e \left(1-c^2 x^2\right)^{3/2} \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{945 c^9}+\frac{b \sqrt{1-c^2 x^2} \left(378 c^4 d^2 e^2+420 c^6 d^3 e+315 c^8 d^4+180 c^2 d e^3+35 e^4\right)}{315 c^9}-\frac{4 b e^3 \left(1-c^2 x^2\right)^{7/2} \left(9 c^2 d+7 e\right)}{441 c^9}+\frac{b e^4 \left(1-c^2 x^2\right)^{9/2}}{81 c^9}","\frac{6}{5} d^2 e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)+\frac{4}{3} d^3 e x^3 \left(a+b \sin ^{-1}(c x)\right)+d^4 x \left(a+b \sin ^{-1}(c x)\right)+\frac{4}{7} d e^3 x^7 \left(a+b \sin ^{-1}(c x)\right)+\frac{1}{9} e^4 x^9 \left(a+b \sin ^{-1}(c x)\right)+\frac{2 b e^2 \left(1-c^2 x^2\right)^{5/2} \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{525 c^9}-\frac{4 b e \left(1-c^2 x^2\right)^{3/2} \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{945 c^9}+\frac{b \sqrt{1-c^2 x^2} \left(378 c^4 d^2 e^2+420 c^6 d^3 e+315 c^8 d^4+180 c^2 d e^3+35 e^4\right)}{315 c^9}-\frac{4 b e^3 \left(1-c^2 x^2\right)^{7/2} \left(9 c^2 d+7 e\right)}{441 c^9}+\frac{b e^4 \left(1-c^2 x^2\right)^{9/2}}{81 c^9}",1,"(b*(315*c^8*d^4 + 420*c^6*d^3*e + 378*c^4*d^2*e^2 + 180*c^2*d*e^3 + 35*e^4)*Sqrt[1 - c^2*x^2])/(315*c^9) - (4*b*e*(105*c^6*d^3 + 189*c^4*d^2*e + 135*c^2*d*e^2 + 35*e^3)*(1 - c^2*x^2)^(3/2))/(945*c^9) + (2*b*e^2*(63*c^4*d^2 + 90*c^2*d*e + 35*e^2)*(1 - c^2*x^2)^(5/2))/(525*c^9) - (4*b*e^3*(9*c^2*d + 7*e)*(1 - c^2*x^2)^(7/2))/(441*c^9) + (b*e^4*(1 - c^2*x^2)^(9/2))/(81*c^9) + d^4*x*(a + b*ArcSin[c*x]) + (4*d^3*e*x^3*(a + b*ArcSin[c*x]))/3 + (6*d^2*e^2*x^5*(a + b*ArcSin[c*x]))/5 + (4*d*e^3*x^7*(a + b*ArcSin[c*x]))/7 + (e^4*x^9*(a + b*ArcSin[c*x]))/9","A",5,5,18,0.2778,1,"{194, 4665, 12, 1799, 1850}"
624,1,653,0,1.0525478,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d + e*x^2),x]","\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 e}-\frac{a d x}{e^2}-\frac{b d \sqrt{1-c^2 x^2}}{c e^2}-\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^3 e}+\frac{b \sqrt{1-c^2 x^2}}{3 c^3 e}-\frac{b d x \sin ^{-1}(c x)}{e^2}","\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{i b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{3 e}-\frac{a d x}{e^2}-\frac{b d \sqrt{1-c^2 x^2}}{c e^2}-\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^3 e}+\frac{b \sqrt{1-c^2 x^2}}{3 c^3 e}-\frac{b d x \sin ^{-1}(c x)}{e^2}",1,"-((a*d*x)/e^2) - (b*d*Sqrt[1 - c^2*x^2])/(c*e^2) + (b*Sqrt[1 - c^2*x^2])/(3*c^3*e) - (b*(1 - c^2*x^2)^(3/2))/(9*c^3*e) - (b*d*x*ArcSin[c*x])/e^2 + (x^3*(a + b*ArcSin[c*x]))/(3*e) + ((-d)^(3/2)*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^(5/2)) - ((-d)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^(5/2)) + ((-d)^(3/2)*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^(5/2)) - ((-d)^(3/2)*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^(5/2)) + ((I/2)*b*(-d)^(3/2)*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e^(5/2) - ((I/2)*b*(-d)^(3/2)*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e^(5/2) + ((I/2)*b*(-d)^(3/2)*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e^(5/2) - ((I/2)*b*(-d)^(3/2)*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e^(5/2)","A",27,12,21,0.5714,1,"{4733, 4619, 261, 4627, 266, 43, 4667, 4741, 4521, 2190, 2279, 2391}"
625,1,559,0,0.9107113,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d + e*x^2),x]","\frac{i b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i d \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e}+\frac{b x \sqrt{1-c^2 x^2}}{4 c e}-\frac{b \sin ^{-1}(c x)}{4 c^2 e}","\frac{i b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{i d \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e^2}+\frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{2 e}+\frac{b x \sqrt{1-c^2 x^2}}{4 c e}-\frac{b \sin ^{-1}(c x)}{4 c^2 e}",1,"(b*x*Sqrt[1 - c^2*x^2])/(4*c*e) - (b*ArcSin[c*x])/(4*c^2*e) + (x^2*(a + b*ArcSin[c*x]))/(2*e) + ((I/2)*d*(a + b*ArcSin[c*x])^2)/(b*e^2) - (d*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^2) - (d*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^2) - (d*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^2) - (d*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^2) + ((I/2)*b*d*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e^2 + ((I/2)*b*d*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e^2 + ((I/2)*b*d*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e^2 + ((I/2)*b*d*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e^2","A",23,9,21,0.4286,1,"{4733, 4627, 321, 216, 4741, 4521, 2190, 2279, 2391}"
626,1,579,0,0.9036571,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d + e*x^2),x]","\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{a x}{e}+\frac{b \sqrt{1-c^2 x^2}}{c e}+\frac{b x \sin ^{-1}(c x)}{e}","\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{a x}{e}+\frac{b \sqrt{1-c^2 x^2}}{c e}+\frac{b x \sin ^{-1}(c x)}{e}",1,"(a*x)/e + (b*Sqrt[1 - c^2*x^2])/(c*e) + (b*x*ArcSin[c*x])/e + (Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^(3/2)) + ((I/2)*b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e^(3/2) - ((I/2)*b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e^(3/2) + ((I/2)*b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e^(3/2) - ((I/2)*b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e^(3/2)","A",23,9,21,0.4286,1,"{4733, 4619, 261, 4667, 4741, 4521, 2190, 2279, 2391}"
627,1,491,0,0.7361624,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d + e*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e}","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 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 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e) - ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e - ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e","A",18,6,19,0.3158,1,"{4733, 4741, 4521, 2190, 2279, 2391}"
628,1,541,0,0.7391387,"\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{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e])","A",18,6,18,0.3333,1,"{4667, 4741, 4521, 2190, 2279, 2391}"
629,1,518,0,0.9295864,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d + e*x^2)),x]","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d}",1,"-((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d) + ((a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/d + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/d + ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/d + ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d","A",25,8,21,0.3810,1,"{4733, 4625, 3717, 2190, 2279, 2391, 4741, 4521}"
630,1,579,0,0.9157627,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d + e*x^2)),x]","\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{d x}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d}","\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{a+b \sin ^{-1}(c x)}{d x}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d}",1,"-((a + b*ArcSin[c*x])/(d*x)) - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d + (Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + ((I/2)*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(-d)^(3/2) - ((I/2)*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(-d)^(3/2) + ((I/2)*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(-d)^(3/2) - ((I/2)*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(-d)^(3/2)","A",24,11,21,0.5238,1,"{4733, 4627, 266, 63, 208, 4667, 4741, 4521, 2190, 2279, 2391}"
631,1,573,0,0.988345,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d + e*x^2)),x]","-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{e \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 d x}","-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{e \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}-\frac{a+b \sin ^{-1}(c x)}{2 d x^2}-\frac{b c \sqrt{1-c^2 x^2}}{2 d x}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*d*x) - (a + b*ArcSin[c*x])/(2*d*x^2) + (e*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^2) + (e*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^2) + (e*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^2) + (e*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^2) - (e*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/d^2 - ((I/2)*b*e*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/d^2 - ((I/2)*b*e*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^2 - ((I/2)*b*e*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/d^2 - ((I/2)*b*e*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^2 + ((I/2)*b*e*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^2","A",27,10,21,0.4762,1,"{4733, 4627, 264, 4625, 3717, 2190, 2279, 2391, 4741, 4521}"
632,1,649,0,0.962196,"\int \frac{a+b \sin ^{-1}(c x)}{x^4 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSin[c*x])/(x^4*(d + e*x^2)),x]","\frac{i b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{i b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{i b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{i b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e \left(a+b \sin ^{-1}(c x)\right)}{d^2 x}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3}+\frac{b c e \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2}-\frac{b c \sqrt{1-c^2 x^2}}{6 d x^2}-\frac{b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d}","\frac{i b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{i b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{i b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{i b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e \left(a+b \sin ^{-1}(c x)\right)}{d^2 x}-\frac{a+b \sin ^{-1}(c x)}{3 d x^3}+\frac{b c e \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2}-\frac{b c \sqrt{1-c^2 x^2}}{6 d x^2}-\frac{b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{6 d}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(6*d*x^2) - (a + b*ArcSin[c*x])/(3*d*x^3) + (e*(a + b*ArcSin[c*x]))/(d^2*x) - (b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/(6*d) + (b*c*e*ArcTanh[Sqrt[1 - c^2*x^2]])/d^2 + (e^(3/2)*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*(-d)^(5/2)) - (e^(3/2)*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*(-d)^(5/2)) + (e^(3/2)*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*(-d)^(5/2)) - (e^(3/2)*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*(-d)^(5/2)) + ((I/2)*b*e^(3/2)*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(-d)^(5/2) - ((I/2)*b*e^(3/2)*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(-d)^(5/2) + ((I/2)*b*e^(3/2)*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(-d)^(5/2) - ((I/2)*b*e^(3/2)*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(-d)^(5/2)","A",29,12,21,0.5714,1,"{4733, 4627, 266, 51, 63, 208, 4667, 4741, 4521, 2190, 2279, 2391}"
