1,1,60,111,0.0502581,"\int e^{\tanh ^{-1}(a x)} x^4 \, dx","Integrate[E^ArcTanh[a*x]*x^4,x]","\frac{45 \sin ^{-1}(a x)-\sqrt{1-a^2 x^2} \left(24 a^4 x^4+30 a^3 x^3+32 a^2 x^2+45 a x+64\right)}{120 a^5}","\frac{3 \sin ^{-1}(a x)}{8 a^5}-\frac{x^4 \sqrt{1-a^2 x^2}}{5 a}-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a^2}-\frac{(45 a x+64) \sqrt{1-a^2 x^2}}{120 a^5}-\frac{4 x^2 \sqrt{1-a^2 x^2}}{15 a^3}",1,"(-(Sqrt[1 - a^2*x^2]*(64 + 45*a*x + 32*a^2*x^2 + 30*a^3*x^3 + 24*a^4*x^4)) + 45*ArcSin[a*x])/(120*a^5)","A",1
2,1,52,87,0.0396645,"\int e^{\tanh ^{-1}(a x)} x^3 \, dx","Integrate[E^ArcTanh[a*x]*x^3,x]","\frac{9 \sin ^{-1}(a x)-\sqrt{1-a^2 x^2} \left(6 a^3 x^3+8 a^2 x^2+9 a x+16\right)}{24 a^4}","\frac{3 \sin ^{-1}(a x)}{8 a^4}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2}-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}-\frac{(9 a x+16) \sqrt{1-a^2 x^2}}{24 a^4}",1,"(-(Sqrt[1 - a^2*x^2]*(16 + 9*a*x + 8*a^2*x^2 + 6*a^3*x^3)) + 9*ArcSin[a*x])/(24*a^4)","A",1
3,1,44,74,0.0337988,"\int e^{\tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^ArcTanh[a*x]*x^2,x]","\frac{3 \sin ^{-1}(a x)-\sqrt{1-a^2 x^2} \left(2 a^2 x^2+3 a x+4\right)}{6 a^3}","\frac{\sin ^{-1}(a x)}{2 a^3}-\frac{x \sqrt{1-a^2 x^2}}{2 a^2}+\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3}-\frac{\sqrt{1-a^2 x^2}}{a^3}",1,"(-(Sqrt[1 - a^2*x^2]*(4 + 3*a*x + 2*a^2*x^2)) + 3*ArcSin[a*x])/(6*a^3)","A",1
4,1,33,38,0.028428,"\int e^{\tanh ^{-1}(a x)} x \, dx","Integrate[E^ArcTanh[a*x]*x,x]","\frac{\sin ^{-1}(a x)-(a x+2) \sqrt{1-a^2 x^2}}{2 a^2}","\frac{\sin ^{-1}(a x)}{2 a^2}-\frac{(a x+2) \sqrt{1-a^2 x^2}}{2 a^2}",1,"(-((2 + a*x)*Sqrt[1 - a^2*x^2]) + ArcSin[a*x])/(2*a^2)","A",1
5,1,25,28,0.0098539,"\int e^{\tanh ^{-1}(a x)} \, dx","Integrate[E^ArcTanh[a*x],x]","\frac{\sin ^{-1}(a x)-\sqrt{1-a^2 x^2}}{a}","\frac{\sin ^{-1}(a x)}{a}-\frac{\sqrt{1-a^2 x^2}}{a}",1,"(-Sqrt[1 - a^2*x^2] + ArcSin[a*x])/a","A",1
6,1,26,22,0.0150783,"\int \frac{e^{\tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^ArcTanh[a*x]/x,x]","-\log \left(\sqrt{1-a^2 x^2}+1\right)+\sin ^{-1}(a x)+\log (x)","\sin ^{-1}(a x)-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"ArcSin[a*x] + Log[x] - Log[1 + Sqrt[1 - a^2*x^2]]","A",0
7,1,44,38,0.0322607,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^ArcTanh[a*x]/x^2,x]","-\frac{\sqrt{1-a^2 x^2}}{x}-a \log \left(\sqrt{1-a^2 x^2}+1\right)+a \log (x)","-\frac{\sqrt{1-a^2 x^2}}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-(Sqrt[1 - a^2*x^2]/x) + a*Log[x] - a*Log[1 + Sqrt[1 - a^2*x^2]]","A",0
8,1,58,64,0.0422745,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^ArcTanh[a*x]/x^3,x]","\frac{1}{2} \left(-\frac{(2 a x+1) \sqrt{1-a^2 x^2}}{x^2}-a^2 \log \left(\sqrt{1-a^2 x^2}+1\right)+a^2 \log (x)\right)","-\frac{a \sqrt{1-a^2 x^2}}{x}-\frac{\sqrt{1-a^2 x^2}}{2 x^2}-\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-(((1 + 2*a*x)*Sqrt[1 - a^2*x^2])/x^2) + a^2*Log[x] - a^2*Log[1 + Sqrt[1 - a^2*x^2]])/2","A",0
9,1,67,90,0.05793,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^ArcTanh[a*x]/x^4,x]","\frac{1}{6} \left(3 a^3 \log (x)-\frac{\sqrt{1-a^2 x^2} \left(4 a^2 x^2+3 a x+2\right)}{x^3}-3 a^3 \log \left(\sqrt{1-a^2 x^2}+1\right)\right)","-\frac{2 a^2 \sqrt{1-a^2 x^2}}{3 x}-\frac{a \sqrt{1-a^2 x^2}}{2 x^2}-\frac{\sqrt{1-a^2 x^2}}{3 x^3}-\frac{1}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-((Sqrt[1 - a^2*x^2]*(2 + 3*a*x + 4*a^2*x^2))/x^3) + 3*a^3*Log[x] - 3*a^3*Log[1 + Sqrt[1 - a^2*x^2]])/6","A",0
10,1,75,114,0.0615373,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[E^ArcTanh[a*x]/x^5,x]","\frac{1}{24} \left(9 a^4 \log (x)-9 a^4 \log \left(\sqrt{1-a^2 x^2}+1\right)-\frac{\sqrt{1-a^2 x^2} \left(16 a^3 x^3+9 a^2 x^2+8 a x+6\right)}{x^4}\right)","-\frac{3 a^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\frac{a \sqrt{1-a^2 x^2}}{3 x^3}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{2 a^3 \sqrt{1-a^2 x^2}}{3 x}",1,"(-((Sqrt[1 - a^2*x^2]*(6 + 8*a*x + 9*a^2*x^2 + 16*a^3*x^3))/x^4) + 9*a^4*Log[x] - 9*a^4*Log[1 + Sqrt[1 - a^2*x^2]])/24","A",0
11,1,44,44,0.0193038,"\int e^{2 \tanh ^{-1}(a x)} x^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3,x]","-\frac{2 \log (1-a x)}{a^4}-\frac{2 x}{a^3}-\frac{x^2}{a^2}-\frac{2 x^3}{3 a}-\frac{x^4}{4}","-\frac{2 \log (1-a x)}{a^4}-\frac{2 x}{a^3}-\frac{x^2}{a^2}-\frac{2 x^3}{3 a}-\frac{x^4}{4}",1,"(-2*x)/a^3 - x^2/a^2 - (2*x^3)/(3*a) - x^4/4 - (2*Log[1 - a*x])/a^4","A",1
12,1,34,34,0.0138137,"\int e^{2 \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2,x]","-\frac{2 \log (1-a x)}{a^3}-\frac{2 x}{a^2}-\frac{x^2}{a}-\frac{x^3}{3}","-\frac{2 \log (1-a x)}{a^3}-\frac{2 x}{a^2}-\frac{x^2}{a}-\frac{x^3}{3}",1,"(-2*x)/a^2 - x^2/a - x^3/3 - (2*Log[1 - a*x])/a^3","A",1
13,1,26,26,0.0119875,"\int e^{2 \tanh ^{-1}(a x)} x \, dx","Integrate[E^(2*ArcTanh[a*x])*x,x]","-\frac{2 \log (1-a x)}{a^2}-\frac{2 x}{a}-\frac{x^2}{2}","-\frac{2 \log (1-a x)}{a^2}-\frac{2 x}{a}-\frac{x^2}{2}",1,"(-2*x)/a - x^2/2 - (2*Log[1 - a*x])/a^2","A",1
14,1,16,16,0.0100705,"\int e^{2 \tanh ^{-1}(a x)} \, dx","Integrate[E^(2*ArcTanh[a*x]),x]","-\frac{2 \log (1-a x)}{a}-x","-\frac{2 \log (1-a x)}{a}-x",1,"-x - (2*Log[1 - a*x])/a","A",1
15,1,12,12,0.0073222,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^(2*ArcTanh[a*x])/x,x]","\log (x)-2 \log (1-a x)","\log (x)-2 \log (1-a x)",1,"Log[x] - 2*Log[1 - a*x]","A",1
16,1,21,21,0.0101661,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/x^2,x]","2 a \log (x)-2 a \log (1-a x)-\frac{1}{x}","2 a \log (x)-2 a \log (1-a x)-\frac{1}{x}",1,"-x^(-1) + 2*a*Log[x] - 2*a*Log[1 - a*x]","A",1
17,1,33,33,0.0117064,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/x^3,x]","2 a^2 \log (x)-2 a^2 \log (1-a x)-\frac{2 a}{x}-\frac{1}{2 x^2}","2 a^2 \log (x)-2 a^2 \log (1-a x)-\frac{2 a}{x}-\frac{1}{2 x^2}",1,"-1/2*1/x^2 - (2*a)/x + 2*a^2*Log[x] - 2*a^2*Log[1 - a*x]","A",1
18,1,41,41,0.0147789,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^(2*ArcTanh[a*x])/x^4,x]","2 a^3 \log (x)-2 a^3 \log (1-a x)-\frac{2 a^2}{x}-\frac{a}{x^2}-\frac{1}{3 x^3}","2 a^3 \log (x)-2 a^3 \log (1-a x)-\frac{2 a^2}{x}-\frac{a}{x^2}-\frac{1}{3 x^3}",1,"-1/3*1/x^3 - a/x^2 - (2*a^2)/x + 2*a^3*Log[x] - 2*a^3*Log[1 - a*x]","A",1
19,1,58,92,0.0598793,"\int e^{3 \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*x^2,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(2 a^3 x^3+7 a^2 x^2+19 a x-52\right)}{a x-1}-33 \sin ^{-1}(a x)}{6 a^3}","-\frac{11 \sin ^{-1}(a x)}{2 a^3}+\frac{(a x+1)^3}{a^3 \sqrt{1-a^2 x^2}}+\frac{(a x+3)^2 \sqrt{1-a^2 x^2}}{3 a^3}+\frac{(3 a x+28) \sqrt{1-a^2 x^2}}{6 a^3}",1,"((Sqrt[1 - a^2*x^2]*(-52 + 19*a*x + 7*a^2*x^2 + 2*a^3*x^3))/(-1 + a*x) - 33*ArcSin[a*x])/(6*a^3)","A",1
20,1,53,88,0.0396804,"\int e^{3 \tanh ^{-1}(a x)} x \, dx","Integrate[E^(3*ArcTanh[a*x])*x,x]","\sqrt{1-a^2 x^2} \left(-\frac{4}{a^2 (a x-1)}+\frac{3}{a^2}+\frac{x}{2 a}\right)-\frac{9 \sin ^{-1}(a x)}{2 a^2}","\frac{\left(1-a^2 x^2\right)^{5/2}}{a^2 (1-a x)^3}+\frac{3 \left(1-a^2 x^2\right)^{3/2}}{2 a^2 (1-a x)}+\frac{9 \sqrt{1-a^2 x^2}}{2 a^2}-\frac{9 \sin ^{-1}(a x)}{2 a^2}",1,"Sqrt[1 - a^2*x^2]*(3/a^2 + x/(2*a) - 4/(a^2*(-1 + a*x))) - (9*ArcSin[a*x])/(2*a^2)","A",1
21,1,39,55,0.0322867,"\int e^{3 \tanh ^{-1}(a x)} \, dx","Integrate[E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{1-a^2 x^2} \left(1-\frac{4}{a x-1}\right)}{a}-\frac{3 \sin ^{-1}(a x)}{a}","\frac{2 (a x+1)^2}{a \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{1-a^2 x^2}}{a}-\frac{3 \sin ^{-1}(a x)}{a}",1,"(Sqrt[1 - a^2*x^2]*(1 - 4/(-1 + a*x)))/a - (3*ArcSin[a*x])/a","A",1
22,1,51,48,0.0458633,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^(3*ArcTanh[a*x])/x,x]","-\frac{4 \sqrt{1-a^2 x^2}}{a x-1}-\log \left(\sqrt{1-a^2 x^2}+1\right)-\sin ^{-1}(a x)+\log (x)","\frac{4 \sqrt{1-a^2 x^2}}{1-a x}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\sin ^{-1}(a x)",1,"(-4*Sqrt[1 - a^2*x^2])/(-1 + a*x) - ArcSin[a*x] + Log[x] - Log[1 + Sqrt[1 - a^2*x^2]]","A",0
23,1,57,63,0.0569795,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])/x^2,x]","\sqrt{1-a^2 x^2} \left(-\frac{4 a}{a x-1}-\frac{1}{x}\right)-3 a \log \left(\sqrt{1-a^2 x^2}+1\right)+3 a \log (x)","\frac{4 a \sqrt{1-a^2 x^2}}{1-a x}-\frac{\sqrt{1-a^2 x^2}}{x}-3 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"Sqrt[1 - a^2*x^2]*(-x^(-1) - (4*a)/(-1 + a*x)) + 3*a*Log[x] - 3*a*Log[1 + Sqrt[1 - a^2*x^2]]","A",0
24,1,75,91,0.0723059,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^(3*ArcTanh[a*x])/x^3,x]","\sqrt{1-a^2 x^2} \left(-\frac{4 a^2}{a x-1}-\frac{3 a}{x}-\frac{1}{2 x^2}\right)-\frac{9}{2} a^2 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{9}{2} a^2 \log (x)","\frac{4 a^2 \sqrt{1-a^2 x^2}}{1-a x}-\frac{3 a \sqrt{1-a^2 x^2}}{x}-\frac{\sqrt{1-a^2 x^2}}{2 x^2}-\frac{9}{2} a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"Sqrt[1 - a^2*x^2]*(-1/2*1/x^2 - (3*a)/x - (4*a^2)/(-1 + a*x)) + (9*a^2*Log[x])/2 - (9*a^2*Log[1 + Sqrt[1 - a^2*x^2]])/2","A",0
25,1,81,117,0.0862151,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^(3*ArcTanh[a*x])/x^4,x]","\frac{1}{6} \left(33 a^3 \log (x)-33 a^3 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{\sqrt{1-a^2 x^2} \left(-52 a^3 x^3+19 a^2 x^2+7 a x+2\right)}{x^3 (a x-1)}\right)","-\frac{14 a^2 \sqrt{1-a^2 x^2}}{3 x}-\frac{3 a \sqrt{1-a^2 x^2}}{2 x^2}-\frac{\sqrt{1-a^2 x^2}}{3 x^3}+\frac{4 a^3 \sqrt{1-a^2 x^2}}{1-a x}-\frac{11}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"((Sqrt[1 - a^2*x^2]*(2 + 7*a*x + 19*a^2*x^2 - 52*a^3*x^3))/(x^3*(-1 + a*x)) + 33*a^3*Log[x] - 33*a^3*Log[1 + Sqrt[1 - a^2*x^2]])/6","A",0
26,1,57,57,0.0500216,"\int e^{4 \tanh ^{-1}(a x)} x^3 \, dx","Integrate[E^(4*ArcTanh[a*x])*x^3,x]","\frac{4}{a^4 (1-a x)}+\frac{16 \log (1-a x)}{a^4}+\frac{12 x}{a^3}+\frac{4 x^2}{a^2}+\frac{4 x^3}{3 a}+\frac{x^4}{4}","\frac{4}{a^4 (1-a x)}+\frac{16 \log (1-a x)}{a^4}+\frac{12 x}{a^3}+\frac{4 x^2}{a^2}+\frac{4 x^3}{3 a}+\frac{x^4}{4}",1,"(12*x)/a^3 + (4*x^2)/a^2 + (4*x^3)/(3*a) + x^4/4 + 4/(a^4*(1 - a*x)) + (16*Log[1 - a*x])/a^4","A",1
27,1,47,47,0.0394775,"\int e^{4 \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^(4*ArcTanh[a*x])*x^2,x]","\frac{4}{a^3 (1-a x)}+\frac{12 \log (1-a x)}{a^3}+\frac{8 x}{a^2}+\frac{2 x^2}{a}+\frac{x^3}{3}","\frac{4}{a^3 (1-a x)}+\frac{12 \log (1-a x)}{a^3}+\frac{8 x}{a^2}+\frac{2 x^2}{a}+\frac{x^3}{3}",1,"(8*x)/a^2 + (2*x^2)/a + x^3/3 + 4/(a^3*(1 - a*x)) + (12*Log[1 - a*x])/a^3","A",1
28,1,39,39,0.0366064,"\int e^{4 \tanh ^{-1}(a x)} x \, dx","Integrate[E^(4*ArcTanh[a*x])*x,x]","\frac{4}{a^2 (1-a x)}+\frac{8 \log (1-a x)}{a^2}+\frac{4 x}{a}+\frac{x^2}{2}","\frac{4}{a^2 (1-a x)}+\frac{8 \log (1-a x)}{a^2}+\frac{4 x}{a}+\frac{x^2}{2}",1,"(4*x)/a + x^2/2 + 4/(a^2*(1 - a*x)) + (8*Log[1 - a*x])/a^2","A",1
29,1,26,27,0.0176425,"\int e^{4 \tanh ^{-1}(a x)} \, dx","Integrate[E^(4*ArcTanh[a*x]),x]","-\frac{4}{a (a x-1)}+\frac{4 \log (1-a x)}{a}+x","\frac{4}{a (1-a x)}+\frac{4 \log (1-a x)}{a}+x",1,"x - 4/(a*(-1 + a*x)) + (4*Log[1 - a*x])/a","A",1
30,1,13,13,0.0097344,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^(4*ArcTanh[a*x])/x,x]","\frac{4}{1-a x}+\log (x)","\frac{4}{1-a x}+\log (x)",1,"4/(1 - a*x) + Log[x]","A",1
31,1,32,32,0.025696,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^(4*ArcTanh[a*x])/x^2,x]","\frac{4 a}{1-a x}+4 a \log (x)-4 a \log (1-a x)-\frac{1}{x}","\frac{4 a}{1-a x}+4 a \log (x)-4 a \log (1-a x)-\frac{1}{x}",1,"-x^(-1) + (4*a)/(1 - a*x) + 4*a*Log[x] - 4*a*Log[1 - a*x]","A",1
32,1,46,46,0.0323678,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^(4*ArcTanh[a*x])/x^3,x]","\frac{4 a^2}{1-a x}+8 a^2 \log (x)-8 a^2 \log (1-a x)-\frac{4 a}{x}-\frac{1}{2 x^2}","\frac{4 a^2}{1-a x}+8 a^2 \log (x)-8 a^2 \log (1-a x)-\frac{4 a}{x}-\frac{1}{2 x^2}",1,"-1/2*1/x^2 - (4*a)/x + (4*a^2)/(1 - a*x) + 8*a^2*Log[x] - 8*a^2*Log[1 - a*x]","A",1
33,1,54,54,0.0462761,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^(4*ArcTanh[a*x])/x^4,x]","\frac{4 a^3}{1-a x}+12 a^3 \log (x)-12 a^3 \log (1-a x)-\frac{8 a^2}{x}-\frac{2 a}{x^2}-\frac{1}{3 x^3}","\frac{4 a^3}{1-a x}+12 a^3 \log (x)-12 a^3 \log (1-a x)-\frac{8 a^2}{x}-\frac{2 a}{x^2}-\frac{1}{3 x^3}",1,"-1/3*1/x^3 - (2*a)/x^2 - (8*a^2)/x + (4*a^3)/(1 - a*x) + 12*a^3*Log[x] - 12*a^3*Log[1 - a*x]","A",1
34,1,51,87,0.0427116,"\int e^{-\tanh ^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^ArcTanh[a*x],x]","\frac{\sqrt{1-a^2 x^2} \left(6 a^3 x^3-8 a^2 x^2+9 a x-16\right)-9 \sin ^{-1}(a x)}{24 a^4}","-\frac{3 \sin ^{-1}(a x)}{8 a^4}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2}+\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}-\frac{(16-9 a x) \sqrt{1-a^2 x^2}}{24 a^4}",1,"(Sqrt[1 - a^2*x^2]*(-16 + 9*a*x - 8*a^2*x^2 + 6*a^3*x^3) - 9*ArcSin[a*x])/(24*a^4)","A",1
35,1,43,73,0.0345725,"\int e^{-\tanh ^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^ArcTanh[a*x],x]","\frac{\sqrt{1-a^2 x^2} \left(2 a^2 x^2-3 a x+4\right)+3 \sin ^{-1}(a x)}{6 a^3}","\frac{\sin ^{-1}(a x)}{2 a^3}-\frac{x \sqrt{1-a^2 x^2}}{2 a^2}-\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3}+\frac{\sqrt{1-a^2 x^2}}{a^3}",1,"(Sqrt[1 - a^2*x^2]*(4 - 3*a*x + 2*a^2*x^2) + 3*ArcSin[a*x])/(6*a^3)","A",1
36,1,34,39,0.0262186,"\int e^{-\tanh ^{-1}(a x)} x \, dx","Integrate[x/E^ArcTanh[a*x],x]","\frac{(a x-2) \sqrt{1-a^2 x^2}-\sin ^{-1}(a x)}{2 a^2}","-\frac{\sqrt{1-a^2 x^2} (2-a x)}{2 a^2}-\frac{\sin ^{-1}(a x)}{2 a^2}",1,"((-2 + a*x)*Sqrt[1 - a^2*x^2] - ArcSin[a*x])/(2*a^2)","A",1
37,1,23,27,0.0130111,"\int e^{-\tanh ^{-1}(a x)} \, dx","Integrate[E^(-ArcTanh[a*x]),x]","\frac{\sqrt{1-a^2 x^2}+\sin ^{-1}(a x)}{a}","\frac{\sqrt{1-a^2 x^2}}{a}+\frac{\sin ^{-1}(a x)}{a}",1,"(Sqrt[1 - a^2*x^2] + ArcSin[a*x])/a","A",1
38,1,28,24,0.0145477,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x} \, dx","Integrate[1/(E^ArcTanh[a*x]*x),x]","-\log \left(\sqrt{1-a^2 x^2}+1\right)-\sin ^{-1}(a x)+\log (x)","-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\sin ^{-1}(a x)",1,"-ArcSin[a*x] + Log[x] - Log[1 + Sqrt[1 - a^2*x^2]]","A",0
39,1,44,37,0.0282569,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^ArcTanh[a*x]*x^2),x]","-\frac{\sqrt{1-a^2 x^2}}{x}+a \log \left(\sqrt{1-a^2 x^2}+1\right)-a \log (x)","a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sqrt{1-a^2 x^2}}{x}",1,"-(Sqrt[1 - a^2*x^2]/x) - a*Log[x] + a*Log[1 + Sqrt[1 - a^2*x^2]]","A",0
40,1,57,63,0.0435655,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^ArcTanh[a*x]*x^3),x]","\frac{1}{2} \left(\frac{(2 a x-1) \sqrt{1-a^2 x^2}}{x^2}-a^2 \log \left(\sqrt{1-a^2 x^2}+1\right)+a^2 \log (x)\right)","\frac{a \sqrt{1-a^2 x^2}}{x}-\frac{\sqrt{1-a^2 x^2}}{2 x^2}-\frac{1}{2} a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(((-1 + 2*a*x)*Sqrt[1 - a^2*x^2])/x^2 + a^2*Log[x] - a^2*Log[1 + Sqrt[1 - a^2*x^2]])/2","A",0
41,1,66,90,0.0548719,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^ArcTanh[a*x]*x^4),x]","\frac{1}{6} \left(-3 a^3 \log (x)+\frac{\left(-4 a^2 x^2+3 a x-2\right) \sqrt{1-a^2 x^2}}{x^3}+3 a^3 \log \left(\sqrt{1-a^2 x^2}+1\right)\right)","-\frac{2 a^2 \sqrt{1-a^2 x^2}}{3 x}+\frac{a \sqrt{1-a^2 x^2}}{2 x^2}-\frac{\sqrt{1-a^2 x^2}}{3 x^3}+\frac{1}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(((-2 + 3*a*x - 4*a^2*x^2)*Sqrt[1 - a^2*x^2])/x^3 - 3*a^3*Log[x] + 3*a^3*Log[1 + Sqrt[1 - a^2*x^2]])/6","A",0
42,1,74,114,0.0581669,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[1/(E^ArcTanh[a*x]*x^5),x]","\frac{1}{24} \left(9 a^4 \log (x)-9 a^4 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{\sqrt{1-a^2 x^2} \left(16 a^3 x^3-9 a^2 x^2+8 a x-6\right)}{x^4}\right)","-\frac{3 a^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}+\frac{a \sqrt{1-a^2 x^2}}{3 x^3}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{2 a^3 \sqrt{1-a^2 x^2}}{3 x}",1,"((Sqrt[1 - a^2*x^2]*(-6 + 8*a*x - 9*a^2*x^2 + 16*a^3*x^3))/x^4 + 9*a^4*Log[x] - 9*a^4*Log[1 + Sqrt[1 - a^2*x^2]])/24","A",0
43,1,43,43,0.0195254,"\int e^{-2 \tanh ^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^(2*ArcTanh[a*x]),x]","-\frac{2 \log (a x+1)}{a^4}+\frac{2 x}{a^3}-\frac{x^2}{a^2}+\frac{2 x^3}{3 a}-\frac{x^4}{4}","-\frac{2 \log (a x+1)}{a^4}+\frac{2 x}{a^3}-\frac{x^2}{a^2}+\frac{2 x^3}{3 a}-\frac{x^4}{4}",1,"(2*x)/a^3 - x^2/a^2 + (2*x^3)/(3*a) - x^4/4 - (2*Log[1 + a*x])/a^4","A",1
44,1,32,32,0.0131026,"\int e^{-2 \tanh ^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^(2*ArcTanh[a*x]),x]","\frac{2 \log (a x+1)}{a^3}-\frac{2 x}{a^2}+\frac{x^2}{a}-\frac{x^3}{3}","\frac{2 \log (a x+1)}{a^3}-\frac{2 x}{a^2}+\frac{x^2}{a}-\frac{x^3}{3}",1,"(-2*x)/a^2 + x^2/a - x^3/3 + (2*Log[1 + a*x])/a^3","A",1
45,1,25,25,0.0109077,"\int e^{-2 \tanh ^{-1}(a x)} x \, dx","Integrate[x/E^(2*ArcTanh[a*x]),x]","-\frac{2 \log (a x+1)}{a^2}+\frac{2 x}{a}-\frac{x^2}{2}","-\frac{2 \log (a x+1)}{a^2}+\frac{2 x}{a}-\frac{x^2}{2}",1,"(2*x)/a - x^2/2 - (2*Log[1 + a*x])/a^2","A",1
46,1,15,15,0.0095619,"\int e^{-2 \tanh ^{-1}(a x)} \, dx","Integrate[E^(-2*ArcTanh[a*x]),x]","\frac{2 \log (a x+1)}{a}-x","\frac{2 \log (a x+1)}{a}-x",1,"-x + (2*Log[1 + a*x])/a","A",1
47,1,11,11,0.0060902,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*x),x]","\log (x)-2 \log (a x+1)","\log (x)-2 \log (a x+1)",1,"Log[x] - 2*Log[1 + a*x]","A",1
48,1,20,20,0.0085406,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*x^2),x]","-2 a \log (x)+2 a \log (a x+1)-\frac{1}{x}","-2 a \log (x)+2 a \log (a x+1)-\frac{1}{x}",1,"-x^(-1) - 2*a*Log[x] + 2*a*Log[1 + a*x]","A",1
49,1,32,32,0.0103588,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*x^3),x]","2 a^2 \log (x)-2 a^2 \log (a x+1)+\frac{2 a}{x}-\frac{1}{2 x^2}","2 a^2 \log (x)-2 a^2 \log (a x+1)+\frac{2 a}{x}-\frac{1}{2 x^2}",1,"-1/2*1/x^2 + (2*a)/x + 2*a^2*Log[x] - 2*a^2*Log[1 + a*x]","A",1
50,1,39,39,0.0118828,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*x^4),x]","-2 a^3 \log (x)+2 a^3 \log (a x+1)-\frac{2 a^2}{x}+\frac{a}{x^2}-\frac{1}{3 x^3}","-2 a^3 \log (x)+2 a^3 \log (a x+1)-\frac{2 a^2}{x}+\frac{a}{x^2}-\frac{1}{3 x^3}",1,"-1/3*1/x^3 + a/x^2 - (2*a^2)/x - 2*a^3*Log[x] + 2*a^3*Log[1 + a*x]","A",1
51,1,70,131,0.0566045,"\int e^{-3 \tanh ^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^(3*ArcTanh[a*x]),x]","\frac{51 \sin ^{-1}(a x)}{8 a^4}+\sqrt{1-a^2 x^2} \left(\frac{4}{a^4 (a x+1)}+\frac{6}{a^4}-\frac{19 x}{8 a^3}+\frac{x^2}{a^2}-\frac{x^3}{4 a}\right)","\frac{51 \sin ^{-1}(a x)}{8 a^4}+\frac{x^2 \sqrt{1-a^2 x^2}}{a^2}-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}+\frac{9 (2-3 a x) \sqrt{1-a^2 x^2}}{8 a^4}+\frac{27 \sqrt{1-a^2 x^2}}{4 a^4}+\frac{(1-a x)^3}{a^4 \sqrt{1-a^2 x^2}}",1,"Sqrt[1 - a^2*x^2]*(6/a^4 - (19*x)/(8*a^3) + x^2/a^2 - x^3/(4*a) + 4/(a^4*(1 + a*x))) + (51*ArcSin[a*x])/(8*a^4)","A",1
52,1,58,95,0.0689916,"\int e^{-3 \tanh ^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^(3*ArcTanh[a*x]),x]","-\frac{\frac{\sqrt{1-a^2 x^2} \left(2 a^3 x^3-7 a^2 x^2+19 a x+52\right)}{a x+1}+33 \sin ^{-1}(a x)}{6 a^3}","-\frac{11 \sin ^{-1}(a x)}{2 a^3}-\frac{(1-a x)^3}{a^3 \sqrt{1-a^2 x^2}}-\frac{(3-a x)^2 \sqrt{1-a^2 x^2}}{3 a^3}-\frac{(28-3 a x) \sqrt{1-a^2 x^2}}{6 a^3}",1,"-1/6*((Sqrt[1 - a^2*x^2]*(52 + 19*a*x - 7*a^2*x^2 + 2*a^3*x^3))/(1 + a*x) + 33*ArcSin[a*x])/a^3","A",1
53,1,44,86,0.0523858,"\int e^{-3 \tanh ^{-1}(a x)} x \, dx","Integrate[x/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{1-a^2 x^2} \left(-a x+\frac{8}{a x+1}+6\right)+9 \sin ^{-1}(a x)}{2 a^2}","\frac{\left(1-a^2 x^2\right)^{5/2}}{a^2 (a x+1)^3}+\frac{3 \left(1-a^2 x^2\right)^{3/2}}{2 a^2 (a x+1)}+\frac{9 \sqrt{1-a^2 x^2}}{2 a^2}+\frac{9 \sin ^{-1}(a x)}{2 a^2}",1,"(Sqrt[1 - a^2*x^2]*(6 - a*x + 8/(1 + a*x)) + 9*ArcSin[a*x])/(2*a^2)","A",1
54,1,39,56,0.0313662,"\int e^{-3 \tanh ^{-1}(a x)} \, dx","Integrate[E^(-3*ArcTanh[a*x]),x]","\frac{\sqrt{1-a^2 x^2} \left(-\frac{4}{a x+1}-1\right)}{a}-\frac{3 \sin ^{-1}(a x)}{a}","-\frac{2 (1-a x)^2}{a \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{1-a^2 x^2}}{a}-\frac{3 \sin ^{-1}(a x)}{a}",1,"(Sqrt[1 - a^2*x^2]*(-1 - 4/(1 + a*x)))/a - (3*ArcSin[a*x])/a","A",1
55,1,49,45,0.0360442,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*x),x]","\frac{4 \sqrt{1-a^2 x^2}}{a x+1}-\log \left(\sqrt{1-a^2 x^2}+1\right)+\sin ^{-1}(a x)+\log (x)","\frac{4 \sqrt{1-a^2 x^2}}{a x+1}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\sin ^{-1}(a x)",1,"(4*Sqrt[1 - a^2*x^2])/(1 + a*x) + ArcSin[a*x] + Log[x] - Log[1 + Sqrt[1 - a^2*x^2]]","A",0
56,1,57,62,0.0577054,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*x^2),x]","\sqrt{1-a^2 x^2} \left(-\frac{4 a}{a x+1}-\frac{1}{x}\right)+3 a \log \left(\sqrt{1-a^2 x^2}+1\right)-3 a \log (x)","-\frac{4 a \sqrt{1-a^2 x^2}}{a x+1}-\frac{\sqrt{1-a^2 x^2}}{x}+3 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"Sqrt[1 - a^2*x^2]*(-x^(-1) - (4*a)/(1 + a*x)) - 3*a*Log[x] + 3*a*Log[1 + Sqrt[1 - a^2*x^2]]","A",0
57,1,75,90,0.0629537,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*x^3),x]","\sqrt{1-a^2 x^2} \left(\frac{4 a^2}{a x+1}+\frac{3 a}{x}-\frac{1}{2 x^2}\right)-\frac{9}{2} a^2 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{9}{2} a^2 \log (x)","\frac{4 a^2 \sqrt{1-a^2 x^2}}{a x+1}+\frac{3 a \sqrt{1-a^2 x^2}}{x}-\frac{\sqrt{1-a^2 x^2}}{2 x^2}-\frac{9}{2} a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"Sqrt[1 - a^2*x^2]*(-1/2*1/x^2 + (3*a)/x + (4*a^2)/(1 + a*x)) + (9*a^2*Log[x])/2 - (9*a^2*Log[1 + Sqrt[1 - a^2*x^2]])/2","A",0
58,1,82,116,0.0796723,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*x^4),x]","\frac{1}{6} \left(-33 a^3 \log (x)+33 a^3 \log \left(\sqrt{1-a^2 x^2}+1\right)-\frac{\sqrt{1-a^2 x^2} \left(52 a^3 x^3+19 a^2 x^2-7 a x+2\right)}{x^3 (a x+1)}\right)","-\frac{14 a^2 \sqrt{1-a^2 x^2}}{3 x}+\frac{3 a \sqrt{1-a^2 x^2}}{2 x^2}-\frac{\sqrt{1-a^2 x^2}}{3 x^3}-\frac{4 a^3 \sqrt{1-a^2 x^2}}{a x+1}+\frac{11}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-((Sqrt[1 - a^2*x^2]*(2 - 7*a*x + 19*a^2*x^2 + 52*a^3*x^3))/(x^3*(1 + a*x))) - 33*a^3*Log[x] + 33*a^3*Log[1 + Sqrt[1 - a^2*x^2]])/6","A",0
59,1,89,135,0.0800928,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*x^5),x]","\frac{1}{8} \left(51 a^4 \log (x)-51 a^4 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{\sqrt{1-a^2 x^2} \left(80 a^4 x^4+29 a^3 x^3-11 a^2 x^2+6 a x-2\right)}{x^4 (a x+1)}\right)","-\frac{19 a^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}+\frac{a \sqrt{1-a^2 x^2}}{x^3}+\frac{4 a^4 \sqrt{1-a^2 x^2}}{a x+1}-\frac{51}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{6 a^3 \sqrt{1-a^2 x^2}}{x}",1,"((Sqrt[1 - a^2*x^2]*(-2 + 6*a*x - 11*a^2*x^2 + 29*a^3*x^3 + 80*a^4*x^4))/(x^4*(1 + a*x)) + 51*a^4*Log[x] - 51*a^4*Log[1 + Sqrt[1 - a^2*x^2]])/8","A",0
60,0,0,31,0.3773866,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^(ArcTanh[a*x]/2)*x^m,x]","\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{1}{4},-\frac{1}{4};m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^(ArcTanh[a*x]/2)*x^m, x]","F",-1
61,1,69,282,0.035742,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^(ArcTanh[a*x]/2)*x^2,x]","-\frac{(1-a x)^{3/4} \left(\sqrt[4]{a x+1} \left(4 a^2 x^2+5 a x+1\right)+6 \sqrt[4]{2} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)\right)}{12 a^3}","-\frac{(1-a x)^{3/4} (a x+1)^{5/4}}{12 a^3}-\frac{3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{8 a^3}-\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{8 \sqrt{2} a^3}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^3}-\frac{x (1-a x)^{3/4} (a x+1)^{5/4}}{3 a^2}",1,"-1/12*((1 - a*x)^(3/4)*((1 + a*x)^(1/4)*(1 + 5*a*x + 4*a^2*x^2) + 6*2^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, (1 - a*x)/2]))/a^3","C",0
62,1,56,255,0.0236967,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x \, dx","Integrate[E^(ArcTanh[a*x]/2)*x,x]","-\frac{(1-a x)^{3/4} \left(2 \sqrt[4]{2} \, _2F_1\left(-\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)+3 (a x+1)^{5/4}\right)}{6 a^2}","-\frac{(1-a x)^{3/4} (a x+1)^{5/4}}{2 a^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 a^2}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a^2}",1,"-1/6*((1 - a*x)^(3/4)*(3*(1 + a*x)^(5/4) + 2*2^(1/4)*Hypergeometric2F1[-1/4, 3/4, 7/4, (1 - a*x)/2]))/a^2","C",0
63,1,149,222,0.2306447,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \, dx","Integrate[E^(ArcTanh[a*x]/2),x]","\frac{-\frac{8 e^{\frac{1}{2} \tanh ^{-1}(a x)}}{e^{2 \tanh ^{-1}(a x)}+1}-\sqrt{2} \log \left(-\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+e^{\tanh ^{-1}(a x)}+1\right)+\sqrt{2} \log \left(\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+e^{\tanh ^{-1}(a x)}+1\right)-2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}\right)+2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+1\right)}{4 a}","-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{a}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{\sqrt{2} a}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}",1,"((-8*E^(ArcTanh[a*x]/2))/(1 + E^(2*ArcTanh[a*x])) - 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*E^(ArcTanh[a*x]/2)] + 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*E^(ArcTanh[a*x]/2)] - Sqrt[2]*Log[1 - Sqrt[2]*E^(ArcTanh[a*x]/2) + E^ArcTanh[a*x]] + Sqrt[2]*Log[1 + Sqrt[2]*E^(ArcTanh[a*x]/2) + E^ArcTanh[a*x]])/(4*a)","A",0
64,1,83,227,0.0323214,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^(ArcTanh[a*x]/2)/x,x]","-\frac{2 (1-a x)^{3/4} \left(\sqrt[4]{2} (a x+1)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)+2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)\right)}{3 (a x+1)^{3/4}}","-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"(-2*(1 - a*x)^(3/4)*(2^(1/4)*(1 + a*x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (1 - a*x)/2] + 2*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(3*(1 + a*x)^(3/4))","C",0
65,1,58,73,0.0151844,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^(ArcTanh[a*x]/2)/x^2,x]","-\frac{(1-a x)^{3/4} \left(2 a x \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+3 a x+3\right)}{3 x (a x+1)^{3/4}}","-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{x}-a \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-a \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"-1/3*((1 - a*x)^(3/4)*(3 + 3*a*x + 2*a*x*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(x*(1 + a*x)^(3/4))","C",0
66,1,70,110,0.0208126,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^(ArcTanh[a*x]/2)/x^3,x]","-\frac{(1-a x)^{3/4} \left(2 a^2 x^2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+9 a^2 x^2+15 a x+6\right)}{12 x^2 (a x+1)^{3/4}}","-\frac{1}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{1}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{(1-a x)^{3/4} (a x+1)^{5/4}}{2 x^2}-\frac{a (1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x}",1,"-1/12*((1 - a*x)^(3/4)*(6 + 15*a*x + 9*a^2*x^2 + 2*a^2*x^2*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(x^2*(1 + a*x)^(3/4))","C",0
67,1,78,139,0.0231146,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^(ArcTanh[a*x]/2)/x^4,x]","-\frac{(1-a x)^{3/4} \left(6 a^3 x^3 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+11 a^3 x^3+21 a^2 x^2+18 a x+8\right)}{24 x^3 (a x+1)^{3/4}}","-\frac{3}{8} a^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{3}{8} a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{11 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{3 x^3}-\frac{5 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{12 x^2}",1,"-1/24*((1 - a*x)^(3/4)*(8 + 18*a*x + 21*a^2*x^2 + 11*a^3*x^3 + 6*a^3*x^3*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(x^3*(1 + a*x)^(3/4))","C",0
68,1,86,168,0.0283584,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[E^(ArcTanh[a*x]/2)/x^5,x]","-\frac{(1-a x)^{3/4} \left(22 a^4 x^4 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+83 a^4 x^4+141 a^3 x^3+114 a^2 x^2+104 a x+48\right)}{192 x^4 (a x+1)^{3/4}}","-\frac{11}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{11}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{83 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{192 x}-\frac{29 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{96 x^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x^4}-\frac{7 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x^3}",1,"-1/192*((1 - a*x)^(3/4)*(48 + 104*a*x + 114*a^2*x^2 + 141*a^3*x^3 + 83*a^4*x^4 + 22*a^4*x^4*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(x^4*(1 + a*x)^(3/4))","C",0
69,1,94,197,0.0325072,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^6} \, dx","Integrate[E^(ArcTanh[a*x]/2)/x^6,x]","-\frac{(1-a x)^{3/4} \left(310 a^5 x^5 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+611 a^5 x^5+1149 a^4 x^4+978 a^3 x^3+872 a^2 x^2+816 a x+384\right)}{1920 x^5 (a x+1)^{3/4}}","-\frac{31}{128} a^5 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{31}{128} a^5 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{611 a^4 (1-a x)^{3/4} \sqrt[4]{a x+1}}{1920 x}-\frac{269 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{960 x^2}-\frac{11 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{48 x^3}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{5 x^5}-\frac{9 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{40 x^4}",1,"-1/1920*((1 - a*x)^(3/4)*(384 + 816*a*x + 872*a^2*x^2 + 978*a^3*x^3 + 1149*a^4*x^4 + 611*a^5*x^5 + 310*a^5*x^5*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(x^5*(1 + a*x)^(3/4))","C",0
70,0,0,31,0.3852833,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^((3*ArcTanh[a*x])/2)*x^m,x]","\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{3}{4},-\frac{3}{4};m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^((3*ArcTanh[a*x])/2)*x^m, x]","F",-1
71,1,131,290,0.1077459,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^3 \, dx","Integrate[E^((3*ArcTanh[a*x])/2)*x^3,x]","-\frac{\sqrt[4]{1-a x} \left(a^3 x^3 (a x+1)^{3/4}+a^2 x^2 (a x+1)^{3/4}+24\ 2^{3/4} \, _2F_1\left(-\frac{11}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)-8\ 2^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)-2\ 2^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)\right)}{4 a^4}","-\frac{\sqrt[4]{1-a x} (a x+1)^{7/4} (4 a x+11)}{32 a^4}-\frac{41 \sqrt[4]{1-a x} (a x+1)^{3/4}}{64 a^4}+\frac{123 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}+\frac{123 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a^4}-\frac{123 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a^4}-\frac{x^2 \sqrt[4]{1-a x} (a x+1)^{7/4}}{4 a^2}",1,"-1/4*((1 - a*x)^(1/4)*(a^2*x^2*(1 + a*x)^(3/4) + a^3*x^3*(1 + a*x)^(3/4) + 24*2^(3/4)*Hypergeometric2F1[-11/4, 1/4, 5/4, (1 - a*x)/2] - 8*2^(3/4)*Hypergeometric2F1[-7/4, 1/4, 5/4, (1 - a*x)/2] - 2*2^(3/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, (1 - a*x)/2]))/a^4","C",0
72,1,69,282,0.0305487,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^((3*ArcTanh[a*x])/2)*x^2,x]","-\frac{\sqrt[4]{1-a x} \left((a x+1)^{3/4} \left(4 a^2 x^2+7 a x+3\right)+34\ 2^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)\right)}{12 a^3}","-\frac{\sqrt[4]{1-a x} (a x+1)^{7/4}}{4 a^3}-\frac{17 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 a^3}+\frac{17 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}-\frac{17 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{8 \sqrt{2} a^3}-\frac{17 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^3}-\frac{x \sqrt[4]{1-a x} (a x+1)^{7/4}}{3 a^2}",1,"-1/12*((1 - a*x)^(1/4)*((1 + a*x)^(3/4)*(3 + 7*a*x + 4*a^2*x^2) + 34*2^(3/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, (1 - a*x)/2]))/a^3","C",0
73,1,54,255,0.0173206,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x \, dx","Integrate[E^((3*ArcTanh[a*x])/2)*x,x]","-\frac{\sqrt[4]{1-a x} \left(6\ 2^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)+(a x+1)^{7/4}\right)}{2 a^2}","-\frac{\sqrt[4]{1-a x} (a x+1)^{7/4}}{2 a^2}-\frac{3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{4 a^2}+\frac{9 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{9 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}+\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a^2}-\frac{9 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a^2}",1,"-1/2*((1 - a*x)^(1/4)*((1 + a*x)^(7/4) + 6*2^(3/4)*Hypergeometric2F1[-3/4, 1/4, 5/4, (1 - a*x)/2]))/a^2","C",0
74,1,48,223,0.0640834,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} \, dx","Integrate[E^((3*ArcTanh[a*x])/2),x]","\frac{8 e^{\frac{3}{2} \tanh ^{-1}(a x)} \left(\, _2F_1\left(\frac{3}{4},2;\frac{7}{4};-e^{2 \tanh ^{-1}(a x)}\right)-\frac{1}{e^{2 \tanh ^{-1}(a x)}+1}\right)}{a}","-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{a}+\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}-\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{\sqrt{2} a}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}",1,"(8*E^((3*ArcTanh[a*x])/2)*(-(1 + E^(2*ArcTanh[a*x]))^(-1) + Hypergeometric2F1[3/4, 2, 7/4, -E^(2*ArcTanh[a*x])]))/a","C",0
75,1,83,227,0.030652,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^((3*ArcTanh[a*x])/2)/x,x]","-2\ 2^{3/4} \sqrt[4]{1-a x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)-\frac{4 \sqrt[4]{1-a x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{1-a x}{-a x-1}\right)}{\sqrt[4]{a x+1}}","\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"-2*2^(3/4)*(1 - a*x)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (1 - a*x)/2] - (4*(1 - a*x)^(1/4)*Hypergeometric2F1[1/4, 1, 5/4, -((1 - a*x)/(-1 - a*x))])/(1 + a*x)^(1/4)","C",0
76,1,55,73,0.0137087,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^((3*ArcTanh[a*x])/2)/x^2,x]","-\frac{\sqrt[4]{1-a x} \left(6 a x \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+a x+1\right)}{x \sqrt[4]{a x+1}}","-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{x}+3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"-(((1 - a*x)^(1/4)*(1 + a*x + 6*a*x*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(x*(1 + a*x)^(1/4)))","C",0
77,1,70,110,0.0178336,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^((3*ArcTanh[a*x])/2)/x^3,x]","-\frac{\sqrt[4]{1-a x} \left(18 a^2 x^2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+5 a^2 x^2+7 a x+2\right)}{4 x^2 \sqrt[4]{a x+1}}","\frac{9}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{9}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{\sqrt[4]{1-a x} (a x+1)^{7/4}}{2 x^2}-\frac{3 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x}",1,"-1/4*((1 - a*x)^(1/4)*(2 + 7*a*x + 5*a^2*x^2 + 18*a^2*x^2*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(x^2*(1 + a*x)^(1/4))","C",0
78,1,78,139,0.0242005,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^((3*ArcTanh[a*x])/2)/x^4,x]","-\frac{\sqrt[4]{1-a x} \left(102 a^3 x^3 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+23 a^3 x^3+37 a^2 x^2+22 a x+8\right)}{24 x^3 \sqrt[4]{a x+1}}","\frac{17}{8} a^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{17}{8} a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{23 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{3 x^3}-\frac{7 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{12 x^2}",1,"-1/24*((1 - a*x)^(1/4)*(8 + 22*a*x + 37*a^2*x^2 + 23*a^3*x^3 + 102*a^3*x^3*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(x^3*(1 + a*x)^(1/4))","C",0
79,1,86,168,0.0294739,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[E^((3*ArcTanh[a*x])/2)/x^5,x]","-\frac{\sqrt[4]{1-a x} \left(246 a^4 x^4 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+63 a^4 x^4+93 a^3 x^3+54 a^2 x^2+40 a x+16\right)}{64 x^4 \sqrt[4]{a x+1}}","\frac{123}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{123}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{63 a^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{64 x}-\frac{15 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{32 x^2}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x^4}-\frac{3 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{8 x^3}",1,"-1/64*((1 - a*x)^(1/4)*(16 + 40*a*x + 54*a^2*x^2 + 93*a^3*x^3 + 63*a^4*x^4 + 246*a^4*x^4*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(x^4*(1 + a*x)^(1/4))","C",0
80,0,0,31,0.4388586,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^((5*ArcTanh[a*x])/2)*x^m,x]","\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{5}{4},-\frac{5}{4};m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^((5*ArcTanh[a*x])/2)*x^m, x]","F",-1
81,1,74,317,0.0464069,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^3 \, dx","Integrate[E^((5*ArcTanh[a*x])/2)*x^3,x]","\frac{(a x+1)^{9/4} \left(-6 a^2 x^2-5 a x+59\right)-380 \sqrt[4]{2} (a x-1) \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)}{24 a^4 \sqrt[4]{1-a x}}","\frac{(1-a x)^{3/4} (a x+1)^{5/4} (452 a x+521)}{96 a^4}+\frac{475 (1-a x)^{3/4} \sqrt[4]{a x+1}}{64 a^4}+\frac{475 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a^4}+\frac{475 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a^4}+\frac{17 x^2 (1-a x)^{3/4} (a x+1)^{5/4}}{4 a^2}+\frac{4 x^3 (a x+1)^{5/4}}{a \sqrt[4]{1-a x}}",1,"((1 + a*x)^(9/4)*(59 - 5*a*x - 6*a^2*x^2) - 380*2^(1/4)*(-1 + a*x)*Hypergeometric2F1[-5/4, 3/4, 7/4, (1 - a*x)/2])/(24*a^4*(1 - a*x)^(1/4))","C",0
82,1,66,305,0.0316153,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^((5*ArcTanh[a*x])/2)*x^2,x]","\frac{(7-a x) (a x+1)^{9/4}-44 \sqrt[4]{2} (a x-1) \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)}{3 a^3 \sqrt[4]{1-a x}}","\frac{(1-a x)^{3/4} (a x+1)^{9/4}}{3 a^3}+\frac{2 (a x+1)^{9/4}}{a^3 \sqrt[4]{1-a x}}+\frac{11 (1-a x)^{3/4} (a x+1)^{5/4}}{4 a^3}+\frac{55 (1-a x)^{3/4} \sqrt[4]{a x+1}}{8 a^3}+\frac{55 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{8 \sqrt{2} a^3}+\frac{55 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^3}",1,"((7 - a*x)*(1 + a*x)^(9/4) - 44*2^(1/4)*(-1 + a*x)*Hypergeometric2F1[-5/4, 3/4, 7/4, (1 - a*x)/2])/(3*a^3*(1 - a*x)^(1/4))","C",0
83,1,61,279,0.0275355,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x \, dx","Integrate[E^((5*ArcTanh[a*x])/2)*x,x]","\frac{6 (a x+1)^{9/4}-40 \sqrt[4]{2} (a x-1) \, _2F_1\left(-\frac{5}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)}{3 a^2 \sqrt[4]{1-a x}}","\frac{2 (a x+1)^{9/4}}{a^2 \sqrt[4]{1-a x}}+\frac{5 (1-a x)^{3/4} (a x+1)^{5/4}}{2 a^2}+\frac{25 (1-a x)^{3/4} \sqrt[4]{a x+1}}{4 a^2}+\frac{25 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{25 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{25 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a^2}+\frac{25 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a^2}",1,"(6*(1 + a*x)^(9/4) - 40*2^(1/4)*(-1 + a*x)*Hypergeometric2F1[-5/4, 3/4, 7/4, (1 - a*x)/2])/(3*a^2*(1 - a*x)^(1/4))","C",0
84,1,174,247,0.2372969,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} \, dx","Integrate[E^((5*ArcTanh[a*x])/2),x]","\frac{\frac{40 e^{\frac{1}{2} \tanh ^{-1}(a x)}}{e^{2 \tanh ^{-1}(a x)}+1}+\frac{32 e^{\frac{5}{2} \tanh ^{-1}(a x)}}{e^{2 \tanh ^{-1}(a x)}+1}+5 \sqrt{2} \log \left(-\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+e^{\tanh ^{-1}(a x)}+1\right)-5 \sqrt{2} \log \left(\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+e^{\tanh ^{-1}(a x)}+1\right)+10 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}\right)-10 \sqrt{2} \tan ^{-1}\left(\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+1\right)}{4 a}","\frac{4 (a x+1)^{5/4}}{a \sqrt[4]{1-a x}}+\frac{5 (1-a x)^{3/4} \sqrt[4]{a x+1}}{a}+\frac{5 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}-\frac{5 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{\sqrt{2} a}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}",1,"((40*E^(ArcTanh[a*x]/2))/(1 + E^(2*ArcTanh[a*x])) + (32*E^((5*ArcTanh[a*x])/2))/(1 + E^(2*ArcTanh[a*x])) + 10*Sqrt[2]*ArcTan[1 - Sqrt[2]*E^(ArcTanh[a*x]/2)] - 10*Sqrt[2]*ArcTan[1 + Sqrt[2]*E^(ArcTanh[a*x]/2)] + 5*Sqrt[2]*Log[1 - Sqrt[2]*E^(ArcTanh[a*x]/2) + E^ArcTanh[a*x]] - 5*Sqrt[2]*Log[1 + Sqrt[2]*E^(ArcTanh[a*x]/2) + E^ArcTanh[a*x]])/(4*a)","A",0
85,1,93,248,0.0400357,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^((5*ArcTanh[a*x])/2)/x,x]","\frac{4 \left(3 \sqrt[4]{2} (a x+1)^{3/4} \, _2F_1\left(-\frac{1}{4},-\frac{1}{4};\frac{3}{4};\frac{1}{2} (1-a x)\right)+(a x-1) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+3 a x+3\right)}{3 \sqrt[4]{1-a x} (a x+1)^{3/4}}","\frac{8 \sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"(4*(3 + 3*a*x + 3*2^(1/4)*(1 + a*x)^(3/4)*Hypergeometric2F1[-1/4, -1/4, 3/4, (1 - a*x)/2] + (-1 + a*x)*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))","C",0
86,1,74,95,0.0213204,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^((5*ArcTanh[a*x])/2)/x^2,x]","\frac{3 \left(9 a^2 x^2+8 a x-1\right)+10 a x (a x-1) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)}{3 x \sqrt[4]{1-a x} (a x+1)^{3/4}}","-\frac{(a x+1)^{5/4}}{x \sqrt[4]{1-a x}}+\frac{10 a \sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}-5 a \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-5 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"(3*(-1 + 8*a*x + 9*a^2*x^2) + 10*a*x*(-1 + a*x)*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)])/(3*x*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))","C",0
87,1,86,136,0.0255101,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^((5*ArcTanh[a*x])/2)/x^3,x]","\frac{50 a^2 x^2 (a x-1) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+3 \left(43 a^3 x^3+34 a^2 x^2-11 a x-2\right)}{12 x^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}","\frac{25 a^2 \sqrt[4]{a x+1}}{2 \sqrt[4]{1-a x}}-\frac{25}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{25}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{(a x+1)^{9/4}}{2 x^2 \sqrt[4]{1-a x}}-\frac{5 a (a x+1)^{5/4}}{4 x \sqrt[4]{1-a x}}",1,"(3*(-2 - 11*a*x + 34*a^2*x^2 + 43*a^3*x^3) + 50*a^2*x^2*(-1 + a*x)*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)])/(12*x^2*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))","C",0
88,1,91,165,0.0290454,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^((5*ArcTanh[a*x])/2)/x^4,x]","\frac{287 a^4 x^4+110 a^3 x^3 (a x-1) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+226 a^3 x^3-87 a^2 x^2-34 a x-8}{24 x^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}","\frac{287 a^3 \sqrt[4]{a x+1}}{24 \sqrt[4]{1-a x}}-\frac{55}{8} a^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{55}{8} a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{61 a^2 \sqrt[4]{a x+1}}{24 x \sqrt[4]{1-a x}}-\frac{\sqrt[4]{a x+1}}{3 x^3 \sqrt[4]{1-a x}}-\frac{13 a \sqrt[4]{a x+1}}{12 x^2 \sqrt[4]{1-a x}}",1,"(-8 - 34*a*x - 87*a^2*x^2 + 226*a^3*x^3 + 287*a^4*x^4 + 110*a^3*x^3*(-1 + a*x)*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)])/(24*x^3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))","C",0
89,1,99,194,0.0337899,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[E^((5*ArcTanh[a*x])/2)/x^5,x]","\frac{2467 a^5 x^5+950 a^4 x^4 (a x-1) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+1946 a^4 x^4-747 a^3 x^3-362 a^2 x^2-184 a x-48}{192 x^4 \sqrt[4]{1-a x} (a x+1)^{3/4}}","\frac{2467 a^4 \sqrt[4]{a x+1}}{192 \sqrt[4]{1-a x}}-\frac{475}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{475}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{521 a^3 \sqrt[4]{a x+1}}{192 x \sqrt[4]{1-a x}}-\frac{113 a^2 \sqrt[4]{a x+1}}{96 x^2 \sqrt[4]{1-a x}}-\frac{\sqrt[4]{a x+1}}{4 x^4 \sqrt[4]{1-a x}}-\frac{17 a \sqrt[4]{a x+1}}{24 x^3 \sqrt[4]{1-a x}}",1,"(-48 - 184*a*x - 362*a^2*x^2 - 747*a^3*x^3 + 1946*a^4*x^4 + 2467*a^5*x^5 + 950*a^4*x^4*(-1 + a*x)*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)])/(192*x^4*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))","C",0
90,0,0,31,0.3966026,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^m \, dx","Integrate[x^m/E^(ArcTanh[a*x]/2),x]","\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;-\frac{1}{4},\frac{1}{4};m+2;a x,-a x\right)}{m+1}",1,"Integrate[x^m/E^(ArcTanh[a*x]/2), x]","F",-1
91,1,116,290,0.1066106,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^(ArcTanh[a*x]/2),x]","\frac{(1-a x)^{5/4} \left(-5 a^2 x^2 (a x+1)^{3/4}+4\ 2^{3/4} \, _2F_1\left(-\frac{7}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)-12\ 2^{3/4} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)+5\ 2^{3/4} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)\right)}{20 a^4}","-\frac{(25-4 a x) (1-a x)^{5/4} (a x+1)^{3/4}}{96 a^4}-\frac{11 \sqrt[4]{1-a x} (a x+1)^{3/4}}{64 a^4}-\frac{11 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}+\frac{11 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{11 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a^4}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a^4}-\frac{x^2 (1-a x)^{5/4} (a x+1)^{3/4}}{4 a^2}",1,"((1 - a*x)^(5/4)*(-5*a^2*x^2*(1 + a*x)^(3/4) + 4*2^(3/4)*Hypergeometric2F1[-7/4, 5/4, 9/4, (1 - a*x)/2] - 12*2^(3/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, (1 - a*x)/2] + 5*2^(3/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (1 - a*x)/2]))/(20*a^4)","C",0
92,1,62,282,0.0282381,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^(ArcTanh[a*x]/2),x]","-\frac{(1-a x)^{5/4} \left(9\ 2^{3/4} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)+5 (a x+1)^{3/4} (4 a x-1)\right)}{60 a^3}","\frac{(a x+1)^{3/4} (1-a x)^{5/4}}{12 a^3}+\frac{3 (a x+1)^{3/4} \sqrt[4]{1-a x}}{8 a^3}+\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}-\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{8 \sqrt{2} a^3}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^3}-\frac{x (a x+1)^{3/4} (1-a x)^{5/4}}{3 a^2}",1,"-1/60*((1 - a*x)^(5/4)*(5*(1 + a*x)^(3/4)*(-1 + 4*a*x) + 9*2^(3/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (1 - a*x)/2]))/a^3","C",0
93,1,55,255,0.0201561,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x \, dx","Integrate[x/E^(ArcTanh[a*x]/2),x]","\frac{(1-a x)^{5/4} \left(2^{3/4} \, _2F_1\left(\frac{1}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)-5 (a x+1)^{3/4}\right)}{10 a^2}","-\frac{(a x+1)^{3/4} (1-a x)^{5/4}}{2 a^2}-\frac{(a x+1)^{3/4} \sqrt[4]{1-a x}}{4 a^2}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a^2}",1,"((1 - a*x)^(5/4)*(-5*(1 + a*x)^(3/4) + 2^(3/4)*Hypergeometric2F1[1/4, 5/4, 9/4, (1 - a*x)/2]))/(10*a^2)","C",0
94,1,35,221,0.0368498,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} \, dx","Integrate[E^(-1/2*ArcTanh[a*x]),x]","\frac{8 e^{\frac{3}{2} \tanh ^{-1}(a x)} \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};-e^{2 \tanh ^{-1}(a x)}\right)}{3 a}","\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{a}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{\sqrt{2} a}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}",1,"(8*E^((3*ArcTanh[a*x])/2)*Hypergeometric2F1[3/4, 2, 7/4, -E^(2*ArcTanh[a*x])])/(3*a)","C",0
95,1,83,227,0.0257875,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[1/(E^(ArcTanh[a*x]/2)*x),x]","2\ 2^{3/4} \sqrt[4]{1-a x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)-\frac{4 \sqrt[4]{1-a x} \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};-\frac{1-a x}{-a x-1}\right)}{\sqrt[4]{a x+1}}","-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"2*2^(3/4)*(1 - a*x)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (1 - a*x)/2] - (4*(1 - a*x)^(1/4)*Hypergeometric2F1[1/4, 1, 5/4, -((1 - a*x)/(-1 - a*x))])/(1 + a*x)^(1/4)","C",0
96,1,55,72,0.0140455,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^(ArcTanh[a*x]/2)*x^2),x]","\frac{\sqrt[4]{1-a x} \left(2 a x \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)-a x-1\right)}{x \sqrt[4]{a x+1}}","-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{x}-a \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+a \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"((1 - a*x)^(1/4)*(-1 - a*x + 2*a*x*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(x*(1 + a*x)^(1/4))","C",0
97,1,69,110,0.0218517,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^(ArcTanh[a*x]/2)*x^3),x]","\frac{\sqrt[4]{1-a x} \left(-2 a^2 x^2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+3 a^2 x^2+a x-2\right)}{4 x^2 \sqrt[4]{a x+1}}","\frac{1}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{1}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{(1-a x)^{5/4} (a x+1)^{3/4}}{2 x^2}+\frac{a \sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x}",1,"((1 - a*x)^(1/4)*(-2 + a*x + 3*a^2*x^2 - 2*a^2*x^2*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(4*x^2*(1 + a*x)^(1/4))","C",0
98,1,78,139,0.0237341,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^(ArcTanh[a*x]/2)*x^4),x]","\frac{\sqrt[4]{1-a x} \left(18 a^3 x^3 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)-11 a^3 x^3-a^2 x^2+2 a x-8\right)}{24 x^3 \sqrt[4]{a x+1}}","-\frac{3}{8} a^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\frac{3}{8} a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{11 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{3 x^3}+\frac{5 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{12 x^2}",1,"((1 - a*x)^(1/4)*(-8 + 2*a*x - a^2*x^2 - 11*a^3*x^3 + 18*a^3*x^3*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(24*x^3*(1 + a*x)^(1/4))","C",0
99,1,86,168,0.0305811,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[1/(E^(ArcTanh[a*x]/2)*x^5),x]","\frac{\sqrt[4]{1-a x} \left(-66 a^4 x^4 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+83 a^4 x^4+25 a^3 x^3-2 a^2 x^2+8 a x-48\right)}{192 x^4 \sqrt[4]{a x+1}}","\frac{11}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{11}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\frac{83 a^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{192 x}-\frac{29 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{96 x^2}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x^4}+\frac{7 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x^3}",1,"((1 - a*x)^(1/4)*(-48 + 8*a*x - 2*a^2*x^2 + 25*a^3*x^3 + 83*a^4*x^4 - 66*a^4*x^4*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(192*x^4*(1 + a*x)^(1/4))","C",0
100,0,0,31,0.3981234,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^m \, dx","Integrate[x^m/E^((3*ArcTanh[a*x])/2),x]","\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;-\frac{3}{4},\frac{3}{4};m+2;a x,-a x\right)}{m+1}",1,"Integrate[x^m/E^((3*ArcTanh[a*x])/2), x]","F",-1
101,1,116,290,0.1076995,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^((3*ArcTanh[a*x])/2),x]","\frac{(1-a x)^{7/4} \left(-7 a^2 x^2 \sqrt[4]{a x+1}+12 \sqrt[4]{2} \, _2F_1\left(-\frac{5}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2} (1-a x)\right)-20 \sqrt[4]{2} \, _2F_1\left(-\frac{1}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2} (1-a x)\right)+7 \sqrt[4]{2} \, _2F_1\left(\frac{3}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2} (1-a x)\right)\right)}{28 a^4}","-\frac{(11-4 a x) (1-a x)^{7/4} \sqrt[4]{a x+1}}{32 a^4}-\frac{41 (1-a x)^{3/4} \sqrt[4]{a x+1}}{64 a^4}+\frac{123 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{123 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a^4}+\frac{123 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a^4}-\frac{x^2 (1-a x)^{7/4} \sqrt[4]{a x+1}}{4 a^2}",1,"((1 - a*x)^(7/4)*(-7*a^2*x^2*(1 + a*x)^(1/4) + 12*2^(1/4)*Hypergeometric2F1[-5/4, 7/4, 11/4, (1 - a*x)/2] - 20*2^(1/4)*Hypergeometric2F1[-1/4, 7/4, 11/4, (1 - a*x)/2] + 7*2^(1/4)*Hypergeometric2F1[3/4, 7/4, 11/4, (1 - a*x)/2]))/(28*a^4)","C",0
102,1,62,282,0.0307095,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^((3*ArcTanh[a*x])/2),x]","-\frac{(1-a x)^{7/4} \left(17 \sqrt[4]{2} \, _2F_1\left(\frac{3}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2} (1-a x)\right)+7 \sqrt[4]{a x+1} (4 a x-3)\right)}{84 a^3}","\frac{\sqrt[4]{a x+1} (1-a x)^{7/4}}{4 a^3}+\frac{17 \sqrt[4]{a x+1} (1-a x)^{3/4}}{24 a^3}-\frac{17 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{17 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{8 \sqrt{2} a^3}-\frac{17 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^3}-\frac{x \sqrt[4]{a x+1} (1-a x)^{7/4}}{3 a^2}",1,"-1/84*((1 - a*x)^(7/4)*(7*(1 + a*x)^(1/4)*(-3 + 4*a*x) + 17*2^(1/4)*Hypergeometric2F1[3/4, 7/4, 11/4, (1 - a*x)/2]))/a^3","C",0
103,1,56,255,0.0224983,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x \, dx","Integrate[x/E^((3*ArcTanh[a*x])/2),x]","\frac{(1-a x)^{7/4} \left(3 \sqrt[4]{2} \, _2F_1\left(\frac{3}{4},\frac{7}{4};\frac{11}{4};\frac{1}{2} (1-a x)\right)-7 \sqrt[4]{a x+1}\right)}{14 a^2}","-\frac{\sqrt[4]{a x+1} (1-a x)^{7/4}}{2 a^2}-\frac{3 \sqrt[4]{a x+1} (1-a x)^{3/4}}{4 a^2}+\frac{9 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{9 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{9 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a^2}+\frac{9 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a^2}",1,"((1 - a*x)^(7/4)*(-7*(1 + a*x)^(1/4) + 3*2^(1/4)*Hypergeometric2F1[3/4, 7/4, 11/4, (1 - a*x)/2]))/(14*a^2)","C",0
104,1,150,222,0.2256391,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} \, dx","Integrate[E^((-3*ArcTanh[a*x])/2),x]","\frac{\frac{8 e^{\frac{1}{2} \tanh ^{-1}(a x)}}{e^{2 \tanh ^{-1}(a x)}+1}-3 \sqrt{2} \log \left(-\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+e^{\tanh ^{-1}(a x)}+1\right)+3 \sqrt{2} \log \left(\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+e^{\tanh ^{-1}(a x)}+1\right)-6 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}\right)+6 \sqrt{2} \tan ^{-1}\left(\sqrt{2} e^{\frac{1}{2} \tanh ^{-1}(a x)}+1\right)}{4 a}","\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{a}-\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{\sqrt{2} a}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}",1,"((8*E^(ArcTanh[a*x]/2))/(1 + E^(2*ArcTanh[a*x])) - 6*Sqrt[2]*ArcTan[1 - Sqrt[2]*E^(ArcTanh[a*x]/2)] + 6*Sqrt[2]*ArcTan[1 + Sqrt[2]*E^(ArcTanh[a*x]/2)] - 3*Sqrt[2]*Log[1 - Sqrt[2]*E^(ArcTanh[a*x]/2) + E^ArcTanh[a*x]] + 3*Sqrt[2]*Log[1 + Sqrt[2]*E^(ArcTanh[a*x]/2) + E^ArcTanh[a*x]])/(4*a)","A",0
105,1,83,227,0.0281574,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[1/(E^((3*ArcTanh[a*x])/2)*x),x]","\frac{2 (1-a x)^{3/4} \left(\sqrt[4]{2} (a x+1)^{3/4} \, _2F_1\left(\frac{3}{4},\frac{3}{4};\frac{7}{4};\frac{1}{2} (1-a x)\right)-2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)\right)}{3 (a x+1)^{3/4}}","\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"(2*(1 - a*x)^(3/4)*(2^(1/4)*(1 + a*x)^(3/4)*Hypergeometric2F1[3/4, 3/4, 7/4, (1 - a*x)/2] - 2*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(3*(1 + a*x)^(3/4))","C",0
106,1,55,73,0.0150016,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^((3*ArcTanh[a*x])/2)*x^2),x]","\frac{(1-a x)^{3/4} \left(2 a x \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)-a x-1\right)}{x (a x+1)^{3/4}}","-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{x}+3 a \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+3 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"((1 - a*x)^(3/4)*(-1 - a*x + 2*a*x*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(x*(1 + a*x)^(3/4))","C",0
107,1,70,110,0.0244739,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^((3*ArcTanh[a*x])/2)*x^3),x]","\frac{(1-a x)^{3/4} \left(-6 a^2 x^2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+5 a^2 x^2+3 a x-2\right)}{4 x^2 (a x+1)^{3/4}}","-\frac{9}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{9}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{(1-a x)^{7/4} \sqrt[4]{a x+1}}{2 x^2}+\frac{3 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x}",1,"((1 - a*x)^(3/4)*(-2 + 3*a*x + 5*a^2*x^2 - 6*a^2*x^2*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(4*x^2*(1 + a*x)^(3/4))","C",0
108,1,78,139,0.0235108,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^((3*ArcTanh[a*x])/2)*x^4),x]","\frac{(1-a x)^{3/4} \left(34 a^3 x^3 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)-23 a^3 x^3-9 a^2 x^2+6 a x-8\right)}{24 x^3 (a x+1)^{3/4}}","\frac{17}{8} a^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\frac{17}{8} a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{23 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{3 x^3}+\frac{7 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{12 x^2}",1,"((1 - a*x)^(3/4)*(-8 + 6*a*x - 9*a^2*x^2 - 23*a^3*x^3 + 34*a^3*x^3*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(24*x^3*(1 + a*x)^(3/4))","C",0
109,1,86,168,0.0322365,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[1/(E^((3*ArcTanh[a*x])/2)*x^5),x]","\frac{(1-a x)^{3/4} \left(-82 a^4 x^4 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};\frac{1-a x}{a x+1}\right)+63 a^4 x^4+33 a^3 x^3-6 a^2 x^2+8 a x-16\right)}{64 x^4 (a x+1)^{3/4}}","-\frac{123}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{123}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\frac{63 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{64 x}-\frac{15 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{32 x^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x^4}+\frac{3 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{8 x^3}",1,"((1 - a*x)^(3/4)*(-16 + 8*a*x - 6*a^2*x^2 + 33*a^3*x^3 + 63*a^4*x^4 - 82*a^4*x^4*Hypergeometric2F1[3/4, 1, 7/4, (1 - a*x)/(1 + a*x)]))/(64*x^4*(1 + a*x)^(3/4))","C",0
110,0,0,31,0.6780242,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^m \, dx","Integrate[x^m/E^((5*ArcTanh[a*x])/2),x]","\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;-\frac{5}{4},\frac{5}{4};m+2;a x,-a x\right)}{m+1}",1,"Integrate[x^m/E^((5*ArcTanh[a*x])/2), x]","F",-1
111,1,79,317,0.0397383,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^3 \, dx","Integrate[x^3/E^((5*ArcTanh[a*x])/2),x]","-\frac{(1-a x)^{9/4} \left(3 \left(6 a^2 x^2-5 a x-59\right)+95\ 2^{3/4} \sqrt[4]{a x+1} \, _2F_1\left(\frac{1}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2} (1-a x)\right)\right)}{72 a^4 \sqrt[4]{a x+1}}","\frac{(521-452 a x) (1-a x)^{5/4} (a x+1)^{3/4}}{96 a^4}+\frac{475 \sqrt[4]{1-a x} (a x+1)^{3/4}}{64 a^4}+\frac{475 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}-\frac{475 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a^4}+\frac{475 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a^4}-\frac{475 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a^4}+\frac{17 x^2 (1-a x)^{5/4} (a x+1)^{3/4}}{4 a^2}-\frac{4 x^3 (1-a x)^{5/4}}{a \sqrt[4]{a x+1}}",1,"-1/72*((1 - a*x)^(9/4)*(3*(-59 - 5*a*x + 6*a^2*x^2) + 95*2^(3/4)*(1 + a*x)^(1/4)*Hypergeometric2F1[1/4, 9/4, 13/4, (1 - a*x)/2]))/(a^4*(1 + a*x)^(1/4))","C",0
112,1,70,305,0.0369388,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[x^2/E^((5*ArcTanh[a*x])/2),x]","\frac{(1-a x)^{9/4} \left(11\ 2^{3/4} \sqrt[4]{a x+1} \, _2F_1\left(\frac{1}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2} (1-a x)\right)-3 (a x+7)\right)}{9 a^3 \sqrt[4]{a x+1}}","-\frac{(a x+1)^{3/4} (1-a x)^{9/4}}{3 a^3}-\frac{2 (1-a x)^{9/4}}{a^3 \sqrt[4]{a x+1}}-\frac{11 (a x+1)^{3/4} (1-a x)^{5/4}}{4 a^3}-\frac{55 (a x+1)^{3/4} \sqrt[4]{1-a x}}{8 a^3}-\frac{55 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}+\frac{55 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{16 \sqrt{2} a^3}-\frac{55 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{8 \sqrt{2} a^3}+\frac{55 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^3}",1,"((1 - a*x)^(9/4)*(-3*(7 + a*x) + 11*2^(3/4)*(1 + a*x)^(1/4)*Hypergeometric2F1[1/4, 9/4, 13/4, (1 - a*x)/2]))/(9*a^3*(1 + a*x)^(1/4))","C",0
113,1,64,279,0.0262012,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x \, dx","Integrate[x/E^((5*ArcTanh[a*x])/2),x]","-\frac{2 (1-a x)^{9/4} \left(5\ 2^{3/4} \sqrt[4]{a x+1} \, _2F_1\left(\frac{1}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2} (1-a x)\right)-9\right)}{9 a^2 \sqrt[4]{a x+1}}","\frac{2 (1-a x)^{9/4}}{a^2 \sqrt[4]{a x+1}}+\frac{5 (a x+1)^{3/4} (1-a x)^{5/4}}{2 a^2}+\frac{25 (a x+1)^{3/4} \sqrt[4]{1-a x}}{4 a^2}+\frac{25 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}-\frac{25 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a^2}+\frac{25 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a^2}-\frac{25 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a^2}",1,"(-2*(1 - a*x)^(9/4)*(-9 + 5*2^(3/4)*(1 + a*x)^(1/4)*Hypergeometric2F1[1/4, 9/4, 13/4, (1 - a*x)/2]))/(9*a^2*(1 + a*x)^(1/4))","C",0
114,1,33,247,0.058827,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} \, dx","Integrate[E^((-5*ArcTanh[a*x])/2),x]","-\frac{8 e^{-\frac{1}{2} \tanh ^{-1}(a x)} \, _2F_1\left(-\frac{1}{4},2;\frac{3}{4};-e^{2 \tanh ^{-1}(a x)}\right)}{a}","-\frac{4 (1-a x)^{5/4}}{a \sqrt[4]{a x+1}}-\frac{5 (a x+1)^{3/4} \sqrt[4]{1-a x}}{a}-\frac{5 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}+\frac{5 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{2 \sqrt{2} a}-\frac{5 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{\sqrt{2} a}+\frac{5 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}",1,"(-8*Hypergeometric2F1[-1/4, 2, 3/4, -E^(2*ArcTanh[a*x])])/(a*E^(ArcTanh[a*x]/2))","C",0
115,1,90,248,0.0677947,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[1/(E^((5*ArcTanh[a*x])/2)*x),x]","\frac{\sqrt[4]{1-a x} \left(-20 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+2^{3/4} (1-a x) \sqrt[4]{a x+1} \, _2F_1\left(\frac{5}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)+20\right)}{5 \sqrt[4]{a x+1}}","\frac{8 \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2}}+2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"((1 - a*x)^(1/4)*(20 - 20*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)] + 2^(3/4)*(1 - a*x)*(1 + a*x)^(1/4)*Hypergeometric2F1[5/4, 5/4, 9/4, (1 - a*x)/2]))/(5*(1 + a*x)^(1/4))","C",0
116,1,55,95,0.0180748,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[1/(E^((5*ArcTanh[a*x])/2)*x^2),x]","\frac{\sqrt[4]{1-a x} \left(10 a x \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)-9 a x-1\right)}{x \sqrt[4]{a x+1}}","-\frac{(1-a x)^{5/4}}{x \sqrt[4]{a x+1}}-\frac{10 a \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-5 a \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+5 a \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)",1,"((1 - a*x)^(1/4)*(-1 - 9*a*x + 10*a*x*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(x*(1 + a*x)^(1/4))","C",0
117,1,70,136,0.0248501,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[1/(E^((5*ArcTanh[a*x])/2)*x^3),x]","\frac{\sqrt[4]{1-a x} \left(-50 a^2 x^2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+43 a^2 x^2+9 a x-2\right)}{4 x^2 \sqrt[4]{a x+1}}","\frac{25 a^2 \sqrt[4]{1-a x}}{2 \sqrt[4]{a x+1}}+\frac{25}{4} a^2 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{25}{4} a^2 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{(1-a x)^{9/4}}{2 x^2 \sqrt[4]{a x+1}}+\frac{5 a (1-a x)^{5/4}}{4 x \sqrt[4]{a x+1}}",1,"((1 - a*x)^(1/4)*(-2 + 9*a*x + 43*a^2*x^2 - 50*a^2*x^2*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(4*x^2*(1 + a*x)^(1/4))","C",0
118,1,78,165,0.0256983,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[1/(E^((5*ArcTanh[a*x])/2)*x^4),x]","\frac{\sqrt[4]{1-a x} \left(330 a^3 x^3 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)-287 a^3 x^3-61 a^2 x^2+26 a x-8\right)}{24 x^3 \sqrt[4]{a x+1}}","-\frac{287 a^3 \sqrt[4]{1-a x}}{24 \sqrt[4]{a x+1}}-\frac{55}{8} a^3 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\frac{55}{8} a^3 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{61 a^2 \sqrt[4]{1-a x}}{24 x \sqrt[4]{a x+1}}-\frac{\sqrt[4]{1-a x}}{3 x^3 \sqrt[4]{a x+1}}+\frac{13 a \sqrt[4]{1-a x}}{12 x^2 \sqrt[4]{a x+1}}",1,"((1 - a*x)^(1/4)*(-8 + 26*a*x - 61*a^2*x^2 - 287*a^3*x^3 + 330*a^3*x^3*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(24*x^3*(1 + a*x)^(1/4))","C",0
119,1,86,194,0.0328731,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Integrate[1/(E^((5*ArcTanh[a*x])/2)*x^5),x]","\frac{\sqrt[4]{1-a x} \left(-2850 a^4 x^4 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};\frac{1-a x}{a x+1}\right)+2467 a^4 x^4+521 a^3 x^3-226 a^2 x^2+136 a x-48\right)}{192 x^4 \sqrt[4]{a x+1}}","\frac{2467 a^4 \sqrt[4]{1-a x}}{192 \sqrt[4]{a x+1}}+\frac{475}{64} a^4 \tan ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)-\frac{475}{64} a^4 \tanh ^{-1}\left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}\right)+\frac{521 a^3 \sqrt[4]{1-a x}}{192 x \sqrt[4]{a x+1}}-\frac{113 a^2 \sqrt[4]{1-a x}}{96 x^2 \sqrt[4]{a x+1}}-\frac{\sqrt[4]{1-a x}}{4 x^4 \sqrt[4]{a x+1}}+\frac{17 a \sqrt[4]{1-a x}}{24 x^3 \sqrt[4]{a x+1}}",1,"((1 - a*x)^(1/4)*(-48 + 136*a*x - 226*a^2*x^2 + 521*a^3*x^3 + 2467*a^4*x^4 - 2850*a^4*x^4*Hypergeometric2F1[1/4, 1, 5/4, (1 - a*x)/(1 + a*x)]))/(192*x^4*(1 + a*x)^(1/4))","C",0
120,0,0,28,0.4842636,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} x^m \, dx","Integrate[E^(ArcTanh[x]/3)*x^m,x]","\int e^{\frac{1}{3} \tanh ^{-1}(x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{1}{6},-\frac{1}{6};m+2;x,-x\right)}{m+1}",1,"Integrate[E^(ArcTanh[x]/3)*x^m, x]","F",-1
121,1,59,245,0.0279071,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} x^2 \, dx","Integrate[E^(ArcTanh[x]/3)*x^2,x]","-\frac{1}{90} (1-x)^{5/6} \left(38 \sqrt[6]{2} \, _2F_1\left(-\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{1-x}{2}\right)+5 \sqrt[6]{x+1} \left(6 x^2+7 x+1\right)\right)","-\frac{1}{3} (1-x)^{5/6} x (x+1)^{7/6}-\frac{1}{18} (1-x)^{5/6} (x+1)^{7/6}-\frac{19}{54} (1-x)^{5/6} \sqrt[6]{x+1}-\frac{19 \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}-\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{108 \sqrt{3}}+\frac{19 \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{108 \sqrt{3}}-\frac{19}{81} \tan ^{-1}\left(\frac{\sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)+\frac{19}{162} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)-\frac{19}{162} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+\sqrt{3}\right)",1,"-1/90*((1 - x)^(5/6)*(5*(1 + x)^(1/6)*(1 + 7*x + 6*x^2) + 38*2^(1/6)*Hypergeometric2F1[-1/6, 5/6, 11/6, (1 - x)/2]))","C",0
122,1,49,224,0.0152264,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} x \, dx","Integrate[E^(ArcTanh[x]/3)*x,x]","-\frac{1}{10} (1-x)^{5/6} \left(2 \sqrt[6]{2} \, _2F_1\left(-\frac{1}{6},\frac{5}{6};\frac{11}{6};\frac{1-x}{2}\right)+5 (x+1)^{7/6}\right)","-\frac{1}{2} (1-x)^{5/6} (x+1)^{7/6}-\frac{1}{6} (1-x)^{5/6} \sqrt[6]{x+1}-\frac{\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}-\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{12 \sqrt{3}}+\frac{\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{12 \sqrt{3}}-\frac{1}{9} \tan ^{-1}\left(\frac{\sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)+\frac{1}{18} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)-\frac{1}{18} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+\sqrt{3}\right)",1,"-1/10*((1 - x)^(5/6)*(5*(1 + x)^(7/6) + 2*2^(1/6)*Hypergeometric2F1[-1/6, 5/6, 11/6, (1 - x)/2]))","C",0
123,1,39,202,0.0466847,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} \, dx","Integrate[E^(ArcTanh[x]/3),x]","2 e^{\frac{1}{3} \tanh ^{-1}(x)} \left(\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};-e^{2 \tanh ^{-1}(x)}\right)-\frac{1}{e^{2 \tanh ^{-1}(x)}+1}\right)","-(1-x)^{5/6} \sqrt[6]{x+1}-\frac{\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}-\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{2 \sqrt{3}}+\frac{\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)}{2 \sqrt{3}}-\frac{2}{3} \tan ^{-1}\left(\frac{\sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)+\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)-\frac{1}{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+\sqrt{3}\right)",1,"2*E^(ArcTanh[x]/3)*(-(1 + E^(2*ArcTanh[x]))^(-1) + Hypergeometric2F1[1/6, 1, 7/6, -E^(2*ArcTanh[x])])","C",0
124,1,74,346,0.0262481,"\int \frac{e^{\frac{1}{3} \tanh ^{-1}(x)}}{x} \, dx","Integrate[E^(ArcTanh[x]/3)/x,x]","-\frac{3 (1-x)^{5/6} \left(\sqrt[6]{2} (x+1)^{5/6} \, _2F_1\left(\frac{5}{6},\frac{5}{6};\frac{11}{6};\frac{1-x}{2}\right)+2 \, _2F_1\left(\frac{5}{6},1;\frac{11}{6};\frac{1-x}{x+1}\right)\right)}{5 (x+1)^{5/6}}","-\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}-\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)+\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+\frac{\sqrt{3} \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+1\right)+\frac{1}{2} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}-\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1\right)-\frac{1}{2} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}+\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)+\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}\right)-\tan ^{-1}\left(\frac{2 \sqrt[6]{1-x}}{\sqrt[6]{x+1}}+\sqrt{3}\right)+\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{x+1}}{\sqrt[6]{1-x}}}{\sqrt{3}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1}{\sqrt{3}}\right)-2 \tanh ^{-1}\left(\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}\right)",1,"(-3*(1 - x)^(5/6)*(2^(1/6)*(1 + x)^(5/6)*Hypergeometric2F1[5/6, 5/6, 11/6, (1 - x)/2] + 2*Hypergeometric2F1[5/6, 1, 11/6, (1 - x)/(1 + x)]))/(5*(1 + x)^(5/6))","C",0
125,1,50,194,0.0123967,"\int \frac{e^{\frac{1}{3} \tanh ^{-1}(x)}}{x^2} \, dx","Integrate[E^(ArcTanh[x]/3)/x^2,x]","-\frac{(1-x)^{5/6} \left(2 x \, _2F_1\left(\frac{5}{6},1;\frac{11}{6};\frac{1-x}{x+1}\right)+5 x+5\right)}{5 x (x+1)^{5/6}}","-\frac{(1-x)^{5/6} \sqrt[6]{x+1}}{x}+\frac{1}{6} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}-\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1\right)-\frac{1}{6} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}+\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1\right)+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{x+1}}{\sqrt[6]{1-x}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{2}{3} \tanh ^{-1}\left(\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}\right)",1,"-1/5*((1 - x)^(5/6)*(5 + 5*x + 2*x*Hypergeometric2F1[5/6, 1, 11/6, (1 - x)/(1 + x)]))/(x*(1 + x)^(5/6))","C",0
126,1,60,224,0.0160371,"\int \frac{e^{\frac{1}{3} \tanh ^{-1}(x)}}{x^3} \, dx","Integrate[E^(ArcTanh[x]/3)/x^3,x]","-\frac{(1-x)^{5/6} \left(2 x^2 \, _2F_1\left(\frac{5}{6},1;\frac{11}{6};\frac{1-x}{x+1}\right)+5 \left(4 x^2+7 x+3\right)\right)}{30 x^2 (x+1)^{5/6}}","-\frac{(1-x)^{5/6} (x+1)^{7/6}}{2 x^2}-\frac{(1-x)^{5/6} \sqrt[6]{x+1}}{6 x}+\frac{1}{36} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}-\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1\right)-\frac{1}{36} \log \left(\frac{\sqrt[3]{x+1}}{\sqrt[3]{1-x}}+\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1\right)+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{x+1}}{\sqrt[6]{1-x}}}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{x+1}}{\sqrt[6]{1-x}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{1}{9} \tanh ^{-1}\left(\frac{\sqrt[6]{x+1}}{\sqrt[6]{1-x}}\right)",1,"-1/30*((1 - x)^(5/6)*(5*(3 + 7*x + 4*x^2) + 2*x^2*Hypergeometric2F1[5/6, 1, 11/6, (1 - x)/(1 + x)]))/(x^2*(1 + x)^(5/6))","C",0
127,0,0,28,0.4388449,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} x^m \, dx","Integrate[E^((2*ArcTanh[x])/3)*x^m,x]","\int e^{\frac{2}{3} \tanh ^{-1}(x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{1}{3},-\frac{1}{3};m+2;x,-x\right)}{m+1}",1,"Integrate[E^((2*ArcTanh[x])/3)*x^m, x]","F",-1
128,1,59,133,0.0275877,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} x^2 \, dx","Integrate[E^((2*ArcTanh[x])/3)*x^2,x]","-\frac{1}{18} (1-x)^{2/3} \left(11 \sqrt[3]{2} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{1-x}{2}\right)+2 \sqrt[3]{x+1} \left(3 x^2+4 x+1\right)\right)","-\frac{1}{3} (1-x)^{2/3} x (x+1)^{4/3}-\frac{1}{9} (1-x)^{2/3} (x+1)^{4/3}-\frac{11}{27} (1-x)^{2/3} \sqrt[3]{x+1}+\frac{11}{81} \log (x+1)+\frac{11}{27} \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+1\right)+\frac{22 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}\right)}{27 \sqrt{3}}",1,"-1/18*((1 - x)^(2/3)*(2*(1 + x)^(1/3)*(1 + 4*x + 3*x^2) + 11*2^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, (1 - x)/2]))","C",0
129,1,46,112,0.0141451,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} x \, dx","Integrate[E^((2*ArcTanh[x])/3)*x,x]","-\frac{1}{2} (1-x)^{2/3} \left(\sqrt[3]{2} \, _2F_1\left(-\frac{1}{3},\frac{2}{3};\frac{5}{3};\frac{1-x}{2}\right)+(x+1)^{4/3}\right)","-\frac{1}{2} (1-x)^{2/3} (x+1)^{4/3}-\frac{1}{3} (1-x)^{2/3} \sqrt[3]{x+1}+\frac{1}{9} \log (x+1)+\frac{1}{3} \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+1\right)+\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}\right)}{3 \sqrt{3}}",1,"-1/2*((1 - x)^(2/3)*((1 + x)^(4/3) + 2^(1/3)*Hypergeometric2F1[-1/3, 2/3, 5/3, (1 - x)/2]))","C",0
130,1,87,84,0.1473509,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} \, dx","Integrate[E^((2*ArcTanh[x])/3),x]","-\frac{2 e^{\frac{2}{3} \tanh ^{-1}(x)}}{e^{2 \tanh ^{-1}(x)}+1}+\frac{2}{3} \log \left(e^{\frac{2}{3} \tanh ^{-1}(x)}+1\right)-\frac{1}{3} \log \left(-e^{\frac{2}{3} \tanh ^{-1}(x)}+e^{\frac{4}{3} \tanh ^{-1}(x)}+1\right)+\frac{2 \tan ^{-1}\left(\frac{2 e^{\frac{2}{3} \tanh ^{-1}(x)}-1}{\sqrt{3}}\right)}{\sqrt{3}}","-(1-x)^{2/3} \sqrt[3]{x+1}+\frac{1}{3} \log (x+1)+\log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+1\right)+\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}\right)}{\sqrt{3}}",1,"(-2*E^((2*ArcTanh[x])/3))/(1 + E^(2*ArcTanh[x])) + (2*ArcTan[(-1 + 2*E^((2*ArcTanh[x])/3))/Sqrt[3]])/Sqrt[3] + (2*Log[1 + E^((2*ArcTanh[x])/3)])/3 - Log[1 - E^((2*ArcTanh[x])/3) + E^((4*ArcTanh[x])/3)]/3","A",0
131,1,74,135,0.0244923,"\int \frac{e^{\frac{2}{3} \tanh ^{-1}(x)}}{x} \, dx","Integrate[E^((2*ArcTanh[x])/3)/x,x]","-\frac{3 (1-x)^{2/3} \left(\sqrt[3]{2} (x+1)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{2}{3};\frac{5}{3};\frac{1-x}{2}\right)+2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1-x}{x+1}\right)\right)}{4 (x+1)^{2/3}}","-\frac{\log (x)}{2}+\frac{1}{2} \log (x+1)+\frac{3}{2} \log \left(\frac{\sqrt[3]{1-x}}{\sqrt[3]{x+1}}+1\right)+\frac{3}{2} \log \left(\sqrt[3]{1-x}-\sqrt[3]{x+1}\right)+\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)",1,"(-3*(1 - x)^(2/3)*(2^(1/3)*(1 + x)^(2/3)*Hypergeometric2F1[2/3, 2/3, 5/3, (1 - x)/2] + 2*Hypergeometric2F1[2/3, 1, 5/3, (1 - x)/(1 + x)]))/(4*(1 + x)^(2/3))","C",0
132,1,45,85,0.0124934,"\int \frac{e^{\frac{2}{3} \tanh ^{-1}(x)}}{x^2} \, dx","Integrate[E^((2*ArcTanh[x])/3)/x^2,x]","-\frac{(1-x)^{2/3} \left(x \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1-x}{x+1}\right)+x+1\right)}{x (x+1)^{2/3}}","-\frac{(1-x)^{2/3} \sqrt[3]{x+1}}{x}-\frac{\log (x)}{3}+\log \left(\sqrt[3]{1-x}-\sqrt[3]{x+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(((1 - x)^(2/3)*(1 + x + x*Hypergeometric2F1[2/3, 1, 5/3, (1 - x)/(1 + x)]))/(x*(1 + x)^(2/3)))","C",0
133,1,57,116,0.0149815,"\int \frac{e^{\frac{2}{3} \tanh ^{-1}(x)}}{x^3} \, dx","Integrate[E^((2*ArcTanh[x])/3)/x^3,x]","-\frac{(1-x)^{2/3} \left(2 x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{1-x}{x+1}\right)+5 x^2+8 x+3\right)}{6 x^2 (x+1)^{2/3}}","-\frac{(1-x)^{2/3} (x+1)^{4/3}}{2 x^2}-\frac{(1-x)^{2/3} \sqrt[3]{x+1}}{3 x}-\frac{\log (x)}{9}+\frac{1}{3} \log \left(\sqrt[3]{1-x}-\sqrt[3]{x+1}\right)+\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x}}{\sqrt{3} \sqrt[3]{x+1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-1/6*((1 - x)^(2/3)*(3 + 8*x + 5*x^2 + 2*x^2*Hypergeometric2F1[2/3, 1, 5/3, (1 - x)/(1 + x)]))/(x^2*(1 + x)^(2/3))","C",0
134,0,0,31,0.3844296,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^(ArcTanh[a*x]/4)*x^m,x]","\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{1}{8},-\frac{1}{8};m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^(ArcTanh[a*x]/4)*x^m, x]","F",-1
135,1,70,646,0.0405841,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^(ArcTanh[a*x]/4)*x^2,x]","-\frac{(1-a x)^{7/8} \left(7 \sqrt[8]{a x+1} \left(8 a^2 x^2+9 a x+1\right)+66 \sqrt[8]{2} \, _2F_1\left(-\frac{1}{8},\frac{7}{8};\frac{15}{8};\frac{1}{2} (1-a x)\right)\right)}{168 a^3}","-\frac{(1-a x)^{7/8} (a x+1)^{9/8}}{24 a^3}-\frac{11 (1-a x)^{7/8} \sqrt[8]{a x+1}}{32 a^3}-\frac{11 \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{256 a^3}+\frac{11 \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{256 a^3}-\frac{11 \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{256 a^3}+\frac{11 \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{256 a^3}+\frac{11 \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2+\sqrt{2}}}\right)}{128 a^3}+\frac{11 \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2-\sqrt{2}}}\right)}{128 a^3}-\frac{11 \sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{128 a^3}-\frac{11 \sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{128 a^3}-\frac{x (1-a x)^{7/8} (a x+1)^{9/8}}{3 a^2}",1,"-1/168*((1 - a*x)^(7/8)*(7*(1 + a*x)^(1/8)*(1 + 9*a*x + 8*a^2*x^2) + 66*2^(1/8)*Hypergeometric2F1[-1/8, 7/8, 15/8, (1 - a*x)/2]))/a^3","C",0
136,1,56,619,0.0235708,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x \, dx","Integrate[E^(ArcTanh[a*x]/4)*x,x]","-\frac{(1-a x)^{7/8} \left(2 \sqrt[8]{2} \, _2F_1\left(-\frac{1}{8},\frac{7}{8};\frac{15}{8};\frac{1}{2} (1-a x)\right)+7 (a x+1)^{9/8}\right)}{14 a^2}","-\frac{(1-a x)^{7/8} (a x+1)^{9/8}}{2 a^2}-\frac{(1-a x)^{7/8} \sqrt[8]{a x+1}}{8 a^2}-\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{64 a^2}+\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{64 a^2}-\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{64 a^2}+\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{64 a^2}+\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2+\sqrt{2}}}\right)}{32 a^2}+\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2-\sqrt{2}}}\right)}{32 a^2}-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{32 a^2}-\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{32 a^2}",1,"-1/14*((1 - a*x)^(7/8)*(7*(1 + a*x)^(9/8) + 2*2^(1/8)*Hypergeometric2F1[-1/8, 7/8, 15/8, (1 - a*x)/2]))/a^2","C",0
137,1,48,591,0.0534658,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} \, dx","Integrate[E^(ArcTanh[a*x]/4),x]","\frac{2 e^{\frac{1}{4} \tanh ^{-1}(a x)} \left(\, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-e^{2 \tanh ^{-1}(a x)}\right)-\frac{1}{e^{2 \tanh ^{-1}(a x)}+1}\right)}{a}","-\frac{(1-a x)^{7/8} \sqrt[8]{a x+1}}{a}-\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{8 a}+\frac{\sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{8 a}-\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{8 a}+\frac{\sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)}{8 a}+\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2+\sqrt{2}}}\right)}{4 a}+\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2-\sqrt{2}}}\right)}{4 a}-\frac{\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{4 a}-\frac{\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{4 a}",1,"(2*E^(ArcTanh[a*x]/4)*(-(1 + E^(2*ArcTanh[a*x]))^(-1) + Hypergeometric2F1[1/8, 1, 9/8, -E^(2*ArcTanh[a*x])]))/a","C",0
138,1,83,759,0.0327379,"\int \frac{e^{\frac{1}{4} \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^(ArcTanh[a*x]/4)/x,x]","-\frac{4 (1-a x)^{7/8} \left(\sqrt[8]{2} (a x+1)^{7/8} \, _2F_1\left(\frac{7}{8},\frac{7}{8};\frac{15}{8};\frac{1}{2} (1-a x)\right)+2 \, _2F_1\left(\frac{7}{8},1;\frac{15}{8};\frac{1-a x}{a x+1}\right)\right)}{7 (a x+1)^{7/8}}","-\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+1\right)+\frac{\log \left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}-\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}+\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{\sqrt{2}}-2 \tan ^{-1}\left(\frac{\sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)+\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2+\sqrt{2}}}\right)+\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}}{\sqrt{2-\sqrt{2}}}\right)-\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)-\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-a x}}{\sqrt[8]{a x+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)-2 \tanh ^{-1}\left(\frac{\sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)",1,"(-4*(1 - a*x)^(7/8)*(2^(1/8)*(1 + a*x)^(7/8)*Hypergeometric2F1[7/8, 7/8, 15/8, (1 - a*x)/2] + 2*Hypergeometric2F1[7/8, 1, 15/8, (1 - a*x)/(1 + a*x)]))/(7*(1 + a*x)^(7/8))","C",0
139,1,58,271,0.0164082,"\int \frac{e^{\frac{1}{4} \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^(ArcTanh[a*x]/4)/x^2,x]","-\frac{(1-a x)^{7/8} \left(2 a x \, _2F_1\left(\frac{7}{8},1;\frac{15}{8};\frac{1-a x}{a x+1}\right)+7 a x+7\right)}{7 x (a x+1)^{7/8}}","-\frac{(1-a x)^{7/8} \sqrt[8]{a x+1}}{x}+\frac{a \log \left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}-\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{4 \sqrt{2}}-\frac{a \log \left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}+\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{4 \sqrt{2}}-\frac{1}{2} a \tan ^{-1}\left(\frac{\sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)+\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)}{2 \sqrt{2}}-\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{2 \sqrt{2}}-\frac{1}{2} a \tanh ^{-1}\left(\frac{\sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)",1,"-1/7*((1 - a*x)^(7/8)*(7 + 7*a*x + 2*a*x*Hypergeometric2F1[7/8, 1, 15/8, (1 - a*x)/(1 + a*x)]))/(x*(1 + a*x)^(7/8))","C",0
140,1,73,312,0.0234032,"\int \frac{e^{\frac{1}{4} \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^(ArcTanh[a*x]/4)/x^3,x]","-\frac{(1-a x)^{7/8} \left(2 a^2 x^2 \, _2F_1\left(\frac{7}{8},1;\frac{15}{8};\frac{1-a x}{a x+1}\right)+7 \left(5 a^2 x^2+9 a x+4\right)\right)}{56 x^2 (a x+1)^{7/8}}","\frac{a^2 \log \left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}-\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{32 \sqrt{2}}-\frac{a^2 \log \left(\frac{\sqrt[4]{a x+1}}{\sqrt[4]{1-a x}}+\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{32 \sqrt{2}}-\frac{1}{16} a^2 \tan ^{-1}\left(\frac{\sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)+\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)}{16 \sqrt{2}}-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}+1\right)}{16 \sqrt{2}}-\frac{1}{16} a^2 \tanh ^{-1}\left(\frac{\sqrt[8]{a x+1}}{\sqrt[8]{1-a x}}\right)-\frac{(1-a x)^{7/8} (a x+1)^{9/8}}{2 x^2}-\frac{a (1-a x)^{7/8} \sqrt[8]{a x+1}}{8 x}",1,"-1/56*((1 - a*x)^(7/8)*(7*(4 + 9*a*x + 5*a^2*x^2) + 2*a^2*x^2*Hypergeometric2F1[7/8, 1, 15/8, (1 - a*x)/(1 + a*x)]))/(x^2*(1 + a*x)^(7/8))","C",0
141,1,47,45,0.0239344,"\int e^{4 \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^(4*ArcTanh[a*x])*x^m,x]","\frac{x^{m+1} (-4 (m+1) (a x-1) \, _2F_1(1,m+1;m+2;a x)+a x-4 m-5)}{(m+1) (a x-1)}","-4 x^{m+1} \, _2F_1(1,m+1;m+2;a x)+\frac{4 x^{m+1}}{1-a x}+\frac{x^{m+1}}{m+1}",1,"(x^(1 + m)*(-5 - 4*m + a*x - 4*(1 + m)*(-1 + a*x)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x]))/((1 + m)*(-1 + a*x))","A",1
142,1,92,151,0.0841178,"\int e^{3 \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^(3*ArcTanh[a*x])*x^m,x]","\frac{\sqrt{-a x-1} \sqrt{1-a x} x^{m+1} \left(F_1\left(m+1;-\frac{1}{2},\frac{1}{2};m+2;-a x,a x\right)-2 F_1\left(m+1;-\frac{1}{2},\frac{3}{2};m+2;-a x,a x\right)\right)}{(m+1) \sqrt{a x-1} \sqrt{a x+1}}","-\frac{3 x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{4 x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}-\frac{a x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}+\frac{4 a x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Sqrt[-1 - a*x]*Sqrt[1 - a*x]*(AppellF1[1 + m, -1/2, 1/2, 2 + m, -(a*x), a*x] - 2*AppellF1[1 + m, -1/2, 3/2, 2 + m, -(a*x), a*x]))/((1 + m)*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","C",0
143,1,26,36,0.0079221,"\int e^{2 \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m,x]","\frac{x^{m+1} (2 \, _2F_1(1,m+1;m+2;a x)-1)}{m+1}","\frac{2 x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{m+1}-\frac{x^{m+1}}{m+1}",1,"(x^(1 + m)*(-1 + 2*Hypergeometric2F1[1, 1 + m, 2 + m, a*x]))/(1 + m)","A",1
144,1,70,74,0.0320103,"\int e^{\tanh ^{-1}(a x)} x^m \, dx","Integrate[E^ArcTanh[a*x]*x^m,x]","-\frac{\sqrt{-a x-1} \sqrt{1-a x} x^{m+1} F_1\left(m+1;-\frac{1}{2},\frac{1}{2};m+2;-a x,a x\right)}{(m+1) \sqrt{a x-1} \sqrt{a x+1}}","\frac{x^{m+1} \, _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} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"-((x^(1 + m)*Sqrt[-1 - a*x]*Sqrt[1 - a*x]*AppellF1[1 + m, -1/2, 1/2, 2 + m, -(a*x), a*x])/((1 + m)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]))","C",0
145,1,31,75,0.0289457,"\int e^{-\tanh ^{-1}(a x)} x^m \, dx","Integrate[x^m/E^ArcTanh[a*x],x]","\frac{x^{m+1} F_1\left(m+1;-\frac{1}{2},\frac{1}{2};m+2;a x,-a x\right)}{m+1}","\frac{x^{m+1} \, _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} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*AppellF1[1 + m, -1/2, 1/2, 2 + m, a*x, -(a*x)])/(1 + m)","C",0
146,1,27,37,0.0083299,"\int e^{-2 \tanh ^{-1}(a x)} x^m \, dx","Integrate[x^m/E^(2*ArcTanh[a*x]),x]","\frac{x^{m+1} (2 \, _2F_1(1,m+1;m+2;-a x)-1)}{m+1}","\frac{2 x^{m+1} \, _2F_1(1,m+1;m+2;-a x)}{m+1}-\frac{x^{m+1}}{m+1}",1,"(x^(1 + m)*(-1 + 2*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)]))/(1 + m)","A",1
147,1,55,150,0.0587228,"\int e^{-3 \tanh ^{-1}(a x)} x^m \, dx","Integrate[x^m/E^(3*ArcTanh[a*x]),x]","-\frac{x^{m+1} \left(F_1\left(m+1;-\frac{1}{2},\frac{1}{2};m+2;a x,-a x\right)-2 F_1\left(m+1;-\frac{1}{2},\frac{3}{2};m+2;a x,-a x\right)\right)}{m+1}","-\frac{3 x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{4 x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}-\frac{4 a x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"-((x^(1 + m)*(AppellF1[1 + m, -1/2, 1/2, 2 + m, a*x, -(a*x)] - 2*AppellF1[1 + m, -1/2, 3/2, 2 + m, a*x, -(a*x)]))/(1 + m))","C",0
148,0,0,35,0.249567,"\int e^{n \tanh ^{-1}(a x)} x^m \, dx","Integrate[E^(n*ArcTanh[a*x])*x^m,x]","\int e^{n \tanh ^{-1}(a x)} x^m \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{n}{2},-\frac{n}{2};m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^(n*ArcTanh[a*x])*x^m, x]","F",-1
149,1,182,155,0.1913499,"\int e^{n \tanh ^{-1}(a x)} x^3 \, dx","Integrate[E^(n*ArcTanh[a*x])*x^3,x]","-\frac{(1-a x)^{1-\frac{n}{2}} \left((n-2) \left(a^2 x^2 (a x+1)^{\frac{n}{2}+1}-2^{\frac{n}{2}+1} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)-2^{\frac{n}{2}+3} n \, _2F_1\left(-\frac{n}{2}-2,1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)+2^{\frac{n}{2}+3} (n-1) \, _2F_1\left(-\frac{n}{2}-1,1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{4 a^4 (n-2)}","-\frac{2^{\frac{n}{2}-2} n \left(n^2+8\right) (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{3 a^4 (2-n)}-\frac{(a x+1)^{\frac{n+2}{2}} \left(2 a n x+n^2+6\right) (1-a x)^{1-\frac{n}{2}}}{24 a^4}-\frac{x^2 (a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{4 a^2}",1,"-1/4*((1 - a*x)^(1 - n/2)*(-(2^(3 + n/2)*n*Hypergeometric2F1[-2 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2]) + 2^(3 + n/2)*(-1 + n)*Hypergeometric2F1[-1 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2] + (-2 + n)*(a^2*x^2*(1 + a*x)^(1 + n/2) - 2^(1 + n/2)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a*x)/2])))/(a^4*(-2 + n))","A",0
150,1,96,141,0.0522846,"\int e^{n \tanh ^{-1}(a x)} x^2 \, dx","Integrate[E^(n*ArcTanh[a*x])*x^2,x]","-\frac{(1-a x)^{1-\frac{n}{2}} \left((n-2) (a x+1)^{\frac{n}{2}+1} (2 a x+n)-2^{\frac{n}{2}+1} \left(n^2+2\right) \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{6 a^3 (n-2)}","-\frac{2^{n/2} \left(n^2+2\right) (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{3 a^3 (2-n)}-\frac{n (a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{6 a^3}-\frac{x (a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{3 a^2}",1,"-1/6*((1 - a*x)^(1 - n/2)*((-2 + n)*(1 + a*x)^(1 + n/2)*(n + 2*a*x) - 2^(1 + n/2)*(2 + n^2)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a*x)/2]))/(a^3*(-2 + n))","A",1
151,1,86,99,0.0263324,"\int e^{n \tanh ^{-1}(a x)} x \, dx","Integrate[E^(n*ArcTanh[a*x])*x,x]","-\frac{(1-a x)^{1-\frac{n}{2}} \left((n-2) (a x+1)^{\frac{n}{2}+1}-2^{\frac{n}{2}+1} n \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{2 a^2 (n-2)}","-\frac{2^{n/2} n (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a^2 (2-n)}-\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{2 a^2}",1,"-1/2*((1 - a*x)^(1 - n/2)*((-2 + n)*(1 + a*x)^(1 + n/2) - 2^(1 + n/2)*n*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a*x)/2]))/(a^2*(-2 + n))","A",1
152,1,46,65,0.0321914,"\int e^{n \tanh ^{-1}(a x)} \, dx","Integrate[E^(n*ArcTanh[a*x]),x]","\frac{4 e^{(n+2) \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)}{a (n+2)}","-\frac{2^{\frac{n}{2}+1} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (2-n)}",1,"(4*E^((2 + n)*ArcTanh[a*x])*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])])/(a*(2 + n))","A",0
153,1,95,111,0.0226325,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x} \, dx","Integrate[E^(n*ArcTanh[a*x])/x,x]","\frac{2 (1-a x)^{-n/2} \left((a x+1)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{1-a x}{a x+1}\right)-2^{n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{n}","\frac{2 (1-a x)^{-n/2} (a x+1)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{n}-\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{n}",1,"(2*((1 + a*x)^(n/2)*Hypergeometric2F1[1, -1/2*n, 1 - n/2, (1 - a*x)/(1 + a*x)] - 2^(n/2)*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a*x)/2]))/(n*(1 - a*x)^(n/2))","A",1
154,1,65,67,0.0166609,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/x^2,x]","\frac{4 a (1-a x)^{1-\frac{n}{2}} (a x+1)^{\frac{n}{2}-1} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{n-2}","-\frac{4 a (1-a x)^{1-\frac{n}{2}} (a x+1)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{2-n}",1,"(4*a*(1 - a*x)^(1 - n/2)*(1 + a*x)^(-1 + n/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(-2 + n)","A",1
155,1,91,105,0.0316699,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3} \, dx","Integrate[E^(n*ArcTanh[a*x])/x^3,x]","\frac{(1-a x)^{1-\frac{n}{2}} (a x+1)^{\frac{n}{2}-1} \left(4 a^2 n x^2 \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-2) (a x+1)^2\right)}{2 (n-2) x^2}","-\frac{2 a^2 n (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{2-n}-\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{2 x^2}",1,"((1 - a*x)^(1 - n/2)*(1 + a*x)^(-1 + n/2)*(-((-2 + n)*(1 + a*x)^2) + 4*a^2*n*x^2*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)]))/(2*(-2 + n)*x^2)","A",1
156,1,101,147,0.0573002,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^4} \, dx","Integrate[E^(n*ArcTanh[a*x])/x^4,x]","\frac{(1-a x)^{1-\frac{n}{2}} (a x+1)^{\frac{n}{2}-1} \left(4 a^3 \left(n^2+2\right) x^3 \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-2) (a x+1)^2 (a n x+2)\right)}{6 (n-2) x^3}","-\frac{2 a^3 \left(n^2+2\right) (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{3 (2-n)}-\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{3 x^3}-\frac{a n (a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{6 x^2}",1,"((1 - a*x)^(1 - n/2)*(1 + a*x)^(-1 + n/2)*(-((-2 + n)*(1 + a*x)^2*(2 + a*n*x)) + 4*a^3*(2 + n^2)*x^3*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)]))/(6*(-2 + n)*x^3)","A",1
157,1,53,65,0.0302762,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^p,x]","-\frac{2 \sqrt{2-2 a x} (c-a c x)^p \, _2F_1\left(-\frac{1}{2},p+\frac{1}{2};p+\frac{3}{2};\frac{1}{2}-\frac{a x}{2}\right)}{2 a p+a}","-\frac{2 \sqrt{2} (c-a c x)^{p+1} \, _2F_1\left(-\frac{1}{2},p+\frac{1}{2};p+\frac{3}{2};\frac{1}{2} (1-a x)\right)}{a c (2 p+1) \sqrt{1-a x}}",1,"(-2*Sqrt[2 - 2*a*x]*(c - a*c*x)^p*Hypergeometric2F1[-1/2, 1/2 + p, 3/2 + p, 1/2 - (a*x)/2])/(a + 2*a*p)","A",1
158,1,75,123,0.1064959,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^4,x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(24 a^4 x^4-90 a^3 x^3+112 a^2 x^2-15 a x-136\right)+210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{120 a}","\frac{c^4 (1-a x)^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}+\frac{7 c^4 (1-a x) \left(1-a^2 x^2\right)^{3/2}}{20 a}+\frac{7 c^4 \left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{7}{8} c^4 x \sqrt{1-a^2 x^2}+\frac{7 c^4 \sin ^{-1}(a x)}{8 a}",1,"-1/120*(c^4*(Sqrt[1 - a^2*x^2]*(-136 - 15*a*x + 112*a^2*x^2 - 90*a^3*x^3 + 24*a^4*x^4) + 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
159,1,67,91,0.0936789,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^3,x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(6 a^3 x^3-16 a^2 x^2+9 a x+16\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{24 a}","\frac{c^3 (1-a x) \left(1-a^2 x^2\right)^{3/2}}{4 a}+\frac{5 c^3 \left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{5}{8} c^3 x \sqrt{1-a^2 x^2}+\frac{5 c^3 \sin ^{-1}(a x)}{8 a}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(16 + 9*a*x - 16*a^2*x^2 + 6*a^3*x^3) - 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(24*a)","A",0
160,1,59,61,0.0822168,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^2,x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(2 a^2 x^2-3 a x-2\right)+6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a}+\frac{1}{2} c^2 x \sqrt{1-a^2 x^2}+\frac{c^2 \sin ^{-1}(a x)}{2 a}",1,"-1/6*(c^2*(Sqrt[1 - a^2*x^2]*(-2 - 3*a*x + 2*a^2*x^2) + 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
161,1,30,33,0.0121366,"\int e^{\tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x),x]","\frac{c \left(a x \sqrt{1-a^2 x^2}+\sin ^{-1}(a x)\right)}{2 a}","\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}",1,"(c*(a*x*Sqrt[1 - a^2*x^2] + ArcSin[a*x]))/(2*a)","A",1
162,1,46,43,0.0238271,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x),x]","\frac{2 \left(\frac{\sqrt{a x+1}}{\sqrt{1-a x}}+\sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{a c}","\frac{2 \sqrt{1-a^2 x^2}}{a c (1-a x)}-\frac{\sin ^{-1}(a x)}{a c}",1,"(2*(Sqrt[1 + a*x]/Sqrt[1 - a*x] + ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*c)","A",0
163,1,29,32,0.0106752,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^2,x]","\frac{(a x+1)^{3/2}}{3 a c^2 (1-a x)^{3/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}",1,"(1 + a*x)^(3/2)/(3*a*c^2*(1 - a*x)^(3/2))","A",0
164,1,35,65,0.0188603,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^3,x]","\frac{(4-a x) (a x+1)^{3/2}}{15 a c^3 (1-a x)^{5/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{15 a c^3 (1-a x)^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a c^3 (1-a x)^4}",1,"((4 - a*x)*(1 + a*x)^(3/2))/(15*a*c^3*(1 - a*x)^(5/2))","A",0
165,1,43,97,0.0234368,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^4,x]","-\frac{(a x+1)^{3/2} \left(-2 a^2 x^2+10 a x-23\right)}{105 a c^4 (1-a x)^{7/2}}","\frac{2 \left(1-a^2 x^2\right)^{3/2}}{105 a c^4 (1-a x)^3}+\frac{2 \left(1-a^2 x^2\right)^{3/2}}{35 a c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a c^4 (1-a x)^5}",1,"-1/105*((1 + a*x)^(3/2)*(-23 + 10*a*x - 2*a^2*x^2))/(a*c^4*(1 - a*x)^(7/2))","A",0
166,1,51,129,0.0277851,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^5,x]","\frac{(a x+1)^{3/2} \left(-2 a^3 x^3+12 a^2 x^2-33 a x+58\right)}{315 a c^5 (1-a x)^{9/2}}","\frac{2 \left(1-a^2 x^2\right)^{3/2}}{315 a c^5 (1-a x)^3}+\frac{2 \left(1-a^2 x^2\right)^{3/2}}{105 a c^5 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{21 a c^5 (1-a x)^5}+\frac{\left(1-a^2 x^2\right)^{3/2}}{9 a c^5 (1-a x)^6}",1,"((1 + a*x)^(3/2)*(58 - 33*a*x + 12*a^2*x^2 - 2*a^3*x^3))/(315*a*c^5*(1 - a*x)^(9/2))","A",0
167,1,29,41,0.0251019,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^p,x]","-\frac{(a p x+p+2) (c-a c x)^p}{a p (p+1)}","\frac{(c-a c x)^{p+1}}{a c (p+1)}-\frac{2 (c-a c x)^p}{a p}",1,"-(((c - a*c*x)^p*(2 + p + a*p*x))/(a*p*(1 + p)))","A",1
168,1,23,37,0.0195648,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^5 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^5,x]","\frac{c^5 (a x-1)^5 (5 a x+7)}{30 a}","\frac{c^5 (1-a x)^6}{6 a}-\frac{2 c^5 (1-a x)^5}{5 a}",1,"(c^5*(-1 + a*x)^5*(7 + 5*a*x))/(30*a)","A",1
169,1,32,37,0.0159432,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^4,x]","c^4 \left(-\frac{1}{5} a^4 x^5+\frac{a^3 x^4}{2}-a x^2+x\right)","\frac{c^4 (1-a x)^5}{5 a}-\frac{c^4 (1-a x)^4}{2 a}",1,"c^4*(x - a*x^2 + (a^3*x^4)/2 - (a^4*x^5)/5)","A",1
170,1,30,37,0.0143806,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^3,x]","\frac{1}{12} c^3 x \left(3 a^3 x^3-4 a^2 x^2-6 a x+12\right)","\frac{c^3 (1-a x)^4}{4 a}-\frac{2 c^3 (1-a x)^3}{3 a}",1,"(c^3*x*(12 - 6*a*x - 4*a^2*x^2 + 3*a^3*x^3))/12","A",1
171,1,16,19,0.007594,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^2,x]","c^2 \left(x-\frac{a^2 x^3}{3}\right)","c^2 x-\frac{1}{3} a^2 c^2 x^3",1,"c^2*(x - (a^2*x^3)/3)","A",1
172,1,26,13,0.0082751,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x),x]","\frac{c \left(1-a^2 x^2\right) e^{2 \tanh ^{-1}(a x)}}{2 a}","\frac{1}{2} a c x^2+c x",1,"(c*E^(2*ArcTanh[a*x])*(1 - a^2*x^2))/(2*a)","C",1
173,1,25,31,0.0183763,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x),x]","\frac{\frac{2}{1-a x}+\log (1-a x)}{a c}","\frac{2}{a c (1-a x)}+\frac{\log (1-a x)}{a c}",1,"(2/(1 - a*x) + Log[1 - a*x])/(a*c)","A",1
174,1,25,13,0.0077712,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x)^2,x]","\frac{(a x+1)^2}{4 a c^2 (1-a x)^2}","\frac{x}{c^2 (1-a x)^2}",1,"(1 + a*x)^2/(4*a*c^2*(1 - a*x)^2)","A",1
175,1,23,37,0.0147144,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x)^3,x]","-\frac{3 a x+1}{6 a c^3 (a x-1)^3}","\frac{2}{3 a c^3 (1-a x)^3}-\frac{1}{2 a c^3 (1-a x)^2}",1,"-1/6*(1 + 3*a*x)/(a*c^3*(-1 + a*x)^3)","A",1
176,1,23,37,0.0139245,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x)^4,x]","\frac{2 a x+1}{6 a c^4 (a x-1)^4}","\frac{1}{2 a c^4 (1-a x)^4}-\frac{1}{3 a c^4 (1-a x)^3}",1,"(1 + 2*a*x)/(6*a*c^4*(-1 + a*x)^4)","A",1
177,1,58,65,0.0254035,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^p,x]","\frac{4 \sqrt{2} (c-a c x)^p \, _2F_1\left(-\frac{3}{2},p-\frac{1}{2};p+\frac{1}{2};\frac{1}{2}-\frac{a x}{2}\right)}{(a-2 a p) \sqrt{1-a x}}","\frac{4 \sqrt{2} (c-a c x)^{p+1} \, _2F_1\left(-\frac{3}{2},p-\frac{1}{2};p+\frac{1}{2};\frac{1}{2} (1-a x)\right)}{a c (1-2 p) (1-a x)^{3/2}}",1,"(4*Sqrt[2]*(c - a*c*x)^p*Hypergeometric2F1[-3/2, -1/2 + p, 1/2 + p, 1/2 - (a*x)/2])/((a - 2*a*p)*Sqrt[1 - a*x])","A",1
178,1,75,83,0.1029255,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^4,x]","\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(8 a^4 x^4-10 a^3 x^3-16 a^2 x^2+25 a x+8\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{40 a}","\frac{c^4 \left(1-a^2 x^2\right)^{5/2}}{5 a}+\frac{1}{4} c^4 x \left(1-a^2 x^2\right)^{3/2}+\frac{3}{8} c^4 x \sqrt{1-a^2 x^2}+\frac{3 c^4 \sin ^{-1}(a x)}{8 a}",1,"(c^4*(Sqrt[1 - a^2*x^2]*(8 + 25*a*x - 16*a^2*x^2 - 10*a^3*x^3 + 8*a^4*x^4) - 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(40*a)","A",0
179,1,44,59,0.0396957,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^3,x]","\frac{c^3 \left(a x \sqrt{1-a^2 x^2} \left(5-2 a^2 x^2\right)+3 \sin ^{-1}(a x)\right)}{8 a}","\frac{1}{4} c^3 x \left(1-a^2 x^2\right)^{3/2}+\frac{3}{8} c^3 x \sqrt{1-a^2 x^2}+\frac{3 c^3 \sin ^{-1}(a x)}{8 a}",1,"(c^3*(a*x*(5 - 2*a^2*x^2)*Sqrt[1 - a^2*x^2] + 3*ArcSin[a*x]))/(8*a)","A",1
180,1,59,61,0.0805097,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^2,x]","\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(2 a^2 x^2+3 a x-2\right)-6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a}+\frac{1}{2} c^2 x \sqrt{1-a^2 x^2}+\frac{c^2 \sin ^{-1}(a x)}{2 a}",1,"(c^2*(Sqrt[1 - a^2*x^2]*(-2 + 3*a*x + 2*a^2*x^2) - 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(6*a)","A",0
181,1,48,65,0.0368217,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x),x]","-\frac{c \left(\sqrt{1-a^2 x^2} (a x+4)+6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{2 a}","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{2 a (1-a x)}-\frac{3 c \sqrt{1-a^2 x^2}}{2 a}+\frac{3 c \sin ^{-1}(a x)}{2 a}",1,"-1/2*(c*((4 + a*x)*Sqrt[1 - a^2*x^2] + 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
182,1,45,74,0.0127889,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x),x]","\frac{4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1}{2} (1-a x)\right)}{3 a c (1-a x)^{3/2}}","\frac{2 \left(1-a^2 x^2\right)^{3/2}}{3 a c (1-a x)^3}-\frac{2 \sqrt{1-a^2 x^2}}{a c (1-a x)}+\frac{\sin ^{-1}(a x)}{a c}",1,"(4*Sqrt[2]*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - a*x)/2])/(3*a*c*(1 - a*x)^(3/2))","C",0
183,1,29,32,0.01086,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^2,x]","\frac{(a x+1)^{5/2}}{5 a c^2 (1-a x)^{5/2}}","\frac{\left(1-a^2 x^2\right)^{5/2}}{5 a c^2 (1-a x)^5}",1,"(1 + a*x)^(5/2)/(5*a*c^2*(1 - a*x)^(5/2))","A",0
184,1,34,65,0.0199873,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^3,x]","-\frac{(a x-6) (a x+1)^{5/2}}{35 a c^3 (1-a x)^{7/2}}","\frac{\left(1-a^2 x^2\right)^{5/2}}{35 a c^3 (1-a x)^5}+\frac{\left(1-a^2 x^2\right)^{5/2}}{7 a c^3 (1-a x)^6}",1,"-1/35*((-6 + a*x)*(1 + a*x)^(5/2))/(a*c^3*(1 - a*x)^(7/2))","A",0
185,1,43,97,0.0244828,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^4,x]","\frac{(a x+1)^{5/2} \left(2 a^2 x^2-14 a x+47\right)}{315 a c^4 (1-a x)^{9/2}}","\frac{2 \left(1-a^2 x^2\right)^{5/2}}{315 a c^4 (1-a x)^5}+\frac{2 \left(1-a^2 x^2\right)^{5/2}}{63 a c^4 (1-a x)^6}+\frac{\left(1-a^2 x^2\right)^{5/2}}{9 a c^4 (1-a x)^7}",1,"((1 + a*x)^(5/2)*(47 - 14*a*x + 2*a^2*x^2))/(315*a*c^4*(1 - a*x)^(9/2))","A",0
186,1,51,129,0.0286714,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^5,x]","-\frac{(a x+1)^{5/2} \left(2 a^3 x^3-16 a^2 x^2+61 a x-152\right)}{1155 a c^5 (1-a x)^{11/2}}","\frac{2 \left(1-a^2 x^2\right)^{5/2}}{1155 a c^5 (1-a x)^5}+\frac{2 \left(1-a^2 x^2\right)^{5/2}}{231 a c^5 (1-a x)^6}+\frac{\left(1-a^2 x^2\right)^{5/2}}{33 a c^5 (1-a x)^7}+\frac{\left(1-a^2 x^2\right)^{5/2}}{11 a c^5 (1-a x)^8}",1,"-1/1155*((1 + a*x)^(5/2)*(-152 + 61*a*x - 16*a^2*x^2 + 2*a^3*x^3))/(a*c^5*(1 - a*x)^(11/2))","A",0
187,1,50,66,0.0926443,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a*c*x)^p,x]","\frac{\left(\frac{a x}{p+1}+\frac{4}{(p-1) (a x-1)}+\frac{3 p+4}{p (p+1)}\right) (c-a c x)^p}{a}","\frac{4 c (c-a c x)^{p-1}}{a (1-p)}+\frac{4 (c-a c x)^p}{a p}-\frac{(c-a c x)^{p+1}}{a c (p+1)}",1,"((c - a*c*x)^p*((4 + 3*p)/(p*(1 + p)) + (a*x)/(1 + p) + 4/((-1 + p)*(-1 + a*x))))/a","A",1
188,1,31,53,0.0206549,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^5 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a*c*x)^5,x]","-\frac{c^5 (a x-1)^4 \left(5 a^2 x^2+14 a x+11\right)}{30 a}","-\frac{c^5 (1-a x)^6}{6 a}+\frac{4 c^5 (1-a x)^5}{5 a}-\frac{c^5 (1-a x)^4}{a}",1,"-1/30*(c^5*(-1 + a*x)^4*(11 + 14*a*x + 5*a^2*x^2))/a","A",1
189,1,26,32,0.0151934,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a*c*x)^4,x]","c^4 \left(\frac{a^4 x^5}{5}-\frac{2 a^2 x^3}{3}+x\right)","\frac{1}{5} a^4 c^4 x^5-\frac{2}{3} a^2 c^4 x^3+c^4 x",1,"c^4*(x - (2*a^2*x^3)/3 + (a^4*x^5)/5)","A",1
190,1,30,35,0.0150068,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a*c*x)^3,x]","-\frac{1}{12} c^3 x \left(3 a^3 x^3+4 a^2 x^2-6 a x-12\right)","\frac{2 c^3 (a x+1)^3}{3 a}-\frac{c^3 (a x+1)^4}{4 a}",1,"-1/12*(c^3*x*(-12 - 6*a*x + 4*a^2*x^2 + 3*a^3*x^3))","A",1
191,1,21,17,0.0120356,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a*c*x)^2,x]","c^2 \left(\frac{a^2 x^3}{3}+a x^2+x\right)","\frac{c^2 (a x+1)^3}{3 a}",1,"c^2*(x + a*x^2 + (a^2*x^3)/3)","A",1
192,1,26,27,0.0111084,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a*c*x),x]","c \left(-\frac{a x^2}{2}-\frac{4 \log (1-a x)}{a}-3 x\right)","-\frac{1}{2} a c x^2-\frac{4 c \log (1-a x)}{a}-3 c x",1,"c*(-3*x - (a*x^2)/2 - (4*Log[1 - a*x])/a)","A",1
193,1,36,48,0.0197682,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a*c*x),x]","\frac{4 a x+(a x-1)^2 (-\log (1-a x))-2}{a c (a x-1)^2}","-\frac{4}{a c (1-a x)}+\frac{2}{a c (1-a x)^2}-\frac{\log (1-a x)}{a c}",1,"(-2 + 4*a*x - (-1 + a*x)^2*Log[1 - a*x])/(a*c*(-1 + a*x)^2)","A",1
194,1,25,25,0.0084325,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a*c*x)^2,x]","\frac{(a x+1)^3}{6 a c^2 (1-a x)^3}","\frac{(a x+1)^3}{6 a c^2 (1-a x)^3}",1,"(1 + a*x)^3/(6*a*c^2*(1 - a*x)^3)","A",1
195,1,31,52,0.018053,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a*c*x)^3,x]","\frac{3 a^2 x^2+2 a x+1}{6 a c^3 (a x-1)^4}","\frac{1}{2 a c^3 (1-a x)^2}-\frac{4}{3 a c^3 (1-a x)^3}+\frac{1}{a c^3 (1-a x)^4}",1,"(1 + 2*a*x + 3*a^2*x^2)/(6*a*c^3*(-1 + a*x)^4)","A",1
196,1,31,53,0.0184541,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a*c*x)^4,x]","-\frac{5 a^2 x^2+5 a x+2}{15 a c^4 (a x-1)^5}","\frac{1}{3 a c^4 (1-a x)^3}-\frac{1}{a c^4 (1-a x)^4}+\frac{4}{5 a c^4 (1-a x)^5}",1,"-1/15*(2 + 5*a*x + 5*a^2*x^2)/(a*c^4*(-1 + a*x)^5)","A",1
197,1,59,65,0.0235649,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[(c - a*c*x)^p/E^ArcTanh[a*x],x]","\frac{\sqrt{2-2 a x} (a x-1) (c-a c x)^p \, _2F_1\left(\frac{1}{2},p+\frac{3}{2};p+\frac{5}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (2 p+3)}","-\frac{\sqrt{2} \sqrt{1-a x} (c-a c x)^{p+1} \, _2F_1\left(\frac{1}{2},p+\frac{3}{2};p+\frac{5}{2};\frac{1}{2} (1-a x)\right)}{a c (2 p+3)}",1,"(Sqrt[2 - 2*a*x]*(-1 + a*x)*(c - a*c*x)^p*Hypergeometric2F1[1/2, 3/2 + p, 5/2 + p, 1/2 - (a*x)/2])/(a*(3 + 2*p))","A",1
198,1,80,133,0.0724587,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[(c - a*c*x)^3/E^ArcTanh[a*x],x]","\frac{c^3 \left(\frac{\sqrt{a x+1} \left(6 a^4 x^4-38 a^3 x^3+113 a^2 x^2-241 a x+160\right)}{\sqrt{1-a x}}-210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{24 a}","\frac{c^3 (1-a x)^3 \sqrt{1-a^2 x^2}}{4 a}+\frac{7 c^3 (1-a x)^2 \sqrt{1-a^2 x^2}}{12 a}+\frac{35 c^3 (1-a x) \sqrt{1-a^2 x^2}}{24 a}+\frac{35 c^3 \sqrt{1-a^2 x^2}}{8 a}+\frac{35 c^3 \sin ^{-1}(a x)}{8 a}",1,"(c^3*((Sqrt[1 + a*x]*(160 - 241*a*x + 113*a^2*x^2 - 38*a^3*x^3 + 6*a^4*x^4))/Sqrt[1 - a*x] - 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(24*a)","A",0
199,1,72,101,0.0841379,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[(c - a*c*x)^2/E^ArcTanh[a*x],x]","\frac{c^2 \left(\frac{\sqrt{a x+1} \left(-2 a^3 x^3+11 a^2 x^2-31 a x+22\right)}{\sqrt{1-a x}}-30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","\frac{c^2 (1-a x)^2 \sqrt{1-a^2 x^2}}{3 a}+\frac{5 c^2 (1-a x) \sqrt{1-a^2 x^2}}{6 a}+\frac{5 c^2 \sqrt{1-a^2 x^2}}{2 a}+\frac{5 c^2 \sin ^{-1}(a x)}{2 a}",1,"(c^2*((Sqrt[1 + a*x]*(22 - 31*a*x + 11*a^2*x^2 - 2*a^3*x^3))/Sqrt[1 - a*x] - 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(6*a)","A",0
200,1,61,63,0.0528094,"\int e^{-\tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[(c - a*c*x)/E^ArcTanh[a*x],x]","\frac{c \left(\frac{\sqrt{a x+1} \left(a^2 x^2-5 a x+4\right)}{\sqrt{1-a x}}-6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{2 a}","\frac{c (1-a x) \sqrt{1-a^2 x^2}}{2 a}+\frac{3 c \sqrt{1-a^2 x^2}}{2 a}+\frac{3 c \sin ^{-1}(a x)}{2 a}",1,"(c*((Sqrt[1 + a*x]*(4 - 5*a*x + a^2*x^2))/Sqrt[1 - a*x] - 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(2*a)","A",0
201,1,11,11,0.0079198,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)),x]","\frac{\sin ^{-1}(a x)}{a c}","\frac{\sin ^{-1}(a x)}{a c}",1,"ArcSin[a*x]/(a*c)","A",1
202,1,26,29,0.009666,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^2),x]","\frac{\sqrt{a x+1}}{a c^2 \sqrt{1-a x}}","\frac{\sqrt{1-a^2 x^2}}{a c^2 (1-a x)}",1,"Sqrt[1 + a*x]/(a*c^2*Sqrt[1 - a*x])","A",0
203,1,34,65,0.0178784,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^3),x]","-\frac{(a x-2) \sqrt{a x+1}}{3 a c^3 (1-a x)^{3/2}}","\frac{\sqrt{1-a^2 x^2}}{3 a c^3 (1-a x)}+\frac{\sqrt{1-a^2 x^2}}{3 a c^3 (1-a x)^2}",1,"-1/3*((-2 + a*x)*Sqrt[1 + a*x])/(a*c^3*(1 - a*x)^(3/2))","A",0
204,1,43,97,0.0220562,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^4),x]","\frac{\sqrt{a x+1} \left(2 a^2 x^2-6 a x+7\right)}{15 a c^4 (1-a x)^{5/2}}","\frac{2 \sqrt{1-a^2 x^2}}{15 a c^4 (1-a x)}+\frac{2 \sqrt{1-a^2 x^2}}{15 a c^4 (1-a x)^2}+\frac{\sqrt{1-a^2 x^2}}{5 a c^4 (1-a x)^3}",1,"(Sqrt[1 + a*x]*(7 - 6*a*x + 2*a^2*x^2))/(15*a*c^4*(1 - a*x)^(5/2))","A",0
205,1,51,129,0.0253398,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^5),x]","-\frac{\sqrt{a x+1} \left(2 a^3 x^3-8 a^2 x^2+13 a x-12\right)}{35 a c^5 (1-a x)^{7/2}}","\frac{2 \sqrt{1-a^2 x^2}}{35 a c^5 (1-a x)}+\frac{2 \sqrt{1-a^2 x^2}}{35 a c^5 (1-a x)^2}+\frac{3 \sqrt{1-a^2 x^2}}{35 a c^5 (1-a x)^3}+\frac{\sqrt{1-a^2 x^2}}{7 a c^5 (1-a x)^4}",1,"-1/35*(Sqrt[1 + a*x]*(-12 + 13*a*x - 8*a^2*x^2 + 2*a^3*x^3))/(a*c^5*(1 - a*x)^(7/2))","A",0
206,1,43,44,0.0164316,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[(c - a*c*x)^p/E^(2*ArcTanh[a*x]),x]","\frac{(a x-1) (c-a c x)^p \left(\, _2F_1\left(1,p+1;p+2;\frac{1}{2} (1-a x)\right)-1\right)}{a (p+1)}","-\frac{(c-a c x)^{p+2} \, _2F_1\left(1,p+2;p+3;\frac{1}{2} (1-a x)\right)}{2 a c^2 (p+2)}",1,"((-1 + a*x)*(c - a*c*x)^p*(-1 + Hypergeometric2F1[1, 1 + p, 2 + p, (1 - a*x)/2]))/(a*(1 + p))","A",0
207,1,56,91,0.0197953,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Integrate[(c - a*c*x)^4/E^(2*ArcTanh[a*x]),x]","-\frac{c^4 \left(6 a^5 x^5-45 a^4 x^4+160 a^3 x^3-390 a^2 x^2+930 a x-960 \log (a x+1)-181\right)}{30 a}","\frac{c^4 (1-a x)^5}{5 a}+\frac{c^4 (1-a x)^4}{2 a}+\frac{4 c^4 (1-a x)^3}{3 a}+\frac{4 c^4 (1-a x)^2}{a}+\frac{32 c^4 \log (a x+1)}{a}-16 c^4 x",1,"-1/30*(c^4*(-181 + 930*a*x - 390*a^2*x^2 + 160*a^3*x^3 - 45*a^4*x^4 + 6*a^5*x^5 - 960*Log[1 + a*x]))/a","A",1
208,1,48,73,0.0174407,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[(c - a*c*x)^3/E^(2*ArcTanh[a*x]),x]","\frac{c^3 \left(3 a^4 x^4-20 a^3 x^3+66 a^2 x^2-180 a x+192 \log (a x+1)+35\right)}{12 a}","\frac{c^3 (1-a x)^4}{4 a}+\frac{2 c^3 (1-a x)^3}{3 a}+\frac{2 c^3 (1-a x)^2}{a}+\frac{16 c^3 \log (a x+1)}{a}-8 c^3 x",1,"(c^3*(35 - 180*a*x + 66*a^2*x^2 - 20*a^3*x^3 + 3*a^4*x^4 + 192*Log[1 + a*x]))/(12*a)","A",1
209,1,39,54,0.0137513,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[(c - a*c*x)^2/E^(2*ArcTanh[a*x]),x]","-\frac{c^2 \left(a^3 x^3-6 a^2 x^2+21 a x-24 \log (a x+1)-4\right)}{3 a}","\frac{c^2 (1-a x)^3}{3 a}+\frac{c^2 (1-a x)^2}{a}+\frac{8 c^2 \log (a x+1)}{a}-4 c^2 x",1,"-1/3*(c^2*(-4 + 21*a*x - 6*a^2*x^2 + a^3*x^3 - 24*Log[1 + a*x]))/a","A",1
210,1,25,26,0.013504,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[(c - a*c*x)/E^(2*ArcTanh[a*x]),x]","c \left(\frac{a x^2}{2}+\frac{4 \log (a x+1)}{a}-3 x\right)","\frac{1}{2} a c x^2+\frac{4 c \log (a x+1)}{a}-3 c x",1,"c*(-3*x + (a*x^2)/2 + (4*Log[1 + a*x])/a)","A",1
211,1,13,13,0.0063994,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)),x]","\frac{\log (a x+1)}{a c}","\frac{\log (a x+1)}{a c}",1,"Log[1 + a*x]/(a*c)","A",1
212,1,11,11,0.007817,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^2),x]","\frac{\tanh ^{-1}(a x)}{a c^2}","\frac{\tanh ^{-1}(a x)}{a c^2}",1,"ArcTanh[a*x]/(a*c^2)","A",1
213,1,31,33,0.0186997,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^3),x]","\frac{\frac{1}{2 a (1-a x)}+\frac{\tanh ^{-1}(a x)}{2 a}}{c^3}","\frac{1}{2 a c^3 (1-a x)}+\frac{\tanh ^{-1}(a x)}{2 a c^3}",1,"(1/(2*a*(1 - a*x)) + ArcTanh[a*x]/(2*a))/c^3","A",1
214,1,35,51,0.0241535,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^4),x]","\frac{-a x+(a x-1)^2 \tanh ^{-1}(a x)+2}{4 a c^4 (a x-1)^2}","\frac{1}{4 a c^4 (1-a x)}+\frac{1}{4 a c^4 (1-a x)^2}+\frac{\tanh ^{-1}(a x)}{4 a c^4}",1,"(2 - a*x + (-1 + a*x)^2*ArcTanh[a*x])/(4*a*c^4*(-1 + a*x)^2)","A",1
215,1,44,69,0.0306646,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^5),x]","\frac{-3 a^2 x^2+9 a x+3 (a x-1)^3 \tanh ^{-1}(a x)-10}{24 a c^5 (a x-1)^3}","\frac{1}{8 a c^5 (1-a x)}+\frac{1}{8 a c^5 (1-a x)^2}+\frac{1}{6 a c^5 (1-a x)^3}+\frac{\tanh ^{-1}(a x)}{8 a c^5}",1,"(-10 + 9*a*x - 3*a^2*x^2 + 3*(-1 + a*x)^3*ArcTanh[a*x])/(24*a*c^5*(-1 + a*x)^3)","A",1
216,1,60,65,0.0300676,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[(c - a*c*x)^p/E^(3*ArcTanh[a*x]),x]","-\frac{(1-a x)^{5/2} (c-a c x)^p \, _2F_1\left(\frac{3}{2},p+\frac{5}{2};p+\frac{7}{2};\frac{1}{2}-\frac{a x}{2}\right)}{\sqrt{2} a (2 p+5)}","-\frac{(1-a x)^{3/2} (c-a c x)^{p+1} \, _2F_1\left(\frac{3}{2},p+\frac{5}{2};p+\frac{7}{2};\frac{1}{2} (1-a x)\right)}{\sqrt{2} a c (2 p+5)}",1,"-(((1 - a*x)^(5/2)*(c - a*c*x)^p*Hypergeometric2F1[3/2, 5/2 + p, 7/2 + p, 1/2 - (a*x)/2])/(Sqrt[2]*a*(5 + 2*p)))","A",1
217,1,45,163,0.0213446,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[(c - a*c*x)^3/E^(3*ArcTanh[a*x]),x]","-\frac{c^3 (1-a x)^{11/2} \, _2F_1\left(\frac{3}{2},\frac{11}{2};\frac{13}{2};\frac{1}{2} (1-a x)\right)}{11 \sqrt{2} a}","-\frac{2 c^3 (1-a x)^5}{a \sqrt{1-a^2 x^2}}-\frac{9 c^3 \sqrt{1-a^2 x^2} (1-a x)^3}{4 a}-\frac{21 c^3 \sqrt{1-a^2 x^2} (1-a x)^2}{4 a}-\frac{105 c^3 \sqrt{1-a^2 x^2} (1-a x)}{8 a}-\frac{315 c^3 \sqrt{1-a^2 x^2}}{8 a}-\frac{315 c^3 \sin ^{-1}(a x)}{8 a}",1,"-1/11*(c^3*(1 - a*x)^(11/2)*Hypergeometric2F1[3/2, 11/2, 13/2, (1 - a*x)/2])/(Sqrt[2]*a)","C",0
218,1,45,131,0.0178398,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[(c - a*c*x)^2/E^(3*ArcTanh[a*x]),x]","-\frac{c^2 (1-a x)^{9/2} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};\frac{1}{2} (1-a x)\right)}{9 \sqrt{2} a}","-\frac{2 c^2 (1-a x)^4}{a \sqrt{1-a^2 x^2}}-\frac{7 c^2 \sqrt{1-a^2 x^2} (1-a x)^2}{3 a}-\frac{35 c^2 \sqrt{1-a^2 x^2} (1-a x)}{6 a}-\frac{35 c^2 \sqrt{1-a^2 x^2}}{2 a}-\frac{35 c^2 \sin ^{-1}(a x)}{2 a}",1,"-1/9*(c^2*(1 - a*x)^(9/2)*Hypergeometric2F1[3/2, 9/2, 11/2, (1 - a*x)/2])/(Sqrt[2]*a)","C",0
219,1,43,91,0.0159726,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[(c - a*c*x)/E^(3*ArcTanh[a*x]),x]","-\frac{c (1-a x)^{7/2} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};\frac{1}{2} (1-a x)\right)}{7 \sqrt{2} a}","-\frac{2 c (1-a x)^3}{a \sqrt{1-a^2 x^2}}-\frac{5 c \sqrt{1-a^2 x^2} (1-a x)}{2 a}-\frac{15 c \sqrt{1-a^2 x^2}}{2 a}-\frac{15 c \sin ^{-1}(a x)}{2 a}",1,"-1/7*(c*(1 - a*x)^(7/2)*Hypergeometric2F1[3/2, 7/2, 9/2, (1 - a*x)/2])/(Sqrt[2]*a)","C",0
220,1,59,41,0.0542299,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)),x]","\frac{2 \left(\sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)+a x-1\right)}{a c \sqrt{1-a^2 x^2}}","-\frac{2 (1-a x)}{a c \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)}{a c}",1,"(2*(-1 + a*x + Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*c*Sqrt[1 - a^2*x^2])","A",0
221,1,27,28,0.0103834,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^2),x]","-\frac{\sqrt{1-a x}}{a c^2 \sqrt{a x+1}}","-\frac{1-a x}{a c^2 \sqrt{1-a^2 x^2}}",1,"-(Sqrt[1 - a*x]/(a*c^2*Sqrt[1 + a*x]))","A",0
222,1,19,19,0.0115343,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^3),x]","\frac{x}{c^3 \sqrt{1-a^2 x^2}}","\frac{x}{c^3 \sqrt{1-a^2 x^2}}",1,"x/(c^3*Sqrt[1 - a^2*x^2])","A",1
223,1,45,55,0.0184377,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^4),x]","\frac{2 a^2 x^2-2 a x-1}{3 a c^4 (a x-1) \sqrt{1-a^2 x^2}}","\frac{2 x}{3 c^4 \sqrt{1-a^2 x^2}}+\frac{1}{3 a c^4 (1-a x) \sqrt{1-a^2 x^2}}",1,"(-1 - 2*a*x + 2*a^2*x^2)/(3*a*c^4*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
224,1,52,87,0.0223766,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^5),x]","\frac{2 a^3 x^3-4 a^2 x^2+a x+2}{5 a c^5 (a x-1)^2 \sqrt{1-a^2 x^2}}","\frac{2 x}{5 c^5 \sqrt{1-a^2 x^2}}+\frac{1}{5 a c^5 (1-a x) \sqrt{1-a^2 x^2}}+\frac{1}{5 a c^5 (1-a x)^2 \sqrt{1-a^2 x^2}}",1,"(2 + a*x - 4*a^2*x^2 + 2*a^3*x^3)/(5*a*c^5*(-1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
225,1,61,119,0.0255422,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^6} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^6),x]","\frac{8 a^4 x^4-24 a^3 x^3+20 a^2 x^2+4 a x-13}{35 a c^6 (a x-1)^3 \sqrt{1-a^2 x^2}}","\frac{8 x}{35 c^6 \sqrt{1-a^2 x^2}}+\frac{4}{35 a c^6 (1-a x) \sqrt{1-a^2 x^2}}+\frac{4}{35 a c^6 (1-a x)^2 \sqrt{1-a^2 x^2}}+\frac{1}{7 a c^6 (1-a x)^3 \sqrt{1-a^2 x^2}}",1,"(-13 + 4*a*x + 20*a^2*x^2 - 24*a^3*x^3 + 8*a^4*x^4)/(35*a*c^6*(-1 + a*x)^3*Sqrt[1 - a^2*x^2])","A",1
226,1,70,176,0.0529008,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^(9/2),x]","\frac{2 c^4 (a x+1)^{3/2} \left(315 a^4 x^4-1820 a^3 x^3+4530 a^2 x^2-6396 a x+5419\right) \sqrt{c-a c x}}{3465 a \sqrt{1-a x}}","\frac{4096 c^6 \left(1-a^2 x^2\right)^{3/2}}{3465 a (c-a c x)^{3/2}}+\frac{1024 c^5 \left(1-a^2 x^2\right)^{3/2}}{1155 a \sqrt{c-a c x}}+\frac{128 c^4 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a c x}}{231 a}+\frac{32 c^3 \left(1-a^2 x^2\right)^{3/2} (c-a c x)^{3/2}}{99 a}+\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2} (c-a c x)^{5/2}}{11 a}",1,"(2*c^4*(1 + a*x)^(3/2)*Sqrt[c - a*c*x]*(5419 - 6396*a*x + 4530*a^2*x^2 - 1820*a^3*x^3 + 315*a^4*x^4))/(3465*a*Sqrt[1 - a*x])","A",0
227,1,62,141,0.0443425,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^(7/2),x]","-\frac{2 c^3 (a x+1)^{3/2} \left(35 a^3 x^3-165 a^2 x^2+321 a x-319\right) \sqrt{c-a c x}}{315 a \sqrt{1-a x}}","\frac{256 c^5 \left(1-a^2 x^2\right)^{3/2}}{315 a (c-a c x)^{3/2}}+\frac{64 c^4 \left(1-a^2 x^2\right)^{3/2}}{105 a \sqrt{c-a c x}}+\frac{8 c^3 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a c x}}{21 a}+\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2} (c-a c x)^{3/2}}{9 a}",1,"(-2*c^3*(1 + a*x)^(3/2)*Sqrt[c - a*c*x]*(-319 + 321*a*x - 165*a^2*x^2 + 35*a^3*x^3))/(315*a*Sqrt[1 - a*x])","A",0
228,1,54,106,0.0370728,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^(5/2),x]","\frac{2 c^2 (a x+1)^{3/2} \left(15 a^2 x^2-54 a x+71\right) \sqrt{c-a c x}}{105 a \sqrt{1-a x}}","\frac{64 c^4 \left(1-a^2 x^2\right)^{3/2}}{105 a (c-a c x)^{3/2}}+\frac{16 c^3 \left(1-a^2 x^2\right)^{3/2}}{35 a \sqrt{c-a c x}}+\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2} \sqrt{c-a c x}}{7 a}",1,"(2*c^2*(1 + a*x)^(3/2)*Sqrt[c - a*c*x]*(71 - 54*a*x + 15*a^2*x^2))/(105*a*Sqrt[1 - a*x])","A",0
229,1,44,71,0.0267755,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^(3/2),x]","-\frac{2 c (a x+1)^{3/2} (3 a x-7) \sqrt{c-a c x}}{15 a \sqrt{1-a x}}","\frac{8 c^3 \left(1-a^2 x^2\right)^{3/2}}{15 a (c-a c x)^{3/2}}+\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{5 a \sqrt{c-a c x}}",1,"(-2*c*(1 + a*x)^(3/2)*(-7 + 3*a*x)*Sqrt[c - a*c*x])/(15*a*Sqrt[1 - a*x])","A",0
230,1,37,35,0.0142051,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - a*c*x],x]","\frac{2 (a x+1)^{3/2} \sqrt{c-a c x}}{3 a \sqrt{1-a x}}","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}",1,"(2*(1 + a*x)^(3/2)*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - a*x])","A",1
231,1,62,83,0.0276401,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[E^ArcTanh[a*x]/Sqrt[c - a*c*x],x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1}-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{a c \sqrt{1-a x}}","\frac{2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{a \sqrt{c}}-\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{c-a c x}}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x] - Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(a*c*Sqrt[1 - a*x])","A",0
232,1,80,82,0.0577545,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^(3/2),x]","-\frac{\sqrt{c-a c x} \left(2 a x+(a x-1) \sqrt{2 a x+2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)+2\right)}{2 a c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{\sqrt{1-a^2 x^2}}{a (c-a c x)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{\sqrt{2} a c^{3/2}}",1,"-1/2*(Sqrt[c - a*c*x]*(2 + 2*a*x + (-1 + a*x)*Sqrt[2 + 2*a*x]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(a*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",0
233,1,57,122,0.0202011,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^(5/2),x]","\frac{(a x+1)^{3/2} \sqrt{c-a c x} \, _2F_1\left(\frac{3}{2},3;\frac{5}{2};\frac{1}{2} (a x+1)\right)}{12 a c^3 \sqrt{1-a x}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{8 \sqrt{2} a c^{5/2}}-\frac{\sqrt{1-a^2 x^2}}{8 a c (c-a c x)^{3/2}}+\frac{\sqrt{1-a^2 x^2}}{2 a (c-a c x)^{5/2}}",1,"((1 + a*x)^(3/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[3/2, 3, 5/2, (1 + a*x)/2])/(12*a*c^3*Sqrt[1 - a*x])","C",0
234,1,57,157,0.0235536,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^(7/2),x]","\frac{(a x+1)^{3/2} \sqrt{c-a c x} \, _2F_1\left(\frac{3}{2},4;\frac{5}{2};\frac{1}{2} (a x+1)\right)}{24 a c^4 \sqrt{1-a x}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{32 \sqrt{2} a c^{7/2}}-\frac{\sqrt{1-a^2 x^2}}{32 a c^2 (c-a c x)^{3/2}}-\frac{\sqrt{1-a^2 x^2}}{24 a c (c-a c x)^{5/2}}+\frac{\sqrt{1-a^2 x^2}}{3 a (c-a c x)^{7/2}}",1,"((1 + a*x)^(3/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[3/2, 4, 5/2, (1 + a*x)/2])/(24*a*c^4*Sqrt[1 - a*x])","C",0
235,1,34,40,0.0426626,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^(7/2),x]","\frac{2 c^3 (a x-1)^3 (7 a x+11) \sqrt{c-a c x}}{63 a}","\frac{2 (c-a c x)^{9/2}}{9 a c}-\frac{4 (c-a c x)^{7/2}}{7 a}",1,"(2*c^3*(-1 + a*x)^3*(11 + 7*a*x)*Sqrt[c - a*c*x])/(63*a)","A",1
236,1,34,40,0.0393312,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^(5/2),x]","-\frac{2 c^2 (a x-1)^2 (5 a x+9) \sqrt{c-a c x}}{35 a}","\frac{2 (c-a c x)^{7/2}}{7 a c}-\frac{4 (c-a c x)^{5/2}}{5 a}",1,"(-2*c^2*(-1 + a*x)^2*(9 + 5*a*x)*Sqrt[c - a*c*x])/(35*a)","A",1
237,1,30,40,0.0305126,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a*c*x)^(3/2),x]","\frac{2 c (a x-1) (3 a x+7) \sqrt{c-a c x}}{15 a}","\frac{2 (c-a c x)^{5/2}}{5 a c}-\frac{4 (c-a c x)^{3/2}}{3 a}",1,"(2*c*(-1 + a*x)*(7 + 3*a*x)*Sqrt[c - a*c*x])/(15*a)","A",1
238,1,23,38,0.0259182,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","-\frac{2 (a x+5) \sqrt{c-a c x}}{3 a}","\frac{2 (c-a c x)^{3/2}}{3 a c}-\frac{4 \sqrt{c-a c x}}{a}",1,"(-2*(5 + a*x)*Sqrt[c - a*c*x])/(3*a)","A",1
239,1,21,36,0.0258752,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[E^(2*ArcTanh[a*x])/Sqrt[c - a*c*x],x]","\frac{6-2 a x}{a \sqrt{c-a c x}}","\frac{2 \sqrt{c-a c x}}{a c}+\frac{4}{a \sqrt{c-a c x}}",1,"(6 - 2*a*x)/(a*Sqrt[c - a*c*x])","A",1
240,1,34,38,0.0455835,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x)^(3/2),x]","\frac{2 (3 a x-1) \sqrt{c-a c x}}{3 a c^2 (a x-1)^2}","\frac{4}{3 a (c-a c x)^{3/2}}-\frac{2}{a c \sqrt{c-a c x}}",1,"(2*(-1 + 3*a*x)*Sqrt[c - a*c*x])/(3*a*c^2*(-1 + a*x)^2)","A",1
241,1,34,40,0.0564149,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x)^(5/2),x]","-\frac{2 (5 a x+1) \sqrt{c-a c x}}{15 a c^3 (a x-1)^3}","\frac{4}{5 a (c-a c x)^{5/2}}-\frac{2}{3 a c (c-a c x)^{3/2}}",1,"(-2*(1 + 5*a*x)*Sqrt[c - a*c*x])/(15*a*c^3*(-1 + a*x)^3)","A",1
242,1,34,40,0.0574402,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a*c*x)^(7/2),x]","\frac{2 (7 a x+3) \sqrt{c-a c x}}{35 a c^4 (a x-1)^4}","\frac{4}{7 a (c-a c x)^{7/2}}-\frac{2}{5 a c (c-a c x)^{5/2}}",1,"(2*(3 + 7*a*x)*Sqrt[c - a*c*x])/(35*a*c^4*(-1 + a*x)^4)","A",1
243,1,62,141,0.0492862,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^(9/2),x]","-\frac{2 c^4 (a x+1)^{5/2} \left(105 a^3 x^3-455 a^2 x^2+755 a x-533\right) \sqrt{c-a c x}}{1155 a \sqrt{1-a x}}","\frac{256 c^7 \left(1-a^2 x^2\right)^{5/2}}{1155 a (c-a c x)^{5/2}}+\frac{64 c^6 \left(1-a^2 x^2\right)^{5/2}}{231 a (c-a c x)^{3/2}}+\frac{8 c^5 \left(1-a^2 x^2\right)^{5/2}}{33 a \sqrt{c-a c x}}+\frac{2 c^4 \left(1-a^2 x^2\right)^{5/2} \sqrt{c-a c x}}{11 a}",1,"(-2*c^4*(1 + a*x)^(5/2)*Sqrt[c - a*c*x]*(-533 + 755*a*x - 455*a^2*x^2 + 105*a^3*x^3))/(1155*a*Sqrt[1 - a*x])","A",0
244,1,54,106,0.0368726,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^(7/2),x]","\frac{2 c^3 (a x+1)^{5/2} \left(35 a^2 x^2-110 a x+107\right) \sqrt{c-a c x}}{315 a \sqrt{1-a x}}","\frac{64 c^6 \left(1-a^2 x^2\right)^{5/2}}{315 a (c-a c x)^{5/2}}+\frac{16 c^5 \left(1-a^2 x^2\right)^{5/2}}{63 a (c-a c x)^{3/2}}+\frac{2 c^4 \left(1-a^2 x^2\right)^{5/2}}{9 a \sqrt{c-a c x}}",1,"(2*c^3*(1 + a*x)^(5/2)*Sqrt[c - a*c*x]*(107 - 110*a*x + 35*a^2*x^2))/(315*a*Sqrt[1 - a*x])","A",0
245,1,46,71,0.0324157,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^(5/2),x]","-\frac{2 c^2 (a x+1)^{5/2} (5 a x-9) \sqrt{c-a c x}}{35 a \sqrt{1-a x}}","\frac{8 c^5 \left(1-a^2 x^2\right)^{5/2}}{35 a (c-a c x)^{5/2}}+\frac{2 c^4 \left(1-a^2 x^2\right)^{5/2}}{7 a (c-a c x)^{3/2}}",1,"(-2*c^2*(1 + a*x)^(5/2)*(-9 + 5*a*x)*Sqrt[c - a*c*x])/(35*a*Sqrt[1 - a*x])","A",0
246,1,37,35,0.0219238,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a*c*x)^(3/2),x]","\frac{2 (a x+1)^{5/2} (c-a c x)^{3/2}}{5 a (1-a x)^{3/2}}","\frac{2 c^4 \left(1-a^2 x^2\right)^{5/2}}{5 a (c-a c x)^{5/2}}",1,"(2*(1 + a*x)^(5/2)*(c - a*c*x)^(3/2))/(5*a*(1 - a*x)^(3/2))","A",1
247,1,67,119,0.0350262,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1} (a x+7)-6 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{3 a \sqrt{1-a x}}","-\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}-\frac{4 c \sqrt{1-a^2 x^2}}{a \sqrt{c-a c x}}+\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{a}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(7 + a*x) - 6*Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(3*a*Sqrt[1 - a*x])","A",0
248,1,57,115,0.0236435,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[E^(3*ArcTanh[a*x])/Sqrt[c - a*c*x],x]","\frac{(a x+1)^{5/2} (c-a c x)^{3/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};\frac{1}{2} (a x+1)\right)}{10 a c^2 (1-a x)^{3/2}}","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{a (c-a c x)^{5/2}}+\frac{3 \sqrt{1-a^2 x^2}}{a \sqrt{c-a c x}}-\frac{3 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{a \sqrt{c}}",1,"((1 + a*x)^(5/2)*(c - a*c*x)^(3/2)*Hypergeometric2F1[2, 5/2, 7/2, (1 + a*x)/2])/(10*a*c^2*(1 - a*x)^(3/2))","C",0
249,1,91,122,0.0780475,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^(3/2),x]","\frac{\sqrt{c-a c x} \left(10 a^2 x^2+8 a x+3 (a x-1)^2 \sqrt{2 a x+2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)-2\right)}{8 a c^2 (a x-1)^2 \sqrt{1-a^2 x^2}}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{4 \sqrt{2} a c^{3/2}}+\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a (c-a c x)^{7/2}}-\frac{3 \sqrt{1-a^2 x^2}}{4 a (c-a c x)^{3/2}}",1,"(Sqrt[c - a*c*x]*(-2 + 8*a*x + 10*a^2*x^2 + 3*(-1 + a*x)^2*Sqrt[2 + 2*a*x]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(8*a*c^2*(-1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",0
250,1,57,157,0.0265241,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^(5/2),x]","\frac{(a x+1)^{5/2} (c-a c x)^{3/2} \, _2F_1\left(\frac{5}{2},4;\frac{7}{2};\frac{1}{2} (a x+1)\right)}{40 a c^4 (1-a x)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{16 \sqrt{2} a c^{5/2}}+\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{9/2}}-\frac{\sqrt{1-a^2 x^2}}{4 a (c-a c x)^{5/2}}+\frac{\sqrt{1-a^2 x^2}}{16 a c (c-a c x)^{3/2}}",1,"((1 + a*x)^(5/2)*(c - a*c*x)^(3/2)*Hypergeometric2F1[5/2, 4, 7/2, (1 + a*x)/2])/(40*a*c^4*(1 - a*x)^(3/2))","C",0
251,1,57,192,0.0257451,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a*c*x)^(7/2),x]","\frac{(a x+1)^{5/2} (c-a c x)^{3/2} \, _2F_1\left(\frac{5}{2},5;\frac{7}{2};\frac{1}{2} (a x+1)\right)}{80 a c^5 (1-a x)^{3/2}}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{256 \sqrt{2} a c^{7/2}}+\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{4 a (c-a c x)^{11/2}}+\frac{3 \sqrt{1-a^2 x^2}}{256 a c^2 (c-a c x)^{3/2}}-\frac{\sqrt{1-a^2 x^2}}{8 a (c-a c x)^{7/2}}+\frac{\sqrt{1-a^2 x^2}}{64 a c (c-a c x)^{5/2}}",1,"((1 + a*x)^(5/2)*(c - a*c*x)^(3/2)*Hypergeometric2F1[5/2, 5, 7/2, (1 + a*x)/2])/(80*a*c^5*(1 - a*x)^(3/2))","C",0
252,1,73,206,0.0593113,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Integrate[(c - a*c*x)^(9/2)/E^ArcTanh[a*x],x]","-\frac{2 c^5 \sqrt{1-a^2 x^2} \left(63 a^5 x^5-455 a^4 x^4+1510 a^3 x^3-3198 a^2 x^2+5419 a x-11531\right)}{693 a \sqrt{c-a c x}}","\frac{16384 c^5 \sqrt{1-a^2 x^2}}{693 a \sqrt{c-a c x}}+\frac{4096 c^4 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{693 a}+\frac{512 c^3 \sqrt{1-a^2 x^2} (c-a c x)^{3/2}}{231 a}+\frac{640 c^2 \sqrt{1-a^2 x^2} (c-a c x)^{5/2}}{693 a}+\frac{40 c \sqrt{1-a^2 x^2} (c-a c x)^{7/2}}{99 a}+\frac{2 \sqrt{1-a^2 x^2} (c-a c x)^{9/2}}{11 a}",1,"(-2*c^5*Sqrt[1 - a^2*x^2]*(-11531 + 5419*a*x - 3198*a^2*x^2 + 1510*a^3*x^3 - 455*a^4*x^4 + 63*a^5*x^5))/(693*a*Sqrt[c - a*c*x])","A",1
253,1,65,171,0.0411873,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Integrate[(c - a*c*x)^(7/2)/E^ArcTanh[a*x],x]","\frac{2 c^4 \sqrt{1-a^2 x^2} \left(35 a^4 x^4-220 a^3 x^3+642 a^2 x^2-1276 a x+2867\right)}{315 a \sqrt{c-a c x}}","\frac{4096 c^4 \sqrt{1-a^2 x^2}}{315 a \sqrt{c-a c x}}+\frac{1024 c^3 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{315 a}+\frac{128 c^2 \sqrt{1-a^2 x^2} (c-a c x)^{3/2}}{105 a}+\frac{32 c \sqrt{1-a^2 x^2} (c-a c x)^{5/2}}{63 a}+\frac{2 \sqrt{1-a^2 x^2} (c-a c x)^{7/2}}{9 a}",1,"(2*c^4*Sqrt[1 - a^2*x^2]*(2867 - 1276*a*x + 642*a^2*x^2 - 220*a^3*x^3 + 35*a^4*x^4))/(315*a*Sqrt[c - a*c*x])","A",1
254,1,57,136,0.038792,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[(c - a*c*x)^(5/2)/E^ArcTanh[a*x],x]","-\frac{2 c^3 \sqrt{1-a^2 x^2} \left(5 a^3 x^3-27 a^2 x^2+71 a x-177\right)}{35 a \sqrt{c-a c x}}","\frac{256 c^3 \sqrt{1-a^2 x^2}}{35 a \sqrt{c-a c x}}+\frac{64 c^2 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{35 a}+\frac{24 c \sqrt{1-a^2 x^2} (c-a c x)^{3/2}}{35 a}+\frac{2 \sqrt{1-a^2 x^2} (c-a c x)^{5/2}}{7 a}",1,"(-2*c^3*Sqrt[1 - a^2*x^2]*(-177 + 71*a*x - 27*a^2*x^2 + 5*a^3*x^3))/(35*a*Sqrt[c - a*c*x])","A",1
255,1,49,101,0.0298006,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[(c - a*c*x)^(3/2)/E^ArcTanh[a*x],x]","\frac{2 c^2 \sqrt{1-a^2 x^2} \left(3 a^2 x^2-14 a x+43\right)}{15 a \sqrt{c-a c x}}","\frac{64 c^2 \sqrt{1-a^2 x^2}}{15 a \sqrt{c-a c x}}+\frac{16 c \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{15 a}+\frac{2 \sqrt{1-a^2 x^2} (c-a c x)^{3/2}}{5 a}",1,"(2*c^2*Sqrt[1 - a^2*x^2]*(43 - 14*a*x + 3*a^2*x^2))/(15*a*Sqrt[c - a*c*x])","A",1
256,1,38,66,0.0219695,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[Sqrt[c - a*c*x]/E^ArcTanh[a*x],x]","-\frac{2 c (a x-5) \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a c x}}","\frac{8 c \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a c x}}+\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{3 a}",1,"(-2*c*(-5 + a*x)*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[c - a*c*x])","A",1
257,1,30,30,0.0155579,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[1/(E^ArcTanh[a*x]*Sqrt[c - a*c*x]),x]","\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{c-a c x}}","\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{c-a c x}}",1,"(2*Sqrt[1 - a^2*x^2])/(a*Sqrt[c - a*c*x])","A",1
258,1,44,51,0.0243046,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^(3/2)),x]","\frac{\sqrt{2-2 a x} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{a c \sqrt{c-a c x}}","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{a c^{3/2}}",1,"(Sqrt[2 - 2*a*x]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(a*c*Sqrt[c - a*c*x])","A",0
259,1,70,90,0.0599453,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^(5/2)),x]","-\frac{\sqrt{2} (a x-1) \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)-2 \sqrt{a x+1}}{4 a c^2 \sqrt{1-a x} \sqrt{c-a c x}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{2 \sqrt{2} a c^{5/2}}+\frac{\sqrt{1-a^2 x^2}}{2 a c (c-a c x)^{3/2}}",1,"-1/4*(-2*Sqrt[1 + a*x] + Sqrt[2]*(-1 + a*x)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(a*c^2*Sqrt[1 - a*x]*Sqrt[c - a*c*x])","A",0
260,1,52,125,0.0270564,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a*c*x)^(7/2)),x]","\frac{\sqrt{1-a^2 x^2} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};\frac{1}{2} (a x+1)\right)}{4 a c^3 \sqrt{c-a c x}}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{16 \sqrt{2} a c^{7/2}}+\frac{3 \sqrt{1-a^2 x^2}}{16 a c^2 (c-a c x)^{3/2}}+\frac{\sqrt{1-a^2 x^2}}{4 a c (c-a c x)^{5/2}}",1,"(Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, 3, 3/2, (1 + a*x)/2])/(4*a*c^3*Sqrt[c - a*c*x])","C",0
261,1,88,137,0.0843172,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Integrate[(c - a*c*x)^(7/2)/E^(2*ArcTanh[a*x]),x]","\frac{2 c^3 \left(\left(35 a^4 x^4-230 a^3 x^3+732 a^2 x^2-1754 a x+6257\right) \sqrt{c-a c x}-5040 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)\right)}{315 a}","-\frac{32 \sqrt{2} c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{32 c^3 \sqrt{c-a c x}}{a}+\frac{16 c^2 (c-a c x)^{3/2}}{3 a}+\frac{2 (c-a c x)^{9/2}}{9 a c}+\frac{4 (c-a c x)^{7/2}}{7 a}+\frac{8 c (c-a c x)^{5/2}}{5 a}",1,"(2*c^3*(Sqrt[c - a*c*x]*(6257 - 1754*a*x + 732*a^2*x^2 - 230*a^3*x^3 + 35*a^4*x^4) - 5040*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]))/(315*a)","A",1
262,1,80,116,0.0619299,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[(c - a*c*x)^(5/2)/E^(2*ArcTanh[a*x]),x]","-\frac{2 c^2 \left(\left(15 a^3 x^3-87 a^2 x^2+269 a x-1037\right) \sqrt{c-a c x}+840 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)\right)}{105 a}","-\frac{16 \sqrt{2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{16 c^2 \sqrt{c-a c x}}{a}+\frac{2 (c-a c x)^{7/2}}{7 a c}+\frac{4 (c-a c x)^{5/2}}{5 a}+\frac{8 c (c-a c x)^{3/2}}{3 a}",1,"(-2*c^2*(Sqrt[c - a*c*x]*(-1037 + 269*a*x - 87*a^2*x^2 + 15*a^3*x^3) + 840*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]))/(105*a)","A",1
263,1,71,95,0.0441795,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[(c - a*c*x)^(3/2)/E^(2*ArcTanh[a*x]),x]","\frac{2 c \left(3 a^2 x^2-16 a x+73\right) \sqrt{c-a c x}-120 \sqrt{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{15 a}","-\frac{8 \sqrt{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{2 (c-a c x)^{5/2}}{5 a c}+\frac{4 (c-a c x)^{3/2}}{3 a}+\frac{8 c \sqrt{c-a c x}}{a}",1,"(2*c*Sqrt[c - a*c*x]*(73 - 16*a*x + 3*a^2*x^2) - 120*Sqrt[2]*c^(3/2)*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/(15*a)","A",1
264,1,61,76,0.043907,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[Sqrt[c - a*c*x]/E^(2*ArcTanh[a*x]),x]","-\frac{2 (a x-7) \sqrt{c-a c x}+12 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{3 a}","\frac{2 (c-a c x)^{3/2}}{3 a c}+\frac{4 \sqrt{c-a c x}}{a}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a}",1,"-1/3*(2*(-7 + a*x)*Sqrt[c - a*c*x] + 12*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",1
265,1,58,58,0.0255163,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x]),x]","\frac{2 \sqrt{c-a c x}}{a c}-\frac{2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a \sqrt{c}}","\frac{2 \sqrt{c-a c x}}{a c}-\frac{2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a \sqrt{c}}",1,"(2*Sqrt[c - a*c*x])/(a*c) - (2*Sqrt[2]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/(a*Sqrt[c])","A",1
266,1,38,38,0.0178265,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(3/2)),x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a c^{3/2}}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a c^{3/2}}",1,"-((Sqrt[2]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/(a*c^(3/2)))","A",1
267,1,36,57,0.0233162,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(5/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (1-a x)\right)}{a c^2 \sqrt{c-a c x}}","\frac{1}{a c^2 \sqrt{c-a c x}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a c^{5/2}}",1,"Hypergeometric2F1[-1/2, 1, 1/2, (1 - a*x)/2]/(a*c^2*Sqrt[c - a*c*x])","C",0
268,1,39,83,0.0260577,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(7/2)),x]","\frac{\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{1}{2} (1-a x)\right)}{3 a c^2 (c-a c x)^{3/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a c^{7/2}}+\frac{1}{2 a c^3 \sqrt{c-a c x}}+\frac{1}{3 a c^2 (c-a c x)^{3/2}}",1,"Hypergeometric2F1[-3/2, 1, -1/2, (1 - a*x)/2]/(3*a*c^2*(c - a*c*x)^(3/2))","C",0
269,1,39,104,0.0312224,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{9/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(9/2)),x]","\frac{\, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{1}{2} (1-a x)\right)}{5 a c^2 (c-a c x)^{5/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a c^{9/2}}+\frac{1}{4 a c^4 \sqrt{c-a c x}}+\frac{1}{6 a c^3 (c-a c x)^{3/2}}+\frac{1}{5 a c^2 (c-a c x)^{5/2}}",1,"Hypergeometric2F1[-5/2, 1, -3/2, (1 - a*x)/2]/(5*a*c^2*(c - a*c*x)^(5/2))","C",0
270,1,70,171,0.0421686,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[(c - a*c*x)^(5/2)/E^(3*ArcTanh[a*x]),x]","\frac{2 c^3 \sqrt{1-a x} \left(5 a^4 x^4-36 a^3 x^3+142 a^2 x^2-708 a x-1451\right)}{35 a \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 (c-a c x)^{9/2}}{7 a c^2 \sqrt{1-a^2 x^2}}-\frac{4096 c^2 \sqrt{c-a c x}}{35 a \sqrt{1-a^2 x^2}}+\frac{32 (c-a c x)^{7/2}}{35 a c \sqrt{1-a^2 x^2}}+\frac{128 (c-a c x)^{5/2}}{35 a \sqrt{1-a^2 x^2}}+\frac{1024 c (c-a c x)^{3/2}}{35 a \sqrt{1-a^2 x^2}}",1,"(2*c^3*Sqrt[1 - a*x]*(-1451 - 708*a*x + 142*a^2*x^2 - 36*a^3*x^3 + 5*a^4*x^4))/(35*a*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",0
271,1,61,136,0.0342372,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[(c - a*c*x)^(3/2)/E^(3*ArcTanh[a*x]),x]","-\frac{2 c^2 \sqrt{1-a x} \left(a^3 x^3-7 a^2 x^2+43 a x+91\right)}{5 a \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 (c-a c x)^{7/2}}{5 a c^2 \sqrt{1-a^2 x^2}}+\frac{8 (c-a c x)^{5/2}}{5 a c \sqrt{1-a^2 x^2}}+\frac{64 (c-a c x)^{3/2}}{5 a \sqrt{1-a^2 x^2}}-\frac{256 c \sqrt{c-a c x}}{5 a \sqrt{1-a^2 x^2}}",1,"(-2*c^2*Sqrt[1 - a*x]*(91 + 43*a*x - 7*a^2*x^2 + a^3*x^3))/(5*a*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",0
272,1,51,103,0.0297035,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[Sqrt[c - a*c*x]/E^(3*ArcTanh[a*x]),x]","\frac{2 c \sqrt{1-a x} \left(a^2 x^2-10 a x-23\right)}{3 a \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 (c-a c x)^{5/2}}{3 a c^2 \sqrt{1-a^2 x^2}}+\frac{16 (c-a c x)^{3/2}}{3 a c \sqrt{1-a^2 x^2}}-\frac{64 \sqrt{c-a c x}}{3 a \sqrt{1-a^2 x^2}}",1,"(2*c*Sqrt[1 - a*x]*(-23 - 10*a*x + a^2*x^2))/(3*a*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",0
273,1,40,67,0.0270228,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x]),x]","-\frac{2 \sqrt{1-a x} (a x+3)}{a \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 (c-a c x)^{3/2}}{a c^2 \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{c-a c x}}{a c \sqrt{1-a^2 x^2}}",1,"(-2*Sqrt[1 - a*x]*(3 + a*x))/(a*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",0
274,1,35,33,0.0253185,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(3/2)),x]","-\frac{2 (1-a x)^{3/2}}{a \sqrt{a x+1} (c-a c x)^{3/2}}","-\frac{2 \sqrt{c-a c x}}{a c^2 \sqrt{1-a^2 x^2}}",1,"(-2*(1 - a*x)^(3/2))/(a*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))","A",0
275,1,55,85,0.027375,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(5/2)),x]","-\frac{(1-a x)^{3/2} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (a x+1)\right)}{a c \sqrt{a x+1} (c-a c x)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{\sqrt{2} a c^{5/2}}-\frac{\sqrt{c-a c x}}{a c^3 \sqrt{1-a^2 x^2}}",1,"-(((1 - a*x)^(3/2)*Hypergeometric2F1[-1/2, 1, 1/2, (1 + a*x)/2])/(a*c*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)))","C",0
276,1,57,125,0.0330164,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(7/2)),x]","-\frac{(1-a x)^{3/2} \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};\frac{1}{2} (a x+1)\right)}{2 a c^2 \sqrt{a x+1} (c-a c x)^{3/2}}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{4 \sqrt{2} a c^{7/2}}-\frac{3 \sqrt{c-a c x}}{4 a c^4 \sqrt{1-a^2 x^2}}+\frac{1}{2 a c^3 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}",1,"-1/2*((1 - a*x)^(3/2)*Hypergeometric2F1[-1/2, 2, 1/2, (1 + a*x)/2])/(a*c^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))","C",0
277,1,57,160,0.0312221,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{9/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(9/2)),x]","-\frac{(1-a x)^{3/2} \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};\frac{1}{2} (a x+1)\right)}{4 a c^3 \sqrt{a x+1} (c-a c x)^{3/2}}","\frac{15 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{32 \sqrt{2} a c^{9/2}}-\frac{15 \sqrt{c-a c x}}{32 a c^5 \sqrt{1-a^2 x^2}}+\frac{5}{16 a c^4 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}+\frac{1}{4 a c^3 \sqrt{1-a^2 x^2} (c-a c x)^{3/2}}",1,"-1/4*((1 - a*x)^(3/2)*Hypergeometric2F1[-1/2, 3, 1/2, (1 + a*x)/2])/(a*c^3*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))","C",0
278,1,80,81,0.0559818,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x)^(7/2),x]","\frac{c^3 2^{\frac{n}{2}+1} \sqrt{c-a c x} (1-a x)^{4-\frac{n}{2}} \, _2F_1\left(\frac{9}{2}-\frac{n}{2},-\frac{n}{2};\frac{11}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (n-9)}","-\frac{2^{\frac{n}{2}+1} (c-a c x)^{9/2} (1-a x)^{-n/2} \, _2F_1\left(\frac{9-n}{2},-\frac{n}{2};\frac{11-n}{2};\frac{1}{2} (1-a x)\right)}{a c (9-n)}",1,"(2^(1 + n/2)*c^3*(1 - a*x)^(4 - n/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[9/2 - n/2, -1/2*n, 11/2 - n/2, 1/2 - (a*x)/2])/(a*(-9 + n))","A",1
279,1,80,81,0.045698,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x)^(5/2),x]","\frac{c^2 2^{\frac{n}{2}+1} \sqrt{c-a c x} (1-a x)^{3-\frac{n}{2}} \, _2F_1\left(\frac{7}{2}-\frac{n}{2},-\frac{n}{2};\frac{9}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (n-7)}","-\frac{2^{\frac{n}{2}+1} (c-a c x)^{7/2} (1-a x)^{-n/2} \, _2F_1\left(\frac{7-n}{2},-\frac{n}{2};\frac{9-n}{2};\frac{1}{2} (1-a x)\right)}{a c (7-n)}",1,"(2^(1 + n/2)*c^2*(1 - a*x)^(3 - n/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[7/2 - n/2, -1/2*n, 9/2 - n/2, 1/2 - (a*x)/2])/(a*(-7 + n))","A",1
280,1,78,81,0.0368496,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x)^(3/2),x]","\frac{c 2^{\frac{n}{2}+1} \sqrt{c-a c x} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(\frac{5}{2}-\frac{n}{2},-\frac{n}{2};\frac{7}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (n-5)}","-\frac{2^{\frac{n}{2}+1} (c-a c x)^{5/2} (1-a x)^{-n/2} \, _2F_1\left(\frac{5-n}{2},-\frac{n}{2};\frac{7-n}{2};\frac{1}{2} (1-a x)\right)}{a c (5-n)}",1,"(2^(1 + n/2)*c*(1 - a*x)^(2 - n/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[5/2 - n/2, -1/2*n, 7/2 - n/2, 1/2 - (a*x)/2])/(a*(-5 + n))","A",1
281,1,77,81,0.0311969,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^(n*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","\frac{2^{\frac{n}{2}+1} \sqrt{c-a c x} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(\frac{3}{2}-\frac{n}{2},-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (n-3)}","-\frac{2^{\frac{n}{2}+1} (c-a c x)^{3/2} (1-a x)^{-n/2} \, _2F_1\left(\frac{3-n}{2},-\frac{n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{a c (3-n)}",1,"(2^(1 + n/2)*(1 - a*x)^(1 - n/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[3/2 - n/2, -1/2*n, 5/2 - n/2, 1/2 - (a*x)/2])/(a*(-3 + n))","A",1
282,1,78,81,0.0249562,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Integrate[E^(n*ArcTanh[a*x])/Sqrt[c - a*c*x],x]","\frac{2^{\frac{n}{2}+1} \sqrt{c-a c x} (1-a x)^{-n/2} \, _2F_1\left(\frac{1}{2}-\frac{n}{2},-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a c (n-1)}","-\frac{2^{\frac{n}{2}+1} \sqrt{c-a c x} (1-a x)^{-n/2} \, _2F_1\left(\frac{1-n}{2},-\frac{n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a c (1-n)}",1,"(2^(1 + n/2)*Sqrt[c - a*c*x]*Hypergeometric2F1[1/2 - n/2, -1/2*n, 3/2 - n/2, 1/2 - (a*x)/2])/(a*c*(-1 + n)*(1 - a*x)^(n/2))","A",1
283,1,78,78,0.0266959,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x)^(3/2),x]","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},-\frac{n}{2};\frac{1}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a c (n+1) \sqrt{c-a c x}}","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(\frac{1}{2} (-n-1),-\frac{n}{2};\frac{1-n}{2};\frac{1}{2} (1-a x)\right)}{a c (n+1) \sqrt{c-a c x}}",1,"(2^(1 + n/2)*Hypergeometric2F1[-1/2 - n/2, -1/2*n, 1/2 - n/2, 1/2 - (a*x)/2])/(a*c*(1 + n)*(1 - a*x)^(n/2)*Sqrt[c - a*c*x])","A",1
284,1,80,78,0.0331976,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x)^(5/2),x]","\frac{2^{\frac{n}{2}+1} (1-a x)^{-\frac{n}{2}-1} \, _2F_1\left(-\frac{n}{2}-\frac{3}{2},-\frac{n}{2};-\frac{n}{2}-\frac{1}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a c^2 (n+3) \sqrt{c-a c x}}","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(\frac{1}{2} (-n-3),-\frac{n}{2};\frac{1}{2} (-n-1);\frac{1}{2} (1-a x)\right)}{a c (n+3) (c-a c x)^{3/2}}",1,"(2^(1 + n/2)*(1 - a*x)^(-1 - n/2)*Hypergeometric2F1[-3/2 - n/2, -1/2*n, -1/2 - n/2, 1/2 - (a*x)/2])/(a*c^2*(3 + n)*Sqrt[c - a*c*x])","A",1
285,1,80,78,0.0440151,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x)^(7/2),x]","\frac{2^{\frac{n}{2}+1} (1-a x)^{-\frac{n}{2}-2} \, _2F_1\left(-\frac{n}{2}-\frac{5}{2},-\frac{n}{2};-\frac{n}{2}-\frac{3}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a c^3 (n+5) \sqrt{c-a c x}}","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(\frac{1}{2} (-n-5),-\frac{n}{2};\frac{1}{2} (-n-3);\frac{1}{2} (1-a x)\right)}{a c (n+5) (c-a c x)^{5/2}}",1,"(2^(1 + n/2)*(1 - a*x)^(-2 - n/2)*Hypergeometric2F1[-5/2 - n/2, -1/2*n, -3/2 - n/2, 1/2 - (a*x)/2])/(a*c^3*(5 + n)*Sqrt[c - a*c*x])","A",1
286,1,50,83,0.0600862,"\int e^{\tanh ^{-1}(a x)} x^4 (c-a c x) \, dx","Integrate[E^ArcTanh[a*x]*x^4*(c - a*c*x),x]","\frac{c \left(a x \sqrt{1-a^2 x^2} \left(8 a^4 x^4-2 a^2 x^2-3\right)+3 \sin ^{-1}(a x)\right)}{48 a^5}","\frac{c \sin ^{-1}(a x)}{16 a^5}+\frac{1}{6} c x^5 \sqrt{1-a^2 x^2}-\frac{c x^3 \sqrt{1-a^2 x^2}}{24 a^2}-\frac{c x \sqrt{1-a^2 x^2}}{16 a^4}",1,"(c*(a*x*Sqrt[1 - a^2*x^2]*(-3 - 2*a^2*x^2 + 8*a^4*x^4) + 3*ArcSin[a*x]))/(48*a^5)","A",1
287,1,32,45,0.0253504,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x) \, dx","Integrate[E^ArcTanh[a*x]*x^3*(c - a*c*x),x]","-\frac{c \left(1-a^2 x^2\right)^{3/2} \left(3 a^2 x^2+2\right)}{15 a^4}","\frac{c \left(1-a^2 x^2\right)^{5/2}}{5 a^4}-\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 a^4}",1,"-1/15*(c*(1 - a^2*x^2)^(3/2)*(2 + 3*a^2*x^2))/a^4","A",1
288,1,40,58,0.0451651,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x) \, dx","Integrate[E^ArcTanh[a*x]*x^2*(c - a*c*x),x]","\frac{c \left(a x \sqrt{1-a^2 x^2} \left(2 a^2 x^2-1\right)+\sin ^{-1}(a x)\right)}{8 a^3}","\frac{c \sin ^{-1}(a x)}{8 a^3}-\frac{c x \sqrt{1-a^2 x^2}}{8 a^2}+\frac{1}{4} c x^3 \sqrt{1-a^2 x^2}",1,"(c*(a*x*Sqrt[1 - a^2*x^2]*(-1 + 2*a^2*x^2) + ArcSin[a*x]))/(8*a^3)","A",1
289,1,22,22,0.0135632,"\int e^{\tanh ^{-1}(a x)} x (c-a c x) \, dx","Integrate[E^ArcTanh[a*x]*x*(c - a*c*x),x]","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 a^2}","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 a^2}",1,"-1/3*(c*(1 - a^2*x^2)^(3/2))/a^2","A",1
290,1,30,33,0.0098452,"\int e^{\tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x),x]","\frac{c \left(a x \sqrt{1-a^2 x^2}+\sin ^{-1}(a x)\right)}{2 a}","\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}",1,"(c*(a*x*Sqrt[1 - a^2*x^2] + ArcSin[a*x]))/(2*a)","A",1
291,1,79,35,0.0821249,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x))/x,x]","c \left(-\frac{a^2 x^2}{\sqrt{1-a^2 x^2}}+\frac{1}{\sqrt{1-a^2 x^2}}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\sin ^{-1}(a x)+2 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)","c \sqrt{1-a^2 x^2}-c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"c*(1/Sqrt[1 - a^2*x^2] - (a^2*x^2)/Sqrt[1 - a^2*x^2] + ArcSin[a*x] + 2*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - ArcTanh[Sqrt[1 - a^2*x^2]])","B",0
292,1,28,29,0.0306056,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x))/x^2,x]","-\frac{c \left(\sqrt{1-a^2 x^2}+a x \sin ^{-1}(a x)\right)}{x}","-\frac{c \sqrt{1-a^2 x^2}}{x}-a c \sin ^{-1}(a x)",1,"-((c*(Sqrt[1 - a^2*x^2] + a*x*ArcSin[a*x]))/x)","A",1
293,1,67,46,0.0240555,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x))/x^3,x]","\frac{c \left(a^2 x^2+a^2 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-1\right)}{2 x^2 \sqrt{1-a^2 x^2}}","\frac{1}{2} a^2 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{c \sqrt{1-a^2 x^2}}{2 x^2}",1,"(c*(-1 + a^2*x^2 + a^2*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(2*x^2*Sqrt[1 - a^2*x^2])","A",1
294,1,22,22,0.0135235,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x^4} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x))/x^4,x]","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 x^3}","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 x^3}",1,"-1/3*(c*(1 - a^2*x^2)^(3/2))/x^3","A",1
295,1,89,124,0.1986257,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x)^2 \, dx","Integrate[E^ArcTanh[a*x]*x^3*(c - a*c*x)^2,x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(40 a^5 x^5-48 a^4 x^4-10 a^3 x^3+16 a^2 x^2-15 a x+32\right)-60 \sin ^{-1}(a x)-150 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{240 a^4}","-\frac{c^2 \sin ^{-1}(a x)}{16 a^4}-\frac{c^2 x^2 \left(1-a^2 x^2\right)^{3/2}}{5 a^2}+\frac{c^2 x^3 \left(1-a^2 x^2\right)^{3/2}}{6 a}-\frac{c^2 (16-15 a x) \left(1-a^2 x^2\right)^{3/2}}{120 a^4}-\frac{c^2 x \sqrt{1-a^2 x^2}}{16 a^3}",1,"-1/240*(c^2*(Sqrt[1 - a^2*x^2]*(32 - 15*a*x + 16*a^2*x^2 - 10*a^3*x^3 - 48*a^4*x^4 + 40*a^5*x^5) - 60*ArcSin[a*x] - 150*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a^4","A",0
296,1,75,113,0.0847088,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x)^2 \, dx","Integrate[E^ArcTanh[a*x]*x^2*(c - a*c*x)^2,x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(24 a^4 x^4-30 a^3 x^3-8 a^2 x^2+15 a x-16\right)+30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{120 a^3}","\frac{c^2 \sin ^{-1}(a x)}{8 a^3}-\frac{c^2 x \left(1-a^2 x^2\right)^{3/2}}{4 a^2}+\frac{c^2 x \sqrt{1-a^2 x^2}}{8 a^2}-\frac{c^2 \left(1-a^2 x^2\right)^{5/2}}{5 a^3}+\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^3}",1,"-1/120*(c^2*(Sqrt[1 - a^2*x^2]*(-16 + 15*a*x - 8*a^2*x^2 - 30*a^3*x^3 + 24*a^4*x^4) + 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a^3","A",0
297,1,67,70,0.1007491,"\int e^{\tanh ^{-1}(a x)} x (c-a c x)^2 \, dx","Integrate[E^ArcTanh[a*x]*x*(c - a*c*x)^2,x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(6 a^3 x^3-8 a^2 x^2-3 a x+8\right)-6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{24 a^2}","-\frac{c^2 (4-3 a x) \left(1-a^2 x^2\right)^{3/2}}{12 a^2}-\frac{c^2 x \sqrt{1-a^2 x^2}}{8 a}-\frac{c^2 \sin ^{-1}(a x)}{8 a^2}",1,"-1/24*(c^2*(Sqrt[1 - a^2*x^2]*(8 - 3*a*x - 8*a^2*x^2 + 6*a^3*x^3) - 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a^2","A",0
298,1,59,61,0.065774,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^2,x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(2 a^2 x^2-3 a x-2\right)+6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a}+\frac{1}{2} c^2 x \sqrt{1-a^2 x^2}+\frac{c^2 \sin ^{-1}(a x)}{2 a}",1,"-1/6*(c^2*(Sqrt[1 - a^2*x^2]*(-2 - 3*a*x + 2*a^2*x^2) + 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
299,1,125,59,0.0835881,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x,x]","\frac{c^2 \left(a^3 x^3-2 a^2 x^2+\sqrt{1-a^2 x^2} \sin ^{-1}(a x)+4 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a x+2\right)}{2 \sqrt{1-a^2 x^2}}","\frac{1}{2} c^2 (2-a x) \sqrt{1-a^2 x^2}-c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{1}{2} c^2 \sin ^{-1}(a x)",1,"(c^2*(2 - a*x - 2*a^2*x^2 + a^3*x^3 + Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 4*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(2*Sqrt[1 - a^2*x^2])","B",0
300,1,84,58,0.1865095,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^2,x]","\frac{1}{2} c^2 \left(\frac{2 (a x-1) (a x+1)^2}{x \sqrt{1-a^2 x^2}}+2 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a \sin ^{-1}(a x)+2 a \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)","-\frac{c^2 (a x+1) \sqrt{1-a^2 x^2}}{x}+a c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a c^2 \sin ^{-1}(a x)",1,"(c^2*((2*(-1 + a*x)*(1 + a*x)^2)/(x*Sqrt[1 - a^2*x^2]) - a*ArcSin[a*x] + 2*a*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] + 2*a*ArcTanh[Sqrt[1 - a^2*x^2]]))/2","A",0
301,1,147,67,0.1063319,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^3,x]","-\frac{c^2 \left(4 a^3 x^3-2 a^2 x^2+a^2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+10 a^2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-2 a^2 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-4 a x+2\right)}{4 x^2 \sqrt{1-a^2 x^2}}","-\frac{c^2 (1-2 a x) \sqrt{1-a^2 x^2}}{2 x^2}+\frac{1}{2} a^2 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a^2 c^2 \sin ^{-1}(a x)",1,"-1/4*(c^2*(2 - 4*a*x - 2*a^2*x^2 + 4*a^3*x^3 + a^2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 10*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 2*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x^2*Sqrt[1 - a^2*x^2])","B",0
302,1,91,75,0.0297748,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^4} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^4,x]","-\frac{c^2 \left(2 a^4 x^4+3 a^3 x^3-4 a^2 x^2+3 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-3 a x+2\right)}{6 x^3 \sqrt{1-a^2 x^2}}","\frac{a c^2 \sqrt{1-a^2 x^2}}{2 x^2}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{1}{2} a^3 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-1/6*(c^2*(2 - 3*a*x - 4*a^2*x^2 + 3*a^3*x^3 + 2*a^4*x^4 + 3*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x^3*Sqrt[1 - a^2*x^2])","A",1
303,1,99,102,0.0328347,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^5} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^5,x]","\frac{c^2 \left(8 a^5 x^5-3 a^4 x^4-16 a^3 x^3+9 a^2 x^2+3 a^4 x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+8 a x-6\right)}{24 x^4 \sqrt{1-a^2 x^2}}","-\frac{a^2 c^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}+\frac{1}{8} a^4 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(c^2*(-6 + 8*a*x + 9*a^2*x^2 - 16*a^3*x^3 - 3*a^4*x^4 + 8*a^5*x^5 + 3*a^4*x^4*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(24*x^4*Sqrt[1 - a^2*x^2])","A",1
304,1,107,129,0.0391696,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^6} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^6,x]","-\frac{c^2 \left(16 a^6 x^6-15 a^5 x^5-8 a^4 x^4+45 a^3 x^3-32 a^2 x^2+15 a^5 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-30 a x+24\right)}{120 x^5 \sqrt{1-a^2 x^2}}","-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{2 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}-\frac{1}{8} a^5 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{a^3 c^2 \sqrt{1-a^2 x^2}}{8 x^2}",1,"-1/120*(c^2*(24 - 30*a*x - 32*a^2*x^2 + 45*a^3*x^3 - 8*a^4*x^4 - 15*a^5*x^5 + 16*a^6*x^6 + 15*a^5*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x^5*Sqrt[1 - a^2*x^2])","A",1
305,1,115,156,0.042555,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^7} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^7,x]","\frac{c^2 \left(32 a^7 x^7-15 a^6 x^6-16 a^5 x^5+5 a^4 x^4-64 a^3 x^3+50 a^2 x^2+15 a^6 x^6 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+48 a x-40\right)}{240 x^6 \sqrt{1-a^2 x^2}}","-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{6 x^6}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}{8 x^4}+\frac{1}{16} a^6 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a^4 c^2 \sqrt{1-a^2 x^2}}{16 x^2}+\frac{2 a^3 c^2 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}",1,"(c^2*(-40 + 48*a*x + 50*a^2*x^2 - 64*a^3*x^3 + 5*a^4*x^4 - 16*a^5*x^5 - 15*a^6*x^6 + 32*a^7*x^7 + 15*a^6*x^6*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(240*x^6*Sqrt[1 - a^2*x^2])","A",1
306,1,91,148,0.1311153,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x)^3 \, dx","Integrate[E^ArcTanh[a*x]*x^3*(c - a*c*x)^3,x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(120 a^6 x^6-280 a^5 x^5+144 a^4 x^4+70 a^3 x^3-88 a^2 x^2+105 a x-176\right)+210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{840 a^4}","-\frac{c^3 \sin ^{-1}(a x)}{8 a^4}-\frac{11 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}{35 a^2}-\frac{1}{7} c^3 x^4 \left(1-a^2 x^2\right)^{3/2}+\frac{c^3 x^3 \left(1-a^2 x^2\right)^{3/2}}{3 a}-\frac{c^3 (88-105 a x) \left(1-a^2 x^2\right)^{3/2}}{420 a^4}-\frac{c^3 x \sqrt{1-a^2 x^2}}{8 a^3}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(-176 + 105*a*x - 88*a^2*x^2 + 70*a^3*x^3 + 144*a^4*x^4 - 280*a^5*x^5 + 120*a^6*x^6) + 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(840*a^4)","A",0