633,1,574,0,0.9563109,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d + e*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{d \left(a+b \sin ^{-1}(c x)\right)}{2 e^2 \left(d+e x^2\right)}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e^2}-\frac{b c \sqrt{d} \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 e^2 \sqrt{c^2 d+e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^2}+\frac{d \left(a+b \sin ^{-1}(c x)\right)}{2 e^2 \left(d+e x^2\right)}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e^2}-\frac{b c \sqrt{d} \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 e^2 \sqrt{c^2 d+e}}",1,"(d*(a + b*ArcSin[c*x]))/(2*e^2*(d + e*x^2)) - ((I/2)*(a + b*ArcSin[c*x])^2)/(b*e^2) - (b*c*Sqrt[d]*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(2*e^2*Sqrt[c^2*d + e]) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^2) - ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e^2 - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e^2 - ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e^2 - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e^2","A",23,9,21,0.4286,1,"{4733, 4729, 377, 205, 4741, 4521, 2190, 2279, 2391}"
634,1,83,0,0.0594234,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d + e*x^2)^2,x]","\frac{b c \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 \sqrt{d} e \sqrt{c^2 d+e}}-\frac{a+b \sin ^{-1}(c x)}{2 e \left(d+e x^2\right)}","\frac{b c \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 \sqrt{d} e \sqrt{c^2 d+e}}-\frac{a+b \sin ^{-1}(c x)}{2 e \left(d+e x^2\right)}",1,"-(a + b*ArcSin[c*x])/(2*e*(d + e*x^2)) + (b*c*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(2*Sqrt[d]*e*Sqrt[c^2*d + e])","A",3,3,19,0.1579,1,"{4729, 377, 205}"
635,1,597,0,1.0092059,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d + e*x^2)^2),x]","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{a+b \sin ^{-1}(c x)}{2 d \left(d+e x^2\right)}-\frac{b c \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 d^{3/2} \sqrt{c^2 d+e}}","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^2}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^2}+\frac{a+b \sin ^{-1}(c x)}{2 d \left(d+e x^2\right)}-\frac{b c \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 d^{3/2} \sqrt{c^2 d+e}}",1,"(a + b*ArcSin[c*x])/(2*d*(d + e*x^2)) - (b*c*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(2*d^(3/2)*Sqrt[c^2*d + e]) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^2) + ((a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/d^2 + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/d^2 + ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^2 + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/d^2 + ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^2 - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^2","A",28,11,21,0.5238,1,"{4733, 4625, 3717, 2190, 2279, 2391, 4729, 377, 205, 4741, 4521}"
636,1,632,0,1.0446989,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d + e*x^2)^2),x]","-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(d+e x^2\right)}-\frac{2 e \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{a+b \sin ^{-1}(c x)}{2 d^2 x^2}+\frac{b c e \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 d^{5/2} \sqrt{c^2 d+e}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d^2 x}","-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{d^3}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{2 d^2 \left(d+e x^2\right)}-\frac{2 e \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}-\frac{a+b \sin ^{-1}(c x)}{2 d^2 x^2}+\frac{b c e \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 d^{5/2} \sqrt{c^2 d+e}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d^2 x}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*d^2*x) - (a + b*ArcSin[c*x])/(2*d^2*x^2) - (e*(a + b*ArcSin[c*x]))/(2*d^2*(d + e*x^2)) + (b*c*e*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(2*d^(5/2)*Sqrt[c^2*d + e]) + (e*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^3 + (e*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^3 + (e*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^3 + (e*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^3 - (2*e*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/d^3 - (I*b*e*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/d^3 - (I*b*e*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^3 - (I*b*e*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/d^3 - (I*b*e*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^3 + (I*b*e*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^3","A",30,13,21,0.6190,1,"{4733, 4627, 264, 4625, 3717, 2190, 2279, 2391, 4729, 377, 205, 4741, 4521}"
637,1,787,0,2.0272337,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d + e*x^2)^2,x]","\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{d \left(a+b \sin ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{a x}{e^2}+\frac{b c d \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{5/2} \sqrt{c^2 d+e}}+\frac{b c d \tanh ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{5/2} \sqrt{c^2 d+e}}+\frac{b \sqrt{1-c^2 x^2}}{c e^2}+\frac{b x \sin ^{-1}(c x)}{e^2}","\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 e^{5/2}}-\frac{d \left(a+b \sin ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{d \left(a+b \sin ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{a x}{e^2}+\frac{b c d \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{5/2} \sqrt{c^2 d+e}}+\frac{b c d \tanh ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{5/2} \sqrt{c^2 d+e}}+\frac{b \sqrt{1-c^2 x^2}}{c e^2}+\frac{b x \sin ^{-1}(c x)}{e^2}",1,"(a*x)/e^2 + (b*Sqrt[1 - c^2*x^2])/(c*e^2) + (b*x*ArcSin[c*x])/e^2 - (d*(a + b*ArcSin[c*x]))/(4*e^(5/2)*(Sqrt[-d] - Sqrt[e]*x)) + (d*(a + b*ArcSin[c*x]))/(4*e^(5/2)*(Sqrt[-d] + Sqrt[e]*x)) + (b*c*d*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*e^(5/2)*Sqrt[c^2*d + e]) + (b*c*d*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*e^(5/2)*Sqrt[c^2*d + e]) + (3*Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*e^(5/2)) + (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e^(5/2) - (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e^(5/2) + (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e^(5/2) - (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e^(5/2)","A",49,12,21,0.5714,1,"{4733, 4619, 261, 4667, 4743, 725, 206, 4741, 4521, 2190, 2279, 2391}"
638,1,745,0,1.943274,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d + e*x^2)^2,x]","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \sin ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{a+b \sin ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{3/2} \sqrt{c^2 d+e}}-\frac{b c \tanh ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{3/2} \sqrt{c^2 d+e}}","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \sin ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{a+b \sin ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{3/2} \sqrt{c^2 d+e}}-\frac{b c \tanh ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 e^{3/2} \sqrt{c^2 d+e}}",1,"(a + b*ArcSin[c*x])/(4*e^(3/2)*(Sqrt[-d] - Sqrt[e]*x)) - (a + b*ArcSin[c*x])/(4*e^(3/2)*(Sqrt[-d] + Sqrt[e]*x)) - (b*c*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*e^(3/2)*Sqrt[c^2*d + e]) - (b*c*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*e^(3/2)*Sqrt[c^2*d + e]) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((I/4)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(3/2)) - ((I/4)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2)) + ((I/4)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(3/2)) - ((I/4)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2))","A",46,10,21,0.4762,1,"{4733, 4667, 4743, 725, 206, 4741, 4521, 2190, 2279, 2391}"
639,1,757,0,0.99458,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \sin ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \sin ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{b c \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d+e}}+\frac{b c \tanh ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d+e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \sin ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \sin ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}+\sqrt{e} x\right)}+\frac{b c \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d+e}}+\frac{b c \tanh ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{1-c^2 x^2} \sqrt{c^2 d+e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d+e}}",1,"-(a + b*ArcSin[c*x])/(4*d*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcSin[c*x])/(4*d*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)) + (b*c*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*d*Sqrt[e]*Sqrt[c^2*d + e]) + (b*c*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*d*Sqrt[e]*Sqrt[c^2*d + e]) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((I/4)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/((-d)^(3/2)*Sqrt[e]) + ((I/4)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e]) - ((I/4)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/((-d)^(3/2)*Sqrt[e]) + ((I/4)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e])","A",26,9,18,0.5000,1,"{4667, 4743, 725, 206, 4741, 4521, 2190, 2279, 2391}"
640,1,795,0,1.9979331,"\int \frac{a+b \sin ^{-1}(c x)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])/(x^2*(d + e*x^2)^2),x]","-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{a+b \sin ^{-1}(c x)}{d^2 x}+\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right)}{4 d^2 \sqrt{d c^2+e}}-\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right)}{4 d^2 \sqrt{d c^2+e}}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}","-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right) \left(a+b \sin ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{a+b \sin ^{-1}(c x)}{d^2 x}+\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{\sqrt{e} \left(a+b \sin ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right)}{4 d^2 \sqrt{d c^2+e}}-\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right)}{4 d^2 \sqrt{d c^2+e}}-\frac{b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{d^2}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}",1,"-((a + b*ArcSin[c*x])/(d^2*x)) + (Sqrt[e]*(a + b*ArcSin[c*x]))/(4*d^2*(Sqrt[-d] - Sqrt[e]*x)) - (Sqrt[e]*(a + b*ArcSin[c*x]))/(4*d^2*(Sqrt[-d] + Sqrt[e]*x)) - (b*c*Sqrt[e]*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*d^2*Sqrt[c^2*d + e]) - (b*c*Sqrt[e]*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(4*d^2*Sqrt[c^2*d + e]) - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d^2 - (3*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (((3*I)/4)*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(-d)^(5/2) + (((3*I)/4)*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(-d)^(5/2) - (((3*I)/4)*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(-d)^(5/2) + (((3*I)/4)*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(-d)^(5/2)","A",50,14,21,0.6667,1,"{4733, 4627, 266, 63, 208, 4667, 4743, 725, 206, 4741, 4521, 2190, 2279, 2391}"
641,1,705,0,1.0945622,"\int \frac{x^5 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*ArcSin[c*x]))/(d + e*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{4 e^3 \left(d+e x^2\right)^2}+\frac{d \left(a+b \sin ^{-1}(c x)\right)}{e^3 \left(d+e x^2\right)}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e^3}+\frac{b c d x \sqrt{1-c^2 x^2}}{8 e^2 \left(c^2 d+e\right) \left(d+e x^2\right)}+\frac{b c \sqrt{d} \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 e^3 \left(c^2 d+e\right)^{3/2}}-\frac{b c \sqrt{d} \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{e^3 \sqrt{c^2 d+e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 e^3}-\frac{d^2 \left(a+b \sin ^{-1}(c x)\right)}{4 e^3 \left(d+e x^2\right)^2}+\frac{d \left(a+b \sin ^{-1}(c x)\right)}{e^3 \left(d+e x^2\right)}-\frac{i \left(a+b \sin ^{-1}(c x)\right)^2}{2 b e^3}+\frac{b c d x \sqrt{1-c^2 x^2}}{8 e^2 \left(c^2 d+e\right) \left(d+e x^2\right)}+\frac{b c \sqrt{d} \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 e^3 \left(c^2 d+e\right)^{3/2}}-\frac{b c \sqrt{d} \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{e^3 \sqrt{c^2 d+e}}",1,"(b*c*d*x*Sqrt[1 - c^2*x^2])/(8*e^2*(c^2*d + e)*(d + e*x^2)) - (d^2*(a + b*ArcSin[c*x]))/(4*e^3*(d + e*x^2)^2) + (d*(a + b*ArcSin[c*x]))/(e^3*(d + e*x^2)) - ((I/2)*(a + b*ArcSin[c*x])^2)/(b*e^3) - (b*c*Sqrt[d]*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(e^3*Sqrt[c^2*d + e]) + (b*c*Sqrt[d]*(2*c^2*d + e)*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(8*e^3*(c^2*d + e)^(3/2)) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*e^3) - ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/e^3 - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/e^3 - ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/e^3 - ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/e^3","A",27,10,21,0.4762,1,"{4733, 4729, 382, 377, 205, 4741, 4521, 2190, 2279, 2391}"
642,1,153,0,0.1938647,"\int \frac{x^3 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSin[c*x]))/(d + e*x^2)^3,x]","\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}+\frac{b c \left(2 c^2 d+3 e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 \sqrt{d} e^2 \left(c^2 d+e\right)^{3/2}}-\frac{b c x \sqrt{1-c^2 x^2}}{8 e \left(c^2 d+e\right) \left(d+e x^2\right)}-\frac{b \sin ^{-1}(c x)}{4 d e^2}","\frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}+\frac{b c \left(2 c^2 d+3 e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 \sqrt{d} e^2 \left(c^2 d+e\right)^{3/2}}-\frac{b c x \sqrt{1-c^2 x^2}}{8 e \left(c^2 d+e\right) \left(d+e x^2\right)}-\frac{b \sin ^{-1}(c x)}{4 d e^2}",1,"-(b*c*x*Sqrt[1 - c^2*x^2])/(8*e*(c^2*d + e)*(d + e*x^2)) - (b*ArcSin[c*x])/(4*d*e^2) + (x^4*(a + b*ArcSin[c*x]))/(4*d*(d + e*x^2)^2) + (b*c*(2*c^2*d + 3*e)*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(8*Sqrt[d]*e^2*(c^2*d + e)^(3/2))","A",7,8,21,0.3810,1,"{264, 4731, 12, 470, 523, 216, 377, 205}"
643,1,133,0,0.0953057,"\int \frac{x \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*ArcSin[c*x]))/(d + e*x^2)^3,x]","-\frac{a+b \sin ^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b c \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 d^{3/2} e \left(c^2 d+e\right)^{3/2}}+\frac{b c x \sqrt{1-c^2 x^2}}{8 d \left(c^2 d+e\right) \left(d+e x^2\right)}","-\frac{a+b \sin ^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b c \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 d^{3/2} e \left(c^2 d+e\right)^{3/2}}+\frac{b c x \sqrt{1-c^2 x^2}}{8 d \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"(b*c*x*Sqrt[1 - c^2*x^2])/(8*d*(c^2*d + e)*(d + e*x^2)) - (a + b*ArcSin[c*x])/(4*e*(d + e*x^2)^2) + (b*c*(2*c^2*d + e)*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(8*d^(3/2)*e*(c^2*d + e)^(3/2))","A",4,4,19,0.2105,1,"{4729, 382, 377, 205}"
644,1,727,0,1.1318665,"\int \frac{a+b \sin ^{-1}(c x)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(x*(d + e*x^2)^3),x]","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{a+b \sin ^{-1}(c x)}{2 d^2 \left(d+e x^2\right)}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}+\frac{a+b \sin ^{-1}(c x)}{4 d \left(d+e x^2\right)^2}-\frac{b c e x \sqrt{1-c^2 x^2}}{8 d^2 \left(c^2 d+e\right) \left(d+e x^2\right)}-\frac{b c \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 d^{5/2} \left(c^2 d+e\right)^{3/2}}-\frac{b c \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 d^{5/2} \sqrt{c^2 d+e}}","\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{i b \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^3}+\frac{a+b \sin ^{-1}(c x)}{2 d^2 \left(d+e x^2\right)}+\frac{\log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^3}+\frac{a+b \sin ^{-1}(c x)}{4 d \left(d+e x^2\right)^2}-\frac{b c e x \sqrt{1-c^2 x^2}}{8 d^2 \left(c^2 d+e\right) \left(d+e x^2\right)}-\frac{b c \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 d^{5/2} \left(c^2 d+e\right)^{3/2}}-\frac{b c \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{2 d^{5/2} \sqrt{c^2 d+e}}",1,"-(b*c*e*x*Sqrt[1 - c^2*x^2])/(8*d^2*(c^2*d + e)*(d + e*x^2)) + (a + b*ArcSin[c*x])/(4*d*(d + e*x^2)^2) + (a + b*ArcSin[c*x])/(2*d^2*(d + e*x^2)) - (b*c*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(2*d^(5/2)*Sqrt[c^2*d + e]) - (b*c*(2*c^2*d + e)*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(8*d^(5/2)*(c^2*d + e)^(3/2)) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^3) + ((a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/d^3 + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/d^3 + ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^3 + ((I/2)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/d^3 + ((I/2)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^3 - ((I/2)*b*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^3","A",32,12,21,0.5714,1,"{4733, 4625, 3717, 2190, 2279, 2391, 4729, 382, 377, 205, 4741, 4521}"
645,1,783,0,1.1748753,"\int \frac{a+b \sin ^{-1}(c x)}{x^3 \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(x^3*(d + e*x^2)^3),x]","-\frac{3 i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{3 i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{3 i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{3 i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{d^3 \left(d+e x^2\right)}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{4 d^2 \left(d+e x^2\right)^2}-\frac{3 e \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^4}-\frac{a+b \sin ^{-1}(c x)}{2 d^3 x^2}+\frac{b c e^2 x \sqrt{1-c^2 x^2}}{8 d^3 \left(c^2 d+e\right) \left(d+e x^2\right)}+\frac{b c e \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 d^{7/2} \left(c^2 d+e\right)^{3/2}}+\frac{b c e \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{d^{7/2} \sqrt{c^2 d+e}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d^3 x}","-\frac{3 i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{3 i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{3 i b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{3 i b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 i b e \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{-\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}+\frac{3 e \left(a+b \sin ^{-1}(c x)\right) \log \left(1+\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 d+e}+i c \sqrt{-d}}\right)}{2 d^4}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{d^3 \left(d+e x^2\right)}-\frac{e \left(a+b \sin ^{-1}(c x)\right)}{4 d^2 \left(d+e x^2\right)^2}-\frac{3 e \log \left(1-e^{2 i \sin ^{-1}(c x)}\right) \left(a+b \sin ^{-1}(c x)\right)}{d^4}-\frac{a+b \sin ^{-1}(c x)}{2 d^3 x^2}+\frac{b c e^2 x \sqrt{1-c^2 x^2}}{8 d^3 \left(c^2 d+e\right) \left(d+e x^2\right)}+\frac{b c e \left(2 c^2 d+e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 d^{7/2} \left(c^2 d+e\right)^{3/2}}+\frac{b c e \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{d^{7/2} \sqrt{c^2 d+e}}-\frac{b c \sqrt{1-c^2 x^2}}{2 d^3 x}",1,"-(b*c*Sqrt[1 - c^2*x^2])/(2*d^3*x) + (b*c*e^2*x*Sqrt[1 - c^2*x^2])/(8*d^3*(c^2*d + e)*(d + e*x^2)) - (a + b*ArcSin[c*x])/(2*d^3*x^2) - (e*(a + b*ArcSin[c*x]))/(4*d^2*(d + e*x^2)^2) - (e*(a + b*ArcSin[c*x]))/(d^3*(d + e*x^2)) + (b*c*e*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(d^(7/2)*Sqrt[c^2*d + e]) + (b*c*e*(2*c^2*d + e)*ArcTan[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[1 - c^2*x^2])])/(8*d^(7/2)*(c^2*d + e)^(3/2)) + (3*e*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^4) + (3*e*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*d^4) + (3*e*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^4) + (3*e*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*d^4) - (3*e*(a + b*ArcSin[c*x])*Log[1 - E^((2*I)*ArcSin[c*x])])/d^4 - (((3*I)/2)*b*e*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/d^4 - (((3*I)/2)*b*e*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/d^4 - (((3*I)/2)*b*e*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/d^4 - (((3*I)/2)*b*e*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/d^4 + (((3*I)/2)*b*e*PolyLog[2, E^((2*I)*ArcSin[c*x])])/d^4","A",34,14,21,0.6667,1,"{4733, 4627, 264, 4625, 3717, 2190, 2279, 2391, 4729, 382, 377, 205, 4741, 4521}"
646,1,1082,0,3.3840682,"\int \frac{x^4 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSin[c*x]))/(d + e*x^2)^3,x]","\frac{b d \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{5/2} \left(d c^2+e\right)^{3/2}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{5/2} \left(d c^2+e\right)^{3/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 e^{5/2} \sqrt{d c^2+e}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 e^{5/2} \sqrt{d c^2+e}}+\frac{b \sqrt{-d} \sqrt{1-c^2 x^2} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b \sqrt{-d} \sqrt{1-c^2 x^2} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}","\frac{b d \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{5/2} \left(d c^2+e\right)^{3/2}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{5/2} \left(d c^2+e\right)^{3/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 e^{5/2} \sqrt{d c^2+e}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 e^{5/2} \sqrt{d c^2+e}}+\frac{b \sqrt{-d} \sqrt{1-c^2 x^2} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b \sqrt{-d} \sqrt{1-c^2 x^2} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{\sqrt{-d} \left(a+b \sin ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}",1,"(b*c*Sqrt[-d]*Sqrt[1 - c^2*x^2])/(16*e^2*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) + (b*c*Sqrt[-d]*Sqrt[1 - c^2*x^2])/(16*e^2*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (Sqrt[-d]*(a + b*ArcSin[c*x]))/(16*e^(5/2)*(Sqrt[-d] - Sqrt[e]*x)^2) + (5*(a + b*ArcSin[c*x]))/(16*e^(5/2)*(Sqrt[-d] - Sqrt[e]*x)) + (Sqrt[-d]*(a + b*ArcSin[c*x]))/(16*e^(5/2)*(Sqrt[-d] + Sqrt[e]*x)^2) - (5*(a + b*ArcSin[c*x]))/(16*e^(5/2)*(Sqrt[-d] + Sqrt[e]*x)) + (b*c^3*d*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*e^(5/2)*(c^2*d + e)^(3/2)) - (5*b*c*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*e^(5/2)*Sqrt[c^2*d + e]) + (b*c^3*d*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*e^(5/2)*(c^2*d + e)^(3/2)) - (5*b*c*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*e^(5/2)*Sqrt[c^2*d + e]) + (3*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (((3*I)/16)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(5/2)) - (((3*I)/16)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2)) + (((3*I)/16)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(5/2)) - (((3*I)/16)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2))","A",80,11,21,0.5238,1,"{4733, 4667, 4743, 731, 725, 206, 4741, 4521, 2190, 2279, 2391}"