307,1,83,121,0.0924788,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x)^3 \, dx","Integrate[E^ArcTanh[a*x]*x^2*(c - a*c*x)^3,x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(40 a^5 x^5-96 a^4 x^4+50 a^3 x^3+32 a^2 x^2-45 a x+64\right)-90 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{240 a^3}","\frac{3 c^3 \sin ^{-1}(a x)}{16 a^3}+\frac{2 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}+\frac{3 c^3 x \sqrt{1-a^2 x^2}}{16 a^2}-\frac{1}{6} c^3 x^3 \left(1-a^2 x^2\right)^{3/2}+\frac{c^3 (32-45 a x) \left(1-a^2 x^2\right)^{3/2}}{120 a^3}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(64 - 45*a*x + 32*a^2*x^2 + 50*a^3*x^3 - 96*a^4*x^4 + 40*a^5*x^5) - 90*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(240*a^3)","A",0
308,1,75,94,0.1121294,"\int e^{\tanh ^{-1}(a x)} x (c-a c x)^3 \, dx","Integrate[E^ArcTanh[a*x]*x*(c - a*c*x)^3,x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(12 a^4 x^4-30 a^3 x^3+16 a^2 x^2+15 a x-28\right)+30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{60 a^2}","-\frac{1}{5} c^3 x^2 \left(1-a^2 x^2\right)^{3/2}-\frac{c^3 (14-15 a x) \left(1-a^2 x^2\right)^{3/2}}{30 a^2}-\frac{c^3 x \sqrt{1-a^2 x^2}}{4 a}-\frac{c^3 \sin ^{-1}(a x)}{4 a^2}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(-28 + 15*a*x + 16*a^2*x^2 - 30*a^3*x^3 + 12*a^4*x^4) + 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(60*a^2)","A",0
309,1,67,91,0.0878591,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^3,x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(6 a^3 x^3-16 a^2 x^2+9 a x+16\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{24 a}","\frac{c^3 (1-a x) \left(1-a^2 x^2\right)^{3/2}}{4 a}+\frac{5 c^3 \left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{5}{8} c^3 x \sqrt{1-a^2 x^2}+\frac{5 c^3 \sin ^{-1}(a x)}{8 a}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(16 + 9*a*x - 16*a^2*x^2 + 6*a^3*x^3) - 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(24*a)","A",0
310,1,135,75,0.1044031,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x,x]","\frac{c^3 \left(-2 a^4 x^4+6 a^3 x^3-2 a^2 x^2+3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+18 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-6 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-6 a x+4\right)}{6 \sqrt{1-a^2 x^2}}","-\frac{1}{3} c^3 \left(1-a^2 x^2\right)^{3/2}+c^3 (1-a x) \sqrt{1-a^2 x^2}-c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-c^3 \sin ^{-1}(a x)",1,"(c^3*(4 - 6*a*x - 2*a^2*x^2 + 6*a^3*x^3 - 2*a^4*x^4 + 3*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 18*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 6*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(6*Sqrt[1 - a^2*x^2])","A",0
311,1,143,83,0.1064022,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^2,x]","-\frac{c^3 \left(a^4 x^4-4 a^3 x^3-3 a^2 x^2+2 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+2 a x \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-4 a x \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+4 a x+2\right)}{2 x \sqrt{1-a^2 x^2}}","-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{x}-\frac{1}{2} a c^3 (a x+4) \sqrt{1-a^2 x^2}+2 a c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{1}{2} a c^3 \sin ^{-1}(a x)",1,"-1/2*(c^3*(2 + 4*a*x - 3*a^2*x^2 - 4*a^3*x^3 + a^4*x^4 + 2*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 2*a*x*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 4*a*x*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x*Sqrt[1 - a^2*x^2])","A",0
312,1,155,92,0.123854,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^3,x]","\frac{c^3 \left(-4 a^4 x^4-8 a^3 x^3+6 a^2 x^2+a^2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-14 a^2 x^2 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-2 a^2 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+8 a x-2\right)}{4 x^2 \sqrt{1-a^2 x^2}}","-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{2 x^2}+\frac{a c^3 (a x+4) \sqrt{1-a^2 x^2}}{2 x}-\frac{1}{2} a^2 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a^2 c^3 \sin ^{-1}(a x)",1,"(c^3*(-2 + 8*a*x + 6*a^2*x^2 - 8*a^3*x^3 - 4*a^4*x^4 + a^2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x] - 14*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 2*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(4*x^2*Sqrt[1 - a^2*x^2])","A",0
313,1,156,88,0.1105341,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^4} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^4,x]","\frac{c^3 \left(4 a^4 x^4-6 a^3 x^3-2 a^2 x^2+3 a^3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+18 a^3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-6 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+6 a x-2\right)}{6 x^3 \sqrt{1-a^2 x^2}}","-a^3 c^3 \sin ^{-1}(a x)+\frac{a c^3 (1-a x) \sqrt{1-a^2 x^2}}{x^2}-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-a^3 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(c^3*(-2 + 6*a*x - 2*a^2*x^2 - 6*a^3*x^3 + 4*a^4*x^4 + 3*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 18*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 6*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(6*x^3*Sqrt[1 - a^2*x^2])","A",0
314,1,99,102,0.0344862,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^5} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^5,x]","\frac{c^3 \left(16 a^5 x^5+9 a^4 x^4-32 a^3 x^3-3 a^2 x^2+15 a^4 x^4 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+16 a x-6\right)}{24 x^4 \sqrt{1-a^2 x^2}}","-\frac{5 a^2 c^3 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}+\frac{2 a c^3 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}+\frac{5}{8} a^4 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(c^3*(-6 + 16*a*x - 3*a^2*x^2 - 32*a^3*x^3 + 9*a^4*x^4 + 16*a^5*x^5 + 15*a^4*x^4*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(24*x^4*Sqrt[1 - a^2*x^2])","A",1
315,1,107,129,0.0366299,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^6} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^6,x]","-\frac{c^3 \left(28 a^6 x^6-15 a^5 x^5-44 a^4 x^4+45 a^3 x^3+4 a^2 x^2+15 a^5 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-30 a x+12\right)}{60 x^5 \sqrt{1-a^2 x^2}}","-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}+\frac{a c^3 \left(1-a^2 x^2\right)^{3/2}}{2 x^4}-\frac{7 a^2 c^3 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}-\frac{1}{4} a^5 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{a^3 c^3 \sqrt{1-a^2 x^2}}{4 x^2}",1,"-1/60*(c^3*(12 - 30*a*x + 4*a^2*x^2 + 45*a^3*x^3 - 44*a^4*x^4 - 15*a^5*x^5 + 28*a^6*x^6 + 15*a^5*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x^5*Sqrt[1 - a^2*x^2])","A",1
316,1,99,173,0.2306584,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x)^4 \, dx","Integrate[E^ArcTanh[a*x]*x^3*(c - a*c*x)^4,x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(1680 a^7 x^7-5760 a^6 x^6+6440 a^5 x^5-1536 a^4 x^4-2030 a^3 x^3+2432 a^2 x^2-3045 a x+4864\right)-6090 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{13440 a^4}","-\frac{29 c^4 \sin ^{-1}(a x)}{128 a^4}-\frac{19 c^4 x^2 \left(1-a^2 x^2\right)^{3/2}}{35 a^2}+\frac{1}{8} a c^4 x^5 \left(1-a^2 x^2\right)^{3/2}-\frac{3}{7} c^4 x^4 \left(1-a^2 x^2\right)^{3/2}+\frac{29 c^4 x^3 \left(1-a^2 x^2\right)^{3/2}}{48 a}-\frac{c^4 (2432-3045 a x) \left(1-a^2 x^2\right)^{3/2}}{6720 a^4}-\frac{29 c^4 x \sqrt{1-a^2 x^2}}{128 a^3}",1,"-1/13440*(c^4*(Sqrt[1 - a^2*x^2]*(4864 - 3045*a*x + 2432*a^2*x^2 - 2030*a^3*x^3 - 1536*a^4*x^4 + 6440*a^5*x^5 - 5760*a^6*x^6 + 1680*a^7*x^7) - 6090*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a^4","A",0
317,1,91,146,0.1110158,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x)^4 \, dx","Integrate[E^ArcTanh[a*x]*x^2*(c - a*c*x)^4,x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(48 a^6 x^6-168 a^5 x^5+192 a^4 x^4-42 a^3 x^3-80 a^2 x^2+105 a x-160\right)+210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{336 a^3}","\frac{5 c^4 \sin ^{-1}(a x)}{16 a^3}+\frac{5 c^4 x^2 \left(1-a^2 x^2\right)^{3/2}}{7 a}+\frac{5 c^4 x \sqrt{1-a^2 x^2}}{16 a^2}+\frac{1}{7} a c^4 x^4 \left(1-a^2 x^2\right)^{3/2}-\frac{1}{2} c^4 x^3 \left(1-a^2 x^2\right)^{3/2}+\frac{5 c^4 (16-21 a x) \left(1-a^2 x^2\right)^{3/2}}{168 a^3}",1,"-1/336*(c^4*(Sqrt[1 - a^2*x^2]*(-160 + 105*a*x - 80*a^2*x^2 - 42*a^3*x^3 + 192*a^4*x^4 - 168*a^5*x^5 + 48*a^6*x^6) + 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a^3","A",0
318,1,83,158,0.1333377,"\int e^{\tanh ^{-1}(a x)} x (c-a c x)^4 \, dx","Integrate[E^ArcTanh[a*x]*x*(c - a*c*x)^4,x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(40 a^5 x^5-144 a^4 x^4+170 a^3 x^3-32 a^2 x^2-105 a x+176\right)-210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{240 a^2}","-\frac{c^4 (1-a x)^3 \left(1-a^2 x^2\right)^{3/2}}{6 a^2}-\frac{c^4 (1-a x)^2 \left(1-a^2 x^2\right)^{3/2}}{10 a^2}-\frac{7 c^4 (1-a x) \left(1-a^2 x^2\right)^{3/2}}{40 a^2}-\frac{7 c^4 \left(1-a^2 x^2\right)^{3/2}}{24 a^2}-\frac{7 c^4 x \sqrt{1-a^2 x^2}}{16 a}-\frac{7 c^4 \sin ^{-1}(a x)}{16 a^2}",1,"-1/240*(c^4*(Sqrt[1 - a^2*x^2]*(176 - 105*a*x - 32*a^2*x^2 + 170*a^3*x^3 - 144*a^4*x^4 + 40*a^5*x^5) - 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a^2","A",0
319,1,75,123,0.100289,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Integrate[E^ArcTanh[a*x]*(c - a*c*x)^4,x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(24 a^4 x^4-90 a^3 x^3+112 a^2 x^2-15 a x-136\right)+210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{120 a}","\frac{c^4 (1-a x)^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}+\frac{7 c^4 (1-a x) \left(1-a^2 x^2\right)^{3/2}}{20 a}+\frac{7 c^4 \left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{7}{8} c^4 x \sqrt{1-a^2 x^2}+\frac{7 c^4 \sin ^{-1}(a x)}{8 a}",1,"-1/120*(c^4*(Sqrt[1 - a^2*x^2]*(-136 - 15*a*x + 112*a^2*x^2 - 90*a^3*x^3 + 24*a^4*x^4) + 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
320,1,142,101,0.097947,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x,x]","\frac{c^4 \left(2 a^5 x^5-8 a^4 x^4+9 a^3 x^3+8 a^2 x^2+4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+34 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-8 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-11 a x\right)}{8 \sqrt{1-a^2 x^2}}","\frac{1}{4} a c^4 x \left(1-a^2 x^2\right)^{3/2}-c^4 \left(1-a^2 x^2\right)^{3/2}+\frac{1}{8} c^4 (8-13 a x) \sqrt{1-a^2 x^2}-c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{13}{8} c^4 \sin ^{-1}(a x)",1,"(c^4*(-11*a*x + 8*a^2*x^2 + 9*a^3*x^3 - 8*a^4*x^4 + 2*a^5*x^5 + 4*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 34*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 8*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(8*Sqrt[1 - a^2*x^2])","A",0
321,1,152,106,0.1293185,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^2,x]","-\frac{c^4 \left(-2 a^5 x^5+9 a^4 x^4-14 a^3 x^3-15 a^2 x^2+9 a x \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+24 a x \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-18 a x \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+16 a x+6\right)}{6 x \sqrt{1-a^2 x^2}}","\frac{1}{3} a c^4 \left(1-a^2 x^2\right)^{3/2}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{x}-\frac{1}{2} a c^4 (6-a x) \sqrt{1-a^2 x^2}+3 a c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{1}{2} a c^4 \sin ^{-1}(a x)",1,"-1/6*(c^4*(6 + 16*a*x - 15*a^2*x^2 - 14*a^3*x^3 + 9*a^4*x^4 - 2*a^5*x^5 + 9*a*x*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 24*a*x*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 18*a*x*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x*Sqrt[1 - a^2*x^2])","A",0
322,1,106,116,0.2272851,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^3,x]","\frac{1}{4} c^4 \left(-10 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+5 a^2 \sin ^{-1}(a x)-10 a^2 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)+\frac{2 (a x+1)^2 \left(a^3 x^3-8 a^2 x^2+8 a x-1\right)}{x^2 \sqrt{1-a^2 x^2}}\right)","\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{x}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{2 x^2}+\frac{5}{2} a^2 c^4 (a x+1) \sqrt{1-a^2 x^2}-\frac{5}{2} a^2 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{5}{2} a^2 c^4 \sin ^{-1}(a x)",1,"(c^4*((2*(1 + a*x)^2*(-1 + 8*a*x - 8*a^2*x^2 + a^3*x^3))/(x^2*Sqrt[1 - a^2*x^2]) + 5*a^2*ArcSin[a*x] - 10*a^2*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 10*a^2*ArcTanh[Sqrt[1 - a^2*x^2]]))/4","A",0
323,1,164,120,0.138171,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^4} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^4,x]","\frac{c^4 \left(12 a^5 x^5+32 a^4 x^4-30 a^3 x^3-28 a^2 x^2+3 a^3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+78 a^3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-6 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+18 a x-4\right)}{12 x^3 \sqrt{1-a^2 x^2}}","-3 a^3 c^4 \sin ^{-1}(a x)+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{2 x^2}-\frac{a^2 c^4 (6-a x) \sqrt{1-a^2 x^2}}{2 x}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{1}{2} a^3 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(c^4*(-4 + 18*a*x - 28*a^2*x^2 - 30*a^3*x^3 + 32*a^4*x^4 + 12*a^5*x^5 + 3*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 78*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] - 6*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(12*x^3*Sqrt[1 - a^2*x^2])","A",0
324,1,125,110,0.2288901,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^5} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^5,x]","\frac{1}{16} c^4 \left(-13 a^4 \sin ^{-1}(a x)+26 a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{2 \left(-11 a^4 x^4+8 a^3 x^3+9 a^2 x^2+29 a^4 x^4 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-8 a x+2\right)}{x^4 \sqrt{1-a^2 x^2}}\right)","a^4 c^4 \sin ^{-1}(a x)-\frac{11 a^2 c^4 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{c^4 \sqrt{1-a^2 x^2}}{4 x^4}+\frac{a c^4 \sqrt{1-a^2 x^2}}{x^3}+\frac{13}{8} a^4 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(c^4*(-13*a^4*ArcSin[a*x] - (2*(2 - 8*a*x + 9*a^2*x^2 + 8*a^3*x^3 - 11*a^4*x^4 + 29*a^4*x^4*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(x^4*Sqrt[1 - a^2*x^2]) + 26*a^4*ArcTanh[Sqrt[1 - a^2*x^2]]))/16","A",0
325,1,107,129,0.0357105,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^6} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^6,x]","-\frac{c^4 \left(136 a^6 x^6+15 a^5 x^5-248 a^4 x^4+75 a^3 x^3+88 a^2 x^2+105 a^5 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-90 a x+24\right)}{120 x^5 \sqrt{1-a^2 x^2}}","-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{17 a^2 c^4 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}-\frac{7}{8} a^5 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{7 a^3 c^4 \sqrt{1-a^2 x^2}}{8 x^2}",1,"-1/120*(c^4*(24 - 90*a*x + 88*a^2*x^2 + 75*a^3*x^3 - 248*a^4*x^4 + 15*a^5*x^5 + 136*a^6*x^6 + 105*a^5*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(x^5*Sqrt[1 - a^2*x^2])","A",1
326,1,115,156,0.0392512,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^7} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^7,x]","\frac{c^4 \left(176 a^7 x^7-105 a^6 x^6-208 a^5 x^5+275 a^4 x^4-112 a^3 x^3-130 a^2 x^2+105 a^6 x^6 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+144 a x-40\right)}{240 x^6 \sqrt{1-a^2 x^2}}","-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{6 x^6}+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{7 a^2 c^4 \left(1-a^2 x^2\right)^{3/2}}{8 x^4}+\frac{7}{16} a^6 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{7 a^4 c^4 \sqrt{1-a^2 x^2}}{16 x^2}+\frac{11 a^3 c^4 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}",1,"(c^4*(-40 + 144*a*x - 130*a^2*x^2 - 112*a^3*x^3 + 275*a^4*x^4 - 208*a^5*x^5 - 105*a^6*x^6 + 176*a^7*x^7 + 105*a^6*x^6*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(240*x^6*Sqrt[1 - a^2*x^2])","A",1
327,1,81,146,0.0681705,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{c-a c x} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a*c*x),x]","\frac{162 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-\frac{\sqrt{a x+1} \left(6 a^4 x^4+10 a^3 x^3+17 a^2 x^2+47 a x-128\right)}{\sqrt{1-a x}}}{24 a^5 c}","-\frac{27 \sin ^{-1}(a x)}{8 a^5 c}+\frac{x^3 \sqrt{1-a^2 x^2}}{4 a^2 c}+\frac{13 \sqrt{1-a^2 x^2}}{3 a^5 c}+\frac{(a x+1)^2}{a^5 c \sqrt{1-a^2 x^2}}+\frac{11 x \sqrt{1-a^2 x^2}}{8 a^4 c}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{3 a^3 c}",1,"(-((Sqrt[1 + a*x]*(-128 + 47*a*x + 17*a^2*x^2 + 10*a^3*x^3 + 6*a^4*x^4))/Sqrt[1 - a*x]) + 162*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(24*a^5*c)","A",0
328,1,72,114,0.0512508,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{c-a c x} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a*c*x),x]","\frac{18 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-\frac{\sqrt{a x+1} \left(a^3 x^3+2 a^2 x^2+5 a x-14\right)}{\sqrt{1-a x}}}{3 a^4 c}","-\frac{3 \sin ^{-1}(a x)}{a^4 c}+\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2 c}+\frac{11 \sqrt{1-a^2 x^2}}{3 a^4 c}+\frac{(a x+1)^2}{a^4 c \sqrt{1-a^2 x^2}}+\frac{x \sqrt{1-a^2 x^2}}{a^3 c}",1,"(-((Sqrt[1 + a*x]*(-14 + 5*a*x + 2*a^2*x^2 + a^3*x^3))/Sqrt[1 - a*x]) + 18*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(3*a^4*c)","A",0
329,1,64,72,0.0458632,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{c-a c x} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a*c*x),x]","\frac{10 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)-\frac{\sqrt{a x+1} \left(a^2 x^2+3 a x-8\right)}{\sqrt{1-a x}}}{2 a^3 c}","-\frac{5 \sin ^{-1}(a x)}{2 a^3 c}+\frac{(a x+1)^2}{a^3 c \sqrt{1-a^2 x^2}}+\frac{(a x+6) \sqrt{1-a^2 x^2}}{2 a^3 c}",1,"(-((Sqrt[1 + a*x]*(-8 + 3*a*x + a^2*x^2))/Sqrt[1 - a*x]) + 10*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(2*a^3*c)","A",0
330,1,53,64,0.038163,"\int \frac{e^{\tanh ^{-1}(a x)} x}{c-a c x} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a*c*x),x]","\frac{\frac{\sqrt{a x+1} (3-a x)}{\sqrt{1-a x}}+4 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{a^2 c}","\frac{\left(1-a^2 x^2\right)^{3/2}}{a^2 c (1-a x)^2}+\frac{2 \sqrt{1-a^2 x^2}}{a^2 c}-\frac{2 \sin ^{-1}(a x)}{a^2 c}",1,"(((3 - a*x)*Sqrt[1 + a*x])/Sqrt[1 - a*x] + 4*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(a^2*c)","A",0
331,1,46,43,0.0232985,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x),x]","\frac{2 \left(\frac{\sqrt{a x+1}}{\sqrt{1-a x}}+\sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{a c}","\frac{2 \sqrt{1-a^2 x^2}}{a c (1-a x)}-\frac{\sin ^{-1}(a x)}{a c}",1,"(2*(Sqrt[1 + a*x]/Sqrt[1 - a*x] + ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*c)","A",0
332,1,55,45,0.0245034,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a*c*x)),x]","\frac{-\sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a x+2}{c \sqrt{1-a^2 x^2}}","\frac{2 (a x+1)}{c \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"(2 + 2*a*x - Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*Sqrt[1 - a^2*x^2])","A",1
333,1,68,69,0.0264782,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a*c*x)),x]","\frac{3 a^2 x^2-2 a x \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a x-1}{c x \sqrt{1-a^2 x^2}}","\frac{2 a (a x+1)}{c \sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2}}{c x}-\frac{2 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"(-1 + 2*a*x + 3*a^2*x^2 - 2*a*x*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*x*Sqrt[1 - a^2*x^2])","A",1
334,1,83,100,0.0407091,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a*c*x)),x]","-\frac{-8 a^3 x^3-5 a^2 x^2+5 a^2 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+4 a x+1}{2 c x^2 \sqrt{1-a^2 x^2}}","\frac{2 a^2 (a x+1)}{c \sqrt{1-a^2 x^2}}-\frac{2 a \sqrt{1-a^2 x^2}}{c x}-\frac{\sqrt{1-a^2 x^2}}{2 c x^2}-\frac{5 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c}",1,"-1/2*(1 + 4*a*x - 5*a^2*x^2 - 8*a^3*x^3 + 5*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*x^2*Sqrt[1 - a^2*x^2])","A",1
335,1,91,125,0.0446027,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 (c-a c x)} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(c - a*c*x)),x]","-\frac{-14 a^4 x^4-9 a^3 x^3+7 a^2 x^2+9 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+3 a x+1}{3 c x^3 \sqrt{1-a^2 x^2}}","-\frac{8 a^2 \sqrt{1-a^2 x^2}}{3 c x}-\frac{a \sqrt{1-a^2 x^2}}{c x^2}-\frac{\sqrt{1-a^2 x^2}}{3 c x^3}+\frac{2 a^3 (a x+1)}{c \sqrt{1-a^2 x^2}}-\frac{3 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"-1/3*(1 + 3*a*x + 7*a^2*x^2 - 9*a^3*x^3 - 14*a^4*x^4 + 9*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*x^3*Sqrt[1 - a^2*x^2])","A",1
336,1,80,159,0.1041527,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{(c-a c x)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a*c*x)^2,x]","-\frac{\frac{\sqrt{a x+1} \left(2 a^4 x^4+5 a^3 x^3+18 a^2 x^2-109 a x+80\right)}{(1-a x)^{3/2}}+102 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{6 a^5 c^2}","\frac{17 \sin ^{-1}(a x)}{2 a^5 c^2}-\frac{2 (a x+1)^3}{a^5 c^2 \sqrt{1-a^2 x^2}}+\frac{(a x+1)^3}{3 a^5 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{(a x+5)^2 \sqrt{1-a^2 x^2}}{3 a^5 c^2}-\frac{(a x+5) \sqrt{1-a^2 x^2}}{6 a^5 c^2}-\frac{5 \sqrt{1-a^2 x^2}}{2 a^5 c^2}",1,"-1/6*((Sqrt[1 + a*x]*(80 - 109*a*x + 18*a^2*x^2 + 5*a^3*x^3 + 2*a^4*x^4))/(1 - a*x)^(3/2) + 102*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(a^5*c^2)","A",0
337,1,72,104,0.0859449,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{(c-a c x)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a*c*x)^2,x]","-\frac{\frac{\sqrt{a x+1} \left(3 a^3 x^3+12 a^2 x^2-71 a x+52\right)}{(1-a x)^{3/2}}+66 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{6 a^4 c^2}","\frac{11 \sin ^{-1}(a x)}{2 a^4 c^2}+\frac{(a x+1)^3}{3 a^4 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{3 (a x+1)^2}{a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{(a x+12) \sqrt{1-a^2 x^2}}{2 a^4 c^2}",1,"-1/6*((Sqrt[1 + a*x]*(52 - 71*a*x + 12*a^2*x^2 + 3*a^3*x^3))/(1 - a*x)^(3/2) + 66*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(a^4*c^2)","A",0
338,1,64,104,0.0758665,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{(c-a c x)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a*c*x)^2,x]","\frac{\frac{\sqrt{a x+1} \left(-3 a^2 x^2+19 a x-14\right)}{(1-a x)^{3/2}}-18 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{3 a^3 c^2}","\frac{3 \sin ^{-1}(a x)}{a^3 c^2}+\frac{\left(1-a^2 x^2\right)^{3/2}}{a^3 c^2 (1-a x)^2}+\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3 c^2 (1-a x)^3}-\frac{6 \sqrt{1-a^2 x^2}}{a^3 c^2 (1-a x)}",1,"((Sqrt[1 + a*x]*(-14 + 19*a*x - 3*a^2*x^2))/(1 - a*x)^(3/2) - 18*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(3*a^3*c^2)","A",0
339,1,57,74,0.0644715,"\int \frac{e^{\tanh ^{-1}(a x)} x}{(c-a c x)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a*c*x)^2,x]","-\frac{(a x+1)^{3/2}-4 \sqrt{2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1}{2} (1-a x)\right)}{3 a^2 c^2 (1-a x)^{3/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^2 c^2 (1-a x)^3}-\frac{2 \sqrt{1-a^2 x^2}}{a^2 c^2 (1-a x)}+\frac{\sin ^{-1}(a x)}{a^2 c^2}",1,"-1/3*((1 + a*x)^(3/2) - 4*Sqrt[2]*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - a*x)/2])/(a^2*c^2*(1 - a*x)^(3/2))","C",0
340,1,29,32,0.0102213,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^2,x]","\frac{(a x+1)^{3/2}}{3 a c^2 (1-a x)^{3/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}",1,"(1 + a*x)^(3/2)/(3*a*c^2*(1 - a*x)^(3/2))","A",0
341,1,78,74,0.0380229,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a*c*x)^2),x]","\frac{5 a^2 x^2-3 (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-2 a x-7}{3 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{4 (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{5 a x+3}{3 c^2 \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^2}",1,"(-7 - 2*a*x + 5*a^2*x^2 - 3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(3*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
342,1,91,99,0.0440944,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a*c*x)^2),x]","\frac{14 a^3 x^3-5 a^2 x^2-9 a x (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-16 a x+3}{3 c^2 x (a x-1) \sqrt{1-a^2 x^2}}","\frac{4 a (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{\sqrt{1-a^2 x^2}}{c^2 x}+\frac{a (11 a x+9)}{3 c^2 \sqrt{1-a^2 x^2}}-\frac{3 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^2}",1,"(3 - 16*a*x - 5*a^2*x^2 + 14*a^3*x^3 - 9*a*x*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(3*c^2*x*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
343,1,103,132,0.053869,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a*c*x)^2),x]","\frac{52 a^4 x^4-19 a^3 x^3-59 a^2 x^2-33 a^2 x^2 (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+15 a x+3}{6 c^2 x^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{a^2 (17 a x+15)}{3 c^2 \sqrt{1-a^2 x^2}}+\frac{4 a^2 (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{3 a \sqrt{1-a^2 x^2}}{c^2 x}-\frac{\sqrt{1-a^2 x^2}}{2 c^2 x^2}-\frac{11 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^2}",1,"(3 + 15*a*x - 59*a^2*x^2 - 19*a^3*x^3 + 52*a^4*x^4 - 33*a^2*x^2*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(6*c^2*x^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
344,1,111,161,0.0587609,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 (c-a c x)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(c - a*c*x)^2),x]","\frac{80 a^5 x^5-29 a^4 x^4-91 a^3 x^3+23 a^2 x^2-51 a^3 x^3 (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+7 a x+2}{6 c^2 x^3 (a x-1) \sqrt{1-a^2 x^2}}","-\frac{17 a^2 \sqrt{1-a^2 x^2}}{3 c^2 x}-\frac{3 a \sqrt{1-a^2 x^2}}{2 c^2 x^2}-\frac{\sqrt{1-a^2 x^2}}{3 c^2 x^3}+\frac{a^3 (23 a x+21)}{3 c^2 \sqrt{1-a^2 x^2}}+\frac{4 a^3 (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{17 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^2}",1,"(2 + 7*a*x + 23*a^2*x^2 - 91*a^3*x^3 - 29*a^4*x^4 + 80*a^5*x^5 - 51*a^3*x^3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(6*c^2*x^3*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
345,1,122,135,0.1482225,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{(c-a c x)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a*c*x)^3,x]","\frac{\sqrt{a x+1} \left(-15 a^4 x^4-75 a^3 x^3+433 a^2 x^2-639 a x+308\right)+140 \sqrt{2} (a x-1) \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1}{2} (1-a x)\right)+360 (1-a x)^{5/2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{30 a^5 c^3 (1-a x)^{5/2}}","-\frac{19 \sin ^{-1}(a x)}{2 a^5 c^3}+\frac{(a x+1)^4}{5 a^5 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{19 (a x+1)^3}{15 a^5 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 (a x+1)^2}{a^5 c^3 \sqrt{1-a^2 x^2}}+\frac{(a x+20) \sqrt{1-a^2 x^2}}{2 a^5 c^3}",1,"(Sqrt[1 + a*x]*(308 - 639*a*x + 433*a^2*x^2 - 75*a^3*x^3 - 15*a^4*x^4) + 360*(1 - a*x)^(5/2)*ArcSin[Sqrt[1 - a*x]/Sqrt[2]] + 140*Sqrt[2]*(-1 + a*x)*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - a*x)/2])/(30*a^5*c^3*(1 - a*x)^(5/2))","C",0
346,1,72,137,0.0756141,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{(c-a c x)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a*c*x)^3,x]","\frac{\frac{\sqrt{a x+1} \left(-15 a^3 x^3+149 a^2 x^2-222 a x+94\right)}{(1-a x)^{5/2}}+120 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{15 a^4 c^3}","-\frac{4 \sin ^{-1}(a x)}{a^4 c^3}-\frac{\left(1-a^2 x^2\right)^{3/2}}{a^4 c^3 (1-a x)^2}-\frac{14 \left(1-a^2 x^2\right)^{3/2}}{15 a^4 c^3 (1-a x)^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a^4 c^3 (1-a x)^4}+\frac{8 \sqrt{1-a^2 x^2}}{a^4 c^3 (1-a x)}",1,"((Sqrt[1 + a*x]*(94 - 222*a*x + 149*a^2*x^2 - 15*a^3*x^3))/(1 - a*x)^(5/2) + 120*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(15*a^4*c^3)","A",0
347,1,77,107,0.0634384,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{(c-a c x)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a*c*x)^3,x]","\frac{\sqrt{a x+1} \left(-a^2 x^2+3 a x+4\right)+20 \sqrt{2} (a x-1) \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1}{2} (1-a x)\right)}{15 a^3 c^3 (1-a x)^{5/2}}","-\frac{\sin ^{-1}(a x)}{a^3 c^3}-\frac{3 \left(1-a^2 x^2\right)^{3/2}}{5 a^3 c^3 (1-a x)^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a^3 c^3 (1-a x)^4}+\frac{2 \sqrt{1-a^2 x^2}}{a^3 c^3 (1-a x)}",1,"(Sqrt[1 + a*x]*(4 + 3*a*x - a^2*x^2) + 20*Sqrt[2]*(-1 + a*x)*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - a*x)/2])/(15*a^3*c^3*(1 - a*x)^(5/2))","C",0
348,1,35,65,0.0195408,"\int \frac{e^{\tanh ^{-1}(a x)} x}{(c-a c x)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a*c*x)^3,x]","\frac{(a x+1)^{3/2} (4 a x-1)}{15 a^2 c^3 (1-a x)^{5/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a^2 c^3 (1-a x)^4}-\frac{4 \left(1-a^2 x^2\right)^{3/2}}{15 a^2 c^3 (1-a x)^3}",1,"((1 + a*x)^(3/2)*(-1 + 4*a*x))/(15*a^2*c^3*(1 - a*x)^(5/2))","A",0
349,1,35,65,0.0171408,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^3,x]","\frac{(4-a x) (a x+1)^{3/2}}{15 a c^3 (1-a x)^{5/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{15 a c^3 (1-a x)^3}+\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a c^3 (1-a x)^4}",1,"((4 - a*x)*(1 + a*x)^(3/2))/(15*a*c^3*(1 - a*x)^(5/2))","A",0
350,1,71,97,0.0930544,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a*c*x)^3),x]","\frac{24 a^5 x^5-60 a^3 x^3+3 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};1-a^2 x^2\right)+5 a^2 x^2+60 a x+16}{15 c^3 \left(1-a^2 x^2\right)^{5/2}}","\frac{4 a x}{5 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{8 a x+5}{5 c^3 \sqrt{1-a^2 x^2}}+\frac{8 (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^3}",1,"(16 + 60*a*x + 5*a^2*x^2 - 60*a^3*x^3 + 24*a^5*x^5 + 3*Hypergeometric2F1[-5/2, 1, -3/2, 1 - a^2*x^2])/(15*c^3*(1 - a^2*x^2)^(5/2))","C",0
351,1,101,127,0.0605568,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a*c*x)^3),x]","\frac{94 a^4 x^4-128 a^3 x^3-73 a^2 x^2-60 a x (a x-1)^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+134 a x-15}{15 c^3 x (a x-1)^2 \sqrt{1-a^2 x^2}}","\frac{8 a (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{\sqrt{1-a^2 x^2}}{c^3 x}+\frac{a (79 a x+60)}{15 c^3 \sqrt{1-a^2 x^2}}+\frac{4 a (8 a x+5)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{4 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^3}",1,"(-15 + 134*a*x - 73*a^2*x^2 - 128*a^3*x^3 + 94*a^4*x^4 - 60*a*x*(-1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(15*c^3*x*(-1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
352,1,113,162,0.0625224,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a*c*x)^3),x]","\frac{448 a^5 x^5-611 a^4 x^4-346 a^3 x^3+638 a^2 x^2-285 a^2 x^2 (a x-1)^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-90 a x-15}{30 c^3 x^2 (a x-1)^2 \sqrt{1-a^2 x^2}}","\frac{a^2 (164 a x+135)}{15 c^3 \sqrt{1-a^2 x^2}}+\frac{4 a^2 (13 a x+10)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{8 a^2 (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{4 a \sqrt{1-a^2 x^2}}{c^3 x}-\frac{\sqrt{1-a^2 x^2}}{2 c^3 x^2}-\frac{19 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^3}",1,"(-15 - 90*a*x + 638*a^2*x^2 - 346*a^3*x^3 - 611*a^4*x^4 + 448*a^5*x^5 - 285*a^2*x^2*(-1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(30*c^3*x^2*(-1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
353,1,121,187,0.0635806,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 (c-a c x)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(c - a*c*x)^3),x]","\frac{424 a^6 x^6-578 a^5 x^5-328 a^4 x^4+604 a^3 x^3-85 a^2 x^2-270 a^3 x^3 (a x-1)^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-20 a x-5}{15 c^3 x^3 (a x-1)^2 \sqrt{1-a^2 x^2}}","-\frac{29 a^2 \sqrt{1-a^2 x^2}}{3 c^3 x}-\frac{2 a \sqrt{1-a^2 x^2}}{c^3 x^2}-\frac{\sqrt{1-a^2 x^2}}{3 c^3 x^3}+\frac{a^3 (93 a x+80)}{5 c^3 \sqrt{1-a^2 x^2}}+\frac{4 a^3 (6 a x+5)}{5 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{8 a^3 (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{18 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^3}",1,"(-5 - 20*a*x - 85*a^2*x^2 + 604*a^3*x^3 - 328*a^4*x^4 - 578*a^5*x^5 + 424*a^6*x^6 - 270*a^3*x^3*(-1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(15*c^3*x^3*(-1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
354,1,126,166,0.3414463,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{(c-a c x)^4} \, dx","Integrate[(E^ArcTanh[a*x]*x^5)/(c - a*c*x)^4,x]","-\frac{(a x+1) \left(\sqrt{1-a^2 x^2} \left(105 a^5 x^5+630 a^4 x^4-8404 a^3 x^3+18916 a^2 x^2-16091 a x+4784\right)-945 (a x-1)^4 \sin ^{-1}(a x)+4200 (a x-1)^4 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{210 a^6 c^4 (a x-1)^3 \left(a^2 x^2-1\right)}","\frac{29 \sin ^{-1}(a x)}{2 a^6 c^4}+\frac{(a x+1)^5}{7 a^6 c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{33 (a x+1)^4}{35 a^6 c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{317 (a x+1)^3}{105 a^6 c^4 \left(1-a^2 x^2\right)^{3/2}}-\frac{10 (a x+1)^2}{a^6 c^4 \sqrt{1-a^2 x^2}}-\frac{(a x+30) \sqrt{1-a^2 x^2}}{2 a^6 c^4}",1,"-1/210*((1 + a*x)*(Sqrt[1 - a^2*x^2]*(4784 - 16091*a*x + 18916*a^2*x^2 - 8404*a^3*x^3 + 630*a^4*x^4 + 105*a^5*x^5) - 945*(-1 + a*x)^4*ArcSin[a*x] + 4200*(-1 + a*x)^4*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a^6*c^4*(-1 + a*x)^3*(-1 + a^2*x^2))","A",0
355,1,95,168,0.0922669,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{(c-a c x)^4} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a*c*x)^4,x]","-\frac{\sqrt{a x+1} \left(105 a^4 x^4-44 a^3 x^3-244 a^2 x^2+29 a x+124\right)-700 \sqrt{2} (a x-1)^2 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};\frac{1}{2} (1-a x)\right)}{105 a^5 c^4 (1-a x)^{7/2}}","\frac{5 \sin ^{-1}(a x)}{a^5 c^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{a^5 c^4 (1-a x)^2}+\frac{184 \left(1-a^2 x^2\right)^{3/2}}{105 a^5 c^4 (1-a x)^3}-\frac{26 \left(1-a^2 x^2\right)^{3/2}}{35 a^5 c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^5 c^4 (1-a x)^5}-\frac{10 \sqrt{1-a^2 x^2}}{a^5 c^4 (1-a x)}",1,"-1/105*(Sqrt[1 + a*x]*(124 + 29*a*x - 244*a^2*x^2 - 44*a^3*x^3 + 105*a^4*x^4) - 700*Sqrt[2]*(-1 + a*x)^2*Hypergeometric2F1[-3/2, -3/2, -1/2, (1 - a*x)/2])/(a^5*c^4*(1 - a*x)^(7/2))","C",0
356,1,94,138,0.2472787,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{(c-a c x)^4} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a*c*x)^4,x]","\frac{\sqrt{a x+1} \left(\sqrt{1-a^2 x^2} \left(296 a^3 x^3-659 a^2 x^2+559 a x-166\right)+105 (a x-1)^4 \sin ^{-1}(a x)\right)}{105 a^4 c^4 (1-a x)^{7/2} \sqrt{1-a^2 x^2}}","\frac{\sin ^{-1}(a x)}{a^4 c^4}+\frac{86 \left(1-a^2 x^2\right)^{3/2}}{105 a^4 c^4 (1-a x)^3}-\frac{19 \left(1-a^2 x^2\right)^{3/2}}{35 a^4 c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^4 c^4 (1-a x)^5}-\frac{2 \sqrt{1-a^2 x^2}}{a^4 c^4 (1-a x)}",1,"(Sqrt[1 + a*x]*(Sqrt[1 - a^2*x^2]*(-166 + 559*a*x - 659*a^2*x^2 + 296*a^3*x^3) + 105*(-1 + a*x)^4*ArcSin[a*x]))/(105*a^4*c^4*(1 - a*x)^(7/2)*Sqrt[1 - a^2*x^2])","A",0
357,1,43,97,0.0277135,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{(c-a c x)^4} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a*c*x)^4,x]","-\frac{(a x+1)^{3/2} \left(-23 a^2 x^2+10 a x-2\right)}{105 a^3 c^4 (1-a x)^{7/2}}","\frac{23 \left(1-a^2 x^2\right)^{3/2}}{105 a^3 c^4 (1-a x)^3}-\frac{12 \left(1-a^2 x^2\right)^{3/2}}{35 a^3 c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^3 c^4 (1-a x)^5}",1,"-1/105*((1 + a*x)^(3/2)*(-2 + 10*a*x - 23*a^2*x^2))/(a^3*c^4*(1 - a*x)^(7/2))","A",0
358,1,42,97,0.0206372,"\int \frac{e^{\tanh ^{-1}(a x)} x}{(c-a c x)^4} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a*c*x)^4,x]","-\frac{(a x+1)^{3/2} \left(a^2 x^2-5 a x+1\right)}{21 a^2 c^4 (1-a x)^{7/2}}","-\frac{\left(1-a^2 x^2\right)^{3/2}}{21 a^2 c^4 (1-a x)^3}-\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^2 c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a^2 c^4 (1-a x)^5}",1,"-1/21*((1 + a*x)^(3/2)*(1 - 5*a*x + a^2*x^2))/(a^2*c^4*(1 - a*x)^(7/2))","A",0
359,1,43,97,0.0211436,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[E^ArcTanh[a*x]/(c - a*c*x)^4,x]","-\frac{(a x+1)^{3/2} \left(-2 a^2 x^2+10 a x-23\right)}{105 a c^4 (1-a x)^{7/2}}","\frac{2 \left(1-a^2 x^2\right)^{3/2}}{105 a c^4 (1-a x)^3}+\frac{2 \left(1-a^2 x^2\right)^{3/2}}{35 a c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a c^4 (1-a x)^5}",1,"-1/105*((1 + a*x)^(3/2)*(-23 + 10*a*x - 2*a^2*x^2))/(a*c^4*(1 - a*x)^(7/2))","A",0
360,1,79,128,0.1827941,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)^4} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a*c*x)^4),x]","\frac{-166 a^7 x^7+581 a^5 x^5-700 a^3 x^3+15 \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};1-a^2 x^2\right)+105 a^2 x^2+525 a x+120}{105 c^4 \left(1-a^2 x^2\right)^{7/2}}","-\frac{4 (7-3 a x)}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{166 a x+105}{105 c^4 \sqrt{1-a^2 x^2}}+\frac{83 a x+35}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{16 (a x+1)}{7 c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^4}",1,"(120 + 525*a*x + 105*a^2*x^2 - 700*a^3*x^3 + 581*a^5*x^5 - 166*a^7*x^7 + 15*Hypergeometric2F1[-7/2, 1, -5/2, 1 - a^2*x^2])/(105*c^4*(1 - a^2*x^2)^(7/2))","C",0
361,1,109,155,0.0673442,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)^4} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a*c*x)^4),x]","\frac{824 a^5 x^5-1947 a^4 x^4+485 a^3 x^3+1812 a^2 x^2-525 a x (a x-1)^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-1339 a x+105}{105 c^4 x (a x-1)^3 \sqrt{1-a^2 x^2}}","\frac{16 a (a x+1)}{7 c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{\sqrt{1-a^2 x^2}}{c^4 x}+\frac{a (719 a x+525)}{105 c^4 \sqrt{1-a^2 x^2}}+\frac{a (307 a x+175)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{4 a (17 a x+7)}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}-\frac{5 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^4}",1,"(105 - 1339*a*x + 1812*a^2*x^2 + 485*a^3*x^3 - 1947*a^4*x^4 + 824*a^5*x^5 - 525*a*x*(-1 + a*x)^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(105*c^4*x*(-1 + a*x)^3*Sqrt[1 - a^2*x^2])","A",1
362,1,121,192,0.0701987,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)^4} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a*c*x)^4),x]","\frac{4784 a^6 x^6-11307 a^5 x^5+2825 a^4 x^4+10512 a^3 x^3-7774 a^2 x^2-3045 a^2 x^2 (a x-1)^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+735 a x+105}{210 c^4 x^2 (a x-1)^3 \sqrt{1-a^2 x^2}}","\frac{a^2 (1867 a x+1470)}{105 c^4 \sqrt{1-a^2 x^2}}+\frac{a^2 (671 a x+455)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{4 a^2 (31 a x+21)}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{16 a^2 (a x+1)}{7 c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{5 a \sqrt{1-a^2 x^2}}{c^4 x}-\frac{\sqrt{1-a^2 x^2}}{2 c^4 x^2}-\frac{29 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^4}",1,"(105 + 735*a*x - 7774*a^2*x^2 + 10512*a^3*x^3 + 2825*a^4*x^4 - 11307*a^5*x^5 + 4784*a^6*x^6 - 3045*a^2*x^2*(-1 + a*x)^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(210*c^4*x^2*(-1 + a*x)^3*Sqrt[1 - a^2*x^2])","A",1
363,1,42,61,0.0302005,"\int e^{\tanh ^{-1}(x)} x (1+x) \, dx","Integrate[E^ArcTanh[x]*x*(1 + x),x]","-\frac{1}{3} \sqrt{1-x^2} \left(x^2+3 x+5\right)-2 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\frac{1}{3} \sqrt{1-x} (x+1)^{5/2}-\frac{1}{3} \sqrt{1-x} (x+1)^{3/2}-\sqrt{1-x} \sqrt{x+1}+\sin ^{-1}(x)",1,"-1/3*(Sqrt[1 - x^2]*(5 + 3*x + x^2)) - 2*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",0
364,1,37,47,0.0132249,"\int e^{\tanh ^{-1}(x)} (1+x) \, dx","Integrate[E^ArcTanh[x]*(1 + x),x]","-\frac{1}{2} \sqrt{1-x^2} (x+4)-3 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\frac{1}{2} \sqrt{1-x} (x+1)^{3/2}-\frac{3}{2} \sqrt{1-x} \sqrt{x+1}+\frac{3}{2} \sin ^{-1}(x)",1,"-1/2*((4 + x)*Sqrt[1 - x^2]) - 3*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",0
365,1,51,87,0.0314466,"\int e^{\tanh ^{-1}(x)} x (1+x)^2 \, dx","Integrate[E^ArcTanh[x]*x*(1 + x)^2,x]","\frac{1}{8} \left(-\sqrt{1-x^2} \left(2 x^3+8 x^2+15 x+24\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)\right)","-\frac{1}{4} \sqrt{1-x} (x+1)^{7/2}-\frac{1}{4} \sqrt{1-x} (x+1)^{5/2}-\frac{5}{8} \sqrt{1-x} (x+1)^{3/2}-\frac{15}{8} \sqrt{1-x} \sqrt{x+1}+\frac{15}{8} \sin ^{-1}(x)",1,"(-(Sqrt[1 - x^2]*(24 + 15*x + 8*x^2 + 2*x^3)) - 30*ArcSin[Sqrt[1 - x]/Sqrt[2]])/8","A",0
366,1,44,67,0.0238444,"\int e^{\tanh ^{-1}(x)} (1+x)^2 \, dx","Integrate[E^ArcTanh[x]*(1 + x)^2,x]","-\frac{1}{6} \sqrt{1-x^2} \left(2 x^2+9 x+22\right)-5 \sin ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\frac{1}{3} \sqrt{1-x} (x+1)^{5/2}-\frac{5}{6} \sqrt{1-x} (x+1)^{3/2}-\frac{5}{2} \sqrt{1-x} \sqrt{x+1}+\frac{5}{2} \sin ^{-1}(x)",1,"-1/6*(Sqrt[1 - x^2]*(22 + 9*x + 2*x^2)) - 5*ArcSin[Sqrt[1 - x]/Sqrt[2]]","A",0
367,1,13,18,0.0056544,"\int \frac{e^{\tanh ^{-1}(x)} x}{1+x} \, dx","Integrate[(E^ArcTanh[x]*x)/(1 + x),x]","-\sqrt{1-x^2}","-\sqrt{1-x} \sqrt{x+1}",1,"-Sqrt[1 - x^2]","A",1
368,1,2,2,0.0032114,"\int \frac{e^{\tanh ^{-1}(x)}}{1+x} \, dx","Integrate[E^ArcTanh[x]/(1 + x),x]","\sin ^{-1}(x)","\sin ^{-1}(x)",1,"ArcSin[x]","A",1
369,1,20,20,0.0348252,"\int \frac{e^{\tanh ^{-1}(x)} x}{(1+x)^2} \, dx","Integrate[(E^ArcTanh[x]*x)/(1 + x)^2,x]","\frac{\sqrt{1-x}}{\sqrt{x+1}}+\sin ^{-1}(x)","\frac{\sqrt{1-x}}{\sqrt{x+1}}+\sin ^{-1}(x)",1,"Sqrt[1 - x]/Sqrt[1 + x] + ArcSin[x]","A",1
370,1,18,18,0.0041873,"\int \frac{e^{\tanh ^{-1}(x)}}{(1+x)^2} \, dx","Integrate[E^ArcTanh[x]/(1 + x)^2,x]","-\frac{\sqrt{1-x}}{\sqrt{x+1}}","-\frac{\sqrt{1-x}}{\sqrt{x+1}}",1,"-(Sqrt[1 - x]/Sqrt[1 + x])","A",1
371,1,28,49,0.0118281,"\int e^{\tanh ^{-1}(x)} x (1+x)^{3/2} \, dx","Integrate[E^ArcTanh[x]*x*(1 + x)^(3/2),x]","-\frac{2}{21} \sqrt{1-x} \left(3 x^3+12 x^2+23 x+46\right)","\frac{2}{7} (1-x)^{7/2}-2 (1-x)^{5/2}+\frac{16}{3} (1-x)^{3/2}-8 \sqrt{1-x}",1,"(-2*Sqrt[1 - x]*(46 + 23*x + 12*x^2 + 3*x^3))/21","A",1
372,1,23,38,0.0088957,"\int e^{\tanh ^{-1}(x)} (1+x)^{3/2} \, dx","Integrate[E^ArcTanh[x]*(1 + x)^(3/2),x]","-\frac{2}{15} \sqrt{1-x} \left(3 x^2+14 x+43\right)","-\frac{2}{5} (1-x)^{5/2}+\frac{8}{3} (1-x)^{3/2}-8 \sqrt{1-x}",1,"(-2*Sqrt[1 - x]*(43 + 14*x + 3*x^2))/15","A",1
373,1,21,34,0.0107148,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} x \, dx","Integrate[E^ArcTanh[x]*(1 - x)^(3/2)*x,x]","-\frac{2}{105} (x+1)^{3/2} \left(15 x^2-33 x+22\right)","-\frac{2}{7} (x+1)^{7/2}+\frac{6}{5} (x+1)^{5/2}-\frac{4}{3} (x+1)^{3/2}",1,"(-2*(1 + x)^(3/2)*(22 - 33*x + 15*x^2))/105","A",1
374,1,16,23,0.0078126,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} \, dx","Integrate[E^ArcTanh[x]*(1 - x)^(3/2),x]","-\frac{2}{15} (x+1)^{3/2} (3 x-7)","\frac{4}{3} (x+1)^{3/2}-\frac{2}{5} (x+1)^{5/2}",1,"(-2*(1 + x)^(3/2)*(-7 + 3*x))/15","A",1
375,1,21,36,0.0084673,"\int e^{\tanh ^{-1}(x)} x \sqrt{1+x} \, dx","Integrate[E^ArcTanh[x]*x*Sqrt[1 + x],x]","-\frac{2}{5} \sqrt{1-x} \left(x^2+3 x+6\right)","-\frac{2}{5} (1-x)^{5/2}+2 (1-x)^{3/2}-4 \sqrt{1-x}",1,"(-2*Sqrt[1 - x]*(6 + 3*x + x^2))/5","A",1
376,1,16,25,0.0060877,"\int e^{\tanh ^{-1}(x)} \sqrt{1+x} \, dx","Integrate[E^ArcTanh[x]*Sqrt[1 + x],x]","-\frac{2}{3} \sqrt{1-x} (x+5)","\frac{2}{3} (1-x)^{3/2}-4 \sqrt{1-x}",1,"(-2*Sqrt[1 - x]*(5 + x))/3","A",1
377,1,16,23,0.007385,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} x \, dx","Integrate[E^ArcTanh[x]*Sqrt[1 - x]*x,x]","\frac{2}{15} (x+1)^{3/2} (3 x-2)","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2)*(-2 + 3*x))/15","A",1
378,1,11,11,0.0046664,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} \, dx","Integrate[E^ArcTanh[x]*Sqrt[1 - x],x]","\frac{2}{3} (x+1)^{3/2}","\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2))/3","A",1
379,1,16,25,0.0072924,"\int \frac{e^{\tanh ^{-1}(x)} x}{\sqrt{1+x}} \, dx","Integrate[(E^ArcTanh[x]*x)/Sqrt[1 + x],x]","-\frac{2}{3} \sqrt{1-x} (x+2)","\frac{2}{3} (1-x)^{3/2}-2 \sqrt{1-x}",1,"(-2*Sqrt[1 - x]*(2 + x))/3","A",1
380,1,11,11,0.0043705,"\int \frac{e^{\tanh ^{-1}(x)}}{\sqrt{1+x}} \, dx","Integrate[E^ArcTanh[x]/Sqrt[1 + x],x]","-2 \sqrt{1-x}","-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x]","A",1
381,1,36,42,0.0225124,"\int \frac{e^{\tanh ^{-1}(x)} x}{\sqrt{1-x}} \, dx","Integrate[(E^ArcTanh[x]*x)/Sqrt[1 - x],x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)-\frac{2}{3} \sqrt{x+1} (x+4)","-\frac{2}{3} (x+1)^{3/2}-2 \sqrt{x+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)",1,"(-2*Sqrt[1 + x]*(4 + x))/3 + 2*Sqrt[2]*ArcTanh[Sqrt[1 + x]/Sqrt[2]]","A",1
382,1,31,31,0.005889,"\int \frac{e^{\tanh ^{-1}(x)}}{\sqrt{1-x}} \, dx","Integrate[E^ArcTanh[x]/Sqrt[1 - x],x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)-2 \sqrt{x+1}","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)-2 \sqrt{x+1}",1,"-2*Sqrt[1 + x] + 2*Sqrt[2]*ArcTanh[Sqrt[1 + x]/Sqrt[2]]","A",1
383,1,34,34,0.0075515,"\int \frac{e^{\tanh ^{-1}(x)} x}{(1+x)^{3/2}} \, dx","Integrate[(E^ArcTanh[x]*x)/(1 + x)^(3/2),x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)-2 \sqrt{1-x}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x] + Sqrt[2]*ArcTanh[Sqrt[1 - x]/Sqrt[2]]","A",1
384,1,23,23,0.0042731,"\int \frac{e^{\tanh ^{-1}(x)}}{(1+x)^{3/2}} \, dx","Integrate[E^ArcTanh[x]/(1 + x)^(3/2),x]","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)","-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{2}}\right)",1,"-(Sqrt[2]*ArcTanh[Sqrt[1 - x]/Sqrt[2]])","A",1
385,1,40,51,0.0222144,"\int \frac{e^{\tanh ^{-1}(x)} x}{(1-x)^{3/2}} \, dx","Integrate[(E^ArcTanh[x]*x)/(1 - x)^(3/2),x]","\frac{\sqrt{x+1} (2 x-3)}{x-1}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{(x+1)^{3/2}}{2 (1-x)}+\frac{5 \sqrt{x+1}}{2}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"(Sqrt[1 + x]*(-3 + 2*x))/(-1 + x) - (5*ArcTanh[Sqrt[1 + x]/Sqrt[2]])/Sqrt[2]","A",1
386,1,36,37,0.0258162,"\int \frac{e^{\tanh ^{-1}(x)}}{(1-x)^{3/2}} \, dx","Integrate[E^ArcTanh[x]/(1 - x)^(3/2),x]","-\frac{\sqrt{x+1}}{x-1}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\sqrt{x+1}}{1-x}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(Sqrt[1 + x]/(-1 + x)) - ArcTanh[Sqrt[1 + x]/Sqrt[2]]/Sqrt[2]","A",1
387,1,46,64,0.0182914,"\int e^{\tanh ^{-1}(a x)} x^m \sqrt{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]*x^m*Sqrt[c - a*c*x],x]","\frac{x^{m+1} \sqrt{c-a c x} \, _2F_1\left(-\frac{1}{2},m+1;m+2;-a x\right)}{(m+1) \sqrt{1-a x}}","\frac{2 c (a x+1) \sqrt{1-a^2 x^2} x^m (-a x)^{-m} \, _2F_1\left(\frac{3}{2},-m;\frac{5}{2};a x+1\right)}{3 a \sqrt{c-a c x}}",1,"(x^(1 + m)*Sqrt[c - a*c*x]*Hypergeometric2F1[-1/2, 1 + m, 2 + m, -(a*x)])/((1 + m)*Sqrt[1 - a*x])","A",0
388,1,51,107,0.0308387,"\int e^{\tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]*x^2*Sqrt[c - a*c*x],x]","\frac{2 (a x+1)^{3/2} \left(15 a^2 x^2-12 a x+8\right) \sqrt{c-a c x}}{105 a^3 \sqrt{1-a x}}","\frac{2 c^2 x^2 \left(1-a^2 x^2\right)^{3/2}}{7 a (c-a c x)^{3/2}}-\frac{8 c^2 \left(1-a^2 x^2\right)^{3/2}}{105 a^3 (c-a c x)^{3/2}}+\frac{8 c \left(1-a^2 x^2\right)^{3/2}}{35 a^3 \sqrt{c-a c x}}",1,"(2*(1 + a*x)^(3/2)*Sqrt[c - a*c*x]*(8 - 12*a*x + 15*a^2*x^2))/(105*a^3*Sqrt[1 - a*x])","A",0
389,1,43,69,0.0232183,"\int e^{\tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]*x*Sqrt[c - a*c*x],x]","\frac{2 (a x+1)^{3/2} (3 a x-2) \sqrt{c-a c x}}{15 a^2 \sqrt{1-a x}}","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{15 a^2 (c-a c x)^{3/2}}-\frac{2 c \left(1-a^2 x^2\right)^{3/2}}{5 a^2 \sqrt{c-a c x}}",1,"(2*(1 + a*x)^(3/2)*(-2 + 3*a*x)*Sqrt[c - a*c*x])/(15*a^2*Sqrt[1 - a*x])","A",0
390,1,37,35,0.0139169,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - a*c*x],x]","\frac{2 (a x+1)^{3/2} \sqrt{c-a c x}}{3 a \sqrt{1-a x}}","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}",1,"(2*(1 + a*x)^(3/2)*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - a*x])","A",1
391,1,46,68,0.0205619,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - a*c*x])/x,x]","\frac{\sqrt{c-a c x} \left(2 \sqrt{a x+1}-2 \tanh ^{-1}\left(\sqrt{a x+1}\right)\right)}{\sqrt{1-a x}}","\frac{2 c \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"(Sqrt[c - a*c*x]*(2*Sqrt[1 + a*x] - 2*ArcTanh[Sqrt[1 + a*x]]))/Sqrt[1 - a*x]","A",0
392,1,57,72,0.0257983,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - a*c*x])/x^2,x]","-\frac{\sqrt{c-a c x} \left(a x+a x \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{a x+1}\right)+1\right)}{x \sqrt{1-a^2 x^2}}","-\frac{c \sqrt{1-a^2 x^2}}{x \sqrt{c-a c x}}-a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"-((Sqrt[c - a*c*x]*(1 + a*x + a*x*Sqrt[1 + a*x]*ArcTanh[Sqrt[1 + a*x]]))/(x*Sqrt[1 - a^2*x^2]))","A",0
393,1,48,101,0.067061,"\int e^{2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*Sqrt[c - a*c*x],x]","-\frac{2 \left(35 a^4 x^4+85 a^3 x^3+102 a^2 x^2+136 a x+272\right) \sqrt{c-a c x}}{315 a^4}","-\frac{2 (c-a c x)^{9/2}}{9 a^4 c^4}+\frac{10 (c-a c x)^{7/2}}{7 a^4 c^3}-\frac{18 (c-a c x)^{5/2}}{5 a^4 c^2}+\frac{14 (c-a c x)^{3/2}}{3 a^4 c}-\frac{4 \sqrt{c-a c x}}{a^4}",1,"(-2*Sqrt[c - a*c*x]*(272 + 136*a*x + 102*a^2*x^2 + 85*a^3*x^3 + 35*a^4*x^4))/(315*a^4)","A",1
394,1,40,80,0.0548611,"\int e^{2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*Sqrt[c - a*c*x],x]","-\frac{2 \left(15 a^3 x^3+39 a^2 x^2+52 a x+104\right) \sqrt{c-a c x}}{105 a^3}","\frac{2 (c-a c x)^{7/2}}{7 a^3 c^3}-\frac{8 (c-a c x)^{5/2}}{5 a^3 c^2}+\frac{10 (c-a c x)^{3/2}}{3 a^3 c}-\frac{4 \sqrt{c-a c x}}{a^3}",1,"(-2*Sqrt[c - a*c*x]*(104 + 52*a*x + 39*a^2*x^2 + 15*a^3*x^3))/(105*a^3)","A",1
395,1,31,57,0.0415665,"\int e^{2 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Integrate[E^(2*ArcTanh[a*x])*x*Sqrt[c - a*c*x],x]","-\frac{2 \left(a^2 x^2+3 a x+6\right) \sqrt{c-a c x}}{5 a^2}","-\frac{2 (c-a c x)^{5/2}}{5 a^2 c^2}+\frac{2 (c-a c x)^{3/2}}{a^2 c}-\frac{4 \sqrt{c-a c x}}{a^2}",1,"(-2*Sqrt[c - a*c*x]*(6 + 3*a*x + a^2*x^2))/(5*a^2)","A",1
396,1,23,38,0.0246397,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","-\frac{2 (a x+5) \sqrt{c-a c x}}{3 a}","\frac{2 (c-a c x)^{3/2}}{3 a c}-\frac{4 \sqrt{c-a c x}}{a}",1,"(-2*(5 + a*x)*Sqrt[c - a*c*x])/(3*a)","A",1
397,1,39,39,0.0319936,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x,x]","-2 \sqrt{c-a c x}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)","-2 \sqrt{c-a c x}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)",1,"-2*Sqrt[c - a*c*x] - 2*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]]","A",1
398,1,43,43,0.0292835,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^2,x]","-\frac{\sqrt{c-a c x}}{x}-3 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)","-\frac{\sqrt{c-a c x}}{x}-3 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)",1,"-(Sqrt[c - a*c*x]/x) - 3*a*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]]","A",1
399,1,55,68,0.0499119,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^3,x]","-\frac{7}{4} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{(7 a x+2) \sqrt{c-a c x}}{4 x^2}","-\frac{7}{4} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{\sqrt{c-a c x}}{2 x^2}-\frac{7 a \sqrt{c-a c x}}{4 x}",1,"-1/4*((2 + 7*a*x)*Sqrt[c - a*c*x])/x^2 - (7*a^2*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/4","A",1
400,1,63,89,0.0655754,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^4,x]","-\frac{11}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{\left(33 a^2 x^2+22 a x+8\right) \sqrt{c-a c x}}{24 x^3}","-\frac{11}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{11 a^2 \sqrt{c-a c x}}{8 x}-\frac{\sqrt{c-a c x}}{3 x^3}-\frac{11 a \sqrt{c-a c x}}{12 x^2}",1,"-1/24*(Sqrt[c - a*c*x]*(8 + 22*a*x + 33*a^2*x^2))/x^3 - (11*a^3*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/8","A",1
401,1,71,110,0.0689671,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^5,x]","-\frac{75}{64} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{\left(75 a^3 x^3+50 a^2 x^2+40 a x+16\right) \sqrt{c-a c x}}{64 x^4}","-\frac{75}{64} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{75 a^3 \sqrt{c-a c x}}{64 x}-\frac{25 a^2 \sqrt{c-a c x}}{32 x^2}-\frac{\sqrt{c-a c x}}{4 x^4}-\frac{5 a \sqrt{c-a c x}}{8 x^3}",1,"-1/64*(Sqrt[c - a*c*x]*(16 + 40*a*x + 50*a^2*x^2 + 75*a^3*x^3))/x^4 - (75*a^4*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/64","A",1
402,1,92,249,0.0840435,"\int e^{3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Integrate[E^(3*ArcTanh[a*x])*x^3*Sqrt[c - a*c*x],x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1} \left(35 a^4 x^4+95 a^3 x^3+138 a^2 x^2+236 a x+788\right)-630 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{315 a^4 \sqrt{1-a x}}","-\frac{2 (a x+1)^{9/2} (c-a c x)^{3/2}}{9 a^4 c (1-a x)^{3/2}}+\frac{2 (a x+1)^{7/2} (c-a c x)^{3/2}}{7 a^4 c (1-a x)^{3/2}}-\frac{2 (a x+1)^{5/2} (c-a c x)^{3/2}}{5 a^4 c (1-a x)^{3/2}}-\frac{2 (a x+1)^{3/2} (c-a c x)^{3/2}}{3 a^4 c (1-a x)^{3/2}}-\frac{4 \sqrt{a x+1} (c-a c x)^{3/2}}{a^4 c (1-a x)^{3/2}}+\frac{4 \sqrt{2} (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{a^4 c (1-a x)^{3/2}}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(788 + 236*a*x + 138*a^2*x^2 + 95*a^3*x^3 + 35*a^4*x^4) - 630*Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(315*a^4*Sqrt[1 - a*x])","A",1
403,1,84,169,0.0676442,"\int e^{3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Integrate[E^(3*ArcTanh[a*x])*x^2*Sqrt[c - a*c*x],x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1} \left(3 a^3 x^3+9 a^2 x^2+16 a x+52\right)-42 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{21 a^3 \sqrt{1-a x}}","-\frac{2 (a x+1)^{7/2} (c-a c x)^{3/2}}{7 a^3 c (1-a x)^{3/2}}-\frac{2 (a x+1)^{3/2} (c-a c x)^{3/2}}{3 a^3 c (1-a x)^{3/2}}-\frac{4 \sqrt{a x+1} (c-a c x)^{3/2}}{a^3 c (1-a x)^{3/2}}+\frac{4 \sqrt{2} (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{a^3 c (1-a x)^{3/2}}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(52 + 16*a*x + 9*a^2*x^2 + 3*a^3*x^3) - 42*Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(21*a^3*Sqrt[1 - a*x])","A",1
404,1,76,169,0.0431273,"\int e^{3 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Integrate[E^(3*ArcTanh[a*x])*x*Sqrt[c - a*c*x],x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1} \left(3 a^2 x^2+11 a x+38\right)-30 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{15 a^2 \sqrt{1-a x}}","-\frac{2 (a x+1)^{5/2} (c-a c x)^{3/2}}{5 a^2 c (1-a x)^{3/2}}-\frac{2 (a x+1)^{3/2} (c-a c x)^{3/2}}{3 a^2 c (1-a x)^{3/2}}-\frac{4 \sqrt{a x+1} (c-a c x)^{3/2}}{a^2 c (1-a x)^{3/2}}+\frac{4 \sqrt{2} (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{a^2 c (1-a x)^{3/2}}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(38 + 11*a*x + 3*a^2*x^2) - 30*Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(15*a^2*Sqrt[1 - a*x])","A",1
405,1,67,119,0.0336839,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1} (a x+7)-6 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{3 a \sqrt{1-a x}}","-\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}-\frac{4 c \sqrt{1-a^2 x^2}}{a \sqrt{c-a c x}}+\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{2} \sqrt{c-a c x}}\right)}{a}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(7 + a*x) - 6*Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(3*a*Sqrt[1 - a*x])","A",0
406,1,66,119,0.0338466,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x,x]","-\frac{2 \sqrt{c-a c x} \left(\sqrt{a x+1}+\tanh ^{-1}\left(\sqrt{a x+1}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{\sqrt{1-a x}}","-\frac{2 \sqrt{a x+1} (c-a c x)^{3/2}}{c (1-a x)^{3/2}}-\frac{2 (c-a c x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{c (1-a x)^{3/2}}+\frac{4 \sqrt{2} (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{c (1-a x)^{3/2}}",1,"(-2*Sqrt[c - a*c*x]*(Sqrt[1 + a*x] + ArcTanh[Sqrt[1 + a*x]] - 2*Sqrt[2]*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/Sqrt[1 - a*x]","A",1
407,1,75,124,0.0367225,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^2,x]","-\frac{\sqrt{c-a c x} \left(\sqrt{a x+1}+5 a x \tanh ^{-1}\left(\sqrt{a x+1}\right)-4 \sqrt{2} a x \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)\right)}{x \sqrt{1-a x}}","-\frac{\sqrt{a x+1} (c-a c x)^{3/2}}{c x (1-a x)^{3/2}}-\frac{5 a (c-a c x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{c (1-a x)^{3/2}}+\frac{4 \sqrt{2} a (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{c (1-a x)^{3/2}}",1,"-((Sqrt[c - a*c*x]*(Sqrt[1 + a*x] + 5*a*x*ArcTanh[Sqrt[1 + a*x]] - 4*Sqrt[2]*a*x*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(x*Sqrt[1 - a*x]))","A",1
408,1,92,173,0.0557584,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^3,x]","-\frac{\sqrt{c-a c x} \left(23 a^2 x^2 \tanh ^{-1}\left(\sqrt{a x+1}\right)-16 \sqrt{2} a^2 x^2 \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)+\sqrt{a x+1} (9 a x+2)\right)}{4 x^2 \sqrt{1-a x}}","-\frac{23 a^2 (c-a c x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{4 c (1-a x)^{3/2}}+\frac{4 \sqrt{2} a^2 (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{c (1-a x)^{3/2}}-\frac{\sqrt{a x+1} (c-a c x)^{3/2}}{2 c x^2 (1-a x)^{3/2}}-\frac{9 a \sqrt{a x+1} (c-a c x)^{3/2}}{4 c x (1-a x)^{3/2}}",1,"-1/4*(Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(2 + 9*a*x) + 23*a^2*x^2*ArcTanh[Sqrt[1 + a*x]] - 16*Sqrt[2]*a^2*x^2*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(x^2*Sqrt[1 - a*x])","A",1
409,1,100,216,0.0666482,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^4,x]","-\frac{\sqrt{c-a c x} \left(135 a^3 x^3 \tanh ^{-1}\left(\sqrt{a x+1}\right)-96 \sqrt{2} a^3 x^3 \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)+\sqrt{a x+1} \left(57 a^2 x^2+26 a x+8\right)\right)}{24 x^3 \sqrt{1-a x}}","-\frac{45 a^3 (c-a c x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{8 c (1-a x)^{3/2}}+\frac{4 \sqrt{2} a^3 (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{c (1-a x)^{3/2}}-\frac{19 a^2 \sqrt{a x+1} (c-a c x)^{3/2}}{8 c x (1-a x)^{3/2}}-\frac{\sqrt{a x+1} (c-a c x)^{3/2}}{3 c x^3 (1-a x)^{3/2}}-\frac{13 a \sqrt{a x+1} (c-a c x)^{3/2}}{12 c x^2 (1-a x)^{3/2}}",1,"-1/24*(Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(8 + 26*a*x + 57*a^2*x^2) + 135*a^3*x^3*ArcTanh[Sqrt[1 + a*x]] - 96*Sqrt[2]*a^3*x^3*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(x^3*Sqrt[1 - a*x])","A",1
410,1,108,259,0.0782453,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^5,x]","-\frac{\sqrt{c-a c x} \left(1089 a^4 x^4 \tanh ^{-1}\left(\sqrt{a x+1}\right)-768 \sqrt{2} a^4 x^4 \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)+\sqrt{a x+1} \left(447 a^3 x^3+214 a^2 x^2+136 a x+48\right)\right)}{192 x^4 \sqrt{1-a x}}","-\frac{363 a^4 (c-a c x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{64 c (1-a x)^{3/2}}+\frac{4 \sqrt{2} a^4 (c-a c x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a x+1}}{\sqrt{2}}\right)}{c (1-a x)^{3/2}}-\frac{149 a^3 \sqrt{a x+1} (c-a c x)^{3/2}}{64 c x (1-a x)^{3/2}}-\frac{107 a^2 \sqrt{a x+1} (c-a c x)^{3/2}}{96 c x^2 (1-a x)^{3/2}}-\frac{\sqrt{a x+1} (c-a c x)^{3/2}}{4 c x^4 (1-a x)^{3/2}}-\frac{17 a \sqrt{a x+1} (c-a c x)^{3/2}}{24 c x^3 (1-a x)^{3/2}}",1,"-1/192*(Sqrt[c - a*c*x]*(Sqrt[1 + a*x]*(48 + 136*a*x + 214*a^2*x^2 + 447*a^3*x^3) + 1089*a^4*x^4*ArcTanh[Sqrt[1 + a*x]] - 768*Sqrt[2]*a^4*x^4*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]]))/(x^4*Sqrt[1 - a*x])","A",1
411,1,77,114,0.0486657,"\int e^{-\tanh ^{-1}(a x)} x^m \sqrt{c-a c x} \, dx","Integrate[(x^m*Sqrt[c - a*c*x])/E^ArcTanh[a*x],x]","-\frac{c \sqrt{1-a x} x^{m+1} \left(2 (m+1) \sqrt{a x+1}-(4 m+5) \, _2F_1\left(\frac{1}{2},m+1;m+2;-a x\right)\right)}{(m+1) (2 m+3) \sqrt{c-a c x}}","\frac{2 (4 m+5) (a x+1) x^m \sqrt{c-a c x} (-a x)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};a x+1\right)}{a (2 m+3) \sqrt{1-a^2 x^2}}-\frac{2 c \sqrt{1-a^2 x^2} x^{m+1}}{(2 m+3) \sqrt{c-a c x}}",1,"-((c*x^(1 + m)*Sqrt[1 - a*x]*(2*(1 + m)*Sqrt[1 + a*x] - (5 + 4*m)*Hypergeometric2F1[1/2, 1 + m, 2 + m, -(a*x)]))/((1 + m)*(3 + 2*m)*Sqrt[c - a*c*x]))","A",0
412,1,55,135,0.0369634,"\int e^{-\tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Integrate[(x^2*Sqrt[c - a*c*x])/E^ArcTanh[a*x],x]","-\frac{2 c \sqrt{1-a^2 x^2} \left(15 a^3 x^3-39 a^2 x^2+52 a x-104\right)}{105 a^3 \sqrt{c-a c x}}","\frac{26 c x^2 \sqrt{1-a^2 x^2}}{35 a \sqrt{c-a c x}}-\frac{2 c x^3 \sqrt{1-a^2 x^2}}{7 \sqrt{c-a c x}}+\frac{104 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{105 a^3}+\frac{104 c \sqrt{1-a^2 x^2}}{105 a^3 \sqrt{c-a c x}}",1,"(-2*c*Sqrt[1 - a^2*x^2]*(-104 + 52*a*x - 39*a^2*x^2 + 15*a^3*x^3))/(105*a^3*Sqrt[c - a*c*x])","A",1
413,1,46,101,0.0316542,"\int e^{-\tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Integrate[(x*Sqrt[c - a*c*x])/E^ArcTanh[a*x],x]","-\frac{2 c \sqrt{1-a^2 x^2} \left(a^2 x^2-3 a x+6\right)}{5 a^2 \sqrt{c-a c x}}","-\frac{2 \sqrt{1-a^2 x^2} (c-a c x)^{3/2}}{5 a^2 c}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{5 a^2}-\frac{8 c \sqrt{1-a^2 x^2}}{5 a^2 \sqrt{c-a c x}}",1,"(-2*c*Sqrt[1 - a^2*x^2]*(6 - 3*a*x + a^2*x^2))/(5*a^2*Sqrt[c - a*c*x])","A",1
414,1,38,66,0.0215646,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[Sqrt[c - a*c*x]/E^ArcTanh[a*x],x]","-\frac{2 c (a x-5) \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a c x}}","\frac{8 c \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a c x}}+\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-a c x}}{3 a}",1,"(-2*c*(-5 + a*x)*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[c - a*c*x])","A",1
415,1,44,68,0.0203026,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Integrate[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x),x]","-\frac{2 c \sqrt{1-a x} \left(\sqrt{a x+1}+\tanh ^{-1}\left(\sqrt{a x+1}\right)\right)}{\sqrt{c-a c x}}","-\frac{2 c \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"(-2*c*Sqrt[1 - a*x]*(Sqrt[1 + a*x] + ArcTanh[Sqrt[1 + a*x]]))/Sqrt[c - a*c*x]","A",0
416,1,52,72,0.030371,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Integrate[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x^2),x]","\frac{\sqrt{1-a x} \left(3 a c \tanh ^{-1}\left(\sqrt{a x+1}\right)-\frac{c \sqrt{a x+1}}{x}\right)}{\sqrt{c-a c x}}","3 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)-\frac{c \sqrt{1-a^2 x^2}}{x \sqrt{c-a c x}}",1,"(Sqrt[1 - a*x]*(-((c*Sqrt[1 + a*x])/x) + 3*a*c*ArcTanh[Sqrt[1 + a*x]]))/Sqrt[c - a*c*x]","A",0
417,1,64,112,0.0370854,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Integrate[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x^3),x]","-\frac{c \sqrt{1-a x} \left(7 a^2 x^2 \tanh ^{-1}\left(\sqrt{a x+1}\right)+(2-7 a x) \sqrt{a x+1}\right)}{4 x^2 \sqrt{c-a c x}}","\frac{7 a c \sqrt{1-a^2 x^2}}{4 x \sqrt{c-a c x}}-\frac{c \sqrt{1-a^2 x^2}}{2 x^2 \sqrt{c-a c x}}-\frac{7}{4} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"-1/4*(c*Sqrt[1 - a*x]*((2 - 7*a*x)*Sqrt[1 + a*x] + 7*a^2*x^2*ArcTanh[Sqrt[1 + a*x]]))/(x^2*Sqrt[c - a*c*x])","A",0
418,1,56,148,0.0233003,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Integrate[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x^4),x]","\frac{c \sqrt{1-a^2 x^2} \left(11 a^3 x^3 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};a x+1\right)-1\right)}{3 x^3 \sqrt{c-a c x}}","-\frac{11 a^2 c \sqrt{1-a^2 x^2}}{8 x \sqrt{c-a c x}}+\frac{11 a c \sqrt{1-a^2 x^2}}{12 x^2 \sqrt{c-a c x}}-\frac{c \sqrt{1-a^2 x^2}}{3 x^3 \sqrt{c-a c x}}+\frac{11}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-a^2 x^2}}{\sqrt{c-a c x}}\right)",1,"(c*Sqrt[1 - a^2*x^2]*(-1 + 11*a^3*x^3*Hypergeometric2F1[1/2, 3, 3/2, 1 + a*x]))/(3*x^3*Sqrt[c - a*c*x])","C",0
419,1,87,139,0.1318351,"\int e^{-2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Integrate[(x^3*Sqrt[c - a*c*x])/E^(2*ArcTanh[a*x]),x]","\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a^4}-\frac{2 \left(35 a^4 x^4-95 a^3 x^3+138 a^2 x^2-236 a x+788\right) \sqrt{c-a c x}}{315 a^4}","-\frac{2 (c-a c x)^{9/2}}{9 a^4 c^4}+\frac{2 (c-a c x)^{7/2}}{7 a^4 c^3}-\frac{2 (c-a c x)^{5/2}}{5 a^4 c^2}-\frac{2 (c-a c x)^{3/2}}{3 a^4 c}-\frac{4 \sqrt{c-a c x}}{a^4}+\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a^4}",1,"(-2*Sqrt[c - a*c*x]*(788 - 236*a*x + 138*a^2*x^2 - 95*a^3*x^3 + 35*a^4*x^4))/(315*a^4) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a^4","A",1
420,1,78,97,0.090644,"\int e^{-2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Integrate[(x^2*Sqrt[c - a*c*x])/E^(2*ArcTanh[a*x]),x]","\frac{2 \left(-3 a^3 x^3+9 a^2 x^2-16 a x+52\right) \sqrt{c-a c x}-84 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{21 a^3}","\frac{2 (c-a c x)^{7/2}}{7 a^3 c^3}+\frac{2 (c-a c x)^{3/2}}{3 a^3 c}+\frac{4 \sqrt{c-a c x}}{a^3}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a^3}",1,"(2*Sqrt[c - a*c*x]*(52 - 16*a*x + 9*a^2*x^2 - 3*a^3*x^3) - 84*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/(21*a^3)","A",1
421,1,70,97,0.083622,"\int e^{-2 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Integrate[(x*Sqrt[c - a*c*x])/E^(2*ArcTanh[a*x]),x]","\frac{60 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)-2 \left(3 a^2 x^2-11 a x+38\right) \sqrt{c-a c x}}{15 a^2}","-\frac{2 (c-a c x)^{5/2}}{5 a^2 c^2}-\frac{2 (c-a c x)^{3/2}}{3 a^2 c}-\frac{4 \sqrt{c-a c x}}{a^2}+\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a^2}",1,"(-2*Sqrt[c - a*c*x]*(38 - 11*a*x + 3*a^2*x^2) + 60*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/(15*a^2)","A",1
422,1,61,76,0.0430837,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[Sqrt[c - a*c*x]/E^(2*ArcTanh[a*x]),x]","-\frac{2 (a x-7) \sqrt{c-a c x}+12 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{3 a}","\frac{2 (c-a c x)^{3/2}}{3 a c}+\frac{4 \sqrt{c-a c x}}{a}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{a}",1,"-1/3*(2*(-7 + a*x)*Sqrt[c - a*c*x] + 12*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",1
423,1,74,74,0.0289011,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x),x]","-2 \sqrt{c-a c x}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)+4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)","-2 \sqrt{c-a c x}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)+4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)",1,"-2*Sqrt[c - a*c*x] - 2*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]] + 4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]","A",1
424,1,79,79,0.0451467,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x^2),x]","-\frac{\sqrt{c-a c x}}{x}+5 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-4 \sqrt{2} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)","-\frac{\sqrt{c-a c x}}{x}+5 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-4 \sqrt{2} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)",1,"-(Sqrt[c - a*c*x]/x) + 5*a*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]] - 4*Sqrt[2]*a*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]","A",1
425,1,93,106,0.0751821,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x^3),x]","-\frac{23}{4} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)+4 \sqrt{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)+\frac{(9 a x-2) \sqrt{c-a c x}}{4 x^2}","-\frac{23}{4} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)+4 \sqrt{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)-\frac{\sqrt{c-a c x}}{2 x^2}+\frac{9 a \sqrt{c-a c x}}{4 x}",1,"((-2 + 9*a*x)*Sqrt[c - a*c*x])/(4*x^2) - (23*a^2*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/4 + 4*Sqrt[2]*a^2*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]","A",1
426,1,101,127,0.0983704,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x^4),x]","\frac{45}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-4 \sqrt{2} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)+\frac{\left(-57 a^2 x^2+26 a x-8\right) \sqrt{c-a c x}}{24 x^3}","\frac{45}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-4 \sqrt{2} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)-\frac{19 a^2 \sqrt{c-a c x}}{8 x}-\frac{\sqrt{c-a c x}}{3 x^3}+\frac{13 a \sqrt{c-a c x}}{12 x^2}",1,"(Sqrt[c - a*c*x]*(-8 + 26*a*x - 57*a^2*x^2))/(24*x^3) + (45*a^3*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/8 - 4*Sqrt[2]*a^3*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]","A",1
427,1,109,148,0.1143673,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x^5),x]","-\frac{363}{64} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)+4 \sqrt{2} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)+\frac{\left(447 a^3 x^3-214 a^2 x^2+136 a x-48\right) \sqrt{c-a c x}}{192 x^4}","-\frac{363}{64} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)+4 \sqrt{2} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)+\frac{149 a^3 \sqrt{c-a c x}}{64 x}-\frac{107 a^2 \sqrt{c-a c x}}{96 x^2}-\frac{\sqrt{c-a c x}}{4 x^4}+\frac{17 a \sqrt{c-a c x}}{24 x^3}",1,"(Sqrt[c - a*c*x]*(-48 + 136*a*x - 214*a^2*x^2 + 447*a^3*x^3))/(192*x^4) - (363*a^4*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/64 + 4*Sqrt[2]*a^4*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]","A",1
428,1,76,235,0.0498615,"\int e^{-3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Integrate[(x^3*Sqrt[c - a*c*x])/E^(3*ArcTanh[a*x]),x]","\frac{2 c \sqrt{1-a x} \left(5 a^5 x^5-20 a^4 x^4+41 a^3 x^3-82 a^2 x^2+328 a x+656\right)}{45 a^4 \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 c^2 (1-a x)^{3/2} (a x+1)^{9/2}}{9 a^4 (c-a c x)^{3/2}}-\frac{2 c^2 (1-a x)^{3/2} (a x+1)^{7/2}}{a^4 (c-a c x)^{3/2}}+\frac{38 c^2 (1-a x)^{3/2} (a x+1)^{5/2}}{5 a^4 (c-a c x)^{3/2}}-\frac{50 c^2 (1-a x)^{3/2} (a x+1)^{3/2}}{3 a^4 (c-a c x)^{3/2}}+\frac{32 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{a^4 (c-a c x)^{3/2}}+\frac{8 c^2 (1-a x)^{3/2}}{a^4 \sqrt{a x+1} (c-a c x)^{3/2}}",1,"(2*c*Sqrt[1 - a*x]*(656 + 328*a*x - 82*a^2*x^2 + 41*a^3*x^3 - 20*a^4*x^4 + 5*a^5*x^5))/(45*a^4*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",1
429,1,68,197,0.0432492,"\int e^{-3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Integrate[(x^2*Sqrt[c - a*c*x])/E^(3*ArcTanh[a*x]),x]","\frac{2 c \sqrt{1-a x} \left(15 a^4 x^4-66 a^3 x^3+167 a^2 x^2-668 a x-1336\right)}{105 a^3 \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 c^2 (1-a x)^{3/2} (a x+1)^{7/2}}{7 a^3 (c-a c x)^{3/2}}-\frac{12 c^2 (1-a x)^{3/2} (a x+1)^{5/2}}{5 a^3 (c-a c x)^{3/2}}+\frac{26 c^2 (1-a x)^{3/2} (a x+1)^{3/2}}{3 a^3 (c-a c x)^{3/2}}-\frac{24 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{a^3 (c-a c x)^{3/2}}-\frac{8 c^2 (1-a x)^{3/2}}{a^3 \sqrt{a x+1} (c-a c x)^{3/2}}",1,"(2*c*Sqrt[1 - a*x]*(-1336 - 668*a*x + 167*a^2*x^2 - 66*a^3*x^3 + 15*a^4*x^4))/(105*a^3*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",1
430,1,60,157,0.0375289,"\int e^{-3 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Integrate[(x*Sqrt[c - a*c*x])/E^(3*ArcTanh[a*x]),x]","\frac{2 c \sqrt{1-a x} \left(3 a^3 x^3-16 a^2 x^2+79 a x+158\right)}{15 a^2 \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 c^2 (1-a x)^{3/2} (a x+1)^{5/2}}{5 a^2 (c-a c x)^{3/2}}-\frac{10 c^2 (1-a x)^{3/2} (a x+1)^{3/2}}{3 a^2 (c-a c x)^{3/2}}+\frac{16 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{a^2 (c-a c x)^{3/2}}+\frac{8 c^2 (1-a x)^{3/2}}{a^2 \sqrt{a x+1} (c-a c x)^{3/2}}",1,"(2*c*Sqrt[1 - a*x]*(158 + 79*a*x - 16*a^2*x^2 + 3*a^3*x^3))/(15*a^2*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",1
431,1,51,103,0.0271988,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Integrate[Sqrt[c - a*c*x]/E^(3*ArcTanh[a*x]),x]","\frac{2 c \sqrt{1-a x} \left(a^2 x^2-10 a x-23\right)}{3 a \sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 (c-a c x)^{5/2}}{3 a c^2 \sqrt{1-a^2 x^2}}+\frac{16 (c-a c x)^{3/2}}{3 a c \sqrt{1-a^2 x^2}}-\frac{64 \sqrt{c-a c x}}{3 a \sqrt{1-a^2 x^2}}",1,"(2*c*Sqrt[1 - a*x]*(-23 - 10*a*x + a^2*x^2))/(3*a*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",0
432,1,51,107,0.0346413,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x),x]","\frac{2 c \sqrt{1-a x} \left(\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};a x+1\right)+a x+4\right)}{\sqrt{a x+1} \sqrt{c-a c x}}","\frac{2 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{(c-a c x)^{3/2}}+\frac{8 c^2 (1-a x)^{3/2}}{\sqrt{a x+1} (c-a c x)^{3/2}}-\frac{2 c^2 (1-a x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{(c-a c x)^{3/2}}",1,"(2*c*Sqrt[1 - a*x]*(4 + a*x + Hypergeometric2F1[-1/2, 1, 1/2, 1 + a*x]))/(Sqrt[1 + a*x]*Sqrt[c - a*c*x])","C",0
433,1,64,112,0.0310459,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^2),x]","\frac{c \sqrt{1-a x} \left(-9 a x+7 a x \sqrt{a x+1} \tanh ^{-1}\left(\sqrt{a x+1}\right)-1\right)}{x \sqrt{a x+1} \sqrt{c-a c x}}","-\frac{9 a c^2 (1-a x)^{3/2}}{\sqrt{a x+1} (c-a c x)^{3/2}}-\frac{c^2 (1-a x)^{3/2}}{x \sqrt{a x+1} (c-a c x)^{3/2}}+\frac{7 a c^2 (1-a x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{(c-a c x)^{3/2}}",1,"(c*Sqrt[1 - a*x]*(-1 - 9*a*x + 7*a*x*Sqrt[1 + a*x]*ArcTanh[Sqrt[1 + a*x]]))/(x*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","A",1
434,1,65,163,0.0285271,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^3),x]","\frac{c \sqrt{1-a x} \left(47 a^2 x^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};a x+1\right)+13 a x-2\right)}{4 x^2 \sqrt{a x+1} \sqrt{c-a c x}}","\frac{47 a^2 c^2 (1-a x)^{3/2}}{4 \sqrt{a x+1} (c-a c x)^{3/2}}-\frac{47 a^2 c^2 (1-a x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{4 (c-a c x)^{3/2}}-\frac{c^2 (1-a x)^{3/2}}{2 x^2 \sqrt{a x+1} (c-a c x)^{3/2}}+\frac{13 a c^2 (1-a x)^{3/2}}{4 x \sqrt{a x+1} (c-a c x)^{3/2}}",1,"(c*Sqrt[1 - a*x]*(-2 + 13*a*x + 47*a^2*x^2*Hypergeometric2F1[-1/2, 1, 1/2, 1 + a*x]))/(4*x^2*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","C",0
435,1,65,206,0.0314826,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^4),x]","-\frac{c \sqrt{1-a x} \left(119 a^3 x^3 \, _2F_1\left(-\frac{1}{2},2;\frac{1}{2};a x+1\right)-19 a x+4\right)}{12 x^3 \sqrt{a x+1} \sqrt{c-a c x}}","-\frac{119 a^3 c^2 (1-a x)^{3/2}}{8 \sqrt{a x+1} (c-a c x)^{3/2}}+\frac{119 a^3 c^2 (1-a x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{8 (c-a c x)^{3/2}}-\frac{119 a^2 c^2 (1-a x)^{3/2}}{24 x \sqrt{a x+1} (c-a c x)^{3/2}}-\frac{c^2 (1-a x)^{3/2}}{3 x^3 \sqrt{a x+1} (c-a c x)^{3/2}}+\frac{19 a c^2 (1-a x)^{3/2}}{12 x^2 \sqrt{a x+1} (c-a c x)^{3/2}}",1,"-1/12*(c*Sqrt[1 - a*x]*(4 - 19*a*x + 119*a^3*x^3*Hypergeometric2F1[-1/2, 2, 1/2, 1 + a*x]))/(x^3*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","C",0
436,1,65,249,0.0291706,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Integrate[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^5),x]","\frac{c \sqrt{1-a x} \left(223 a^4 x^4 \, _2F_1\left(-\frac{1}{2},3;\frac{1}{2};a x+1\right)+25 a x-6\right)}{24 x^4 \sqrt{a x+1} \sqrt{c-a c x}}","\frac{1115 a^4 c^2 (1-a x)^{3/2}}{64 \sqrt{a x+1} (c-a c x)^{3/2}}-\frac{1115 a^4 c^2 (1-a x)^{3/2} \tanh ^{-1}\left(\sqrt{a x+1}\right)}{64 (c-a c x)^{3/2}}+\frac{1115 a^3 c^2 (1-a x)^{3/2}}{192 x \sqrt{a x+1} (c-a c x)^{3/2}}-\frac{223 a^2 c^2 (1-a x)^{3/2}}{96 x^2 \sqrt{a x+1} (c-a c x)^{3/2}}-\frac{c^2 (1-a x)^{3/2}}{4 x^4 \sqrt{a x+1} (c-a c x)^{3/2}}+\frac{25 a c^2 (1-a x)^{3/2}}{24 x^3 \sqrt{a x+1} (c-a c x)^{3/2}}",1,"(c*Sqrt[1 - a*x]*(-6 + 25*a*x + 223*a^4*x^4*Hypergeometric2F1[-1/2, 3, 1/2, 1 + a*x]))/(24*x^4*Sqrt[1 + a*x]*Sqrt[c - a*c*x])","C",0
437,1,56,61,0.0264331,"\int e^{-2 p \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[(c - a*c*x)^p/E^(2*p*ArcTanh[a*x]),x]","-\frac{2^{-p} (1-a x)^{p+1} (c-a c x)^p \, _2F_1\left(p,2 p+1;2 p+2;\frac{1}{2}-\frac{a x}{2}\right)}{2 a p+a}","-\frac{2^{-p} (1-a x)^p (c-a c x)^{p+1} \, _2F_1\left(p,2 p+1;2 (p+1);\frac{1}{2} (1-a x)\right)}{a c (2 p+1)}",1,"-(((1 - a*x)^(1 + p)*(c - a*c*x)^p*Hypergeometric2F1[p, 1 + 2*p, 2 + 2*p, 1/2 - (a*x)/2])/(2^p*(a + 2*a*p)))","A",1
438,1,32,37,0.0268683,"\int e^{2 p \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[E^(2*p*ArcTanh[a*x])*(c - a*c*x)^p,x]","\frac{(a x+1) (c-a c x)^p e^{2 p \tanh ^{-1}(a x)}}{a (p+1)}","\frac{(1-a x)^{-p} (a x+1)^{p+1} (c-a c x)^p}{a (p+1)}",1,"(E^(2*p*ArcTanh[a*x])*(1 + a*x)*(c - a*c*x)^p)/(a*(1 + p))","A",1
439,1,77,82,0.0247697,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x)^p,x]","\frac{2^{\frac{n}{2}+1} (1-a x)^{1-\frac{n}{2}} (c-a c x)^p \, _2F_1\left(-\frac{n}{2},-\frac{n}{2}+p+1;-\frac{n}{2}+p+2;\frac{1}{2}-\frac{a x}{2}\right)}{a (n-2 (p+1))}","-\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} (c-a c x)^{p+1} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2}+p+1;-\frac{n}{2}+p+2;\frac{1}{2} (1-a x)\right)}{a c (-n+2 p+2)}",1,"(2^(1 + n/2)*(1 - a*x)^(1 - n/2)*(c - a*c*x)^p*Hypergeometric2F1[-1/2*n, 1 - n/2 + p, 2 - n/2 + p, 1/2 - (a*x)/2])/(a*(n - 2*(1 + p)))","A",1
440,1,65,68,0.0223208,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x)^3,x]","\frac{c^3 2^{\frac{n}{2}+1} (1-a x)^{4-\frac{n}{2}} \, _2F_1\left(4-\frac{n}{2},-\frac{n}{2};5-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (n-8)}","-\frac{c^3 2^{\frac{n}{2}+1} (1-a x)^{4-\frac{n}{2}} \, _2F_1\left(4-\frac{n}{2},-\frac{n}{2};5-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (8-n)}",1,"(2^(1 + n/2)*c^3*(1 - a*x)^(4 - n/2)*Hypergeometric2F1[4 - n/2, -1/2*n, 5 - n/2, (1 - a*x)/2])/(a*(-8 + n))","A",1
441,1,65,68,0.0182184,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x)^2,x]","\frac{c^2 2^{\frac{n}{2}+1} (1-a x)^{3-\frac{n}{2}} \, _2F_1\left(3-\frac{n}{2},-\frac{n}{2};4-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (n-6)}","-\frac{c^2 2^{\frac{n}{2}+1} (1-a x)^{3-\frac{n}{2}} \, _2F_1\left(3-\frac{n}{2},-\frac{n}{2};4-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (6-n)}",1,"(2^(1 + n/2)*c^2*(1 - a*x)^(3 - n/2)*Hypergeometric2F1[3 - n/2, -1/2*n, 4 - n/2, (1 - a*x)/2])/(a*(-6 + n))","A",1
442,1,63,66,0.0172667,"\int e^{n \tanh ^{-1}(a x)} (c-a c x) \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a*c*x),x]","\frac{c 2^{\frac{n}{2}+1} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(2-\frac{n}{2},-\frac{n}{2};3-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (n-4)}","-\frac{c 2^{\frac{n}{2}+1} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(2-\frac{n}{2},-\frac{n}{2};3-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (4-n)}",1,"(2^(1 + n/2)*c*(1 - a*x)^(2 - n/2)*Hypergeometric2F1[2 - n/2, -1/2*n, 3 - n/2, (1 - a*x)/2])/(a*(-4 + n))","A",1
443,1,59,59,0.0099124,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-a c x} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x),x]","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a c n}","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a c n}",1,"(2^(1 + n/2)*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a*x)/2])/(a*c*n*(1 - a*x)^(n/2))","A",1
444,1,39,39,0.0199071,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x)^2,x]","\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n}{2}+1}}{a c^2 (n+2)}","\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n+2}{2}}}{a c^2 (n+2)}",1,"((1 - a*x)^(-1 - n/2)*(1 + a*x)^(1 + n/2))/(a*c^2*(2 + n))","A",1
445,1,51,84,0.0331395,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x)^3,x]","\frac{(1-a x)^{-\frac{n}{2}-2} (-a x+n+3) (a x+1)^{\frac{n}{2}+1}}{a c^3 (n+2) (n+4)}","\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a c^3 \left(n^2+6 n+8\right)}+\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-2}}{a c^3 (n+4)}",1,"((1 - a*x)^(-2 - n/2)*(3 + n - a*x)*(1 + a*x)^(1 + n/2))/(a*c^3*(2 + n)*(4 + n))","A",1
446,1,74,135,0.0464535,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a*c*x)^4,x]","\frac{(1-a x)^{-\frac{n}{2}-3} (a x+1)^{\frac{n}{2}+1} \left(2 a^2 x^2-2 a n x-8 a x+n^2+8 n+14\right)}{a c^4 (n+2) (n+4) (n+6)}","\frac{2 (a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a c^4 (n+6) \left(n^2+6 n+8\right)}+\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-3}}{a c^4 (n+6)}+\frac{2 (a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-2}}{a c^4 (n+4) (n+6)}",1,"((1 - a*x)^(-3 - n/2)*(1 + a*x)^(1 + n/2)*(14 + 8*n + n^2 - 8*a*x - 2*a*n*x + 2*a^2*x^2))/(a*c^4*(2 + n)*(4 + n)*(6 + n))","A",1
447,0,0,60,1.3969883,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^p,x]","\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","\frac{x (1-a x)^{-p} F_1\left(1-p;\frac{1}{2}-p,-\frac{1}{2};2-p;a x,-a x\right) \left(c-\frac{c}{a x}\right)^p}{1-p}",1,"Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^p, x]","F",-1
448,1,86,125,0.2552016,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^4,x]","\frac{c^4 \left(-3 \log \left(\sqrt{1-a^2 x^2}+1\right)-\frac{\sqrt{1-a^2 x^2} \left(6 a^3 x^3+16 a^2 x^2-9 a x+2\right)}{a^3 x^3}+3 \log (a x)-18 \sin ^{-1}(a x)\right)}{6 a}","-\frac{c^4 (6-a x) \sqrt{1-a^2 x^2}}{2 a^2 x}-\frac{c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}+\frac{3 c^4 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{3 c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*(-((Sqrt[1 - a^2*x^2]*(2 - 9*a*x + 16*a^2*x^2 + 6*a^3*x^3))/(a^3*x^3)) - 18*ArcSin[a*x] + 3*Log[a*x] - 3*Log[1 + Sqrt[1 - a^2*x^2]]))/(6*a)","A",0
449,1,75,97,0.1989787,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^3,x]","\frac{c^3 \left(\frac{\sqrt{1-a^2 x^2} \left(-2 a^2 x^2-4 a x+1\right)}{a^2 x^2}+\log \left(\sqrt{1-a^2 x^2}+1\right)-\log (a x)-4 \sin ^{-1}(a x)\right)}{2 a}","-\frac{c^3 (a x+4) \sqrt{1-a^2 x^2}}{2 a^2 x}+\frac{c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{2 c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*(((1 - 4*a*x - 2*a^2*x^2)*Sqrt[1 - a^2*x^2])/(a^2*x^2) - 4*ArcSin[a*x] - Log[a*x] + Log[1 + Sqrt[1 - a^2*x^2]]))/(2*a)","A",0
450,1,78,65,0.1055224,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^2,x]","-\frac{c^2 \left(a x \sqrt{1-a^2 x^2}+\sqrt{1-a^2 x^2}-a x \log \left(\sqrt{1-a^2 x^2}+1\right)+a x \log (a x)+a x \sin ^{-1}(a x)\right)}{a^2 x}","-\frac{c^2 (a x+1) \sqrt{1-a^2 x^2}}{a^2 x}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{c^2 \sin ^{-1}(a x)}{a}",1,"-((c^2*(Sqrt[1 - a^2*x^2] + a*x*Sqrt[1 - a^2*x^2] + a*x*ArcSin[a*x] + a*x*Log[a*x] - a*x*Log[1 + Sqrt[1 - a^2*x^2]]))/(a^2*x))","A",0
451,1,42,41,0.0440909,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x)),x]","-\frac{c \left(\sqrt{1-a^2 x^2}-\log \left(\sqrt{1-a^2 x^2}+1\right)+\log (x)\right)}{a}","\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{c \sqrt{1-a^2 x^2}}{a}",1,"-((c*(Sqrt[1 - a^2*x^2] + Log[x] - Log[1 + Sqrt[1 - a^2*x^2]]))/a)","A",0
452,1,52,65,0.0406796,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a*x)),x]","\frac{\frac{(a x-3) \sqrt{a x+1}}{\sqrt{1-a x}}-4 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{a c}","-\frac{\left(1-a^2 x^2\right)^{3/2}}{a c (1-a x)^2}-\frac{2 \sqrt{1-a^2 x^2}}{a c}+\frac{2 \sin ^{-1}(a x)}{a c}",1,"(((-3 + a*x)*Sqrt[1 + a*x])/Sqrt[1 - a*x] - 4*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(a*c)","A",0
453,1,53,104,0.1358242,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a*x))^2,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(-3 a^2 x^2+19 a x-14\right)}{(a x-1)^2}+9 \sin ^{-1}(a x)}{3 a c^2}","\frac{\left(1-a^2 x^2\right)^{3/2}}{a c^2 (1-a x)^2}+\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}-\frac{6 \sqrt{1-a^2 x^2}}{a c^2 (1-a x)}+\frac{3 \sin ^{-1}(a x)}{a c^2}",1,"(((-14 + 19*a*x - 3*a^2*x^2)*Sqrt[1 - a^2*x^2])/(-1 + a*x)^2 + 9*ArcSin[a*x])/(3*a*c^2)","A",1
454,1,61,136,0.1561981,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a*x))^3,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(-15 a^3 x^3+149 a^2 x^2-222 a x+94\right)}{(a x-1)^3}+60 \sin ^{-1}(a x)}{15 a c^3}","\frac{\left(1-a^2 x^2\right)^{3/2}}{a c^3 (1-a x)^2}+\frac{14 \left(1-a^2 x^2\right)^{3/2}}{15 a c^3 (1-a x)^3}-\frac{\left(1-a^2 x^2\right)^{3/2}}{5 a c^3 (1-a x)^4}-\frac{8 \sqrt{1-a^2 x^2}}{a c^3 (1-a x)}+\frac{4 \sin ^{-1}(a x)}{a c^3}",1,"((Sqrt[1 - a^2*x^2]*(94 - 222*a*x + 149*a^2*x^2 - 15*a^3*x^3))/(-1 + a*x)^3 + 60*ArcSin[a*x])/(15*a*c^3)","A",1
455,1,69,168,0.1913073,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a*x))^4,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(-105 a^4 x^4+1444 a^3 x^3-3256 a^2 x^2+2771 a x-824\right)}{(a x-1)^4}+525 \sin ^{-1}(a x)}{105 a c^4}","\frac{\left(1-a^2 x^2\right)^{3/2}}{a c^4 (1-a x)^2}+\frac{184 \left(1-a^2 x^2\right)^{3/2}}{105 a c^4 (1-a x)^3}-\frac{26 \left(1-a^2 x^2\right)^{3/2}}{35 a c^4 (1-a x)^4}+\frac{\left(1-a^2 x^2\right)^{3/2}}{7 a c^4 (1-a x)^5}-\frac{10 \sqrt{1-a^2 x^2}}{a c^4 (1-a x)}+\frac{5 \sin ^{-1}(a x)}{a c^4}",1,"((Sqrt[1 - a^2*x^2]*(-824 + 2771*a*x - 3256*a^2*x^2 + 1444*a^3*x^3 - 105*a^4*x^4))/(-1 + a*x)^4 + 525*ArcSin[a*x])/(105*a*c^4)","A",1
456,1,46,59,0.0294828,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^p,x]","\frac{\left(c-\frac{c}{a x}\right)^p \left((p-2) \, _2F_1\left(1,p;p+1;1-\frac{1}{a x}\right)-a p x\right)}{a p}","-\frac{(2-p) \left(c-\frac{c}{a x}\right)^p \, _2F_1\left(1,p;p+1;1-\frac{1}{a x}\right)}{a p}-x \left(c-\frac{c}{a x}\right)^p",1,"((c - c/(a*x))^p*(-(a*p*x) + (-2 + p)*Hypergeometric2F1[1, p, 1 + p, 1 - 1/(a*x)]))/(a*p)","A",1
457,1,64,62,0.2250296,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^5 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^5,x]","\frac{c^5}{4 a^5 x^4}-\frac{c^5}{a^4 x^3}+\frac{c^5}{a^3 x^2}+\frac{2 c^5}{a^2 x}+\frac{3 c^5 \log (a x)}{a}+c^5 (-x)","\frac{c^5}{4 a^5 x^4}-\frac{c^5}{a^4 x^3}+\frac{c^5}{a^3 x^2}+\frac{2 c^5}{a^2 x}+\frac{3 c^5 \log (x)}{a}+c^5 (-x)",1,"c^5/(4*a^5*x^4) - c^5/(a^4*x^3) + c^5/(a^3*x^2) + (2*c^5)/(a^2*x) - c^5*x + (3*c^5*Log[a*x])/a","A",0
458,1,42,40,0.1588915,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^4,x]","-\frac{c^4}{3 a^4 x^3}+\frac{c^4}{a^3 x^2}+\frac{2 c^4 \log (a x)}{a}+c^4 (-x)","-\frac{c^4}{3 a^4 x^3}+\frac{c^4}{a^3 x^2}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)",1,"-1/3*c^4/(a^4*x^3) + c^4/(a^3*x^2) - c^4*x + (2*c^4*Log[a*x])/a","A",0
459,1,42,40,0.1257999,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^3,x]","\frac{c^3}{2 a^3 x^2}-\frac{c^3}{a^2 x}+\frac{c^3 \log (a x)}{a}+c^3 (-x)","\frac{c^3}{2 a^3 x^2}-\frac{c^3}{a^2 x}+\frac{c^3 \log (x)}{a}+c^3 (-x)",1,"c^3/(2*a^3*x^2) - c^3/(a^2*x) - c^3*x + (c^3*Log[a*x])/a","A",0
460,1,18,18,0.095949,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^2,x]","c^2 (-x)-\frac{c^2}{a^2 x}","c^2 (-x)-\frac{c^2}{a^2 x}",1,"-(c^2/(a^2*x)) - c^2*x","A",1
461,1,13,13,0.037488,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x)),x]","-\frac{c \log (x)}{a}-c x","-\frac{c \log (x)}{a}-c x",1,"-(c*x) - (c*Log[x])/a","A",1
462,1,31,38,0.0296631,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x)),x]","-\frac{a x+\frac{2}{1-a x}+3 \log (1-a x)}{a c}","-\frac{2}{a c (1-a x)}-\frac{3 \log (1-a x)}{a c}-\frac{x}{c}",1,"-((a*x + 2/(1 - a*x) + 3*Log[1 - a*x])/(a*c))","A",1
463,1,51,53,0.0984757,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x))^2,x]","\frac{5}{a c^2 (a x-1)}+\frac{1}{a c^2 (a x-1)^2}-\frac{4 \log (1-a x)}{a c^2}-\frac{x}{c^2}","-\frac{5}{a c^2 (1-a x)}+\frac{1}{a c^2 (1-a x)^2}-\frac{4 \log (1-a x)}{a c^2}-\frac{x}{c^2}",1,"-(x/c^2) + 1/(a*c^2*(-1 + a*x)^2) + 5/(a*c^2*(-1 + a*x)) - (4*Log[1 - a*x])/(a*c^2)","A",1
464,1,63,74,0.1255492,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x))^3,x]","\frac{-6 a^4 x^4+18 a^3 x^3+36 a^2 x^2-81 a x-30 (a x-1)^3 \log (1-a x)+37}{6 a c^3 (a x-1)^3}","-\frac{9}{a c^3 (1-a x)}+\frac{7}{2 a c^3 (1-a x)^2}-\frac{2}{3 a c^3 (1-a x)^3}-\frac{5 \log (1-a x)}{a c^3}-\frac{x}{c^3}",1,"(37 - 81*a*x + 36*a^2*x^2 + 18*a^3*x^3 - 6*a^4*x^4 - 30*(-1 + a*x)^3*Log[1 - a*x])/(6*a*c^3*(-1 + a*x)^3)","A",1
465,1,71,88,0.1542439,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x))^4,x]","\frac{-2 a^5 x^5+8 a^4 x^4+16 a^3 x^3-60 a^2 x^2+56 a x-12 (a x-1)^4 \log (1-a x)-17}{2 a c^4 (a x-1)^4}","-\frac{14}{a c^4 (1-a x)}+\frac{8}{a c^4 (1-a x)^2}-\frac{3}{a c^4 (1-a x)^3}+\frac{1}{2 a c^4 (1-a x)^4}-\frac{6 \log (1-a x)}{a c^4}-\frac{x}{c^4}",1,"(-17 + 56*a*x - 60*a^2*x^2 + 16*a^3*x^3 + 8*a^4*x^4 - 2*a^5*x^5 - 12*(-1 + a*x)^4*Log[1 - a*x])/(2*a*c^4*(-1 + a*x)^4)","A",1
466,1,85,103,0.260164,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^4,x]","\frac{c^4 \left(-9 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{\sqrt{1-a^2 x^2} \left(6 a^3 x^3+8 a^2 x^2+3 a x-2\right)}{a^3 x^3}+9 \log (a x)+6 \sin ^{-1}(a x)\right)}{6 a}","\frac{c^4 (3 a x+2) \sqrt{1-a^2 x^2}}{2 a^2 x}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^4 (2-3 a x) \left(1-a^2 x^2\right)^{3/2}}{6 a^4 x^3}+\frac{c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*((Sqrt[1 - a^2*x^2]*(-2 + 3*a*x + 8*a^2*x^2 + 6*a^3*x^3))/(a^3*x^3) + 6*ArcSin[a*x] + 9*Log[a*x] - 9*Log[1 + Sqrt[1 - a^2*x^2]]))/(6*a)","A",0
467,1,77,77,0.1355007,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^3,x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{c^3}{2 a^2 x^2}+c^3\right)}{a}-\frac{3 c^3 \log \left(\sqrt{1-a^2 x^2}+1\right)}{2 a}+\frac{3 c^3 \log (a x)}{2 a}","\frac{3 c^3 \sqrt{1-a^2 x^2}}{2 a}-\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}",1,"((c^3 + c^3/(2*a^2*x^2))*Sqrt[1 - a^2*x^2])/a + (3*c^3*Log[a*x])/(2*a) - (3*c^3*Log[1 + Sqrt[1 - a^2*x^2]])/(2*a)","A",0
468,1,82,67,0.1101186,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^2,x]","\frac{\sqrt{1-a^2 x^2} \left(c^2-\frac{c^2}{a x}\right)}{a}-\frac{c^2 \log \left(\sqrt{1-a^2 x^2}+1\right)}{a}+\frac{c^2 \log (a x)}{a}-\frac{c^2 \sin ^{-1}(a x)}{a}","-\frac{c^2 (1-a x) \sqrt{1-a^2 x^2}}{a^2 x}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{c^2 \sin ^{-1}(a x)}{a}",1,"((c^2 - c^2/(a*x))*Sqrt[1 - a^2*x^2])/a - (c^2*ArcSin[a*x])/a + (c^2*Log[a*x])/a - (c^2*Log[1 + Sqrt[1 - a^2*x^2]])/a","A",0
469,1,47,50,0.0551538,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x)),x]","\frac{c \left(\sqrt{1-a^2 x^2}+\log \left(\sqrt{1-a^2 x^2}+1\right)-2 \sin ^{-1}(a x)-\log (x)\right)}{a}","\frac{c \sqrt{1-a^2 x^2}}{a}+\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{2 c \sin ^{-1}(a x)}{a}",1,"(c*(Sqrt[1 - a^2*x^2] - 2*ArcSin[a*x] - Log[x] + Log[1 + Sqrt[1 - a^2*x^2]]))/a","A",0
470,1,62,99,0.0355544,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a*x)),x]","-\frac{16 \sqrt{2} (a x-1) \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};\frac{1}{2} (1-a x)\right)+(a x+1)^{5/2}}{3 a c (1-a x)^{3/2}}","-\frac{\left(1-a^2 x^2\right)^{5/2}}{3 a c (1-a x)^4}+\frac{8 \left(1-a^2 x^2\right)^{3/2}}{3 a c (1-a x)^2}+\frac{4 \sqrt{1-a^2 x^2}}{a c}-\frac{4 \sin ^{-1}(a x)}{a c}",1,"-1/3*((1 + a*x)^(5/2) + 16*Sqrt[2]*(-1 + a*x)*Hypergeometric2F1[-3/2, -1/2, 1/2, (1 - a*x)/2])/(a*c*(1 - a*x)^(3/2))","C",0
471,1,61,128,0.1349437,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a*x))^2,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(15 a^3 x^3-188 a^2 x^2+279 a x-118\right)}{(a x-1)^3}-75 \sin ^{-1}(a x)}{15 a c^2}","\frac{(a x+1)^5}{5 a c^2 \left(1-a^2 x^2\right)^{5/2}}-\frac{2 (a x+1)^4}{3 a c^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{10 (a x+1)^2}{3 a c^2 \sqrt{1-a^2 x^2}}+\frac{5 \sqrt{1-a^2 x^2}}{a c^2}-\frac{5 \sin ^{-1}(a x)}{a c^2}",1,"((Sqrt[1 - a^2*x^2]*(-118 + 279*a*x - 188*a^2*x^2 + 15*a^3*x^3))/(-1 + a*x)^3 - 75*ArcSin[a*x])/(15*a*c^2)","A",1
472,1,69,155,0.1630359,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a*x))^3,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(7 a^4 x^4-116 a^3 x^3+261 a^2 x^2-222 a x+66\right)}{(a x-1)^4}-42 \sin ^{-1}(a x)}{7 a c^3}","-\frac{(a x+1)^6}{7 a c^3 \left(1-a^2 x^2\right)^{7/2}}+\frac{4 (a x+1)^5}{7 a c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{(a x+1)^4}{a c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{4 (a x+1)^2}{a c^3 \sqrt{1-a^2 x^2}}+\frac{6 \sqrt{1-a^2 x^2}}{a c^3}-\frac{6 \sin ^{-1}(a x)}{a c^3}",1,"((Sqrt[1 - a^2*x^2]*(66 - 222*a*x + 261*a^2*x^2 - 116*a^3*x^3 + 7*a^4*x^4))/(-1 + a*x)^4 - 42*ArcSin[a*x])/(7*a*c^3)","A",1
473,1,77,190,0.1950056,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a*x))^4,x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(315 a^5 x^5-6539 a^4 x^4+19780 a^3 x^3-25347 a^2 x^2+15115 a x-3464\right)}{(a x-1)^5}-2205 \sin ^{-1}(a x)}{315 a c^4}","\frac{(a x+1)^7}{9 a c^4 \left(1-a^2 x^2\right)^{9/2}}-\frac{34 (a x+1)^6}{63 a c^4 \left(1-a^2 x^2\right)^{7/2}}+\frac{344 (a x+1)^5}{315 a c^4 \left(1-a^2 x^2\right)^{5/2}}-\frac{4 (a x+1)^4}{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{14 (a x+1)^2}{3 a c^4 \sqrt{1-a^2 x^2}}+\frac{7 \sqrt{1-a^2 x^2}}{a c^4}-\frac{7 \sin ^{-1}(a x)}{a c^4}",1,"((Sqrt[1 - a^2*x^2]*(-3464 + 15115*a*x - 25347*a^2*x^2 + 19780*a^3*x^3 - 6539*a^4*x^4 + 315*a^5*x^5))/(-1 + a*x)^5 - 2205*ArcSin[a*x])/(315*a*c^4)","A",1
474,1,81,93,0.0519655,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a*x))^p,x]","\frac{\left(c-\frac{c}{a x}\right)^p \left(a p x (p (a x-1)-a x+5)-\left(p^2-5 p+4\right) (a x-1) \, _2F_1\left(1,p;p+1;1-\frac{1}{a x}\right)\right)}{a (p-1) p (a x-1)}","\frac{(4-p) \left(c-\frac{c}{a x}\right)^p \, _2F_1\left(1,p;p+1;1-\frac{1}{a x}\right)}{a p}-\frac{c (5-p) \left(c-\frac{c}{a x}\right)^{p-1}}{a (1-p)}+c x \left(c-\frac{c}{a x}\right)^{p-1}",1,"((c - c/(a*x))^p*(a*p*x*(5 - a*x + p*(-1 + a*x)) - (4 - 5*p + p^2)*(-1 + a*x)*Hypergeometric2F1[1, p, 1 + p, 1 - 1/(a*x)]))/(a*(-1 + p)*p*(-1 + a*x))","A",1
475,1,66,64,0.2757463,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^5 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a*x))^5,x]","\frac{c^5}{4 a^5 x^4}-\frac{c^5}{3 a^4 x^3}-\frac{c^5}{a^3 x^2}+\frac{2 c^5}{a^2 x}-\frac{c^5 \log (a x)}{a}+c^5 x","\frac{c^5}{4 a^5 x^4}-\frac{c^5}{3 a^4 x^3}-\frac{c^5}{a^3 x^2}+\frac{2 c^5}{a^2 x}-\frac{c^5 \log (x)}{a}+c^5 x",1,"c^5/(4*a^5*x^4) - c^5/(3*a^4*x^3) - c^5/(a^3*x^2) + (2*c^5)/(a^2*x) + c^5*x - (c^5*Log[a*x])/a","A",0
476,1,30,30,0.1894284,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a*x))^4,x]","-\frac{c^4}{3 a^4 x^3}+\frac{2 c^4}{a^2 x}+c^4 x","-\frac{c^4}{3 a^4 x^3}+\frac{2 c^4}{a^2 x}+c^4 x",1,"-1/3*c^4/(a^4*x^3) + (2*c^4)/(a^2*x) + c^4*x","A",1
477,1,40,38,0.1420788,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a*x))^3,x]","\frac{c^3}{2 a^3 x^2}+\frac{c^3}{a^2 x}+\frac{c^3 \log (a x)}{a}+c^3 x","\frac{c^3}{2 a^3 x^2}+\frac{c^3}{a^2 x}+\frac{c^3 \log (x)}{a}+c^3 x",1,"c^3/(2*a^3*x^2) + c^3/(a^2*x) + c^3*x + (c^3*Log[a*x])/a","A",0
478,1,29,27,0.1001157,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a*x))^2,x]","-\frac{c^2}{a^2 x}+\frac{2 c^2 \log (a x)}{a}+c^2 x","-\frac{c^2}{a^2 x}+\frac{2 c^2 \log (x)}{a}+c^2 x",1,"-(c^2/(a^2*x)) + c^2*x + (2*c^2*Log[a*x])/a","A",0
479,1,25,25,0.0393394,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a*x)),x]","-\frac{c \log (x)}{a}+\frac{4 c \log (1-a x)}{a}+c x","-\frac{c \log (x)}{a}+\frac{4 c \log (1-a x)}{a}+c x",1,"c*x - (c*Log[x])/a + (4*c*Log[1 - a*x])/a","A",1
480,1,51,53,0.033006,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a*x)),x]","-\frac{a \left(-\frac{8}{a^2 (1-a x)}+\frac{2}{a^2 (1-a x)^2}-\frac{5 \log (1-a x)}{a^2}-\frac{x}{a}\right)}{c}","\frac{8}{a c (1-a x)}-\frac{2}{a c (1-a x)^2}+\frac{5 \log (1-a x)}{a c}+\frac{x}{c}",1,"-((a*(-(x/a) + 2/(a^2*(1 - a*x)^2) - 8/(a^2*(1 - a*x)) - (5*Log[1 - a*x])/a^2))/c)","A",1
481,1,63,71,0.1095317,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a*x))^2,x]","\frac{3 a^4 x^4-9 a^3 x^3-30 a^2 x^2+57 a x+18 (a x-1)^3 \log (1-a x)-25}{3 a c^2 (a x-1)^3}","\frac{13}{a c^2 (1-a x)}-\frac{6}{a c^2 (1-a x)^2}+\frac{4}{3 a c^2 (1-a x)^3}+\frac{6 \log (1-a x)}{a c^2}+\frac{x}{c^2}",1,"(-25 + 57*a*x - 30*a^2*x^2 - 9*a^3*x^3 + 3*a^4*x^4 + 18*(-1 + a*x)^3*Log[1 - a*x])/(3*a*c^2*(-1 + a*x)^3)","A",1
482,1,71,89,0.1424229,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a*x))^3,x]","\frac{6 a^5 x^5-24 a^4 x^4-78 a^3 x^3+243 a^2 x^2-218 a x+42 (a x-1)^4 \log (1-a x)+65}{6 a c^3 (a x-1)^4}","\frac{19}{a c^3 (1-a x)}-\frac{25}{2 a c^3 (1-a x)^2}+\frac{16}{3 a c^3 (1-a x)^3}-\frac{1}{a c^3 (1-a x)^4}+\frac{7 \log (1-a x)}{a c^3}+\frac{x}{c^3}",1,"(65 - 218*a*x + 243*a^2*x^2 - 78*a^3*x^3 - 24*a^4*x^4 + 6*a^5*x^5 + 42*(-1 + a*x)^4*Log[1 - a*x])/(6*a*c^3*(-1 + a*x)^4)","A",1
483,1,79,105,0.1723941,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a*x))^4,x]","\frac{15 a^6 x^6-75 a^5 x^5-240 a^4 x^4+1080 a^3 x^3-1480 a^2 x^2+890 a x+120 (a x-1)^5 \log (1-a x)-202}{15 a c^4 (a x-1)^5}","\frac{26}{a c^4 (1-a x)}-\frac{22}{a c^4 (1-a x)^2}+\frac{41}{3 a c^4 (1-a x)^3}-\frac{5}{a c^4 (1-a x)^4}+\frac{4}{5 a c^4 (1-a x)^5}+\frac{8 \log (1-a x)}{a c^4}+\frac{x}{c^4}",1,"(-202 + 890*a*x - 1480*a^2*x^2 + 1080*a^3*x^3 - 240*a^4*x^4 - 75*a^5*x^5 + 15*a^6*x^6 + 120*(-1 + a*x)^5*Log[1 - a*x])/(15*a*c^4*(-1 + a*x)^5)","A",1
484,0,0,60,1.1195584,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[(c - c/(a*x))^p/E^ArcTanh[a*x],x]","\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","\frac{x (1-a x)^{-p} F_1\left(1-p;-p-\frac{1}{2},\frac{1}{2};2-p;a x,-a x\right) \left(c-\frac{c}{a x}\right)^p}{1-p}",1,"Integrate[(c - c/(a*x))^p/E^ArcTanh[a*x], x]","F",-1
485,1,85,140,0.2525855,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Integrate[(c - c/(a*x))^4/E^ArcTanh[a*x],x]","\frac{c^4 \left(75 \log \left(\sqrt{1-a^2 x^2}+1\right)+\frac{\sqrt{1-a^2 x^2} \left(6 a^3 x^3-64 a^2 x^2+15 a x-2\right)}{a^3 x^3}-75 \log (a x)+30 \sin ^{-1}(a x)\right)}{6 a}","\frac{c^4 \sqrt{1-a^2 x^2}}{a}-\frac{32 c^4 \sqrt{1-a^2 x^2}}{3 a^2 x}+\frac{25 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^4 \sqrt{1-a^2 x^2}}{3 a^4 x^3}+\frac{5 c^4 \sqrt{1-a^2 x^2}}{2 a^3 x^2}+\frac{5 c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*((Sqrt[1 - a^2*x^2]*(-2 + 15*a*x - 64*a^2*x^2 + 6*a^3*x^3))/(a^3*x^3) + 30*ArcSin[a*x] - 75*Log[a*x] + 75*Log[1 + Sqrt[1 - a^2*x^2]]))/(6*a)","A",0
486,1,77,111,0.1926535,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[(c - c/(a*x))^3/E^ArcTanh[a*x],x]","\frac{c^3 \left(\frac{\sqrt{1-a^2 x^2} \left(2 a^2 x^2-8 a x+1\right)}{a^2 x^2}+13 \log \left(\sqrt{1-a^2 x^2}+1\right)-13 \log (a x)+8 \sin ^{-1}(a x)\right)}{2 a}","\frac{c^3 \sqrt{1-a^2 x^2}}{a}-\frac{4 c^3 \sqrt{1-a^2 x^2}}{a^2 x}+\frac{13 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{c^3 \sqrt{1-a^2 x^2}}{2 a^3 x^2}+\frac{4 c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*((Sqrt[1 - a^2*x^2]*(1 - 8*a*x + 2*a^2*x^2))/(a^2*x^2) + 8*ArcSin[a*x] - 13*Log[a*x] + 13*Log[1 + Sqrt[1 - a^2*x^2]]))/(2*a)","A",0
487,1,83,82,0.125586,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[(c - c/(a*x))^2/E^ArcTanh[a*x],x]","\frac{\sqrt{1-a^2 x^2} \left(c^2-\frac{c^2}{a x}\right)}{a}+\frac{3 c^2 \log \left(\sqrt{1-a^2 x^2}+1\right)}{a}-\frac{3 c^2 \log (a x)}{a}+\frac{3 c^2 \sin ^{-1}(a x)}{a}","\frac{c^2 \sqrt{1-a^2 x^2}}{a}-\frac{c^2 \sqrt{1-a^2 x^2}}{a^2 x}+\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}+\frac{3 c^2 \sin ^{-1}(a x)}{a}",1,"((c^2 - c^2/(a*x))*Sqrt[1 - a^2*x^2])/a + (3*c^2*ArcSin[a*x])/a - (3*c^2*Log[a*x])/a + (3*c^2*Log[1 + Sqrt[1 - a^2*x^2]])/a","A",0
488,1,47,50,0.0552754,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[(c - c/(a*x))/E^ArcTanh[a*x],x]","\frac{c \left(\sqrt{1-a^2 x^2}+\log \left(\sqrt{1-a^2 x^2}+1\right)+2 \sin ^{-1}(a x)-\log (x)\right)}{a}","\frac{c \sqrt{1-a^2 x^2}}{a}+\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}+\frac{2 c \sin ^{-1}(a x)}{a}",1,"(c*(Sqrt[1 - a^2*x^2] + 2*ArcSin[a*x] - Log[x] + Log[1 + Sqrt[1 - a^2*x^2]]))/a","A",0
489,1,21,21,0.0140327,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))),x]","\frac{\sqrt{1-a^2 x^2}}{a c}","\frac{\sqrt{1-a^2 x^2}}{a c}",1,"Sqrt[1 - a^2*x^2]/(a*c)","A",1
490,1,47,63,0.0991441,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))^2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{c^2}-\frac{1}{c^2 (a x-1)}\right)}{a}-\frac{\sin ^{-1}(a x)}{a c^2}","\frac{\sqrt{1-a^2 x^2}}{a c^2 (1-a x)}+\frac{\sqrt{1-a^2 x^2}}{a c^2}-\frac{\sin ^{-1}(a x)}{a c^2}",1,"(Sqrt[1 - a^2*x^2]*(c^(-2) - 1/(c^2*(-1 + a*x))))/a - ArcSin[a*x]/(a*c^2)","A",1
491,1,53,94,0.1361627,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))^3),x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(3 a^2 x^2-14 a x+10\right)}{(a x-1)^2}-6 \sin ^{-1}(a x)}{3 a c^3}","-\frac{(a x+1)^2}{3 a c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{8 (a x+1)}{3 a c^3 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2}}{a c^3}-\frac{2 \sin ^{-1}(a x)}{a c^3}",1,"((Sqrt[1 - a^2*x^2]*(10 - 14*a*x + 3*a^2*x^2))/(-1 + a*x)^2 - 6*ArcSin[a*x])/(3*a*c^3)","A",1
492,1,61,125,0.1654631,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))^4),x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(5 a^3 x^3-39 a^2 x^2+57 a x-24\right)}{(a x-1)^3}-15 \sin ^{-1}(a x)}{5 a c^4}","\frac{(a x+1)^3}{5 a c^4 \left(1-a^2 x^2\right)^{5/2}}-\frac{6 (a x+1)^2}{5 a c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{24 (a x+1)}{5 a c^4 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2}}{a c^4}-\frac{3 \sin ^{-1}(a x)}{a c^4}",1,"((Sqrt[1 - a^2*x^2]*(-24 + 57*a*x - 39*a^2*x^2 + 5*a^3*x^3))/(-1 + a*x)^3 - 15*ArcSin[a*x])/(5*a*c^4)","A",1
493,1,87,114,0.0514897,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[(c - c/(a*x))^p/E^(2*ArcTanh[a*x]),x]","-\frac{(a x-1)^2 \left(c-\frac{c}{a x}\right)^p \left(\, _2F_1\left(1,p+2;p+3;\frac{a-\frac{1}{x}}{2 a}\right)+2 (p+2) \left(a x-\, _2F_1\left(1,p+2;p+3;1-\frac{1}{a x}\right)\right)\right)}{2 a^3 (p+2) x^2}","-\frac{\left(c-\frac{c}{a x}\right)^{p+2} \, _2F_1\left(1,p+2;p+3;\frac{a-\frac{1}{x}}{2 a}\right)}{2 a c^2 (p+2)}+\frac{\left(c-\frac{c}{a x}\right)^{p+2} \, _2F_1\left(1,p+2;p+3;1-\frac{1}{a x}\right)}{a c^2}-\frac{x \left(c-\frac{c}{a x}\right)^{p+2}}{c^2}",1,"-1/2*((c - c/(a*x))^p*(-1 + a*x)^2*(Hypergeometric2F1[1, 2 + p, 3 + p, (a - x^(-1))/(2*a)] + 2*(2 + p)*(a*x - Hypergeometric2F1[1, 2 + p, 3 + p, 1 - 1/(a*x)])))/(a^3*(2 + p)*x^2)","A",1
494,1,68,66,0.1758716,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Integrate[(c - c/(a*x))^4/E^(2*ArcTanh[a*x]),x]","-\frac{c^4}{3 a^4 x^3}+\frac{3 c^4}{a^3 x^2}-\frac{16 c^4}{a^2 x}-\frac{26 c^4 \log (a x)}{a}+\frac{32 c^4 \log (a x+1)}{a}+c^4 (-x)","-\frac{c^4}{3 a^4 x^3}+\frac{3 c^4}{a^3 x^2}-\frac{16 c^4}{a^2 x}-\frac{26 c^4 \log (x)}{a}+\frac{32 c^4 \log (a x+1)}{a}+c^4 (-x)",1,"-1/3*c^4/(a^4*x^3) + (3*c^4)/(a^3*x^2) - (16*c^4)/(a^2*x) - c^4*x - (26*c^4*Log[a*x])/a + (32*c^4*Log[1 + a*x])/a","A",0
495,1,57,55,0.129997,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[(c - c/(a*x))^3/E^(2*ArcTanh[a*x]),x]","\frac{c^3}{2 a^3 x^2}-\frac{5 c^3}{a^2 x}-\frac{11 c^3 \log (a x)}{a}+\frac{16 c^3 \log (a x+1)}{a}+c^3 (-x)","\frac{c^3}{2 a^3 x^2}-\frac{5 c^3}{a^2 x}-\frac{11 c^3 \log (x)}{a}+\frac{16 c^3 \log (a x+1)}{a}+c^3 (-x)",1,"c^3/(2*a^3*x^2) - (5*c^3)/(a^2*x) - c^3*x - (11*c^3*Log[a*x])/a + (16*c^3*Log[1 + a*x])/a","A",0
496,1,44,42,0.0996612,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[(c - c/(a*x))^2/E^(2*ArcTanh[a*x]),x]","-\frac{c^2}{a^2 x}-\frac{4 c^2 \log (a x)}{a}+\frac{8 c^2 \log (a x+1)}{a}+c^2 (-x)","-\frac{c^2}{a^2 x}-\frac{4 c^2 \log (x)}{a}+\frac{8 c^2 \log (a x+1)}{a}+c^2 (-x)",1,"-(c^2/(a^2*x)) - c^2*x - (4*c^2*Log[a*x])/a + (8*c^2*Log[1 + a*x])/a","A",0
497,1,25,25,0.0401271,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[(c - c/(a*x))/E^(2*ArcTanh[a*x]),x]","-\frac{c \log (x)}{a}+\frac{4 c \log (a x+1)}{a}-c x","-\frac{c \log (x)}{a}+\frac{4 c \log (a x+1)}{a}-c x",1,"-(c*x) - (c*Log[x])/a + (4*c*Log[1 + a*x])/a","A",1
498,1,18,20,0.0162382,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))),x]","\frac{\log (a x+1)-a x}{a c}","\frac{\log (a x+1)}{a c}-\frac{x}{c}",1,"(-(a*x) + Log[1 + a*x])/(a*c)","A",1
499,1,40,18,0.0774441,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^2),x]","-\frac{\log (1-a x)}{2 a c^2}+\frac{\log (a x+1)}{2 a c^2}-\frac{x}{c^2}","\frac{\tanh ^{-1}(a x)}{a c^2}-\frac{x}{c^2}",1,"-(x/c^2) - Log[1 - a*x]/(2*a*c^2) + Log[1 + a*x]/(2*a*c^2)","B",0
500,1,57,58,0.111619,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^3),x]","\frac{1}{2 a c^3 (a x-1)}-\frac{5 \log (1-a x)}{4 a c^3}+\frac{\log (a x+1)}{4 a c^3}-\frac{x}{c^3}","-\frac{1}{2 a c^3 (1-a x)}-\frac{5 \log (1-a x)}{4 a c^3}+\frac{\log (a x+1)}{4 a c^3}-\frac{x}{c^3}",1,"-(x/c^3) + 1/(2*a*c^3*(-1 + a*x)) - (5*Log[1 - a*x])/(4*a*c^3) + Log[1 + a*x]/(4*a*c^3)","A",1
501,1,69,76,0.1521469,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^4),x]","\frac{-8 a^3 x^3+16 a^2 x^2+6 a x-17 (a x-1)^2 \log (1-a x)+(a x-1)^2 \log (a x+1)-12}{8 a c^4 (a x-1)^2}","-\frac{7}{4 a c^4 (1-a x)}+\frac{1}{4 a c^4 (1-a x)^2}-\frac{17 \log (1-a x)}{8 a c^4}+\frac{\log (a x+1)}{8 a c^4}-\frac{x}{c^4}",1,"(-12 + 6*a*x + 16*a^2*x^2 - 8*a^3*x^3 - 17*(-1 + a*x)^2*Log[1 - a*x] + (-1 + a*x)^2*Log[1 + a*x])/(8*a*c^4*(-1 + a*x)^2)","A",1
502,1,93,140,0.3016741,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Integrate[(c - c/(a*x))^3/E^(3*ArcTanh[a*x]),x]","\frac{c^3 \left(33 \log \left(\sqrt{1-a^2 x^2}+1\right)-\frac{\sqrt{1-a^2 x^2} \left(2 a^3 x^3+78 a^2 x^2+11 a x-1\right)}{a^2 x^2 (a x+1)}-33 \log (a x)-12 \sin ^{-1}(a x)\right)}{2 a}","-\frac{c^3 \sqrt{1-a^2 x^2}}{a}-\frac{6 c^3 \sqrt{1-a^2 x^2}}{a^2 x}-\frac{32 c^3 (1-a x)}{a \sqrt{1-a^2 x^2}}+\frac{33 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{c^3 \sqrt{1-a^2 x^2}}{2 a^3 x^2}-\frac{6 c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*(-((Sqrt[1 - a^2*x^2]*(-1 + 11*a*x + 78*a^2*x^2 + 2*a^3*x^3))/(a^2*x^2*(1 + a*x))) - 12*ArcSin[a*x] - 33*Log[a*x] + 33*Log[1 + Sqrt[1 - a^2*x^2]]))/(2*a)","A",0
503,1,81,111,0.2299701,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[(c - c/(a*x))^2/E^(3*ArcTanh[a*x]),x]","\frac{c^2 \left(-\frac{\sqrt{1-a^2 x^2} \left(a^2 x^2+18 a x+1\right)}{a x (a x+1)}+5 \log \left(\sqrt{1-a^2 x^2}+1\right)-5 \log (a x)-5 \sin ^{-1}(a x)\right)}{a}","-\frac{c^2 \sqrt{1-a^2 x^2}}{a}-\frac{c^2 \sqrt{1-a^2 x^2}}{a^2 x}-\frac{16 c^2 (1-a x)}{a \sqrt{1-a^2 x^2}}+\frac{5 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{5 c^2 \sin ^{-1}(a x)}{a}",1,"(c^2*(-((Sqrt[1 - a^2*x^2]*(1 + 18*a*x + a^2*x^2))/(a*x*(1 + a*x))) - 5*ArcSin[a*x] - 5*Log[a*x] + 5*Log[1 + Sqrt[1 - a^2*x^2]]))/a","A",0
504,1,61,77,0.1454676,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[(c - c/(a*x))/E^(3*ArcTanh[a*x]),x]","\frac{c \left(-\frac{\sqrt{1-a^2 x^2} (a x+9)}{a x+1}+\log \left(\sqrt{1-a^2 x^2}+1\right)-4 \sin ^{-1}(a x)-\log (x)\right)}{a}","-\frac{c \sqrt{1-a^2 x^2}}{a}-\frac{8 c (1-a x)}{a \sqrt{1-a^2 x^2}}+\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{4 c \sin ^{-1}(a x)}{a}",1,"(c*(-(((9 + a*x)*Sqrt[1 - a^2*x^2])/(1 + a*x)) - 4*ArcSin[a*x] - Log[x] + Log[1 + Sqrt[1 - a^2*x^2]]))/a","A",0
505,1,67,65,0.0324597,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))),x]","\frac{a^2 x^2+4 \sqrt{1-a^2 x^2} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)+2 a x-3}{a c \sqrt{1-a^2 x^2}}","-\frac{(1-a x)^2}{a c \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2}}{a c}-\frac{2 \sin ^{-1}(a x)}{a c}",1,"(-3 + 2*a*x + a^2*x^2 + 4*Sqrt[1 - a^2*x^2]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]])/(a*c*Sqrt[1 - a^2*x^2])","A",0
506,1,46,63,0.1469547,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^2),x]","-\frac{\sqrt{1-a^2 x^2} (a x+2)+(a x+1) \sin ^{-1}(a x)}{a c^2 (a x+1)}","-\frac{1-a x}{a c^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2}}{a c^2}-\frac{\sin ^{-1}(a x)}{a c^2}",1,"-(((2 + a*x)*Sqrt[1 - a^2*x^2] + (1 + a*x)*ArcSin[a*x])/(a*c^2*(1 + a*x)))","A",1
507,1,30,45,0.1371006,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^3),x]","\frac{a^2 x^2-2}{a c^3 \sqrt{1-a^2 x^2}}","-\frac{\sqrt{1-a^2 x^2}}{a c^3}-\frac{1}{a c^3 \sqrt{1-a^2 x^2}}",1,"(-2 + a^2*x^2)/(a*c^3*Sqrt[1 - a^2*x^2])","A",1
508,1,68,96,0.1895179,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^4),x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(-3 a^3 x^3+7 a^2 x^2+5 a x-8\right)}{(a x-1)^2 (a x+1)}+3 \sin ^{-1}(a x)}{3 a c^4}","-\frac{x (4 a x+3)}{3 c^4 \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{1-a^2 x^2}}{3 a c^4}+\frac{a^2 x^3 (a x+1)}{3 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{\sin ^{-1}(a x)}{a c^4}",1,"((Sqrt[1 - a^2*x^2]*(-8 + 5*a*x + 7*a^2*x^2 - 3*a^3*x^3))/((-1 + a*x)^2*(1 + a*x)) + 3*ArcSin[a*x])/(3*a*c^4)","A",1
509,1,76,125,0.2352302,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^5} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^5),x]","\frac{\frac{\sqrt{1-a^2 x^2} \left(-15 a^4 x^4+76 a^3 x^3-32 a^2 x^2-82 a x+56\right)}{(a x-1)^3 (a x+1)}+30 \sin ^{-1}(a x)}{15 a c^5}","-\frac{(a x+1)^2}{5 a c^5 \left(1-a^2 x^2\right)^{5/2}}+\frac{22 (a x+1)}{15 a c^5 \left(1-a^2 x^2\right)^{3/2}}-\frac{\sqrt{1-a^2 x^2}}{a c^5}-\frac{2 (23 a x+30)}{15 a c^5 \sqrt{1-a^2 x^2}}+\frac{2 \sin ^{-1}(a x)}{a c^5}",1,"((Sqrt[1 - a^2*x^2]*(56 - 82*a*x - 32*a^2*x^2 + 76*a^3*x^3 - 15*a^4*x^4))/((-1 + a*x)^3*(1 + a*x)) + 30*ArcSin[a*x])/(15*a*c^5)","A",1
510,1,101,225,0.0815315,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^(9/2),x]","\frac{c^4 \sqrt{c-\frac{c}{a x}} \left(245 a^2 x^2 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-a x\right)+\sqrt{a x+1} \left(105 a^4 x^4-688 a^3 x^3-601 a^2 x^2+162 a x-30\right)\right)}{105 a^4 x^3 \sqrt{1-a x}}","-\frac{7 a^{7/2} x^{9/2} \left(c-\frac{c}{a x}\right)^{9/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{9/2}}-\frac{a^3 x^4 (54-227 a x) \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{105 (1-a x)^{9/2}}-\frac{10 a^2 x^3 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{21 (1-a x)^{5/2}}+\frac{2 a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{5 (1-a x)^{3/2}}-\frac{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{7 \sqrt{1-a x}}",1,"(c^4*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x]*(-30 + 162*a*x - 601*a^2*x^2 - 688*a^3*x^3 + 105*a^4*x^4) + 245*a^2*x^2*Hypergeometric2F1[-3/2, -3/2, -1/2, -(a*x)]))/(105*a^4*x^3*Sqrt[1 - a*x])","C",0
511,1,95,181,0.0747075,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^(7/2),x]","\frac{c^3 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1} \left(15 a^3 x^3+56 a^2 x^2-28 a x+6\right)-75 a^{5/2} x^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{15 a^3 x^2 \sqrt{1-a x}}","\frac{5 a^{5/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{7/2}}-\frac{a^2 x^3 \sqrt{a x+1} (31 a x+18) \left(c-\frac{c}{a x}\right)^{7/2}}{15 (1-a x)^{7/2}}+\frac{2 a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}{3 (1-a x)^{3/2}}-\frac{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 \sqrt{1-a x}}",1,"(c^3*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x]*(6 - 28*a*x + 56*a^2*x^2 + 15*a^3*x^3) - 75*a^(5/2)*x^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]]))/(15*a^3*x^2*Sqrt[1 - a*x])","A",1
512,1,87,171,0.0640099,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^(5/2),x]","\frac{c^2 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1} \left(3 a^2 x^2+10 a x-2\right)-9 a^{3/2} x^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{3 a^2 x \sqrt{1-a x}}","-\frac{3 a^{3/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{5/2}}-\frac{3 a^2 x^3 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{5/2}}{(1-a x)^{5/2}}+\frac{4 a x^2 (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{5/2}}{(1-a x)^{5/2}}-\frac{2 x (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{5/2}}{3 (1-a x)^{5/2}}",1,"(c^2*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x]*(-2 + 10*a*x + 3*a^2*x^2) - 9*a^(3/2)*x^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]]))/(3*a^2*x*Sqrt[1 - a*x])","A",1
513,1,70,128,0.0518694,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a*x))^(3/2),x]","\frac{c \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1} (a x+2)-\sqrt{a} \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{a \sqrt{1-a x}}","-\frac{2 x \left(1-a^2 x^2\right)^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^3}+\frac{\sqrt{a} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{3/2}}+\frac{a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}",1,"(c*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x]*(2 + a*x) - Sqrt[a]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a*Sqrt[1 - a*x])","A",0
514,1,69,84,0.0420515,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)],x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}+\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{\sqrt{a} \sqrt{1-a x}}","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}-\frac{c \sqrt{1-a^2 x^2}}{a \sqrt{c-\frac{c}{a x}}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] + ArcSinh[Sqrt[a]*Sqrt[x]]))/(Sqrt[a]*Sqrt[1 - a*x])","A",0
515,1,105,157,0.067691,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[E^ArcTanh[a*x]/Sqrt[c - c/(a*x)],x]","-\frac{\sqrt{1-a x} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}+3 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}","-\frac{3 \sqrt{1-a x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}+\frac{2 \sqrt{2} \sqrt{1-a x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}-\frac{\sqrt{1-a x} \sqrt{a x+1}}{a \sqrt{c-\frac{c}{a x}}}",1,"-((Sqrt[1 - a*x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] + 3*ArcSinh[Sqrt[a]*Sqrt[x]] - 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x]))","A",1
516,1,126,198,0.1581141,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a*x))^(3/2),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{a x+1} (a x-2)+10 (a x-1) \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-7 \sqrt{2} (a x-1) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{2 a^{3/2} c \sqrt{x} \sqrt{1-a x} \sqrt{c-\frac{c}{a x}}}","\frac{5 (1-a x)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{7 (1-a x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{2} a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{2 \sqrt{a x+1} (1-a x)^{3/2}}{a^2 x \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{\sqrt{a x+1} \sqrt{1-a x}}{a \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(2*Sqrt[a]*Sqrt[x]*(-2 + a*x)*Sqrt[1 + a*x] + 10*(-1 + a*x)*ArcSinh[Sqrt[a]*Sqrt[x]] - 7*Sqrt[2]*(-1 + a*x)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(2*a^(3/2)*c*Sqrt[c - c/(a*x)]*Sqrt[x]*Sqrt[1 - a*x])","A",1
517,1,139,249,0.1812734,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a*x))^(5/2),x]","\frac{-2 \sqrt{a} \sqrt{x} \sqrt{a x+1} \left(8 a^2 x^2-35 a x+23\right)-112 (a x-1)^2 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+79 \sqrt{2} (a x-1)^2 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{16 a^{3/2} c^2 \sqrt{x} (1-a x)^{3/2} \sqrt{c-\frac{c}{a x}}}","-\frac{7 (1-a x)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{79 (1-a x)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{8 \sqrt{2} a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{23 \sqrt{a x+1} (1-a x)^{5/2}}{8 a^3 x^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{11 \sqrt{a x+1} (1-a x)^{3/2}}{8 a^2 x \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{\sqrt{a x+1} \sqrt{1-a x}}{2 a \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(-2*Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(23 - 35*a*x + 8*a^2*x^2) - 112*(-1 + a*x)^2*ArcSinh[Sqrt[a]*Sqrt[x]] + 79*Sqrt[2]*(-1 + a*x)^2*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(16*a^(3/2)*c^2*Sqrt[c - c/(a*x)]*Sqrt[x]*(1 - a*x)^(3/2))","A",1
518,1,91,145,0.1478674,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(9/2),x]","\frac{5 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{c^4 \left(21 a^4 x^4+92 a^3 x^3+4 a^2 x^2-18 a x+6\right) \sqrt{c-\frac{c}{a x}}}{21 a^4 x^3}","\frac{5 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{5 c^4 \sqrt{c-\frac{c}{a x}}}{a}-\frac{5 c^3 \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-\frac{c^2 \left(c-\frac{c}{a x}\right)^{5/2}}{a}-\frac{5 c \left(c-\frac{c}{a x}\right)^{7/2}}{7 a}-x \left(c-\frac{c}{a x}\right)^{9/2}",1,"-1/21*(c^4*Sqrt[c - c/(a*x)]*(6 - 18*a*x + 4*a^2*x^2 + 92*a^3*x^3 + 21*a^4*x^4))/(a^4*x^3) + (5*c^(9/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",1
519,1,83,120,0.0910568,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(7/2),x]","\frac{3 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{c^3 \left(5 a^3 x^3+8 a^2 x^2+4 a x-2\right) \sqrt{c-\frac{c}{a x}}}{5 a^3 x^2}","\frac{3 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{3 c^3 \sqrt{c-\frac{c}{a x}}}{a}-\frac{c^2 \left(c-\frac{c}{a x}\right)^{3/2}}{a}-\frac{3 c \left(c-\frac{c}{a x}\right)^{5/2}}{5 a}-x \left(c-\frac{c}{a x}\right)^{7/2}",1,"-1/5*(c^3*Sqrt[c - c/(a*x)]*(-2 + 4*a*x + 8*a^2*x^2 + 5*a^3*x^3))/(a^3*x^2) + (3*c^(7/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",1
520,1,75,96,0.0644621,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(5/2),x]","\frac{c^2 \left(-3 a^2 x^2+2 a x-2\right) \sqrt{c-\frac{c}{a x}}+3 a c^{5/2} x \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{3 a^2 x}","\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{c^2 \sqrt{c-\frac{c}{a x}}}{a}-\frac{c \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-x \left(c-\frac{c}{a x}\right)^{5/2}",1,"(c^2*Sqrt[c - c/(a*x)]*(-2 + 2*a*x - 3*a^2*x^2) + 3*a*c^(5/2)*x*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(3*a^2*x)","A",1
521,1,57,71,0.0497591,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(3/2),x]","\frac{c (2-a x) \sqrt{c-\frac{c}{a x}}-c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}+\frac{c \sqrt{c-\frac{c}{a x}}}{a}-x \left(c-\frac{c}{a x}\right)^{3/2}",1,"(c*Sqrt[c - c/(a*x)]*(2 - a*x) - c^(3/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",1
522,1,51,51,0.0308663,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)],x]","x \left(-\sqrt{c-\frac{c}{a x}}\right)-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}","x \left(-\sqrt{c-\frac{c}{a x}}\right)-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}",1,"-(Sqrt[c - c/(a*x)]*x) - (3*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",1
523,1,44,71,0.0283889,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[E^(2*ArcTanh[a*x])/Sqrt[c - c/(a*x)],x]","\frac{5 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-\frac{1}{a x}\right)-a x}{a \sqrt{c-\frac{c}{a x}}}","-\frac{x}{\sqrt{c-\frac{c}{a x}}}+\frac{5}{a \sqrt{c-\frac{c}{a x}}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a \sqrt{c}}",1,"(-(a*x) + 5*Hypergeometric2F1[-1/2, 1, 1/2, 1 - 1/(a*x)])/(a*Sqrt[c - c/(a*x)])","C",0
524,1,55,96,0.0306378,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x))^(3/2),x]","\frac{x \left(7 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};1-\frac{1}{a x}\right)-3 a x\right)}{3 c (a x-1) \sqrt{c-\frac{c}{a x}}}","-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{3/2}}-\frac{x}{\left(c-\frac{c}{a x}\right)^{3/2}}+\frac{7}{a c \sqrt{c-\frac{c}{a x}}}+\frac{7}{3 a \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(x*(-3*a*x + 7*Hypergeometric2F1[-3/2, 1, -1/2, 1 - 1/(a*x)]))/(3*c*Sqrt[c - c/(a*x)]*(-1 + a*x))","C",0
525,1,59,119,0.0302998,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x))^(5/2),x]","\frac{9 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};1-\frac{1}{a x}\right)}{5 a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{x}{\left(c-\frac{c}{a x}\right)^{5/2}}","-\frac{9 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{5/2}}+\frac{9}{a c^2 \sqrt{c-\frac{c}{a x}}}-\frac{x}{\left(c-\frac{c}{a x}\right)^{5/2}}+\frac{3}{a c \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{9}{5 a \left(c-\frac{c}{a x}\right)^{5/2}}",1,"-(x/(c - c/(a*x))^(5/2)) + (9*Hypergeometric2F1[-5/2, 1, -3/2, 1 - 1/(a*x)])/(5*a*(c - c/(a*x))^(5/2))","C",0
526,1,46,146,0.0417822,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a*x))^(7/2),x]","\frac{\frac{11 \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};1-\frac{1}{a x}\right)}{a}-7 x}{7 \left(c-\frac{c}{a x}\right)^{7/2}}","-\frac{11 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{7/2}}+\frac{11}{a c^3 \sqrt{c-\frac{c}{a x}}}+\frac{11}{3 a c^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{x}{\left(c-\frac{c}{a x}\right)^{7/2}}+\frac{11}{5 a c \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{11}{7 a \left(c-\frac{c}{a x}\right)^{7/2}}",1,"(-7*x + (11*Hypergeometric2F1[-7/2, 1, -5/2, 1 - 1/(a*x)])/a)/(7*(c - c/(a*x))^(7/2))","C",0
527,1,85,223,0.0681669,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(9/2),x]","-\frac{c^4 \sqrt{c-\frac{c}{a x}} \left(35 a^2 x^2 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};-a x\right)+\left(35 a^2 x^2-46 a x+10\right) (a x+1)^{5/2}\right)}{35 a^4 x^3 \sqrt{1-a x}}","\frac{3 a^{7/2} x^{9/2} \left(c-\frac{c}{a x}\right)^{9/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{9/2}}-\frac{3 a^3 x^4 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{(1-a x)^{9/2}}+\frac{3 a^2 x^3 (6-17 a x) (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{35 (1-a x)^{9/2}}+\frac{6 a x^2 (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{35 (1-a x)^{5/2}}-\frac{2 x (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{7 (1-a x)^{3/2}}",1,"-1/35*(c^4*Sqrt[c - c/(a*x)]*((1 + a*x)^(5/2)*(10 - 46*a*x + 35*a^2*x^2) + 35*a^2*x^2*Hypergeometric2F1[-3/2, -3/2, -1/2, -(a*x)]))/(a^4*x^3*Sqrt[1 - a*x])","C",0
528,1,77,217,0.0563397,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(7/2),x]","-\frac{2 c^3 \sqrt{c-\frac{c}{a x}} \left(5 a^2 x^2 \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-a x\right)+(10 a x-3) (a x+1)^{5/2}\right)}{15 a^3 x^2 \sqrt{1-a x}}","-\frac{a^{5/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{7/2}}-\frac{a^3 x^4 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}{(1-a x)^{7/2}}+\frac{2 a^2 x^3 (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{7/2}}{3 (1-a x)^{7/2}}+\frac{4 a x^2 (a x+1)^{5/2} \left(c-\frac{c}{a x}\right)^{7/2}}{3 (1-a x)^{7/2}}-\frac{2 x (a x+1)^{5/2} \left(c-\frac{c}{a x}\right)^{7/2}}{5 (1-a x)^{7/2}}",1,"(-2*c^3*Sqrt[c - c/(a*x)]*((1 + a*x)^(5/2)*(-3 + 10*a*x) + 5*a^2*x^2*Hypergeometric2F1[-3/2, -1/2, 1/2, -(a*x)]))/(15*a^3*x^2*Sqrt[1 - a*x])","C",0
529,1,66,176,0.0423624,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(5/2),x]","-\frac{2 c^2 \sqrt{c-\frac{c}{a x}} \left((a x+1)^{5/2}-a x \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-a x\right)\right)}{3 a^2 x \sqrt{1-a x}}","-\frac{a^{3/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{5/2}}-\frac{a^2 x^3 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{5/2}}{(1-a x)^{5/2}}-\frac{2 x \left(1-a^2 x^2\right)^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}{3 (1-a x)^5}+\frac{2 a x^2 (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{5/2}}{3 (1-a x)^{5/2}}",1,"(-2*c^2*Sqrt[c - c/(a*x)]*((1 + a*x)^(5/2) - a*x*Hypergeometric2F1[-3/2, -1/2, 1/2, -(a*x)]))/(3*a^2*x*Sqrt[1 - a*x])","C",0
530,1,42,127,0.0257882,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(3/2),x]","-\frac{2 x \left(c-\frac{c}{a x}\right)^{3/2} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-a x\right)}{(1-a x)^{3/2}}","\frac{3 \sqrt{a} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{3/2}}+\frac{3 a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}-\frac{2 x (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}",1,"(-2*(c - c/(a*x))^(3/2)*x*Hypergeometric2F1[-3/2, -1/2, 1/2, -(a*x)])/(1 - a*x)^(3/2)","C",0
531,1,105,155,0.0731783,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)],x]","-\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}+5 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{\sqrt{a} \sqrt{1-a x}}","-\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}-\frac{5 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}+\frac{4 \sqrt{2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{a} \sqrt{1-a x}}",1,"-((Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] + 5*ArcSinh[Sqrt[a]*Sqrt[x]] - 4*Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(Sqrt[a]*Sqrt[1 - a*x]))","A",1
532,1,120,195,0.1057321,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[E^(3*ArcTanh[a*x])/Sqrt[c - c/(a*x)],x]","\frac{\sqrt{a} \sqrt{x} \sqrt{a x+1} (3-a x)+(7-7 a x) \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+5 \sqrt{2} (a x-1) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{3/2} \sqrt{x} \sqrt{1-a x} \sqrt{c-\frac{c}{a x}}}","\frac{7 \sqrt{1-a x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}-\frac{5 \sqrt{2} \sqrt{1-a x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}+\frac{(a x+1)^{3/2}}{a \sqrt{1-a x} \sqrt{c-\frac{c}{a x}}}+\frac{2 \sqrt{1-a x} \sqrt{a x+1}}{a \sqrt{c-\frac{c}{a x}}}",1,"(Sqrt[a]*Sqrt[x]*(3 - a*x)*Sqrt[1 + a*x] + (7 - 7*a*x)*ArcSinh[Sqrt[a]*Sqrt[x]] + 5*Sqrt[2]*(-1 + a*x)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x]*Sqrt[1 - a*x])","A",1
533,1,139,249,0.1424993,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a*x))^(3/2),x]","-\frac{-2 \sqrt{a} \sqrt{x} \sqrt{a x+1} \left(4 a^2 x^2-23 a x+15\right)-72 (a x-1)^2 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+51 \sqrt{2} (a x-1)^2 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{8 a^{3/2} c \sqrt{x} (1-a x)^{3/2} \sqrt{c-\frac{c}{a x}}}","-\frac{9 (1-a x)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{51 (1-a x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{4 \sqrt{2} a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{21 \sqrt{a x+1} (1-a x)^{3/2}}{8 a^2 x \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{9 (a x+1)^{3/2} \sqrt{1-a x}}{8 a^2 x \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{(a x+1)^{3/2}}{2 a \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{3/2}}",1,"-1/8*(-2*Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(15 - 23*a*x + 4*a^2*x^2) - 72*(-1 + a*x)^2*ArcSinh[Sqrt[a]*Sqrt[x]] + 51*Sqrt[2]*(-1 + a*x)^2*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(3/2)*c*Sqrt[c - c/(a*x)]*Sqrt[x]*(1 - a*x)^(3/2))","A",1
534,1,147,293,0.1683597,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a*x))^(5/2),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{a x+1} \left(-48 a^3 x^3+415 a^2 x^2-554 a x+219\right)-1056 (a x-1)^3 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+747 \sqrt{2} (a x-1)^3 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{96 a^{3/2} c^2 \sqrt{x} (1-a x)^{5/2} \sqrt{c-\frac{c}{a x}}}","\frac{11 (1-a x)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{249 (1-a x)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{16 \sqrt{2} a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{103 \sqrt{a x+1} (1-a x)^{5/2}}{32 a^3 x^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{43 (a x+1)^{3/2} (1-a x)^{3/2}}{32 a^3 x^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{13 (a x+1)^{3/2} \sqrt{1-a x}}{24 a^2 x \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{(a x+1)^{3/2}}{3 a \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(2*Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(219 - 554*a*x + 415*a^2*x^2 - 48*a^3*x^3) - 1056*(-1 + a*x)^3*ArcSinh[Sqrt[a]*Sqrt[x]] + 747*Sqrt[2]*(-1 + a*x)^3*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(96*a^(3/2)*c^2*Sqrt[c - c/(a*x)]*Sqrt[x]*(1 - a*x)^(5/2))","A",1
535,1,108,225,2.8316937,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Integrate[(c - c/(a*x))^(9/2)/E^ArcTanh[a*x],x]","\frac{c^4 \sqrt{c-\frac{c}{a x}} \left(\sqrt{-a x (a x+1)} \left(105 a^4 x^4-4156 a^3 x^3+1028 a^2 x^2-246 a x+30\right)-1155 a^4 x^4 \sin ^{-1}\left(\sqrt{-a x}\right)\right)}{105 a^3 x^2 (-a x)^{3/2} \sqrt{1-a x}}","\frac{11 a^{7/2} x^{9/2} \left(c-\frac{c}{a x}\right)^{9/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{9/2}}+\frac{a^3 x^4 \sqrt{a x+1} (521 a x+2718) \left(c-\frac{c}{a x}\right)^{9/2}}{105 (1-a x)^{9/2}}-\frac{94 a^2 x^3 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{21 (1-a x)^{5/2}}+\frac{6 a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{5 (1-a x)^{3/2}}-\frac{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{9/2}}{7 \sqrt{1-a x}}",1,"(c^4*Sqrt[c - c/(a*x)]*(Sqrt[-(a*x*(1 + a*x))]*(30 - 246*a*x + 1028*a^2*x^2 - 4156*a^3*x^3 + 105*a^4*x^4) - 1155*a^4*x^4*ArcSin[Sqrt[-(a*x)]]))/(105*a^3*x^2*(-(a*x))^(3/2)*Sqrt[1 - a*x])","A",0
536,1,95,179,0.0955077,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Integrate[(c - c/(a*x))^(7/2)/E^ArcTanh[a*x],x]","-\frac{c^3 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1} \left(5 a^3 x^3-92 a^2 x^2+16 a x-2\right)-45 a^{5/2} x^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{5 a^3 x^2 \sqrt{1-a x}}","-\frac{9 a^{5/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{7/2}}-\frac{a^2 x^3 \sqrt{a x+1} (7 a x+66) \left(c-\frac{c}{a x}\right)^{7/2}}{5 (1-a x)^{7/2}}+\frac{2 a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}{(1-a x)^{3/2}}-\frac{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 \sqrt{1-a x}}",1,"-1/5*(c^3*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x]*(-2 + 16*a*x - 92*a^2*x^2 + 5*a^3*x^3) - 45*a^(5/2)*x^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a^3*x^2*Sqrt[1 - a*x])","A",1
537,1,87,137,0.0654146,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Integrate[(c - c/(a*x))^(5/2)/E^ArcTanh[a*x],x]","-\frac{c^2 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1} \left(3 a^2 x^2-22 a x+2\right)-21 a^{3/2} x^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{3 a^2 x \sqrt{1-a x}}","\frac{7 a^{3/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{5/2}}+\frac{a x^2 (18-a x) \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{5/2}}{3 (1-a x)^{5/2}}-\frac{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{5/2}}{3 \sqrt{1-a x}}",1,"-1/3*(c^2*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x]*(2 - 22*a*x + 3*a^2*x^2) - 21*a^(3/2)*x^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a^2*x*Sqrt[1 - a*x])","A",1
538,1,71,126,0.0522086,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[(c - c/(a*x))^(3/2)/E^ArcTanh[a*x],x]","-\frac{c \sqrt{c-\frac{c}{a x}} \left((a x-2) \sqrt{a x+1}-5 \sqrt{a} \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{a \sqrt{1-a x}}","-\frac{5 \sqrt{a} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{3/2}}+\frac{a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}-\frac{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}",1,"-((c*Sqrt[c - c/(a*x)]*((-2 + a*x)*Sqrt[1 + a*x] - 5*Sqrt[a]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a*Sqrt[1 - a*x]))","A",1
539,1,67,90,0.0520814,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[Sqrt[c - c/(a*x)]/E^ArcTanh[a*x],x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\frac{3 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}-\sqrt{x} \sqrt{a x+1}\right)}{\sqrt{1-a x}}","\frac{3 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}-\frac{x \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{1-a x}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(-(Sqrt[x]*Sqrt[1 + a*x]) + (3*ArcSinh[Sqrt[a]*Sqrt[x]])/Sqrt[a]))/Sqrt[1 - a*x]","A",0
540,1,71,88,0.0404562,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[1/(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]),x]","\frac{\sqrt{1-a x} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}-\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}","\frac{\sqrt{1-a x} \sqrt{a x+1}}{a \sqrt{c-\frac{c}{a x}}}-\frac{\sqrt{1-a x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}",1,"(Sqrt[1 - a*x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] - ArcSinh[Sqrt[a]*Sqrt[x]]))/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x])","A",1
541,1,105,159,0.0660567,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))^(3/2)),x]","\frac{\sqrt{1-a x} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}+\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{a^{3/2} c \sqrt{x} \sqrt{c-\frac{c}{a x}}}","-\frac{(1-a x)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{\sqrt{2} (1-a x)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{\sqrt{a x+1} (1-a x)^{3/2}}{a^2 x \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(Sqrt[1 - a*x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] + ArcSinh[Sqrt[a]*Sqrt[x]] - Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(a^(3/2)*c*Sqrt[c - c/(a*x)]*Sqrt[x])","A",1
542,1,127,208,0.1833811,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))^(5/2)),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{a x+1} (3-2 a x)-12 (a x-1) \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+9 \sqrt{2} (a x-1) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{4 a^{3/2} c^2 \sqrt{x} \sqrt{1-a x} \sqrt{c-\frac{c}{a x}}}","\frac{3 (1-a x)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{9 (1-a x)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{2 \sqrt{2} a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{3 \sqrt{a x+1} (1-a x)^{5/2}}{2 a^3 x^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{\sqrt{a x+1} (1-a x)^{3/2}}{2 a^2 x \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(2*Sqrt[a]*Sqrt[x]*(3 - 2*a*x)*Sqrt[1 + a*x] - 12*(-1 + a*x)*ArcSinh[Sqrt[a]*Sqrt[x]] + 9*Sqrt[2]*(-1 + a*x)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(4*a^(3/2)*c^2*Sqrt[c - c/(a*x)]*Sqrt[x]*Sqrt[1 - a*x])","A",1
543,1,139,252,0.2287456,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a*x))^(7/2)),x]","\frac{2 \sqrt{a} \sqrt{x} \sqrt{a x+1} \left(16 a^2 x^2-55 a x+35\right)+160 (a x-1)^2 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-115 \sqrt{2} (a x-1)^2 \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{32 a^{3/2} c^3 \sqrt{x} (1-a x)^{3/2} \sqrt{c-\frac{c}{a x}}}","-\frac{5 (1-a x)^{7/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{9/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{115 (1-a x)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{16 \sqrt{2} a^{9/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{35 \sqrt{a x+1} (1-a x)^{7/2}}{16 a^4 x^3 \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{15 \sqrt{a x+1} (1-a x)^{5/2}}{16 a^3 x^2 \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{\sqrt{a x+1} (1-a x)^{3/2}}{4 a^2 x \left(c-\frac{c}{a x}\right)^{7/2}}",1,"(2*Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(35 - 55*a*x + 16*a^2*x^2) + 160*(-1 + a*x)^2*ArcSinh[Sqrt[a]*Sqrt[x]] - 115*Sqrt[2]*(-1 + a*x)^2*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(32*a^(3/2)*c^3*Sqrt[c - c/(a*x)]*Sqrt[x]*(1 - a*x)^(3/2))","A",1
544,1,133,189,0.3515219,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Integrate[(c - c/(a*x))^(9/2)/E^(2*ArcTanh[a*x]),x]","\frac{c^4 \left(-105 a^4 x^4+6428 a^3 x^3-1196 a^2 x^2+258 a x-30\right) \sqrt{c-\frac{c}{a x}}}{105 a^4 x^3}+\frac{13 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{64 \sqrt{2} c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}","\frac{13 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{64 \sqrt{2} c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{51 c^4 \sqrt{c-\frac{c}{a x}}}{a}+\frac{19 c^3 \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}+\frac{3 c^2 \left(c-\frac{c}{a x}\right)^{5/2}}{5 a}-\frac{5 c \left(c-\frac{c}{a x}\right)^{7/2}}{7 a}-x \left(c-\frac{c}{a x}\right)^{9/2}",1,"(c^4*Sqrt[c - c/(a*x)]*(-30 + 258*a*x - 1196*a^2*x^2 + 6428*a^3*x^3 - 105*a^4*x^4))/(105*a^4*x^3) + (13*c^(9/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a - (64*Sqrt[2]*c^(9/2)*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",1
545,1,125,164,0.1837804,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Integrate[(c - c/(a*x))^(7/2)/E^(2*ArcTanh[a*x]),x]","\frac{c^3 \left(-15 a^3 x^3+376 a^2 x^2-52 a x+6\right) \sqrt{c-\frac{c}{a x}}}{15 a^3 x^2}+\frac{11 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{32 \sqrt{2} c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}","\frac{11 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{32 \sqrt{2} c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{21 c^3 \sqrt{c-\frac{c}{a x}}}{a}+\frac{5 c^2 \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-\frac{3 c \left(c-\frac{c}{a x}\right)^{5/2}}{5 a}-x \left(c-\frac{c}{a x}\right)^{7/2}",1,"(c^3*Sqrt[c - c/(a*x)]*(6 - 52*a*x + 376*a^2*x^2 - 15*a^3*x^3))/(15*a^3*x^2) + (11*c^(7/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a - (32*Sqrt[2]*c^(7/2)*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",1
546,1,116,139,0.1069205,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Integrate[(c - c/(a*x))^(5/2)/E^(2*ArcTanh[a*x]),x]","\frac{c^2 \left(-3 a^2 x^2+26 a x-2\right) \sqrt{c-\frac{c}{a x}}+27 a c^{5/2} x \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)-48 \sqrt{2} a c^{5/2} x \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{3 a^2 x}","\frac{9 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{16 \sqrt{2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{7 c^2 \sqrt{c-\frac{c}{a x}}}{a}-\frac{c \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-x \left(c-\frac{c}{a x}\right)^{5/2}",1,"(c^2*Sqrt[c - c/(a*x)]*(-2 + 26*a*x - 3*a^2*x^2) + 27*a*c^(5/2)*x*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]] - 48*Sqrt[2]*a*c^(5/2)*x*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/(3*a^2*x)","A",1
547,1,96,113,0.0834179,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[(c - c/(a*x))^(3/2)/E^(2*ArcTanh[a*x]),x]","\frac{7 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)-8 \sqrt{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)+c (2-a x) \sqrt{c-\frac{c}{a x}}}{a}","\frac{7 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{8 \sqrt{2} c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}+\frac{c \sqrt{c-\frac{c}{a x}}}{a}-x \left(c-\frac{c}{a x}\right)^{3/2}",1,"(c*Sqrt[c - c/(a*x)]*(2 - a*x) + 7*c^(3/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]] - 8*Sqrt[2]*c^(3/2)*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",1
548,1,93,93,0.0496676,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[Sqrt[c - c/(a*x)]/E^(2*ArcTanh[a*x]),x]","x \left(-\sqrt{c-\frac{c}{a x}}\right)+\frac{5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}","x \left(-\sqrt{c-\frac{c}{a x}}\right)+\frac{5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}",1,"-(Sqrt[c - c/(a*x)]*x) + (5*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a - (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",1
549,1,96,96,0.0497481,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]),x]","-\frac{x \sqrt{c-\frac{c}{a x}}}{c}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a \sqrt{c}}-\frac{2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a \sqrt{c}}","-\frac{x \sqrt{c-\frac{c}{a x}}}{c}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a \sqrt{c}}-\frac{2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a \sqrt{c}}",1,"-((Sqrt[c - c/(a*x)]*x)/c) + (3*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*Sqrt[c]) - (2*Sqrt[2]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/(a*Sqrt[c])","A",1
550,1,95,95,0.0541572,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(3/2)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{3/2}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a c^{3/2}}-\frac{x \sqrt{c-\frac{c}{a x}}}{c^2}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{3/2}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a c^{3/2}}-\frac{x \sqrt{c-\frac{c}{a x}}}{c^2}",1,"-((Sqrt[c - c/(a*x)]*x)/c^2) + ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]]/(a*c^(3/2)) - (Sqrt[2]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/(a*c^(3/2))","A",1
551,1,67,119,0.0543002,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(5/2)),x]","\frac{\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{a-\frac{1}{x}}{2 a}\right)+\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-\frac{1}{a x}\right)-a x}{a c^2 \sqrt{c-\frac{c}{a x}}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a c^{5/2}}-\frac{x}{c^2 \sqrt{c-\frac{c}{a x}}}+\frac{2}{a c^2 \sqrt{c-\frac{c}{a x}}}",1,"(-(a*x) + Hypergeometric2F1[-1/2, 1, 1/2, (a - x^(-1))/(2*a)] + Hypergeometric2F1[-1/2, 1, 1/2, 1 - 1/(a*x)])/(a*c^2*Sqrt[c - c/(a*x)])","C",0
552,1,77,148,0.0584905,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(7/2)),x]","\frac{x \left(\, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};\frac{a-\frac{1}{x}}{2 a}\right)+3 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};1-\frac{1}{a x}\right)-3 a x\right)}{3 c^3 (a x-1) \sqrt{c-\frac{c}{a x}}}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a c^{7/2}}+\frac{7}{2 a c^3 \sqrt{c-\frac{c}{a x}}}-\frac{x}{c^2 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4}{3 a c^2 \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(x*(-3*a*x + Hypergeometric2F1[-3/2, 1, -1/2, (a - x^(-1))/(2*a)] + 3*Hypergeometric2F1[-3/2, 1, -1/2, 1 - 1/(a*x)]))/(3*c^3*Sqrt[c - c/(a*x)]*(-1 + a*x))","C",0
553,1,82,173,0.0620485,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{9/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(9/2)),x]","-\frac{a x^2 \left(-\, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};\frac{a-\frac{1}{x}}{2 a}\right)-5 \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};1-\frac{1}{a x}\right)+5 a x\right)}{5 c^4 (a x-1)^2 \sqrt{c-\frac{c}{a x}}}","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a c^{9/2}}+\frac{21}{4 a c^4 \sqrt{c-\frac{c}{a x}}}+\frac{11}{6 a c^3 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{x}{c^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{6}{5 a c^2 \left(c-\frac{c}{a x}\right)^{5/2}}",1,"-1/5*(a*x^2*(5*a*x - Hypergeometric2F1[-5/2, 1, -3/2, (a - x^(-1))/(2*a)] - 5*Hypergeometric2F1[-5/2, 1, -3/2, 1 - 1/(a*x)]))/(c^4*Sqrt[c - c/(a*x)]*(-1 + a*x)^2)","C",0
554,1,234,267,10.4825972,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Integrate[(c - c/(a*x))^(9/2)/E^(3*ArcTanh[a*x]),x]","-\frac{c^4 \sqrt{c-\frac{c}{a x}} \left(-\frac{7168 (-a x (a x+1))^{5/2} (a x-1)^4 \, _5F_4\left(-\frac{3}{2},2,2,2,\frac{5}{2};1,1,1,\frac{7}{2};-a x\right)}{(a x+1)^{3/2}}+105 \left(101 a^5 x^5+209 a^4 x^4-54 a^3 x^3-54 a^2 x^2+81 a x-27\right) \sin ^{-1}\left(\sqrt{-a x}\right)+\sqrt{-a x (a x+1)} \left(70000 a^8 x^8-214760 a^7 x^7+165830 a^6 x^6+84329 a^5 x^5-375805 a^4 x^4-59750 a^3 x^3+34100 a^2 x^2-12955 a x+3091\right)\right)}{896 a^4 x^3 \sqrt{-a x (a x+1)} \sqrt{1-a^2 x^2}}","-\frac{15 a^{7/2} x^{9/2} \left(c-\frac{c}{a x}\right)^{9/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{9/2}}+\frac{5 a^4 x^5 (587-109 a x) \left(c-\frac{c}{a x}\right)^{9/2}}{7 (1-a x)^{9/2} \sqrt{a x+1}}+\frac{70 a^3 x^4 \left(c-\frac{c}{a x}\right)^{9/2}}{(1-a x)^{5/2} \sqrt{a x+1}}-\frac{50 a^2 x^3 \left(c-\frac{c}{a x}\right)^{9/2}}{7 (1-a x)^{3/2} \sqrt{a x+1}}+\frac{10 a x^2 \left(c-\frac{c}{a x}\right)^{9/2}}{7 \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 x \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{9/2}}{7 \sqrt{a x+1}}",1,"-1/896*(c^4*Sqrt[c - c/(a*x)]*(Sqrt[-(a*x*(1 + a*x))]*(3091 - 12955*a*x + 34100*a^2*x^2 - 59750*a^3*x^3 - 375805*a^4*x^4 + 84329*a^5*x^5 + 165830*a^6*x^6 - 214760*a^7*x^7 + 70000*a^8*x^8) + 105*(-27 + 81*a*x - 54*a^2*x^2 - 54*a^3*x^3 + 209*a^4*x^4 + 101*a^5*x^5)*ArcSin[Sqrt[-(a*x)]] - (7168*(-1 + a*x)^4*(-(a*x*(1 + a*x)))^(5/2)*HypergeometricPFQ[{-3/2, 2, 2, 2, 5/2}, {1, 1, 1, 7/2}, -(a*x)])/(1 + a*x)^(3/2)))/(a^4*x^3*Sqrt[-(a*x*(1 + a*x))]*Sqrt[1 - a^2*x^2])","C",0
555,1,200,225,3.755826,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Integrate[(c - c/(a*x))^(7/2)/E^(3*ArcTanh[a*x]),x]","-\frac{c^3 x \sqrt{c-\frac{c}{a x}} \left(1040 a^4 x^4 (a x-1)^3 \sqrt{a x+1} \sqrt{-a x (a x+1)} \, _2F_1\left(\frac{3}{2},\frac{9}{2};\frac{11}{2};-a x\right)+585 \left(19 a^4 x^4-86 a^3 x^3+70 a x-35\right) \sin ^{-1}\left(\sqrt{-a x}\right)-3 \sqrt{-a x (a x+1)} \left(520 a^6 x^6-2470 a^5 x^5+6325 a^4 x^4-28706 a^3 x^3-21508 a^2 x^2+19192 a x-6921\right)\right)}{720 (-a x)^{7/2} \sqrt{a x+1} \sqrt{1-a^2 x^2}}","\frac{13 a^{5/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{7/2}}-\frac{a^3 x^4 (2525-427 a x) \left(c-\frac{c}{a x}\right)^{7/2}}{15 (1-a x)^{7/2} \sqrt{a x+1}}-\frac{398 a^2 x^3 \left(c-\frac{c}{a x}\right)^{7/2}}{15 (1-a x)^{3/2} \sqrt{a x+1}}+\frac{38 a x^2 \left(c-\frac{c}{a x}\right)^{7/2}}{15 \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 x \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{7/2}}{5 \sqrt{a x+1}}",1,"-1/720*(c^3*Sqrt[c - c/(a*x)]*x*(-3*Sqrt[-(a*x*(1 + a*x))]*(-6921 + 19192*a*x - 21508*a^2*x^2 - 28706*a^3*x^3 + 6325*a^4*x^4 - 2470*a^5*x^5 + 520*a^6*x^6) + 585*(-35 + 70*a*x - 86*a^3*x^3 + 19*a^4*x^4)*ArcSin[Sqrt[-(a*x)]] + 1040*a^4*x^4*(-1 + a*x)^3*Sqrt[1 + a*x]*Sqrt[-(a*x*(1 + a*x))]*Hypergeometric2F1[3/2, 9/2, 11/2, -(a*x)]))/((-(a*x))^(7/2)*Sqrt[1 + a*x]*Sqrt[1 - a^2*x^2])","C",0
556,1,97,181,0.0794009,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Integrate[(c - c/(a*x))^(5/2)/E^(3*ArcTanh[a*x]),x]","\frac{c^2 \sqrt{c-\frac{c}{a x}} \left(-33 a^{3/2} x^{3/2} \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+3 a^3 x^3+133 a^2 x^2+32 a x-2\right)}{3 a^2 x \sqrt{1-a^2 x^2}}","-\frac{11 a^{3/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{5/2}}+\frac{a^2 x^3 (191-25 a x) \left(c-\frac{c}{a x}\right)^{5/2}}{3 (1-a x)^{5/2} \sqrt{a x+1}}+\frac{26 a x^2 \left(c-\frac{c}{a x}\right)^{5/2}}{3 \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 x \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{5/2}}{3 \sqrt{a x+1}}",1,"(c^2*Sqrt[c - c/(a*x)]*(-2 + 32*a*x + 133*a^2*x^2 + 3*a^3*x^3 - 33*a^(3/2)*x^(3/2)*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(3*a^2*x*Sqrt[1 - a^2*x^2])","A",0
557,1,80,133,0.0549845,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[(c - c/(a*x))^(3/2)/E^(3*ArcTanh[a*x]),x]","\frac{c \sqrt{c-\frac{c}{a x}} \left(a^2 x^2+19 a x-9 \sqrt{a} \sqrt{x} \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+2\right)}{a \sqrt{1-a^2 x^2}}","\frac{9 \sqrt{a} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{(1-a x)^{3/2}}-\frac{a x^2 (23-a x) \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2} \sqrt{a x+1}}-\frac{2 x \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{3/2}}{\sqrt{a x+1}}",1,"(c*Sqrt[c - c/(a*x)]*(2 + 19*a*x + a^2*x^2 - 9*Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a*Sqrt[1 - a^2*x^2])","A",0
558,1,80,123,0.0526365,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[Sqrt[c - c/(a*x)]/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} (a x+9)-7 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{\sqrt{a} \sqrt{1-a^2 x^2}}","\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}+\frac{8 x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{7 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*(9 + a*x) - 7*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(Sqrt[a]*Sqrt[1 - a^2*x^2])","A",0
559,1,86,127,0.0652194,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]),x]","\frac{\sqrt{1-a x} \left(5 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-\sqrt{a} \sqrt{x} (a x+5)\right)}{a^{3/2} \sqrt{x} \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}","\frac{5 \sqrt{1-a x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}-\frac{x (1-a x)}{\sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}-\frac{5 \sqrt{1-a x}}{a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}",1,"(Sqrt[1 - a*x]*(-(Sqrt[a]*Sqrt[x]*(5 + a*x)) + 5*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x]*Sqrt[1 + a*x])","A",0
560,1,44,131,0.0420584,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^(3/2)),x]","\frac{2 x (1-a x)^{3/2} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-a x\right)}{5 \left(c-\frac{c}{a x}\right)^{3/2}}","-\frac{3 (1-a x)^{3/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{5/2} x^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{3 \sqrt{a x+1} (1-a x)^{3/2}}{a^2 x \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 (1-a x)^{3/2}}{a \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(2*x*(1 - a*x)^(3/2)*Hypergeometric2F1[3/2, 5/2, 7/2, -(a*x)])/(5*(c - c/(a*x))^(3/2))","C",0
561,1,162,199,0.164,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^(5/2)),x]","\frac{\sqrt{1-a x} \left(5 \left(2 \sqrt{a} \sqrt{x}-4 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+\sqrt{2 a x+2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)-4 a^{5/2} x^{5/2} \sqrt{a x+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-a x\right)\right)}{10 a^{3/2} c^2 \sqrt{x} \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}","\frac{(1-a x)^{5/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{(1-a x)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{2} a^{7/2} x^{5/2} \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{2 \sqrt{a x+1} (1-a x)^{5/2}}{a^3 x^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{(1-a x)^{5/2}}{a^2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(Sqrt[1 - a*x]*(5*(2*Sqrt[a]*Sqrt[x] - 4*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]] + Sqrt[2 + 2*a*x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]) - 4*a^(5/2)*x^(5/2)*Sqrt[1 + a*x]*Hypergeometric2F1[3/2, 5/2, 7/2, -(a*x)]))/(10*a^(3/2)*c^2*Sqrt[c - c/(a*x)]*Sqrt[x]*Sqrt[1 + a*x])","C",0
562,1,234,251,0.6491457,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^(7/2)),x]","\frac{-40 a^{7/2} x^{7/2} (a x-1) \sqrt{a x+1} \, _2F_1\left(\frac{3}{2},\frac{7}{2};\frac{9}{2};-a x\right)-56 a^{5/2} x^{5/2} (a x-1) \sqrt{a x+1} \, _2F_1\left(\frac{3}{2},\frac{5}{2};\frac{7}{2};-a x\right)+35 \left(\sqrt{a} \sqrt{x} \left(2 a^3 x^3+13 a^2 x^2+2 a x-25\right)+19 (a x-1) \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-22 (a x-1) \sqrt{2 a x+2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{560 a^{3/2} c^3 \sqrt{x} \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}","\frac{(1-a x)^{7/2} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{9/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{11 (1-a x)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{4 \sqrt{2} a^{9/2} x^{7/2} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{7 \sqrt{a x+1} (1-a x)^{7/2}}{4 a^4 x^3 \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{(1-a x)^{7/2}}{4 a^3 x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{(1-a x)^{5/2}}{2 a^2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}",1,"(35*(Sqrt[a]*Sqrt[x]*(-25 + 2*a*x + 13*a^2*x^2 + 2*a^3*x^3) + 19*(-1 + a*x)*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]] - 22*(-1 + a*x)*Sqrt[2 + 2*a*x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]) - 56*a^(5/2)*x^(5/2)*(-1 + a*x)*Sqrt[1 + a*x]*Hypergeometric2F1[3/2, 5/2, 7/2, -(a*x)] - 40*a^(7/2)*x^(7/2)*(-1 + a*x)*Sqrt[1 + a*x]*Hypergeometric2F1[3/2, 7/2, 9/2, -(a*x)])/(560*a^(3/2)*c^3*Sqrt[c - c/(a*x)]*Sqrt[x]*Sqrt[1 - a^2*x^2])","C",0
563,1,92,105,0.0420698,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right) x^3} \, dx","Integrate[E^(3*ArcTanh[a*x])/((c - c/(a*x))*x^3),x]","\frac{a \left(-19 a^3 x^3+7 a^2 x^2+12 a x (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+23 a x-3\right)}{3 c x (a x-1) \sqrt{1-a^2 x^2}}","-\frac{4 a^2 (4 a x+3)}{3 c \sqrt{1-a^2 x^2}}-\frac{8 a^2 (a x+1)}{3 c \left(1-a^2 x^2\right)^{3/2}}+\frac{a \sqrt{1-a^2 x^2}}{c x}+\frac{4 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"(a*(-3 + 23*a*x + 7*a^2*x^2 - 19*a^3*x^3 + 12*a*x*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(3*c*x*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
564,1,56,57,0.0250605,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^m \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]*x^m,x]","\frac{x^{m+1} \sqrt{c-\frac{c}{a x}} \, _2F_1\left(-\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};-a x\right)}{\left(m+\frac{1}{2}\right) \sqrt{1-a x}}","\frac{2 x^{m+1} \sqrt{c-\frac{c}{a x}} \, _2F_1\left(-\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};-a x\right)}{(2 m+1) \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*x^(1 + m)*Hypergeometric2F1[-1/2, 1/2 + m, 3/2 + m, -(a*x)])/((1/2 + m)*Sqrt[1 - a*x])","A",1
565,1,88,179,0.0578455,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]*x^2,x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1} \left(8 a^2 x^2+2 a x-3\right)+3 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{24 a^{5/2} \sqrt{1-a x}}","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{8 a^{5/2} \sqrt{1-a x}}-\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-a x}}+\frac{x^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-a x}}+\frac{x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(-3 + 2*a*x + 8*a^2*x^2) + 3*ArcSinh[Sqrt[a]*Sqrt[x]]))/(24*a^(5/2)*Sqrt[1 - a*x])","A",1
566,1,80,135,0.0509356,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]*x,x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1} (2 a x+1)-\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{4 a^{3/2} \sqrt{1-a x}}","-\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2} \sqrt{1-a x}}+\frac{x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{2 \sqrt{1-a x}}+\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(1 + 2*a*x) - ArcSinh[Sqrt[a]*Sqrt[x]]))/(4*a^(3/2)*Sqrt[1 - a*x])","A",1
567,1,69,85,0.0363644,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)],x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}+\sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{\sqrt{a} \sqrt{1-a x}}","\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}+\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] + ArcSinh[Sqrt[a]*Sqrt[x]]))/(Sqrt[a]*Sqrt[1 - a*x])","A",1
568,1,61,86,0.039095,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x,x]","-\frac{2 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1}-\sqrt{a} \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{\sqrt{1-a x}}","\frac{2 \sqrt{a} \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x] - Sqrt[a]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/Sqrt[1 - a*x]","A",1
569,1,41,41,0.0215789,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^2,x]","-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a x}}","-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(3*x*Sqrt[1 - a*x])","A",1
570,1,47,84,0.025117,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^3,x]","\frac{2 (a x+1)^{3/2} (2 a x-3) \sqrt{c-\frac{c}{a x}}}{15 x^2 \sqrt{1-a x}}","\frac{4 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{15 x \sqrt{1-a x}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{5 x^2 \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2)*(-3 + 2*a*x))/(15*x^2*Sqrt[1 - a*x])","A",1
571,1,55,128,0.0290529,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^4,x]","-\frac{2 (a x+1)^{3/2} \left(8 a^2 x^2-12 a x+15\right) \sqrt{c-\frac{c}{a x}}}{105 x^3 \sqrt{1-a x}}","-\frac{16 a^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{105 x \sqrt{1-a x}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{7 x^3 \sqrt{1-a x}}+\frac{8 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{35 x^2 \sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2)*(15 - 12*a*x + 8*a^2*x^2))/(105*x^3*Sqrt[1 - a*x])","A",1
572,1,63,172,0.0330216,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^5,x]","\frac{2 (a x+1)^{3/2} \left(16 a^3 x^3-24 a^2 x^2+30 a x-35\right) \sqrt{c-\frac{c}{a x}}}{315 x^4 \sqrt{1-a x}}","\frac{32 a^3 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{315 x \sqrt{1-a x}}-\frac{16 a^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{105 x^2 \sqrt{1-a x}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{9 x^4 \sqrt{1-a x}}+\frac{4 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{21 x^3 \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2)*(-35 + 30*a*x - 24*a^2*x^2 + 16*a^3*x^3))/(315*x^4*Sqrt[1 - a*x])","A",1