647,1,1092,0,2.6106283,"\int \frac{x^2 \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSin[c*x]))/(d + e*x^2)^3,x]","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{3/2} \left(d c^2+e\right)^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{3/2} \left(d c^2+e\right)^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d e^{3/2} \sqrt{d c^2+e}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d e^{3/2} \sqrt{d c^2+e}}+\frac{b \sqrt{1-c^2 x^2} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b \sqrt{1-c^2 x^2} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \sin ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \sin ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \sin ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \sin ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{3/2} \left(d c^2+e\right)^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 e^{3/2} \left(d c^2+e\right)^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d e^{3/2} \sqrt{d c^2+e}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d e^{3/2} \sqrt{d c^2+e}}+\frac{b \sqrt{1-c^2 x^2} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b \sqrt{1-c^2 x^2} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \sin ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \sin ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \sin ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \sin ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}",1,"(b*c*Sqrt[1 - c^2*x^2])/(16*Sqrt[-d]*e*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) + (b*c*Sqrt[1 - c^2*x^2])/(16*Sqrt[-d]*e*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (a + b*ArcSin[c*x])/(16*Sqrt[-d]*e^(3/2)*(Sqrt[-d] - Sqrt[e]*x)^2) - (a + b*ArcSin[c*x])/(16*d*e^(3/2)*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcSin[c*x])/(16*Sqrt[-d]*e^(3/2)*(Sqrt[-d] + Sqrt[e]*x)^2) + (a + b*ArcSin[c*x])/(16*d*e^(3/2)*(Sqrt[-d] + Sqrt[e]*x)) - (b*c^3*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*e^(3/2)*(c^2*d + e)^(3/2)) + (b*c*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d*e^(3/2)*Sqrt[c^2*d + e]) - (b*c^3*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*e^(3/2)*(c^2*d + e)^(3/2)) + (b*c*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d*e^(3/2)*Sqrt[c^2*d + e]) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((I/16)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/((-d)^(3/2)*e^(3/2)) + ((I/16)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2)) - ((I/16)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/((-d)^(3/2)*e^(3/2)) + ((I/16)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2))","A",62,11,21,0.5238,1,"{4733, 4667, 4743, 731, 725, 206, 4741, 4521, 2190, 2279, 2391}"
648,1,1092,0,1.2478686,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x^2)^3,x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 d \sqrt{e} \left(d c^2+e\right)^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 d \sqrt{e} \left(d c^2+e\right)^{3/2}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d^2 \sqrt{e} \sqrt{d c^2+e}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d^2 \sqrt{e} \sqrt{d c^2+e}}+\frac{b \sqrt{1-c^2 x^2} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b \sqrt{1-c^2 x^2} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \sin ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \sin ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 d \sqrt{e} \left(d c^2+e\right)^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c^3}{16 d \sqrt{e} \left(d c^2+e\right)^{3/2}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d^2 \sqrt{e} \sqrt{d c^2+e}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{-d} x c^2+\sqrt{e}}{\sqrt{d c^2+e} \sqrt{1-c^2 x^2}}\right) c}{16 d^2 \sqrt{e} \sqrt{d c^2+e}}+\frac{b \sqrt{1-c^2 x^2} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{b \sqrt{1-c^2 x^2} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \sin ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \sin ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sin ^{-1}(c x)\right) \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}",1,"(b*c*Sqrt[1 - c^2*x^2])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) + (b*c*Sqrt[1 - c^2*x^2])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (a + b*ArcSin[c*x])/(16*(-d)^(3/2)*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)^2) - (3*(a + b*ArcSin[c*x]))/(16*d^2*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcSin[c*x])/(16*(-d)^(3/2)*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)^2) + (3*(a + b*ArcSin[c*x]))/(16*d^2*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)) + (b*c^3*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d*Sqrt[e]*(c^2*d + e)^(3/2)) + (3*b*c*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^2*Sqrt[e]*Sqrt[c^2*d + e]) + (b*c^3*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d*Sqrt[e]*(c^2*d + e)^(3/2)) + (3*b*c*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^2*Sqrt[e]*Sqrt[c^2*d + e]) + (3*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (((3*I)/16)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/((-d)^(5/2)*Sqrt[e]) - (((3*I)/16)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e]) + (((3*I)/16)*b*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/((-d)^(5/2)*Sqrt[e]) - (((3*I)/16)*b*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e])","A",34,10,18,0.5556,1,"{4667, 4743, 731, 725, 206, 4741, 4521, 2190, 2279, 2391}"
649,0,0,0,0.0217492,"\int \sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcSin[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
650,0,0,0,0.0225675,"\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSin[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \sin ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \sin ^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSin[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
651,1,70,0,0.0985282,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{d \sqrt{e}}","\frac{x \left(a+b \sin ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{d \sqrt{e}}",1,"(x*(a + b*ArcSin[c*x]))/(d*Sqrt[d + e*x^2]) + (b*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(d*Sqrt[e])","A",6,7,20,0.3500,1,"{191, 4665, 12, 444, 63, 217, 203}"
652,1,146,0,0.1600703,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{2 b \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e}}+\frac{b c \sqrt{1-c^2 x^2}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}","\frac{2 x \left(a+b \sin ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{2 b \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e}}+\frac{b c \sqrt{1-c^2 x^2}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}",1,"(b*c*Sqrt[1 - c^2*x^2])/(3*d*(c^2*d + e)*Sqrt[d + e*x^2]) + (x*(a + b*ArcSin[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcSin[c*x]))/(3*d^2*Sqrt[d + e*x^2]) + (2*b*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(3*d^2*Sqrt[e])","A",7,9,20,0.4500,1,"{192, 191, 4665, 12, 571, 78, 63, 217, 203}"
653,1,226,0,0.8245667,"\int \frac{a+b \sin ^{-1}(c x)}{\left(d+e x^2\right)^{7/2}} \, dx","Int[(a + b*ArcSin[c*x])/(d + e*x^2)^(7/2),x]","\frac{8 x \left(a+b \sin ^{-1}(c x)\right)}{15 d^3 \sqrt{d+e x^2}}+\frac{4 x \left(a+b \sin ^{-1}(c x)\right)}{15 d^2 \left(d+e x^2\right)^{3/2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{5 d \left(d+e x^2\right)^{5/2}}+\frac{2 b c \sqrt{1-c^2 x^2} \left(3 c^2 d+2 e\right)}{15 d^2 \left(c^2 d+e\right)^2 \sqrt{d+e x^2}}+\frac{8 b \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{15 d^3 \sqrt{e}}+\frac{b c \sqrt{1-c^2 x^2}}{15 d \left(c^2 d+e\right) \left(d+e x^2\right)^{3/2}}","\frac{8 x \left(a+b \sin ^{-1}(c x)\right)}{15 d^3 \sqrt{d+e x^2}}+\frac{4 x \left(a+b \sin ^{-1}(c x)\right)}{15 d^2 \left(d+e x^2\right)^{3/2}}+\frac{x \left(a+b \sin ^{-1}(c x)\right)}{5 d \left(d+e x^2\right)^{5/2}}+\frac{2 b c \sqrt{1-c^2 x^2} \left(3 c^2 d+2 e\right)}{15 d^2 \left(c^2 d+e\right)^2 \sqrt{d+e x^2}}+\frac{8 b \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{15 d^3 \sqrt{e}}+\frac{b c \sqrt{1-c^2 x^2}}{15 d \left(c^2 d+e\right) \left(d+e x^2\right)^{3/2}}",1,"(b*c*Sqrt[1 - c^2*x^2])/(15*d*(c^2*d + e)*(d + e*x^2)^(3/2)) + (2*b*c*(3*c^2*d + 2*e)*Sqrt[1 - c^2*x^2])/(15*d^2*(c^2*d + e)^2*Sqrt[d + e*x^2]) + (x*(a + b*ArcSin[c*x]))/(5*d*(d + e*x^2)^(5/2)) + (4*x*(a + b*ArcSin[c*x]))/(15*d^2*(d + e*x^2)^(3/2)) + (8*x*(a + b*ArcSin[c*x]))/(15*d^3*Sqrt[d + e*x^2]) + (8*b*ArcTan[(Sqrt[e]*Sqrt[1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(15*d^3*Sqrt[e])","A",8,10,20,0.5000,1,"{192, 191, 4665, 12, 6715, 949, 78, 63, 217, 203}"
654,1,455,0,2.3762853,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*ArcSin[c*x]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \sin ^{-1}(c x)\right)}{f^7 (m+7)}-\frac{b c (f x)^{m+2} \left(\frac{e \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{c^6 (m+3)^2 (m+5)^2 (m+7)^2}+\frac{d^3}{m^2+3 m+2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2}+\frac{b e \sqrt{1-c^2 x^2} (f x)^{m+2} \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{c^5 f^2 (m+3)^2 (m+5)^2 (m+7)^2}+\frac{b e^2 \sqrt{1-c^2 x^2} (f x)^{m+4} \left(3 c^2 d (m+7)^2+e \left(m^2+11 m+30\right)\right)}{c^3 f^4 (m+5)^2 (m+7)^2}+\frac{b e^3 \sqrt{1-c^2 x^2} (f x)^{m+6}}{c f^6 (m+7)^2}","\frac{3 d^2 e (f x)^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \sin ^{-1}(c x)\right)}{f^7 (m+7)}-\frac{b (f x)^{m+2} \left(\frac{e (m+2) \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{(m+3) (m+5) (m+7)}+\frac{c^6 d^3 (m+3) (m+5) (m+7)}{m+1}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c^5 f^2 (m+2) (m+3) (m+5) (m+7)}+\frac{b e \sqrt{1-c^2 x^2} (f x)^{m+2} \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{c^5 f^2 (m+3)^2 (m+5)^2 (m+7)^2}+\frac{b e^2 \sqrt{1-c^2 x^2} (f x)^{m+4} \left(3 c^2 d (m+7)^2+e \left(m^2+11 m+30\right)\right)}{c^3 f^4 (m+5)^2 (m+7)^2}+\frac{b e^3 \sqrt{1-c^2 x^2} (f x)^{m+6}}{c f^6 (m+7)^2}",1,"(b*e*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4))*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2])/(c^5*f^2*(3 + m)^2*(5 + m)^2*(7 + m)^2) + (b*e^2*(3*c^2*d*(7 + m)^2 + e*(30 + 11*m + m^2))*(f*x)^(4 + m)*Sqrt[1 - c^2*x^2])/(c^3*f^4*(5 + m)^2*(7 + m)^2) + (b*e^3*(f*x)^(6 + m)*Sqrt[1 - c^2*x^2])/(c*f^6*(7 + m)^2) + (d^3*(f*x)^(1 + m)*(a + b*ArcSin[c*x]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*ArcSin[c*x]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*ArcSin[c*x]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*ArcSin[c*x]))/(f^7*(7 + m)) - (b*c*(d^3/(2 + 3*m + m^2) + (e*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4)))/(c^6*(3 + m)^2*(5 + m)^2*(7 + m)^2))*(f*x)^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/f^2","A",6,7,23,0.3043,1,"{270, 4731, 12, 1809, 1267, 459, 364}"
655,1,272,0,0.4152642,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*ArcSin[c*x]),x]","\frac{d^2 (f x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{f^5 (m+5)}-\frac{b c (f x)^{m+2} \left(\frac{e \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{c^4 (m+3)^2 (m+5)^2}+\frac{d^2}{m^2+3 m+2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2}+\frac{b e \sqrt{1-c^2 x^2} (f x)^{m+2} \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{c^3 f^2 (m+3)^2 (m+5)^2}+\frac{b e^2 \sqrt{1-c^2 x^2} (f x)^{m+4}}{c f^4 (m+5)^2}","\frac{d^2 (f x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \sin ^{-1}(c x)\right)}{f^5 (m+5)}-\frac{b (f x)^{m+2} \left(\frac{c^4 d^2 (m+3) (m+5)}{m+1}+\frac{e (m+2) \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{(m+3) (m+5)}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c^3 f^2 (m+2) (m+3) (m+5)}+\frac{b e \sqrt{1-c^2 x^2} (f x)^{m+2} \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{c^3 f^2 (m+3)^2 (m+5)^2}+\frac{b e^2 \sqrt{1-c^2 x^2} (f x)^{m+4}}{c f^4 (m+5)^2}",1,"(b*e*(2*c^2*d*(5 + m)^2 + e*(12 + 7*m + m^2))*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2])/(c^3*f^2*(3 + m)^2*(5 + m)^2) + (b*e^2*(f*x)^(4 + m)*Sqrt[1 - c^2*x^2])/(c*f^4*(5 + m)^2) + (d^2*(f*x)^(1 + m)*(a + b*ArcSin[c*x]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*ArcSin[c*x]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*ArcSin[c*x]))/(f^5*(5 + m)) - (b*c*(d^2/(2 + 3*m + m^2) + (e*(2*c^2*d*(5 + m)^2 + e*(12 + 7*m + m^2)))/(c^4*(3 + m)^2*(5 + m)^2))*(f*x)^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/f^2","A",5,6,23,0.2609,1,"{270, 4731, 12, 1267, 459, 364}"
656,1,148,0,0.1661871,"\int (f x)^m \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*ArcSin[c*x]),x]","\frac{d (f x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{f^3 (m+3)}-\frac{b c (f x)^{m+2} \left(\frac{e}{c^2 (m+3)^2}+\frac{d}{m^2+3 m+2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2}+\frac{b e \sqrt{1-c^2 x^2} (f x)^{m+2}}{c f^2 (m+3)^2}","\frac{d (f x)^{m+1} \left(a+b \sin ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \sin ^{-1}(c x)\right)}{f^3 (m+3)}-\frac{b (f x)^{m+2} \left(c^2 d (m+3)^2+e (m+1) (m+2)\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c f^2 (m+1) (m+2) (m+3)^2}+\frac{b e \sqrt{1-c^2 x^2} (f x)^{m+2}}{c f^2 (m+3)^2}",1,"(b*e*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2])/(c*f^2*(3 + m)^2) + (d*(f*x)^(1 + m)*(a + b*ArcSin[c*x]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*ArcSin[c*x]))/(f^3*(3 + m)) - (b*c*(e/(c^2*(3 + m)^2) + d/(2 + 3*m + m^2))*(f*x)^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/f^2","A",4,5,21,0.2381,1,"{14, 4731, 12, 459, 364}"
657,0,0,0,0.0622664,"\int \frac{(f x)^m \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*ArcSin[c*x]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \sin ^{-1}(c x)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSin[c*x]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
658,0,0,0,0.0593164,"\int \frac{(f x)^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcSin[c*x]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \sin ^{-1}(c x)\right)}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSin[c*x]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
659,1,569,0,0.9626797,"\int \left(d+e x^2\right)^3 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)^3*(a + b*ArcSin[c*x])^2,x]","\frac{2 b d^2 e x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{4 b d^2 e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^3}+\frac{2 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{6 b d e^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b d e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c^3}+\frac{16 b d e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c^5}+\frac{2 b e^3 x^6 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{49 c}+\frac{12 b e^3 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{245 c^3}+\frac{16 b e^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{245 c^5}+\frac{32 b e^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{245 c^7}+d^2 e x^3 \left(a+b \sin ^{-1}(c x)\right)^2+d^3 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{5} d e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{7} e^3 x^7 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 d^2 e x}{3 c^2}-\frac{8 b^2 d e^2 x^3}{75 c^2}-\frac{16 b^2 d e^2 x}{25 c^4}-\frac{12 b^2 e^3 x^5}{1225 c^2}-\frac{16 b^2 e^3 x^3}{735 c^4}-\frac{32 b^2 e^3 x}{245 c^6}-\frac{2}{9} b^2 d^2 e x^3-2 b^2 d^3 x-\frac{6}{125} b^2 d e^2 x^5-\frac{2}{343} b^2 e^3 x^7","\frac{2 b d^2 e x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c}+\frac{4 b d^2 e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{3 c^3}+\frac{2 b d^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{6 b d e^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b d e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c^3}+\frac{16 b d e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c^5}+\frac{2 b e^3 x^6 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{49 c}+\frac{12 b e^3 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{245 c^3}+\frac{16 b e^3 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{245 c^5}+\frac{32 b e^3 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{245 c^7}+d^2 e x^3 \left(a+b \sin ^{-1}(c x)\right)^2+d^3 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{3}{5} d e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{7} e^3 x^7 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 d^2 e x}{3 c^2}-\frac{8 b^2 d e^2 x^3}{75 c^2}-\frac{16 b^2 d e^2 x}{25 c^4}-\frac{12 b^2 e^3 x^5}{1225 c^2}-\frac{16 b^2 e^3 x^3}{735 c^4}-\frac{32 b^2 e^3 x}{245 c^6}-\frac{2}{9} b^2 d^2 e x^3-2 b^2 d^3 x-\frac{6}{125} b^2 d e^2 x^5-\frac{2}{343} b^2 e^3 x^7",1,"-2*b^2*d^3*x - (4*b^2*d^2*e*x)/(3*c^2) - (16*b^2*d*e^2*x)/(25*c^4) - (32*b^2*e^3*x)/(245*c^6) - (2*b^2*d^2*e*x^3)/9 - (8*b^2*d*e^2*x^3)/(75*c^2) - (16*b^2*e^3*x^3)/(735*c^4) - (6*b^2*d*e^2*x^5)/125 - (12*b^2*e^3*x^5)/(1225*c^2) - (2*b^2*e^3*x^7)/343 + (2*b*d^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (4*b*d^2*e*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c^3) + (16*b*d*e^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c^5) + (32*b*e^3*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(245*c^7) + (2*b*d^2*e*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(3*c) + (8*b*d*e^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c^3) + (16*b*e^3*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(245*c^5) + (6*b*d*e^2*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c) + (12*b*e^3*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(245*c^3) + (2*b*e^3*x^6*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(49*c) + d^3*x*(a + b*ArcSin[c*x])^2 + d^2*e*x^3*(a + b*ArcSin[c*x])^2 + (3*d*e^2*x^5*(a + b*ArcSin[c*x])^2)/5 + (e^3*x^7*(a + b*ArcSin[c*x])^2)/7","A",26,7,20,0.3500,1,"{4667, 4619, 4677, 8, 4627, 4707, 30}"
660,1,335,0,0.5565169,"\int \left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)^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{4 b d e x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{8 b d e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{2 b e^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^3}+\frac{16 b e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^5}+d^2 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{3} d e x^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{5} e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{8 b^2 d e x}{9 c^2}-\frac{8 b^2 e^2 x^3}{225 c^2}-\frac{16 b^2 e^2 x}{75 c^4}-2 b^2 d^2 x-\frac{4}{27} b^2 d e x^3-\frac{2}{125} b^2 e^2 x^5","\frac{2 b d^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{4 b d e x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{8 b d e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+\frac{2 b e^2 x^4 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{25 c}+\frac{8 b e^2 x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^3}+\frac{16 b e^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{75 c^5}+d^2 x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{2}{3} d e x^3 \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{5} e^2 x^5 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{8 b^2 d e x}{9 c^2}-\frac{8 b^2 e^2 x^3}{225 c^2}-\frac{16 b^2 e^2 x}{75 c^4}-2 b^2 d^2 x-\frac{4}{27} b^2 d e x^3-\frac{2}{125} b^2 e^2 x^5",1,"-2*b^2*d^2*x - (8*b^2*d*e*x)/(9*c^2) - (16*b^2*e^2*x)/(75*c^4) - (4*b^2*d*e*x^3)/27 - (8*b^2*e^2*x^3)/(225*c^2) - (2*b^2*e^2*x^5)/125 + (2*b*d^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (8*b*d*e*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (16*b*e^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(75*c^5) + (4*b*d*e*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) + (8*b*e^2*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(75*c^3) + (2*b*e^2*x^4*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(25*c) + d^2*x*(a + b*ArcSin[c*x])^2 + (2*d*e*x^3*(a + b*ArcSin[c*x])^2)/3 + (e^2*x^5*(a + b*ArcSin[c*x])^2)/5","A",17,7,20,0.3500,1,"{4667, 4619, 4677, 8, 4627, 4707, 30}"