573,1,50,130,0.0337298,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^3,x]","-\frac{\sqrt{c-\frac{c}{a x}} \left(a^4 x^4+15 \, _2F_1\left(\frac{1}{2},4;\frac{3}{2};1-\frac{1}{a x}\right)\right)}{4 a^4}","-\frac{75 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{64 a^4}-\frac{75 x \sqrt{c-\frac{c}{a x}}}{64 a^3}-\frac{25 x^2 \sqrt{c-\frac{c}{a x}}}{32 a^2}-\frac{1}{4} x^4 \sqrt{c-\frac{c}{a x}}-\frac{5 x^3 \sqrt{c-\frac{c}{a x}}}{8 a}",1,"-1/4*(Sqrt[c - c/(a*x)]*(a^4*x^4 + 15*Hypergeometric2F1[1/2, 4, 3/2, 1 - 1/(a*x)]))/a^4","C",0
574,1,50,105,0.032334,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^2,x]","-\frac{\sqrt{c-\frac{c}{a x}} \left(a^3 x^3+11 \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-\frac{1}{a x}\right)\right)}{3 a^3}","-\frac{11 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{8 a^3}-\frac{11 x \sqrt{c-\frac{c}{a x}}}{8 a^2}-\frac{1}{3} x^3 \sqrt{c-\frac{c}{a x}}-\frac{11 x^2 \sqrt{c-\frac{c}{a x}}}{12 a}",1,"-1/3*(Sqrt[c - c/(a*x)]*(a^3*x^3 + 11*Hypergeometric2F1[1/2, 3, 3/2, 1 - 1/(a*x)]))/a^3","C",0
575,1,77,80,0.0747701,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x,x]","-\frac{\sqrt{c-\frac{c}{a x}} \left(a x \sqrt{1-\frac{1}{a x}} (2 a x+7)+7 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}}\right)\right)}{4 a^2 \sqrt{1-\frac{1}{a x}}}","-\frac{7 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{4 a^2}-\frac{1}{2} x^2 \sqrt{c-\frac{c}{a x}}-\frac{7 x \sqrt{c-\frac{c}{a x}}}{4 a}",1,"-1/4*(Sqrt[c - c/(a*x)]*(a*Sqrt[1 - 1/(a*x)]*x*(7 + 2*a*x) + 7*ArcTanh[Sqrt[1 - 1/(a*x)]]))/(a^2*Sqrt[1 - 1/(a*x)])","A",0
576,1,51,51,0.0388896,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)],x]","x \left(-\sqrt{c-\frac{c}{a x}}\right)-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}","x \left(-\sqrt{c-\frac{c}{a x}}\right)-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}",1,"-(Sqrt[c - c/(a*x)]*x) - (3*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",1
577,1,47,47,0.0327862,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x,x]","-2 \sqrt{c-\frac{c}{a x}}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)","-2 \sqrt{c-\frac{c}{a x}}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)",1,"-2*Sqrt[c - c/(a*x)] - 2*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]]","A",1
578,1,28,42,0.0334513,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^2,x]","-\frac{2 (5 a x+1) \sqrt{c-\frac{c}{a x}}}{3 x}","\frac{2 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a \sqrt{c-\frac{c}{a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + 5*a*x))/(3*x)","A",1
579,1,36,69,0.041745,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^3,x]","-\frac{2 \left(6 a^2 x^2+3 a x+1\right) \sqrt{c-\frac{c}{a x}}}{5 x^2}","-\frac{2 a^2 \left(c-\frac{c}{a x}\right)^{5/2}}{5 c^2}+\frac{2 a^2 \left(c-\frac{c}{a x}\right)^{3/2}}{c}-4 a^2 \sqrt{c-\frac{c}{a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + 3*a*x + 6*a^2*x^2))/(5*x^2)","A",1
580,1,44,96,0.0502712,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^4,x]","-\frac{2 \left(104 a^3 x^3+52 a^2 x^2+39 a x+15\right) \sqrt{c-\frac{c}{a x}}}{105 x^3}","\frac{2 a^3 \left(c-\frac{c}{a x}\right)^{7/2}}{7 c^3}-\frac{8 a^3 \left(c-\frac{c}{a x}\right)^{5/2}}{5 c^2}+\frac{10 a^3 \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a^3 \sqrt{c-\frac{c}{a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(15 + 39*a*x + 52*a^2*x^2 + 104*a^3*x^3))/(105*x^3)","A",1
581,1,52,121,0.058494,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^5,x]","-\frac{2 \left(272 a^4 x^4+136 a^3 x^3+102 a^2 x^2+85 a x+35\right) \sqrt{c-\frac{c}{a x}}}{315 x^4}","-\frac{2 a^4 \left(c-\frac{c}{a x}\right)^{9/2}}{9 c^4}+\frac{10 a^4 \left(c-\frac{c}{a x}\right)^{7/2}}{7 c^3}-\frac{18 a^4 \left(c-\frac{c}{a x}\right)^{5/2}}{5 c^2}+\frac{14 a^4 \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a^4 \sqrt{c-\frac{c}{a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(35 + 85*a*x + 102*a^2*x^2 + 136*a^3*x^3 + 272*a^4*x^4))/(315*x^4)","A",1
582,1,130,292,0.1011152,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^3,x]","-\frac{\sqrt{c-\frac{c}{a x}} \left(\sqrt{a} x \sqrt{a x+1} \left(48 a^3 x^3+136 a^2 x^2+214 a x+447\right)+1089 \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-768 \sqrt{2} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{192 a^{7/2} \sqrt{1-a x}}","-\frac{363 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{64 a^{7/2} \sqrt{1-a x}}+\frac{4 \sqrt{2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{7/2} \sqrt{1-a x}}-\frac{21 x (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{32 a^3 \sqrt{1-a x}}-\frac{107 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{64 a^3 \sqrt{1-a x}}-\frac{11 x^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{24 a^2 \sqrt{1-a x}}-\frac{x^3 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"-1/192*(Sqrt[c - c/(a*x)]*(Sqrt[a]*x*Sqrt[1 + a*x]*(447 + 214*a*x + 136*a^2*x^2 + 48*a^3*x^3) + 1089*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]] - 768*Sqrt[2]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(a^(7/2)*Sqrt[1 - a*x])","A",1
583,1,122,248,0.0864576,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^2,x]","-\frac{\sqrt{c-\frac{c}{a x}} \left(\sqrt{a} x \sqrt{a x+1} \left(8 a^2 x^2+26 a x+57\right)+135 \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-96 \sqrt{2} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{24 a^{5/2} \sqrt{1-a x}}","-\frac{45 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{8 a^{5/2} \sqrt{1-a x}}+\frac{4 \sqrt{2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{5/2} \sqrt{1-a x}}-\frac{3 x (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{4 a^2 \sqrt{1-a x}}-\frac{13 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-a x}}-\frac{x^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 a \sqrt{1-a x}}",1,"-1/24*(Sqrt[c - c/(a*x)]*(Sqrt[a]*x*Sqrt[1 + a*x]*(57 + 26*a*x + 8*a^2*x^2) + 135*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]] - 96*Sqrt[2]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(a^(5/2)*Sqrt[1 - a*x])","A",1
584,1,114,204,0.0725577,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x,x]","-\frac{\sqrt{c-\frac{c}{a x}} \left(\sqrt{a} x \sqrt{a x+1} (2 a x+9)+23 \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-16 \sqrt{2} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{4 a^{3/2} \sqrt{1-a x}}","-\frac{23 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2} \sqrt{1-a x}}+\frac{4 \sqrt{2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{a^{3/2} \sqrt{1-a x}}-\frac{x (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{2 a \sqrt{1-a x}}-\frac{7 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"-1/4*(Sqrt[c - c/(a*x)]*(Sqrt[a]*x*Sqrt[1 + a*x]*(9 + 2*a*x) + 23*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]] - 16*Sqrt[2]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(a^(3/2)*Sqrt[1 - a*x])","A",1
585,1,105,155,0.0681626,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)],x]","-\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1}+5 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{\sqrt{a} \sqrt{1-a x}}","-\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}-\frac{5 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}+\frac{4 \sqrt{2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{a} \sqrt{1-a x}}",1,"-((Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x] + 5*ArcSinh[Sqrt[a]*Sqrt[x]] - 4*Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(Sqrt[a]*Sqrt[1 - a*x]))","A",1
586,1,103,154,0.0512545,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x,x]","-\frac{2 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1}+\sqrt{a} \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)-2 \sqrt{2} \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)\right)}{\sqrt{1-a x}}","-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}-\frac{2 \sqrt{a} \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{1-a x}}+\frac{4 \sqrt{2} \sqrt{a} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x] + Sqrt[a]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]] - 2*Sqrt[2]*Sqrt[a]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/Sqrt[1 - a*x]","A",1
587,1,93,147,0.052796,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^2,x]","\frac{2 \sqrt{c-\frac{c}{a x}} \left(6 \sqrt{2} a^{3/2} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)-\sqrt{a x+1} (7 a x+1)\right)}{3 x \sqrt{1-a x}}","\frac{4 \sqrt{2} a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{1-a x}}-\frac{4 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*(-(Sqrt[1 + a*x]*(1 + 7*a*x)) + 6*Sqrt[2]*a^(3/2)*x^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(3*x*Sqrt[1 - a*x])","A",1
588,1,101,191,0.0619077,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^3,x]","\frac{2 \sqrt{c-\frac{c}{a x}} \left(30 \sqrt{2} a^{5/2} x^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)-\sqrt{a x+1} \left(38 a^2 x^2+11 a x+3\right)\right)}{15 x^2 \sqrt{1-a x}}","\frac{4 \sqrt{2} a^{5/2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{1-a x}}-\frac{4 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}-\frac{2 (a x+1)^{5/2} \sqrt{c-\frac{c}{a x}}}{5 x^2 \sqrt{1-a x}}-\frac{2 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*(-(Sqrt[1 + a*x]*(3 + 11*a*x + 38*a^2*x^2)) + 30*Sqrt[2]*a^(5/2)*x^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(15*x^2*Sqrt[1 - a*x])","A",1
589,1,109,237,0.0679551,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^4,x]","\frac{2 \sqrt{c-\frac{c}{a x}} \left(42 \sqrt{2} a^{7/2} x^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)-\sqrt{a x+1} \left(52 a^3 x^3+16 a^2 x^2+9 a x+3\right)\right)}{21 x^3 \sqrt{1-a x}}","\frac{4 \sqrt{2} a^{7/2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{1-a x}}-\frac{104 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{21 \sqrt{1-a x}}-\frac{32 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{21 x \sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{7 x^3 \sqrt{1-a x}}-\frac{6 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{7 x^2 \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*(-(Sqrt[1 + a*x]*(3 + 9*a*x + 16*a^2*x^2 + 52*a^3*x^3)) + 42*Sqrt[2]*a^(7/2)*x^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(21*x^3*Sqrt[1 - a*x])","A",1
590,1,117,281,0.0793838,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^5,x]","\frac{2 \sqrt{c-\frac{c}{a x}} \left(630 \sqrt{2} a^{9/2} x^{9/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)-\sqrt{a x+1} \left(788 a^4 x^4+236 a^3 x^3+138 a^2 x^2+95 a x+35\right)\right)}{315 x^4 \sqrt{1-a x}}","\frac{4 \sqrt{2} a^{9/2} \sqrt{x} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{x}}{\sqrt{a x+1}}\right)}{\sqrt{1-a x}}-\frac{1576 a^4 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{315 \sqrt{1-a x}}-\frac{472 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{315 x \sqrt{1-a x}}-\frac{92 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 x^2 \sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{9 x^4 \sqrt{1-a x}}-\frac{38 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{63 x^3 \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*(-(Sqrt[1 + a*x]*(35 + 95*a*x + 138*a^2*x^2 + 236*a^3*x^3 + 788*a^4*x^4)) + 630*Sqrt[2]*a^(9/2)*x^(9/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]]))/(315*x^4*Sqrt[1 - a*x])","A",1
591,1,87,116,0.0597289,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^m \, dx","Integrate[(Sqrt[c - c/(a*x)]*x^m)/E^ArcTanh[a*x],x]","-\frac{2 x^{m+1} \sqrt{c-\frac{c}{a x}} \left(a (4 m+3) x \, _2F_1\left(\frac{1}{2},m+\frac{3}{2};m+\frac{5}{2};-a x\right)-(2 m+3) \sqrt{a x+1}\right)}{\left(4 m^2+8 m+3\right) \sqrt{1-a x}}","\frac{(4 m+3) x^{m+1} \sqrt{c-\frac{c}{a x}} \, _2F_1\left(\frac{1}{2},m+\frac{1}{2};m+\frac{3}{2};-a x\right)}{(m+1) (2 m+1) \sqrt{1-a x}}-\frac{\sqrt{1-a^2 x^2} x^{m+1} \sqrt{c-\frac{c}{a x}}}{(m+1) (1-a x)}",1,"(-2*Sqrt[c - c/(a*x)]*x^(1 + m)*(-((3 + 2*m)*Sqrt[1 + a*x]) + a*(3 + 4*m)*x*Hypergeometric2F1[1/2, 3/2 + m, 5/2 + m, -(a*x)]))/((3 + 8*m + 4*m^2)*Sqrt[1 - a*x])","A",0
592,1,88,182,0.0887079,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Integrate[(Sqrt[c - c/(a*x)]*x^2)/E^ArcTanh[a*x],x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1} \left(-8 a^2 x^2+22 a x-33\right)+33 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{24 a^{5/2} \sqrt{1-a x}}","\frac{11 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{8 a^{5/2} \sqrt{1-a x}}-\frac{x^3 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{3 (1-a x)}-\frac{11 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-a x}}+\frac{11 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(-33 + 22*a*x - 8*a^2*x^2) + 33*ArcSinh[Sqrt[a]*Sqrt[x]]))/(24*a^(5/2)*Sqrt[1 - a*x])","A",0
593,1,80,138,0.050408,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Integrate[(Sqrt[c - c/(a*x)]*x)/E^ArcTanh[a*x],x]","-\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \sqrt{a x+1} (2 a x-7)+7 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{4 a^{3/2} \sqrt{1-a x}}","-\frac{7 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2} \sqrt{1-a x}}-\frac{x^2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{2 (1-a x)}+\frac{7 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"-1/4*(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*(-7 + 2*a*x) + 7*ArcSinh[Sqrt[a]*Sqrt[x]]))/(a^(3/2)*Sqrt[1 - a*x])","A",0
594,1,67,90,0.0545601,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[Sqrt[c - c/(a*x)]/E^ArcTanh[a*x],x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\frac{3 \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a}}-\sqrt{x} \sqrt{a x+1}\right)}{\sqrt{1-a x}}","\frac{3 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}-\frac{x \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{1-a x}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(-(Sqrt[x]*Sqrt[1 + a*x]) + (3*ArcSinh[Sqrt[a]*Sqrt[x]])/Sqrt[a]))/Sqrt[1 - a*x]","A",0
595,1,60,89,0.050794,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x),x]","-\frac{2 \sqrt{c-\frac{c}{a x}} \left(\sqrt{a x+1}+\sqrt{a} \sqrt{x} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{\sqrt{1-a x}}","-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{1-a x}-\frac{2 \sqrt{a} \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(Sqrt[1 + a*x] + Sqrt[a]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/Sqrt[1 - a*x]","A",0
596,1,47,84,0.0321756,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x^2),x]","\frac{2 \sqrt{a x+1} (5 a x-1) \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a x}}","\frac{10 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-a x}}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{3 x (1-a x)}",1,"(2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x]*(-1 + 5*a*x))/(3*x*Sqrt[1 - a*x])","A",0
597,1,55,128,0.0322699,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x^3),x]","-\frac{2 \sqrt{a x+1} \left(6 a^2 x^2-3 a x+1\right) \sqrt{c-\frac{c}{a x}}}{5 x^2 \sqrt{1-a x}}","-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{5 x^2 (1-a x)}-\frac{12 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{5 \sqrt{1-a x}}+\frac{6 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{5 x \sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x]*(1 - 3*a*x + 6*a^2*x^2))/(5*x^2*Sqrt[1 - a*x])","A",0
598,1,63,172,0.0363392,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x^4),x]","\frac{2 \sqrt{a x+1} \left(104 a^3 x^3-52 a^2 x^2+39 a x-15\right) \sqrt{c-\frac{c}{a x}}}{105 x^3 \sqrt{1-a x}}","\frac{208 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 \sqrt{1-a x}}-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{7 x^3 (1-a x)}-\frac{104 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 x \sqrt{1-a x}}+\frac{26 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{35 x^2 \sqrt{1-a x}}",1,"(2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x]*(-15 + 39*a*x - 52*a^2*x^2 + 104*a^3*x^3))/(105*x^3*Sqrt[1 - a*x])","A",0
599,1,116,172,0.1469954,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Integrate[(Sqrt[c - c/(a*x)]*x^3)/E^(2*ArcTanh[a*x]),x]","\frac{a x \left(-48 a^3 x^3+136 a^2 x^2-214 a x+447\right) \sqrt{c-\frac{c}{a x}}-1089 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)+768 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{192 a^4}","-\frac{363 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{64 a^4}+\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a^4}+\frac{149 x \sqrt{c-\frac{c}{a x}}}{64 a^3}-\frac{107 x^2 \sqrt{c-\frac{c}{a x}}}{96 a^2}-\frac{1}{4} x^4 \sqrt{c-\frac{c}{a x}}+\frac{17 x^3 \sqrt{c-\frac{c}{a x}}}{24 a}",1,"(a*Sqrt[c - c/(a*x)]*x*(447 - 214*a*x + 136*a^2*x^2 - 48*a^3*x^3) - 1089*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]] + 768*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/(192*a^4)","A",1
600,1,108,147,0.1017761,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Integrate[(Sqrt[c - c/(a*x)]*x^2)/E^(2*ArcTanh[a*x]),x]","\frac{a x \left(-8 a^2 x^2+26 a x-57\right) \sqrt{c-\frac{c}{a x}}+135 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)-96 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{24 a^3}","\frac{45 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{8 a^3}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a^3}-\frac{19 x \sqrt{c-\frac{c}{a x}}}{8 a^2}-\frac{1}{3} x^3 \sqrt{c-\frac{c}{a x}}+\frac{13 x^2 \sqrt{c-\frac{c}{a x}}}{12 a}",1,"(a*Sqrt[c - c/(a*x)]*x*(-57 + 26*a*x - 8*a^2*x^2) + 135*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]] - 96*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/(24*a^3)","A",1
601,1,100,122,0.0838817,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Integrate[(Sqrt[c - c/(a*x)]*x)/E^(2*ArcTanh[a*x]),x]","\frac{a x (9-2 a x) \sqrt{c-\frac{c}{a x}}-23 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)+16 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{4 a^2}","-\frac{23 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{4 a^2}+\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a^2}-\frac{1}{2} x^2 \sqrt{c-\frac{c}{a x}}+\frac{9 x \sqrt{c-\frac{c}{a x}}}{4 a}",1,"(a*Sqrt[c - c/(a*x)]*x*(9 - 2*a*x) - 23*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]] + 16*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/(4*a^2)","A",1
602,1,93,93,0.0482116,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[Sqrt[c - c/(a*x)]/E^(2*ArcTanh[a*x]),x]","x \left(-\sqrt{c-\frac{c}{a x}}\right)+\frac{5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}","x \left(-\sqrt{c-\frac{c}{a x}}\right)+\frac{5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)}{a}",1,"-(Sqrt[c - c/(a*x)]*x) + (5*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a - (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",1
603,1,86,86,0.0366886,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x),x]","-2 \sqrt{c-\frac{c}{a x}}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)+4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)","-2 \sqrt{c-\frac{c}{a x}}-2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)+4 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)",1,"-2*Sqrt[c - c/(a*x)] - 2*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]] + 4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",1
604,1,69,82,0.0659973,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^2),x]","\frac{2 (7 a x-1) \sqrt{c-\frac{c}{a x}}}{3 x}-4 \sqrt{2} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)","\frac{2 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}+4 a \sqrt{c-\frac{c}{a x}}-4 \sqrt{2} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)",1,"(2*Sqrt[c - c/(a*x)]*(-1 + 7*a*x))/(3*x) - 4*Sqrt[2]*a*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",1
605,1,79,113,0.0840381,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^3),x]","4 \sqrt{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)-\frac{2 \left(38 a^2 x^2-11 a x+3\right) \sqrt{c-\frac{c}{a x}}}{15 x^2}","-\frac{2 a^2 \left(c-\frac{c}{a x}\right)^{5/2}}{5 c^2}-\frac{2 a^2 \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a^2 \sqrt{c-\frac{c}{a x}}+4 \sqrt{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)",1,"(-2*Sqrt[c - c/(a*x)]*(3 - 11*a*x + 38*a^2*x^2))/(15*x^2) + 4*Sqrt[2]*a^2*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",1
606,1,87,113,0.1297727,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^4),x]","\frac{2 \left(52 a^3 x^3-16 a^2 x^2+9 a x-3\right) \sqrt{c-\frac{c}{a x}}}{21 x^3}-4 \sqrt{2} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)","\frac{2 a^3 \left(c-\frac{c}{a x}\right)^{7/2}}{7 c^3}+\frac{2 a^3 \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}+4 a^3 \sqrt{c-\frac{c}{a x}}-4 \sqrt{2} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)",1,"(2*Sqrt[c - c/(a*x)]*(-3 + 9*a*x - 16*a^2*x^2 + 52*a^3*x^3))/(21*x^3) - 4*Sqrt[2]*a^3*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",1
607,1,95,163,0.1383727,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^5),x]","4 \sqrt{2} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)-\frac{2 \left(788 a^4 x^4-236 a^3 x^3+138 a^2 x^2-95 a x+35\right) \sqrt{c-\frac{c}{a x}}}{315 x^4}","-\frac{2 a^4 \left(c-\frac{c}{a x}\right)^{9/2}}{9 c^4}+\frac{2 a^4 \left(c-\frac{c}{a x}\right)^{7/2}}{7 c^3}-\frac{2 a^4 \left(c-\frac{c}{a x}\right)^{5/2}}{5 c^2}-\frac{2 a^4 \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a^4 \sqrt{c-\frac{c}{a x}}+4 \sqrt{2} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{2} \sqrt{c}}\right)",1,"(-2*Sqrt[c - c/(a*x)]*(35 - 95*a*x + 138*a^2*x^2 - 236*a^3*x^3 + 788*a^4*x^4))/(315*x^4) + 4*Sqrt[2]*a^4*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",1
608,1,108,262,0.0648875,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Integrate[(Sqrt[c - c/(a*x)]*x^3)/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \left(48 a^4 x^4-200 a^3 x^3+446 a^2 x^2-1115 a x-3345\right)+3345 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{192 a^{7/2} \sqrt{1-a^2 x^2}}","\frac{1115 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{64 a^{7/2} \sqrt{1-a x}}-\frac{1115 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{64 a^3 \sqrt{1-a x}}+\frac{1115 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{96 a^2 \sqrt{1-a x}}+\frac{x^4 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 \sqrt{1-a x}}+\frac{8 x^4 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{223 x^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{24 a \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*(-3345 - 1115*a*x + 446*a^2*x^2 - 200*a^3*x^3 + 48*a^4*x^4) + 3345*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(192*a^(7/2)*Sqrt[1 - a^2*x^2])","A",0
609,1,100,218,0.0648566,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Integrate[(Sqrt[c - c/(a*x)]*x^2)/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \left(8 a^3 x^3-38 a^2 x^2+119 a x+357\right)-357 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{24 a^{5/2} \sqrt{1-a^2 x^2}}","-\frac{119 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{8 a^{5/2} \sqrt{1-a x}}+\frac{119 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-a x}}+\frac{x^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-a x}}+\frac{8 x^3 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{119 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*(357 + 119*a*x - 38*a^2*x^2 + 8*a^3*x^3) - 357*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(24*a^(5/2)*Sqrt[1 - a^2*x^2])","A",0
610,1,92,174,0.0565358,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Integrate[(Sqrt[c - c/(a*x)]*x)/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} \left(2 a^2 x^2-13 a x-47\right)+47 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{4 a^{3/2} \sqrt{1-a^2 x^2}}","\frac{47 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{4 a^{3/2} \sqrt{1-a x}}+\frac{x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{2 \sqrt{1-a x}}+\frac{8 x^2 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{47 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*(-47 - 13*a*x + 2*a^2*x^2) + 47*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(4*a^(3/2)*Sqrt[1 - a^2*x^2])","A",0
611,1,80,123,0.0492981,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[Sqrt[c - c/(a*x)]/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{x} \sqrt{c-\frac{c}{a x}} \left(\sqrt{a} \sqrt{x} (a x+9)-7 \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{\sqrt{a} \sqrt{1-a^2 x^2}}","\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x}}+\frac{8 x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{7 \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{1-a x}}",1,"(Sqrt[c - c/(a*x)]*Sqrt[x]*(Sqrt[a]*Sqrt[x]*(9 + a*x) - 7*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/(Sqrt[a]*Sqrt[1 - a^2*x^2])","A",0
612,1,70,124,0.0532238,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x),x]","-\frac{2 \sqrt{c-\frac{c}{a x}} \left(5 a x-\sqrt{a} \sqrt{x} \sqrt{a x+1} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+1\right)}{\sqrt{1-a^2 x^2}}","-\frac{10 a x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{2 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-a x} \sqrt{a x+1}}+\frac{2 \sqrt{a} \sqrt{x} \sqrt{c-\frac{c}{a x}} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + 5*a*x - Sqrt[a]*Sqrt[x]*Sqrt[1 + a*x]*ArcSinh[Sqrt[a]*Sqrt[x]]))/Sqrt[1 - a^2*x^2]","A",0
613,1,50,123,0.0315867,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^2),x]","\frac{2 \left(23 a^2 x^2+10 a x-1\right) \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a^2 x^2}}","\frac{46 a^2 x \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-a x} \sqrt{a x+1}}+\frac{20 a \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 \sqrt{c-\frac{c}{a x}}}{3 x \sqrt{1-a x} \sqrt{a x+1}}",1,"(2*Sqrt[c - c/(a*x)]*(-1 + 10*a*x + 23*a^2*x^2))/(3*x*Sqrt[1 - a^2*x^2])","A",1
614,1,58,166,0.0321892,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^3),x]","-\frac{2 \left(158 a^3 x^3+79 a^2 x^2-16 a x+3\right) \sqrt{c-\frac{c}{a x}}}{15 x^2 \sqrt{1-a^2 x^2}}","-\frac{316 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{15 \sqrt{1-a x}}+\frac{158 a^2 \sqrt{c-\frac{c}{a x}}}{15 \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 \sqrt{c-\frac{c}{a x}}}{5 x^2 \sqrt{1-a x} \sqrt{a x+1}}+\frac{32 a \sqrt{c-\frac{c}{a x}}}{15 x \sqrt{1-a x} \sqrt{a x+1}}",1,"(-2*Sqrt[c - c/(a*x)]*(3 - 16*a*x + 79*a^2*x^2 + 158*a^3*x^3))/(15*x^2*Sqrt[1 - a^2*x^2])","A",1
615,1,66,213,0.0342103,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^4),x]","\frac{2 \left(1336 a^4 x^4+668 a^3 x^3-167 a^2 x^2+66 a x-15\right) \sqrt{c-\frac{c}{a x}}}{105 x^3 \sqrt{1-a^2 x^2}}","\frac{2672 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 \sqrt{1-a x}}-\frac{1336 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 x \sqrt{1-a x}}+\frac{334 a^2 \sqrt{c-\frac{c}{a x}}}{35 x \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 \sqrt{c-\frac{c}{a x}}}{7 x^3 \sqrt{1-a x} \sqrt{a x+1}}+\frac{44 a \sqrt{c-\frac{c}{a x}}}{35 x^2 \sqrt{1-a x} \sqrt{a x+1}}",1,"(2*Sqrt[c - c/(a*x)]*(-15 + 66*a*x - 167*a^2*x^2 + 668*a^3*x^3 + 1336*a^4*x^4))/(105*x^3*Sqrt[1 - a^2*x^2])","A",1
616,1,74,257,0.0370039,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Integrate[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^5),x]","-\frac{2 \left(656 a^5 x^5+328 a^4 x^4-82 a^3 x^3+41 a^2 x^2-20 a x+5\right) \sqrt{c-\frac{c}{a x}}}{45 x^4 \sqrt{1-a^2 x^2}}","-\frac{1312 a^4 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{45 \sqrt{1-a x}}+\frac{656 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{45 x \sqrt{1-a x}}-\frac{164 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{15 x^2 \sqrt{1-a x}}+\frac{82 a^2 \sqrt{c-\frac{c}{a x}}}{9 x^2 \sqrt{1-a x} \sqrt{a x+1}}-\frac{2 \sqrt{c-\frac{c}{a x}}}{9 x^4 \sqrt{1-a x} \sqrt{a x+1}}+\frac{8 a \sqrt{c-\frac{c}{a x}}}{9 x^3 \sqrt{1-a x} \sqrt{a x+1}}",1,"(-2*Sqrt[c - c/(a*x)]*(5 - 20*a*x + 41*a^2*x^2 - 82*a^3*x^3 + 328*a^4*x^4 + 656*a^5*x^5))/(45*x^4*Sqrt[1 - a^2*x^2])","A",1
617,0,0,64,0.6393026,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a*x))^p,x]","\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","\frac{x (1-a x)^{-p} \left(c-\frac{c}{a x}\right)^p F_1\left(1-p;\frac{1}{2} (n-2 p),-\frac{n}{2};2-p;a x,-a x\right)}{1-p}",1,"Integrate[E^(n*ArcTanh[a*x])*(c - c/(a*x))^p, x]","F",-1
618,0,0,54,0.4409806,"\int e^{-2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[(c - c/(a*x))^p/E^(2*p*ArcTanh[a*x]),x]","\int e^{-2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","\frac{x (1-a x)^{-p} F_1(1-p;-2 p,p;2-p;a x,-a x) \left(c-\frac{c}{a x}\right)^p}{1-p}",1,"Integrate[(c - c/(a*x))^p/E^(2*p*ArcTanh[a*x]), x]","F",-1
619,1,50,50,0.0181956,"\int e^{2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Integrate[E^(2*p*ArcTanh[a*x])*(c - c/(a*x))^p,x]","\frac{x (1-a x)^{-p} \left(c-\frac{c}{a x}\right)^p \, _2F_1(1-p,-p;2-p;-a x)}{1-p}","\frac{x (1-a x)^{-p} \left(c-\frac{c}{a x}\right)^p \, _2F_1(1-p,-p;2-p;-a x)}{1-p}",1,"((c - c/(a*x))^p*x*Hypergeometric2F1[1 - p, -p, 2 - p, -(a*x)])/((1 - p)*(1 - a*x)^p)","A",1
620,1,262,130,0.4974214,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a*x))^2,x]","-\frac{c^2 e^{n \tanh ^{-1}(a x)} \left(a n^2 x \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;e^{2 \tanh ^{-1}(a x)}\right)-2 a n x e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+a (n-2) n x e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;e^{2 \tanh ^{-1}(a x)}\right)+2 a n x \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;-e^{2 \tanh ^{-1}(a x)}\right)-4 a n x e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+4 a x \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;-e^{2 \tanh ^{-1}(a x)}\right)-4 a x \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;e^{2 \tanh ^{-1}(a x)}\right)+n^2+2 n\right)}{a^2 n (n+2) x}","\frac{c^2 2^{n/2} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},2-\frac{n}{2};3-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (4-n)}+\frac{4 c^2 (a x+1)^{n/2} (1-a x)^{-n/2} \, _2F_1\left(2,\frac{n}{2};\frac{n+2}{2};\frac{a x+1}{1-a x}\right)}{a n}",1,"-((c^2*E^(n*ArcTanh[a*x])*(2*n + n^2 - 2*a*E^(2*ArcTanh[a*x])*n*x*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])] + a*E^(2*ArcTanh[a*x])*(-2 + n)*n*x*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, E^(2*ArcTanh[a*x])] + 4*a*x*Hypergeometric2F1[1, n/2, 1 + n/2, -E^(2*ArcTanh[a*x])] + 2*a*n*x*Hypergeometric2F1[1, n/2, 1 + n/2, -E^(2*ArcTanh[a*x])] - 4*a*x*Hypergeometric2F1[1, n/2, 1 + n/2, E^(2*ArcTanh[a*x])] + a*n^2*x*Hypergeometric2F1[1, n/2, 1 + n/2, E^(2*ArcTanh[a*x])] - 4*a*E^(2*ArcTanh[a*x])*n*x*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])]))/(a^2*n*(2 + n)*x))","B",0
621,1,180,187,0.263363,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a*x)),x]","\frac{c e^{n \tanh ^{-1}(a x)} \left(e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;e^{2 \tanh ^{-1}(a x)}\right)-\frac{(n+2) \left(\, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;-e^{2 \tanh ^{-1}(a x)}\right)-\, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;e^{2 \tanh ^{-1}(a x)}\right)\right)}{n}+4 e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)\right)}{a (n+2)}","-\frac{2 c (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1,\frac{n-2}{2};\frac{n}{2};\frac{a x+1}{1-a x}\right)}{a (2-n)}+\frac{c 2^{n/2} (1-n) (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(\frac{2-n}{2},2-\frac{n}{2};3-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (2-n) (4-n)}+\frac{c (a x+1)^{\frac{n-2}{2}} (1-a x)^{2-\frac{n}{2}}}{a (2-n)}",1,"(c*E^(n*ArcTanh[a*x])*(E^(2*ArcTanh[a*x])*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])] + E^(2*ArcTanh[a*x])*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, E^(2*ArcTanh[a*x])] - ((2 + n)*(Hypergeometric2F1[1, n/2, 1 + n/2, -E^(2*ArcTanh[a*x])] - Hypergeometric2F1[1, n/2, 1 + n/2, E^(2*ArcTanh[a*x])]))/n + 4*E^(2*ArcTanh[a*x])*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])]))/(a*(2 + n))","A",0
622,1,95,111,0.043423,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a*x)),x]","\frac{(1-a x)^{-n/2} \left(-2^{\frac{n}{2}+1} (n+1) (a x-1) \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)-\left((n-2) (a x+1)^{\frac{n}{2}+1}\right)\right)}{a c (n-2) n}","-\frac{2^{\frac{n}{2}+1} (n+1) (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a c (2-n) n}-\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{-n/2}}{a c n}",1,"(-((-2 + n)*(1 + a*x)^(1 + n/2)) - 2^(1 + n/2)*(1 + n)*(-1 + a*x)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a*x)/2])/(a*c*(-2 + n)*n*(1 - a*x)^(n/2))","A",1
623,1,194,139,0.4719018,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a*x))^2,x]","\frac{e^{n \tanh ^{-1}(a x)} \left(-2 n (a x-1) e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)-4 n e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+4 a n x e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+2 (n+2) (a x-1) \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;-e^{2 \tanh ^{-1}(a x)}\right)-3 a n x-4 a x+n+4\right)}{a c^2 n (n+2) (a x-1)}","-\frac{2^{\frac{n}{2}+1} (n+2) (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a c^2 n}+\frac{(n+3) (a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a c^2 (n+2)}-\frac{x (a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-1}}{c^2}",1,"(E^(n*ArcTanh[a*x])*(4 + n - 4*a*x - 3*a*n*x - 2*E^(2*ArcTanh[a*x])*n*(-1 + a*x)*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])] + 2*(2 + n)*(-1 + a*x)*Hypergeometric2F1[1, n/2, 1 + n/2, -E^(2*ArcTanh[a*x])] - 4*E^(2*ArcTanh[a*x])*n*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])] + 4*a*E^(2*ArcTanh[a*x])*n*x*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])]))/(a*c^2*n*(2 + n)*(-1 + a*x))","A",0
624,-1,0,54,180.0070176,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a*x))^(3/2),x]","\text{\$Aborted}","-\frac{2 x \left(c-\frac{c}{a x}\right)^{3/2} F_1\left(-\frac{1}{2};\frac{n-3}{2},-\frac{n}{2};\frac{1}{2};a x,-a x\right)}{(1-a x)^{3/2}}",1,"$Aborted","F",-1
625,-1,0,54,180.0070471,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Integrate[E^(n*ArcTanh[a*x])*Sqrt[c - c/(a*x)],x]","\text{\$Aborted}","\frac{2 x \sqrt{c-\frac{c}{a x}} F_1\left(\frac{1}{2};\frac{n-1}{2},-\frac{n}{2};\frac{3}{2};a x,-a x\right)}{\sqrt{1-a x}}",1,"$Aborted","F",-1
626,-1,0,56,180.0068911,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Integrate[E^(n*ArcTanh[a*x])/Sqrt[c - c/(a*x)],x]","\text{\$Aborted}","\frac{2 x \sqrt{1-a x} F_1\left(\frac{3}{2};\frac{n+1}{2},-\frac{n}{2};\frac{5}{2};a x,-a x\right)}{3 \sqrt{c-\frac{c}{a x}}}",1,"$Aborted","F",-1
627,-1,0,56,180.0065269,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a*x))^(3/2),x]","\text{\$Aborted}","\frac{2 x (1-a x)^{3/2} F_1\left(\frac{5}{2};\frac{n+3}{2},-\frac{n}{2};\frac{7}{2};a x,-a x\right)}{5 \left(c-\frac{c}{a x}\right)^{3/2}}",1,"$Aborted","F",-1
628,1,70,169,0.0322709,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^4,x]","\frac{c^4 \left(-\frac{9 \, _2F_1\left(-\frac{7}{2},-\frac{7}{2};-\frac{5}{2};a^2 x^2\right)}{x^7}-7 a^7 \left(1-a^2 x^2\right)^{9/2} \, _2F_1\left(4,\frac{9}{2};\frac{11}{2};1-a^2 x^2\right)\right)}{63 a^8}","\frac{c^4 (16-35 a x) \sqrt{1-a^2 x^2}}{16 a^2 x}+\frac{35 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{16 a}-\frac{c^4 (7 a x+6) \left(1-a^2 x^2\right)^{7/2}}{42 a^8 x^7}+\frac{c^4 (35 a x+24) \left(1-a^2 x^2\right)^{5/2}}{120 a^6 x^5}-\frac{c^4 (35 a x+16) \left(1-a^2 x^2\right)^{3/2}}{48 a^4 x^3}+\frac{c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*((-9*Hypergeometric2F1[-7/2, -7/2, -5/2, a^2*x^2])/x^7 - 7*a^7*(1 - a^2*x^2)^(9/2)*Hypergeometric2F1[4, 9/2, 11/2, 1 - a^2*x^2]))/(63*a^8)","C",0
629,1,70,136,0.0285256,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^3,x]","\frac{c^3 \left(\frac{7 \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};a^2 x^2\right)}{x^5}+5 a^5 \left(1-a^2 x^2\right)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};1-a^2 x^2\right)\right)}{35 a^6}","\frac{c^3 (8-15 a x) \sqrt{1-a^2 x^2}}{8 a^2 x}+\frac{15 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{8 a}+\frac{c^3 (5 a x+4) \left(1-a^2 x^2\right)^{5/2}}{20 a^6 x^5}-\frac{c^3 (15 a x+8) \left(1-a^2 x^2\right)^{3/2}}{24 a^4 x^3}+\frac{c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*((7*Hypergeometric2F1[-5/2, -5/2, -3/2, a^2*x^2])/x^5 + 5*a^5*(1 - a^2*x^2)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 - a^2*x^2]))/(35*a^6)","C",0
630,1,70,103,0.0259516,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^2,x]","\frac{c^2 \left(-\frac{5 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};a^2 x^2\right)}{x^3}-3 a^3 \left(1-a^2 x^2\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};1-a^2 x^2\right)\right)}{15 a^4}","\frac{c^2 (2-3 a x) \sqrt{1-a^2 x^2}}{2 a^2 x}+\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^2 (3 a x+2) \left(1-a^2 x^2\right)^{3/2}}{6 a^4 x^3}+\frac{c^2 \sin ^{-1}(a x)}{a}",1,"(c^2*((-5*Hypergeometric2F1[-3/2, -3/2, -1/2, a^2*x^2])/x^3 - 3*a^3*(1 - a^2*x^2)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 - a^2*x^2]))/(15*a^4)","C",0
631,1,55,58,0.0429575,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2)),x]","\frac{c \left(\sqrt{1-a^2 x^2} (1-a x)+a x \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a x \sin ^{-1}(a x)\right)}{a^2 x}","\frac{c \sqrt{1-a^2 x^2} (1-a x)}{a^2 x}+\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}+\frac{c \sin ^{-1}(a x)}{a}",1,"(c*((1 - a*x)*Sqrt[1 - a^2*x^2] + a*x*ArcSin[a*x] + a*x*ArcTanh[Sqrt[1 - a^2*x^2]]))/(a^2*x)","A",1
632,1,53,61,0.0284562,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2)),x]","\frac{a^2 x^2+\sqrt{1-a^2 x^2} \sin ^{-1}(a x)-a x-2}{a c \sqrt{1-a^2 x^2}}","-\frac{a x+1}{a c \sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2}}{a c}+\frac{\sin ^{-1}(a x)}{a c}",1,"(-2 - a*x + a^2*x^2 + Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(a*c*Sqrt[1 - a^2*x^2])","A",1
633,1,78,96,0.0506258,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^2,x]","\frac{3 a^3 x^3-7 a^2 x^2+3 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-5 a x+8}{3 a c^2 (a x-1) \sqrt{1-a^2 x^2}}","-\frac{x (4 a x+3)}{3 c^2 \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{1-a^2 x^2}}{3 a c^2}+\frac{a^2 x^3 (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{\sin ^{-1}(a x)}{a c^2}",1,"(8 - 5*a*x - 7*a^2*x^2 + 3*a^3*x^3 + 3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
634,1,108,129,0.0738324,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^3,x]","\frac{15 a^5 x^5-38 a^4 x^4-52 a^3 x^3+87 a^2 x^2+15 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+33 a x-48}{15 a c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{x (8 a x+5)}{5 c^3 \sqrt{1-a^2 x^2}}-\frac{16 \sqrt{1-a^2 x^2}}{5 a c^3}+\frac{a^2 x^3 (6 a x+5)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{a^4 x^5 (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{\sin ^{-1}(a x)}{a c^3}",1,"(-48 + 33*a*x + 87*a^2*x^2 - 52*a^3*x^3 - 38*a^4*x^4 + 15*a^5*x^5 + 15*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(15*a*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
635,1,126,162,0.0989744,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^4,x]","\frac{105 a^7 x^7-281 a^6 x^6-559 a^5 x^5+965 a^4 x^4+715 a^3 x^3-1065 a^2 x^2+105 (a x-1)^3 (a x+1)^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-279 a x+384}{105 a c^4 (a x-1)^3 (a x+1)^2 \sqrt{1-a^2 x^2}}","-\frac{x (64 a x+35)}{35 c^4 \sqrt{1-a^2 x^2}}-\frac{128 \sqrt{1-a^2 x^2}}{35 a c^4}+\frac{a^2 x^3 (48 a x+35)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{a^6 x^7 (a x+1)}{7 c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^4 x^5 (8 a x+7)}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{\sin ^{-1}(a x)}{a c^4}",1,"(384 - 279*a*x - 1065*a^2*x^2 + 715*a^3*x^3 + 965*a^4*x^4 - 559*a^5*x^5 - 281*a^6*x^6 + 105*a^7*x^7 + 105*(-1 + a*x)^3*(1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(105*a*c^4*(-1 + a*x)^3*(1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
636,1,128,128,0.0386836,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^5 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^5,x]","\frac{c^5}{9 a^{10} x^9}+\frac{c^5}{4 a^9 x^8}-\frac{3 c^5}{7 a^8 x^7}-\frac{4 c^5}{3 a^7 x^6}+\frac{2 c^5}{5 a^6 x^5}+\frac{3 c^5}{a^5 x^4}+\frac{2 c^5}{3 a^4 x^3}-\frac{4 c^5}{a^3 x^2}-\frac{3 c^5}{a^2 x}-\frac{2 c^5 \log (x)}{a}+c^5 (-x)","\frac{c^5}{9 a^{10} x^9}+\frac{c^5}{4 a^9 x^8}-\frac{3 c^5}{7 a^8 x^7}-\frac{4 c^5}{3 a^7 x^6}+\frac{2 c^5}{5 a^6 x^5}+\frac{3 c^5}{a^5 x^4}+\frac{2 c^5}{3 a^4 x^3}-\frac{4 c^5}{a^3 x^2}-\frac{3 c^5}{a^2 x}-\frac{2 c^5 \log (x)}{a}+c^5 (-x)",1,"c^5/(9*a^10*x^9) + c^5/(4*a^9*x^8) - (3*c^5)/(7*a^8*x^7) - (4*c^5)/(3*a^7*x^6) + (2*c^5)/(5*a^6*x^5) + (3*c^5)/(a^5*x^4) + (2*c^5)/(3*a^4*x^3) - (4*c^5)/(a^3*x^2) - (3*c^5)/(a^2*x) - c^5*x - (2*c^5*Log[x])/a","A",1
637,1,91,91,0.0262815,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^4,x]","-\frac{c^4}{7 a^8 x^7}-\frac{c^4}{3 a^7 x^6}+\frac{2 c^4}{5 a^6 x^5}+\frac{3 c^4}{2 a^5 x^4}-\frac{3 c^4}{a^3 x^2}-\frac{2 c^4}{a^2 x}-\frac{2 c^4 \log (x)}{a}+c^4 (-x)","-\frac{c^4}{7 a^8 x^7}-\frac{c^4}{3 a^7 x^6}+\frac{2 c^4}{5 a^6 x^5}+\frac{3 c^4}{2 a^5 x^4}-\frac{3 c^4}{a^3 x^2}-\frac{2 c^4}{a^2 x}-\frac{2 c^4 \log (x)}{a}+c^4 (-x)",1,"-1/7*c^4/(a^8*x^7) - c^4/(3*a^7*x^6) + (2*c^4)/(5*a^6*x^5) + (3*c^4)/(2*a^5*x^4) - (3*c^4)/(a^3*x^2) - (2*c^4)/(a^2*x) - c^4*x - (2*c^4*Log[x])/a","A",1
638,1,78,78,0.0221905,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^3,x]","\frac{c^3}{5 a^6 x^5}+\frac{c^3}{2 a^5 x^4}-\frac{c^3}{3 a^4 x^3}-\frac{2 c^3}{a^3 x^2}-\frac{c^3}{a^2 x}-\frac{2 c^3 \log (x)}{a}+c^3 (-x)","\frac{c^3}{5 a^6 x^5}+\frac{c^3}{2 a^5 x^4}-\frac{c^3}{3 a^4 x^3}-\frac{2 c^3}{a^3 x^2}-\frac{c^3}{a^2 x}-\frac{2 c^3 \log (x)}{a}+c^3 (-x)",1,"c^3/(5*a^6*x^5) + c^3/(2*a^5*x^4) - c^3/(3*a^4*x^3) - (2*c^3)/(a^3*x^2) - c^3/(a^2*x) - c^3*x - (2*c^3*Log[x])/a","A",1
639,1,41,41,0.0150843,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{c^2}{3 a^4 x^3}-\frac{c^2}{a^3 x^2}-\frac{2 c^2 \log (x)}{a}+c^2 (-x)","-\frac{c^2}{3 a^4 x^3}-\frac{c^2}{a^3 x^2}-\frac{2 c^2 \log (x)}{a}+c^2 (-x)",1,"-1/3*c^2/(a^4*x^3) - c^2/(a^3*x^2) - c^2*x - (2*c^2*Log[x])/a","A",1
640,1,21,21,0.0118621,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2)),x]","\frac{c}{a^2 x}-\frac{2 c \log (x)}{a}+c (-x)","\frac{c}{a^2 x}-\frac{2 c \log (x)}{a}+c (-x)",1,"c/(a^2*x) - c*x - (2*c*Log[x])/a","A",1
641,1,38,38,0.021243,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2)),x]","-\frac{1}{a c (1-a x)}-\frac{2 \log (1-a x)}{a c}-\frac{x}{c}","-\frac{1}{a c (1-a x)}-\frac{2 \log (1-a x)}{a c}-\frac{x}{c}",1,"-(x/c) - 1/(a*c*(1 - a*x)) - (2*Log[1 - a*x])/(a*c)","A",1
642,1,69,76,0.0436688,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","\frac{-8 a^3 x^3+16 a^2 x^2+6 a x-17 (a x-1)^2 \log (1-a x)+(a x-1)^2 \log (a x+1)-12}{8 a c^2 (a x-1)^2}","-\frac{7}{4 a c^2 (1-a x)}+\frac{1}{4 a c^2 (1-a x)^2}-\frac{17 \log (1-a x)}{8 a c^2}+\frac{\log (a x+1)}{8 a c^2}-\frac{x}{c^2}",1,"(-12 + 6*a*x + 16*a^2*x^2 - 8*a^3*x^3 - 17*(-1 + a*x)^2*Log[1 - a*x] + (-1 + a*x)^2*Log[1 + a*x])/(8*a*c^2*(-1 + a*x)^2)","A",1
643,1,103,111,0.0593692,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^3,x]","\frac{-12 a^5 x^5+24 a^4 x^4+30 a^3 x^3-48 a^2 x^2-14 a x-27 (a x-1)^3 (a x+1) \log (1-a x)+3 (a x-1)^3 (a x+1) \log (a x+1)+22}{12 a c^3 (a x-1)^3 (a x+1)}","-\frac{39}{16 a c^3 (1-a x)}+\frac{1}{16 a c^3 (a x+1)}+\frac{5}{8 a c^3 (1-a x)^2}-\frac{1}{12 a c^3 (1-a x)^3}-\frac{9 \log (1-a x)}{4 a c^3}+\frac{\log (a x+1)}{4 a c^3}-\frac{x}{c^3}",1,"(22 - 14*a*x - 48*a^2*x^2 + 30*a^3*x^3 + 24*a^4*x^4 - 12*a^5*x^5 - 27*(-1 + a*x)^3*(1 + a*x)*Log[1 - a*x] + 3*(-1 + a*x)^3*(1 + a*x)*Log[1 + a*x])/(12*a*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
644,1,123,146,0.089151,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^4,x]","\frac{-384 a^7 x^7+768 a^6 x^6+1638 a^5 x^5-2508 a^4 x^4-1732 a^3 x^3+2516 a^2 x^2+550 a x-909 (a x-1)^4 (a x+1)^2 \log (1-a x)+141 (a x-1)^4 (a x+1)^2 \log (a x+1)-800}{384 a c^4 (a x-1)^4 (a x+1)^2}","-\frac{99}{32 a c^4 (1-a x)}+\frac{11}{64 a c^4 (a x+1)}+\frac{35}{32 a c^4 (1-a x)^2}-\frac{1}{64 a c^4 (a x+1)^2}-\frac{13}{48 a c^4 (1-a x)^3}+\frac{1}{32 a c^4 (1-a x)^4}-\frac{303 \log (1-a x)}{128 a c^4}+\frac{47 \log (a x+1)}{128 a c^4}-\frac{x}{c^4}",1,"(-800 + 550*a*x + 2516*a^2*x^2 - 1732*a^3*x^3 - 2508*a^4*x^4 + 1638*a^5*x^5 + 768*a^6*x^6 - 384*a^7*x^7 - 909*(-1 + a*x)^4*(1 + a*x)^2*Log[1 - a*x] + 141*(-1 + a*x)^4*(1 + a*x)^2*Log[1 + a*x])/(384*a*c^4*(-1 + a*x)^4*(1 + a*x)^2)","A",1
645,1,191,191,0.2111688,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^4,x]","\frac{c^4 \left(-336 a^2 x^2 \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};a^2 x^2\right)-\frac{5 \left(16 a^8 x^8-231 a^7 x^7-64 a^6 x^6+413 a^5 x^5+96 a^4 x^4-238 a^3 x^3-64 a^2 x^2+16 a^7 x^7 \left(a^2 x^2-1\right)^4 \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};1-a^2 x^2\right)-105 a^7 x^7 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+56 a x+16\right)}{\sqrt{1-a^2 x^2}}\right)}{560 a^8 x^7}","-\frac{3 c^4 (16-5 a x) \sqrt{1-a^2 x^2}}{16 a^2 x}-\frac{15 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{16 a}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{7 a^8 x^7}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{2 a^7 x^6}-\frac{c^4 (5 a x+24) \left(1-a^2 x^2\right)^{5/2}}{40 a^6 x^5}+\frac{c^4 (5 a x+16) \left(1-a^2 x^2\right)^{3/2}}{16 a^4 x^3}-\frac{3 c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*(-336*a^2*x^2*Hypergeometric2F1[-5/2, -5/2, -3/2, a^2*x^2] - (5*(16 + 56*a*x - 64*a^2*x^2 - 238*a^3*x^3 + 96*a^4*x^4 + 413*a^5*x^5 - 64*a^6*x^6 - 231*a^7*x^7 + 16*a^8*x^8 - 105*a^7*x^7*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]] + 16*a^7*x^7*(-1 + a^2*x^2)^4*Hypergeometric2F1[3, 7/2, 9/2, 1 - a^2*x^2]))/Sqrt[1 - a^2*x^2]))/(560*a^8*x^7)","C",0
646,1,186,157,0.1040113,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^3,x]","\frac{c^3 \left(-8 a^6 x^6+75 a^5 x^5+24 a^4 x^4-105 a^3 x^3+40 a^2 x^2 \sqrt{1-a^2 x^2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};a^2 x^2\right)-24 a^2 x^2-8 a^5 x^5 \left(a^2 x^2-1\right)^3 \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};1-a^2 x^2\right)+45 a^5 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+30 a x+8\right)}{40 a^6 x^5 \sqrt{1-a^2 x^2}}","-\frac{3 c^3 (8-a x) \sqrt{1-a^2 x^2}}{8 a^2 x}-\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{8 a}+\frac{c^3 \left(1-a^2 x^2\right)^{5/2}}{5 a^6 x^5}+\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{4 a^5 x^4}+\frac{c^3 (a x+8) \left(1-a^2 x^2\right)^{3/2}}{8 a^4 x^3}-\frac{3 c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*(8 + 30*a*x - 24*a^2*x^2 - 105*a^3*x^3 + 24*a^4*x^4 + 75*a^5*x^5 - 8*a^6*x^6 + 45*a^5*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]] + 40*a^2*x^2*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[-3/2, -3/2, -1/2, a^2*x^2] - 8*a^5*x^5*(-1 + a^2*x^2)^3*Hypergeometric2F1[2, 5/2, 7/2, 1 - a^2*x^2]))/(40*a^6*x^5*Sqrt[1 - a^2*x^2])","C",0
647,1,128,124,0.066542,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{c^2 \left(6 a^5 x^5-16 a^4 x^4-15 a^3 x^3+14 a^2 x^2+18 a^3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-3 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+9 a x+2\right)}{6 a^4 x^3 \sqrt{1-a^2 x^2}}","-\frac{c^2 (a x+6) \sqrt{1-a^2 x^2}}{2 a^2 x}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\frac{3 c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{3 c^2 \sin ^{-1}(a x)}{a}",1,"-1/6*(c^2*(2 + 9*a*x + 14*a^2*x^2 - 15*a^3*x^3 - 16*a^4*x^4 + 6*a^5*x^5 + 18*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x] - 3*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(a^4*x^3*Sqrt[1 - a^2*x^2])","A",1
648,1,56,73,0.0468451,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2)),x]","\frac{c \left(\sqrt{1-a^2 x^2} (a x+1)+3 a x \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-3 a x \sin ^{-1}(a x)\right)}{a^2 x}","\frac{c \sqrt{1-a^2 x^2}}{a}+\frac{c \sqrt{1-a^2 x^2}}{a^2 x}+\frac{3 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{3 c \sin ^{-1}(a x)}{a}",1,"(c*((1 + a*x)*Sqrt[1 - a^2*x^2] - 3*a*x*ArcSin[a*x] + 3*a*x*ArcTanh[Sqrt[1 - a^2*x^2]]))/(a^2*x)","A",1
649,1,78,95,0.0799163,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2)),x]","\frac{-3 a^3 x^3+16 a^2 x^2-9 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+5 a x-14}{3 a c (a x-1) \sqrt{1-a^2 x^2}}","-\frac{(a x+1)^3}{3 a c \left(1-a^2 x^2\right)^{3/2}}+\frac{2 (a x+1)^2}{a c \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{1-a^2 x^2}}{a c}-\frac{3 \sin ^{-1}(a x)}{a c}",1,"(-14 + 5*a*x + 16*a^2*x^2 - 3*a^3*x^3 - 9*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a*c*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
650,1,88,125,0.1025913,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","\frac{-5 a^4 x^4+34 a^3 x^3-18 a^2 x^2-15 (a x-1)^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-33 a x+24}{5 a c^2 (a x-1)^2 \sqrt{1-a^2 x^2}}","\frac{(a x+1)^3}{5 a c^2 \left(1-a^2 x^2\right)^{5/2}}-\frac{6 (a x+1)^2}{5 a c^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{24 (a x+1)}{5 a c^2 \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2}}{a c^2}-\frac{3 \sin ^{-1}(a x)}{a c^2}",1,"(24 - 33*a*x - 18*a^2*x^2 + 34*a^3*x^3 - 5*a^4*x^4 - 15*(-1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(5*a*c^2*(-1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
651,1,96,155,0.1180739,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^3,x]","\frac{-35 a^5 x^5+286 a^4 x^4-368 a^3 x^3-125 a^2 x^2-105 (a x-1)^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+423 a x-176}{35 a c^3 (a x-1)^3 \sqrt{1-a^2 x^2}}","-\frac{(a x+1)^3}{7 a c^3 \left(1-a^2 x^2\right)^{7/2}}+\frac{38 (a x+1)^2}{35 a c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{137 (a x+1)}{35 a c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{\sqrt{1-a^2 x^2}}{a c^3}+\frac{181 a x+245}{35 a c^3 \sqrt{1-a^2 x^2}}-\frac{3 \sin ^{-1}(a x)}{a c^3}",1,"(-176 + 423*a*x - 125*a^2*x^2 - 368*a^3*x^3 + 286*a^4*x^4 - 35*a^5*x^5 - 105*(-1 + a*x)^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(35*a*c^3*(-1 + a*x)^3*Sqrt[1 - a^2*x^2])","A",1
652,1,124,185,0.1474942,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^4,x]","\frac{-315 a^7 x^7+2669 a^6 x^6-2967 a^5 x^5-4029 a^4 x^4+7399 a^3 x^3-339 a^2 x^2-945 (a x-1)^4 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-4047 a x+1664}{315 a c^4 (a x-1)^4 (a x+1) \sqrt{1-a^2 x^2}}","\frac{(a x+1)^3}{9 a c^4 \left(1-a^2 x^2\right)^{9/2}}-\frac{22 (a x+1)^2}{21 a c^4 \left(1-a^2 x^2\right)^{7/2}}+\frac{478 (a x+1)}{105 a c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{\sqrt{1-a^2 x^2}}{a c^4}+\frac{4 (431 a x+630)}{315 a c^4 \sqrt{1-a^2 x^2}}-\frac{2 (829 a x+1155)}{315 a c^4 \left(1-a^2 x^2\right)^{3/2}}-\frac{3 \sin ^{-1}(a x)}{a c^4}",1,"(1664 - 4047*a*x - 339*a^2*x^2 + 7399*a^3*x^3 - 4029*a^4*x^4 - 2967*a^5*x^5 + 2669*a^6*x^6 - 315*a^7*x^7 - 945*(-1 + a*x)^4*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(315*a*c^4*(-1 + a*x)^4*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
653,1,116,116,0.0388614,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^5 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^5,x]","\frac{c^5}{9 a^{10} x^9}+\frac{c^5}{2 a^9 x^8}+\frac{3 c^5}{7 a^8 x^7}-\frac{4 c^5}{3 a^7 x^6}-\frac{14 c^5}{5 a^6 x^5}+\frac{14 c^5}{3 a^4 x^3}+\frac{4 c^5}{a^3 x^2}-\frac{3 c^5}{a^2 x}+\frac{4 c^5 \log (x)}{a}+c^5 x","\frac{c^5}{9 a^{10} x^9}+\frac{c^5}{2 a^9 x^8}+\frac{3 c^5}{7 a^8 x^7}-\frac{4 c^5}{3 a^7 x^6}-\frac{14 c^5}{5 a^6 x^5}+\frac{14 c^5}{3 a^4 x^3}+\frac{4 c^5}{a^3 x^2}-\frac{3 c^5}{a^2 x}+\frac{4 c^5 \log (x)}{a}+c^5 x",1,"c^5/(9*a^10*x^9) + c^5/(2*a^9*x^8) + (3*c^5)/(7*a^8*x^7) - (4*c^5)/(3*a^7*x^6) - (14*c^5)/(5*a^6*x^5) + (14*c^5)/(3*a^4*x^3) + (4*c^5)/(a^3*x^2) - (3*c^5)/(a^2*x) + c^5*x + (4*c^5*Log[x])/a","A",1
654,1,100,100,0.0280832,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^4,x]","-\frac{c^4}{7 a^8 x^7}-\frac{2 c^4}{3 a^7 x^6}-\frac{4 c^4}{5 a^6 x^5}+\frac{c^4}{a^5 x^4}+\frac{10 c^4}{3 a^4 x^3}+\frac{2 c^4}{a^3 x^2}-\frac{4 c^4}{a^2 x}+\frac{4 c^4 \log (x)}{a}+c^4 x","-\frac{c^4}{7 a^8 x^7}-\frac{2 c^4}{3 a^7 x^6}-\frac{4 c^4}{5 a^6 x^5}+\frac{c^4}{a^5 x^4}+\frac{10 c^4}{3 a^4 x^3}+\frac{2 c^4}{a^3 x^2}-\frac{4 c^4}{a^2 x}+\frac{4 c^4 \log (x)}{a}+c^4 x",1,"-1/7*c^4/(a^8*x^7) - (2*c^4)/(3*a^7*x^6) - (4*c^4)/(5*a^6*x^5) + c^4/(a^5*x^4) + (10*c^4)/(3*a^4*x^3) + (2*c^4)/(a^3*x^2) - (4*c^4)/(a^2*x) + c^4*x + (4*c^4*Log[x])/a","A",1
655,1,63,63,0.0214127,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^3,x]","\frac{c^3}{5 a^6 x^5}+\frac{c^3}{a^5 x^4}+\frac{5 c^3}{3 a^4 x^3}-\frac{5 c^3}{a^2 x}+\frac{4 c^3 \log (x)}{a}+c^3 x","\frac{c^3}{5 a^6 x^5}+\frac{c^3}{a^5 x^4}+\frac{5 c^3}{3 a^4 x^3}-\frac{5 c^3}{a^2 x}+\frac{4 c^3 \log (x)}{a}+c^3 x",1,"c^3/(5*a^6*x^5) + c^3/(a^5*x^4) + (5*c^3)/(3*a^4*x^3) - (5*c^3)/(a^2*x) + c^3*x + (4*c^3*Log[x])/a","A",1
656,1,51,51,0.0180973,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{c^2}{3 a^4 x^3}-\frac{2 c^2}{a^3 x^2}-\frac{6 c^2}{a^2 x}+\frac{4 c^2 \log (x)}{a}+c^2 x","-\frac{c^2}{3 a^4 x^3}-\frac{2 c^2}{a^3 x^2}-\frac{6 c^2}{a^2 x}+\frac{4 c^2 \log (x)}{a}+c^2 x",1,"-1/3*c^2/(a^4*x^3) - (2*c^2)/(a^3*x^2) - (6*c^2)/(a^2*x) + c^2*x + (4*c^2*Log[x])/a","A",1
657,1,33,33,0.0190696,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2)),x]","\frac{c}{a^2 x}-\frac{4 c \log (x)}{a}+\frac{8 c \log (1-a x)}{a}+c x","\frac{c}{a^2 x}-\frac{4 c \log (x)}{a}+\frac{8 c \log (1-a x)}{a}+c x",1,"c/(a^2*x) + c*x - (4*c*Log[x])/a + (8*c*Log[1 - a*x])/a","A",1
658,1,53,53,0.0319308,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2)),x]","\frac{5}{a c (1-a x)}-\frac{1}{a c (1-a x)^2}+\frac{4 \log (1-a x)}{a c}+\frac{x}{c}","\frac{5}{a c (1-a x)}-\frac{1}{a c (1-a x)^2}+\frac{4 \log (1-a x)}{a c}+\frac{x}{c}",1,"x/c - 1/(a*c*(1 - a*x)^2) + 5/(a*c*(1 - a*x)) + (4*Log[1 - a*x])/(a*c)","A",1
659,1,63,71,0.0374283,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","\frac{3 a^4 x^4-9 a^3 x^3-9 a^2 x^2+27 a x+12 (a x-1)^3 \log (1-a x)-13}{3 a c^2 (a x-1)^3}","\frac{6}{a c^2 (1-a x)}-\frac{2}{a c^2 (1-a x)^2}+\frac{1}{3 a c^2 (1-a x)^3}+\frac{4 \log (1-a x)}{a c^2}+\frac{x}{c^2}",1,"(-13 + 27*a*x - 9*a^2*x^2 - 9*a^3*x^3 + 3*a^4*x^4 + 12*(-1 + a*x)^3*Log[1 - a*x])/(3*a*c^2*(-1 + a*x)^3)","A",1
660,1,89,111,0.0633325,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2))^3,x]","\frac{2 \left(48 a^5 x^5-192 a^4 x^4-45 a^3 x^3+660 a^2 x^2-701 a x+224\right)+387 (a x-1)^4 \log (1-a x)-3 (a x-1)^4 \log (a x+1)}{96 a c^3 (a x-1)^4}","\frac{111}{16 a c^3 (1-a x)}-\frac{49}{16 a c^3 (1-a x)^2}+\frac{11}{12 a c^3 (1-a x)^3}-\frac{1}{8 a c^3 (1-a x)^4}+\frac{129 \log (1-a x)}{32 a c^3}-\frac{\log (a x+1)}{32 a c^3}+\frac{x}{c^3}",1,"(2*(224 - 701*a*x + 660*a^2*x^2 - 45*a^3*x^3 - 192*a^4*x^4 + 48*a^5*x^5) + 387*(-1 + a*x)^4*Log[1 - a*x] - 3*(-1 + a*x)^4*Log[1 + a*x])/(96*a*c^3*(-1 + a*x)^4)","A",1
661,1,98,146,0.0991516,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2))^4,x]","\frac{\frac{2 \left(480 a^7 x^7-1920 a^6 x^6-1365 a^5 x^5+9300 a^4 x^4-6800 a^3 x^3-4900 a^2 x^2+7541 a x-2384\right)}{(a x-1)^5 (a x+1)}+3915 \log (1-a x)-75 \log (a x+1)}{960 a c^4}","\frac{501}{64 a c^4 (1-a x)}-\frac{1}{64 a c^4 (a x+1)}-\frac{67}{16 a c^4 (1-a x)^2}+\frac{83}{48 a c^4 (1-a x)^3}-\frac{7}{16 a c^4 (1-a x)^4}+\frac{1}{20 a c^4 (1-a x)^5}+\frac{261 \log (1-a x)}{64 a c^4}-\frac{5 \log (a x+1)}{64 a c^4}+\frac{x}{c^4}",1,"((2*(-2384 + 7541*a*x - 4900*a^2*x^2 - 6800*a^3*x^3 + 9300*a^4*x^4 - 1365*a^5*x^5 - 1920*a^6*x^6 + 480*a^7*x^7))/((-1 + a*x)^5*(1 + a*x)) + 3915*Log[1 - a*x] - 75*Log[1 + a*x])/(960*a*c^4)","A",1
662,1,70,169,0.0287723,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[(c - c/(a^2*x^2))^4/E^ArcTanh[a*x],x]","\frac{c^4 \left(7 a^7 \left(1-a^2 x^2\right)^{9/2} \, _2F_1\left(4,\frac{9}{2};\frac{11}{2};1-a^2 x^2\right)-\frac{9 \, _2F_1\left(-\frac{7}{2},-\frac{7}{2};-\frac{5}{2};a^2 x^2\right)}{x^7}\right)}{63 a^8}","\frac{c^4 (35 a x+16) \sqrt{1-a^2 x^2}}{16 a^2 x}-\frac{35 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{16 a}-\frac{c^4 (6-7 a x) \left(1-a^2 x^2\right)^{7/2}}{42 a^8 x^7}+\frac{c^4 (24-35 a x) \left(1-a^2 x^2\right)^{5/2}}{120 a^6 x^5}-\frac{c^4 (16-35 a x) \left(1-a^2 x^2\right)^{3/2}}{48 a^4 x^3}+\frac{c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*((-9*Hypergeometric2F1[-7/2, -7/2, -5/2, a^2*x^2])/x^7 + 7*a^7*(1 - a^2*x^2)^(9/2)*Hypergeometric2F1[4, 9/2, 11/2, 1 - a^2*x^2]))/(63*a^8)","C",0
663,1,70,136,0.0260972,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[(c - c/(a^2*x^2))^3/E^ArcTanh[a*x],x]","\frac{c^3 \left(\frac{7 \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};a^2 x^2\right)}{x^5}-5 a^5 \left(1-a^2 x^2\right)^{7/2} \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};1-a^2 x^2\right)\right)}{35 a^6}","\frac{c^3 (15 a x+8) \sqrt{1-a^2 x^2}}{8 a^2 x}-\frac{15 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{8 a}+\frac{c^3 (4-5 a x) \left(1-a^2 x^2\right)^{5/2}}{20 a^6 x^5}-\frac{c^3 (8-15 a x) \left(1-a^2 x^2\right)^{3/2}}{24 a^4 x^3}+\frac{c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*((7*Hypergeometric2F1[-5/2, -5/2, -3/2, a^2*x^2])/x^5 - 5*a^5*(1 - a^2*x^2)^(7/2)*Hypergeometric2F1[3, 7/2, 9/2, 1 - a^2*x^2]))/(35*a^6)","C",0
664,1,70,103,0.0266587,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[(c - c/(a^2*x^2))^2/E^ArcTanh[a*x],x]","\frac{c^2 \left(3 a^3 \left(1-a^2 x^2\right)^{5/2} \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};1-a^2 x^2\right)-\frac{5 \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};a^2 x^2\right)}{x^3}\right)}{15 a^4}","\frac{c^2 (3 a x+2) \sqrt{1-a^2 x^2}}{2 a^2 x}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^2 (2-3 a x) \left(1-a^2 x^2\right)^{3/2}}{6 a^4 x^3}+\frac{c^2 \sin ^{-1}(a x)}{a}",1,"(c^2*((-5*Hypergeometric2F1[-3/2, -3/2, -1/2, a^2*x^2])/x^3 + 3*a^3*(1 - a^2*x^2)^(5/2)*Hypergeometric2F1[2, 5/2, 7/2, 1 - a^2*x^2]))/(15*a^4)","C",0
665,1,55,58,0.0397132,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[(c - c/(a^2*x^2))/E^ArcTanh[a*x],x]","\frac{c \left(\sqrt{1-a^2 x^2} (a x+1)-a x \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a x \sin ^{-1}(a x)\right)}{a^2 x}","\frac{c \sqrt{1-a^2 x^2} (a x+1)}{a^2 x}-\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}+\frac{c \sin ^{-1}(a x)}{a}",1,"(c*((1 + a*x)*Sqrt[1 - a^2*x^2] + a*x*ArcSin[a*x] - a*x*ArcTanh[Sqrt[1 - a^2*x^2]]))/(a^2*x)","A",1
666,1,54,60,0.0294792,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))),x]","\frac{-a^2 x^2+\sqrt{1-a^2 x^2} \sin ^{-1}(a x)-a x+2}{a c \sqrt{1-a^2 x^2}}","\frac{1-a x}{a c \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2}}{a c}+\frac{\sin ^{-1}(a x)}{a c}",1,"(2 - a*x - a^2*x^2 + Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(a*c*Sqrt[1 - a^2*x^2])","A",1
667,1,78,97,0.0532945,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^2),x]","\frac{-3 a^3 x^3-7 a^2 x^2+3 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+5 a x+8}{3 a c^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{x (3-4 a x)}{3 c^2 \sqrt{1-a^2 x^2}}+\frac{8 \sqrt{1-a^2 x^2}}{3 a c^2}+\frac{a^2 x^3 (1-a x)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{\sin ^{-1}(a x)}{a c^2}",1,"(8 + 5*a*x - 7*a^2*x^2 - 3*a^3*x^3 + 3*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a*c^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
668,1,108,130,0.0781177,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^3),x]","\frac{-15 a^5 x^5-38 a^4 x^4+52 a^3 x^3+87 a^2 x^2+15 (a x-1) (a x+1)^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-33 a x-48}{15 a c^3 (a x-1) (a x+1)^2 \sqrt{1-a^2 x^2}}","-\frac{x (5-8 a x)}{5 c^3 \sqrt{1-a^2 x^2}}+\frac{16 \sqrt{1-a^2 x^2}}{5 a c^3}+\frac{a^2 x^3 (5-6 a x)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{a^4 x^5 (1-a x)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{\sin ^{-1}(a x)}{a c^3}",1,"(-48 - 33*a*x + 87*a^2*x^2 + 52*a^3*x^3 - 38*a^4*x^4 - 15*a^5*x^5 + 15*(-1 + a*x)*(1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(15*a*c^3*(-1 + a*x)*(1 + a*x)^2*Sqrt[1 - a^2*x^2])","A",1
669,1,126,163,0.0981753,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^4),x]","\frac{-105 a^7 x^7-281 a^6 x^6+559 a^5 x^5+965 a^4 x^4-715 a^3 x^3-1065 a^2 x^2+105 (a x-1)^2 (a x+1)^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+279 a x+384}{105 a c^4 (a x-1)^2 (a x+1)^3 \sqrt{1-a^2 x^2}}","-\frac{x (35-64 a x)}{35 c^4 \sqrt{1-a^2 x^2}}+\frac{128 \sqrt{1-a^2 x^2}}{35 a c^4}+\frac{a^2 x^3 (35-48 a x)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{a^6 x^7 (1-a x)}{7 c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^4 x^5 (7-8 a x)}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{\sin ^{-1}(a x)}{a c^4}",1,"(384 + 279*a*x - 1065*a^2*x^2 - 715*a^3*x^3 + 965*a^4*x^4 + 559*a^5*x^5 - 281*a^6*x^6 - 105*a^7*x^7 + 105*(-1 + a*x)^2*(1 + a*x)^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(105*a*c^4*(-1 + a*x)^2*(1 + a*x)^3*Sqrt[1 - a^2*x^2])","A",1
670,1,91,91,0.0273879,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[(c - c/(a^2*x^2))^4/E^(2*ArcTanh[a*x]),x]","-\frac{c^4}{7 a^8 x^7}+\frac{c^4}{3 a^7 x^6}+\frac{2 c^4}{5 a^6 x^5}-\frac{3 c^4}{2 a^5 x^4}+\frac{3 c^4}{a^3 x^2}-\frac{2 c^4}{a^2 x}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)","-\frac{c^4}{7 a^8 x^7}+\frac{c^4}{3 a^7 x^6}+\frac{2 c^4}{5 a^6 x^5}-\frac{3 c^4}{2 a^5 x^4}+\frac{3 c^4}{a^3 x^2}-\frac{2 c^4}{a^2 x}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)",1,"-1/7*c^4/(a^8*x^7) + c^4/(3*a^7*x^6) + (2*c^4)/(5*a^6*x^5) - (3*c^4)/(2*a^5*x^4) + (3*c^4)/(a^3*x^2) - (2*c^4)/(a^2*x) - c^4*x + (2*c^4*Log[x])/a","A",1
671,1,78,78,0.0212096,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[(c - c/(a^2*x^2))^3/E^(2*ArcTanh[a*x]),x]","\frac{c^3}{5 a^6 x^5}-\frac{c^3}{2 a^5 x^4}-\frac{c^3}{3 a^4 x^3}+\frac{2 c^3}{a^3 x^2}-\frac{c^3}{a^2 x}+\frac{2 c^3 \log (x)}{a}+c^3 (-x)","\frac{c^3}{5 a^6 x^5}-\frac{c^3}{2 a^5 x^4}-\frac{c^3}{3 a^4 x^3}+\frac{2 c^3}{a^3 x^2}-\frac{c^3}{a^2 x}+\frac{2 c^3 \log (x)}{a}+c^3 (-x)",1,"c^3/(5*a^6*x^5) - c^3/(2*a^5*x^4) - c^3/(3*a^4*x^3) + (2*c^3)/(a^3*x^2) - c^3/(a^2*x) - c^3*x + (2*c^3*Log[x])/a","A",1
672,1,40,40,0.0157402,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[(c - c/(a^2*x^2))^2/E^(2*ArcTanh[a*x]),x]","-\frac{c^2}{3 a^4 x^3}+\frac{c^2}{a^3 x^2}+\frac{2 c^2 \log (x)}{a}+c^2 (-x)","-\frac{c^2}{3 a^4 x^3}+\frac{c^2}{a^3 x^2}+\frac{2 c^2 \log (x)}{a}+c^2 (-x)",1,"-1/3*c^2/(a^4*x^3) + c^2/(a^3*x^2) - c^2*x + (2*c^2*Log[x])/a","A",1
673,1,21,21,0.0114248,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[(c - c/(a^2*x^2))/E^(2*ArcTanh[a*x]),x]","\frac{c}{a^2 x}+\frac{2 c \log (x)}{a}+c (-x)","\frac{c}{a^2 x}+\frac{2 c \log (x)}{a}+c (-x)",1,"c/(a^2*x) - c*x + (2*c*Log[x])/a","A",1
674,1,28,35,0.0280374,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))),x]","\frac{\frac{1}{a^2 x+a}+\frac{2 \log (a x+1)}{a}-x}{c}","\frac{1}{a c (a x+1)}+\frac{2 \log (a x+1)}{a c}-\frac{x}{c}",1,"(-x + (a + a^2*x)^(-1) + (2*Log[1 + a*x])/a)/c","A",1
675,1,68,74,0.0441784,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^2),x]","\frac{-8 a^3 x^3-16 a^2 x^2+6 a x-(a x+1)^2 \log (1-a x)+17 (a x+1)^2 \log (a x+1)+12}{8 a (a c x+c)^2}","\frac{7}{4 a c^2 (a x+1)}-\frac{1}{4 a c^2 (a x+1)^2}-\frac{\log (1-a x)}{8 a c^2}+\frac{17 \log (a x+1)}{8 a c^2}-\frac{x}{c^2}",1,"(12 + 6*a*x - 16*a^2*x^2 - 8*a^3*x^3 - (1 + a*x)^2*Log[1 - a*x] + 17*(1 + a*x)^2*Log[1 + a*x])/(8*a*(c + a*c*x)^2)","A",1
676,1,104,109,0.0638256,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^3),x]","\frac{-2 \left(6 a^5 x^5+12 a^4 x^4-15 a^3 x^3-24 a^2 x^2+7 a x+11\right)-3 (a x-1) (a x+1)^3 \log (1-a x)+27 (a x-1) (a x+1)^3 \log (a x+1)}{12 a (a x-1) (a c x+c)^3}","-\frac{1}{16 a c^3 (1-a x)}+\frac{39}{16 a c^3 (a x+1)}-\frac{5}{8 a c^3 (a x+1)^2}+\frac{1}{12 a c^3 (a x+1)^3}-\frac{\log (1-a x)}{4 a c^3}+\frac{9 \log (a x+1)}{4 a c^3}-\frac{x}{c^3}",1,"(-2*(11 + 7*a*x - 24*a^2*x^2 - 15*a^3*x^3 + 12*a^4*x^4 + 6*a^5*x^5) - 3*(-1 + a*x)*(1 + a*x)^3*Log[1 - a*x] + 27*(-1 + a*x)*(1 + a*x)^3*Log[1 + a*x])/(12*a*(-1 + a*x)*(c + a*c*x)^3)","A",1
677,1,121,144,0.093872,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^4),x]","\frac{-384 a^7 x^7-768 a^6 x^6+1638 a^5 x^5+2508 a^4 x^4-1732 a^3 x^3-2516 a^2 x^2+550 a x-141 (a x-1)^2 (a x+1)^4 \log (1-a x)+909 (a x-1)^2 (a x+1)^4 \log (a x+1)+800}{384 a (a x-1)^2 (a c x+c)^4}","-\frac{11}{64 a c^4 (1-a x)}+\frac{99}{32 a c^4 (a x+1)}+\frac{1}{64 a c^4 (1-a x)^2}-\frac{35}{32 a c^4 (a x+1)^2}+\frac{13}{48 a c^4 (a x+1)^3}-\frac{1}{32 a c^4 (a x+1)^4}-\frac{47 \log (1-a x)}{128 a c^4}+\frac{303 \log (a x+1)}{128 a c^4}-\frac{x}{c^4}",1,"(800 + 550*a*x - 2516*a^2*x^2 - 1732*a^3*x^3 + 2508*a^4*x^4 + 1638*a^5*x^5 - 768*a^6*x^6 - 384*a^7*x^7 - 141*(-1 + a*x)^2*(1 + a*x)^4*Log[1 - a*x] + 909*(-1 + a*x)^2*(1 + a*x)^4*Log[1 + a*x])/(384*a*(-1 + a*x)^2*(c + a*c*x)^4)","A",1
678,1,191,191,0.1816398,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Integrate[(c - c/(a^2*x^2))^4/E^(3*ArcTanh[a*x]),x]","\frac{c^4 \left(\frac{5 \left(-16 a^8 x^8-231 a^7 x^7+64 a^6 x^6+413 a^5 x^5-96 a^4 x^4-238 a^3 x^3+64 a^2 x^2+16 a^7 x^7 \left(a^2 x^2-1\right)^4 \, _2F_1\left(3,\frac{7}{2};\frac{9}{2};1-a^2 x^2\right)-105 a^7 x^7 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+56 a x-16\right)}{\sqrt{1-a^2 x^2}}-336 a^2 x^2 \, _2F_1\left(-\frac{5}{2},-\frac{5}{2};-\frac{3}{2};a^2 x^2\right)\right)}{560 a^8 x^7}","-\frac{3 c^4 (5 a x+16) \sqrt{1-a^2 x^2}}{16 a^2 x}+\frac{15 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{16 a}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{7 a^8 x^7}+\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{2 a^7 x^6}-\frac{c^4 (24-5 a x) \left(1-a^2 x^2\right)^{5/2}}{40 a^6 x^5}+\frac{c^4 (16-5 a x) \left(1-a^2 x^2\right)^{3/2}}{16 a^4 x^3}-\frac{3 c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*(-336*a^2*x^2*Hypergeometric2F1[-5/2, -5/2, -3/2, a^2*x^2] + (5*(-16 + 56*a*x + 64*a^2*x^2 - 238*a^3*x^3 - 96*a^4*x^4 + 413*a^5*x^5 + 64*a^6*x^6 - 231*a^7*x^7 - 16*a^8*x^8 - 105*a^7*x^7*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]] + 16*a^7*x^7*(-1 + a^2*x^2)^4*Hypergeometric2F1[3, 7/2, 9/2, 1 - a^2*x^2]))/Sqrt[1 - a^2*x^2]))/(560*a^8*x^7)","C",0
679,1,186,157,0.1042612,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Integrate[(c - c/(a^2*x^2))^3/E^(3*ArcTanh[a*x]),x]","\frac{c^3 \left(-8 a^6 x^6-75 a^5 x^5+24 a^4 x^4+105 a^3 x^3+40 a^2 x^2 \sqrt{1-a^2 x^2} \, _2F_1\left(-\frac{3}{2},-\frac{3}{2};-\frac{1}{2};a^2 x^2\right)-24 a^2 x^2+8 a^5 x^5 \left(a^2 x^2-1\right)^3 \, _2F_1\left(2,\frac{5}{2};\frac{7}{2};1-a^2 x^2\right)-45 a^5 x^5 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-30 a x+8\right)}{40 a^6 x^5 \sqrt{1-a^2 x^2}}","-\frac{3 c^3 (a x+8) \sqrt{1-a^2 x^2}}{8 a^2 x}+\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{8 a}+\frac{c^3 \left(1-a^2 x^2\right)^{5/2}}{5 a^6 x^5}-\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{4 a^5 x^4}+\frac{c^3 (8-a x) \left(1-a^2 x^2\right)^{3/2}}{8 a^4 x^3}-\frac{3 c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*(8 - 30*a*x - 24*a^2*x^2 + 105*a^3*x^3 + 24*a^4*x^4 - 75*a^5*x^5 - 8*a^6*x^6 - 45*a^5*x^5*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]] + 40*a^2*x^2*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[-3/2, -3/2, -1/2, a^2*x^2] + 8*a^5*x^5*(-1 + a^2*x^2)^3*Hypergeometric2F1[2, 5/2, 7/2, 1 - a^2*x^2]))/(40*a^6*x^5*Sqrt[1 - a^2*x^2])","C",0
680,1,128,125,0.084025,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[(c - c/(a^2*x^2))^2/E^(3*ArcTanh[a*x]),x]","-\frac{c^2 \left(-6 a^5 x^5-16 a^4 x^4+15 a^3 x^3+14 a^2 x^2+18 a^3 x^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+3 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-9 a x+2\right)}{6 a^4 x^3 \sqrt{1-a^2 x^2}}","-\frac{c^2 (6-a x) \sqrt{1-a^2 x^2}}{2 a^2 x}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}+\frac{3 c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{3 c^2 \sin ^{-1}(a x)}{a}",1,"-1/6*(c^2*(2 - 9*a*x + 14*a^2*x^2 + 15*a^3*x^3 - 16*a^4*x^4 - 6*a^5*x^5 + 18*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x] + 3*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]]))/(a^4*x^3*Sqrt[1 - a^2*x^2])","A",1
681,1,57,74,0.0643276,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[(c - c/(a^2*x^2))/E^(3*ArcTanh[a*x]),x]","-\frac{c \left(\sqrt{1-a^2 x^2} (a x-1)+3 a x \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+3 a x \sin ^{-1}(a x)\right)}{a^2 x}","-\frac{c \sqrt{1-a^2 x^2}}{a}+\frac{c \sqrt{1-a^2 x^2}}{a^2 x}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{a}-\frac{3 c \sin ^{-1}(a x)}{a}",1,"-((c*((-1 + a*x)*Sqrt[1 - a^2*x^2] + 3*a*x*ArcSin[a*x] + 3*a*x*ArcTanh[Sqrt[1 - a^2*x^2]]))/(a^2*x))","A",1
682,1,78,97,0.0825904,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))),x]","\frac{3 a^3 x^3+16 a^2 x^2-9 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-5 a x-14}{3 a c (a x+1) \sqrt{1-a^2 x^2}}","\frac{(1-a x)^3}{3 a c \left(1-a^2 x^2\right)^{3/2}}-\frac{2 (1-a x)^2}{a c \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{1-a^2 x^2}}{a c}-\frac{3 \sin ^{-1}(a x)}{a c}",1,"(-14 - 5*a*x + 16*a^2*x^2 + 3*a^3*x^3 - 9*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a*c*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
683,1,86,129,0.1060567,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^2),x]","\frac{5 a^4 x^4+34 a^3 x^3+18 a^2 x^2-15 (a x+1)^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-33 a x-24}{5 a \sqrt{1-a^2 x^2} (a c x+c)^2}","-\frac{(1-a x)^3}{5 a c^2 \left(1-a^2 x^2\right)^{5/2}}+\frac{6 (1-a x)^2}{5 a c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{24 (1-a x)}{5 a c^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{1-a^2 x^2}}{a c^2}-\frac{3 \sin ^{-1}(a x)}{a c^2}",1,"(-24 - 33*a*x + 18*a^2*x^2 + 34*a^3*x^3 + 5*a^4*x^4 - 15*(1 + a*x)^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(5*a*(c + a*c*x)^2*Sqrt[1 - a^2*x^2])","A",1
684,1,94,159,0.1293391,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^3),x]","\frac{35 a^5 x^5+286 a^4 x^4+368 a^3 x^3-125 a^2 x^2-105 (a x+1)^3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-423 a x-176}{35 a \sqrt{1-a^2 x^2} (a c x+c)^3}","\frac{(1-a x)^3}{7 a c^3 \left(1-a^2 x^2\right)^{7/2}}-\frac{38 (1-a x)^2}{35 a c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{137 (1-a x)}{35 a c^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{\sqrt{1-a^2 x^2}}{a c^3}-\frac{245-181 a x}{35 a c^3 \sqrt{1-a^2 x^2}}-\frac{3 \sin ^{-1}(a x)}{a c^3}",1,"(-176 - 423*a*x - 125*a^2*x^2 + 368*a^3*x^3 + 286*a^4*x^4 + 35*a^5*x^5 - 105*(1 + a*x)^3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(35*a*(c + a*c*x)^3*Sqrt[1 - a^2*x^2])","A",1
685,1,122,189,0.1568198,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^4),x]","\frac{315 a^7 x^7+2669 a^6 x^6+2967 a^5 x^5-4029 a^4 x^4-7399 a^3 x^3-339 a^2 x^2-945 (a x-1) (a x+1)^4 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+4047 a x+1664}{315 a (a x-1) \sqrt{1-a^2 x^2} (a c x+c)^4}","-\frac{(1-a x)^3}{9 a c^4 \left(1-a^2 x^2\right)^{9/2}}+\frac{22 (1-a x)^2}{21 a c^4 \left(1-a^2 x^2\right)^{7/2}}-\frac{478 (1-a x)}{105 a c^4 \left(1-a^2 x^2\right)^{5/2}}-\frac{\sqrt{1-a^2 x^2}}{a c^4}-\frac{4 (630-431 a x)}{315 a c^4 \sqrt{1-a^2 x^2}}+\frac{2 (1155-829 a x)}{315 a c^4 \left(1-a^2 x^2\right)^{3/2}}-\frac{3 \sin ^{-1}(a x)}{a c^4}",1,"(1664 + 4047*a*x - 339*a^2*x^2 - 7399*a^3*x^3 - 4029*a^4*x^4 + 2967*a^5*x^5 + 2669*a^6*x^6 + 315*a^7*x^7 - 945*(-1 + a*x)*(1 + a*x)^4*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(315*a*(-1 + a*x)*(c + a*c*x)^4*Sqrt[1 - a^2*x^2])","A",1
686,1,114,374,0.1041228,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(9/2),x]","\frac{x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \left(a^9 x+a^8 \log (x)+\frac{4 a^7}{x}+\frac{2 a^6}{x^2}-\frac{2 a^5}{x^3}-\frac{3 a^4}{2 x^4}+\frac{4 a^3}{5 x^5}+\frac{2 a^2}{3 x^6}-\frac{a}{7 x^7}-\frac{1}{8 x^8}\right)}{\left(1-a^2 x^2\right)^{9/2}}","-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{7 \left(1-a^2 x^2\right)^{9/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{8 \left(1-a^2 x^2\right)^{9/2}}+\frac{2 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{3 \left(1-a^2 x^2\right)^{9/2}}+\frac{a^9 x^{10} \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{a^8 x^9 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{4 a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{2 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{2 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{3 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{2 \left(1-a^2 x^2\right)^{9/2}}+\frac{4 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{5 \left(1-a^2 x^2\right)^{9/2}}",1,"((c - c/(a^2*x^2))^(9/2)*x^9*(-1/8*1/x^8 - a/(7*x^7) + (2*a^2)/(3*x^6) + (4*a^3)/(5*x^5) - (3*a^4)/(2*x^4) - (2*a^5)/x^3 + (2*a^6)/x^2 + (4*a^7)/x + a^9*x + a^8*Log[x]))/(1 - a^2*x^2)^(9/2)","A",1
687,1,98,299,0.0595582,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(7/2),x]","\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}} \left(60 a^7 x^7+60 a^6 x^6 \log (x)+180 a^5 x^5+90 a^4 x^4-60 a^3 x^3-45 a^2 x^2+12 a x+10\right)}{60 a^6 x^5 \sqrt{1-a^2 x^2}}","-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{5 \left(1-a^2 x^2\right)^{7/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{6 \left(1-a^2 x^2\right)^{7/2}}+\frac{3 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{4 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}-\frac{a^6 x^7 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}-\frac{3 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}-\frac{3 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{2 \left(1-a^2 x^2\right)^{7/2}}+\frac{a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}",1,"(c^3*Sqrt[c - c/(a^2*x^2)]*(10 + 12*a*x - 45*a^2*x^2 - 60*a^3*x^3 + 90*a^4*x^4 + 180*a^5*x^5 + 60*a^7*x^7 + 60*a^6*x^6*Log[x]))/(60*a^6*x^5*Sqrt[1 - a^2*x^2])","A",1
688,1,82,219,0.0474304,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(5/2),x]","\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}} \left(12 a^5 x^5+12 a^4 x^4 \log (x)+24 a^3 x^3+12 a^2 x^2-4 a x-3\right)}{12 a^4 x^3 \sqrt{1-a^2 x^2}}","-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{3 \left(1-a^2 x^2\right)^{5/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{4 \left(1-a^2 x^2\right)^{5/2}}+\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}+\frac{a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}+\frac{a^4 x^5 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}+\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}",1,"(c^2*Sqrt[c - c/(a^2*x^2)]*(-3 - 4*a*x + 12*a^2*x^2 + 24*a^3*x^3 + 12*a^5*x^5 + 12*a^4*x^4*Log[x]))/(12*a^4*x^3*Sqrt[1 - a^2*x^2])","A",1
689,1,72,146,0.0355516,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(3/2),x]","\frac{c \sqrt{c-\frac{c}{a^2 x^2}} \left(2 a^3 x^3+3 a^2 x^2+2 a^2 x^2 \log (x)+2 a x+1\right)}{2 a^2 x \sqrt{1-a^2 x^2}}","-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 \left(1-a^2 x^2\right)^{3/2}}-\frac{a^2 x^3 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}-\frac{a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}",1,"(c*Sqrt[c - c/(a^2*x^2)]*(1 + 2*a*x + 3*a^2*x^2 + 2*a^3*x^3 + 2*a^2*x^2*Log[x]))/(2*a^2*x*Sqrt[1 - a^2*x^2])","A",0
690,1,37,68,0.0223877,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (a x+\log (x))}{\sqrt{1-a^2 x^2}}","\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(a*x + Log[x]))/Sqrt[1 - a^2*x^2]","A",1
691,1,48,79,0.0298766,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[E^ArcTanh[a*x]/Sqrt[c - c/(a^2*x^2)],x]","-\frac{\sqrt{1-a^2 x^2} (a x+\log (1-a x))}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}","-\frac{\sqrt{1-a^2 x^2}}{a \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"-((Sqrt[1 - a^2*x^2]*(a*x + Log[1 - a*x]))/(a^2*Sqrt[c - c/(a^2*x^2)]*x))","A",1
692,1,91,175,0.0539813,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^(3/2),x]","-\frac{\sqrt{1-a^2 x^2} \left(a^2 x^2-1\right) \left(\frac{1}{2 a^4 (1-a x)}+\frac{5 \log (1-a x)}{4 a^4}-\frac{\log (a x+1)}{4 a^4}+\frac{x}{a^3}\right)}{x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{2 a^4 x^3 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{5 \left(1-a^2 x^2\right)^{3/2} \log (1-a x)}{4 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{\left(1-a^2 x^2\right)^{3/2} \log (a x+1)}{4 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{\left(1-a^2 x^2\right)^{3/2}}{a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"-((Sqrt[1 - a^2*x^2]*(-1 + a^2*x^2)*(x/a^3 + 1/(2*a^4*(1 - a*x)) + (5*Log[1 - a*x])/(4*a^4) - Log[1 + a*x]/(4*a^4)))/((c - c/(a^2*x^2))^(3/2)*x^3))","A",1
693,1,87,267,0.1354691,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^(5/2),x]","\frac{\left(1-a^2 x^2\right)^{5/2} \left(2 \left(-8 a x+\frac{8}{a x-1}+\frac{1}{a x+1}+\frac{1}{(a x-1)^2}\right)-23 \log (1-a x)+7 \log (a x+1)\right)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}","-\frac{\left(1-a^2 x^2\right)^{5/2}}{a^6 x^5 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (1-a x)^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{23 \left(1-a^2 x^2\right)^{5/2} \log (1-a x)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{7 \left(1-a^2 x^2\right)^{5/2} \log (a x+1)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}",1,"((1 - a^2*x^2)^(5/2)*(2*(-8*a*x + (-1 + a*x)^(-2) + 8/(-1 + a*x) + (1 + a*x)^(-1)) - 23*Log[1 - a*x] + 7*Log[1 + a*x]))/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",1