661,1,156,0,0.2614113,"\int \left(d+e x^2\right) \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 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{2 b e x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+d x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{3} e x^3 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 e x}{9 c^2}-2 b^2 d x-\frac{2}{27} b^2 e x^3","\frac{2 b d \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{c}+\frac{2 b e x^2 \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c}+\frac{4 b e \sqrt{1-c^2 x^2} \left(a+b \sin ^{-1}(c x)\right)}{9 c^3}+d x \left(a+b \sin ^{-1}(c x)\right)^2+\frac{1}{3} e x^3 \left(a+b \sin ^{-1}(c x)\right)^2-\frac{4 b^2 e x}{9 c^2}-2 b^2 d x-\frac{2}{27} b^2 e x^3",1,"-2*b^2*d*x - (4*b^2*e*x)/(9*c^2) - (2*b^2*e*x^3)/27 + (2*b*d*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/c + (4*b*e*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c^3) + (2*b*e*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcSin[c*x]))/(9*c) + d*x*(a + b*ArcSin[c*x])^2 + (e*x^3*(a + b*ArcSin[c*x])^2)/3","A",10,7,18,0.3889,1,"{4667, 4619, 4677, 8, 4627, 4707, 30}"
662,1,47,0,0.0601597,"\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}"
663,1,821,0,1.3420182,"\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{\text{PolyLog}\left(3,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}+\frac{\text{PolyLog}\left(3,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}-\frac{\text{PolyLog}\left(3,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}+\frac{\text{PolyLog}\left(3,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}+\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}-\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}+\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}-\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{\text{PolyLog}\left(3,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}+\frac{\text{PolyLog}\left(3,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}-\frac{\text{PolyLog}\left(3,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}+\frac{\text{PolyLog}\left(3,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b^2}{\sqrt{-d} \sqrt{e}}+\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}-\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}+\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}-\frac{i \left(a+b \sin ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right) b}{\sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i c \sqrt{-d}-\sqrt{d c^2+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i c \sqrt{-d}-\sqrt{d c^2+e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{i \sin ^{-1}(c x)}}{i \sqrt{-d} c+\sqrt{d c^2+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sin ^{-1}(c x)\right)^2 \log \left(\frac{e^{i \sin ^{-1}(c x)} \sqrt{e}}{i \sqrt{-d} c+\sqrt{d c^2+e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcSin[c*x])^2*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSin[c*x])^2*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcSin[c*x])^2*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSin[c*x])^2*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) + (I*b*(a + b*ArcSin[c*x])*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) - (I*b*(a + b*ArcSin[c*x])*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) - (b^2*PolyLog[3, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) + (b^2*PolyLog[3, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) - (b^2*PolyLog[3, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) + (b^2*PolyLog[3, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e])","A",22,7,20,0.3500,1,"{4667, 4741, 4521, 2190, 2531, 2282, 6589}"
664,0,0,0,0.0371079,"\int \sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcSin[c*x])^2,x]","\int \sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)^2 \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
665,0,0,0,0.0389481,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSin[c*x])^2/Sqrt[d + e*x^2],x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSin[c*x])^2/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
666,0,0,0,0.043805,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(d + e*x^2)^(3/2),x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcSin[c*x])^2/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
667,0,0,0,0.0441763,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSin[c*x])^2/(d + e*x^2)^(5/2),x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcSin[c*x])^2/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
668,1,379,0,0.7703224,"\int \frac{\left(d+e x^2\right)^2}{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x^2)^2/(a + b*ArcSin[c*x]),x]","\frac{d e \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{2 b c^3}-\frac{d e \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{2 b c^3}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^5}-\frac{3 e^2 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^5}+\frac{e^2 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^5}+\frac{d e \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{2 b c^3}-\frac{d e \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{2 b c^3}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b c^5}-\frac{3 e^2 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b c^5}+\frac{e^2 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b c^5}+\frac{d^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}+\frac{d^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}","\frac{d e \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{2 b c^3}-\frac{d e \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^3}+\frac{e^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^5}-\frac{3 e^2 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{e^2 \cos \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{d e \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{2 b c^3}-\frac{d e \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b c^3}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b c^5}-\frac{3 e^2 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{e^2 \sin \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{d^2 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}+\frac{d^2 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}",1,"(d*e*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(2*b*c^3) + (e^2*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(8*b*c^5) - (d*e*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(2*b*c^3) - (3*e^2*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b*c^5) + (e^2*Cos[(5*a)/b]*CosIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b*c^5) + (d^2*Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/(b*c) + (d*e*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(2*b*c^3) + (e^2*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b*c^5) - (d*e*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(2*b*c^3) - (3*e^2*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b*c^5) + (e^2*Sin[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b*c^5) + (d^2*Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(b*c)","A",27,7,20,0.3500,1,"{4667, 4623, 3303, 3299, 3302, 4635, 4406}"
669,1,175,0,0.3354668,"\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{e \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{e \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 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{4 b c^3}-\frac{e \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 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}+\frac{d \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}","\frac{e \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{e \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{e \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{e \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{d \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}+\frac{d \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{b c}",1,"(e*Cos[a/b]*CosIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) - (e*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3) + (d*Cos[a/b]*CosIntegral[(a + b*ArcSin[c*x])/b])/(b*c) + (e*Sin[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b*c^3) - (e*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b*c^3) + (d*Sin[a/b]*SinIntegral[(a + b*ArcSin[c*x])/b])/(b*c)","A",15,7,18,0.3889,1,"{4667, 4623, 3303, 3299, 3302, 4635, 4406}"
670,1,53,0,0.0634425,"\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}"
671,0,0,0,0.0357308,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \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,"{}"
672,0,0,0,0.0343192,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
673,0,0,0,0.0421287,"\int \frac{\sqrt{d+e x^2}}{a+b \sin ^{-1}(c x)} \, dx","Int[Sqrt[d + e*x^2]/(a + b*ArcSin[c*x]),x]","\int \frac{\sqrt{d+e x^2}}{a+b \sin ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2}}{a+b \sin ^{-1}(c x)},x\right)",0,"Defer[Int][Sqrt[d + e*x^2]/(a + b*ArcSin[c*x]), x]","A",0,0,0,0,-1,"{}"
674,0,0,0,0.0439177,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(Sqrt[d + e*x^2]*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
675,0,0,0,0.0470364,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^(3/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
676,0,0,0,0.0477665,"\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^(5/2)*(a + b*ArcSin[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^(5/2)*(a + b*ArcSin[c*x])), x]","A",0,0,0,0,-1,"{}"
677,1,486,0,0.7612875,"\int \frac{\left(d+e x^2\right)^2}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x^2)^2/(a + b*ArcSin[c*x])^2,x]","\frac{d e \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{3 d e \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^5}-\frac{9 e^2 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^5}+\frac{5 e^2 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{d e \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{3 d e \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sin ^{-1}(c x)\right)}{8 b^2 c^5}+\frac{9 e^2 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sin ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{5 e^2 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 a}{b}+5 \sin ^{-1}(c x)\right)}{16 b^2 c^5}+\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^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{e^2 x^4 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{d e \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{2 b^2 c^3}-\frac{3 d e \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}+\frac{e^2 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^5}-\frac{9 e^2 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}+\frac{5 e^2 \sin \left(\frac{5 a}{b}\right) \text{CosIntegral}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{d e \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{2 b^2 c^3}+\frac{3 d e \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}-\frac{e^2 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \sin ^{-1}(c x)}{b}\right)}{8 b^2 c^5}+\frac{9 e^2 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{5 e^2 \cos \left(\frac{5 a}{b}\right) \text{Si}\left(\frac{5 \left(a+b \sin ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}+\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^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}-\frac{e^2 x^4 \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^2*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x])) - (e^2*x^4*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x])) + (d^2*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(b^2*c) + (d*e*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(2*b^2*c^3) + (e^2*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(8*b^2*c^5) - (3*d*e*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(2*b^2*c^3) - (9*e^2*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(16*b^2*c^5) + (5*e^2*CosIntegral[(5*a)/b + 5*ArcSin[c*x]]*Sin[(5*a)/b])/(16*b^2*c^5) - (d^2*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b^2*c) - (d*e*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(2*b^2*c^3) - (e^2*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(8*b^2*c^5) + (3*d*e*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(2*b^2*c^3) + (9*e^2*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(16*b^2*c^5) - (5*e^2*Cos[(5*a)/b]*SinIntegral[(5*a)/b + 5*ArcSin[c*x]])/(16*b^2*c^5)","A",26,7,20,0.3500,1,"{4667, 4621, 4723, 3303, 3299, 3302, 4631}"
678,1,241,0,0.4182017,"\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{e \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 \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{e \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 \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 \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^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \sin ^{-1}(c x)\right)}","\frac{e \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 \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{e \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 \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 \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^2 \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^2*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcSin[c*x])) + (d*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(b^2*c) + (e*CosIntegral[a/b + ArcSin[c*x]]*Sin[a/b])/(4*b^2*c^3) - (3*e*CosIntegral[(3*a)/b + 3*ArcSin[c*x]]*Sin[(3*a)/b])/(4*b^2*c^3) - (d*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(b^2*c) - (e*Cos[a/b]*SinIntegral[a/b + ArcSin[c*x]])/(4*b^2*c^3) + (3*e*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSin[c*x]])/(4*b^2*c^3)","A",15,7,18,0.3889,1,"{4667, 4621, 4723, 3303, 3299, 3302, 4631}"
679,1,82,0,0.1676404,"\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}"
680,0,0,0,0.0340797,"\int \frac{1}{\left(d+e x^2\right) \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}{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \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,"{}"
681,0,0,0,0.0327086,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
682,0,0,0,0.040308,"\int \frac{\sqrt{d+e x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[d + e*x^2]/(a + b*ArcSin[c*x])^2,x]","\int \frac{\sqrt{d+e x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2}}{\left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[d + e*x^2]/(a + b*ArcSin[c*x])^2, x]","A",0,0,0,0,-1,"{}"
683,0,0,0,0.0407799,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\sqrt{d+e x^2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(Sqrt[d + e*x^2]*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
684,0,0,0,0.0443735,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^(3/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
685,0,0,0,0.0432489,"\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^(5/2)*(a + b*ArcSin[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sin ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^(5/2)*(a + b*ArcSin[c*x])^2), x]","A",0,0,0,0,-1,"{}"
686,1,754,0,2.2648846,"\int \left(d+e x^2\right)^2 \sqrt{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x^2)^2*Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d e \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} d e \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{6 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d e \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c^3}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} d e \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{6 c^3}+\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 x)}}{\sqrt{b}}\right)}{8 c^5}-\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 x)}}{\sqrt{b}}\right)}{16 c^5}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{b} e^2 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{80 c^5}-\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 x)}}{\sqrt{b}}\right)}{8 c^5}+\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 x)}}{\sqrt{b}}\right)}{16 c^5}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{b} e^2 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{80 c^5}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d e \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} d e \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{6 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d e \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c^3}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} d e \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{6 c^3}+\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 x)}}{\sqrt{b}}\right)}{8 c^5}-\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 x)}}{\sqrt{b}}\right)}{16 c^5}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{b} e^2 \sin \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{80 c^5}-\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 x)}}{\sqrt{b}}\right)}{8 c^5}+\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 x)}}{\sqrt{b}}\right)}{16 c^5}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{b} e^2 \cos \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{80 c^5}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d^2 \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d^2 \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+d^2 x \sqrt{a+b \sin ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sin ^{-1}(c x)}",1,"d^2*x*Sqrt[a + b*ArcSin[c*x]] + (2*d*e*x^3*Sqrt[a + b*ArcSin[c*x]])/3 + (e^2*x^5*Sqrt[a + b*ArcSin[c*x]])/5 - (Sqrt[b]*d^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/c - (Sqrt[b]*d*e*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*c^3) - (Sqrt[b]*e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*c^5) + (Sqrt[b]*d*e*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(6*c^3) + (Sqrt[b]*e^2*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(16*c^5) - (Sqrt[b]*e^2*Sqrt[Pi/10]*Cos[(5*a)/b]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(80*c^5) + (Sqrt[b]*d^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/c + (Sqrt[b]*d*e*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*c^3) + (Sqrt[b]*e^2*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(8*c^5) - (Sqrt[b]*d*e*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(6*c^3) - (Sqrt[b]*e^2*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(16*c^5) + (Sqrt[b]*e^2*Sqrt[Pi/10]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(5*a)/b])/(80*c^5)","A",42,10,22,0.4545,1,"{4667, 4619, 4723, 3306, 3305, 3351, 3304, 3352, 4629, 3312}"
687,1,369,0,1.0265721,"\int \left(d+e x^2\right) \sqrt{a+b \sin ^{-1}(c x)} \, dx","Int[(d + e*x^2)*Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+d x \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{3} e x^3 \sqrt{a+b \sin ^{-1}(c x)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} e \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+d x \sqrt{a+b \sin ^{-1}(c x)}+\frac{1}{3} e x^3 \sqrt{a+b \sin ^{-1}(c x)}",1,"d*x*Sqrt[a + b*ArcSin[c*x]] + (e*x^3*Sqrt[a + b*ArcSin[c*x]])/3 - (Sqrt[b]*d*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/c - (Sqrt[b]*e*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*c^3) + (Sqrt[b]*e*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(12*c^3) + (Sqrt[b]*d*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/c + (Sqrt[b]*e*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(4*c^3) - (Sqrt[b]*e*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(12*c^3)","A",23,10,20,0.5000,1,"{4667, 4619, 4723, 3306, 3305, 3351, 3304, 3352, 4629, 3312}"
688,1,120,0,0.2709505,"\int \sqrt{a+b \sin ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+x \sqrt{a+b \sin ^{-1}(c x)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+x \sqrt{a+b \sin ^{-1}(c x)}",1,"x*Sqrt[a + b*ArcSin[c*x]] - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/c + (Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/c","A",7,7,12,0.5833,1,"{4619, 4723, 3306, 3305, 3351, 3304, 3352}"
689,0,0,0,0.0529863,"\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{d+e x^2} \, dx","Int[Sqrt[a + b*ArcSin[c*x]]/(d + e*x^2),x]","\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{d+e x^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \sin ^{-1}(c x)}}{d+e x^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcSin[c*x]]/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
690,0,0,0,0.0488776,"\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{\left(d+e x^2\right)^2} \, dx","Int[Sqrt[a + b*ArcSin[c*x]]/(d + e*x^2)^2,x]","\int \frac{\sqrt{a+b \sin ^{-1}(c x)}}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \sin ^{-1}(c x)}}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcSin[c*x]]/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
691,1,482,0,1.4243762,"\int \left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Int[(d + e*x^2)*(a + b*ArcSin[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} d \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} d \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 b d \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{2 c}+\frac{b e x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{6 c}+\frac{b e \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{3 c^3}+d x \left(a+b \sin ^{-1}(c x)\right)^{3/2}+\frac{1}{3} e x^3 \left(a+b \sin ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} e \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} d \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} d \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 b d \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{2 c}+\frac{b e x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{6 c}+\frac{b e \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{3 c^3}+d x \left(a+b \sin ^{-1}(c x)\right)^{3/2}+\frac{1}{3} e x^3 \left(a+b \sin ^{-1}(c x)\right)^{3/2}",1,"(3*b*d*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(2*c) + (b*e*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(3*c^3) + (b*e*x^2*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(6*c) + d*x*(a + b*ArcSin[c*x])^(3/2) + (e*x^3*(a + b*ArcSin[c*x])^(3/2))/3 - (3*b^(3/2)*d*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*c) - (3*b^(3/2)*e*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*c^3) + (b^(3/2)*e*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(24*c^3) - (3*b^(3/2)*d*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*c) - (3*b^(3/2)*e*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(8*c^3) + (b^(3/2)*e*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(24*c^3)","A",32,13,20,0.6500,1,"{4667, 4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352, 4629, 4707, 4635, 4406}"