694,1,147,361,0.1216909,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^(7/2),x]","\frac{\sqrt{1-a^2 x^2} \left(-96 a^6 x^6+96 a^5 x^5+366 a^4 x^4-222 a^3 x^3-338 a^2 x^2+122 a x-153 (a x-1)^3 (a x+1)^2 \log (1-a x)+57 (a x-1)^3 (a x+1)^2 \log (a x+1)+88\right)}{96 a^2 c^3 x (a x-1)^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{3 \left(1-a^2 x^2\right)^{7/2}}{2 a^8 x^7 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{5 \left(1-a^2 x^2\right)^{7/2}}{16 a^8 x^7 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{11 \left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (1-a x)^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (a x+1)^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{24 a^8 x^7 (1-a x)^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{51 \left(1-a^2 x^2\right)^{7/2} \log (1-a x)}{32 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{19 \left(1-a^2 x^2\right)^{7/2} \log (a x+1)}{32 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}",1,"(Sqrt[1 - a^2*x^2]*(88 + 122*a*x - 338*a^2*x^2 - 222*a^3*x^3 + 366*a^4*x^4 + 96*a^5*x^5 - 96*a^6*x^6 - 153*(-1 + a*x)^3*(1 + a*x)^2*Log[1 - a*x] + 57*(-1 + a*x)^3*(1 + a*x)^2*Log[1 + a*x]))/(96*a^2*c^3*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^3*(1 + a*x)^2)","A",1
695,1,166,450,0.1961031,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(9/2),x]","-\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}} \left(26880 a^8 x^8 \log \left(\sqrt{a^2 x^2-1}+a x\right)+25725 a^8 x^8 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(13440 a^8 x^8-45056 a^7 x^7+14595 a^6 x^6+31232 a^5 x^5+770 a^4 x^4-16896 a^3 x^3-4760 a^2 x^2+3840 a x+1680\right)\right)}{13440 a^8 x^7 \sqrt{a^2 x^2-1}}","-\frac{a x^2 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{28 (1-a x)^2}-\frac{x (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{8 (1-a x)}+\frac{71 a^2 x^3 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{336 (1-a x)^3}-\frac{501 a^8 x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{128 (1-a x)^4 (a x+1)^4}+\frac{2 a^8 x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \sin ^{-1}(a x)}{(1-a x)^{9/2} (a x+1)^{9/2}}+\frac{245 a^8 x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{128 (1-a x)^{9/2} (a x+1)^{9/2}}+\frac{373 a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{192 (1-a x)^4 (a x+1)^3}+\frac{501 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{640 (1-a x)^4 (a x+1)^2}+\frac{661 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{1680 (1-a x)^4 (a x+1)}+\frac{295 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{1344 (1-a x)^4}-\frac{127 a^3 x^4 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{420 (1-a x)^4}",1,"-1/13440*(c^4*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(1680 + 3840*a*x - 4760*a^2*x^2 - 16896*a^3*x^3 + 770*a^4*x^4 + 31232*a^5*x^5 + 14595*a^6*x^6 - 45056*a^7*x^7 + 13440*a^8*x^8) + 25725*a^8*x^8*ArcTan[1/Sqrt[-1 + a^2*x^2]] + 26880*a^8*x^8*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^8*x^7*Sqrt[-1 + a^2*x^2])","A",0
696,1,150,372,0.160849,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2),x]","-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}} \left(480 a^6 x^6 \log \left(\sqrt{a^2 x^2-1}+a x\right)+375 a^6 x^6 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(240 a^6 x^6-736 a^5 x^5+105 a^4 x^4+352 a^3 x^3+70 a^2 x^2-96 a x-40\right)\right)}{240 a^6 x^5 \sqrt{a^2 x^2-1}}","-\frac{a x^2 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{15 (1-a x)^2}-\frac{x (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{6 (1-a x)}+\frac{13 a^2 x^3 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{40 (1-a x)^3}+\frac{57 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{16 (1-a x)^3 (a x+1)^3}-\frac{2 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \sin ^{-1}(a x)}{(1-a x)^{7/2} (a x+1)^{7/2}}-\frac{25 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{16 (1-a x)^{7/2} (a x+1)^{7/2}}-\frac{41 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{24 (1-a x)^3 (a x+1)^2}-\frac{57 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{80 (1-a x)^3 (a x+1)}-\frac{11 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{30 (1-a x)^3}",1,"-1/240*(c^3*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(-40 - 96*a*x + 70*a^2*x^2 + 352*a^3*x^3 + 105*a^4*x^4 - 736*a^5*x^5 + 240*a^6*x^6) + 375*a^6*x^6*ArcTan[1/Sqrt[-1 + a^2*x^2]] + 480*a^6*x^6*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^6*x^5*Sqrt[-1 + a^2*x^2])","A",0
697,1,134,294,0.1318257,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2),x]","-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}} \left(48 a^4 x^4 \log \left(\sqrt{a^2 x^2-1}+a x\right)+27 a^4 x^4 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(24 a^4 x^4-64 a^3 x^3-3 a^2 x^2+16 a x+6\right)\right)}{24 a^4 x^3 \sqrt{a^2 x^2-1}}","-\frac{a x^2 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{6 (1-a x)^2}-\frac{x (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{4 (1-a x)}+\frac{5 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2}-\frac{25 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 (a x+1)^2}+\frac{2 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \sin ^{-1}(a x)}{(1-a x)^{5/2} (a x+1)^{5/2}}+\frac{9 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{8 (1-a x)^{5/2} (a x+1)^{5/2}}+\frac{17 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{12 (1-a x)^2 (a x+1)}",1,"-1/24*(c^2*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(6 + 16*a*x - 3*a^2*x^2 - 64*a^3*x^3 + 24*a^4*x^4) + 27*a^4*x^4*ArcTan[1/Sqrt[-1 + a^2*x^2]] + 48*a^4*x^4*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^4*x^3*Sqrt[-1 + a^2*x^2])","A",0
698,1,115,214,0.1041512,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2),x]","-\frac{c \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1} \left(2 a^2 x^2-4 a x-1\right)+4 a^2 x^2 \log \left(\sqrt{a^2 x^2-1}+a x\right)+a^2 x^2 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{2 a^2 x \sqrt{a^2 x^2-1}}","-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{1-a x}-\frac{x (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 (1-a x)}+\frac{5 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 (1-a x) (a x+1)}-\frac{2 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \sin ^{-1}(a x)}{(1-a x)^{3/2} (a x+1)^{3/2}}-\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{2 (1-a x)^{3/2} (a x+1)^{3/2}}",1,"-1/2*(c*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(-1 - 4*a*x + 2*a^2*x^2) + a^2*x^2*ArcTan[1/Sqrt[-1 + a^2*x^2]] + 4*a^2*x^2*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^2*x*Sqrt[-1 + a^2*x^2])","A",0
699,1,81,118,0.0848484,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1}+2 \log \left(\sqrt{a^2 x^2-1}+a x\right)-\tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{\sqrt{a^2 x^2-1}}","-x \sqrt{c-\frac{c}{a^2 x^2}}+\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"-((Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[-1 + a^2*x^2] - ArcTan[1/Sqrt[-1 + a^2*x^2]] + 2*Log[a*x + Sqrt[-1 + a^2*x^2]]))/Sqrt[-1 + a^2*x^2])","A",0
700,1,69,110,0.0675115,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[E^(2*ArcTanh[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\frac{-a^2 x^2-2 \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)+2 a x+3}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(a x+1)^2}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 (1-a x) (a x+1)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{2 \sqrt{1-a x} \sqrt{a x+1} \sin ^{-1}(a x)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(3 + 2*a*x - a^2*x^2 - 2*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",0
701,1,95,123,0.083703,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(3/2),x]","\frac{-3 a^3 x^3+11 a^2 x^2-6 (a x-1) \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)+4 a x-10}{3 a^2 c x (a x-1) \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(a x+1)^2}{3 a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{2 (5-2 a x) (1-a x) (a x+1)^2}{3 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{2 (1-a x)^{3/2} (a x+1)^{3/2} \sin ^{-1}(a x)}{a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"(-10 + 4*a*x + 11*a^2*x^2 - 3*a^3*x^3 - 6*(-1 + a*x)*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(3*a^2*c*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x))","A",0
702,1,105,203,0.0988938,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(5/2),x]","\frac{-15 a^4 x^4+76 a^3 x^3-32 a^2 x^2-30 (a x-1)^2 \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)-82 a x+56}{15 a^2 c^2 x (a x-1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(a x+1)^2}{5 a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{2 (a x+1)^2 (43 a x+28) (1-a x)^3}{15 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{2 (a x+1)^{5/2} (1-a x)^{5/2} \sin ^{-1}(a x)}{a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{58 (a x+1)^2 (1-a x)^2}{15 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{2 (a x+1)^2 (1-a x)}{3 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}",1,"(56 - 82*a*x - 32*a^2*x^2 + 76*a^3*x^3 - 15*a^4*x^4 - 30*(-1 + a*x)^2*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(15*a^2*c^2*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^2)","A",0
703,1,133,283,0.1179788,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(7/2),x]","\frac{-105 a^6 x^6+562 a^5 x^5-74 a^4 x^4-1226 a^3 x^3+636 a^2 x^2-210 (a x-1)^3 (a x+1) \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)+654 a x-432}{105 a^2 c^3 x (a x-1)^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(a x+1)^2}{7 a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{2 (a x+1)^3 (107 a x+72) (1-a x)^4}{35 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{2 (a x+1)^{7/2} (1-a x)^{7/2} \sin ^{-1}(a x)}{a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{142 (a x+1)^2 (1-a x)^4}{35 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{782 (a x+1)^2 (1-a x)^3}{105 a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{124 (a x+1)^2 (1-a x)^2}{105 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{2 (a x+1)^2 (1-a x)}{5 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}",1,"(-432 + 654*a*x + 636*a^2*x^2 - 1226*a^3*x^3 - 74*a^4*x^4 + 562*a^5*x^5 - 105*a^6*x^6 - 210*(-1 + a*x)^3*(1 + a*x)*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(105*a^2*c^3*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^3*(1 + a*x))","A",0
704,1,151,363,0.1495733,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{9/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(9/2),x]","\frac{-315 a^8 x^8+1756 a^7 x^7+268 a^6 x^6-5784 a^5 x^5+2060 a^4 x^4+6200 a^3 x^3-3372 a^2 x^2-630 (a x-1)^4 (a x+1)^2 \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)-2186 a x+1408}{315 a^2 c^4 x (a x-1)^4 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(a x+1)^2}{9 a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}+\frac{2 (a x+1)^4 (1019 a x+704) (1-a x)^5}{315 a^{10} x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}-\frac{2 (a x+1)^{9/2} (1-a x)^{9/2} \sin ^{-1}(a x)}{a^{10} x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}+\frac{1334 (a x+1)^3 (1-a x)^5}{315 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}+\frac{2458 (a x+1)^2 (1-a x)^5}{315 a^7 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}+\frac{302 (a x+1)^2 (1-a x)^4}{21 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}-\frac{646 (a x+1)^2 (1-a x)^3}{315 a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}+\frac{214 (a x+1)^2 (1-a x)^2}{315 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}-\frac{2 (a x+1)^2 (1-a x)}{7 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}",1,"(1408 - 2186*a*x - 3372*a^2*x^2 + 6200*a^3*x^3 + 2060*a^4*x^4 - 5784*a^5*x^5 + 268*a^6*x^6 + 1756*a^7*x^7 - 315*a^8*x^8 - 630*(-1 + a*x)^4*(1 + a*x)^2*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(315*a^2*c^4*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^4*(1 + a*x)^2)","A",0
705,1,98,300,0.0668844,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(9/2),x]","-\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}} \left(280 a^9 x^9+840 a^8 x^8 \log (x)+1120 a^6 x^6+560 a^5 x^5-420 a^4 x^4-448 a^3 x^3+120 a x+35\right)}{280 a^8 x^7 \sqrt{1-a^2 x^2}}","-\frac{3 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{7 \left(1-a^2 x^2\right)^{9/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{8 \left(1-a^2 x^2\right)^{9/2}}-\frac{a^9 x^{10} \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{3 a^8 x^9 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{4 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{2 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{3 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{2 \left(1-a^2 x^2\right)^{9/2}}+\frac{8 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{5 \left(1-a^2 x^2\right)^{9/2}}",1,"-1/280*(c^4*Sqrt[c - c/(a^2*x^2)]*(35 + 120*a*x - 448*a^3*x^3 - 420*a^4*x^4 + 560*a^5*x^5 + 1120*a^6*x^6 + 280*a^9*x^9 + 840*a^8*x^8*Log[x]))/(a^8*x^7*Sqrt[1 - a^2*x^2])","A",1
706,1,98,301,0.0615578,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2),x]","-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}} \left(60 a^7 x^7+180 a^6 x^6 \log (x)-60 a^5 x^5+150 a^4 x^4+100 a^3 x^3-15 a^2 x^2-36 a x-10\right)}{60 a^6 x^5 \sqrt{1-a^2 x^2}}","-\frac{3 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{5 \left(1-a^2 x^2\right)^{7/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{6 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{4 \left(1-a^2 x^2\right)^{7/2}}+\frac{a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}+\frac{3 a^6 x^7 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}-\frac{a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}+\frac{5 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{2 \left(1-a^2 x^2\right)^{7/2}}+\frac{5 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{3 \left(1-a^2 x^2\right)^{7/2}}",1,"-1/60*(c^3*Sqrt[c - c/(a^2*x^2)]*(-10 - 36*a*x - 15*a^2*x^2 + 100*a^3*x^3 + 150*a^4*x^4 - 60*a^5*x^5 + 60*a^7*x^7 + 180*a^6*x^6*Log[x]))/(a^6*x^5*Sqrt[1 - a^2*x^2])","A",1
707,1,90,220,0.0481759,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2),x]","-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^5 x^5+5 a^4 x^4+12 a^4 x^4 \log (x)-8 a^3 x^3+4 a^2 x^2+4 a x+1\right)}{4 a^4 x^3 \sqrt{1-a^2 x^2}}","-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{4 \left(1-a^2 x^2\right)^{5/2}}-\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{3 a^4 x^5 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}+\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}",1,"-1/4*(c^2*Sqrt[c - c/(a^2*x^2)]*(1 + 4*a*x + 4*a^2*x^2 - 8*a^3*x^3 + 5*a^4*x^4 + 4*a^5*x^5 + 12*a^4*x^4*Log[x]))/(a^4*x^3*Sqrt[1 - a^2*x^2])","A",0
708,1,64,145,0.0365708,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2),x]","-\frac{c \sqrt{c-\frac{c}{a^2 x^2}} \left(2 a^3 x^3+6 a^2 x^2 \log (x)-6 a x-1\right)}{2 a^2 x \sqrt{1-a^2 x^2}}","-\frac{3 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 \left(1-a^2 x^2\right)^{3/2}}+\frac{3 a^2 x^3 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}+\frac{a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}",1,"-1/2*(c*Sqrt[c - c/(a^2*x^2)]*(-1 - 6*a*x + 2*a^3*x^3 + 6*a^2*x^2*Log[x]))/(a^2*x*Sqrt[1 - a^2*x^2])","A",1
709,1,47,108,0.0303661,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (-a x-4 \log (1-a x)+\log (x))}{\sqrt{1-a^2 x^2}}","-\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-(a*x) + Log[x] - 4*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
710,1,59,123,0.0459628,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[E^(3*ArcTanh[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\frac{\sqrt{1-a^2 x^2} \left(a x+\frac{2}{1-a x}+3 \log (1-a x)\right)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{\sqrt{1-a^2 x^2}}{a \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 \sqrt{1-a^2 x^2}}{a^2 x (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-a^2 x^2} \log (1-a x)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - a^2*x^2]*(a*x + 2/(1 - a*x) + 3*Log[1 - a*x]))/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",1
711,1,87,174,0.0556761,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(2 a^3 x^3-4 a^2 x^2-4 a x+6 (a x-1)^2 \log (1-a x)+5\right)}{2 a^2 c x (a x-1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}","-\frac{3 \left(1-a^2 x^2\right)^{3/2}}{a^4 x^3 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{\left(1-a^2 x^2\right)^{3/2}}{2 a^4 x^3 (1-a x)^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{3 \left(1-a^2 x^2\right)^{3/2} \log (1-a x)}{a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{\left(1-a^2 x^2\right)^{3/2}}{a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"(Sqrt[1 - a^2*x^2]*(5 - 4*a*x - 4*a^2*x^2 + 2*a^3*x^3 + 6*(-1 + a*x)^2*Log[1 - a*x]))/(2*a^2*c*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^2)","A",1
712,1,113,269,0.0819778,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(2 \left(24 a^4 x^4-72 a^3 x^3-21 a^2 x^2+135 a x-70\right)+147 (a x-1)^3 \log (1-a x)-3 (a x-1)^3 \log (a x+1)\right)}{48 a^2 c^2 x (a x-1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{31 \left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{9 \left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (1-a x)^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{6 a^6 x^5 (1-a x)^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{49 \left(1-a^2 x^2\right)^{5/2} \log (1-a x)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{\left(1-a^2 x^2\right)^{5/2} \log (a x+1)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}",1,"(Sqrt[1 - a^2*x^2]*(2*(-70 + 135*a*x - 21*a^2*x^2 - 72*a^3*x^3 + 24*a^4*x^4) + 147*(-1 + a*x)^3*Log[1 - a*x] - 3*(-1 + a*x)^3*Log[1 + a*x]))/(48*a^2*c^2*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^3)","A",1
713,1,146,363,0.1193307,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^(7/2),x]","\frac{\sqrt{1-a^2 x^2} \left(2 \left(32 a^6 x^6-96 a^5 x^5-87 a^4 x^4+309 a^3 x^3-59 a^2 x^2-207 a x+104\right)+201 (a x+1) (a x-1)^4 \log (1-a x)-9 (a x+1) (a x-1)^4 \log (a x+1)\right)}{64 a^2 c^3 x (a x-1)^4 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}","-\frac{75 \left(1-a^2 x^2\right)^{7/2}}{16 a^8 x^7 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{59 \left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (1-a x)^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{\left(1-a^2 x^2\right)^{7/2}}{2 a^8 x^7 (1-a x)^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{16 a^8 x^7 (1-a x)^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{201 \left(1-a^2 x^2\right)^{7/2} \log (1-a x)}{64 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{9 \left(1-a^2 x^2\right)^{7/2} \log (a x+1)}{64 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}",1,"(Sqrt[1 - a^2*x^2]*(2*(104 - 207*a*x - 59*a^2*x^2 + 309*a^3*x^3 - 87*a^4*x^4 - 96*a^5*x^5 + 32*a^6*x^6) + 201*(-1 + a*x)^4*(1 + a*x)*Log[1 - a*x] - 9*(-1 + a*x)^4*(1 + a*x)*Log[1 + a*x]))/(64*a^2*c^3*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^4*(1 + a*x))","A",1
714,1,115,375,0.1076804,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Integrate[(c - c/(a^2*x^2))^(9/2)/E^ArcTanh[a*x],x]","\frac{x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \left(a^9 (-x)+a^8 \log (x)-\frac{4 a^7}{x}+\frac{2 a^6}{x^2}+\frac{2 a^5}{x^3}-\frac{3 a^4}{2 x^4}-\frac{4 a^3}{5 x^5}+\frac{2 a^2}{3 x^6}+\frac{a}{7 x^7}-\frac{1}{8 x^8}\right)}{\left(1-a^2 x^2\right)^{9/2}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{7 \left(1-a^2 x^2\right)^{9/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{8 \left(1-a^2 x^2\right)^{9/2}}+\frac{2 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{3 \left(1-a^2 x^2\right)^{9/2}}-\frac{a^9 x^{10} \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{a^8 x^9 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{4 a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{2 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{2 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{3 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{2 \left(1-a^2 x^2\right)^{9/2}}-\frac{4 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{5 \left(1-a^2 x^2\right)^{9/2}}",1,"((c - c/(a^2*x^2))^(9/2)*x^9*(-1/8*1/x^8 + a/(7*x^7) + (2*a^2)/(3*x^6) - (4*a^3)/(5*x^5) - (3*a^4)/(2*x^4) + (2*a^5)/x^3 + (2*a^6)/x^2 - (4*a^7)/x - a^9*x + a^8*Log[x]))/(1 - a^2*x^2)^(9/2)","A",1
715,1,98,299,0.0569508,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Integrate[(c - c/(a^2*x^2))^(7/2)/E^ArcTanh[a*x],x]","-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}} \left(60 a^7 x^7-60 a^6 x^6 \log (x)+180 a^5 x^5-90 a^4 x^4-60 a^3 x^3+45 a^2 x^2+12 a x-10\right)}{60 a^6 x^5 \sqrt{1-a^2 x^2}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{5 \left(1-a^2 x^2\right)^{7/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{6 \left(1-a^2 x^2\right)^{7/2}}+\frac{3 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{4 \left(1-a^2 x^2\right)^{7/2}}+\frac{a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}-\frac{a^6 x^7 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}+\frac{3 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}-\frac{3 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{2 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}",1,"-1/60*(c^3*Sqrt[c - c/(a^2*x^2)]*(-10 + 12*a*x + 45*a^2*x^2 - 60*a^3*x^3 - 90*a^4*x^4 + 180*a^5*x^5 + 60*a^7*x^7 - 60*a^6*x^6*Log[x]))/(a^6*x^5*Sqrt[1 - a^2*x^2])","A",1
716,1,82,220,0.0487761,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Integrate[(c - c/(a^2*x^2))^(5/2)/E^ArcTanh[a*x],x]","-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}} \left(12 a^5 x^5-12 a^4 x^4 \log (x)+24 a^3 x^3-12 a^2 x^2-4 a x+3\right)}{12 a^4 x^3 \sqrt{1-a^2 x^2}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{3 \left(1-a^2 x^2\right)^{5/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{4 \left(1-a^2 x^2\right)^{5/2}}+\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}+\frac{a^4 x^5 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}",1,"-1/12*(c^2*Sqrt[c - c/(a^2*x^2)]*(3 - 4*a*x - 12*a^2*x^2 + 24*a^3*x^3 + 12*a^5*x^5 - 12*a^4*x^4*Log[x]))/(a^4*x^3*Sqrt[1 - a^2*x^2])","A",1
717,1,72,144,0.0357853,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[(c - c/(a^2*x^2))^(3/2)/E^ArcTanh[a*x],x]","-\frac{c \sqrt{c-\frac{c}{a^2 x^2}} \left(2 a^3 x^3-3 a^2 x^2-2 a^2 x^2 \log (x)+2 a x-1\right)}{2 a^2 x \sqrt{1-a^2 x^2}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 \left(1-a^2 x^2\right)^{3/2}}-\frac{a^2 x^3 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}+\frac{a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}",1,"-1/2*(c*Sqrt[c - c/(a^2*x^2)]*(-1 + 2*a*x - 3*a^2*x^2 + 2*a^3*x^3 - 2*a^2*x^2*Log[x]))/(a^2*x*Sqrt[1 - a^2*x^2])","A",0
718,1,38,69,0.0238512,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/E^ArcTanh[a*x],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (\log (x)-a x)}{\sqrt{1-a^2 x^2}}","\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-(a*x) + Log[x]))/Sqrt[1 - a^2*x^2]","A",1
719,1,50,77,0.0296172,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[1/(E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{x}{a}-\frac{\log (a x+1)}{a^2}\right)}{x \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{\sqrt{1-a^2 x^2}}{a \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - a^2*x^2]*(x/a - Log[1 + a*x]/a^2))/(Sqrt[c - c/(a^2*x^2)]*x)","A",1
720,1,91,175,0.0562265,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(3/2)),x]","-\frac{\sqrt{1-a^2 x^2} \left(a^2 x^2-1\right) \left(\frac{1}{2 a^4 (a x+1)}-\frac{\log (1-a x)}{4 a^4}+\frac{5 \log (a x+1)}{4 a^4}-\frac{x}{a^3}\right)}{x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}","\frac{\left(1-a^2 x^2\right)^{3/2}}{2 a^4 x^3 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{\left(1-a^2 x^2\right)^{3/2} \log (1-a x)}{4 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{5 \left(1-a^2 x^2\right)^{3/2} \log (a x+1)}{4 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{\left(1-a^2 x^2\right)^{3/2}}{a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"-((Sqrt[1 - a^2*x^2]*(-1 + a^2*x^2)*(-(x/a^3) + 1/(2*a^4*(1 + a*x)) - Log[1 - a*x]/(4*a^4) + (5*Log[1 + a*x])/(4*a^4)))/((c - c/(a^2*x^2))^(3/2)*x^3))","A",1
721,1,88,265,0.1239496,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(5/2)),x]","\frac{\left(1-a^2 x^2\right)^{5/2} \left(2 \left(8 a x+\frac{1}{1-a x}-\frac{8}{a x+1}+\frac{1}{(a x+1)^2}\right)+7 \log (1-a x)-23 \log (a x+1)\right)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}","\frac{\left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{\left(1-a^2 x^2\right)^{5/2}}{a^6 x^5 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (a x+1)^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{7 \left(1-a^2 x^2\right)^{5/2} \log (1-a x)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{23 \left(1-a^2 x^2\right)^{5/2} \log (a x+1)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}",1,"((1 - a^2*x^2)^(5/2)*(2*(8*a*x + (1 - a*x)^(-1) + (1 + a*x)^(-2) - 8/(1 + a*x)) + 7*Log[1 - a*x] - 23*Log[1 + a*x]))/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",1
722,1,145,361,0.1166543,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(7/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(96 a^6 x^6+96 a^5 x^5-366 a^4 x^4-222 a^3 x^3+338 a^2 x^2+122 a x+57 (a x-1)^2 (a x+1)^3 \log (1-a x)-153 (a x-1)^2 (a x+1)^3 \log (a x+1)-88\right)}{96 a^2 x (a x-1)^2 \sqrt{c-\frac{c}{a^2 x^2}} (a c x+c)^3}","-\frac{5 \left(1-a^2 x^2\right)^{7/2}}{16 a^8 x^7 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{3 \left(1-a^2 x^2\right)^{7/2}}{2 a^8 x^7 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (1-a x)^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{11 \left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (a x+1)^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{24 a^8 x^7 (a x+1)^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{19 \left(1-a^2 x^2\right)^{7/2} \log (1-a x)}{32 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{51 \left(1-a^2 x^2\right)^{7/2} \log (a x+1)}{32 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}",1,"(Sqrt[1 - a^2*x^2]*(-88 + 122*a*x + 338*a^2*x^2 - 222*a^3*x^3 - 366*a^4*x^4 + 96*a^5*x^5 + 96*a^6*x^6 + 57*(-1 + a*x)^2*(1 + a*x)^3*Log[1 - a*x] - 153*(-1 + a*x)^2*(1 + a*x)^3*Log[1 + a*x]))/(96*a^2*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)^2*(c + a*c*x)^3)","A",1
723,1,166,455,0.194946,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Integrate[(c - c/(a^2*x^2))^(9/2)/E^(2*ArcTanh[a*x]),x]","-\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}} \left(-26880 a^8 x^8 \log \left(\sqrt{a^2 x^2-1}+a x\right)+25725 a^8 x^8 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(13440 a^8 x^8+45056 a^7 x^7+14595 a^6 x^6-31232 a^5 x^5+770 a^4 x^4+16896 a^3 x^3-4760 a^2 x^2-3840 a x+1680\right)\right)}{13440 a^8 x^7 \sqrt{a^2 x^2-1}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{28 (a x+1)}-\frac{x (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{8 (a x+1)}+\frac{47 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{336 (1-a x) (a x+1)}+\frac{11 a^8 x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{128 (1-a x)^4 (a x+1)^4}-\frac{2 a^8 x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \sin ^{-1}(a x)}{(1-a x)^{9/2} (a x+1)^{9/2}}+\frac{245 a^8 x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{128 (1-a x)^{9/2} (a x+1)^{9/2}}+\frac{39 a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{64 (1-a x)^4 (a x+1)^3}-\frac{11 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{640 (1-a x)^4 (a x+1)^2}-\frac{103 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{160 (1-a x)^4 (a x+1)}+\frac{629 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{960 (1-a x)^3 (a x+1)}-\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{5 (1-a x)^2 (a x+1)}",1,"-1/13440*(c^4*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(1680 - 3840*a*x - 4760*a^2*x^2 + 16896*a^3*x^3 + 770*a^4*x^4 - 31232*a^5*x^5 + 14595*a^6*x^6 + 45056*a^7*x^7 + 13440*a^8*x^8) + 25725*a^8*x^8*ArcTan[1/Sqrt[-1 + a^2*x^2]] - 26880*a^8*x^8*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^8*x^7*Sqrt[-1 + a^2*x^2])","A",0
724,1,150,375,0.161395,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Integrate[(c - c/(a^2*x^2))^(7/2)/E^(2*ArcTanh[a*x]),x]","-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}} \left(-480 a^6 x^6 \log \left(\sqrt{a^2 x^2-1}+a x\right)+375 a^6 x^6 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(240 a^6 x^6+736 a^5 x^5+105 a^4 x^4-352 a^3 x^3+70 a^2 x^2+96 a x-40\right)\right)}{240 a^6 x^5 \sqrt{a^2 x^2-1}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{15 (a x+1)}-\frac{x (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{6 (a x+1)}+\frac{23 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{120 (1-a x) (a x+1)}-\frac{7 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{16 (1-a x)^3 (a x+1)^3}+\frac{2 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \sin ^{-1}(a x)}{(1-a x)^{7/2} (a x+1)^{7/2}}-\frac{25 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{16 (1-a x)^{7/2} (a x+1)^{7/2}}-\frac{3 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{8 (1-a x)^3 (a x+1)^2}+\frac{19 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{16 (1-a x)^3 (a x+1)}-\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{3 (1-a x)^2 (a x+1)}",1,"-1/240*(c^3*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(-40 + 96*a*x + 70*a^2*x^2 - 352*a^3*x^3 + 105*a^4*x^4 + 736*a^5*x^5 + 240*a^6*x^6) + 375*a^6*x^6*ArcTan[1/Sqrt[-1 + a^2*x^2]] - 480*a^6*x^6*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^6*x^5*Sqrt[-1 + a^2*x^2])","A",0
725,1,134,293,0.1406798,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Integrate[(c - c/(a^2*x^2))^(5/2)/E^(2*ArcTanh[a*x]),x]","-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}} \left(-48 a^4 x^4 \log \left(\sqrt{a^2 x^2-1}+a x\right)+27 a^4 x^4 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(24 a^4 x^4+64 a^3 x^3-3 a^2 x^2-16 a x+6\right)\right)}{24 a^4 x^3 \sqrt{a^2 x^2-1}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{6 (a x+1)}-\frac{x (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{4 (a x+1)}+\frac{7 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{24 (1-a x) (a x+1)}+\frac{7 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 (a x+1)^2}-\frac{2 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \sin ^{-1}(a x)}{(1-a x)^{5/2} (a x+1)^{5/2}}+\frac{9 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{8 (1-a x)^{5/2} (a x+1)^{5/2}}-\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{(1-a x)^2 (a x+1)}",1,"-1/24*(c^2*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(6 - 16*a*x - 3*a^2*x^2 + 64*a^3*x^3 + 24*a^4*x^4) + 27*a^4*x^4*ArcTan[1/Sqrt[-1 + a^2*x^2]] - 48*a^4*x^4*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^4*x^3*Sqrt[-1 + a^2*x^2])","A",0
726,1,115,212,0.109181,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[(c - c/(a^2*x^2))^(3/2)/E^(2*ArcTanh[a*x]),x]","-\frac{c \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1} \left(2 a^2 x^2+4 a x-1\right)-4 a^2 x^2 \log \left(\sqrt{a^2 x^2-1}+a x\right)+a^2 x^2 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{2 a^2 x \sqrt{a^2 x^2-1}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{a x+1}-\frac{x (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 (a x+1)}+\frac{5 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 (1-a x) (a x+1)}+\frac{2 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \sin ^{-1}(a x)}{(1-a x)^{3/2} (a x+1)^{3/2}}-\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{2 (1-a x)^{3/2} (a x+1)^{3/2}}",1,"-1/2*(c*Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(-1 + 4*a*x + 2*a^2*x^2) + a^2*x^2*ArcTan[1/Sqrt[-1 + a^2*x^2]] - 4*a^2*x^2*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^2*x*Sqrt[-1 + a^2*x^2])","A",0
727,1,80,118,0.0907381,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/E^(2*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-\sqrt{a^2 x^2-1}+2 \log \left(\sqrt{a^2 x^2-1}+a x\right)+\tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{\sqrt{a^2 x^2-1}}","-x \sqrt{c-\frac{c}{a^2 x^2}}-\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-Sqrt[-1 + a^2*x^2] + ArcTan[1/Sqrt[-1 + a^2*x^2]] + 2*Log[a*x + Sqrt[-1 + a^2*x^2]]))/Sqrt[-1 + a^2*x^2]","A",0
728,1,69,111,0.0692068,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]),x]","\frac{-a^2 x^2+2 \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)-2 a x+3}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(1-a x)^2}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 (a x+1) (1-a x)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 \sqrt{a x+1} \sqrt{1-a x} \sin ^{-1}(a x)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(3 - 2*a*x - a^2*x^2 + 2*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",0
729,1,95,124,0.0840735,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2)),x]","\frac{-3 a^3 x^3-11 a^2 x^2+6 (a x+1) \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)+4 a x+10}{3 a^2 c x (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(1-a x)^2}{3 a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{2 (a x+1) (2 a x+5) (1-a x)^2}{3 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{2 (a x+1)^{3/2} (1-a x)^{3/2} \sin ^{-1}(a x)}{a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"(10 + 4*a*x - 11*a^2*x^2 - 3*a^3*x^3 + 6*(1 + a*x)*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(3*a^2*c*Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x))","A",0
730,1,105,194,0.0974353,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2)),x]","\frac{-15 a^4 x^4-76 a^3 x^3-32 a^2 x^2+30 (a x+1)^2 \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)+82 a x+56}{15 a^2 c^2 x (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{(1-a x)^2}{a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{2 (a x+1)^2 (13 a x+28) (1-a x)^3}{15 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{2 (a x+1)^{5/2} (1-a x)^{5/2} \sin ^{-1}(a x)}{a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{2 (a x+1) (1-a x)^3}{15 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{2 (1-a x)^3}{5 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}",1,"(56 + 82*a*x - 32*a^2*x^2 - 76*a^3*x^3 - 15*a^4*x^4 + 30*(1 + a*x)^2*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(15*a^2*c^2*Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x)^2)","A",0
731,1,131,270,0.1185999,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2)),x]","\frac{-105 a^6 x^6-562 a^5 x^5-74 a^4 x^4+1226 a^3 x^3+636 a^2 x^2+210 (a x-1) (a x+1)^3 \sqrt{a^2 x^2-1} \log \left(\sqrt{a^2 x^2-1}+a x\right)-654 a x-432}{105 a^2 x (a x-1) \sqrt{c-\frac{c}{a^2 x^2}} (a c x+c)^3}","\frac{(1-a x)^2}{3 a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{2 (a x+1)^3 (37 a x+72) (1-a x)^4}{35 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{2 (a x+1)^{7/2} (1-a x)^{7/2} \sin ^{-1}(a x)}{a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{2 (a x+1)^2 (1-a x)^4}{35 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{82 (a x+1) (1-a x)^4}{105 a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{12 (1-a x)^4}{7 a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{10 (1-a x)^3}{3 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}",1,"(-432 - 654*a*x + 636*a^2*x^2 + 1226*a^3*x^3 - 74*a^4*x^4 - 562*a^5*x^5 - 105*a^6*x^6 + 210*(-1 + a*x)*(1 + a*x)^3*Sqrt[-1 + a^2*x^2]*Log[a*x + Sqrt[-1 + a^2*x^2]])/(105*a^2*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)*(c + a*c*x)^3)","A",0
732,1,97,299,0.0947625,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Integrate[(c - c/(a^2*x^2))^(9/2)/E^(3*ArcTanh[a*x]),x]","\frac{x^9 \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \left(a^9 x-3 a^8 \log (x)-\frac{4 a^6}{x^2}+\frac{2 a^5}{x^3}+\frac{3 a^4}{2 x^4}-\frac{8 a^3}{5 x^5}+\frac{3 a}{7 x^7}-\frac{1}{8 x^8}\right)}{\left(1-a^2 x^2\right)^{9/2}}","\frac{3 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{7 \left(1-a^2 x^2\right)^{9/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{8 \left(1-a^2 x^2\right)^{9/2}}+\frac{a^9 x^{10} \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{3 a^8 x^9 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}-\frac{4 a^6 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{2 a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{\left(1-a^2 x^2\right)^{9/2}}+\frac{3 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{2 \left(1-a^2 x^2\right)^{9/2}}-\frac{8 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{9/2}}{5 \left(1-a^2 x^2\right)^{9/2}}",1,"((c - c/(a^2*x^2))^(9/2)*x^9*(-1/8*1/x^8 + (3*a)/(7*x^7) - (8*a^3)/(5*x^5) + (3*a^4)/(2*x^4) + (2*a^5)/x^3 - (4*a^6)/x^2 + a^9*x - 3*a^8*Log[x]))/(1 - a^2*x^2)^(9/2)","A",1
733,1,98,301,0.0600769,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Integrate[(c - c/(a^2*x^2))^(7/2)/E^(3*ArcTanh[a*x]),x]","\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}} \left(60 a^7 x^7-180 a^6 x^6 \log (x)-60 a^5 x^5-150 a^4 x^4+100 a^3 x^3+15 a^2 x^2-36 a x+10\right)}{60 a^6 x^5 \sqrt{1-a^2 x^2}}","\frac{3 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{5 \left(1-a^2 x^2\right)^{7/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{6 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{4 \left(1-a^2 x^2\right)^{7/2}}-\frac{a^7 x^8 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}+\frac{3 a^6 x^7 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}+\frac{a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{\left(1-a^2 x^2\right)^{7/2}}+\frac{5 a^4 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{2 \left(1-a^2 x^2\right)^{7/2}}-\frac{5 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}{3 \left(1-a^2 x^2\right)^{7/2}}",1,"(c^3*Sqrt[c - c/(a^2*x^2)]*(10 - 36*a*x + 15*a^2*x^2 + 100*a^3*x^3 - 150*a^4*x^4 - 60*a^5*x^5 + 60*a^7*x^7 - 180*a^6*x^6*Log[x]))/(60*a^6*x^5*Sqrt[1 - a^2*x^2])","A",1
734,1,90,218,0.0490479,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Integrate[(c - c/(a^2*x^2))^(5/2)/E^(3*ArcTanh[a*x]),x]","\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^5 x^5-5 a^4 x^4-12 a^4 x^4 \log (x)-8 a^3 x^3-4 a^2 x^2+4 a x-1\right)}{4 a^4 x^3 \sqrt{1-a^2 x^2}}","\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{4 \left(1-a^2 x^2\right)^{5/2}}-\frac{a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}+\frac{a^5 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{3 a^4 x^5 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}-\frac{2 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{\left(1-a^2 x^2\right)^{5/2}}",1,"(c^2*Sqrt[c - c/(a^2*x^2)]*(-1 + 4*a*x - 4*a^2*x^2 - 8*a^3*x^3 - 5*a^4*x^4 + 4*a^5*x^5 - 12*a^4*x^4*Log[x]))/(4*a^4*x^3*Sqrt[1 - a^2*x^2])","A",0
735,1,64,146,0.03854,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[(c - c/(a^2*x^2))^(3/2)/E^(3*ArcTanh[a*x]),x]","\frac{c \sqrt{c-\frac{c}{a^2 x^2}} \left(2 a^3 x^3-6 a^2 x^2 \log (x)-6 a x+1\right)}{2 a^2 x \sqrt{1-a^2 x^2}}","\frac{3 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{2 \left(1-a^2 x^2\right)^{3/2}}+\frac{3 a^2 x^3 \log (x) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}-\frac{a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}{\left(1-a^2 x^2\right)^{3/2}}",1,"(c*Sqrt[c - c/(a^2*x^2)]*(1 - 6*a*x + 2*a^3*x^3 - 6*a^2*x^2*Log[x]))/(2*a^2*x*Sqrt[1 - a^2*x^2])","A",1
736,1,45,106,0.0281108,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/E^(3*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (a x-4 \log (a x+1)+\log (x))}{\sqrt{1-a^2 x^2}}","\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(a*x + Log[x] - 4*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
737,1,58,122,0.0471053,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]),x]","\frac{\sqrt{1-a^2 x^2} \left(-a x+\frac{2}{a x+1}+3 \log (a x+1)\right)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}","-\frac{\sqrt{1-a^2 x^2}}{a \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 \sqrt{1-a^2 x^2}}{a^2 x (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-a^2 x^2} \log (a x+1)}{a^2 x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - a^2*x^2]*(-(a*x) + 2/(1 + a*x) + 3*Log[1 + a*x]))/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",1
738,1,86,170,0.0558812,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2)),x]","-\frac{\sqrt{1-a^2 x^2} \left(a^2 x^2-1\right) \left(-\frac{3}{a^4 (a x+1)}+\frac{1}{2 a^4 (a x+1)^2}-\frac{3 \log (a x+1)}{a^4}+\frac{x}{a^3}\right)}{x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}","-\frac{3 \left(1-a^2 x^2\right)^{3/2}}{a^4 x^3 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{\left(1-a^2 x^2\right)^{3/2}}{2 a^4 x^3 (a x+1)^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{3 \left(1-a^2 x^2\right)^{3/2} \log (a x+1)}{a^4 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{\left(1-a^2 x^2\right)^{3/2}}{a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"-((Sqrt[1 - a^2*x^2]*(-1 + a^2*x^2)*(x/a^3 + 1/(2*a^4*(1 + a*x)^2) - 3/(a^4*(1 + a*x)) - (3*Log[1 + a*x])/a^4))/((c - c/(a^2*x^2))^(3/2)*x^3))","A",1
739,1,110,267,0.0925922,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(-48 a^4 x^4-144 a^3 x^3+42 a^2 x^2+270 a x-3 (a x+1)^3 \log (1-a x)+147 (a x+1)^3 \log (a x+1)+140\right)}{48 a^2 c^2 x (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{31 \left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{9 \left(1-a^2 x^2\right)^{5/2}}{8 a^6 x^5 (a x+1)^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{\left(1-a^2 x^2\right)^{5/2}}{6 a^6 x^5 (a x+1)^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{\left(1-a^2 x^2\right)^{5/2} \log (1-a x)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{49 \left(1-a^2 x^2\right)^{5/2} \log (a x+1)}{16 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}-\frac{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}",1,"(Sqrt[1 - a^2*x^2]*(140 + 270*a*x + 42*a^2*x^2 - 144*a^3*x^3 - 48*a^4*x^4 - 3*(1 + a*x)^3*Log[1 - a*x] + 147*(1 + a*x)^3*Log[1 + a*x]))/(48*a^2*c^2*Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x)^3)","A",1
740,1,146,359,0.1244704,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(-2 \left(32 a^6 x^6+96 a^5 x^5-87 a^4 x^4-309 a^3 x^3-59 a^2 x^2+207 a x+104\right)-9 (a x-1) (a x+1)^4 \log (1-a x)+201 (a x-1) (a x+1)^4 \log (a x+1)\right)}{64 a^2 c^3 x (a x-1) (a x+1)^4 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{\left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (1-a x) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{75 \left(1-a^2 x^2\right)^{7/2}}{16 a^8 x^7 (a x+1) \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{59 \left(1-a^2 x^2\right)^{7/2}}{32 a^8 x^7 (a x+1)^2 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{\left(1-a^2 x^2\right)^{7/2}}{2 a^8 x^7 (a x+1)^3 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{16 a^8 x^7 (a x+1)^4 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{9 \left(1-a^2 x^2\right)^{7/2} \log (1-a x)}{64 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}-\frac{201 \left(1-a^2 x^2\right)^{7/2} \log (a x+1)}{64 a^8 x^7 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}+\frac{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \left(c-\frac{c}{a^2 x^2}\right)^{7/2}}",1,"(Sqrt[1 - a^2*x^2]*(-2*(104 + 207*a*x - 59*a^2*x^2 - 309*a^3*x^3 - 87*a^4*x^4 + 96*a^5*x^5 + 32*a^6*x^6) - 9*(-1 + a*x)*(1 + a*x)^4*Log[1 - a*x] + 201*(-1 + a*x)*(1 + a*x)^4*Log[1 + a*x]))/(64*a^2*c^3*Sqrt[c - c/(a^2*x^2)]*x*(-1 + a*x)*(1 + a*x)^4)","A",1
741,1,51,80,0.0332205,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^m \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]*x^m,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{a x^{m+1}}{m+1}+\frac{x^m}{m}\right)}{\sqrt{1-a^2 x^2}}","\frac{x^{m+1} \sqrt{c-\frac{c}{a^2 x^2}}}{m \sqrt{1-a^2 x^2}}+\frac{a x^{m+2} \sqrt{c-\frac{c}{a^2 x^2}}}{(m+1) \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(x^m/m + (a*x^(1 + m))/(1 + m)))/Sqrt[1 - a^2*x^2]","A",1
742,1,42,74,0.0211678,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]*x^2,x]","\frac{x^3 (2 a x+3) \sqrt{c-\frac{c}{a^2 x^2}}}{6 \sqrt{1-a^2 x^2}}","\frac{a x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-a^2 x^2}}+\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x^3*(3 + 2*a*x))/(6*Sqrt[1 - a^2*x^2])","A",1
743,1,41,71,0.020118,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]*x,x]","\frac{x \left(\frac{a x^2}{2}+x\right) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(x + (a*x^2)/2))/Sqrt[1 - a^2*x^2]","A",1
744,1,37,68,0.0184567,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (a x+\log (x))}{\sqrt{1-a^2 x^2}}","\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(a*x + Log[x]))/Sqrt[1 - a^2*x^2]","A",1
745,1,37,66,0.0207746,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)])/x,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} (a x \log (x)-1)}{\sqrt{1-a^2 x^2}}","\frac{a x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-1 + a*x*Log[x]))/Sqrt[1 - a^2*x^2]","A",1
746,1,42,43,0.0192828,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)])/x^2,x]","-\frac{(2 a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}","-\frac{(a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}",1,"-1/2*(Sqrt[c - c/(a^2*x^2)]*(1 + 2*a*x))/(x*Sqrt[1 - a^2*x^2])","A",0
747,1,93,160,0.0907601,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^3,x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(21 \log \left(\sqrt{a^2 x^2-1}+a x\right)+\sqrt{a^2 x^2-1} \left(6 a^3 x^3+16 a^2 x^2+21 a x+32\right)\right)}{24 a^3 \sqrt{a^2 x^2-1}}","-\frac{x^2 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^2}-\frac{x (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^3}-\frac{7 x (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}{24 a^3}-\frac{7 x \sqrt{c-\frac{c}{a^2 x^2}}}{8 a^3}+\frac{7 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{8 a^3 \sqrt{1-a x} \sqrt{a x+1}}",1,"-1/24*(Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[-1 + a^2*x^2]*(32 + 21*a*x + 16*a^2*x^2 + 6*a^3*x^3) + 21*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^3*Sqrt[-1 + a^2*x^2])","A",0
748,1,84,123,0.065391,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^2,x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1} \left(a^2 x^2+3 a x+5\right)+3 \log \left(\sqrt{a^2 x^2-1}+a x\right)\right)}{3 a^2 \sqrt{a^2 x^2-1}}","-\frac{x (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^2}-\frac{x (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^2}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{a^2}+\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{a^2 \sqrt{1-a x} \sqrt{a x+1}}",1,"-1/3*(Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[-1 + a^2*x^2]*(5 + 3*a*x + a^2*x^2) + 3*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^2*Sqrt[-1 + a^2*x^2])","A",0
749,1,77,98,0.0626627,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x,x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{1-a^2 x^2} (a x+4)+6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{2 a \sqrt{1-a^2 x^2}}","-\frac{x (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}{2 a}-\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}}}{2 a}+\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{2 a \sqrt{1-a x} \sqrt{a x+1}}",1,"-1/2*(Sqrt[c - c/(a^2*x^2)]*x*((4 + a*x)*Sqrt[1 - a^2*x^2] + 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a^2*x^2])","A",0
750,1,81,118,0.0764697,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1}+2 \log \left(\sqrt{a^2 x^2-1}+a x\right)-\tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{\sqrt{a^2 x^2-1}}","-x \sqrt{c-\frac{c}{a^2 x^2}}+\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"-((Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[-1 + a^2*x^2] - ArcTan[1/Sqrt[-1 + a^2*x^2]] + 2*Log[a*x + Sqrt[-1 + a^2*x^2]]))/Sqrt[-1 + a^2*x^2])","A",0
751,1,85,118,0.0715402,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(-\sqrt{a^2 x^2-1}-a x \log \left(\sqrt{a^2 x^2-1}+a x\right)+2 a x \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{\sqrt{a^2 x^2-1}}","-\sqrt{c-\frac{c}{a^2 x^2}}+\frac{a x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{2 a x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-Sqrt[-1 + a^2*x^2] + 2*a*x*ArcTan[1/Sqrt[-1 + a^2*x^2]] - a*x*Log[a*x + Sqrt[-1 + a^2*x^2]]))/Sqrt[-1 + a^2*x^2]","A",0
752,1,79,111,0.0687674,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^2,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(3 a^2 x^2 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)-(4 a x+1) \sqrt{a^2 x^2-1}\right)}{2 x \sqrt{a^2 x^2-1}}","-\frac{3}{2} a \sqrt{c-\frac{c}{a^2 x^2}}-\frac{(a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}{2 x}-\frac{3 a^2 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{2 \sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-((1 + 4*a*x)*Sqrt[-1 + a^2*x^2]) + 3*a^2*x^2*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(2*x*Sqrt[-1 + a^2*x^2])","A",0
753,1,71,139,0.082769,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^3,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(-5 a^2 x^2+\frac{3 a^3 x^3 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)}{\sqrt{a^2 x^2-1}}-3 a x-1\right)}{3 x^2}","-a^2 \sqrt{c-\frac{c}{a^2 x^2}}-\frac{a (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}{3 x}-\frac{(a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2}-\frac{a^3 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-1 - 3*a*x - 5*a^2*x^2 + (3*a^3*x^3*ArcTan[1/Sqrt[-1 + a^2*x^2]])/Sqrt[-1 + a^2*x^2]))/(3*x^2)","A",0
754,1,95,156,0.0817674,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^4,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(21 a^4 x^4 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)-\sqrt{a^2 x^2-1} \left(32 a^3 x^3+21 a^2 x^2+16 a x+6\right)\right)}{24 x^3 \sqrt{a^2 x^2-1}}","-\frac{7 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{8 x}-\frac{2 a \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 x^3}-\frac{7 a^4 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{8 \sqrt{1-a x} \sqrt{a x+1}}-\frac{4}{3} a^3 \sqrt{c-\frac{c}{a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-(Sqrt[-1 + a^2*x^2]*(6 + 16*a*x + 21*a^2*x^2 + 32*a^3*x^3)) + 21*a^4*x^4*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(24*x^3*Sqrt[-1 + a^2*x^2])","A",0
755,1,103,181,0.0894767,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^5,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(15 a^5 x^5 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)-\sqrt{a^2 x^2-1} \left(24 a^4 x^4+15 a^3 x^3+12 a^2 x^2+10 a x+4\right)\right)}{20 x^4 \sqrt{a^2 x^2-1}}","-\frac{3 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{5 x^2}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4}-\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^3}-\frac{3 a^5 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{4 \sqrt{1-a x} \sqrt{a x+1}}-\frac{6}{5} a^4 \sqrt{c-\frac{c}{a^2 x^2}}-\frac{3 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 x}",1,"(Sqrt[c - c/(a^2*x^2)]*(-(Sqrt[-1 + a^2*x^2]*(4 + 10*a*x + 12*a^2*x^2 + 15*a^3*x^3 + 24*a^4*x^4)) + 15*a^5*x^5*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(20*x^4*Sqrt[-1 + a^2*x^2])","A",0
756,1,71,188,0.0504805,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^3,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-\frac{4 \log (1-a x)}{a^3}-\frac{4 x}{a^2}-\frac{a x^4}{4}-\frac{2 x^2}{a}-x^3\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-a^2 x^2}}-\frac{a x^5 \sqrt{c-\frac{c}{a^2 x^2}}}{4 \sqrt{1-a^2 x^2}}-\frac{x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{2 x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*((-4*x)/a^2 - (2*x^2)/a - x^3 - (a*x^4)/4 - (4*Log[1 - a*x])/a^3))/Sqrt[1 - a^2*x^2]","A",1
757,1,65,153,0.0410174,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^2,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-\frac{4 \log (1-a x)}{a^2}-\frac{a x^3}{3}-\frac{4 x}{a}-\frac{3 x^2}{2}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^2 \sqrt{1-a^2 x^2}}-\frac{a x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-a^2 x^2}}-\frac{3 x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*((-4*x)/a - (3*x^2)/2 - (a*x^3)/3 - (4*Log[1 - a*x])/a^2))/Sqrt[1 - a^2*x^2]","A",1
758,1,55,114,0.0264366,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-\frac{a x^2}{2}-\frac{4 \log (1-a x)}{a}-3 x\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a \sqrt{1-a^2 x^2}}-\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-3*x - (a*x^2)/2 - (4*Log[1 - a*x])/a))/Sqrt[1 - a^2*x^2]","A",1
759,1,47,108,0.0290523,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (-a x-4 \log (1-a x)+\log (x))}{\sqrt{1-a^2 x^2}}","-\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-(a*x) + Log[x] - 4*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
760,1,49,107,0.0328421,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} (3 a x \log (x)-4 a x \log (1-a x)-1)}{\sqrt{1-a^2 x^2}}","-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{3 a x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-1 + 3*a*x*Log[x] - 4*a*x*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
761,1,64,148,0.0444033,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^2,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^2 \log (x)-4 a^2 \log (1-a x)-\frac{3 a}{x}-\frac{1}{2 x^2}\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 a \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}+\frac{4 a^2 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a^2 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/2*1/x^2 - (3*a)/x + 4*a^2*Log[x] - 4*a^2*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
762,1,74,187,0.0495539,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^3,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^3 \log (x)-4 a^3 \log (1-a x)-\frac{4 a^2}{x}-\frac{3 a}{2 x^2}-\frac{1}{3 x^3}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{3 a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \sqrt{1-a^2 x^2}}+\frac{4 a^3 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a^3 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/3*1/x^3 - (3*a)/(2*x^2) - (4*a^2)/x + 4*a^3*Log[x] - 4*a^3*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
763,1,80,222,0.0582792,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^4,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^4 \log (x)-4 a^4 \log (1-a x)-\frac{4 a^3}{x}-\frac{2 a^2}{x^2}-\frac{a}{x^3}-\frac{1}{4 x^4}\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-a^2 x^2}}-\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 x^3 \sqrt{1-a^2 x^2}}+\frac{4 a^4 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a^4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}-\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/4*1/x^4 - a/x^3 - (2*a^2)/x^2 - (4*a^3)/x + 4*a^4*Log[x] - 4*a^4*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
764,1,92,263,0.0631616,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^5,x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^5 \log (x)-4 a^5 \log (1-a x)-\frac{4 a^4}{x}-\frac{2 a^3}{x^2}-\frac{4 a^2}{3 x^3}-\frac{3 a}{4 x^4}-\frac{1}{5 x^5}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4 \sqrt{1-a^2 x^2}}-\frac{3 a \sqrt{c-\frac{c}{a^2 x^2}}}{4 x^3 \sqrt{1-a^2 x^2}}+\frac{4 a^5 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a^5 x \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-a^2 x^2}}-\frac{4 a^4 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{2 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/5*1/x^5 - (3*a)/(4*x^4) - (4*a^2)/(3*x^3) - (2*a^3)/x^2 - (4*a^4)/x + 4*a^5*Log[x] - 4*a^5*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
765,1,52,81,0.0382238,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^m \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x^m)/E^ArcTanh[a*x],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{x^m}{m}-\frac{a x^{m+1}}{m+1}\right)}{\sqrt{1-a^2 x^2}}","\frac{x^{m+1} \sqrt{c-\frac{c}{a^2 x^2}}}{m \sqrt{1-a^2 x^2}}-\frac{a x^{m+2} \sqrt{c-\frac{c}{a^2 x^2}}}{(m+1) \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(x^m/m - (a*x^(1 + m))/(1 + m)))/Sqrt[1 - a^2*x^2]","A",1
766,1,42,74,0.0237071,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x^2)/E^ArcTanh[a*x],x]","-\frac{x^3 (2 a x-3) \sqrt{c-\frac{c}{a^2 x^2}}}{6 \sqrt{1-a^2 x^2}}","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}-\frac{a x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-a^2 x^2}}",1,"-1/6*(Sqrt[c - c/(a^2*x^2)]*x^3*(-3 + 2*a*x))/Sqrt[1 - a^2*x^2]","A",1
767,1,41,71,0.0201689,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x)/E^ArcTanh[a*x],x]","\frac{x \left(x-\frac{a x^2}{2}\right) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(x - (a*x^2)/2))/Sqrt[1 - a^2*x^2]","A",1
768,1,38,69,0.0205328,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/E^ArcTanh[a*x],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (\log (x)-a x)}{\sqrt{1-a^2 x^2}}","\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-(a*x) + Log[x]))/Sqrt[1 - a^2*x^2]","A",1
769,1,38,67,0.0231746,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^ArcTanh[a*x]*x),x]","-\frac{\sqrt{c-\frac{c}{a^2 x^2}} (a x \log (x)+1)}{\sqrt{1-a^2 x^2}}","-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{a x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"-((Sqrt[c - c/(a^2*x^2)]*(1 + a*x*Log[x]))/Sqrt[1 - a^2*x^2])","A",1
770,1,44,44,0.0201819,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^ArcTanh[a*x]*x^2),x]","\frac{x \left(\frac{a}{x}-\frac{1}{2 x^2}\right) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}","-\frac{(1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-1/2*1/x^2 + a/x)*x)/Sqrt[1 - a^2*x^2]","A",0
771,1,93,163,0.0858874,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x^3)/E^(2*ArcTanh[a*x]),x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(21 \log \left(\sqrt{a^2 x^2-1}+a x\right)+\sqrt{a^2 x^2-1} \left(6 a^3 x^3-16 a^2 x^2+21 a x-32\right)\right)}{24 a^3 \sqrt{a^2 x^2-1}}","-\frac{x^2 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^2}+\frac{x (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^3}+\frac{7 x (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}{24 a^3}+\frac{7 x \sqrt{c-\frac{c}{a^2 x^2}}}{8 a^3}+\frac{7 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{8 a^3 \sqrt{a x+1} \sqrt{1-a x}}",1,"-1/24*(Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[-1 + a^2*x^2]*(-32 + 21*a*x - 16*a^2*x^2 + 6*a^3*x^3) + 21*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^3*Sqrt[-1 + a^2*x^2])","A",0
772,1,84,126,0.0671549,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x^2)/E^(2*ArcTanh[a*x]),x]","-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1} \left(a^2 x^2-3 a x+5\right)-3 \log \left(\sqrt{a^2 x^2-1}+a x\right)\right)}{3 a^2 \sqrt{a^2 x^2-1}}","-\frac{x (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^2}-\frac{x (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^2}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{a^2}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{a^2 \sqrt{a x+1} \sqrt{1-a x}}",1,"-1/3*(Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[-1 + a^2*x^2]*(5 - 3*a*x + a^2*x^2) - 3*Log[a*x + Sqrt[-1 + a^2*x^2]]))/(a^2*Sqrt[-1 + a^2*x^2])","A",0
773,1,100,99,0.0587403,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x)/E^(2*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a x+1} \left(a^2 x^2-5 a x+4\right)-6 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{2 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{x (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}{2 a}+\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}}}{2 a}+\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{2 a \sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(Sqrt[1 + a*x]*(4 - 5*a*x + a^2*x^2) - 6*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(2*a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
774,1,80,118,0.0848143,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/E^(2*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-\sqrt{a^2 x^2-1}+2 \log \left(\sqrt{a^2 x^2-1}+a x\right)+\tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{\sqrt{a^2 x^2-1}}","-x \sqrt{c-\frac{c}{a^2 x^2}}-\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{\sqrt{1-a x} \sqrt{a x+1}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-Sqrt[-1 + a^2*x^2] + ArcTan[1/Sqrt[-1 + a^2*x^2]] + 2*Log[a*x + Sqrt[-1 + a^2*x^2]]))/Sqrt[-1 + a^2*x^2]","A",0
775,1,83,118,0.0668986,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x),x]","-\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1}+a x \log \left(\sqrt{a^2 x^2-1}+a x\right)+2 a x \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{\sqrt{a^2 x^2-1}}","-\sqrt{c-\frac{c}{a^2 x^2}}+\frac{a x \sqrt{c-\frac{c}{a^2 x^2}} \sin ^{-1}(a x)}{\sqrt{1-a x} \sqrt{a x+1}}+\frac{2 a x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"-((Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2] + 2*a*x*ArcTan[1/Sqrt[-1 + a^2*x^2]] + a*x*Log[a*x + Sqrt[-1 + a^2*x^2]]))/Sqrt[-1 + a^2*x^2])","A",0
776,1,78,112,0.0649174,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^2),x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left((4 a x-1) \sqrt{a^2 x^2-1}+3 a^2 x^2 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{2 x \sqrt{a^2 x^2-1}}","\frac{3}{2} a \sqrt{c-\frac{c}{a^2 x^2}}-\frac{(1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}{2 x}-\frac{3 a^2 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{2 \sqrt{1-a x} \sqrt{a x+1}}",1,"(Sqrt[c - c/(a^2*x^2)]*((-1 + 4*a*x)*Sqrt[-1 + a^2*x^2] + 3*a^2*x^2*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(2*x*Sqrt[-1 + a^2*x^2])","A",0
777,1,86,140,0.0720487,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^3),x]","-\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(\sqrt{a^2 x^2-1} \left(5 a^2 x^2-3 a x+1\right)+3 a^3 x^3 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)\right)}{3 x^2 \sqrt{a^2 x^2-1}}","-a^2 \sqrt{c-\frac{c}{a^2 x^2}}+\frac{a (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}{3 x}-\frac{(1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2}+\frac{a^3 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{\sqrt{1-a x} \sqrt{a x+1}}",1,"-1/3*(Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(1 - 3*a*x + 5*a^2*x^2) + 3*a^3*x^3*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(x^2*Sqrt[-1 + a^2*x^2])","A",0
778,1,94,156,0.0796355,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^4),x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(21 a^4 x^4 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(32 a^3 x^3-21 a^2 x^2+16 a x-6\right)\right)}{24 x^3 \sqrt{a^2 x^2-1}}","-\frac{7 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{8 x}+\frac{2 a \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 x^3}-\frac{7 a^4 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{8 \sqrt{1-a x} \sqrt{a x+1}}+\frac{4}{3} a^3 \sqrt{c-\frac{c}{a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(-6 + 16*a*x - 21*a^2*x^2 + 32*a^3*x^3) + 21*a^4*x^4*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(24*x^3*Sqrt[-1 + a^2*x^2])","A",0
779,1,102,181,0.0869503,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^5),x]","-\frac{\sqrt{c-\frac{c}{a^2 x^2}} \left(15 a^5 x^5 \tan ^{-1}\left(\frac{1}{\sqrt{a^2 x^2-1}}\right)+\sqrt{a^2 x^2-1} \left(24 a^4 x^4-15 a^3 x^3+12 a^2 x^2-10 a x+4\right)\right)}{20 x^4 \sqrt{a^2 x^2-1}}","-\frac{3 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{5 x^2}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4}+\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^3}+\frac{3 a^5 x \sqrt{c-\frac{c}{a^2 x^2}} \tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)}{4 \sqrt{1-a x} \sqrt{a x+1}}-\frac{6}{5} a^4 \sqrt{c-\frac{c}{a^2 x^2}}+\frac{3 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 x}",1,"-1/20*(Sqrt[c - c/(a^2*x^2)]*(Sqrt[-1 + a^2*x^2]*(4 - 10*a*x + 12*a^2*x^2 - 15*a^3*x^3 + 24*a^4*x^4) + 15*a^5*x^5*ArcTan[1/Sqrt[-1 + a^2*x^2]]))/(x^4*Sqrt[-1 + a^2*x^2])","A",0
780,1,70,187,0.0525419,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x^3)/E^(3*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{4 \log (a x+1)}{a^3}-\frac{4 x}{a^2}+\frac{a x^4}{4}+\frac{2 x^2}{a}-x^3\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-a^2 x^2}}+\frac{a x^5 \sqrt{c-\frac{c}{a^2 x^2}}}{4 \sqrt{1-a^2 x^2}}-\frac{x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{2 x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-a^2 x^2}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*((-4*x)/a^2 + (2*x^2)/a - x^3 + (a*x^4)/4 + (4*Log[1 + a*x])/a^3))/Sqrt[1 - a^2*x^2]","A",1
781,1,64,152,0.0473013,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x^2)/E^(3*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-\frac{4 \log (a x+1)}{a^2}+\frac{a x^3}{3}+\frac{4 x}{a}-\frac{3 x^2}{2}\right)}{\sqrt{1-a^2 x^2}}","\frac{4 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^2 \sqrt{1-a^2 x^2}}+\frac{a x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-a^2 x^2}}-\frac{3 x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*((4*x)/a - (3*x^2)/2 + (a*x^3)/3 - (4*Log[1 + a*x])/a^2))/Sqrt[1 - a^2*x^2]","A",1
782,1,54,113,0.0321373,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Integrate[(Sqrt[c - c/(a^2*x^2)]*x)/E^(3*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{a x^2}{2}+\frac{4 \log (a x+1)}{a}-3 x\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a \sqrt{1-a^2 x^2}}+\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-3*x + (a*x^2)/2 + (4*Log[1 + a*x])/a))/Sqrt[1 - a^2*x^2]","A",1
783,1,45,106,0.0272044,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/E^(3*ArcTanh[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (a x-4 \log (a x+1)+\log (x))}{\sqrt{1-a^2 x^2}}","\frac{a x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(a*x + Log[x] - 4*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
784,1,48,106,0.033704,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x),x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}} (-3 a x \log (x)+4 a x \log (a x+1)-1)}{\sqrt{1-a^2 x^2}}","-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{3 a x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{4 a x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*(-1 - 3*a*x*Log[x] + 4*a*x*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
785,1,63,147,0.0407169,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^2),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^2 \log (x)-4 a^2 \log (a x+1)+\frac{3 a}{x}-\frac{1}{2 x^2}\right)}{\sqrt{1-a^2 x^2}}","\frac{3 a \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}+\frac{4 a^2 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a^2 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/2*1/x^2 + (3*a)/x + 4*a^2*Log[x] - 4*a^2*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
786,1,73,186,0.0448422,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^3),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-4 a^3 \log (x)+4 a^3 \log (a x+1)-\frac{4 a^2}{x}+\frac{3 a}{2 x^2}-\frac{1}{3 x^3}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{3 a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \sqrt{1-a^2 x^2}}-\frac{4 a^3 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{4 a^3 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/3*1/x^3 + (3*a)/(2*x^2) - (4*a^2)/x - 4*a^3*Log[x] + 4*a^3*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
787,1,78,220,0.0536704,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^4),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(4 a^4 \log (x)-4 a^4 \log (a x+1)+\frac{4 a^3}{x}-\frac{2 a^2}{x^2}+\frac{a}{x^3}-\frac{1}{4 x^4}\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-a^2 x^2}}+\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 x^3 \sqrt{1-a^2 x^2}}+\frac{4 a^4 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}-\frac{4 a^4 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}+\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/4*1/x^4 + a/x^3 - (2*a^2)/x^2 + (4*a^3)/x + 4*a^4*Log[x] - 4*a^4*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
788,1,87,262,0.0660453,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Integrate[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^5),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(-4 a^5 \log (x)+4 a^5 \log (a x+1)-\frac{240 a^4 x^4-120 a^3 x^3+80 a^2 x^2-45 a x+12}{60 x^5}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4 \sqrt{1-a^2 x^2}}+\frac{3 a \sqrt{c-\frac{c}{a^2 x^2}}}{4 x^3 \sqrt{1-a^2 x^2}}-\frac{4 a^5 x \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{4 a^5 x \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-a^2 x^2}}-\frac{4 a^4 \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-a^2 x^2}}+\frac{2 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - c/(a^2*x^2)]*x*(-1/60*(12 - 45*a*x + 80*a^2*x^2 - 120*a^3*x^3 + 240*a^4*x^4)/x^5 - 4*a^5*Log[x] + 4*a^5*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
789,1,53,53,0.0203364,"\int e^{-2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[(c - c/(a^2*x^2))^p/E^(2*p*ArcTanh[a*x]),x]","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1(1-2 p,-2 p;2-2 p;a x)}{1-2 p}","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1(1-2 p,-2 p;2-2 p;a x)}{1-2 p}",1,"((c - c/(a^2*x^2))^p*x*Hypergeometric2F1[1 - 2*p, -2*p, 2 - 2*p, a*x])/((1 - 2*p)*(1 - a^2*x^2)^p)","A",1
790,1,54,54,0.0161312,"\int e^{2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[E^(2*p*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1(1-2 p,-2 p;2-2 p;-a x)}{1-2 p}","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1(1-2 p,-2 p;2-2 p;-a x)}{1-2 p}",1,"((c - c/(a^2*x^2))^p*x*Hypergeometric2F1[1 - 2*p, -2*p, 2 - 2*p, -(a*x)])/((1 - 2*p)*(1 - a^2*x^2)^p)","A",1
791,1,229,331,0.8534265,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{c^2 e^{n \tanh ^{-1}(a x)} \left(a^3 \left(n^2-10\right) n x^3 e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;e^{2 \tanh ^{-1}(a x)}\right)+a^3 \left(n^3+2 n^2-10 n-20\right) x^3 \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;e^{2 \tanh ^{-1}(a x)}\right)-24 a^3 x^3 e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)-a^3 n^2 x^3-2 a^3 n x^3+a^2 n^3 x^2+2 a^2 n^2 x^2-12 a^2 n x^2-24 a^2 x^2+a n^2 x+2 a n x+2 n+4\right)}{6 a^4 (n+2) x^3}","-\frac{c^2 (a x+1)^{\frac{n-4}{2}} (1-a x)^{3-\frac{n}{2}}}{3 a^4 x^3}-\frac{c^2 (n+10) (a x+1)^{\frac{n-4}{2}} (1-a x)^{3-\frac{n}{2}}}{6 a^3 x^2}-\frac{c^2 \left(n^2+5 n+14\right) (a x+1)^{\frac{n-4}{2}} (1-a x)^{3-\frac{n}{2}}}{6 a^2 x}-\frac{c^2 n \left(10-n^2\right) (a x+1)^{\frac{n-4}{2}} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(1,\frac{n-4}{2};\frac{n-2}{2};\frac{a x+1}{1-a x}\right)}{3 a (4-n)}+\frac{c^2 2^{\frac{n}{2}-1} n (1-a x)^{3-\frac{n}{2}} \, _2F_1\left(\frac{4-n}{2},3-\frac{n}{2};4-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a \left(n^2-10 n+24\right)}-\frac{4 c^2 (a x+1)^{\frac{n-4}{2}} (1-a x)^{3-\frac{n}{2}}}{a (4-n)}",1,"-1/6*(c^2*E^(n*ArcTanh[a*x])*(4 + 2*n + 2*a*n*x + a*n^2*x - 24*a^2*x^2 - 12*a^2*n*x^2 + 2*a^2*n^2*x^2 + a^2*n^3*x^2 - 2*a^3*n*x^3 - a^3*n^2*x^3 + a^3*E^(2*ArcTanh[a*x])*n*(-10 + n^2)*x^3*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, E^(2*ArcTanh[a*x])] + a^3*(-20 - 10*n + 2*n^2 + n^3)*x^3*Hypergeometric2F1[1, n/2, 1 + n/2, E^(2*ArcTanh[a*x])] - 24*a^3*E^(2*ArcTanh[a*x])*x^3*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])]))/(a^4*(2 + n)*x^3)","A",0
792,1,126,137,0.2245535,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2)),x]","\frac{c e^{n \tanh ^{-1}(a x)} \left(a n x e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;e^{2 \tanh ^{-1}(a x)}\right)+a (n+2) x \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;e^{2 \tanh ^{-1}(a x)}\right)+4 a x e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+n+2\right)}{a^2 (n+2) x}","\frac{4 c (1-a x)^{1-\frac{n}{2}} (a x+1)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{a (2-n)}-\frac{c 2^{\frac{n}{2}+1} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (2-n)}",1,"(c*E^(n*ArcTanh[a*x])*(2 + n + a*E^(2*ArcTanh[a*x])*n*x*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, E^(2*ArcTanh[a*x])] + a*(2 + n)*x*Hypergeometric2F1[1, n/2, 1 + n/2, E^(2*ArcTanh[a*x])] + 4*a*E^(2*ArcTanh[a*x])*x*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])]))/(a^2*(2 + n)*x)","A",0
793,1,82,125,0.1060207,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2)),x]","\frac{(1-a x)^{-n/2} \left((a x+1)^{n/2} (a n x+n-1)-2^{\frac{n}{2}+1} n \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{a c n}","-\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a c}+\frac{x (a x+1)^{n/2} (1-a x)^{-n/2}}{c}-\frac{(1-n) (a x+1)^{n/2} (1-a x)^{-n/2}}{a c n}",1,"((1 + a*x)^(n/2)*(-1 + n + a*n*x) - 2^(1 + n/2)*n*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a*x)/2])/(a*c*n*(1 - a*x)^(n/2))","A",1
794,1,178,373,0.1593976,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","-\frac{(1-a x)^{-\frac{n}{2}-1} \left((a x+1)^{n/2} \left(n^2 \left(1-2 a^2 x^2\right)+6 a^2 x^2+n \left(-4 a^3 x^3+4 a^2 x^2+6 a x-4\right)+n^3 (a x-1)^2 (a x+1)-6\right)-2^{n/2} n^2 (n+2) (a x-1)^2 (a x+1) \, _2F_1\left(1-\frac{n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{a c^2 (n-2) n (n+2) (a x+1)}","-\frac{a^2 x^3 (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{c^2}-\frac{2^{n/2} n (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(\frac{2-n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a c^2 (2-n)}-\frac{(n+3) \left(2-n^2\right) (a x+1)^{n/2} (1-a x)^{-\frac{n}{2}-1}}{a c^2 \left(4-n^2\right)}-\frac{(n+3) \left(2-n^2\right) (a x+1)^{n/2} (1-a x)^{-n/2}}{a c^2 n \left(4-n^2\right)}+\frac{(1-n) (n+3) (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a c^2 (2-n)}+\frac{(n+3) x (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{c^2}+\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}}}{a c^2 (2-n)}-\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{-n/2}}{a c^2}",1,"-(((1 - a*x)^(-1 - n/2)*((1 + a*x)^(n/2)*(-6 + 6*a^2*x^2 + n^3*(-1 + a*x)^2*(1 + a*x) + n^2*(1 - 2*a^2*x^2) + n*(-4 + 6*a*x + 4*a^2*x^2 - 4*a^3*x^3)) - 2^(n/2)*n^2*(2 + n)*(-1 + a*x)^2*(1 + a*x)*Hypergeometric2F1[1 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2]))/(a*c^2*(-2 + n)*n*(2 + n)*(1 + a*x)))","A",1
795,1,190,430,1.6863655,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2),x]","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}} e^{n \tanh ^{-1}(a x)} \text{csch}\left(\frac{1}{2} \tanh ^{-1}(a x)\right) \text{sech}\left(\frac{1}{2} \tanh ^{-1}(a x)\right) \left(-(n+1) \text{csch}\left(\frac{1}{2} \tanh ^{-1}(a x)\right) \text{sech}\left(\frac{1}{2} \tanh ^{-1}(a x)\right) \left(\left(1-a^2 x^2\right) \cosh \left(2 \tanh ^{-1}(a x)\right)+a x (a x+n)\right)-4 a \left(n^2-3\right) x e^{\tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};e^{2 \tanh ^{-1}(a x)}\right)+8 a n x e^{\tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-e^{2 \tanh ^{-1}(a x)}\right)\right)}{8 (n+1) \left(a^2 x^2-1\right)}","-\frac{a^2 \left(3-n^2\right) x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{n-3}{2};\frac{n-1}{2};\frac{a x+1}{1-a x}\right)}{(3-n) \left(1-a^2 x^2\right)^{3/2}}+\frac{a^2 2^{\frac{n-1}{2}} n x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} (1-a x)^{\frac{5-n}{2}} \, _2F_1\left(\frac{3-n}{2},\frac{5-n}{2};\frac{7-n}{2};\frac{1}{2} (1-a x)\right)}{(3-n) (5-n) \left(1-a^2 x^2\right)^{3/2}}-\frac{a (n+4) x^2 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{5-n}{2}}}{2 \left(1-a^2 x^2\right)^{3/2}}-\frac{x \left(c-\frac{c}{a^2 x^2}\right)^{3/2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{5-n}{2}}}{2 \left(1-a^2 x^2\right)^{3/2}}-\frac{3 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{5-n}{2}}}{(3-n) \left(1-a^2 x^2\right)^{3/2}}",1,"(c*E^(n*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x*Csch[ArcTanh[a*x]/2]*Sech[ArcTanh[a*x]/2]*(8*a*E^ArcTanh[a*x]*n*x*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -E^(2*ArcTanh[a*x])] - 4*a*E^ArcTanh[a*x]*(-3 + n^2)*x*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, E^(2*ArcTanh[a*x])] - (1 + n)*(a*x*(n + a*x) + (1 - a^2*x^2)*Cosh[2*ArcTanh[a*x]])*Csch[ArcTanh[a*x]/2]*Sech[ArcTanh[a*x]/2]))/(8*(1 + n)*(-1 + a^2*x^2))","A",1
796,1,208,272,0.173074,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Integrate[E^(n*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} (1-a x)^{\frac{1}{2} (-n-1)} \left((n-1) (a x+1)^{\frac{n+1}{2}} \, _2F_1\left(1,-\frac{n}{2}-\frac{1}{2};\frac{1}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)+2^{\frac{n+1}{2}} \left((n+1) (a x-1) \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)-(n-1) \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},-\frac{n}{2}-\frac{1}{2};\frac{1}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)\right)\right)}{\left(n^2-1\right) \sqrt{1-a^2 x^2}}","\frac{2^{\frac{n+1}{2}} n x \sqrt{c-\frac{c}{a^2 x^2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{\left(n^2-4 n+3\right) \sqrt{1-a^2 x^2}}+\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{(1-n) \sqrt{1-a^2 x^2}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{3-n}{2}}}{(1-n) \sqrt{1-a^2 x^2}}",1,"(2*Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x)^((-1 - n)/2)*((-1 + n)*(1 + a*x)^((1 + n)/2)*Hypergeometric2F1[1, -1/2 - n/2, 1/2 - n/2, (1 - a*x)/(1 + a*x)] + 2^((1 + n)/2)*(-((-1 + n)*Hypergeometric2F1[-1/2 - n/2, -1/2 - n/2, 1/2 - n/2, 1/2 - (a*x)/2]) + (1 + n)*(-1 + a*x)*Hypergeometric2F1[-1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2])))/((-1 + n^2)*Sqrt[1 - a^2*x^2])","A",0
797,1,130,182,0.1051694,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Integrate[E^(n*ArcTanh[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} \left(2^{\frac{n+3}{2}} n \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)-(n-1) (a x+1)^{\frac{n+1}{2}}\right)}{a^2 (n-1) (n+1) x \sqrt{c-\frac{c}{a^2 x^2}}}","-\frac{2^{\frac{n+3}{2}} n \sqrt{1-a^2 x^2} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{1-n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a^2 \left(1-n^2\right) x \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{a^2 (n+1) x \sqrt{c-\frac{c}{a^2 x^2}}}",1,"((1 - a*x)^(1/2 - n/2)*Sqrt[1 - a^2*x^2]*(-((-1 + n)*(1 + a*x)^((1 + n)/2)) + 2^((3 + n)/2)*n*Hypergeometric2F1[-1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2]))/(a^2*(-1 + n)*(1 + n)*Sqrt[c - c/(a^2*x^2)]*x)","A",1
798,1,186,267,0.2503806,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2))^(3/2),x]","\frac{\left(1-a^2 x^2\right)^{3/2} (1-a x)^{\frac{1}{2} (-n-1)} \left(-4 a^4 x^2 (a x+1)^{\frac{n-1}{2}}+\frac{a^2 2^{\frac{n+3}{2}} n (a x-1)^2 \, _2F_1\left(\frac{3}{2}-\frac{n}{2},\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{n-3}+\frac{4 a^2 \left(n^2 (2 a x-1)+n (3 a x-2)-2\right) (a x+1)^{\frac{n-1}{2}}}{n^2-1}\right)}{4 a^6 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}","-\frac{\left(1-a^2 x^2\right)^{3/2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}-\frac{2^{\frac{n-1}{2}} n \left(1-a^2 x^2\right)^{3/2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{3-n}{2},\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{a^4 (3-n) x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}+\frac{\left(1-a^2 x^2\right)^{3/2} (a x+1)^{\frac{n-1}{2}} \left(-a (2 n+3) n x+n^2+2 n+2\right) (1-a x)^{\frac{1}{2} (-n-1)}}{a^4 \left(1-n^2\right) x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2}}",1,"((1 - a*x)^((-1 - n)/2)*(1 - a^2*x^2)^(3/2)*(-4*a^4*x^2*(1 + a*x)^((-1 + n)/2) + (4*a^2*(1 + a*x)^((-1 + n)/2)*(-2 + n^2*(-1 + 2*a*x) + n*(-2 + 3*a*x)))/(-1 + n^2) + (2^((3 + n)/2)*a^2*n*(-1 + a*x)^2*Hypergeometric2F1[3/2 - n/2, 3/2 - n/2, 5/2 - n/2, 1/2 - (a*x)/2])/(-3 + n)))/(4*a^6*(c - c/(a^2*x^2))^(3/2)*x^3)","A",1
799,1,227,1039,6.3229312,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2))^(5/2),x]","\frac{\left(a^2 x^2-1\right)^2 \left(-\frac{4 \left(a^2 x^2-1\right) \left(\frac{2 n e^{(n+1) \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-e^{2 \tanh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-(n+1) e^{n \tanh ^{-1}(a x)}\right)}{n+1}-\frac{e^{n \tanh ^{-1}(a x)} \left(3 \left(n^2-1\right) \sqrt{1-a^2 x^2} \cosh \left(3 \tanh ^{-1}(a x)\right)-2 a n^3 x-2 a \left(n^2-1\right) n x \cosh \left(2 \tanh ^{-1}(a x)\right)+10 a n x+n^2-9\right)}{n^4-10 n^2+9}-\frac{8 (a n x-1) e^{n \tanh ^{-1}(a x)}}{n^2-1}\right)}{4 a^6 x^5 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}","-\frac{(a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-3)}}{a^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x}+\frac{(n+4) (a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-3)}}{a^3 (n+3) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^2}-\frac{3 (n+4) (a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-1)}}{a^5 (n+3) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^4}+\frac{n (a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-1)}}{a^6 (n+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}-\frac{3 (2-n) (n+4) (a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-1)}}{a^6 \left(9-n^2\right) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}+\frac{3 (n+4) \left(-n^2+2 n+1\right) (a x+1)^{\frac{n-1}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-1)}}{a^6 (3-n) (n+1) (n+3) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}-\frac{3 n (a x+1)^{\frac{n-1}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-1)}}{a^6 (n+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}+\frac{3 n (a x+1)^{\frac{n+1}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1}{2} (-n-1)}}{a^6 (n+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}-\frac{2^{\frac{n+3}{2}} n \left(1-a^2 x^2\right)^{5/2} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{1}{2} (-n-1);\frac{1-n}{2};\frac{1}{2} (1-a x)\right) (1-a x)^{\frac{1}{2} (-n-1)}}{a^6 (n+1) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}-\frac{2 n (a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1-n}{2}}}{a^6 \left(1-n^2\right) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}+\frac{3 n (a x+1)^{\frac{n-1}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1-n}{2}}}{a^6 \left(1-n^2\right) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}-\frac{3 (n+4) \left(-n^2+2 n+1\right) (a x+1)^{\frac{n-1}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{1-n}{2}}}{a^6 \left(n^4-10 n^2+9\right) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}+\frac{2 n (a x+1)^{\frac{n-3}{2}} \left(1-a^2 x^2\right)^{5/2} (1-a x)^{\frac{3-n}{2}}}{a^6 (n+1) \left(n^2-4 n+3\right) \left(c-\frac{c}{a^2 x^2}\right)^{5/2} x^5}",1,"((-1 + a^2*x^2)^2*((-8*E^(n*ArcTanh[a*x])*(-1 + a*n*x))/(-1 + n^2) - (E^(n*ArcTanh[a*x])*(-9 + n^2 + 10*a*n*x - 2*a*n^3*x - 2*a*n*(-1 + n^2)*x*Cosh[2*ArcTanh[a*x]] + 3*(-1 + n^2)*Sqrt[1 - a^2*x^2]*Cosh[3*ArcTanh[a*x]]))/(9 - 10*n^2 + n^4) - (4*(-1 + a^2*x^2)*(-(E^(n*ArcTanh[a*x])*(1 + n)) + (2*E^((1 + n)*ArcTanh[a*x])*n*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -E^(2*ArcTanh[a*x])])/Sqrt[1 - a^2*x^2]))/(1 + n)))/(4*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",0
800,0,0,72,0.3873969,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p F_1\left(1-2 p;\frac{1}{2} (n-2 p),-\frac{n}{2}-p;2-2 p;a x,-a x\right)}{1-2 p}",1,"Integrate[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2))^p, x]","F",-1
801,1,217,339,0.2099189,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","-\frac{x (1-a x)^{-p} \left(-\left(a^2 x^2-1\right)^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(-4 (a x+1) (a x-1)^p \left(1-a^2 x^2\right)^p F_1(1-2 p;1-p,-p;2-2 p;a x,-a x)+4 (a x-1)^p (a x+1)^{2 p} \left(1-a^2 x^2\right)^p \, _2F_1\left(1-2 p,2-p;2-2 p;\frac{2 a x}{a x+1}\right)+(a x+1) (1-a x)^p \left(a^2 x^2-1\right)^p \, _2F_1\left(\frac{1}{2}-p,-p;\frac{3}{2}-p;a^2 x^2\right)\right)}{(2 p-1) (a x+1)}","\frac{x (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (1-2 p),2-p;\frac{1}{2} (3-2 p);a^2 x^2\right)}{1-2 p}+\frac{6 a^2 x^3 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (3-2 p),2-p;\frac{1}{2} (5-2 p);a^2 x^2\right)}{3-2 p}+\frac{2 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^p}{(1-p) (1-a x) (a x+1)}+\frac{a^4 x^5 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (5-2 p),2-p;\frac{1}{2} (7-2 p);a^2 x^2\right)}{5-2 p}+\frac{2 a^3 x^4 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(2-p,2-p;3-p;a^2 x^2\right)}{2-p}",1,"-(((c - c/(a^2*x^2))^p*x*(-4*(-1 + a*x)^p*(1 + a*x)*(1 - a^2*x^2)^p*AppellF1[1 - 2*p, 1 - p, -p, 2 - 2*p, a*x, -(a*x)] + 4*(-1 + a*x)^p*(1 + a*x)^(2*p)*(1 - a^2*x^2)^p*Hypergeometric2F1[1 - 2*p, 2 - p, 2 - 2*p, (2*a*x)/(1 + a*x)] + (1 - a*x)^p*(1 + a*x)*(-1 + a^2*x^2)^p*Hypergeometric2F1[1/2 - p, -p, 3/2 - p, a^2*x^2]))/((-1 + 2*p)*(1 - a*x)^p*(1 + a*x)*(-(-1 + a^2*x^2)^2)^p))","C",0
802,1,175,217,0.1633643,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\frac{1}{2} x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(-\frac{3 a x \, _2F_1\left(1-p,\frac{3}{2}-p;2-p;a^2 x^2\right)}{p-1}+\frac{6 a^2 x^2 \, _2F_1\left(\frac{3}{2}-p,\frac{3}{2}-p;\frac{5}{2}-p;a^2 x^2\right)}{3-2 p}+\frac{2 \left(1-a^2 x^2\right)^{p-\frac{1}{2}}}{1-2 p}+\frac{a^3 x^3 \, _2F_1\left(\frac{3}{2}-p,2-p;3-p;a^2 x^2\right)}{2-p}\right)","\frac{a (5-2 p) x^2 \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(1-p,\frac{3}{2}-p;2-p;a^2 x^2\right)}{2 (1-p)}+\frac{3 a^2 x^3 \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (3-2 p),\frac{3}{2}-p;\frac{1}{2} (5-2 p);a^2 x^2\right)}{3-2 p}-\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^p}{\sqrt{1-a^2 x^2}}+\frac{x \left(c-\frac{c}{a^2 x^2}\right)^p}{(1-2 p) \sqrt{1-a^2 x^2}}",1,"((c - c/(a^2*x^2))^p*x*((2*(1 - a^2*x^2)^(-1/2 + p))/(1 - 2*p) - (3*a*x*Hypergeometric2F1[1 - p, 3/2 - p, 2 - p, a^2*x^2])/(-1 + p) + (6*a^2*x^2*Hypergeometric2F1[3/2 - p, 3/2 - p, 5/2 - p, a^2*x^2])/(3 - 2*p) + (a^3*x^3*Hypergeometric2F1[3/2 - p, 2 - p, 3 - p, a^2*x^2])/(2 - p)))/(2*(1 - a^2*x^2)^p)","A",0
803,1,142,217,0.1082986,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\frac{x (1-a x)^{-p} \left(-\left(a^2 x^2-1\right)^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left((1-a x)^p \left(a^2 x^2-1\right)^p \, _2F_1\left(\frac{1}{2}-p,-p;\frac{3}{2}-p;a^2 x^2\right)-2 (a x-1)^p \left(1-a^2 x^2\right)^p F_1(1-2 p;1-p,-p;2-2 p;a x,-a x)\right)}{2 p-1}","\frac{x (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (1-2 p),1-p;\frac{1}{2} (3-2 p);a^2 x^2\right)}{1-2 p}+\frac{a x^2 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(1-p,1-p;2-p;a^2 x^2\right)}{1-p}+\frac{a^2 x^3 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (3-2 p),1-p;\frac{1}{2} (5-2 p);a^2 x^2\right)}{3-2 p}",1,"((c - c/(a^2*x^2))^p*x*(-2*(-1 + a*x)^p*(1 - a^2*x^2)^p*AppellF1[1 - 2*p, 1 - p, -p, 2 - 2*p, a*x, -(a*x)] + (1 - a*x)^p*(-1 + a^2*x^2)^p*Hypergeometric2F1[1/2 - p, -p, 3/2 - p, a^2*x^2]))/((-1 + 2*p)*(1 - a*x)^p*(-(-1 + a^2*x^2)^2)^p)","C",0
804,1,112,137,0.0432068,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^p,x]","-\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(2 (p-1) \, _2F_1\left(\frac{1}{2}-p,\frac{1}{2}-p;\frac{3}{2}-p;a^2 x^2\right)+a (2 p-1) x \, _2F_1\left(\frac{1}{2}-p,1-p;2-p;a^2 x^2\right)\right)}{2 (p-1) (2 p-1)}","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (1-2 p),\frac{1}{2}-p;\frac{1}{2} (3-2 p);a^2 x^2\right)}{1-2 p}+\frac{a x^2 \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2}-p,1-p;2-p;a^2 x^2\right)}{2 (1-p)}",1,"-1/2*((c - c/(a^2*x^2))^p*x*(2*(-1 + p)*Hypergeometric2F1[1/2 - p, 1/2 - p, 3/2 - p, a^2*x^2] + a*(-1 + 2*p)*x*Hypergeometric2F1[1/2 - p, 1 - p, 2 - p, a^2*x^2]))/((-1 + p)*(-1 + 2*p)*(1 - a^2*x^2)^p)","A",1
805,1,112,137,0.0300095,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[(c - c/(a^2*x^2))^p/E^ArcTanh[a*x],x]","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(a (2 p-1) x \, _2F_1\left(\frac{1}{2}-p,1-p;2-p;a^2 x^2\right)-2 (p-1) \, _2F_1\left(\frac{1}{2}-p,\frac{1}{2}-p;\frac{3}{2}-p;a^2 x^2\right)\right)}{2 (p-1) (2 p-1)}","\frac{x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (1-2 p),\frac{1}{2}-p;\frac{1}{2} (3-2 p);a^2 x^2\right)}{1-2 p}-\frac{a x^2 \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2}-p,1-p;2-p;a^2 x^2\right)}{2 (1-p)}",1,"((c - c/(a^2*x^2))^p*x*(-2*(-1 + p)*Hypergeometric2F1[1/2 - p, 1/2 - p, 3/2 - p, a^2*x^2] + a*(-1 + 2*p)*x*Hypergeometric2F1[1/2 - p, 1 - p, 2 - p, a^2*x^2]))/(2*(-1 + p)*(-1 + 2*p)*(1 - a^2*x^2)^p)","A",1
806,1,142,218,0.1058835,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[(c - c/(a^2*x^2))^p/E^(2*ArcTanh[a*x]),x]","\frac{x (1-a x)^{-p} \left(-\left(a^2 x^2-1\right)^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left((1-a x)^p \left(a^2 x^2-1\right)^p \, _2F_1\left(\frac{1}{2}-p,-p;\frac{3}{2}-p;a^2 x^2\right)-2 (a x-1)^p \left(1-a^2 x^2\right)^p F_1(1-2 p;-p,1-p;2-2 p;a x,-a x)\right)}{2 p-1}","\frac{x (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (1-2 p),1-p;\frac{1}{2} (3-2 p);a^2 x^2\right)}{1-2 p}-\frac{a x^2 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(1-p,1-p;2-p;a^2 x^2\right)}{1-p}+\frac{a^2 x^3 (1-a x)^{-p} (a x+1)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (3-2 p),1-p;\frac{1}{2} (5-2 p);a^2 x^2\right)}{3-2 p}",1,"((c - c/(a^2*x^2))^p*x*(-2*(-1 + a*x)^p*(1 - a^2*x^2)^p*AppellF1[1 - 2*p, -p, 1 - p, 2 - 2*p, a*x, -(a*x)] + (1 - a*x)^p*(-1 + a^2*x^2)^p*Hypergeometric2F1[1/2 - p, -p, 3/2 - p, a^2*x^2]))/((-1 + 2*p)*(1 - a*x)^p*(-(-1 + a^2*x^2)^2)^p)","C",0
807,1,173,216,0.1415771,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Integrate[(c - c/(a^2*x^2))^p/E^(3*ArcTanh[a*x]),x]","\frac{1}{2} x \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(\frac{3 a x \, _2F_1\left(1-p,\frac{3}{2}-p;2-p;a^2 x^2\right)}{p-1}+\frac{6 a^2 x^2 \, _2F_1\left(\frac{3}{2}-p,\frac{3}{2}-p;\frac{5}{2}-p;a^2 x^2\right)}{3-2 p}+\frac{2 \left(1-a^2 x^2\right)^{p-\frac{1}{2}}}{1-2 p}+\frac{a^3 x^3 \, _2F_1\left(\frac{3}{2}-p,2-p;3-p;a^2 x^2\right)}{p-2}\right)","-\frac{a (5-2 p) x^2 \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(1-p,\frac{3}{2}-p;2-p;a^2 x^2\right)}{2 (1-p)}+\frac{3 a^2 x^3 \left(1-a^2 x^2\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(\frac{1}{2} (3-2 p),\frac{3}{2}-p;\frac{1}{2} (5-2 p);a^2 x^2\right)}{3-2 p}+\frac{a x^2 \left(c-\frac{c}{a^2 x^2}\right)^p}{\sqrt{1-a^2 x^2}}+\frac{x \left(c-\frac{c}{a^2 x^2}\right)^p}{(1-2 p) \sqrt{1-a^2 x^2}}",1,"((c - c/(a^2*x^2))^p*x*((2*(1 - a^2*x^2)^(-1/2 + p))/(1 - 2*p) + (3*a*x*Hypergeometric2F1[1 - p, 3/2 - p, 2 - p, a^2*x^2])/(-1 + p) + (6*a^2*x^2*Hypergeometric2F1[3/2 - p, 3/2 - p, 5/2 - p, a^2*x^2])/(3 - 2*p) + (a^3*x^3*Hypergeometric2F1[3/2 - p, 2 - p, 3 - p, a^2*x^2])/(-2 + p)))/(2*(1 - a^2*x^2)^p)","A",0
808,1,184,240,9.2692511,"\int e^{\tanh ^{-1}(x)} x \sqrt{1+x} \sin (x) \, dx","Integrate[E^ArcTanh[x]*x*Sqrt[1 + x]*Sin[x],x]","-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt{x+1} \left((\cos (x+1)-i \sin (x+1)) \left((2+2 i) \left(2 x^2+(2-3 i) x-(4-3 i)\right) (\cos (1)+i \sin (1))-(6+5 i) \sqrt{2 \pi } \sqrt{x-1} \text{erf}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\cos (x)+i \sin (x))\right)+(-6+5 i) \sqrt{2 \pi } \sqrt{x-1} \text{erfi}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\cos (1)+i \sin (1))+(2+2 i) \left(2 x^2+(2+3 i) x-(4+3 i)\right) (\cos (x)+i \sin (x))\right)}{\sqrt{1-x^2}}","-2 \sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-3 \sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-3 \sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+2 \sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\frac{3}{2} \sqrt{\frac{\pi }{2}} \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\frac{3}{2} \sqrt{1-x} \sin (x)+(1-x)^{3/2} (-\cos (x))+3 \sqrt{1-x} \cos (x)",1,"((-1/16 + I/16)*Sqrt[1 + x]*((-6 + 5*I)*Sqrt[2*Pi]*Sqrt[-1 + x]*Erfi[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*(Cos[1] + I*Sin[1]) + (2 + 2*I)*((-4 - 3*I) + (2 + 3*I)*x + 2*x^2)*(Cos[x] + I*Sin[x]) + ((2 + 2*I)*((-4 + 3*I) + (2 - 3*I)*x + 2*x^2)*(Cos[1] + I*Sin[1]) - (6 + 5*I)*Sqrt[2*Pi]*Sqrt[-1 + x]*Erf[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*(Cos[x] + I*Sin[x]))*(Cos[1 + x] - I*Sin[1 + x])))/Sqrt[1 - x^2]","C",0
809,1,134,141,8.4152914,"\int e^{\tanh ^{-1}(x)} \sqrt{1+x} \sin (x) \, dx","Integrate[E^ArcTanh[x]*Sqrt[1 + x]*Sin[x],x]","\left(\frac{1}{8}+\frac{i}{8}\right) \left(\frac{e^{-i x} \sqrt{1-x^2} \left((4+i) \sqrt{2 \pi } e^{i (x+1)} \text{erfi}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right)+(2-2 i) \sqrt{x-1} \left(1+e^{2 i x}\right)\right)}{\sqrt{x-1} \sqrt{x+1}}-(4-i) e^{-i} \sqrt{2 \pi } \text{erfi}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{2-2 x}\right)\right)","-2 \sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+2 \sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\sqrt{1-x} \cos (x)",1,"(1/8 + I/8)*(((-4 + I)*Sqrt[2*Pi]*Erfi[(1/2 + I/2)*Sqrt[2 - 2*x]])/E^I + (Sqrt[1 - x^2]*((2 - 2*I)*(1 + E^((2*I)*x))*Sqrt[-1 + x] + (4 + I)*E^(I*(1 + x))*Sqrt[2*Pi]*Erfi[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]))/(E^(I*x)*Sqrt[-1 + x]*Sqrt[1 + x]))","C",0
810,1,168,163,8.6764624,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} x \sin (x) \, dx","Integrate[E^ArcTanh[x]*Sqrt[1 - x]*x*Sin[x],x]","\frac{\left(\frac{1}{16}+\frac{i}{16}\right) e^{-i (x+1)} \sqrt{1-x} \left(e^i \left((3-2 i) \sqrt{2 \pi } e^{i (x+1)} \sqrt{-x-1} \text{erfi}\left(\frac{(1+i) \sqrt{-x-1}}{\sqrt{2}}\right)+(2+2 i) \left(e^{2 i x} (-3+2 i x)+2 i x+3\right) (x+1)\right)-(3+2 i) \sqrt{2 \pi } e^{i x} \sqrt{-x-1} \text{erf}\left(\frac{(1+i) \sqrt{-x-1}}{\sqrt{2}}\right)\right)}{\sqrt{1-x^2}}","\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\frac{3}{2} \sqrt{\frac{\pi }{2}} \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\frac{3}{2} \sqrt{x+1} \sin (x)+(x+1)^{3/2} (-\cos (x))+\sqrt{x+1} \cos (x)",1,"((1/16 + I/16)*Sqrt[1 - x]*((-3 - 2*I)*E^(I*x)*Sqrt[2*Pi]*Sqrt[-1 - x]*Erf[((1 + I)*Sqrt[-1 - x])/Sqrt[2]] + E^I*((2 + 2*I)*(3 + E^((2*I)*x)*(-3 + (2*I)*x) + (2*I)*x)*(1 + x) + (3 - 2*I)*E^(I*(1 + x))*Sqrt[2*Pi]*Sqrt[-1 - x]*Erfi[((1 + I)*Sqrt[-1 - x])/Sqrt[2]])))/(E^(I*(1 + x))*Sqrt[1 - x^2])","C",0
811,1,77,72,0.0248943,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} \sin (x) \, dx","Integrate[E^ArcTanh[x]*Sqrt[1 - x]*Sin[x],x]","-\frac{e^{-i} \sqrt{x+1} \Gamma \left(\frac{3}{2},-i (x+1)\right)}{2 \sqrt{-i (x+1)}}-\frac{e^i \sqrt{x+1} \Gamma \left(\frac{3}{2},i (x+1)\right)}{2 \sqrt{i (x+1)}}","\sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{x+1} \cos (x)",1,"-1/2*(Sqrt[1 + x]*Gamma[3/2, (-I)*(1 + x)])/(E^I*Sqrt[(-I)*(1 + x)]) - (E^I*Sqrt[1 + x]*Gamma[3/2, I*(1 + x)])/(2*Sqrt[I*(1 + x)])","C",0
812,1,200,335,9.7701184,"\int e^{\tanh ^{-1}(x)} x (1+x)^{3/2} \sin (x) \, dx","Integrate[E^ArcTanh[x]*x*(1 + x)^(3/2)*Sin[x],x]","\frac{\left(\frac{1}{32}+\frac{i}{32}\right) \sqrt{x+1} \left((\cos (x+1)-i \sin (x+1)) \left((17+2 i) \sqrt{2 \pi } \sqrt{x-1} \text{erf}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\sin (x)-i \cos (x))+(2+2 i) \left(4 i x^3+(10+8 i) x^2+(10-11 i) x-(20+i)\right) (\cos (1)+i \sin (1))\right)+(-2-17 i) \sqrt{2 \pi } \sqrt{x-1} \text{erfi}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\cos (1)+i \sin (1))-(2-2 i) \left(4 x^3+(8+10 i) x^2-(11-10 i) x-(1+20 i)\right) (\cos (x)+i \sin (x))\right)}{\sqrt{1-x^2}}","-4 \sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{2} \sqrt{\frac{\pi }{2}} \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-4 \sqrt{2 \pi } \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{4} \sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-4 \sqrt{2 \pi } \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{4} \sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+4 \sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\frac{15}{2} \sqrt{\frac{\pi }{2}} \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{5}{2} (1-x)^{3/2} \sin (x)-\frac{15}{2} \sqrt{1-x} \sin (x)+(1-x)^{5/2} \cos (x)-5 (1-x)^{3/2} \cos (x)+\frac{17}{4} \sqrt{1-x} \cos (x)",1,"((1/32 + I/32)*Sqrt[1 + x]*((-2 - 17*I)*Sqrt[2*Pi]*Sqrt[-1 + x]*Erfi[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*(Cos[1] + I*Sin[1]) - (2 - 2*I)*((-1 - 20*I) - (11 - 10*I)*x + (8 + 10*I)*x^2 + 4*x^3)*(Cos[x] + I*Sin[x]) + ((2 + 2*I)*((-20 - I) + (10 - 11*I)*x + (10 + 8*I)*x^2 + (4*I)*x^3)*(Cos[1] + I*Sin[1]) + (17 + 2*I)*Sqrt[2*Pi]*Sqrt[-1 + x]*Erf[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*((-I)*Cos[x] + Sin[x]))*(Cos[1 + x] - I*Sin[1 + x])))/Sqrt[1 - x^2]","C",0
813,1,178,236,8.6897079,"\int e^{\tanh ^{-1}(x)} (1+x)^{3/2} \sin (x) \, dx","Integrate[E^ArcTanh[x]*(1 + x)^(3/2)*Sin[x],x]","\frac{i \sqrt{1-x^2} \left(-(\cos (x+1)-i \sin (x+1)) \left((21+5 i) \sqrt{\frac{\pi }{2}} \text{erf}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\sin (x)-i \cos (x))+2 \sqrt{x-1} (2 i x+(3+6 i)) (\cos (1)+i \sin (1))\right)+(5+21 i) \sqrt{\frac{\pi }{2}} \text{erfi}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\sin (1)-i \cos (1))+2 \sqrt{x-1} (2 x+(6+3 i)) (\sin (x)-i \cos (x))\right)}{8 \sqrt{x-1} \sqrt{x+1}}","-4 \sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-2 \sqrt{2 \pi } \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-2 \sqrt{2 \pi } \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+4 \sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\frac{3}{2} \sqrt{\frac{\pi }{2}} \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\frac{3}{2} \sqrt{1-x} \sin (x)+(1-x)^{3/2} (-\cos (x))+4 \sqrt{1-x} \cos (x)",1,"((I/8)*Sqrt[1 - x^2]*((5 + 21*I)*Sqrt[Pi/2]*Erfi[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*((-I)*Cos[1] + Sin[1]) + 2*Sqrt[-1 + x]*((6 + 3*I) + 2*x)*((-I)*Cos[x] + Sin[x]) - (2*((3 + 6*I) + (2*I)*x)*Sqrt[-1 + x]*(Cos[1] + I*Sin[1]) + (21 + 5*I)*Sqrt[Pi/2]*Erf[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*((-I)*Cos[x] + Sin[x]))*(Cos[1 + x] - I*Sin[1 + x])))/(Sqrt[-1 + x]*Sqrt[1 + x])","C",0
814,1,193,193,8.5945138,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} x \sin (x) \, dx","Integrate[E^ArcTanh[x]*(1 - x)^(3/2)*x*Sin[x],x]","\frac{\left(\frac{1}{32}+\frac{i}{32}\right) \sqrt{1-x} \left((\cos (1)-i \sin (1)) \left((2+2 i) \left(-4 i x^3+10 x^2+(2+19 i) x-(8-15 i)\right) (\cos (x+1)+i \sin (x+1))-(18-7 i) \sqrt{2 \pi } \sqrt{-x-1} \text{erf}\left(\frac{(1+i) \sqrt{-x-1}}{\sqrt{2}}\right)\right)+(18+7 i) e^i \sqrt{2 \pi } \sqrt{-x-1} \text{erfi}\left(\frac{(1+i) \sqrt{-x-1}}{\sqrt{2}}\right)+(2+2 i) e^{-i x} \left(-4 i x^3-10 x^2-(2-19 i) x+(8+15 i)\right)\right)}{\sqrt{1-x^2}}","\frac{9}{2} \sqrt{\frac{\pi }{2}} \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\frac{7}{4} \sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\frac{7}{4} \sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\frac{9}{2} \sqrt{\frac{\pi }{2}} \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\frac{5}{2} (x+1)^{3/2} \sin (x)+\frac{9}{2} \sqrt{x+1} \sin (x)+(x+1)^{5/2} \cos (x)-3 (x+1)^{3/2} \cos (x)-\frac{7}{4} \sqrt{x+1} \cos (x)",1,"((1/32 + I/32)*Sqrt[1 - x]*(((2 + 2*I)*((8 + 15*I) - (2 - 19*I)*x - 10*x^2 - (4*I)*x^3))/E^(I*x) + (18 + 7*I)*E^I*Sqrt[2*Pi]*Sqrt[-1 - x]*Erfi[((1 + I)*Sqrt[-1 - x])/Sqrt[2]] + (Cos[1] - I*Sin[1])*((-18 + 7*I)*Sqrt[2*Pi]*Sqrt[-1 - x]*Erf[((1 + I)*Sqrt[-1 - x])/Sqrt[2]] + (2 + 2*I)*((-8 + 15*I) + (2 + 19*I)*x + 10*x^2 - (4*I)*x^3)*(Cos[1 + x] + I*Sin[1 + x]))))/Sqrt[1 - x^2]","C",0
815,1,176,157,7.1971029,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} \sin (x) \, dx","Integrate[E^ArcTanh[x]*(1 - x)^(3/2)*Sin[x],x]","\frac{\left(\frac{1}{16}+\frac{i}{16}\right) e^{-i x} \sqrt{1-x^2} \left(-(3+4 i) \sqrt{2 \pi } e^{i x} \text{erf}\left(\frac{(1+i) \sqrt{-x-1}}{\sqrt{2}}\right) (\cos (1)-i \sin (1))+(4+3 i) \sqrt{2 \pi } e^{i x} \text{erfi}\left(\frac{(1+i) \sqrt{-x-1}}{\sqrt{2}}\right) (\sin (1)-i \cos (1))+(2+2 i) \sqrt{-x-1} \left(e^{2 i x} ((3+2 i)-2 i x)-2 i x-(3-2 i)\right)\right)}{\sqrt{-x-1} \sqrt{1-x}}","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\sqrt{2 \pi } \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\sqrt{2 \pi } \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\frac{3}{2} \sqrt{x+1} \sin (x)+(x+1)^{3/2} \cos (x)-2 \sqrt{x+1} \cos (x)",1,"((1/16 + I/16)*Sqrt[1 - x^2]*((2 + 2*I)*Sqrt[-1 - x]*((-3 + 2*I) + E^((2*I)*x)*((3 + 2*I) - (2*I)*x) - (2*I)*x) - (3 + 4*I)*E^(I*x)*Sqrt[2*Pi]*Erf[((1 + I)*Sqrt[-1 - x])/Sqrt[2]]*(Cos[1] - I*Sin[1]) + (4 + 3*I)*E^(I*x)*Sqrt[2*Pi]*Erfi[((1 + I)*Sqrt[-1 - x])/Sqrt[2]]*((-I)*Cos[1] + Sin[1])))/(E^(I*x)*Sqrt[-1 - x]*Sqrt[1 - x])","C",0
816,1,162,140,8.1747177,"\int \frac{e^{\tanh ^{-1}(x)} x \sin (x)}{\sqrt{1+x}} \, dx","Integrate[(E^ArcTanh[x]*x*Sin[x])/Sqrt[1 + x],x]","\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \sqrt{x+1} \left((\cos (x+1)-i \sin (x+1)) \left((1+2 i) \sqrt{2 \pi } \sqrt{x-1} \text{erf}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\sin (x)-i \cos (x))-(2-2 i) (x-1) (\cos (1)+i \sin (1))\right)+(-2-i) \sqrt{2 \pi } \sqrt{x-1} \text{erfi}\left(\frac{(1+i) \sqrt{x-1}}{\sqrt{2}}\right) (\cos (1)+i \sin (1))-(2-2 i) (x-1) (\cos (x)+i \sin (x))\right)}{\sqrt{1-x^2}}","-\sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \cos (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \sin (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\sqrt{1-x} \cos (x)",1,"((1/8 + I/8)*Sqrt[1 + x]*((-2 - I)*Sqrt[2*Pi]*Sqrt[-1 + x]*Erfi[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*(Cos[1] + I*Sin[1]) - (2 - 2*I)*(-1 + x)*(Cos[x] + I*Sin[x]) + ((-2 + 2*I)*(-1 + x)*(Cos[1] + I*Sin[1]) + (1 + 2*I)*Sqrt[2*Pi]*Sqrt[-1 + x]*Erf[((1 + I)*Sqrt[-1 + x])/Sqrt[2]]*((-I)*Cos[x] + Sin[x]))*(Cos[1 + x] - I*Sin[1 + x])))/Sqrt[1 - x^2]","C",0
817,1,70,62,0.0286204,"\int \frac{e^{\tanh ^{-1}(x)} \sin (x)}{\sqrt{1+x}} \, dx","Integrate[(E^ArcTanh[x]*Sin[x])/Sqrt[1 + x],x]","-\frac{e^{-i} \left(e^{2 i} \sqrt{-i (x-1)} \Gamma \left(\frac{1}{2},-i (x-1)\right)+\sqrt{i (x-1)} \Gamma \left(\frac{1}{2},i (x-1)\right)\right)}{2 \sqrt{1-x}}","\sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{2 \pi } \sin (1) C\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)",1,"-1/2*(E^(2*I)*Sqrt[(-I)*(-1 + x)]*Gamma[1/2, (-I)*(-1 + x)] + Sqrt[I*(-1 + x)]*Gamma[1/2, I*(-1 + x)])/(E^I*Sqrt[1 - x])","C",0
818,1,149,156,0.3935118,"\int e^{\tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[E^ArcTanh[a + b*x]*x^3,x]","-\frac{\left(8 a^3-12 a^2+12 a-3\right) \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{4 b^{9/2}}-\frac{\sqrt{-a^2-2 a b x-b^2 x^2+1} \left(-6 a^3+a^2 (6 b x+44)-a \left(6 b^2 x^2+20 b x+39\right)+6 b^3 x^3+8 b^2 x^2+9 b x+16\right)}{24 b^4}","-\frac{\sqrt{-a-b x+1} (a+b x+1)^{3/2} \left(18 a^2+2 (1-6 a) b x-10 a+7\right)}{24 b^4}-\frac{\left(-8 a^3+12 a^2-12 a+3\right) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{8 b^4}+\frac{\left(-8 a^3+12 a^2-12 a+3\right) \sin ^{-1}(a+b x)}{8 b^4}-\frac{x^2 \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{4 b^2}",1,"-1/24*(Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*(16 - 6*a^3 + 9*b*x + 8*b^2*x^2 + 6*b^3*x^3 + a^2*(44 + 6*b*x) - a*(39 + 20*b*x + 6*b^2*x^2)))/b^4 - ((-3 + 12*a - 12*a^2 + 8*a^3)*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/(4*b^(9/2))","A",0
819,1,159,130,0.1750085,"\int e^{\tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[E^ArcTanh[a + b*x]*x^2,x]","\frac{-\sqrt{b} \sqrt{-a^2-2 a b x-b^2 x^2+1} \left(2 a^2-a (2 b x+9)+2 b^2 x^2+3 b x+4\right)+6 \left(2 a^2+1\right) \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)+12 a \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)}{6 b^{7/2}}","-\frac{\left(2 a^2-2 a+1\right) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{2 b^3}+\frac{\left(2 a^2-2 a+1\right) \sin ^{-1}(a+b x)}{2 b^3}-\frac{(1-4 a) \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{6 b^3}-\frac{x \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{3 b^2}",1,"(-(Sqrt[b]*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*(4 + 2*a^2 + 3*b*x + 2*b^2*x^2 - a*(9 + 2*b*x))) + 6*(1 + 2*a^2)*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])] + 12*a*Sqrt[-b]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(6*b^(7/2))","A",0
820,1,130,84,0.0927635,"\int e^{\tanh ^{-1}(a+b x)} x \, dx","Integrate[E^ArcTanh[a + b*x]*x,x]","\frac{\sqrt{b} \sqrt{-a^2-2 a b x-b^2 x^2+1} (a-b x-2)+2 \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)+4 a \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)}{2 b^{5/2}}","-\frac{\sqrt{-a-b x+1} (a+b x+1)^{3/2}}{2 b^2}-\frac{(1-2 a) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{2 b^2}+\frac{(1-2 a) \sin ^{-1}(a+b x)}{2 b^2}",1,"(Sqrt[b]*(-2 + a - b*x)*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2] + 2*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])] + 4*a*Sqrt[-b]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(2*b^(5/2))","A",0
821,1,28,39,0.0170385,"\int e^{\tanh ^{-1}(a+b x)} \, dx","Integrate[E^ArcTanh[a + b*x],x]","\frac{\sin ^{-1}(a+b x)-\sqrt{1-(a+b x)^2}}{b}","\frac{\sin ^{-1}(a+b x)}{b}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{b}",1,"(-Sqrt[1 - (a + b*x)^2] + ArcSin[a + b*x])/b","A",1
822,1,106,64,0.0613687,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[E^ArcTanh[a + b*x]/x,x]","\frac{2 \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b}}-\frac{2 \sqrt{-a-1} \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{\sqrt{a-1}}","\sin ^{-1}(a+b x)-\frac{2 (a+1) \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{\sqrt{1-a^2}}",1,"(2*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/Sqrt[b] - (2*Sqrt[-1 - a]*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/Sqrt[-1 + a]","A",0
823,1,88,98,0.0525568,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[E^ArcTanh[a + b*x]/x^2,x]","\frac{\sqrt{-((a+b x-1) (a+b x+1))}}{(a-1) x}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{\sqrt{-a-1} (a-1)^{3/2}}","-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a) \sqrt{1-a^2}}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{(1-a) x}",1,"Sqrt[-((-1 + a + b*x)*(1 + a + b*x))]/((-1 + a)*x) - (2*b*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/(Sqrt[-1 - a]*(-1 + a)^(3/2))","A",0
824,1,123,162,0.1311516,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[E^ArcTanh[a + b*x]/x^3,x]","\frac{\left(a^2-a b x-2 b x-1\right) \sqrt{-a^2-2 a b x-b^2 x^2+1}}{2 (a-1)^2 (a+1) x^2}-\frac{(2 a+1) b^2 \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(-a-1)^{3/2} (a-1)^{5/2}}","-\frac{(2 a+1) b^2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a)^2 (a+1) \sqrt{1-a^2}}-\frac{\sqrt{-a-b x+1} (a+b x+1)^{3/2}}{2 \left(1-a^2\right) x^2}-\frac{(2 a+1) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{2 (1-a)^2 (a+1) x}",1,"((-1 + a^2 - 2*b*x - a*b*x)*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2])/(2*(-1 + a)^2*(1 + a)*x^2) - ((1 + 2*a)*b^2*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/((-1 - a)^(3/2)*(-1 + a)^(5/2))","A",0
825,1,193,213,0.2659636,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[E^ArcTanh[a + b*x]/x^4,x]","\frac{\frac{3 \left(2 a^2+2 a+1\right) b^2 x^2 \left(\sqrt{-a-1} \sqrt{a-1} \sqrt{-((a+b x-1) (a+b x+1))}-2 b x \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)\right)}{\sqrt{-a-1} (a-1)^{3/2}}-(4 a+1) b x \sqrt{-a-b x+1} (a+b x+1)^{3/2}+2 (a-1) (a+1) \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{6 \left(a^2-1\right)^2 x^3}","-\frac{\left(2 a^2+2 a+1\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a) \left(1-a^2\right)^{5/2}}-\frac{(a+4) (2 a+1) b^2 \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a)^3 (a+1)^2 x}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{3 (1-a) x^3}-\frac{(2 a+3) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a)^2 (a+1) x^2}",1,"(2*(-1 + a)*(1 + a)*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2) - (1 + 4*a)*b*x*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2) + (3*(1 + 2*a + 2*a^2)*b^2*x^2*(Sqrt[-1 - a]*Sqrt[-1 + a]*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))] - 2*b*x*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])]))/(Sqrt[-1 - a]*(-1 + a)^(3/2)))/(6*(-1 + a^2)^2*x^3)","A",0
826,1,75,83,0.0634431,"\int e^{2 \tanh ^{-1}(a+b x)} x^4 \, dx","Integrate[E^(2*ArcTanh[a + b*x])*x^4,x]","-\frac{2 (a-1)^4 \log (-a-b x+1)}{b^5}+\frac{2 (a-1)^3 x}{b^4}-\frac{(a-1)^2 x^2}{b^3}+\frac{2 (a-1) x^3}{3 b^2}-\frac{x^4}{2 b}-\frac{x^5}{5}","-\frac{2 (1-a)^4 \log (-a-b x+1)}{b^5}-\frac{2 (1-a)^3 x}{b^4}-\frac{(1-a)^2 x^2}{b^3}-\frac{2 (1-a) x^3}{3 b^2}-\frac{x^4}{2 b}-\frac{x^5}{5}",1,"(2*(-1 + a)^3*x)/b^4 - ((-1 + a)^2*x^2)/b^3 + (2*(-1 + a)*x^3)/(3*b^2) - x^4/(2*b) - x^5/5 - (2*(-1 + a)^4*Log[1 - a - b*x])/b^5","A",1
827,1,66,66,0.0424401,"\int e^{2 \tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[E^(2*ArcTanh[a + b*x])*x^3,x]","-\frac{2 (1-a)^3 \log (-a-b x+1)}{b^4}-\frac{2 (1-a)^2 x}{b^3}-\frac{(1-a) x^2}{b^2}-\frac{2 x^3}{3 b}-\frac{x^4}{4}","-\frac{2 (1-a)^3 \log (-a-b x+1)}{b^4}-\frac{2 (1-a)^2 x}{b^3}-\frac{(1-a) x^2}{b^2}-\frac{2 x^3}{3 b}-\frac{x^4}{4}",1,"(-2*(1 - a)^2*x)/b^3 - ((1 - a)*x^2)/b^2 - (2*x^3)/(3*b) - x^4/4 - (2*(1 - a)^3*Log[1 - a - b*x])/b^4","A",1
828,1,44,49,0.031546,"\int e^{2 \tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[E^(2*ArcTanh[a + b*x])*x^2,x]","-\frac{b x \left(-6 a+b^2 x^2+3 b x+6\right)+6 (a-1)^2 \log (-a-b x+1)}{3 b^3}","-\frac{2 (1-a)^2 \log (-a-b x+1)}{b^3}-\frac{2 (1-a) x}{b^2}-\frac{x^2}{b}-\frac{x^3}{3}",1,"-1/3*(b*x*(6 - 6*a + 3*b*x + b^2*x^2) + 6*(-1 + a)^2*Log[1 - a - b*x])/b^3","A",1
829,1,34,34,0.0181934,"\int e^{2 \tanh ^{-1}(a+b x)} x \, dx","Integrate[E^(2*ArcTanh[a + b*x])*x,x]","-\frac{2 (1-a) \log (-a-b x+1)}{b^2}-\frac{2 x}{b}-\frac{x^2}{2}","-\frac{2 (1-a) \log (-a-b x+1)}{b^2}-\frac{2 x}{b}-\frac{x^2}{2}",1,"(-2*x)/b - x^2/2 - (2*(1 - a)*Log[1 - a - b*x])/b^2","A",1
830,1,19,19,0.0104654,"\int e^{2 \tanh ^{-1}(a+b x)} \, dx","Integrate[E^(2*ArcTanh[a + b*x]),x]","-\frac{2 \log (-a-b x+1)}{b}-x","-\frac{2 \log (-a-b x+1)}{b}-x",1,"-x - (2*Log[1 - a - b*x])/b","A",1
831,1,26,33,0.0172385,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[E^(2*ArcTanh[a + b*x])/x,x]","\frac{2 \log (-a-b x+1)-(a+1) \log (x)}{a-1}","\frac{(a+1) \log (x)}{1-a}-\frac{2 \log (-a-b x+1)}{1-a}",1,"(-((1 + a)*Log[x]) + 2*Log[1 - a - b*x])/(-1 + a)","A",1
832,1,34,48,0.0226024,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[E^(2*ArcTanh[a + b*x])/x^2,x]","\frac{a^2-2 b x \log (-a-b x+1)+2 b x \log (x)-1}{(a-1)^2 x}","\frac{2 b \log (x)}{(1-a)^2}-\frac{2 b \log (-a-b x+1)}{(1-a)^2}-\frac{a+1}{(1-a) x}",1,"(-1 + a^2 + 2*b*x*Log[x] - 2*b*x*Log[1 - a - b*x])/((-1 + a)^2*x)","A",1
833,1,54,67,0.0341068,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[E^(2*ArcTanh[a + b*x])/x^3,x]","\frac{(a-1) \left(a^2-4 b x-1\right)+4 b^2 x^2 \log (-a-b x+1)-4 b^2 x^2 \log (x)}{2 (a-1)^3 x^2}","\frac{2 b^2 \log (x)}{(1-a)^3}-\frac{2 b^2 \log (-a-b x+1)}{(1-a)^3}-\frac{2 b}{(1-a)^2 x}-\frac{a+1}{2 (1-a) x^2}",1,"((-1 + a)*(-1 + a^2 - 4*b*x) - 4*b^2*x^2*Log[x] + 4*b^2*x^2*Log[1 - a - b*x])/(2*(-1 + a)^3*x^2)","A",1
834,1,75,82,0.0470231,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[E^(2*ArcTanh[a + b*x])/x^4,x]","\frac{(a-1) \left(a^3-a^2-3 a b x-a+6 b^2 x^2+3 b x+1\right)-6 b^3 x^3 \log (-a-b x+1)+6 b^3 x^3 \log (x)}{3 (a-1)^4 x^3}","\frac{2 b^3 \log (x)}{(1-a)^4}-\frac{2 b^3 \log (-a-b x+1)}{(1-a)^4}-\frac{2 b^2}{(1-a)^3 x}-\frac{b}{(1-a)^2 x^2}-\frac{a+1}{3 (1-a) x^3}",1,"((-1 + a)*(1 - a - a^2 + a^3 + 3*b*x - 3*a*b*x + 6*b^2*x^2) + 6*b^3*x^3*Log[x] - 6*b^3*x^3*Log[1 - a - b*x])/(3*(-1 + a)^4*x^3)","A",1
835,1,203,187,0.2885158,"\int e^{3 \tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[E^(3*ArcTanh[a + b*x])*x^3,x]","\frac{24 a \left(2 a^2+11\right) \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)+6 \left(36 a^2+17\right) \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)-\frac{\sqrt{b} \sqrt{a+b x+1} \left(-2 a^4+78 a^3+a^2 (22 b x-233)+a \left(-10 b^2 x^2-54 b x+237\right)+2 b^4 x^4+6 b^3 x^3+11 b^2 x^2+29 b x-80\right)}{\sqrt{-a-b x+1}}}{8 b^{9/2}}","\frac{\sqrt{-a-b x+1} (a+b x+1)^{3/2} \left(22 a^2+2 (11-10 a) b x-54 a+29\right)}{8 b^4}+\frac{3 \left(-8 a^3+36 a^2-44 a+17\right) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{8 b^4}-\frac{3 \left(-8 a^3+36 a^2-44 a+17\right) \sin ^{-1}(a+b x)}{8 b^4}+\frac{9 x^2 \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{4 b^2}+\frac{2 x^3 (a+b x+1)^{3/2}}{b \sqrt{-a-b x+1}}",1,"(-((Sqrt[b]*Sqrt[1 + a + b*x]*(-80 + 78*a^3 - 2*a^4 + 29*b*x + 11*b^2*x^2 + 6*b^3*x^3 + 2*b^4*x^4 + a^2*(-233 + 22*b*x) + a*(237 - 54*b*x - 10*b^2*x^2)))/Sqrt[1 - a - b*x]) + 24*a*(11 + 2*a^2)*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])] + 6*(17 + 36*a^2)*Sqrt[-b]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(8*b^(9/2))","A",0
836,1,170,168,0.2218012,"\int e^{3 \tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[E^(3*ArcTanh[a + b*x])*x^2,x]","\frac{6 \left(6 a^2+11\right) \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)-\frac{\sqrt{b} \sqrt{a+b x+1} \left(2 a^3-53 a^2+a (103-16 b x)+2 b^3 x^3+7 b^2 x^2+19 b x-52\right)}{\sqrt{-a-b x+1}}+108 a \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{6 b^{7/2}}","\frac{\left(6 a^2-18 a+11\right) \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{6 b^3}+\frac{\left(6 a^2-18 a+11\right) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{2 b^3}-\frac{\left(6 a^2-18 a+11\right) \sin ^{-1}(a+b x)}{2 b^3}+\frac{\sqrt{-a-b x+1} (a+b x+1)^{5/2}}{3 b^3}+\frac{(1-a)^2 (a+b x+1)^{5/2}}{b^3 \sqrt{-a-b x+1}}",1,"(-((Sqrt[b]*Sqrt[1 + a + b*x]*(-52 - 53*a^2 + 2*a^3 + 19*b*x + 7*b^2*x^2 + 2*b^3*x^3 + a*(103 - 16*b*x)))/Sqrt[1 - a - b*x]) + 108*a*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])] + 6*(11 + 6*a^2)*Sqrt[-b]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(6*b^(7/2))","A",0
837,1,142,121,0.1637241,"\int e^{3 \tanh ^{-1}(a+b x)} x \, dx","Integrate[E^(3*ArcTanh[a + b*x])*x,x]","\frac{\frac{\sqrt{b} \sqrt{a+b x+1} \left(a^2-15 a-b^2 x^2-5 b x+14\right)}{\sqrt{-a-b x+1}}+12 a \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)+18 \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)}{2 b^{5/2}}","\frac{(1-a) (a+b x+1)^{5/2}}{b^2 \sqrt{-a-b x+1}}+\frac{(3-2 a) \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{2 b^2}+\frac{3 (3-2 a) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{2 b^2}-\frac{3 (3-2 a) \sin ^{-1}(a+b x)}{2 b^2}",1,"((Sqrt[b]*Sqrt[1 + a + b*x]*(14 - 15*a + a^2 - 5*b*x - b^2*x^2))/Sqrt[1 - a - b*x] + 12*a*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])] + 18*Sqrt[-b]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(2*b^(5/2))","A",0
838,1,43,68,0.0413193,"\int e^{3 \tanh ^{-1}(a+b x)} \, dx","Integrate[E^(3*ArcTanh[a + b*x]),x]","\frac{\left(1-\frac{4}{a+b x-1}\right) \sqrt{1-(a+b x)^2}}{b}-\frac{3 \sin ^{-1}(a+b x)}{b}","\frac{2 (a+b x+1)^{3/2}}{b \sqrt{-a-b x+1}}+\frac{3 \sqrt{-a-b x+1} \sqrt{a+b x+1}}{b}-\frac{3 \sin ^{-1}(a+b x)}{b}",1,"((1 - 4/(-1 + a + b*x))*Sqrt[1 - (a + b*x)^2])/b - (3*ArcSin[a + b*x])/b","A",0
839,1,153,107,0.5897487,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[E^(3*ArcTanh[a + b*x])/x,x]","\frac{2 \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{-b}}-\frac{2 \left(2 \sqrt{a-1} \sqrt{a+b x+1}+(-a-1)^{3/2} \sqrt{-a-b x+1} \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)\right)}{(a-1)^{3/2} \sqrt{-a-b x+1}}","-\frac{2 (a+1)^2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a) \sqrt{1-a^2}}+\frac{4 \sqrt{a+b x+1}}{(1-a) \sqrt{-a-b x+1}}-\sin ^{-1}(a+b x)",1,"(2*Sqrt[b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/Sqrt[-b] - (2*(2*Sqrt[-1 + a]*Sqrt[1 + a + b*x] + (-1 - a)^(3/2)*Sqrt[1 - a - b*x]*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])]))/((-1 + a)^(3/2)*Sqrt[1 - a - b*x])","A",0
840,1,106,134,0.0788606,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[E^(3*ArcTanh[a + b*x])/x^2,x]","\frac{\sqrt{a+b x+1} \left(a^2+a b x+5 b x-1\right)}{(a-1)^2 x \sqrt{-a-b x+1}}-\frac{6 \sqrt{-a-1} b \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(a-1)^{5/2}}","-\frac{6 (a+1) b \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a)^2 \sqrt{1-a^2}}-\frac{(a+b x+1)^{3/2}}{(1-a) x \sqrt{-a-b x+1}}+\frac{6 b \sqrt{a+b x+1}}{(1-a)^2 \sqrt{-a-b x+1}}",1,"(Sqrt[1 + a + b*x]*(-1 + a^2 + 5*b*x + a*b*x))/((-1 + a)^2*x*Sqrt[1 - a - b*x]) - (6*Sqrt[-1 - a]*b*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/(-1 + a)^(5/2)","A",0
841,1,141,202,0.1680424,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[E^(3*ArcTanh[a + b*x])/x^3,x]","\frac{\sqrt{a+b x+1} \left(a^3-a^2-a \left(b^2 x^2+5 b x+1\right)-14 b^2 x^2+5 b x+1\right)}{2 (a-1)^3 x^2 \sqrt{-a-b x+1}}-\frac{3 (2 a+3) b^2 \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{\sqrt{-a-1} (a-1)^{7/2}}","-\frac{3 (2 a+3) b^2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a)^3 \sqrt{1-a^2}}-\frac{(a+b x+1)^{5/2}}{2 \left(1-a^2\right) x^2 \sqrt{-a-b x+1}}+\frac{3 (2 a+3) b^2 \sqrt{a+b x+1}}{(1-a)^3 (a+1) \sqrt{-a-b x+1}}-\frac{(2 a+3) b (a+b x+1)^{3/2}}{2 (1-a)^2 (a+1) x \sqrt{-a-b x+1}}",1,"(Sqrt[1 + a + b*x]*(1 - a^2 + a^3 + 5*b*x - 14*b^2*x^2 - a*(1 + 5*b*x + b^2*x^2)))/(2*(-1 + a)^3*x^2*Sqrt[1 - a - b*x]) - (3*(3 + 2*a)*b^2*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/(Sqrt[-1 - a]*(-1 + a)^(7/2))","A",0
842,1,199,260,0.309307,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[E^(3*ArcTanh[a + b*x])/x^4,x]","-\frac{-\left(6 a^2+18 a+11\right) b^2 x^2 \left(\sqrt{a-1} \sqrt{a+b x+1} \left(a^2+a b x+5 b x-1\right)-6 \sqrt{-a-1} b x \sqrt{-a-b x+1} \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)\right)-2 (a+1) (a-1)^{7/2} (a+b x+1)^{5/2}+(4 a+3) (a-1)^{5/2} b x (a+b x+1)^{5/2}}{6 (a-1)^{5/2} \left(a^2-1\right)^2 x^3 \sqrt{-a-b x+1}}","\frac{\left(2 a^2+51 a+52\right) b^3 \sqrt{a+b x+1}}{6 (1-a)^4 (a+1) \sqrt{-a-b x+1}}-\frac{\left(6 a^2+18 a+11\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a)^4 (a+1) \sqrt{1-a^2}}-\frac{(16 a+19) b^2 \sqrt{a+b x+1}}{6 (1-a)^3 (a+1) x \sqrt{-a-b x+1}}-\frac{(a+1) \sqrt{a+b x+1}}{3 (1-a) x^3 \sqrt{-a-b x+1}}-\frac{7 b \sqrt{a+b x+1}}{6 (1-a)^2 x^2 \sqrt{-a-b x+1}}",1,"-1/6*(-2*(-1 + a)^(7/2)*(1 + a)*(1 + a + b*x)^(5/2) + (-1 + a)^(5/2)*(3 + 4*a)*b*x*(1 + a + b*x)^(5/2) - (11 + 18*a + 6*a^2)*b^2*x^2*(Sqrt[-1 + a]*Sqrt[1 + a + b*x]*(-1 + a^2 + 5*b*x + a*b*x) - 6*Sqrt[-1 - a]*b*x*Sqrt[1 - a - b*x]*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])]))/((-1 + a)^(5/2)*(-1 + a^2)^2*x^3*Sqrt[1 - a - b*x])","A",0
843,1,160,156,0.4359945,"\int e^{-\tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[x^3/E^ArcTanh[a + b*x],x]","\frac{\frac{6 \left(8 a^3+12 a^2+12 a+3\right) \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{-b}}+\frac{\sqrt{a+b x+1} \left(6 a^4+38 a^3+5 a^2 (6 b x-1)+a \left(-18 b^2 x^2+50 b x-23\right)-6 b^4 x^4+14 b^3 x^3-17 b^2 x^2+25 b x-16\right)}{\sqrt{-a-b x+1}}}{24 b^4}","-\frac{(-a-b x+1)^{3/2} \sqrt{a+b x+1} \left(18 a^2-2 (6 a+1) b x+10 a+7\right)}{24 b^4}-\frac{\left(8 a^3+12 a^2+12 a+3\right) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{8 b^4}-\frac{\left(8 a^3+12 a^2+12 a+3\right) \sin ^{-1}(a+b x)}{8 b^4}-\frac{x^2 (-a-b x+1)^{3/2} \sqrt{a+b x+1}}{4 b^2}",1,"((Sqrt[1 + a + b*x]*(-16 + 38*a^3 + 6*a^4 + 25*b*x - 17*b^2*x^2 + 14*b^3*x^3 - 6*b^4*x^4 + 5*a^2*(-1 + 6*b*x) + a*(-23 + 50*b*x - 18*b^2*x^2)))/Sqrt[1 - a - b*x] + (6*(3 + 12*a + 12*a^2 + 8*a^3)*Sqrt[b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/Sqrt[-b])/(24*b^4)","A",0
844,1,126,130,0.1603276,"\int e^{-\tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[x^2/E^ArcTanh[a + b*x],x]","\frac{\left(2 a^2+2 a+1\right) \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{b^{7/2}}-\frac{\sqrt{a+b x+1} \left(2 a^3+7 a^2+a (8 b x-5)+2 b^3 x^3-5 b^2 x^2+7 b x-4\right)}{6 b^3 \sqrt{-a-b x+1}}","\frac{\left(2 a^2+2 a+1\right) \sqrt{a+b x+1} \sqrt{-a-b x+1}}{2 b^3}+\frac{\left(2 a^2+2 a+1\right) \sin ^{-1}(a+b x)}{2 b^3}+\frac{(4 a+1) \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{6 b^3}-\frac{x \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{3 b^2}",1,"-1/6*(Sqrt[1 + a + b*x]*(-4 + 7*a^2 + 2*a^3 + 7*b*x - 5*b^2*x^2 + 2*b^3*x^3 + a*(-5 + 8*b*x)))/(b^3*Sqrt[1 - a - b*x]) + ((1 + 2*a + 2*a^2)*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/b^(7/2)","A",0
845,1,99,84,0.1139928,"\int e^{-\tanh ^{-1}(a+b x)} x \, dx","Integrate[x/E^ArcTanh[a + b*x],x]","\frac{\sqrt{a+b x+1} \left(a^2+a-b^2 x^2+3 b x-2\right)}{2 b^2 \sqrt{-a-b x+1}}+\frac{(2 a+1) \sqrt{b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{(-b)^{5/2}}","-\frac{\sqrt{a+b x+1} (-a-b x+1)^{3/2}}{2 b^2}-\frac{(2 a+1) \sqrt{a+b x+1} \sqrt{-a-b x+1}}{2 b^2}-\frac{(2 a+1) \sin ^{-1}(a+b x)}{2 b^2}",1,"(Sqrt[1 + a + b*x]*(-2 + a + a^2 + 3*b*x - b^2*x^2))/(2*b^2*Sqrt[1 - a - b*x]) + ((1 + 2*a)*Sqrt[b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/(-b)^(5/2)","A",0
846,1,26,38,0.0189609,"\int e^{-\tanh ^{-1}(a+b x)} \, dx","Integrate[E^(-ArcTanh[a + b*x]),x]","\frac{\sqrt{1-(a+b x)^2}+\sin ^{-1}(a+b x)}{b}","\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{b}+\frac{\sin ^{-1}(a+b x)}{b}",1,"(Sqrt[1 - (a + b*x)^2] + ArcSin[a + b*x])/b","A",1
847,1,106,68,0.0392813,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[1/(E^ArcTanh[a + b*x]*x),x]","\frac{2 \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)}{\sqrt{b}}-\frac{2 \sqrt{a-1} \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{\sqrt{-a-1}}","-\frac{2 (1-a) \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{\sqrt{1-a^2}}-\sin ^{-1}(a+b x)",1,"(2*Sqrt[-b]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/Sqrt[b] - (2*Sqrt[-1 + a]*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/Sqrt[-1 - a]","A",0
848,1,89,94,0.0651466,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[1/(E^ArcTanh[a + b*x]*x^2),x]","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(-a-1)^{3/2} \sqrt{a-1}}-\frac{\sqrt{-((a+b x-1) (a+b x+1))}}{(a+1) x}","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(a+1) \sqrt{1-a^2}}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{(a+1) x}",1,"-(Sqrt[-((-1 + a + b*x)*(1 + a + b*x))]/((1 + a)*x)) + (2*b*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/((-1 - a)^(3/2)*Sqrt[-1 + a])","A",0
849,1,122,162,0.1345987,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[1/(E^ArcTanh[a + b*x]*x^3),x]","\frac{(2 a-1) b^2 \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(-a-1)^{5/2} (a-1)^{3/2}}-\frac{\left(a^2-a b x+2 b x-1\right) \sqrt{-a^2-2 a b x-b^2 x^2+1}}{2 (a-1) (a+1)^2 x^2}","-\frac{(1-2 a) b^2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a) (a+1)^2 \sqrt{1-a^2}}-\frac{(-a-b x+1)^{3/2} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x^2}+\frac{(1-2 a) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{2 (1-a) (a+1)^2 x}",1,"-1/2*((-1 + a^2 + 2*b*x - a*b*x)*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2])/((-1 + a)*(1 + a)^2*x^2) + ((-1 + 2*a)*b^2*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/((-1 - a)^(5/2)*(-1 + a)^(3/2))","A",0
850,1,194,210,0.2424651,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[1/(E^ArcTanh[a + b*x]*x^4),x]","\frac{\frac{3 \left(2 a^2-2 a+1\right) b^2 x^2 \left(\sqrt{-a-1} \sqrt{a-1} \sqrt{-((a+b x-1) (a+b x+1))}+2 b x \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)\right)}{(-a-1)^{3/2} \sqrt{a-1}}+(1-4 a) b x (-a-b x+1)^{3/2} \sqrt{a+b x+1}-2 (1-a) (a+1) (-a-b x+1)^{3/2} \sqrt{a+b x+1}}{6 \left(a^2-1\right)^2 x^3}","\frac{\left(2 a^2-2 a+1\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(a+1) \left(1-a^2\right)^{5/2}}-\frac{(1-2 a) (4-a) b^2 \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a)^2 (a+1)^3 x}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{3 (a+1) x^3}+\frac{(3-2 a) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a) (a+1)^2 x^2}",1,"(-2*(1 - a)*(1 + a)*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x] + (1 - 4*a)*b*x*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x] + (3*(1 - 2*a + 2*a^2)*b^2*x^2*(Sqrt[-1 - a]*Sqrt[-1 + a]*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))] + 2*b*x*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])]))/((-1 - a)^(3/2)*Sqrt[-1 + a]))/(6*(-1 + a^2)^2*x^3)","A",0
851,1,71,71,0.0577171,"\int e^{-2 \tanh ^{-1}(a+b x)} x^4 \, dx","Integrate[x^4/E^(2*ArcTanh[a + b*x]),x]","\frac{2 (a+1)^4 \log (a+b x+1)}{b^5}-\frac{2 (a+1)^3 x}{b^4}+\frac{(a+1)^2 x^2}{b^3}-\frac{2 (a+1) x^3}{3 b^2}+\frac{x^4}{2 b}-\frac{x^5}{5}","\frac{2 (a+1)^4 \log (a+b x+1)}{b^5}-\frac{2 (a+1)^3 x}{b^4}+\frac{(a+1)^2 x^2}{b^3}-\frac{2 (a+1) x^3}{3 b^2}+\frac{x^4}{2 b}-\frac{x^5}{5}",1,"(-2*(1 + a)^3*x)/b^4 + ((1 + a)^2*x^2)/b^3 - (2*(1 + a)*x^3)/(3*b^2) + x^4/(2*b) - x^5/5 + (2*(1 + a)^4*Log[1 + a + b*x])/b^5","A",1
852,1,57,57,0.0424463,"\int e^{-2 \tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[x^3/E^(2*ArcTanh[a + b*x]),x]","-\frac{2 (a+1)^3 \log (a+b x+1)}{b^4}+\frac{2 (a+1)^2 x}{b^3}-\frac{(a+1) x^2}{b^2}+\frac{2 x^3}{3 b}-\frac{x^4}{4}","-\frac{2 (a+1)^3 \log (a+b x+1)}{b^4}+\frac{2 (a+1)^2 x}{b^3}-\frac{(a+1) x^2}{b^2}+\frac{2 x^3}{3 b}-\frac{x^4}{4}",1,"(2*(1 + a)^2*x)/b^3 - ((1 + a)*x^2)/b^2 + (2*x^3)/(3*b) - x^4/4 - (2*(1 + a)^3*Log[1 + a + b*x])/b^4","A",1
853,1,41,41,0.0286822,"\int e^{-2 \tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[x^2/E^(2*ArcTanh[a + b*x]),x]","\frac{2 (a+1)^2 \log (a+b x+1)}{b^3}-\frac{2 (a+1) x}{b^2}+\frac{x^2}{b}-\frac{x^3}{3}","\frac{2 (a+1)^2 \log (a+b x+1)}{b^3}-\frac{2 (a+1) x}{b^2}+\frac{x^2}{b}-\frac{x^3}{3}",1,"(-2*(1 + a)*x)/b^2 + x^2/b - x^3/3 + (2*(1 + a)^2*Log[1 + a + b*x])/b^3","A",1
854,1,29,29,0.0180821,"\int e^{-2 \tanh ^{-1}(a+b x)} x \, dx","Integrate[x/E^(2*ArcTanh[a + b*x]),x]","-\frac{2 (a+1) \log (a+b x+1)}{b^2}+\frac{2 x}{b}-\frac{x^2}{2}","-\frac{2 (a+1) \log (a+b x+1)}{b^2}+\frac{2 x}{b}-\frac{x^2}{2}",1,"(2*x)/b - x^2/2 - (2*(1 + a)*Log[1 + a + b*x])/b^2","A",1
855,1,16,16,0.010932,"\int e^{-2 \tanh ^{-1}(a+b x)} \, dx","Integrate[E^(-2*ArcTanh[a + b*x]),x]","\frac{2 \log (a+b x+1)}{b}-x","\frac{2 \log (a+b x+1)}{b}-x",1,"-x + (2*Log[1 + a + b*x])/b","A",1
856,1,23,28,0.0159826,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[1/(E^(2*ArcTanh[a + b*x])*x),x]","\frac{-2 \log (a+b x+1)-a \log (x)+\log (x)}{a+1}","\frac{(1-a) \log (x)}{a+1}-\frac{2 \log (a+b x+1)}{a+1}",1,"(Log[x] - a*Log[x] - 2*Log[1 + a + b*x])/(1 + a)","A",1
857,1,31,41,0.0222734,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[1/(E^(2*ArcTanh[a + b*x])*x^2),x]","\frac{a^2+2 b x \log (a+b x+1)-2 b x \log (x)-1}{(a+1)^2 x}","-\frac{2 b \log (x)}{(a+1)^2}+\frac{2 b \log (a+b x+1)}{(a+1)^2}-\frac{1-a}{(a+1) x}",1,"(-1 + a^2 - 2*b*x*Log[x] + 2*b*x*Log[1 + a + b*x])/((1 + a)^2*x)","A",1
858,1,51,58,0.0355153,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[1/(E^(2*ArcTanh[a + b*x])*x^3),x]","\frac{(a+1) \left(a^2+4 b x-1\right)-4 b^2 x^2 \log (a+b x+1)+4 b^2 x^2 \log (x)}{2 (a+1)^3 x^2}","\frac{2 b^2 \log (x)}{(a+1)^3}-\frac{2 b^2 \log (a+b x+1)}{(a+1)^3}+\frac{2 b}{(a+1)^2 x}-\frac{1-a}{2 (a+1) x^2}",1,"((1 + a)*(-1 + a^2 + 4*b*x) + 4*b^2*x^2*Log[x] - 4*b^2*x^2*Log[1 + a + b*x])/(2*(1 + a)^3*x^2)","A",1
859,1,70,70,0.047221,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[1/(E^(2*ArcTanh[a + b*x])*x^4),x]","-\frac{2 b^3 \log (x)}{(a+1)^4}+\frac{2 b^3 \log (a+b x+1)}{(a+1)^4}-\frac{2 b^2}{(a+1)^3 x}+\frac{b}{(a+1)^2 x^2}-\frac{1-a}{3 (a+1) x^3}","-\frac{2 b^3 \log (x)}{(a+1)^4}+\frac{2 b^3 \log (a+b x+1)}{(a+1)^4}-\frac{2 b^2}{(a+1)^3 x}+\frac{b}{(a+1)^2 x^2}-\frac{1-a}{3 (a+1) x^3}",1,"-1/3*(1 - a)/((1 + a)*x^3) + b/((1 + a)^2*x^2) - (2*b^2)/((1 + a)^3*x) - (2*b^3*Log[x])/(1 + a)^4 + (2*b^3*Log[1 + a + b*x])/(1 + a)^4","A",1
860,1,231,187,0.2111788,"\int e^{-3 \tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[x^3/E^(3*ArcTanh[a + b*x]),x]","\frac{6 \left(8 a^3+36 a^2+44 a+17\right) \sqrt{b} \sqrt{-a^2-2 a b x-b^2 x^2+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)+\sqrt{-b} \left(-2 a^5-2 a^4 (b x+38)-5 a^3 (20 b x+31)-a^2 \left(12 b^2 x^2+265 b x+4\right)+a \left(2 b^4 x^4+4 b^3 x^3-53 b^2 x^2-212 b x+157\right)+2 b^5 x^5-8 b^4 x^4+17 b^3 x^3-40 b^2 x^2-51 b x+80\right)}{8 (-b)^{9/2} \sqrt{-((a+b x-1) (a+b x+1))}}","\frac{(-a-b x+1)^{3/2} \sqrt{a+b x+1} \left(22 a^2-2 (10 a+11) b x+54 a+29\right)}{8 b^4}+\frac{3 \left(8 a^3+36 a^2+44 a+17\right) \sqrt{-a-b x+1} \sqrt{a+b x+1}}{8 b^4}+\frac{3 \left(8 a^3+36 a^2+44 a+17\right) \sin ^{-1}(a+b x)}{8 b^4}+\frac{9 x^2 (-a-b x+1)^{3/2} \sqrt{a+b x+1}}{4 b^2}-\frac{2 x^3 (-a-b x+1)^{3/2}}{b \sqrt{a+b x+1}}",1,"(Sqrt[-b]*(80 - 2*a^5 - 51*b*x - 40*b^2*x^2 + 17*b^3*x^3 - 8*b^4*x^4 + 2*b^5*x^5 - 2*a^4*(38 + b*x) - 5*a^3*(31 + 20*b*x) - a^2*(4 + 265*b*x + 12*b^2*x^2) + a*(157 - 212*b*x - 53*b^2*x^2 + 4*b^3*x^3 + 2*b^4*x^4)) + 6*(17 + 44*a + 36*a^2 + 8*a^3)*Sqrt[b]*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(8*(-b)^(9/2)*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))])","A",0
861,1,190,167,0.1703751,"\int e^{-3 \tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[x^2/E^(3*ArcTanh[a + b*x]),x]","-\frac{6 \left(6 a^2+18 a+11\right) \sqrt{b} \sqrt{-a^2-2 a b x-b^2 x^2+1} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{-b} \left(2 a^4+a^3 (2 b x+51)+a^2 (69 b x+50)+a \left(2 b^3 x^3+9 b^2 x^2+106 b x-51\right)+2 b^4 x^4-9 b^3 x^3+26 b^2 x^2+33 b x-52\right)}{6 (-b)^{7/2} \sqrt{-((a+b x-1) (a+b x+1))}}","-\frac{\left(6 a^2+18 a+11\right) \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{6 b^3}-\frac{\left(6 a^2+18 a+11\right) \sqrt{a+b x+1} \sqrt{-a-b x+1}}{2 b^3}-\frac{\left(6 a^2+18 a+11\right) \sin ^{-1}(a+b x)}{2 b^3}-\frac{\sqrt{a+b x+1} (-a-b x+1)^{5/2}}{3 b^3}-\frac{(a+1)^2 (-a-b x+1)^{5/2}}{b^3 \sqrt{a+b x+1}}",1,"-1/6*(Sqrt[-b]*(-52 + 2*a^4 + 33*b*x + 26*b^2*x^2 - 9*b^3*x^3 + 2*b^4*x^4 + a^3*(51 + 2*b*x) + a^2*(50 + 69*b*x) + a*(-51 + 106*b*x + 9*b^2*x^2 + 2*b^3*x^3)) + 6*(11 + 18*a + 6*a^2)*Sqrt[b]*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/((-b)^(7/2)*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))])","A",0
862,1,157,119,0.1326081,"\int e^{-3 \tanh ^{-1}(a+b x)} x \, dx","Integrate[x/E^(3*ArcTanh[a + b*x]),x]","\frac{6 (2 a+3) \sqrt{b} \sqrt{-a^2-2 a b x-b^2 x^2+1} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{-b}}\right)+\sqrt{-b} \left(-a^3-a^2 (b x+14)+a \left(b^2 x^2-20 b x+1\right)+b^3 x^3-6 b^2 x^2-9 b x+14\right)}{2 (-b)^{5/2} \sqrt{-((a+b x-1) (a+b x+1))}}","\frac{(a+1) (-a-b x+1)^{5/2}}{b^2 \sqrt{a+b x+1}}+\frac{(2 a+3) \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{2 b^2}+\frac{3 (2 a+3) \sqrt{a+b x+1} \sqrt{-a-b x+1}}{2 b^2}+\frac{3 (2 a+3) \sin ^{-1}(a+b x)}{2 b^2}",1,"(Sqrt[-b]*(14 - a^3 - 9*b*x - 6*b^2*x^2 + b^3*x^3 - a^2*(14 + b*x) + a*(1 - 20*b*x + b^2*x^2)) + 6*(3 + 2*a)*Sqrt[b]*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*ArcSinh[(Sqrt[b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[-b])])/(2*(-b)^(5/2)*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))])","A",0
863,1,43,68,0.0442669,"\int e^{-3 \tanh ^{-1}(a+b x)} \, dx","Integrate[E^(-3*ArcTanh[a + b*x]),x]","\frac{\sqrt{1-(a+b x)^2} \left(-\frac{4}{a+b x+1}-1\right)}{b}-\frac{3 \sin ^{-1}(a+b x)}{b}","-\frac{2 (-a-b x+1)^{3/2}}{b \sqrt{a+b x+1}}-\frac{3 \sqrt{a+b x+1} \sqrt{-a-b x+1}}{b}-\frac{3 \sin ^{-1}(a+b x)}{b}",1,"(Sqrt[1 - (a + b*x)^2]*(-1 - 4/(1 + a + b*x)))/b - (3*ArcSin[a + b*x])/b","A",0
864,1,137,103,0.4433723,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[1/(E^(3*ArcTanh[a + b*x])*x),x]","-\frac{4 (a+b x-1)}{(a+1) \sqrt{-((a+b x-1) (a+b x+1))}}+\frac{2 \sqrt{-b} \sinh ^{-1}\left(\frac{\sqrt{-b} \sqrt{-a-b x+1}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b}}-\frac{2 (a-1)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(-a-1)^{3/2}}","-\frac{2 (1-a)^2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(a+1) \sqrt{1-a^2}}+\frac{4 \sqrt{-a-b x+1}}{(a+1) \sqrt{a+b x+1}}+\sin ^{-1}(a+b x)",1,"(-4*(-1 + a + b*x))/((1 + a)*Sqrt[-((-1 + a + b*x)*(1 + a + b*x))]) + (2*Sqrt[-b]*ArcSinh[(Sqrt[-b]*Sqrt[1 - a - b*x])/(Sqrt[2]*Sqrt[b])])/Sqrt[b] - (2*(-1 + a)^(3/2)*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/(-1 - a)^(3/2)","A",0
865,1,106,130,0.0961822,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[1/(E^(3*ArcTanh[a + b*x])*x^2),x]","\frac{\sqrt{-a-b x+1} \left(a^2+a b x-5 b x-1\right)}{(a+1)^2 x \sqrt{a+b x+1}}+\frac{6 \sqrt{a-1} b \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(-a-1)^{5/2}}","\frac{6 (1-a) b \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(a+1)^2 \sqrt{1-a^2}}-\frac{(-a-b x+1)^{3/2}}{(a+1) x \sqrt{a+b x+1}}-\frac{6 b \sqrt{-a-b x+1}}{(a+1)^2 \sqrt{a+b x+1}}",1,"(Sqrt[1 - a - b*x]*(-1 + a^2 - 5*b*x + a*b*x))/((1 + a)^2*x*Sqrt[1 + a + b*x]) + (6*Sqrt[-1 + a]*b*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/(-1 - a)^(5/2)","A",0
866,1,139,200,0.158515,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[1/(E^(3*ArcTanh[a + b*x])*x^3),x]","\frac{\sqrt{-a-b x+1} \left(a^3+a^2-a \left(b^2 x^2-5 b x+1\right)+14 b^2 x^2+5 b x-1\right)}{2 (a+1)^3 x^2 \sqrt{a+b x+1}}+\frac{3 (2 a-3) b^2 \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)}{(-a-1)^{7/2} \sqrt{a-1}}","-\frac{3 (3-2 a) b^2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(a+1)^3 \sqrt{1-a^2}}-\frac{(-a-b x+1)^{5/2}}{2 \left(1-a^2\right) x^2 \sqrt{a+b x+1}}+\frac{3 (3-2 a) b^2 \sqrt{-a-b x+1}}{(1-a) (a+1)^3 \sqrt{a+b x+1}}+\frac{(3-2 a) b (-a-b x+1)^{3/2}}{2 (1-a) (a+1)^2 x \sqrt{a+b x+1}}",1,"(Sqrt[1 - a - b*x]*(-1 + a^2 + a^3 + 5*b*x + 14*b^2*x^2 - a*(1 - 5*b*x + b^2*x^2)))/(2*(1 + a)^3*x^2*Sqrt[1 + a + b*x]) + (3*(-3 + 2*a)*b^2*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])])/((-1 - a)^(7/2)*Sqrt[-1 + a])","A",0
867,1,194,257,0.3214366,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[1/(E^(3*ArcTanh[a + b*x])*x^4),x]","\frac{\frac{\left(6 a^2-18 a+11\right) b^2 x^2 \left(\sqrt{-a-1} \sqrt{-a-b x+1} \left(a^2+a b x-5 b x-1\right)+6 \sqrt{a-1} b x \sqrt{a+b x+1} \tanh ^{-1}\left(\frac{\sqrt{-a-1} \sqrt{-a-b x+1}}{\sqrt{a-1} \sqrt{a+b x+1}}\right)\right)}{(-a-1)^{5/2}}-2 (1-a) (a+1) (-a-b x+1)^{5/2}+(3-4 a) b x (-a-b x+1)^{5/2}}{6 \left(a^2-1\right)^2 x^3 \sqrt{a+b x+1}}","-\frac{\left(2 a^2-51 a+52\right) b^3 \sqrt{-a-b x+1}}{6 (1-a) (a+1)^4 \sqrt{a+b x+1}}+\frac{\left(6 a^2-18 a+11\right) b^3 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a) (a+1)^4 \sqrt{1-a^2}}-\frac{(19-16 a) b^2 \sqrt{-a-b x+1}}{6 (1-a) (a+1)^3 x \sqrt{a+b x+1}}-\frac{(1-a) \sqrt{-a-b x+1}}{3 (a+1) x^3 \sqrt{a+b x+1}}+\frac{7 b \sqrt{-a-b x+1}}{6 (a+1)^2 x^2 \sqrt{a+b x+1}}",1,"(-2*(1 - a)*(1 + a)*(1 - a - b*x)^(5/2) + (3 - 4*a)*b*x*(1 - a - b*x)^(5/2) + ((11 - 18*a + 6*a^2)*b^2*x^2*(Sqrt[-1 - a]*Sqrt[1 - a - b*x]*(-1 + a^2 - 5*b*x + a*b*x) + 6*Sqrt[-1 + a]*b*x*Sqrt[1 + a + b*x]*ArcTanh[(Sqrt[-1 - a]*Sqrt[1 - a - b*x])/(Sqrt[-1 + a]*Sqrt[1 + a + b*x])]))/(-1 - a)^(5/2))/(6*(-1 + a^2)^2*x^3*Sqrt[1 + a + b*x])","A",0
868,1,37,10,0.0126621,"\int \frac{e^{\tanh ^{-1}(1+b x)}}{2+b x} \, dx","Integrate[E^ArcTanh[1 + b*x]/(2 + b*x),x]","-\frac{2 \sqrt{-b x} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{2}}\right)}{b^{3/2} \sqrt{x}}","\frac{\sin ^{-1}(b x+1)}{b}",1,"(-2*Sqrt[-(b*x)]*ArcSinh[(Sqrt[b]*Sqrt[x])/Sqrt[2]])/(b^(3/2)*Sqrt[x])","B",0
869,1,90,109,0.3685833,"\int \frac{e^{\tanh ^{-1}(a+b x)} x^3}{1-a^2-2 a b x-b^2 x^2} \, dx","Integrate[(E^ArcTanh[a + b*x]*x^3)/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","-\frac{3 \left(2 a^2-2 a+1\right) \sin ^{-1}(a+b x)-\frac{\sqrt{-a^2-2 a b x-b^2 x^2+1} \left(2 a^3-11 a^2+a (13-4 b x)+b^2 x^2+b x-4\right)}{a+b x-1}}{2 b^4}","-\frac{3 \left(2 a^2-2 a+1\right) \sin ^{-1}(a+b x)}{2 b^4}+\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1} ((3-2 a) b x+(1-2 a) (4-a))}{2 b^4}+\frac{(1-a) x^2 \sqrt{a+b x+1}}{b^2 \sqrt{-a-b x+1}}",1,"-1/2*(-((Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*(-4 - 11*a^2 + 2*a^3 + b*x + b^2*x^2 + a*(13 - 4*b*x)))/(-1 + a + b*x)) + 3*(1 - 2*a + 2*a^2)*ArcSin[a + b*x])/b^4","A",0
870,1,64,78,0.2119921,"\int \frac{e^{\tanh ^{-1}(a+b x)} x^2}{1-a^2-2 a b x-b^2 x^2} \, dx","Integrate[(E^ArcTanh[a + b*x]*x^2)/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","-\frac{\frac{\left(a^2-3 a-b x+2\right) \sqrt{-a^2-2 a b x-b^2 x^2+1}}{a+b x-1}-(2 a-1) \sin ^{-1}(a+b x)}{b^3}","\frac{(1-a)^2 \sqrt{a+b x+1}}{b^3 \sqrt{-a-b x+1}}+\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{b^3}-\frac{(1-2 a) \sin ^{-1}(a+b x)}{b^3}",1,"-((((2 - 3*a + a^2 - b*x)*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2])/(-1 + a + b*x) - (-1 + 2*a)*ArcSin[a + b*x])/b^3)","A",0
871,1,49,44,0.1371936,"\int \frac{e^{\tanh ^{-1}(a+b x)} x}{1-a^2-2 a b x-b^2 x^2} \, dx","Integrate[(E^ArcTanh[a + b*x]*x)/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","-\frac{\sin ^{-1}(a+b x)-\frac{(a-1) \sqrt{-a^2-2 a b x-b^2 x^2+1}}{a+b x-1}}{b^2}","\frac{(1-a) \sqrt{a+b x+1}}{b^2 \sqrt{-a-b x+1}}-\frac{\sin ^{-1}(a+b x)}{b^2}",1,"-((-(((-1 + a)*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2])/(-1 + a + b*x)) + ArcSin[a + b*x])/b^2)","A",0
872,1,12,27,0.0813825,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{1-a^2-2 a b x-b^2 x^2} \, dx","Integrate[E^ArcTanh[a + b*x]/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","\frac{e^{\tanh ^{-1}(a+b x)}}{b}","\frac{\sqrt{a+b x+1}}{b \sqrt{-a-b x+1}}",1,"E^ArcTanh[a + b*x]/b","C",1
873,1,118,93,0.2484268,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x \left(1-a^2-2 a b x-b^2 x^2\right)} \, dx","Integrate[E^ArcTanh[a + b*x]/(x*(1 - a^2 - 2*a*b*x - b^2*x^2)),x]","-\frac{-\frac{\sqrt{-a^2-2 a b x-b^2 x^2+1}}{a+b x-1}-\frac{\log \left(\sqrt{1-a^2} \sqrt{-a^2-2 a b x-b^2 x^2+1}-a^2-a b x+1\right)}{\sqrt{1-a^2}}+\frac{\log (x)}{\sqrt{1-a^2}}}{a-1}","\frac{\sqrt{a+b x+1}}{(1-a) \sqrt{-a-b x+1}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a) \sqrt{1-a^2}}",1,"-((-(Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]/(-1 + a + b*x)) + Log[x]/Sqrt[1 - a^2] - Log[1 - a^2 - a*b*x + Sqrt[1 - a^2]*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]]/Sqrt[1 - a^2])/(-1 + a))","A",0
874,1,149,150,0.3196971,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^2 \left(1-a^2-2 a b x-b^2 x^2\right)} \, dx","Integrate[E^ArcTanh[a + b*x]/(x^2*(1 - a^2 - 2*a*b*x - b^2*x^2)),x]","-\frac{\sqrt{-a^2-2 a b x-b^2 x^2+1} \left(\frac{b}{a+b x-1}+\frac{1}{a x+x}\right)+\frac{(2 a+1) b \log \left(\sqrt{1-a^2} \sqrt{-a^2-2 a b x-b^2 x^2+1}-a^2-a b x+1\right)}{(a+1) \sqrt{1-a^2}}-\frac{(2 a+1) b \log (x)}{(a+1) \sqrt{1-a^2}}}{(a-1)^2}","-\frac{\sqrt{a+b x+1}}{\left(1-a^2\right) x \sqrt{-a-b x+1}}-\frac{2 (2 a+1) b \tanh ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{-a-b x+1}}\right)}{(1-a)^2 (a+1) \sqrt{1-a^2}}+\frac{(a+2) b \sqrt{a+b x+1}}{(1-a)^2 (a+1) \sqrt{-a-b x+1}}",1,"-((Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]*((x + a*x)^(-1) + b/(-1 + a + b*x)) - ((1 + 2*a)*b*Log[x])/((1 + a)*Sqrt[1 - a^2]) + ((1 + 2*a)*b*Log[1 - a^2 - a*b*x + Sqrt[1 - a^2]*Sqrt[1 - a^2 - 2*a*b*x - b^2*x^2]])/((1 + a)*Sqrt[1 - a^2]))/(-1 + a)^2)","A",0
875,0,0,109,0.8404866,"\int e^{n \tanh ^{-1}(a+b x)} x^m \, dx","Integrate[E^(n*ArcTanh[a + b*x])*x^m,x]","\int e^{n \tanh ^{-1}(a+b x)} x^m \, dx","\frac{x^{m+1} (-a-b x+1)^{-n/2} (a+b x+1)^{n/2} \left(1-\frac{b x}{1-a}\right)^{n/2} \left(\frac{b x}{a+1}+1\right)^{-n/2} F_1\left(m+1;\frac{n}{2},-\frac{n}{2};m+2;\frac{b x}{1-a},-\frac{b x}{a+1}\right)}{m+1}",1,"Integrate[E^(n*ArcTanh[a + b*x])*x^m, x]","F",-1
876,1,220,206,0.2510254,"\int e^{n \tanh ^{-1}(a+b x)} x^3 \, dx","Integrate[E^(n*ArcTanh[a + b*x])*x^3,x]","\frac{(-a-b x+1)^{1-\frac{n}{2}} \left(b^2 (n-2) x^2 (a+b x+1)^{\frac{n}{2}+1}-2^{\frac{n}{2}+3} (n-6 a) \, _2F_1\left(-\frac{n}{2}-2,1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)-(a+1) 2^{\frac{n}{2}+3} (5 a-n+1) \, _2F_1\left(-\frac{n}{2}-1,1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)+(a+1)^2 2^{\frac{n}{2}+1} (4 a-n+2) \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)\right)}{4 b^4 (2-n)}","-\frac{(a+b x+1)^{\frac{n+2}{2}} \left(18 a^2-2 b x (6 a-n)-10 a n+n^2+6\right) (-a-b x+1)^{1-\frac{n}{2}}}{24 b^4}+\frac{2^{\frac{n}{2}-2} \left(24 a^3-36 a^2 n+12 a \left(n^2+2\right)-n \left(n^2+8\right)\right) (-a-b x+1)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{3 b^4 (2-n)}-\frac{x^2 (a+b x+1)^{\frac{n+2}{2}} (-a-b x+1)^{1-\frac{n}{2}}}{4 b^2}",1,"((1 - a - b*x)^(1 - n/2)*(b^2*(-2 + n)*x^2*(1 + a + b*x)^(1 + n/2) - 2^(3 + n/2)*(-6*a + n)*Hypergeometric2F1[-2 - n/2, 1 - n/2, 2 - n/2, (1 - a - b*x)/2] - 2^(3 + n/2)*(1 + a)*(1 + 5*a - n)*Hypergeometric2F1[-1 - n/2, 1 - n/2, 2 - n/2, (1 - a - b*x)/2] + 2^(1 + n/2)*(1 + a)^2*(2 + 4*a - n)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a - b*x)/2]))/(4*b^4*(2 - n))","A",0
877,1,127,170,0.1135864,"\int e^{n \tanh ^{-1}(a+b x)} x^2 \, dx","Integrate[E^(n*ArcTanh[a + b*x])*x^2,x]","\frac{(-a-b x+1)^{1-\frac{n}{2}} \left(\frac{2^{\frac{n}{2}+1} \left(6 a^2-6 a n+n^2+2\right) \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{n-2}+(4 a-n) (a+b x+1)^{\frac{n}{2}+1}-2 b x (a+b x+1)^{\frac{n}{2}+1}\right)}{6 b^3}","-\frac{2^{n/2} \left(6 a^2-6 a n+n^2+2\right) (-a-b x+1)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{3 b^3 (2-n)}+\frac{(4 a-n) (a+b x+1)^{\frac{n+2}{2}} (-a-b x+1)^{1-\frac{n}{2}}}{6 b^3}-\frac{x (a+b x+1)^{\frac{n+2}{2}} (-a-b x+1)^{1-\frac{n}{2}}}{3 b^2}",1,"((1 - a - b*x)^(1 - n/2)*((4*a - n)*(1 + a + b*x)^(1 + n/2) - 2*b*x*(1 + a + b*x)^(1 + n/2) + (2^(1 + n/2)*(2 + 6*a^2 - 6*a*n + n^2)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a - b*x)/2])/(-2 + n)))/(6*b^3)","A",1
878,1,96,114,0.0429124,"\int e^{n \tanh ^{-1}(a+b x)} x \, dx","Integrate[E^(n*ArcTanh[a + b*x])*x,x]","\frac{(-a-b x+1)^{1-\frac{n}{2}} \left(\frac{b 2^{\frac{n}{2}+1} (n-2 a) \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{n-2}-b (a+b x+1)^{\frac{n}{2}+1}\right)}{2 b^3}","\frac{2^{n/2} (2 a-n) (-a-b x+1)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{b^2 (2-n)}-\frac{(-a-b x+1)^{1-\frac{n}{2}} (a+b x+1)^{\frac{n+2}{2}}}{2 b^2}",1,"((1 - a - b*x)^(1 - n/2)*(-(b*(1 + a + b*x)^(1 + n/2)) + (2^(1 + n/2)*b*(-2*a + n)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a - b*x)/2])/(-2 + n)))/(2*b^3)","A",1
879,1,50,71,0.0224468,"\int e^{n \tanh ^{-1}(a+b x)} \, dx","Integrate[E^(n*ArcTanh[a + b*x]),x]","\frac{4 e^{(n+2) \tanh ^{-1}(a+b x)} \, _2F_1\left(2,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a+b x)}\right)}{b (n+2)}","-\frac{2^{\frac{n}{2}+1} (-a-b x+1)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{b (2-n)}",1,"(4*E^((2 + n)*ArcTanh[a + b*x])*Hypergeometric2F1[2, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a + b*x])])/(b*(2 + n))","A",0
880,1,111,135,0.037053,"\int \frac{e^{n \tanh ^{-1}(a+b x)}}{x} \, dx","Integrate[E^(n*ArcTanh[a + b*x])/x,x]","\frac{2 (-a-b x+1)^{-n/2} \left((a+b x+1)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{(a+1) (a+b x-1)}{(a-1) (a+b x+1)}\right)-2^{n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)\right)}{n}","\frac{2 (-a-b x+1)^{-n/2} (a+b x+1)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{(a+1) (-a-b x+1)}{(1-a) (a+b x+1)}\right)}{n}-\frac{2^{\frac{n}{2}+1} (-a-b x+1)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (-a-b x+1)\right)}{n}",1,"(2*((1 + a + b*x)^(n/2)*Hypergeometric2F1[1, -1/2*n, 1 - n/2, ((1 + a)*(-1 + a + b*x))/((-1 + a)*(1 + a + b*x))] - 2^(n/2)*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a - b*x)/2]))/(n*(1 - a - b*x)^(n/2))","A",1
881,1,83,92,0.0234705,"\int \frac{e^{n \tanh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[E^(n*ArcTanh[a + b*x])/x^2,x]","\frac{4 b (-a-b x+1)^{1-\frac{n}{2}} (a+b x+1)^{\frac{n}{2}-1} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{(a+1) (a+b x-1)}{(a-1) (a+b x+1)}\right)}{(a-1)^2 (n-2)}","-\frac{4 b (-a-b x+1)^{1-\frac{n}{2}} (a+b x+1)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{(a+1) (-a-b x+1)}{(1-a) (a+b x+1)}\right)}{(1-a)^2 (2-n)}",1,"(4*b*(1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^(-1 + n/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, ((1 + a)*(-1 + a + b*x))/((-1 + a)*(1 + a + b*x))])/((-1 + a)^2*(-2 + n))","A",1
882,1,123,152,0.0620403,"\int \frac{e^{n \tanh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[E^(n*ArcTanh[a + b*x])/x^3,x]","\frac{(-a-b x+1)^{1-\frac{n}{2}} (a+b x+1)^{\frac{n}{2}-1} \left((a-1)^2 (n-2) (a+b x+1)^2-4 b^2 x^2 (2 a+n) \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{(a+1) (a+b x-1)}{(a-1) (a+b x+1)}\right)\right)}{2 (a-1)^3 (a+1) (n-2) x^2}","-\frac{(a+b x+1)^{\frac{n+2}{2}} (-a-b x+1)^{1-\frac{n}{2}}}{2 \left(1-a^2\right) x^2}-\frac{2 b^2 (2 a+n) (a+b x+1)^{\frac{n-2}{2}} (-a-b x+1)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{(a+1) (-a-b x+1)}{(1-a) (a+b x+1)}\right)}{(1-a)^3 (a+1) (2-n)}",1,"((1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^(-1 + n/2)*((-1 + a)^2*(-2 + n)*(1 + a + b*x)^2 - 4*b^2*(2*a + n)*x^2*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, ((1 + a)*(-1 + a + b*x))/((-1 + a)*(1 + a + b*x))]))/(2*(-1 + a)^3*(1 + a)*(-2 + n)*x^2)","A",1
883,1,107,127,0.1567734,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^4,x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(128 a^8 x^8+144 a^7 x^7-512 a^6 x^6-600 a^5 x^5+768 a^4 x^4+978 a^3 x^3-512 a^2 x^2-837 a x+128\right)+630 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{1152 a}","-\frac{c^4 \left(1-a^2 x^2\right)^{9/2}}{9 a}+\frac{1}{8} c^4 x \left(1-a^2 x^2\right)^{7/2}+\frac{7}{48} c^4 x \left(1-a^2 x^2\right)^{5/2}+\frac{35}{192} c^4 x \left(1-a^2 x^2\right)^{3/2}+\frac{35}{128} c^4 x \sqrt{1-a^2 x^2}+\frac{35 c^4 \sin ^{-1}(a x)}{128 a}",1,"-1/1152*(c^4*(Sqrt[1 - a^2*x^2]*(128 - 837*a*x - 512*a^2*x^2 + 978*a^3*x^3 + 768*a^4*x^4 - 600*a^5*x^5 - 512*a^6*x^6 + 144*a^7*x^7 + 128*a^8*x^8) + 630*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
884,1,91,105,0.1299173,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^3,x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(48 a^6 x^6+56 a^5 x^5-144 a^4 x^4-182 a^3 x^3+144 a^2 x^2+231 a x-48\right)-210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{336 a}","-\frac{c^3 \left(1-a^2 x^2\right)^{7/2}}{7 a}+\frac{1}{6} c^3 x \left(1-a^2 x^2\right)^{5/2}+\frac{5}{24} c^3 x \left(1-a^2 x^2\right)^{3/2}+\frac{5}{16} c^3 x \sqrt{1-a^2 x^2}+\frac{5 c^3 \sin ^{-1}(a x)}{16 a}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(-48 + 231*a*x + 144*a^2*x^2 - 182*a^3*x^3 - 144*a^4*x^4 + 56*a^5*x^5 + 48*a^6*x^6) - 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(336*a)","A",0
885,1,75,83,0.1018572,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^2,x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(8 a^4 x^4+10 a^3 x^3-16 a^2 x^2-25 a x+8\right)+30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{40 a}","-\frac{c^2 \left(1-a^2 x^2\right)^{5/2}}{5 a}+\frac{1}{4} c^2 x \left(1-a^2 x^2\right)^{3/2}+\frac{3}{8} c^2 x \sqrt{1-a^2 x^2}+\frac{3 c^2 \sin ^{-1}(a x)}{8 a}",1,"-1/40*(c^2*(Sqrt[1 - a^2*x^2]*(8 - 25*a*x - 16*a^2*x^2 + 10*a^3*x^3 + 8*a^4*x^4) + 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
886,1,57,55,0.0749451,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2),x]","\frac{c \left(\sqrt{1-a^2 x^2} \left(2 a^2 x^2+3 a x-2\right)-6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","-\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 a}+\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}",1,"(c*(Sqrt[1 - a^2*x^2]*(-2 + 3*a*x + 2*a^2*x^2) - 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(6*a)","A",0
887,1,74,101,0.0455346,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{c-a^2 c x^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2),x]","-\frac{2 a^4 x^4+3 a^3 x^3+8 a^2 x^2+9 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-9 a x-16}{6 a^5 c \sqrt{1-a^2 x^2}}","-\frac{3 \sin ^{-1}(a x)}{2 a^5 c}+\frac{x^3 (a x+1)}{a^2 c \sqrt{1-a^2 x^2}}+\frac{(9 a x+16) \sqrt{1-a^2 x^2}}{6 a^5 c}+\frac{4 x^2 \sqrt{1-a^2 x^2}}{3 a^3 c}",1,"-1/6*(-16 - 9*a*x + 8*a^2*x^2 + 3*a^3*x^3 + 2*a^4*x^4 + 9*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(a^5*c*Sqrt[1 - a^2*x^2])","A",1
888,1,65,74,0.0396429,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{c-a^2 c x^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2),x]","-\frac{a^3 x^3+2 a^2 x^2+3 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-3 a x-4}{2 a^4 c \sqrt{1-a^2 x^2}}","-\frac{3 \sin ^{-1}(a x)}{2 a^4 c}+\frac{x^2 (a x+1)}{a^2 c \sqrt{1-a^2 x^2}}+\frac{(3 a x+4) \sqrt{1-a^2 x^2}}{2 a^4 c}",1,"-1/2*(-4 - 3*a*x + 2*a^2*x^2 + a^3*x^3 + 3*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(a^4*c*Sqrt[1 - a^2*x^2])","A",1
889,1,54,60,0.028264,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2),x]","\frac{-a^2 x^2-\sqrt{1-a^2 x^2} \sin ^{-1}(a x)+a x+2}{a^3 c \sqrt{1-a^2 x^2}}","-\frac{\sin ^{-1}(a x)}{a^3 c}+\frac{a x+1}{a^3 c \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2}}{a^3 c}",1,"(2 + a*x - a^2*x^2 - Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(a^3*c*Sqrt[1 - a^2*x^2])","A",1
890,1,45,39,0.0296338,"\int \frac{e^{\tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2),x]","\frac{\frac{a x}{\sqrt{1-a^2 x^2}}+\frac{1}{\sqrt{1-a^2 x^2}}-\sin ^{-1}(a x)}{a^2 c}","\frac{a x+1}{a^2 c \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)}{a^2 c}",1,"(1/Sqrt[1 - a^2*x^2] + (a*x)/Sqrt[1 - a^2*x^2] - ArcSin[a*x])/(a^2*c)","A",1
891,1,26,13,0.008862,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2),x]","\frac{\sqrt{a x+1}}{a c \sqrt{1-a x}}","\frac{e^{\tanh ^{-1}(a x)}}{a c}",1,"Sqrt[1 + a*x]/(a*c*Sqrt[1 - a*x])","A",0
892,1,55,44,0.0220834,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)),x]","-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}-\frac{a^3 (-x)-a^2}{a^2 c \sqrt{1-a^2 x^2}}","\frac{a x+1}{c \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"-((-a^2 - a^3*x)/(a^2*c*Sqrt[1 - a^2*x^2])) - ArcTanh[Sqrt[1 - a^2*x^2]]/c","A",1
893,1,67,70,0.0250209,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)),x]","\frac{2 a^2 x^2-a x \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a x-1}{c x \sqrt{1-a^2 x^2}}","\frac{a x+1}{c x \sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a^2 x^2}}{c x}-\frac{a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"(-1 + a*x + 2*a^2*x^2 - a*x*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*x*Sqrt[1 - a^2*x^2])","A",1
894,1,83,99,0.0402271,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)),x]","-\frac{-4 a^3 x^3-3 a^2 x^2+3 a^2 x^2 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a x+1}{2 c x^2 \sqrt{1-a^2 x^2}}","-\frac{2 a \sqrt{1-a^2 x^2}}{c x}-\frac{3 \sqrt{1-a^2 x^2}}{2 c x^2}+\frac{a x+1}{c x^2 \sqrt{1-a^2 x^2}}-\frac{3 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c}",1,"-1/2*(1 + 2*a*x - 3*a^2*x^2 - 4*a^3*x^3 + 3*a^2*x^2*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*x^2*Sqrt[1 - a^2*x^2])","A",1
895,1,91,128,0.0399021,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(c - a^2*c*x^2)),x]","-\frac{-16 a^4 x^4-9 a^3 x^3+8 a^2 x^2+9 a^3 x^3 \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+3 a x+2}{6 c x^3 \sqrt{1-a^2 x^2}}","-\frac{8 a^2 \sqrt{1-a^2 x^2}}{3 c x}-\frac{3 a \sqrt{1-a^2 x^2}}{2 c x^2}-\frac{4 \sqrt{1-a^2 x^2}}{3 c x^3}+\frac{a x+1}{c x^3 \sqrt{1-a^2 x^2}}-\frac{3 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c}",1,"-1/6*(2 + 3*a*x + 8*a^2*x^2 - 9*a^3*x^3 - 16*a^4*x^4 + 9*a^3*x^3*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(c*x^3*Sqrt[1 - a^2*x^2])","A",1
896,1,93,137,0.0603227,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^6)/(c - a^2*c*x^2)^2,x]","\frac{2 a^5 x^5+a^4 x^4+11 a^3 x^3-31 a^2 x^2+15 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-17 a x+32}{6 a^7 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{5 \sin ^{-1}(a x)}{2 a^7 c^2}+\frac{x^5 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{(15 a x+32) \sqrt{1-a^2 x^2}}{6 a^7 c^2}-\frac{8 x^2 \sqrt{1-a^2 x^2}}{3 a^5 c^2}-\frac{x^3 (6 a x+5)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}",1,"(32 - 17*a*x - 31*a^2*x^2 + 11*a^3*x^3 + a^4*x^4 + 2*a^5*x^5 + 15*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(6*a^7*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
897,1,86,110,0.0463501,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^2,x]","\frac{3 a^4 x^4+3 a^3 x^3-23 a^2 x^2+15 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-a x+16}{6 a^6 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{5 \sin ^{-1}(a x)}{2 a^6 c^2}+\frac{x^4 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{(15 a x+16) \sqrt{1-a^2 x^2}}{6 a^6 c^2}-\frac{x^2 (5 a x+4)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}",1,"(16 - a*x - 23*a^2*x^2 + 3*a^3*x^3 + 3*a^4*x^4 + 15*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(6*a^6*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
898,1,78,99,0.0484511,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^2,x]","\frac{3 a^3 x^3-7 a^2 x^2+3 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-5 a x+8}{3 a^5 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{\sin ^{-1}(a x)}{a^5 c^2}+\frac{x^3 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{8 \sqrt{1-a^2 x^2}}{3 a^5 c^2}-\frac{x (4 a x+3)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}",1,"(8 - 5*a*x - 7*a^2*x^2 + 3*a^3*x^3 + 3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a^5*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
899,1,69,74,0.0405392,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^2,x]","\frac{-4 a^2 x^2+3 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+a x+2}{3 a^4 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{\sin ^{-1}(a x)}{a^4 c^2}+\frac{x^2 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{3 a x+2}{3 a^4 c^2 \sqrt{1-a^2 x^2}}",1,"(2 + a*x - 4*a^2*x^2 + 3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a^4*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
900,1,45,57,0.0195468,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^2,x]","\frac{-a^2 x^2-2 a x+2}{3 a^3 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{x^2 (a x+1)}{3 a c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{2}{3 a^3 c^2 \sqrt{1-a^2 x^2}}",1,"(2 - 2*a*x - a^2*x^2)/(3*a^3*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
901,1,44,55,0.019522,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^2,x]","\frac{-a^2 x^2+a x-1}{3 a^2 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{a x+1}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{x}{3 a c^2 \sqrt{1-a^2 x^2}}",1,"(-1 + a*x - a^2*x^2)/(3*a^2*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
902,1,45,52,0.0137519,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^2,x]","\frac{2 a^2 x^2-2 a x-1}{3 a c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{2 x}{3 c^2 \sqrt{1-a^2 x^2}}+\frac{a x+1}{3 a c^2 \left(1-a^2 x^2\right)^{3/2}}",1,"(-1 - 2*a*x + 2*a^2*x^2)/(3*a*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