692,1,159,0,0.2322866,"\int \left(a+b \sin ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcSin[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 b \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{2 c}+x \left(a+b \sin ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 b \sqrt{1-c^2 x^2} \sqrt{a+b \sin ^{-1}(c x)}}{2 c}+x \left(a+b \sin ^{-1}(c x)\right)^{3/2}",1,"(3*b*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcSin[c*x]])/(2*c) + x*(a + b*ArcSin[c*x])^(3/2) - (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*c) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*c)","A",8,8,12,0.6667,1,"{4619, 4677, 4623, 3306, 3305, 3351, 3304, 3352}"
693,0,0,0,0.0619877,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{d+e x^2} \, dx","Int[(a + b*ArcSin[c*x])^(3/2)/(d + e*x^2),x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{d+e x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{d+e x^2},x\right)",0,"Defer[Int][(a + b*ArcSin[c*x])^(3/2)/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
694,0,0,0,0.0587861,"\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSin[c*x])^(3/2)/(d + e*x^2)^2,x]","\int \frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\left(a+b \sin ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][(a + b*ArcSin[c*x])^(3/2)/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
695,1,679,0,1.5043518,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[(d + e*x^2)^2/Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} d e \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} d e \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{2}} d e \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} d e \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}+\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 x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^5}-\frac{\sqrt{\frac{3 \pi }{2}} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\frac{\sqrt{\frac{\pi }{10}} e^2 \cos \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\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 x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^5}-\frac{\sqrt{\frac{3 \pi }{2}} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\frac{\sqrt{\frac{\pi }{10}} e^2 \sin \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\frac{\sqrt{2 \pi } d^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } d^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}","\frac{\sqrt{\frac{\pi }{2}} d e \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} d e \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{2}} d e \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} d e \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c^3}+\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 x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^5}-\frac{\sqrt{\frac{3 \pi }{2}} e^2 \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\frac{\sqrt{\frac{\pi }{10}} e^2 \cos \left(\frac{5 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\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 x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^5}-\frac{\sqrt{\frac{3 \pi }{2}} e^2 \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\frac{\sqrt{\frac{\pi }{10}} e^2 \sin \left(\frac{5 a}{b}\right) S\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^5}+\frac{\sqrt{2 \pi } d^2 \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } d^2 \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}",1,"(d*e*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(Sqrt[b]*c^3) + (e^2*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^5) + (d^2*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(Sqrt[b]*c) - (d*e*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(Sqrt[b]*c^3) - (e^2*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^5) + (e^2*Sqrt[Pi/10]*Cos[(5*a)/b]*FresnelC[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^5) + (d*e*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*c^3) + (e^2*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(4*Sqrt[b]*c^5) + (d^2*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*c) - (d*e*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(Sqrt[b]*c^3) - (e^2*Sqrt[(3*Pi)/2]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(8*Sqrt[b]*c^5) + (e^2*Sqrt[Pi/10]*FresnelS[(Sqrt[10/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(5*a)/b])/(8*Sqrt[b]*c^5)","A",39,9,22,0.4091,1,"{4667, 4623, 3306, 3305, 3351, 3304, 3352, 4635, 4406}"
696,1,329,0,0.6370463,"\int \frac{d+e x^2}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[(d + e*x^2)/Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} e \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{2}} e \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} e \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{2 \pi } d \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } d \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}","\frac{\sqrt{\frac{\pi }{2}} e \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} e \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{2}} e \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} e \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{2 \pi } d \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } d \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}",1,"(e*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*Sqrt[b]*c^3) + (d*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(Sqrt[b]*c) - (e*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(2*Sqrt[b]*c^3) + (e*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(2*Sqrt[b]*c^3) + (d*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*c) - (e*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(2*Sqrt[b]*c^3)","A",21,9,20,0.4500,1,"{4667, 4623, 3306, 3305, 3351, 3304, 3352, 4635, 4406}"
697,1,101,0,0.0950421,"\int \frac{1}{\sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcSin[c*x]],x]","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}","\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}+\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}",1,"(Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(Sqrt[b]*c) + (Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*c)","A",6,6,12,0.5000,1,"{4623, 3306, 3305, 3351, 3304, 3352}"
698,0,0,0,0.0567442,"\int \frac{1}{\left(d+e x^2\right) \sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[1/((d + e*x^2)*Sqrt[a + b*ArcSin[c*x]]),x]","\int \frac{1}{\left(d+e x^2\right) \sqrt{a+b \sin ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \sqrt{a+b \sin ^{-1}(c x)}},x\right)",0,"Defer[Int][1/((d + e*x^2)*Sqrt[a + b*ArcSin[c*x]]), x]","A",0,0,0,0,-1,"{}"
699,0,0,0,0.0537331,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \sin ^{-1}(c x)}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[a + b*ArcSin[c*x]]),x]","\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \sin ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \sin ^{-1}(c x)}},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*Sqrt[a + b*ArcSin[c*x]]), x]","A",0,0,0,0,-1,"{}"
700,1,394,0,0.7976107,"\int \frac{d+e x^2}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + e*x^2)/(a + b*ArcSin[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} e \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{\pi }{2}} e \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{\sqrt{\frac{3 \pi }{2}} e \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{2 \sqrt{2 \pi } d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}-\frac{2 e x^2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} e \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} e \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{\pi }{2}} e \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{\sqrt{\frac{3 \pi }{2}} e \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{2 \sqrt{2 \pi } d \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } d \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}-\frac{2 e x^2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*d*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (2*e*x^2*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (e*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) - (2*d*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c) + (e*Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) + (e*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c^3) + (2*d*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c) - (e*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(3/2)*c^3)","A",21,9,20,0.4500,1,"{4667, 4621, 4723, 3306, 3305, 3351, 3304, 3352, 4631}"
701,1,137,0,0.2680306,"\int \frac{1}{\left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcSin[c*x])^(-3/2),x]","\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}","\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \sin ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \sin ^{-1}(c x)}}",1,"(-2*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcSin[c*x]]) - (2*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]])/(b^(3/2)*c) + (2*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcSin[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c)","A",7,7,12,0.5833,1,"{4621, 4723, 3306, 3305, 3351, 3304, 3352}"
702,0,0,0,0.0639963,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/((d + e*x^2)*(a + b*ArcSin[c*x])^(3/2)),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \left(a+b \sin ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/((d + e*x^2)*(a + b*ArcSin[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
703,0,0,0,0.0604461,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcSin[c*x])^(3/2)),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \sin ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcSin[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"