903,1,77,74,0.0336852,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^2),x]","\frac{2 a^2 x^2-3 (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a x-4}{3 c^2 (a x-1) \sqrt{1-a^2 x^2}}","\frac{a x+1}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{2 a x+3}{3 c^2 \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^2}",1,"(-4 + a*x + 2*a^2*x^2 - 3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(3*c^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
904,1,91,105,0.042042,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^2),x]","\frac{8 a^3 x^3-5 a^2 x^2-3 a x (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-7 a x+3}{3 c^2 x (a x-1) \sqrt{1-a^2 x^2}}","\frac{a x+1}{3 c^2 x \left(1-a^2 x^2\right)^{3/2}}-\frac{8 \sqrt{1-a^2 x^2}}{3 c^2 x}+\frac{3 a x+4}{3 c^2 x \sqrt{1-a^2 x^2}}-\frac{a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^2}",1,"(3 - 7*a*x - 5*a^2*x^2 + 8*a^3*x^3 - 3*a*x*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(3*c^2*x*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
905,1,103,134,0.0468377,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^2),x]","\frac{16 a^4 x^4-a^3 x^3-23 a^2 x^2-15 a^2 x^2 (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+3 a x+3}{6 c^2 x^2 (a x-1) \sqrt{1-a^2 x^2}}","-\frac{8 a \sqrt{1-a^2 x^2}}{3 c^2 x}-\frac{5 \sqrt{1-a^2 x^2}}{2 c^2 x^2}+\frac{4 a x+5}{3 c^2 x^2 \sqrt{1-a^2 x^2}}+\frac{a x+1}{3 c^2 x^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{5 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^2}",1,"(3 + 3*a*x - 23*a^2*x^2 - a^3*x^3 + 16*a^4*x^4 - 15*a^2*x^2*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(6*c^2*x^2*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
906,1,110,161,0.051199,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(c - a^2*c*x^2)^2),x]","\frac{32 a^5 x^5-17 a^4 x^4-31 a^3 x^3+11 a^2 x^2-15 a^3 x^3 (a x-1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a x+2}{6 c^2 x^3 (a x-1) \sqrt{1-a^2 x^2}}","-\frac{16 a^2 \sqrt{1-a^2 x^2}}{3 c^2 x}-\frac{5 a \sqrt{1-a^2 x^2}}{2 c^2 x^2}-\frac{8 \sqrt{1-a^2 x^2}}{3 c^2 x^3}+\frac{5 a x+6}{3 c^2 x^3 \sqrt{1-a^2 x^2}}+\frac{a x+1}{3 c^2 x^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{5 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^2}",1,"(2 + a*x + 11*a^2*x^2 - 31*a^3*x^3 - 17*a^4*x^4 + 32*a^5*x^5 - 15*a^3*x^3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(6*c^2*x^3*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
907,1,116,143,0.0822282,"\int \frac{e^{\tanh ^{-1}(a x)} x^7}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^7)/(c - a^2*c*x^2)^3,x]","\frac{-15 a^6 x^6-15 a^5 x^5+176 a^4 x^4+4 a^3 x^3-249 a^2 x^2-105 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+9 a x+96}{30 a^8 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{7 \sin ^{-1}(a x)}{2 a^8 c^3}+\frac{x^6 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{(35 a x+32) \sqrt{1-a^2 x^2}}{10 a^8 c^3}+\frac{x^2 (35 a x+24)}{15 a^6 c^3 \sqrt{1-a^2 x^2}}-\frac{x^4 (7 a x+6)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}",1,"(96 + 9*a*x - 249*a^2*x^2 + 4*a^3*x^3 + 176*a^4*x^4 - 15*a^5*x^5 - 15*a^6*x^6 - 105*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(30*a^8*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
908,1,108,133,0.0745294,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^6)/(c - a^2*c*x^2)^3,x]","\frac{-15 a^5 x^5+38 a^4 x^4+52 a^3 x^3-87 a^2 x^2-15 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-33 a x+48}{15 a^7 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{\sin ^{-1}(a x)}{a^7 c^3}+\frac{x^5 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{16 \sqrt{1-a^2 x^2}}{5 a^7 c^3}+\frac{x (8 a x+5)}{5 a^6 c^3 \sqrt{1-a^2 x^2}}-\frac{x^3 (6 a x+5)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}",1,"(48 - 33*a*x - 87*a^2*x^2 + 52*a^3*x^3 + 38*a^4*x^4 - 15*a^5*x^5 - 15*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(15*a^7*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
909,1,100,108,0.0595597,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^3,x]","\frac{23 a^4 x^4-8 a^3 x^3-27 a^2 x^2-15 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)+7 a x+8}{15 a^6 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{\sin ^{-1}(a x)}{a^6 c^3}+\frac{x^4 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{15 a x+8}{15 a^6 c^3 \sqrt{1-a^2 x^2}}-\frac{x^2 (5 a x+4)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}",1,"(8 + 7*a*x - 27*a^2*x^2 - 8*a^3*x^3 + 23*a^4*x^4 - 15*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(15*a^6*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
910,1,68,81,0.0264702,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^3,x]","\frac{3 a^4 x^4+12 a^3 x^3-12 a^2 x^2-8 a x+8}{15 a^5 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","\frac{x^4 (a x+1)}{5 a c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{4}{5 a^5 c^3 \sqrt{1-a^2 x^2}}-\frac{4}{15 a^5 c^3 \left(1-a^2 x^2\right)^{3/2}}",1,"(8 - 8*a*x - 12*a^2*x^2 + 12*a^3*x^3 + 3*a^4*x^4)/(15*a^5*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
911,1,68,74,0.0248893,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^3,x]","\frac{3 a^4 x^4-3 a^3 x^3+3 a^2 x^2+2 a x-2}{15 a^4 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","\frac{a x^5}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{1}{3 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{1}{5 a^4 c^3 \left(1-a^2 x^2\right)^{5/2}}",1,"(-2 + 2*a*x + 3*a^2*x^2 - 3*a^3*x^3 + 3*a^4*x^4)/(15*a^4*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
912,1,68,88,0.026362,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^3,x]","\frac{-2 a^4 x^4+2 a^3 x^3+3 a^2 x^2+2 a x-2}{15 a^3 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","\frac{x^2 (a x+1)}{5 a c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{2 x}{15 a^2 c^3 \sqrt{1-a^2 x^2}}-\frac{2 (1-a x)}{15 a^3 c^3 \left(1-a^2 x^2\right)^{3/2}}",1,"(-2 + 2*a*x + 3*a^2*x^2 + 2*a^3*x^3 - 2*a^4*x^4)/(15*a^3*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
913,1,68,80,0.0328605,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^3,x]","\frac{-2 a^4 x^4+2 a^3 x^3+3 a^2 x^2-3 a x+3}{15 a^2 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{2 x}{15 a c^3 \sqrt{1-a^2 x^2}}-\frac{x}{15 a c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{a x+1}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}",1,"(3 - 3*a*x + 3*a^2*x^2 + 2*a^3*x^3 - 2*a^4*x^4)/(15*a^2*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
914,1,59,74,0.0236572,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^3,x]","\frac{8 a^4 x^4-8 a^3 x^3-12 a^2 x^2+12 a x+3}{15 a c^3 (1-a x)^{5/2} (a x+1)^{3/2}}","\frac{8 x}{15 c^3 \sqrt{1-a^2 x^2}}+\frac{4 x}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{a x+1}{5 a c^3 \left(1-a^2 x^2\right)^{5/2}}",1,"(3 + 12*a*x - 12*a^2*x^2 - 8*a^3*x^3 + 8*a^4*x^4)/(15*a*c^3*(1 - a*x)^(5/2)*(1 + a*x)^(3/2))","A",1
915,1,108,101,0.0493435,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^3),x]","\frac{8 a^4 x^4+7 a^3 x^3-27 a^2 x^2-15 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-8 a x+23}{15 c^3 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","\frac{a x+1}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{8 a x+15}{15 c^3 \sqrt{1-a^2 x^2}}+\frac{4 a x+5}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^3}",1,"(23 - 8*a*x - 27*a^2*x^2 + 7*a^3*x^3 + 8*a^4*x^4 - 15*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(15*c^3*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
916,1,121,135,0.0589541,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^3),x]","\frac{48 a^5 x^5-33 a^4 x^4-87 a^3 x^3+52 a^2 x^2-15 a x (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+38 a x-15}{15 c^3 x (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","\frac{a x+1}{5 c^3 x \left(1-a^2 x^2\right)^{5/2}}-\frac{16 \sqrt{1-a^2 x^2}}{5 c^3 x}+\frac{5 a x+8}{5 c^3 x \sqrt{1-a^2 x^2}}+\frac{5 a x+6}{15 c^3 x \left(1-a^2 x^2\right)^{3/2}}-\frac{a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^3}",1,"(-15 + 38*a*x + 52*a^2*x^2 - 87*a^3*x^3 - 33*a^4*x^4 + 48*a^5*x^5 - 15*a*x*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(15*c^3*x*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
917,1,133,164,0.0649802,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^3),x]","\frac{96 a^6 x^6+9 a^5 x^5-249 a^4 x^4+4 a^3 x^3+176 a^2 x^2-105 a^2 x^2 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-15 a x-15}{30 c^3 x^2 (a x-1)^2 (a x+1) \sqrt{1-a^2 x^2}}","-\frac{16 a \sqrt{1-a^2 x^2}}{5 c^3 x}-\frac{7 \sqrt{1-a^2 x^2}}{2 c^3 x^2}+\frac{24 a x+35}{15 c^3 x^2 \sqrt{1-a^2 x^2}}+\frac{6 a x+7}{15 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{a x+1}{5 c^3 x^2 \left(1-a^2 x^2\right)^{5/2}}-\frac{7 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^3}",1,"(-15 - 15*a*x + 176*a^2*x^2 + 4*a^3*x^3 - 249*a^4*x^4 + 9*a^5*x^5 + 96*a^6*x^6 - 105*a^2*x^2*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2]*ArcTanh[Sqrt[1 - a^2*x^2]])/(30*c^3*x^2*(-1 + a*x)^2*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
918,1,75,96,0.0329553,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^4,x]","\frac{-16 a^6 x^6+16 a^5 x^5+40 a^4 x^4-40 a^3 x^3-30 a^2 x^2+30 a x+5}{35 a c^4 (1-a x)^{7/2} (a x+1)^{5/2}}","\frac{16 x}{35 c^4 \sqrt{1-a^2 x^2}}+\frac{8 x}{35 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}+\frac{a x+1}{7 a c^4 \left(1-a^2 x^2\right)^{7/2}}",1,"(5 + 30*a*x - 30*a^2*x^2 - 40*a^3*x^3 + 40*a^4*x^4 + 16*a^5*x^5 - 16*a^6*x^6)/(35*a*c^4*(1 - a*x)^(7/2)*(1 + a*x)^(5/2))","A",0
919,1,91,118,0.0325852,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^5} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^5,x]","\frac{128 a^8 x^8-128 a^7 x^7-448 a^6 x^6+448 a^5 x^5+560 a^4 x^4-560 a^3 x^3-280 a^2 x^2+280 a x+35}{315 a c^5 (1-a x)^{9/2} (a x+1)^{7/2}}","\frac{128 x}{315 c^5 \sqrt{1-a^2 x^2}}+\frac{64 x}{315 c^5 \left(1-a^2 x^2\right)^{3/2}}+\frac{16 x}{105 c^5 \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x}{63 c^5 \left(1-a^2 x^2\right)^{7/2}}+\frac{a x+1}{9 a c^5 \left(1-a^2 x^2\right)^{9/2}}",1,"(35 + 280*a*x - 280*a^2*x^2 - 560*a^3*x^3 + 560*a^4*x^4 + 448*a^5*x^5 - 448*a^6*x^6 - 128*a^7*x^7 + 128*a^8*x^8)/(315*a*c^5*(1 - a*x)^(9/2)*(1 + a*x)^(7/2))","A",0
920,1,49,49,0.0263056,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\sqrt{1-a^2 x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/Sqrt[1 - a^2*x^2],x]","-\frac{\log (1-a x)}{a^5}-\frac{x}{a^4}-\frac{x^2}{2 a^3}-\frac{x^3}{3 a^2}-\frac{x^4}{4 a}","-\frac{\log (1-a x)}{a^5}-\frac{x}{a^4}-\frac{x^2}{2 a^3}-\frac{x^3}{3 a^2}-\frac{x^4}{4 a}",1,"-(x/a^4) - x^2/(2*a^3) - x^3/(3*a^2) - x^4/(4*a) - Log[1 - a*x]/a^5","A",1
921,1,39,39,0.0194681,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\sqrt{1-a^2 x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/Sqrt[1 - a^2*x^2],x]","-\frac{\log (1-a x)}{a^4}-\frac{x}{a^3}-\frac{x^2}{2 a^2}-\frac{x^3}{3 a}","-\frac{\log (1-a x)}{a^4}-\frac{x}{a^3}-\frac{x^2}{2 a^2}-\frac{x^3}{3 a}",1,"-(x/a^3) - x^2/(2*a^2) - x^3/(3*a) - Log[1 - a*x]/a^4","A",1
922,1,29,29,0.0166946,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\sqrt{1-a^2 x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/Sqrt[1 - a^2*x^2],x]","-\frac{\log (1-a x)}{a^3}-\frac{x}{a^2}-\frac{x^2}{2 a}","-\frac{\log (1-a x)}{a^3}-\frac{x}{a^2}-\frac{x^2}{2 a}",1,"-(x/a^2) - x^2/(2*a) - Log[1 - a*x]/a^3","A",1
923,1,19,19,0.0128798,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\sqrt{1-a^2 x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x)/Sqrt[1 - a^2*x^2],x]","-\frac{\log (1-a x)}{a^2}-\frac{x}{a}","-\frac{\log (1-a x)}{a^2}-\frac{x}{a}",1,"-(x/a) - Log[1 - a*x]/a^2","A",1
924,1,12,12,0.0050309,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{1-a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]/Sqrt[1 - a^2*x^2],x]","-\frac{\log (1-a x)}{a}","-\frac{\log (1-a x)}{a}",1,"-(Log[1 - a*x]/a)","A",1
925,1,12,12,0.006669,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \sqrt{1-a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x*Sqrt[1 - a^2*x^2]),x]","\log (x)-\log (1-a x)","\log (x)-\log (1-a x)",1,"Log[x] - Log[1 - a*x]","A",1
926,1,20,20,0.0126867,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \sqrt{1-a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*Sqrt[1 - a^2*x^2]),x]","a \log (x)-a \log (1-a x)-\frac{1}{x}","a \log (x)-a \log (1-a x)-\frac{1}{x}",1,"-x^(-1) + a*Log[x] - a*Log[1 - a*x]","A",1
927,1,32,32,0.0144164,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \sqrt{1-a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*Sqrt[1 - a^2*x^2]),x]","a^2 \log (x)-a^2 \log (1-a x)-\frac{a}{x}-\frac{1}{2 x^2}","a^2 \log (x)-a^2 \log (1-a x)-\frac{a}{x}-\frac{1}{2 x^2}",1,"-1/2*1/x^2 - a/x + a^2*Log[x] - a^2*Log[1 - a*x]","A",1
928,1,42,42,0.0156238,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \sqrt{1-a^2 x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*Sqrt[1 - a^2*x^2]),x]","a^3 \log (x)-a^3 \log (1-a x)-\frac{a^2}{x}-\frac{a}{2 x^2}-\frac{1}{3 x^3}","a^3 \log (x)-a^3 \log (1-a x)-\frac{a^2}{x}-\frac{a}{2 x^2}-\frac{1}{3 x^3}",1,"-1/3*1/x^3 - a/(2*x^2) - a^2/x + a^3*Log[x] - a^3*Log[1 - a*x]","A",1
929,1,45,58,0.0479055,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(1 - a^2*x^2)^(3/2),x]","\frac{2 \left(a^2 x^2+2 a x+\frac{1}{1-a x}\right)+7 \log (1-a x)+\log (a x+1)}{4 a^5}","\frac{1}{2 a^5 (1-a x)}+\frac{7 \log (1-a x)}{4 a^5}+\frac{\log (a x+1)}{4 a^5}+\frac{x}{a^4}+\frac{x^2}{2 a^3}",1,"(2*(2*a*x + a^2*x^2 + (1 - a*x)^(-1)) + 7*Log[1 - a*x] + Log[1 + a*x])/(4*a^5)","A",1
930,1,39,48,0.0315441,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(1 - a^2*x^2)^(3/2),x]","\frac{4 a x+\frac{2}{1-a x}+5 \log (1-a x)-\log (a x+1)}{4 a^4}","\frac{1}{2 a^4 (1-a x)}+\frac{5 \log (1-a x)}{4 a^4}-\frac{\log (a x+1)}{4 a^4}+\frac{x}{a^3}",1,"(4*a*x + 2/(1 - a*x) + 5*Log[1 - a*x] - Log[1 + a*x])/(4*a^4)","A",1
931,1,33,43,0.0261565,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(1 - a^2*x^2)^(3/2),x]","\frac{\frac{2}{1-a x}+3 \log (1-a x)+\log (a x+1)}{4 a^3}","\frac{1}{2 a^3 (1-a x)}+\frac{3 \log (1-a x)}{4 a^3}+\frac{\log (a x+1)}{4 a^3}",1,"(2/(1 - a*x) + 3*Log[1 - a*x] + Log[1 + a*x])/(4*a^3)","A",1
932,1,22,27,0.0182997,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(1 - a^2*x^2)^(3/2),x]","\frac{\frac{1}{1-a x}-\tanh ^{-1}(a x)}{2 a^2}","\frac{1}{2 a^2 (1-a x)}-\frac{\tanh ^{-1}(a x)}{2 a^2}",1,"((1 - a*x)^(-1) - ArcTanh[a*x])/(2*a^2)","A",1
933,1,20,27,0.0148467,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(1 - a^2*x^2)^(3/2),x]","\frac{\frac{1}{1-a x}+\tanh ^{-1}(a x)}{2 a}","\frac{1}{2 a (1-a x)}+\frac{\tanh ^{-1}(a x)}{2 a}",1,"((1 - a*x)^(-1) + ArcTanh[a*x])/(2*a)","A",1
934,1,32,36,0.031474,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x*(1 - a^2*x^2)^(3/2)),x]","\frac{1}{2-2 a x}-\frac{3}{4} \log (1-a x)-\frac{1}{4} \log (a x+1)+\log (x)","\frac{1}{2 (1-a x)}-\frac{3}{4} \log (1-a x)-\frac{1}{4} \log (a x+1)+\log (x)",1,"(2 - 2*a*x)^(-1) + Log[x] - (3*Log[1 - a*x])/4 - Log[1 + a*x]/4","A",1
935,1,46,46,0.0399693,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(1 - a^2*x^2)^(3/2)),x]","\frac{a}{2 (1-a x)}+a \log (x)-\frac{5}{4} a \log (1-a x)+\frac{1}{4} a \log (a x+1)-\frac{1}{x}","\frac{a}{2 (1-a x)}+a \log (x)-\frac{5}{4} a \log (1-a x)+\frac{1}{4} a \log (a x+1)-\frac{1}{x}",1,"-x^(-1) + a/(2*(1 - a*x)) + a*Log[x] - (5*a*Log[1 - a*x])/4 + (a*Log[1 + a*x])/4","A",1
936,1,59,63,0.0514337,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(1 - a^2*x^2)^(3/2)),x]","\frac{1}{4} \left(\frac{2 a^2}{1-a x}+8 a^2 \log (x)-7 a^2 \log (1-a x)-a^2 \log (a x+1)-\frac{4 a}{x}-\frac{2}{x^2}\right)","\frac{a^2}{2 (1-a x)}+2 a^2 \log (x)-\frac{7}{4} a^2 \log (1-a x)-\frac{1}{4} a^2 \log (a x+1)-\frac{a}{x}-\frac{1}{2 x^2}",1,"(-2/x^2 - (4*a)/x + (2*a^2)/(1 - a*x) + 8*a^2*Log[x] - 7*a^2*Log[1 - a*x] - a^2*Log[1 + a*x])/4","A",1
937,1,67,73,0.0593712,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(1 - a^2*x^2)^(3/2)),x]","\frac{1}{12} \left(\frac{6 a^3}{1-a x}+24 a^3 \log (x)-27 a^3 \log (1-a x)+3 a^3 \log (a x+1)-\frac{24 a^2}{x}-\frac{6 a}{x^2}-\frac{4}{x^3}\right)","\frac{a^3}{2 (1-a x)}+2 a^3 \log (x)-\frac{9}{4} a^3 \log (1-a x)+\frac{1}{4} a^3 \log (a x+1)-\frac{2 a^2}{x}-\frac{a}{2 x^2}-\frac{1}{3 x^3}",1,"(-4/x^3 - (6*a)/x^2 - (24*a^2)/x + (6*a^3)/(1 - a*x) + 24*a^3*Log[x] - 27*a^3*Log[1 - a*x] + 3*a^3*Log[1 + a*x])/12","A",1
938,1,65,88,0.0943809,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^6)/(1 - a^2*x^2)^(5/2),x]","\frac{2 \left(-4 a^2 x^2-8 a x+\frac{10}{a x-1}-\frac{1}{a x+1}+\frac{1}{(a x-1)^2}\right)-39 \log (1-a x)-9 \log (a x+1)}{16 a^7}","-\frac{5}{4 a^7 (1-a x)}-\frac{1}{8 a^7 (a x+1)}+\frac{1}{8 a^7 (1-a x)^2}-\frac{39 \log (1-a x)}{16 a^7}-\frac{9 \log (a x+1)}{16 a^7}-\frac{x}{a^6}-\frac{x^2}{2 a^5}",1,"(2*(-8*a*x - 4*a^2*x^2 + (-1 + a*x)^(-2) + 10/(-1 + a*x) - (1 + a*x)^(-1)) - 39*Log[1 - a*x] - 9*Log[1 + a*x])/(16*a^7)","A",1
939,1,55,76,0.0759007,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^5)/(1 - a^2*x^2)^(5/2),x]","\frac{2 \left(-8 a x+\frac{8}{a x-1}+\frac{1}{a x+1}+\frac{1}{(a x-1)^2}\right)-23 \log (1-a x)+7 \log (a x+1)}{16 a^6}","-\frac{1}{a^6 (1-a x)}+\frac{1}{8 a^6 (a x+1)}+\frac{1}{8 a^6 (1-a x)^2}-\frac{23 \log (1-a x)}{16 a^6}+\frac{7 \log (a x+1)}{16 a^6}-\frac{x}{a^5}",1,"(2*(-8*a*x + (-1 + a*x)^(-2) + 8/(-1 + a*x) + (1 + a*x)^(-1)) - 23*Log[1 - a*x] + 7*Log[1 + a*x])/(16*a^6)","A",1
940,1,55,72,0.0655274,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(1 - a^2*x^2)^(5/2),x]","\frac{\frac{2 \left(5 a^2 x^2+3 a x-6\right)}{(a x-1)^2 (a x+1)}-11 \log (1-a x)-5 \log (a x+1)}{16 a^5}","-\frac{3}{4 a^5 (1-a x)}-\frac{1}{8 a^5 (a x+1)}+\frac{1}{8 a^5 (1-a x)^2}-\frac{11 \log (1-a x)}{16 a^5}-\frac{5 \log (a x+1)}{16 a^5}",1,"((2*(-6 + 3*a*x + 5*a^2*x^2))/((-1 + a*x)^2*(1 + a*x)) - 11*Log[1 - a*x] - 5*Log[1 + a*x])/(16*a^5)","A",1
941,1,53,56,0.0337204,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(1 - a^2*x^2)^(5/2),x]","\frac{5 a^2 x^2-a x+3 (a x-1)^2 (a x+1) \tanh ^{-1}(a x)-2}{8 a^4 (a x-1)^2 (a x+1)}","-\frac{1}{2 a^4 (1-a x)}+\frac{1}{8 a^4 (a x+1)}+\frac{1}{8 a^4 (1-a x)^2}+\frac{3 \tanh ^{-1}(a x)}{8 a^4}",1,"(-2 - a*x + 5*a^2*x^2 + 3*(-1 + a*x)^2*(1 + a*x)*ArcTanh[a*x])/(8*a^4*(-1 + a*x)^2*(1 + a*x))","A",1
942,1,52,56,0.031688,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(1 - a^2*x^2)^(5/2),x]","\frac{a^2 x^2+3 a x-(a x-1)^2 (a x+1) \tanh ^{-1}(a x)-2}{8 a^3 (a x-1)^2 (a x+1)}","-\frac{1}{4 a^3 (1-a x)}-\frac{1}{8 a^3 (a x+1)}+\frac{1}{8 a^3 (1-a x)^2}-\frac{\tanh ^{-1}(a x)}{8 a^3}",1,"(-2 + 3*a*x + a^2*x^2 - (-1 + a*x)^2*(1 + a*x)*ArcTanh[a*x])/(8*a^3*(-1 + a*x)^2*(1 + a*x))","A",1
943,1,28,41,0.0282476,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(1 - a^2*x^2)^(5/2),x]","\frac{\frac{1}{a x+1}+\frac{1}{(a x-1)^2}-\tanh ^{-1}(a x)}{8 a^2}","\frac{1}{8 a^2 (a x+1)}+\frac{1}{8 a^2 (1-a x)^2}-\frac{\tanh ^{-1}(a x)}{8 a^2}",1,"((-1 + a*x)^(-2) + (1 + a*x)^(-1) - ArcTanh[a*x])/(8*a^2)","A",1
944,1,53,56,0.025635,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(1 - a^2*x^2)^(5/2),x]","\frac{-3 a^2 x^2+3 a x+3 (a x-1)^2 (a x+1) \tanh ^{-1}(a x)+2}{8 a (a x-1)^2 (a x+1)}","\frac{1}{4 a (1-a x)}-\frac{1}{8 a (a x+1)}+\frac{1}{8 a (1-a x)^2}+\frac{3 \tanh ^{-1}(a x)}{8 a}",1,"(2 + 3*a*x - 3*a^2*x^2 + 3*(-1 + a*x)^2*(1 + a*x)*ArcTanh[a*x])/(8*a*(-1 + a*x)^2*(1 + a*x))","A",1
945,1,54,59,0.0477743,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x*(1 - a^2*x^2)^(5/2)),x]","\frac{1}{16} \left(\frac{8}{1-a x}+\frac{2}{a x+1}+\frac{2}{(a x-1)^2}-11 \log (1-a x)-5 \log (a x+1)+16 \log (x)\right)","\frac{1}{2 (1-a x)}+\frac{1}{8 (a x+1)}+\frac{1}{8 (1-a x)^2}-\frac{11}{16} \log (1-a x)-\frac{5}{16} \log (a x+1)+\log (x)",1,"(8/(1 - a*x) + 2/(-1 + a*x)^2 + 2/(1 + a*x) + 16*Log[x] - 11*Log[1 - a*x] - 5*Log[1 + a*x])/16","A",1
946,1,65,71,0.0620371,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(1 - a^2*x^2)^(5/2)),x]","\frac{1}{16} \left(\frac{12 a}{1-a x}-\frac{2 a}{a x+1}+\frac{2 a}{(a x-1)^2}+16 a \log (x)-23 a \log (1-a x)+7 a \log (a x+1)-\frac{16}{x}\right)","\frac{3 a}{4 (1-a x)}-\frac{a}{8 (a x+1)}+\frac{a}{8 (1-a x)^2}+a \log (x)-\frac{23}{16} a \log (1-a x)+\frac{7}{16} a \log (a x+1)-\frac{1}{x}",1,"(-16/x + (12*a)/(1 - a*x) + (2*a)/(-1 + a*x)^2 - (2*a)/(1 + a*x) + 16*a*Log[x] - 23*a*Log[1 - a*x] + 7*a*Log[1 + a*x])/16","A",1
947,1,83,89,0.0747029,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(1 - a^2*x^2)^(5/2)),x]","\frac{1}{16} \left(\frac{16 a^2}{1-a x}+\frac{2 a^2}{a x+1}+\frac{2 a^2}{(a x-1)^2}+48 a^2 \log (x)-39 a^2 \log (1-a x)-9 a^2 \log (a x+1)-\frac{16 a}{x}-\frac{8}{x^2}\right)","\frac{a^2}{1-a x}+\frac{a^2}{8 (a x+1)}+\frac{a^2}{8 (1-a x)^2}+3 a^2 \log (x)-\frac{39}{16} a^2 \log (1-a x)-\frac{9}{16} a^2 \log (a x+1)-\frac{a}{x}-\frac{1}{2 x^2}",1,"(-8/x^2 - (16*a)/x + (16*a^2)/(1 - a*x) + (2*a^2)/(-1 + a*x)^2 + (2*a^2)/(1 + a*x) + 48*a^2*Log[x] - 39*a^2*Log[1 - a*x] - 9*a^2*Log[1 + a*x])/16","A",1
948,1,91,102,0.0865084,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(1 - a^2*x^2)^(5/2)),x]","\frac{1}{48} \left(\frac{60 a^3}{1-a x}-\frac{6 a^3}{a x+1}+\frac{6 a^3}{(a x-1)^2}+144 a^3 \log (x)-177 a^3 \log (1-a x)+33 a^3 \log (a x+1)-\frac{144 a^2}{x}-\frac{24 a}{x^2}-\frac{16}{x^3}\right)","\frac{5 a^3}{4 (1-a x)}-\frac{a^3}{8 (a x+1)}+\frac{a^3}{8 (1-a x)^2}+3 a^3 \log (x)-\frac{59}{16} a^3 \log (1-a x)+\frac{11}{16} a^3 \log (a x+1)-\frac{3 a^2}{x}-\frac{a}{2 x^2}-\frac{1}{3 x^3}",1,"(-16/x^3 - (24*a)/x^2 - (144*a^2)/x + (60*a^3)/(1 - a*x) + (6*a^3)/(-1 + a*x)^2 - (6*a^3)/(1 + a*x) + 144*a^3*Log[x] - 177*a^3*Log[1 - a*x] + 33*a^3*Log[1 + a*x])/48","A",1
949,1,42,74,0.0268915,"\int e^{\tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^ArcTanh[a*x]*x^2*Sqrt[c - a^2*c*x^2],x]","\frac{x^3 (3 a x+4) \sqrt{c-a^2 c x^2}}{12 \sqrt{1-a^2 x^2}}","\frac{a x^4 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-a^2 x^2}}+\frac{x^3 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-a^2 x^2}}",1,"(x^3*(4 + 3*a*x)*Sqrt[c - a^2*c*x^2])/(12*Sqrt[1 - a^2*x^2])","A",1
950,1,42,74,0.0200512,"\int e^{\tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[E^ArcTanh[a*x]*x*Sqrt[c - a^2*c*x^2],x]","\frac{x^2 (2 a x+3) \sqrt{c-a^2 c x^2}}{6 \sqrt{1-a^2 x^2}}","\frac{x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}+\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-a^2 x^2}}",1,"(x^2*(3 + 2*a*x)*Sqrt[c - a^2*c*x^2])/(6*Sqrt[1 - a^2*x^2])","A",1
951,1,40,69,0.0157977,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2],x]","\frac{\left(\frac{a x^2}{2}+x\right) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}","\frac{a x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}+\frac{x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}",1,"((x + (a*x^2)/2)*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]","A",1
952,1,36,65,0.019621,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2])/x,x]","\frac{\sqrt{c-a^2 c x^2} (a x+\log (x))}{\sqrt{1-a^2 x^2}}","\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(a*x + Log[x]))/Sqrt[1 - a^2*x^2]","A",1
953,1,40,68,0.0203467,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2])/x^2,x]","\frac{\sqrt{c-a^2 c x^2} \left(a \log (x)-\frac{1}{x}\right)}{\sqrt{1-a^2 x^2}}","\frac{a \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-x^(-1) + a*Log[x]))/Sqrt[1 - a^2*x^2]","A",1
954,1,57,89,0.0280174,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^(3/2),x]","-\frac{c x \left(3 a^3 x^3+4 a^2 x^2-6 a x-12\right) \sqrt{c-a^2 c x^2}}{12 \sqrt{1-a^2 x^2}}","\frac{2 c (a x+1)^3 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}-\frac{c (a x+1)^4 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-a^2 x^2}}",1,"-1/12*(c*x*Sqrt[c - a^2*c*x^2]*(-12 - 6*a*x + 4*a^2*x^2 + 3*a^3*x^3))/Sqrt[1 - a^2*x^2]","A",0
955,1,60,136,0.0393601,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^(5/2),x]","\frac{c^2 (a x+1)^4 \left(5 a^2 x^2-14 a x+11\right) \sqrt{c-a^2 c x^2}}{30 a \sqrt{1-a^2 x^2}}","\frac{c^2 (a x+1)^6 \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{4 c^2 (a x+1)^5 \sqrt{c-a^2 c x^2}}{5 a \sqrt{1-a^2 x^2}}+\frac{c^2 (a x+1)^4 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}",1,"(c^2*(1 + a*x)^4*(11 - 14*a*x + 5*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(30*a*Sqrt[1 - a^2*x^2])","A",1
956,1,68,183,0.048683,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^(7/2),x]","-\frac{c^3 (a x+1)^5 \left(35 a^3 x^3-135 a^2 x^2+185 a x-93\right) \sqrt{c-a^2 c x^2}}{280 a \sqrt{1-a^2 x^2}}","-\frac{c^3 (a x+1)^8 \sqrt{c-a^2 c x^2}}{8 a \sqrt{1-a^2 x^2}}+\frac{6 c^3 (a x+1)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}-\frac{2 c^3 (a x+1)^6 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}+\frac{8 c^3 (a x+1)^5 \sqrt{c-a^2 c x^2}}{5 a \sqrt{1-a^2 x^2}}",1,"-1/280*(c^3*(1 + a*x)^5*Sqrt[c - a^2*c*x^2]*(-93 + 185*a*x - 135*a^2*x^2 + 35*a^3*x^3))/(a*Sqrt[1 - a^2*x^2])","A",1
957,1,71,194,0.0472031,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{1-a^2 x^2} \left(a x \left(3 a^3 x^3+4 a^2 x^2+6 a x+12\right)+12 \log (1-a x)\right)}{12 a^5 \sqrt{c-a^2 c x^2}}","-\frac{x^4 \sqrt{1-a^2 x^2}}{4 a \sqrt{c-a^2 c x^2}}-\frac{x^3 \sqrt{1-a^2 x^2}}{3 a^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a^5 \sqrt{c-a^2 c x^2}}-\frac{x \sqrt{1-a^2 x^2}}{a^4 \sqrt{c-a^2 c x^2}}-\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^3 \sqrt{c-a^2 c x^2}}",1,"-1/12*(Sqrt[1 - a^2*x^2]*(a*x*(12 + 6*a*x + 4*a^2*x^2 + 3*a^3*x^3) + 12*Log[1 - a*x]))/(a^5*Sqrt[c - a^2*c*x^2])","A",1
958,1,63,155,0.0381832,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{1-a^2 x^2} \left(a x \left(2 a^2 x^2+3 a x+6\right)+6 \log (1-a x)\right)}{6 a^4 \sqrt{c-a^2 c x^2}}","-\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^2 \sqrt{c-a^2 c x^2}}-\frac{x^3 \sqrt{1-a^2 x^2}}{3 a \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a^4 \sqrt{c-a^2 c x^2}}-\frac{x \sqrt{1-a^2 x^2}}{a^3 \sqrt{c-a^2 c x^2}}",1,"-1/6*(Sqrt[1 - a^2*x^2]*(a*x*(6 + 3*a*x + 2*a^2*x^2) + 6*Log[1 - a*x]))/(a^4*Sqrt[c - a^2*c*x^2])","A",1
959,1,54,116,0.0326776,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{1-a^2 x^2} (a x (a x+2)+2 \log (1-a x))}{2 a^3 \sqrt{c-a^2 c x^2}}","-\frac{x^2 \sqrt{1-a^2 x^2}}{2 a \sqrt{c-a^2 c x^2}}-\frac{x \sqrt{1-a^2 x^2}}{a^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a^3 \sqrt{c-a^2 c x^2}}",1,"-1/2*(Sqrt[1 - a^2*x^2]*(a*x*(2 + a*x) + 2*Log[1 - a*x]))/(a^3*Sqrt[c - a^2*c*x^2])","A",1
960,1,45,77,0.0254012,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x)/Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{1-a^2 x^2} (a x+\log (1-a x))}{a^2 \sqrt{c-a^2 c x^2}}","-\frac{x \sqrt{1-a^2 x^2}}{a \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a^2 \sqrt{c-a^2 c x^2}}",1,"-((Sqrt[1 - a^2*x^2]*(a*x + Log[1 - a*x]))/(a^2*Sqrt[c - a^2*c*x^2]))","A",1
961,1,41,41,0.0129358,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[E^ArcTanh[a*x]/Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a \sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a \sqrt{c-a^2 c x^2}}",1,"-((Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a*Sqrt[c - a^2*c*x^2]))","A",1
962,1,42,71,0.0171138,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} (\log (x)-\log (1-a x))}{\sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} \log (x)}{\sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{\sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(Log[x] - Log[1 - a*x]))/Sqrt[c - a^2*c*x^2]","A",1
963,1,50,107,0.0292866,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} \left(a \log (x)-a \log (1-a x)-\frac{1}{x}\right)}{\sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2}}{x \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2} \log (x)}{\sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2} \log (1-a x)}{\sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-x^(-1) + a*Log[x] - a*Log[1 - a*x]))/Sqrt[c - a^2*c*x^2]","A",1
964,1,62,148,0.0400184,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} \left(a^2 \log (x)-a^2 \log (1-a x)-\frac{a}{x}-\frac{1}{2 x^2}\right)}{\sqrt{c-a^2 c x^2}}","-\frac{a \sqrt{1-a^2 x^2}}{x \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{2 x^2 \sqrt{c-a^2 c x^2}}+\frac{a^2 \sqrt{1-a^2 x^2} \log (x)}{\sqrt{c-a^2 c x^2}}-\frac{a^2 \sqrt{1-a^2 x^2} \log (1-a x)}{\sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-1/2*1/x^2 - a/x + a^2*Log[x] - a^2*Log[1 - a*x]))/Sqrt[c - a^2*c*x^2]","A",1
965,1,72,187,0.0427154,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} \left(a^3 \log (x)-a^3 \log (1-a x)-\frac{a^2}{x}-\frac{a}{2 x^2}-\frac{1}{3 x^3}\right)}{\sqrt{c-a^2 c x^2}}","-\frac{a^2 \sqrt{1-a^2 x^2}}{x \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2}}{2 x^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{3 x^3 \sqrt{c-a^2 c x^2}}+\frac{a^3 \sqrt{1-a^2 x^2} \log (x)}{\sqrt{c-a^2 c x^2}}-\frac{a^3 \sqrt{1-a^2 x^2} \log (1-a x)}{\sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-1/3*1/x^3 - a/(2*x^2) - a^2/x + a^3*Log[x] - a^3*Log[1 - a*x]))/Sqrt[c - a^2*c*x^2]","A",1
966,1,87,261,0.0748043,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(4 a^3 x^3+6 a^2 x^2+24 a x+\frac{6}{1-a x}+27 \log (1-a x)-3 \log (a x+1)\right)}{12 a^6 c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a^6 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{9 \sqrt{1-a^2 x^2} \log (1-a x)}{4 a^6 c \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{4 a^6 c \sqrt{c-a^2 c x^2}}+\frac{2 x \sqrt{1-a^2 x^2}}{a^5 c \sqrt{c-a^2 c x^2}}+\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^4 c \sqrt{c-a^2 c x^2}}+\frac{x^3 \sqrt{1-a^2 x^2}}{3 a^3 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(24*a*x + 6*a^2*x^2 + 4*a^3*x^3 + 6/(1 - a*x) + 27*Log[1 - a*x] - 3*Log[1 + a*x]))/(12*a^6*c*Sqrt[c - a^2*c*x^2])","A",1
967,1,77,218,0.0634549,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(2 \left(a^2 x^2+2 a x+\frac{1}{1-a x}\right)+7 \log (1-a x)+\log (a x+1)\right)}{4 a^5 c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a^5 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{7 \sqrt{1-a^2 x^2} \log (1-a x)}{4 a^5 c \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{4 a^5 c \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{1-a^2 x^2}}{a^4 c \sqrt{c-a^2 c x^2}}+\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^3 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(2*(2*a*x + a^2*x^2 + (1 - a*x)^(-1)) + 7*Log[1 - a*x] + Log[1 + a*x]))/(4*a^5*c*Sqrt[c - a^2*c*x^2])","A",1
968,1,71,176,0.0534725,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(4 a x+\frac{2}{1-a x}+5 \log (1-a x)-\log (a x+1)\right)}{4 a^4 c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a^4 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{5 \sqrt{1-a^2 x^2} \log (1-a x)}{4 a^4 c \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{4 a^4 c \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{1-a^2 x^2}}{a^3 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(4*a*x + 2/(1 - a*x) + 5*Log[1 - a*x] - Log[1 + a*x]))/(4*a^4*c*Sqrt[c - a^2*c*x^2])","A",1
969,1,76,139,0.0427292,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{2 a^3 (1-a x)}+\frac{3 \log (1-a x)}{4 a^3}+\frac{\log (a x+1)}{4 a^3}\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a^3 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \log (1-a x)}{4 a^3 c \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{4 a^3 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(1/(2*a^3*(1 - a*x)) + (3*Log[1 - a*x])/(4*a^3) + Log[1 + a*x]/(4*a^3)))/(c*Sqrt[c - a^2*c*x^2])","A",1
970,1,60,91,0.0360673,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{2 a^2 (1-a x)}-\frac{\tanh ^{-1}(a x)}{2 a^2}\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a^2 c (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 a^2 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(1/(2*a^2*(1 - a*x)) - ArcTanh[a*x]/(2*a^2)))/(c*Sqrt[c - a^2*c*x^2])","A",1
971,1,60,91,0.0289818,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{2 a (1-a x)}+\frac{\tanh ^{-1}(a x)}{2 a}\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 a c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(1/(2*a*(1 - a*x)) + ArcTanh[a*x]/(2*a)))/(c*Sqrt[c - a^2*c*x^2])","A",1
972,1,65,165,0.0549149,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{2-2 a x}-\frac{3}{4} \log (1-a x)-\frac{1}{4} \log (a x+1)+\log (x)\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log (x)}{c \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{1-a^2 x^2} \log (1-a x)}{4 c \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{4 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*((2 - 2*a*x)^(-1) + Log[x] - (3*Log[1 - a*x])/4 - Log[1 + a*x]/4))/(c*Sqrt[c - a^2*c*x^2])","A",1
973,1,76,206,0.0625481,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{2 a}{1-a x}+4 a \log (x)-5 a \log (1-a x)+a \log (a x+1)-\frac{4}{x}\right)}{4 c \sqrt{c-a^2 c x^2}}","\frac{a \sqrt{1-a^2 x^2}}{2 c (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{c x \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2} \log (x)}{c \sqrt{c-a^2 c x^2}}-\frac{5 a \sqrt{1-a^2 x^2} \log (1-a x)}{4 c \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2} \log (a x+1)}{4 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-4/x + (2*a)/(1 - a*x) + 4*a*Log[x] - 5*a*Log[1 - a*x] + a*Log[1 + a*x]))/(4*c*Sqrt[c - a^2*c*x^2])","A",1
974,1,91,255,0.066247,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{2 a^2}{1-a x}+8 a^2 \log (x)-7 a^2 \log (1-a x)-a^2 \log (a x+1)-\frac{4 a}{x}-\frac{2}{x^2}\right)}{4 c \sqrt{c-a^2 c x^2}}","\frac{a^2 \sqrt{1-a^2 x^2}}{2 c (1-a x) \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2}}{c x \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{2 c x^2 \sqrt{c-a^2 c x^2}}+\frac{2 a^2 \sqrt{1-a^2 x^2} \log (x)}{c \sqrt{c-a^2 c x^2}}-\frac{7 a^2 \sqrt{1-a^2 x^2} \log (1-a x)}{4 c \sqrt{c-a^2 c x^2}}-\frac{a^2 \sqrt{1-a^2 x^2} \log (a x+1)}{4 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-2/x^2 - (4*a)/x + (2*a^2)/(1 - a*x) + 8*a^2*Log[x] - 7*a^2*Log[1 - a*x] - a^2*Log[1 + a*x]))/(4*c*Sqrt[c - a^2*c*x^2])","A",1
975,1,99,297,0.0779299,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^4*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{6 a^3}{1-a x}+24 a^3 \log (x)-27 a^3 \log (1-a x)+3 a^3 \log (a x+1)-\frac{24 a^2}{x}-\frac{6 a}{x^2}-\frac{4}{x^3}\right)}{12 c \sqrt{c-a^2 c x^2}}","-\frac{2 a^2 \sqrt{1-a^2 x^2}}{c x \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2}}{2 c x^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{3 c x^3 \sqrt{c-a^2 c x^2}}+\frac{a^3 \sqrt{1-a^2 x^2}}{2 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{2 a^3 \sqrt{1-a^2 x^2} \log (x)}{c \sqrt{c-a^2 c x^2}}-\frac{9 a^3 \sqrt{1-a^2 x^2} \log (1-a x)}{4 c \sqrt{c-a^2 c x^2}}+\frac{a^3 \sqrt{1-a^2 x^2} \log (a x+1)}{4 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-4/x^3 - (6*a)/x^2 - (24*a^2)/x + (6*a^3)/(1 - a*x) + 24*a^3*Log[x] - 27*a^3*Log[1 - a*x] + 3*a^3*Log[1 + a*x]))/(12*c*Sqrt[c - a^2*c*x^2])","A",1
976,1,97,312,0.1337451,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^6)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(2 \left(-4 a^2 x^2-8 a x+\frac{10}{a x-1}-\frac{1}{a x+1}+\frac{1}{(a x-1)^2}\right)-39 \log (1-a x)-9 \log (a x+1)\right)}{16 a^7 c^2 \sqrt{c-a^2 c x^2}}","-\frac{5 \sqrt{1-a^2 x^2}}{4 a^7 c^2 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a^7 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^7 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{39 \sqrt{1-a^2 x^2} \log (1-a x)}{16 a^7 c^2 \sqrt{c-a^2 c x^2}}-\frac{9 \sqrt{1-a^2 x^2} \log (a x+1)}{16 a^7 c^2 \sqrt{c-a^2 c x^2}}-\frac{x \sqrt{1-a^2 x^2}}{a^6 c^2 \sqrt{c-a^2 c x^2}}-\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^5 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(2*(-8*a*x - 4*a^2*x^2 + (-1 + a*x)^(-2) + 10/(-1 + a*x) - (1 + a*x)^(-1)) - 39*Log[1 - a*x] - 9*Log[1 + a*x]))/(16*a^7*c^2*Sqrt[c - a^2*c*x^2])","A",1
977,1,87,268,0.1220328,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(2 \left(-8 a x+\frac{8}{a x-1}+\frac{1}{a x+1}+\frac{1}{(a x-1)^2}\right)-23 \log (1-a x)+7 \log (a x+1)\right)}{16 a^6 c^2 \sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2}}{a^6 c^2 (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^6 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^6 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{23 \sqrt{1-a^2 x^2} \log (1-a x)}{16 a^6 c^2 \sqrt{c-a^2 c x^2}}+\frac{7 \sqrt{1-a^2 x^2} \log (a x+1)}{16 a^6 c^2 \sqrt{c-a^2 c x^2}}-\frac{x \sqrt{1-a^2 x^2}}{a^5 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(2*(-8*a*x + (-1 + a*x)^(-2) + 8/(-1 + a*x) + (1 + a*x)^(-1)) - 23*Log[1 - a*x] + 7*Log[1 + a*x]))/(16*a^6*c^2*Sqrt[c - a^2*c*x^2])","A",1
978,1,87,232,0.1038447,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{2 \left(5 a^2 x^2+3 a x-6\right)}{(a x-1)^2 (a x+1)}-11 \log (1-a x)-5 \log (a x+1)\right)}{16 a^5 c^2 \sqrt{c-a^2 c x^2}}","-\frac{3 \sqrt{1-a^2 x^2}}{4 a^5 c^2 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a^5 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^5 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{11 \sqrt{1-a^2 x^2} \log (1-a x)}{16 a^5 c^2 \sqrt{c-a^2 c x^2}}-\frac{5 \sqrt{1-a^2 x^2} \log (a x+1)}{16 a^5 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*((2*(-6 + 3*a*x + 5*a^2*x^2))/((-1 + a*x)^2*(1 + a*x)) - 11*Log[1 - a*x] - 5*Log[1 + a*x]))/(16*a^5*c^2*Sqrt[c - a^2*c*x^2])","A",1
979,1,85,184,0.0667073,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(5 a^2 x^2-a x+3 (a x-1)^2 (a x+1) \tanh ^{-1}(a x)-2\right)}{8 a^4 c^2 (a x-1)^2 (a x+1) \sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2}}{2 a^4 c^2 (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^4 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^4 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^4 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-2 - a*x + 5*a^2*x^2 + 3*(-1 + a*x)^2*(1 + a*x)*ArcTanh[a*x]))/(8*a^4*c^2*(-1 + a*x)^2*(1 + a*x)*Sqrt[c - a^2*c*x^2])","A",1
980,1,84,184,0.0598318,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(a^2 x^2+3 a x-(a x-1)^2 (a x+1) \tanh ^{-1}(a x)-2\right)}{8 a^3 c^2 (a x-1)^2 (a x+1) \sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2}}{4 a^3 c^2 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a^3 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^3 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^3 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-2 + 3*a*x + a^2*x^2 - (-1 + a*x)^2*(1 + a*x)*ArcTanh[a*x]))/(8*a^3*c^2*(-1 + a*x)^2*(1 + a*x)*Sqrt[c - a^2*c*x^2])","A",1
981,1,60,137,0.0693582,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{a x+1}+\frac{1}{(a x-1)^2}-\tanh ^{-1}(a x)\right)}{8 a^2 c^2 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{8 a^2 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a^2 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a^2 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*((-1 + a*x)^(-2) + (1 + a*x)^(-1) - ArcTanh[a*x]))/(8*a^2*c^2*Sqrt[c - a^2*c*x^2])","A",1
982,1,85,184,0.0497044,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(-3 a^2 x^2+3 a x+3 (a x-1)^2 (a x+1) \tanh ^{-1}(a x)+2\right)}{8 a c^2 (a x-1)^2 (a x+1) \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{4 a c^2 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(2 + 3*a*x - 3*a^2*x^2 + 3*(-1 + a*x)^2*(1 + a*x)*ArcTanh[a*x]))/(8*a*c^2*(-1 + a*x)^2*(1 + a*x)*Sqrt[c - a^2*c*x^2])","A",1
983,1,86,252,0.0705937,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{8}{1-a x}+\frac{2}{a x+1}+\frac{2}{(a x-1)^2}-11 \log (1-a x)-5 \log (a x+1)+16 \log (x)\right)}{16 c^2 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 c^2 (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log (x)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{11 \sqrt{1-a^2 x^2} \log (1-a x)}{16 c^2 \sqrt{c-a^2 c x^2}}-\frac{5 \sqrt{1-a^2 x^2} \log (a x+1)}{16 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(8/(1 - a*x) + 2/(-1 + a*x)^2 + 2/(1 + a*x) + 16*Log[x] - 11*Log[1 - a*x] - 5*Log[1 + a*x]))/(16*c^2*Sqrt[c - a^2*c*x^2])","A",1
984,1,97,295,0.0933226,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{12 a}{1-a x}-\frac{2 a}{a x+1}+\frac{2 a}{(a x-1)^2}+16 a \log (x)-23 a \log (1-a x)+7 a \log (a x+1)-\frac{16}{x}\right)}{16 c^2 \sqrt{c-a^2 c x^2}}","\frac{3 a \sqrt{1-a^2 x^2}}{4 c^2 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2}}{8 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2}}{8 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{c^2 x \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2} \log (x)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{23 a \sqrt{1-a^2 x^2} \log (1-a x)}{16 c^2 \sqrt{c-a^2 c x^2}}+\frac{7 a \sqrt{1-a^2 x^2} \log (a x+1)}{16 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-16/x + (12*a)/(1 - a*x) + (2*a)/(-1 + a*x)^2 - (2*a)/(1 + a*x) + 16*a*Log[x] - 23*a*Log[1 - a*x] + 7*a*Log[1 + a*x]))/(16*c^2*Sqrt[c - a^2*c*x^2])","A",1
985,1,115,345,0.1216301,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{16 a^2}{1-a x}+\frac{2 a^2}{a x+1}+\frac{2 a^2}{(a x-1)^2}+48 a^2 \log (x)-39 a^2 \log (1-a x)-9 a^2 \log (a x+1)-\frac{16 a}{x}-\frac{8}{x^2}\right)}{16 c^2 \sqrt{c-a^2 c x^2}}","\frac{a^2 \sqrt{1-a^2 x^2}}{c^2 (1-a x) \sqrt{c-a^2 c x^2}}+\frac{a^2 \sqrt{1-a^2 x^2}}{8 c^2 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{a^2 \sqrt{1-a^2 x^2}}{8 c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{a \sqrt{1-a^2 x^2}}{c^2 x \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{2 c^2 x^2 \sqrt{c-a^2 c x^2}}+\frac{3 a^2 \sqrt{1-a^2 x^2} \log (x)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{39 a^2 \sqrt{1-a^2 x^2} \log (1-a x)}{16 c^2 \sqrt{c-a^2 c x^2}}-\frac{9 a^2 \sqrt{1-a^2 x^2} \log (a x+1)}{16 c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-8/x^2 - (16*a)/x + (16*a^2)/(1 - a*x) + (2*a^2)/(-1 + a*x)^2 + (2*a^2)/(1 + a*x) + 48*a^2*Log[x] - 39*a^2*Log[1 - a*x] - 9*a^2*Log[1 + a*x]))/(16*c^2*Sqrt[c - a^2*c*x^2])","A",1
986,1,103,277,0.083053,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[E^ArcTanh[a*x]/(c - a^2*c*x^2)^(7/2),x]","\frac{\sqrt{1-a^2 x^2} \left(-15 a^4 x^4+15 a^3 x^3+25 a^2 x^2-25 a x+15 (a x-1)^3 (a x+1)^2 \tanh ^{-1}(a x)-8\right)}{48 a c^3 (a x-1)^3 (a x+1)^2 \sqrt{c-a^2 c x^2}}","\frac{3 \sqrt{1-a^2 x^2}}{16 a c^3 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a c^3 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2}}{32 a c^3 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{32 a c^3 (a x+1)^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{24 a c^3 (1-a x)^3 \sqrt{c-a^2 c x^2}}+\frac{5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 a c^3 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-8 - 25*a*x + 25*a^2*x^2 + 15*a^3*x^3 - 15*a^4*x^4 + 15*(-1 + a*x)^3*(1 + a*x)^2*ArcTanh[a*x]))/(48*a*c^3*(-1 + a*x)^3*(1 + a*x)^2*Sqrt[c - a^2*c*x^2])","A",1
987,1,82,80,0.0350662,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2)^2,x]","c^2 \left(\frac{x^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}\right)","\frac{c^2 x^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a c^2 x^{m+2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"c^2*((x^(1 + m)*Hypergeometric2F1[-3/2, (1 + m)/2, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[-3/2, (2 + m)/2, 1 + (2 + m)/2, a^2*x^2])/(2 + m))","A",1
988,1,72,76,0.0448116,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","Integrate[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2),x]","c x^{m+1} \left(\frac{a x \, _2F_1\left(-\frac{1}{2},\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\frac{c x^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a c x^{m+2} \, _2F_1\left(-\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"c*x^(1 + m)*((a*x*Hypergeometric2F1[-1/2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
989,1,82,80,0.0316571,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{c-a^2 c x^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2),x]","\frac{\frac{x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}}{c}","\frac{x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{c (m+1)}+\frac{a x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{c (m+2)}",1,"((x^(1 + m)*Hypergeometric2F1[3/2, (1 + m)/2, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, 1 + (2 + m)/2, a^2*x^2])/(2 + m))/c","A",1
990,1,82,80,0.0317264,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^2,x]","\frac{\frac{x^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}}{c^2}","\frac{x^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{c^2 (m+1)}+\frac{a x^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{c^2 (m+2)}",1,"((x^(1 + m)*Hypergeometric2F1[5/2, (1 + m)/2, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[5/2, (2 + m)/2, 1 + (2 + m)/2, a^2*x^2])/(2 + m))/c^2","A",1
991,1,82,80,0.0339817,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^3,x]","\frac{\frac{x^{m+1} \, _2F_1\left(\frac{7}{2},\frac{m+1}{2};\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(\frac{7}{2},\frac{m+2}{2};\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}}{c^3}","\frac{x^{m+1} \, _2F_1\left(\frac{7}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{c^3 (m+1)}+\frac{a x^{m+2} \, _2F_1\left(\frac{7}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{c^3 (m+2)}",1,"((x^(1 + m)*Hypergeometric2F1[7/2, (1 + m)/2, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[7/2, (2 + m)/2, 1 + (2 + m)/2, a^2*x^2])/(2 + m))/c^3","A",1
992,1,70,82,0.0493133,"\int e^{\tanh ^{-1}(a x)} x^m \left(1-a^2 x^2\right)^{5/2} \, dx","Integrate[E^ArcTanh[a*x]*x^m*(1 - a^2*x^2)^(5/2),x]","x^{m+1} \left(\frac{a^5 x^5}{m+6}+\frac{a^4 x^4}{m+5}-\frac{2 a^3 x^3}{m+4}-\frac{2 a^2 x^2}{m+3}+\frac{a x}{m+2}+\frac{1}{m+1}\right)","\frac{a^5 x^{m+6}}{m+6}+\frac{a^4 x^{m+5}}{m+5}-\frac{2 a^3 x^{m+4}}{m+4}-\frac{2 a^2 x^{m+3}}{m+3}+\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)*((1 + m)^(-1) + (a*x)/(2 + m) - (2*a^2*x^2)/(3 + m) - (2*a^3*x^3)/(4 + m) + (a^4*x^4)/(5 + m) + (a^5*x^5)/(6 + m))","A",1
993,1,54,54,0.1324646,"\int e^{\tanh ^{-1}(a x)} x^m \left(1-a^2 x^2\right)^{3/2} \, dx","Integrate[E^ArcTanh[a*x]*x^m*(1 - a^2*x^2)^(3/2),x]","\frac{x^{m+1} \left((2 m+5) \left(\frac{a^2 x^2}{m+3}+\frac{2 a x}{m+2}+\frac{1}{m+1}\right)-(a x+1)^3\right)}{m+4}","-\frac{a^3 x^{m+4}}{m+4}-\frac{a^2 x^{m+3}}{m+3}+\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}",1,"(x^(1 + m)*(-(1 + a*x)^3 + (5 + 2*m)*((1 + m)^(-1) + (2*a*x)/(2 + m) + (a^2*x^2)/(3 + m))))/(4 + m)","A",1
994,1,20,24,0.0176438,"\int e^{\tanh ^{-1}(a x)} x^m \sqrt{1-a^2 x^2} \, dx","Integrate[E^ArcTanh[a*x]*x^m*Sqrt[1 - a^2*x^2],x]","x^{m+1} \left(\frac{a x}{m+2}+\frac{1}{m+1}\right)","\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)*((1 + m)^(-1) + (a*x)/(2 + m))","A",1
995,1,22,22,0.0105535,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\sqrt{1-a^2 x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/Sqrt[1 - a^2*x^2],x]","\frac{x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{m+1}","\frac{x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{m+1}",1,"(x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/(1 + m)","A",1
996,1,67,70,0.034911,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(1 - a^2*x^2)^(3/2),x]","x^{m+1} \left(\frac{a x \, _2F_1\left(2,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"x^(1 + m)*((a*x*Hypergeometric2F1[2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
997,1,67,70,0.0339856,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(1 - a^2*x^2)^(5/2),x]","x^{m+1} \left(\frac{a x \, _2F_1\left(3,\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}\right)","\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"x^(1 + m)*((a*x*Hypergeometric2F1[3, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) + Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m))","A",1
998,1,102,274,0.0949486,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2)^(5/2),x]","\frac{c^2 x^{m+1} \sqrt{c-a^2 c x^2} \left(\frac{a^5 x^5}{m+6}+\frac{a^4 x^4}{m+5}-\frac{2 a^3 x^3}{m+4}-\frac{2 a^2 x^2}{m+3}+\frac{a x}{m+2}+\frac{1}{m+1}\right)}{\sqrt{1-a^2 x^2}}","\frac{c^2 x^{m+1} \sqrt{c-a^2 c x^2}}{(m+1) \sqrt{1-a^2 x^2}}+\frac{a c^2 x^{m+2} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-a^2 x^2}}-\frac{2 a^2 c^2 x^{m+3} \sqrt{c-a^2 c x^2}}{(m+3) \sqrt{1-a^2 x^2}}+\frac{a^5 c^2 x^{m+6} \sqrt{c-a^2 c x^2}}{(m+6) \sqrt{1-a^2 x^2}}+\frac{a^4 c^2 x^{m+5} \sqrt{c-a^2 c x^2}}{(m+5) \sqrt{1-a^2 x^2}}-\frac{2 a^3 c^2 x^{m+4} \sqrt{c-a^2 c x^2}}{(m+4) \sqrt{1-a^2 x^2}}",1,"(c^2*x^(1 + m)*Sqrt[c - a^2*c*x^2]*((1 + m)^(-1) + (a*x)/(2 + m) - (2*a^2*x^2)/(3 + m) - (2*a^3*x^3)/(4 + m) + (a^4*x^4)/(5 + m) + (a^5*x^5)/(6 + m)))/Sqrt[1 - a^2*x^2]","A",1
999,1,84,174,0.0961516,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2)^(3/2),x]","\frac{c x^{m+1} \sqrt{c-a^2 c x^2} \left((2 m+5) \left(\frac{a^2 x^2}{m+3}+\frac{2 a x}{m+2}+\frac{1}{m+1}\right)-(a x+1)^3\right)}{(m+4) \sqrt{1-a^2 x^2}}","\frac{c x^{m+1} \sqrt{c-a^2 c x^2}}{(m+1) \sqrt{1-a^2 x^2}}+\frac{a c x^{m+2} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-a^2 x^2}}-\frac{a^2 c x^{m+3} \sqrt{c-a^2 c x^2}}{(m+3) \sqrt{1-a^2 x^2}}-\frac{a^3 c x^{m+4} \sqrt{c-a^2 c x^2}}{(m+4) \sqrt{1-a^2 x^2}}",1,"(c*x^(1 + m)*Sqrt[c - a^2*c*x^2]*(-(1 + a*x)^3 + (5 + 2*m)*((1 + m)^(-1) + (2*a*x)/(2 + m) + (a^2*x^2)/(3 + m))))/((4 + m)*Sqrt[1 - a^2*x^2])","A",1
1000,1,49,82,0.0333609,"\int e^{\tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Integrate[E^ArcTanh[a*x]*x^m*Sqrt[c - a^2*c*x^2],x]","\frac{x^{m+1} \sqrt{c-a^2 c x^2} \left(\frac{a x}{m+2}+\frac{1}{m+1}\right)}{\sqrt{1-a^2 x^2}}","\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+1) \sqrt{1-a^2 x^2}}+\frac{a x^{m+2} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-a^2 x^2}}",1,"(x^(1 + m)*((1 + m)^(-1) + (a*x)/(2 + m))*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]","A",1
1001,1,51,51,0.0275441,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{(m+1) \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{(m+1) \sqrt{c-a^2 c x^2}}",1,"(x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/((1 + m)*Sqrt[c - a^2*c*x^2])","A",1
1002,1,107,134,0.0431647,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{c (m+1) \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{c (m+2) \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*((x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, 1 + (2 + m)/2, a^2*x^2])/(2 + m)))/(c*Sqrt[c - a^2*c*x^2])","A",1
1003,1,107,134,0.0408389,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{x^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}\right)}{c^2 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} x^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{c^2 (m+1) \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{c^2 (m+2) \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*((x^(1 + m)*Hypergeometric2F1[3, (1 + m)/2, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[3, (2 + m)/2, 1 + (2 + m)/2, a^2*x^2])/(2 + m)))/(c^2*Sqrt[c - a^2*c*x^2])","A",1
1004,1,114,136,0.0428711,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2)^p,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{x^{m+1} \, _2F_1\left(\frac{m+1}{2},\frac{1}{2}-p;\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(\frac{m+2}{2},\frac{1}{2}-p;\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}\right)","\frac{x^{m+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{m+1}{2},\frac{1}{2}-p;\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{m+2}{2},\frac{1}{2}-p;\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"((c - a^2*c*x^2)^p*((x^(1 + m)*Hypergeometric2F1[(1 + m)/2, 1/2 - p, 1 + (1 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[(2 + m)/2, 1/2 - p, 1 + (2 + m)/2, a^2*x^2])/(2 + m)))/(1 - a^2*x^2)^p","A",1
1005,1,77,85,0.0701193,"\int e^{\tanh ^{-1}(a x)} x^3 \left(1-a^2 x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x^3*(1 - a^2*x^2)^p,x]","\frac{1}{5} a x^5 \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \left(a^2 (2 p+1) x^2+2\right)}{a^4 \left(4 p^2+8 p+3\right)}","\frac{1}{5} a x^5 \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^4 (2 p+1)}+\frac{\left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^4 (2 p+3)}",1,"-(((1 - a^2*x^2)^(1/2 + p)*(2 + a^2*(1 + 2*p)*x^2))/(a^4*(3 + 8*p + 4*p^2))) + (a*x^5*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/5","A",1
1006,1,76,84,0.0494218,"\int e^{\tanh ^{-1}(a x)} x^2 \left(1-a^2 x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x^2*(1 - a^2*x^2)^p,x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \left(a^2 (2 p+1) x^2+2\right)}{a^3 \left(4 p^2+8 p+3\right)}","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^3 (2 p+1)}+\frac{\left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^3 (2 p+3)}",1,"-(((1 - a^2*x^2)^(1/2 + p)*(2 + a^2*(1 + 2*p)*x^2))/(a^3*(3 + 8*p + 4*p^2))) + (x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3","A",1
1007,1,60,58,0.0238905,"\int e^{\tanh ^{-1}(a x)} x \left(1-a^2 x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x*(1 - a^2*x^2)^p,x]","\frac{1}{3} a x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{2 a^2 \left(p+\frac{1}{2}\right)}","\frac{1}{3} a x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^2 (2 p+1)}",1,"-1/2*(1 - a^2*x^2)^(1/2 + p)/(a^2*(1/2 + p)) + (a*x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3","A",1
1008,1,59,59,0.0146424,"\int e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*(1 - a^2*x^2)^p,x]","-\frac{2^{p+\frac{1}{2}} (1-a x)^{p+\frac{1}{2}} \, _2F_1\left(-p-\frac{1}{2},p+\frac{1}{2};p+\frac{3}{2};\frac{1}{2} (1-a x)\right)}{a \left(p+\frac{1}{2}\right)}","-\frac{2^{p+\frac{3}{2}} (1-a x)^{p+\frac{1}{2}} \, _2F_1\left(-p-\frac{1}{2},p+\frac{1}{2};p+\frac{3}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+1)}",1,"-((2^(1/2 + p)*(1 - a*x)^(1/2 + p)*Hypergeometric2F1[-1/2 - p, 1/2 + p, 3/2 + p, (1 - a*x)/2])/(a*(1/2 + p)))","A",1
1009,1,74,72,0.0276166,"\int \frac{e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x} \, dx","Integrate[(E^ArcTanh[a*x]*(1 - a^2*x^2)^p)/x,x]","a x \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}","a x \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}",1,"a*x*Hypergeometric2F1[1/2, 1/2 - p, 3/2, a^2*x^2] - ((1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))","A",1
1010,1,77,75,0.0284748,"\int \frac{e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*(1 - a^2*x^2)^p)/x^2,x]","-\frac{a \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}-\frac{\, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}","-\frac{a \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{\, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}",1,"-(Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2]/x) - (a*(1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))","A",1
1011,1,80,78,0.0223651,"\int \frac{e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*(1 - a^2*x^2)^p)/x^3,x]","-\frac{a^2 \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(2,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}-\frac{a \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}","-\frac{a^2 \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(2,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{a \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}",1,"-((a*Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2])/x) - (a^2*(1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[2, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))","A",1
1012,1,105,134,0.0925003,"\int e^{\tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x^3*(c - a^2*c*x^2)^p,x]","\frac{\left(c-a^2 c x^2\right)^p \left(a^5 x^5 \left(1-a^2 x^2\right)^{-p} \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)-\frac{5 \sqrt{1-a^2 x^2} \left(a^2 (2 p+1) x^2+2\right)}{4 p^2+8 p+3}\right)}{5 a^4}","\frac{1}{5} a x^5 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)+\frac{\left(1-a^2 x^2\right)^{3/2} \left(c-a^2 c x^2\right)^p}{a^4 (2 p+3)}-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^4 (2 p+1)}",1,"((c - a^2*c*x^2)^p*((-5*Sqrt[1 - a^2*x^2]*(2 + a^2*(1 + 2*p)*x^2))/(3 + 8*p + 4*p^2) + (a^5*x^5*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/(1 - a^2*x^2)^p))/(5*a^4)","A",1
1013,1,102,133,0.0906743,"\int e^{\tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x^2*(c - a^2*c*x^2)^p,x]","\frac{1}{3} \left(c-a^2 c x^2\right)^p \left(x^3 \left(1-a^2 x^2\right)^{-p} \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{3 \sqrt{1-a^2 x^2} \left(a^2 (2 p+1) x^2+2\right)}{a^3 \left(4 p^2+8 p+3\right)}\right)","\frac{1}{3} x^3 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)+\frac{\left(1-a^2 x^2\right)^{3/2} \left(c-a^2 c x^2\right)^p}{a^3 (2 p+3)}-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^3 (2 p+1)}",1,"((c - a^2*c*x^2)^p*((-3*Sqrt[1 - a^2*x^2]*(2 + a^2*(1 + 2*p)*x^2))/(a^3*(3 + 8*p + 4*p^2)) + (x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/(1 - a^2*x^2)^p))/3","A",1
1014,1,88,96,0.0365638,"\int e^{\tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*x*(c - a^2*c*x^2)^p,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{1}{3} a x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{2 a^2 \left(p+\frac{1}{2}\right)}\right)","\frac{1}{3} a x^3 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^2 (2 p+1)}",1,"((c - a^2*c*x^2)^p*(-1/2*(1 - a^2*x^2)^(1/2 + p)/(a^2*(1/2 + p)) + (a*x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3))/(1 - a^2*x^2)^p","A",1
1015,1,86,86,0.0178855,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^ArcTanh[a*x]*(c - a^2*c*x^2)^p,x]","-\frac{2^{p+\frac{1}{2}} (1-a x)^{p+\frac{1}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-\frac{1}{2},p+\frac{1}{2};p+\frac{3}{2};\frac{1}{2} (1-a x)\right)}{a \left(p+\frac{1}{2}\right)}","-\frac{2^{p+\frac{3}{2}} (1-a x)^{p+\frac{1}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-\frac{1}{2},p+\frac{1}{2};p+\frac{3}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+1)}",1,"-((2^(1/2 + p)*(1 - a*x)^(1/2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1/2 - p, 1/2 + p, 3/2 + p, (1 - a*x)/2])/(a*(1/2 + p)*(1 - a^2*x^2)^p))","A",1
1016,1,102,110,0.0288495,"\int \frac{e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a^2*c*x^2)^p)/x,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(a x \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}\right)","a x \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}",1,"((c - a^2*c*x^2)^p*(a*x*Hypergeometric2F1[1/2, 1/2 - p, 3/2, a^2*x^2] - ((1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))))/(1 - a^2*x^2)^p","A",1
1017,1,105,113,0.0383458,"\int \frac{e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^2} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a^2*c*x^2)^p)/x^2,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(-\frac{a \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}-\frac{\, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}\right)","-\frac{\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}-\frac{a \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}",1,"((c - a^2*c*x^2)^p*(-(Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2]/x) - (a*(1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))))/(1 - a^2*x^2)^p","A",1
1018,1,108,116,0.0225261,"\int \frac{e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^3} \, dx","Integrate[(E^ArcTanh[a*x]*(c - a^2*c*x^2)^p)/x^3,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(-\frac{a^2 \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(2,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}-\frac{a \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}\right)","-\frac{a \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}-\frac{a^2 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(2,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}",1,"((c - a^2*c*x^2)^p*(-((a*Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2])/x) - (a^2*(1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[2, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))))/(1 - a^2*x^2)^p","A",1
1019,1,22,29,0.0170896,"\int e^{2 \tanh ^{-1}(a x)} x^4 \left(c-a^2 c x^2\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*x^4*(c - a^2*c*x^2),x]","\frac{1}{105} c x^5 \left(15 a^2 x^2+35 a x+21\right)","\frac{1}{7} a^2 c x^7+\frac{1}{3} a c x^6+\frac{c x^5}{5}",1,"(c*x^5*(21 + 35*a*x + 15*a^2*x^2))/105","A",1
1020,1,22,29,0.0175742,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2),x]","\frac{1}{60} c x^4 \left(10 a^2 x^2+24 a x+15\right)","\frac{1}{6} a^2 c x^6+\frac{2}{5} a c x^5+\frac{c x^4}{4}",1,"(c*x^4*(15 + 24*a*x + 10*a^2*x^2))/60","A",1
1021,1,22,29,0.0150138,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2),x]","\frac{1}{30} c x^3 \left(6 a^2 x^2+15 a x+10\right)","\frac{1}{5} a^2 c x^5+\frac{1}{2} a c x^4+\frac{c x^3}{3}",1,"(c*x^3*(10 + 15*a*x + 6*a^2*x^2))/30","A",1
1022,1,22,29,0.0151255,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2),x]","\frac{1}{12} c x^2 \left(3 a^2 x^2+8 a x+6\right)","\frac{1}{4} a^2 c x^4+\frac{2}{3} a c x^3+\frac{c x^2}{2}",1,"(c*x^2*(6 + 8*a*x + 3*a^2*x^2))/12","A",1
1023,1,19,15,0.0121801,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2),x]","c \left(\frac{a^2 x^3}{3}+a x^2+x\right)","\frac{c (a x+1)^3}{3 a}",1,"c*(x + a*x^2 + (a^2*x^3)/3)","A",1
1024,1,19,21,0.0145721,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x,x]","c \left(\frac{a^2 x^2}{2}+2 a x+\log (x)\right)","\frac{1}{2} a^2 c x^2+2 a c x+c \log (x)",1,"c*(2*a*x + (a^2*x^2)/2 + Log[x])","A",1
1025,1,18,19,0.0129252,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x^2,x]","c \left(a^2 x+2 a \log (x)-\frac{1}{x}\right)","a^2 c x+2 a c \log (x)-\frac{c}{x}",1,"c*(-x^(-1) + a^2*x + 2*a*Log[x])","A",1
1026,1,22,23,0.0179716,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x^3,x]","c \left(a^2 \log (x)-\frac{2 a}{x}-\frac{1}{2 x^2}\right)","a^2 c \log (x)-\frac{2 a c}{x}-\frac{c}{2 x^2}",1,"c*(-1/2*1/x^2 - (2*a)/x + a^2*Log[x])","A",1
1027,1,15,15,0.0090554,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x^4,x]","-\frac{c (a x+1)^3}{3 x^3}","-\frac{c (a x+1)^3}{3 x^3}",1,"-1/3*(c*(1 + a*x)^3)/x^3","A",1
1028,1,32,48,0.0247364,"\int e^{2 \tanh ^{-1}(a x)} x^4 \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^4*(c - a^2*c*x^2)^2,x]","-\frac{1}{180} c^2 x^5 \left(20 a^4 x^4+45 a^3 x^3-60 a x-36\right)","-\frac{1}{9} a^4 c^2 x^9-\frac{1}{4} a^3 c^2 x^8+\frac{1}{3} a c^2 x^6+\frac{c^2 x^5}{5}",1,"-1/180*(c^2*x^5*(-36 - 60*a*x + 45*a^3*x^3 + 20*a^4*x^4))","A",1
1029,1,40,48,0.0225378,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^2,x]","c^2 \left(-\frac{1}{8} a^4 x^8-\frac{2 a^3 x^7}{7}+\frac{2 a x^5}{5}+\frac{x^4}{4}\right)","-\frac{1}{8} a^4 c^2 x^8-\frac{2}{7} a^3 c^2 x^7+\frac{2}{5} a c^2 x^5+\frac{c^2 x^4}{4}",1,"c^2*(x^4/4 + (2*a*x^5)/5 - (2*a^3*x^7)/7 - (a^4*x^8)/8)","A",1
1030,1,32,48,0.0212778,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^2,x]","-\frac{1}{42} c^2 x^3 \left(6 a^4 x^4+14 a^3 x^3-21 a x-14\right)","-\frac{1}{7} a^4 c^2 x^7-\frac{1}{3} a^3 c^2 x^6+\frac{1}{2} a c^2 x^4+\frac{c^2 x^3}{3}",1,"-1/42*(c^2*x^3*(-14 - 21*a*x + 14*a^3*x^3 + 6*a^4*x^4))","A",1
1031,1,32,48,0.0191319,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^2,x]","-\frac{1}{30} c^2 x^2 \left(5 a^4 x^4+12 a^3 x^3-20 a x-15\right)","-\frac{1}{6} a^4 c^2 x^6-\frac{2}{5} a^3 c^2 x^5+\frac{2}{3} a c^2 x^3+\frac{c^2 x^2}{2}",1,"-1/30*(c^2*x^2*(-15 - 20*a*x + 12*a^3*x^3 + 5*a^4*x^4))","A",1
1032,1,23,35,0.014754,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","-\frac{c^2 (a x+1)^4 (2 a x-3)}{10 a}","\frac{c^2 (a x+1)^4}{2 a}-\frac{c^2 (a x+1)^5}{5 a}",1,"-1/10*(c^2*(1 + a*x)^4*(-3 + 2*a*x))/a","A",1
1033,1,33,40,0.015416,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x,x]","-\frac{1}{12} c^2 \left(3 a^4 x^4+8 a^3 x^3-24 a x-12 \log (x)+3\right)","-\frac{1}{4} a^4 c^2 x^4-\frac{2}{3} a^3 c^2 x^3+2 a c^2 x+c^2 \log (x)",1,"-1/12*(c^2*(3 - 24*a*x + 8*a^3*x^3 + 3*a^4*x^4 - 12*Log[x]))","A",1
1034,1,41,41,0.0120679,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^2,x]","-\frac{1}{3} a^4 c^2 x^3-a^3 c^2 x^2+2 a c^2 \log (x)-\frac{c^2}{x}","-\frac{1}{3} a^4 c^2 x^3-a^3 c^2 x^2+2 a c^2 \log (x)-\frac{c^2}{x}",1,"-(c^2/x) - a^3*c^2*x^2 - (a^4*c^2*x^3)/3 + 2*a*c^2*Log[x]","A",1
1035,1,17,17,0.0149147,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^3,x]","-\frac{c^2 (a x+1)^4}{2 x^2}","-\frac{c^2 (a x+1)^4}{2 x^2}",1,"-1/2*(c^2*(1 + a*x)^4)/x^2","A",1
1036,1,39,39,0.0154221,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^4,x]","a^4 \left(-c^2\right) x-2 a^3 c^2 \log (x)-\frac{a c^2}{x^2}-\frac{c^2}{3 x^3}","a^4 \left(-c^2\right) x-2 a^3 c^2 \log (x)-\frac{a c^2}{x^2}-\frac{c^2}{3 x^3}",1,"-1/3*c^2/x^3 - (a*c^2)/x^2 - a^4*c^2*x - 2*a^3*c^2*Log[x]","A",1
1037,1,35,43,0.0179031,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^5,x]","c^2 \left(a^4 (-\log (x))+\frac{2 a^3}{x}-\frac{2 a}{3 x^3}-\frac{1}{4 x^4}\right)","a^4 \left(-c^2\right) \log (x)+\frac{2 a^3 c^2}{x}-\frac{2 a c^2}{3 x^3}-\frac{c^2}{4 x^4}",1,"c^2*(-1/4*1/x^4 - (2*a)/(3*x^3) + (2*a^3)/x - a^4*Log[x])","A",1
1038,1,23,42,0.0097069,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^6} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^6,x]","\frac{c^2 (a x+1)^4 (3 a x-2)}{10 x^5}","\frac{a^4 c^2}{x}+\frac{a^3 c^2}{x^2}-\frac{a c^2}{2 x^4}-\frac{c^2}{5 x^5}",1,"(c^2*(1 + a*x)^4*(-2 + 3*a*x))/(10*x^5)","A",1
1039,1,70,87,0.0363009,"\int e^{2 \tanh ^{-1}(a x)} x^4 \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^4*(c - a^2*c*x^2)^3,x]","c^3 \left(\frac{a^6 x^{11}}{11}+\frac{a^5 x^{10}}{5}-\frac{a^4 x^9}{9}-\frac{a^3 x^8}{2}-\frac{a^2 x^7}{7}+\frac{a x^6}{3}+\frac{x^5}{5}\right)","\frac{1}{11} a^6 c^3 x^{11}+\frac{1}{5} a^5 c^3 x^{10}-\frac{1}{9} a^4 c^3 x^9-\frac{1}{2} a^3 c^3 x^8-\frac{1}{7} a^2 c^3 x^7+\frac{1}{3} a c^3 x^6+\frac{c^3 x^5}{5}",1,"c^3*(x^5/5 + (a*x^6)/3 - (a^2*x^7)/7 - (a^3*x^8)/2 - (a^4*x^9)/9 + (a^5*x^10)/5 + (a^6*x^11)/11)","A",1
1040,1,70,87,0.0335248,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^3,x]","c^3 \left(\frac{a^6 x^{10}}{10}+\frac{2 a^5 x^9}{9}-\frac{a^4 x^8}{8}-\frac{4 a^3 x^7}{7}-\frac{a^2 x^6}{6}+\frac{2 a x^5}{5}+\frac{x^4}{4}\right)","\frac{1}{10} a^6 c^3 x^{10}+\frac{2}{9} a^5 c^3 x^9-\frac{1}{8} a^4 c^3 x^8-\frac{4}{7} a^3 c^3 x^7-\frac{1}{6} a^2 c^3 x^6+\frac{2}{5} a c^3 x^5+\frac{c^3 x^4}{4}",1,"c^3*(x^4/4 + (2*a*x^5)/5 - (a^2*x^6)/6 - (4*a^3*x^7)/7 - (a^4*x^8)/8 + (2*a^5*x^9)/9 + (a^6*x^10)/10)","A",1
1041,1,70,84,0.0308829,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^3,x]","c^3 \left(\frac{a^6 x^9}{9}+\frac{a^5 x^8}{4}-\frac{a^4 x^7}{7}-\frac{2 a^3 x^6}{3}-\frac{a^2 x^5}{5}+\frac{a x^4}{2}+\frac{x^3}{3}\right)","\frac{c^3 (a x+1)^9}{9 a^3}-\frac{3 c^3 (a x+1)^8}{4 a^3}+\frac{13 c^3 (a x+1)^7}{7 a^3}-\frac{2 c^3 (a x+1)^6}{a^3}+\frac{4 c^3 (a x+1)^5}{5 a^3}",1,"c^3*(x^3/3 + (a*x^4)/2 - (a^2*x^5)/5 - (2*a^3*x^6)/3 - (a^4*x^7)/7 + (a^5*x^8)/4 + (a^6*x^9)/9)","A",1
1042,1,70,69,0.0290214,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^3,x]","c^3 \left(\frac{a^6 x^8}{8}+\frac{2 a^5 x^7}{7}-\frac{a^4 x^6}{6}-\frac{4 a^3 x^5}{5}-\frac{a^2 x^4}{4}+\frac{2 a x^3}{3}+\frac{x^2}{2}\right)","\frac{c^3 (a x+1)^8}{8 a^2}-\frac{5 c^3 (a x+1)^7}{7 a^2}+\frac{4 c^3 (a x+1)^6}{3 a^2}-\frac{4 c^3 (a x+1)^5}{5 a^2}",1,"c^3*(x^2/2 + (2*a*x^3)/3 - (a^2*x^4)/4 - (4*a^3*x^5)/5 - (a^4*x^6)/6 + (2*a^5*x^7)/7 + (a^6*x^8)/8)","A",1
1043,1,31,52,0.0189747,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","\frac{c^3 (a x+1)^5 \left(15 a^2 x^2-40 a x+29\right)}{105 a}","\frac{c^3 (a x+1)^7}{7 a}-\frac{2 c^3 (a x+1)^6}{3 a}+\frac{4 c^3 (a x+1)^5}{5 a}",1,"(c^3*(1 + a*x)^5*(29 - 40*a*x + 15*a^2*x^2))/(105*a)","A",1
1044,1,51,79,0.0278247,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x,x]","c^3 \left(\frac{1}{60} a x \left(10 a^5 x^5+24 a^4 x^4-15 a^3 x^3-80 a^2 x^2-30 a x+120\right)+\log (x)\right)","\frac{1}{6} a^6 c^3 x^6+\frac{2}{5} a^5 c^3 x^5-\frac{1}{4} a^4 c^3 x^4-\frac{4}{3} a^3 c^3 x^3-\frac{1}{2} a^2 c^3 x^2+2 a c^3 x+c^3 \log (x)",1,"c^3*((a*x*(120 - 30*a*x - 80*a^2*x^2 - 15*a^3*x^3 + 24*a^4*x^4 + 10*a^5*x^5))/60 + Log[x])","A",1
1045,1,59,76,0.025304,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x^2,x]","c^3 \left(\frac{a^6 x^5}{5}+\frac{a^5 x^4}{2}-\frac{a^4 x^3}{3}-2 a^3 x^2-a^2 x+2 a \log (x)-\frac{1}{x}\right)","\frac{1}{5} a^6 c^3 x^5+\frac{1}{2} a^5 c^3 x^4-\frac{1}{3} a^4 c^3 x^3-2 a^3 c^3 x^2-a^2 c^3 x+2 a c^3 \log (x)-\frac{c^3}{x}",1,"c^3*(-x^(-1) - a^2*x - 2*a^3*x^2 - (a^4*x^3)/3 + (a^5*x^4)/2 + (a^6*x^5)/5 + 2*a*Log[x])","A",1
1046,1,58,78,0.0235956,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x^3,x]","\frac{c^3 \left(3 a^6 x^6+8 a^5 x^5-6 a^4 x^4-48 a^3 x^3-12 a^2 x^2 \log (x)-24 a x-6\right)}{12 x^2}","\frac{1}{4} a^6 c^3 x^4+\frac{2}{3} a^5 c^3 x^3-\frac{1}{2} a^4 c^3 x^2-4 a^3 c^3 x-a^2 c^3 \log (x)-\frac{2 a c^3}{x}-\frac{c^3}{2 x^2}",1,"(c^3*(-6 - 24*a*x - 48*a^3*x^3 - 6*a^4*x^4 + 8*a^5*x^5 + 3*a^6*x^6 - 12*a^2*x^2*Log[x]))/(12*x^2)","A",1
1047,1,55,72,0.028475,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x^4,x]","c^3 \left(\frac{a^6 x^3}{3}+a^5 x^2-a^4 x-4 a^3 \log (x)+\frac{a^2}{x}-\frac{a}{x^2}-\frac{1}{3 x^3}\right)","\frac{1}{3} a^6 c^3 x^3+a^5 c^3 x^2-a^4 c^3 x-4 a^3 c^3 \log (x)+\frac{a^2 c^3}{x}-\frac{a c^3}{x^2}-\frac{c^3}{3 x^3}",1,"c^3*(-1/3*1/x^3 - a/x^2 + a^2/x - a^4*x + a^5*x^2 + (a^6*x^3)/3 - 4*a^3*Log[x])","A",1
1048,1,39,69,0.0254601,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^4,x]","-\frac{c^4 (a x+1)^6 \left(28 a^3 x^3-105 a^2 x^2+138 a x-65\right)}{252 a}","-\frac{c^4 (a x+1)^9}{9 a}+\frac{3 c^4 (a x+1)^8}{4 a}-\frac{12 c^4 (a x+1)^7}{7 a}+\frac{4 c^4 (a x+1)^6}{3 a}",1,"-1/252*(c^4*(1 + a*x)^6*(-65 + 138*a*x - 105*a^2*x^2 + 28*a^3*x^3))/a","A",1
1049,1,49,63,0.0387329,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^4}{c-a^2 c x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2),x]","\frac{a^3 x^3+3 a^2 x^2+9 a x+\frac{3}{1-a x}+12 \log (1-a x)}{3 a^5 c}","\frac{1}{a^5 c (1-a x)}+\frac{4 \log (1-a x)}{a^5 c}+\frac{3 x}{a^4 c}+\frac{x^2}{a^3 c}+\frac{x^3}{3 a^2 c}",1,"(9*a*x + 3*a^2*x^2 + a^3*x^3 + 3/(1 - a*x) + 12*Log[1 - a*x])/(3*a^5*c)","A",1
1050,1,41,53,0.030175,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{c-a^2 c x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2),x]","\frac{a^2 x^2+4 a x+\frac{2}{1-a x}+6 \log (1-a x)}{2 a^4 c}","\frac{1}{a^4 c (1-a x)}+\frac{3 \log (1-a x)}{a^4 c}+\frac{2 x}{a^3 c}+\frac{x^2}{2 a^2 c}",1,"(4*a*x + a^2*x^2 + 2/(1 - a*x) + 6*Log[1 - a*x])/(2*a^4*c)","A",1
1051,1,28,39,0.0235975,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2),x]","\frac{a x+\frac{1}{1-a x}+2 \log (1-a x)}{a^3 c}","\frac{1}{a^3 c (1-a x)}+\frac{2 \log (1-a x)}{a^3 c}+\frac{x}{a^2 c}",1,"(a*x + (1 - a*x)^(-1) + 2*Log[1 - a*x])/(a^3*c)","A",1
1052,1,23,30,0.0188804,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2),x]","\frac{\frac{1}{1-a x}+\log (1-a x)}{a^2 c}","\frac{1}{a^2 c (1-a x)}+\frac{\log (1-a x)}{a^2 c}",1,"((1 - a*x)^(-1) + Log[1 - a*x])/(a^2*c)","A",1
1053,1,18,15,0.0114777,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{e^{2 \tanh ^{-1}(a x)}}{2 a c}","\frac{1}{a c (1-a x)}",1,"E^(2*ArcTanh[a*x])/(2*a*c)","C",1
1054,1,24,31,0.0236807,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)),x]","\frac{\frac{1}{1-a x}-\log (1-a x)+\log (x)}{c}","\frac{1}{c (1-a x)}-\frac{\log (1-a x)}{c}+\frac{\log (x)}{c}",1,"((1 - a*x)^(-1) + Log[x] - Log[1 - a*x])/c","A",1
1055,1,35,43,0.0335409,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)),x]","\frac{\frac{a}{1-a x}+2 a \log (x)-2 a \log (1-a x)-\frac{1}{x}}{c}","\frac{a}{c (1-a x)}+\frac{2 a \log (x)}{c}-\frac{2 a \log (1-a x)}{c}-\frac{1}{c x}",1,"(-x^(-1) + a/(1 - a*x) + 2*a*Log[x] - 2*a*Log[1 - a*x])/c","A",1
1056,1,52,60,0.0509812,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)),x]","\frac{\frac{-6 a^2 x^2+3 a x+1}{x^2 (a x-1)}+6 a^2 \log (x)-6 a^2 \log (1-a x)}{2 c}","\frac{a^2}{c (1-a x)}+\frac{3 a^2 \log (x)}{c}-\frac{3 a^2 \log (1-a x)}{c}-\frac{2 a}{c x}-\frac{1}{2 c x^2}",1,"((1 + 3*a*x - 6*a^2*x^2)/(x^2*(-1 + a*x)) + 6*a^2*Log[x] - 6*a^2*Log[1 - a*x])/(2*c)","A",1
1057,1,71,71,0.0410294,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^4*(c - a^2*c*x^2)),x]","\frac{a^3}{c (1-a x)}+\frac{4 a^3 \log (x)}{c}-\frac{4 a^3 \log (1-a x)}{c}-\frac{3 a^2}{c x}-\frac{a}{c x^2}-\frac{1}{3 c x^3}","\frac{a^3}{c (1-a x)}+\frac{4 a^3 \log (x)}{c}-\frac{4 a^3 \log (1-a x)}{c}-\frac{3 a^2}{c x}-\frac{a}{c x^2}-\frac{1}{3 c x^3}",1,"-1/3*1/(c*x^3) - a/(c*x^2) - (3*a^2)/(c*x) + a^3/(c*(1 - a*x)) + (4*a^3*Log[x])/c - (4*a^3*Log[1 - a*x])/c","A",1
1058,1,68,79,0.0451779,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2)^2,x]","\frac{-\frac{7}{4 a^5 (1-a x)}+\frac{1}{4 a^5 (1-a x)^2}-\frac{17 \log (1-a x)}{8 a^5}+\frac{\log (a x+1)}{8 a^5}-\frac{x}{a^4}}{c^2}","-\frac{7}{4 a^5 c^2 (1-a x)}+\frac{1}{4 a^5 c^2 (1-a x)^2}-\frac{17 \log (1-a x)}{8 a^5 c^2}+\frac{\log (a x+1)}{8 a^5 c^2}-\frac{x}{a^4 c^2}",1,"(-(x/a^4) + 1/(4*a^5*(1 - a*x)^2) - 7/(4*a^5*(1 - a*x)) - (17*Log[1 - a*x])/(8*a^5) + Log[1 + a*x]/(8*a^5))/c^2","A",1
1059,1,53,70,0.0429294,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^2,x]","-\frac{-10 a x+7 (a x-1)^2 \log (1-a x)+(a x-1)^2 \log (a x+1)+8}{8 a^4 c^2 (a x-1)^2}","-\frac{5}{4 a^4 c^2 (1-a x)}+\frac{1}{4 a^4 c^2 (1-a x)^2}-\frac{7 \log (1-a x)}{8 a^4 c^2}-\frac{\log (a x+1)}{8 a^4 c^2}",1,"-1/8*(8 - 10*a*x + 7*(-1 + a*x)^2*Log[1 - a*x] + (-1 + a*x)^2*Log[1 + a*x])/(a^4*c^2*(-1 + a*x)^2)","A",1
1060,1,35,51,0.0292362,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^2,x]","\frac{3 a x+(a x-1)^2 \tanh ^{-1}(a x)-2}{4 a^3 c^2 (a x-1)^2}","-\frac{3}{4 a^3 c^2 (1-a x)}+\frac{1}{4 a^3 c^2 (1-a x)^2}+\frac{\tanh ^{-1}(a x)}{4 a^3 c^2}",1,"(-2 + 3*a*x + (-1 + a*x)^2*ArcTanh[a*x])/(4*a^3*c^2*(-1 + a*x)^2)","A",1
1061,1,34,51,0.0257885,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^2,x]","\frac{a x-(a x-1)^2 \tanh ^{-1}(a x)}{4 a^2 c^2 (a x-1)^2}","-\frac{1}{4 a^2 c^2 (1-a x)}+\frac{1}{4 a^2 c^2 (1-a x)^2}-\frac{\tanh ^{-1}(a x)}{4 a^2 c^2}",1,"(a*x - (-1 + a*x)^2*ArcTanh[a*x])/(4*a^2*c^2*(-1 + a*x)^2)","A",1
1062,1,35,51,0.0198798,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","\frac{-a x+(a x-1)^2 \tanh ^{-1}(a x)+2}{4 a c^2 (a x-1)^2}","\frac{1}{4 a c^2 (1-a x)}+\frac{1}{4 a c^2 (1-a x)^2}+\frac{\tanh ^{-1}(a x)}{4 a c^2}",1,"(2 - a*x + (-1 + a*x)^2*ArcTanh[a*x])/(4*a*c^2*(-1 + a*x)^2)","A",1
1063,1,48,64,0.0434029,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^2),x]","\frac{\frac{6}{1-a x}+\frac{2}{(a x-1)^2}-7 \log (1-a x)-\log (a x+1)+8 \log (x)}{8 c^2}","\frac{3}{4 c^2 (1-a x)}+\frac{1}{4 c^2 (1-a x)^2}-\frac{7 \log (1-a x)}{8 c^2}-\frac{\log (a x+1)}{8 c^2}+\frac{\log (x)}{c^2}",1,"(6/(1 - a*x) + 2/(-1 + a*x)^2 + 8*Log[x] - 7*Log[1 - a*x] - Log[1 + a*x])/(8*c^2)","A",1
1064,1,57,78,0.0536599,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^2),x]","\frac{\frac{10 a}{1-a x}+\frac{2 a}{(a x-1)^2}+16 a \log (x)-17 a \log (1-a x)+a \log (a x+1)-\frac{8}{x}}{8 c^2}","\frac{5 a}{4 c^2 (1-a x)}+\frac{a}{4 c^2 (1-a x)^2}+\frac{2 a \log (x)}{c^2}-\frac{17 a \log (1-a x)}{8 c^2}+\frac{a \log (a x+1)}{8 c^2}-\frac{1}{c^2 x}",1,"(-8/x + (10*a)/(1 - a*x) + (2*a)/(-1 + a*x)^2 + 16*a*Log[x] - 17*a*Log[1 - a*x] + a*Log[1 + a*x])/(8*c^2)","A",1
1065,1,72,99,0.09969,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^2),x]","-\frac{\frac{14 a^2}{a x-1}-\frac{2 a^2}{(a x-1)^2}-32 a^2 \log (x)+31 a^2 \log (1-a x)+a^2 \log (a x+1)+\frac{16 a}{x}+\frac{4}{x^2}}{8 c^2}","\frac{7 a^2}{4 c^2 (1-a x)}+\frac{a^2}{4 c^2 (1-a x)^2}+\frac{4 a^2 \log (x)}{c^2}-\frac{31 a^2 \log (1-a x)}{8 c^2}-\frac{a^2 \log (a x+1)}{8 c^2}-\frac{2 a}{c^2 x}-\frac{1}{2 c^2 x^2}",1,"-1/8*(4/x^2 + (16*a)/x - (2*a^2)/(-1 + a*x)^2 + (14*a^2)/(-1 + a*x) - 32*a^2*Log[x] + 31*a^2*Log[1 - a*x] + a^2*Log[1 + a*x])/c^2","A",1
1066,1,87,110,0.0884008,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^4*(c - a^2*c*x^2)^2),x]","\frac{\frac{9 a^3}{4-4 a x}+\frac{a^3}{4 (a x-1)^2}+6 a^3 \log (x)-\frac{49}{8} a^3 \log (1-a x)+\frac{1}{8} a^3 \log (a x+1)-\frac{4 a^2}{x}-\frac{a}{x^2}-\frac{1}{3 x^3}}{c^2}","\frac{9 a^3}{4 c^2 (1-a x)}+\frac{a^3}{4 c^2 (1-a x)^2}+\frac{6 a^3 \log (x)}{c^2}-\frac{49 a^3 \log (1-a x)}{8 c^2}+\frac{a^3 \log (a x+1)}{8 c^2}-\frac{4 a^2}{c^2 x}-\frac{a}{c^2 x^2}-\frac{1}{3 c^2 x^3}",1,"(-1/3*1/x^3 - a/x^2 - (4*a^2)/x + (9*a^3)/(4 - 4*a*x) + a^3/(4*(-1 + a*x)^2) + 6*a^3*Log[x] - (49*a^3*Log[1 - a*x])/8 + (a^3*Log[1 + a*x])/8)/c^2","A",1
1067,1,87,105,0.0596456,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^5)/(c - a^2*c*x^2)^3,x]","\frac{-66 a^3 x^3+36 a^2 x^2+74 a x+39 (a x-1)^3 (a x+1) \log (1-a x)+9 (a x-1)^3 (a x+1) \log (a x+1)-52}{48 a^6 c^3 (a x-1)^3 (a x+1)}","\frac{23}{16 a^6 c^3 (1-a x)}+\frac{1}{16 a^6 c^3 (a x+1)}-\frac{1}{2 a^6 c^3 (1-a x)^2}+\frac{1}{12 a^6 c^3 (1-a x)^3}+\frac{13 \log (1-a x)}{16 a^6 c^3}+\frac{3 \log (a x+1)}{16 a^6 c^3}",1,"(-52 + 74*a*x + 36*a^2*x^2 - 66*a^3*x^3 + 39*(-1 + a*x)^3*(1 + a*x)*Log[1 - a*x] + 9*(-1 + a*x)^3*(1 + a*x)*Log[1 + a*x])/(48*a^6*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
1068,1,64,86,0.0419321,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2)^3,x]","\frac{-9 a^3 x^3+6 a^2 x^2+5 a x-3 (a x-1)^3 (a x+1) \tanh ^{-1}(a x)-4}{12 a^5 c^3 (a x-1)^3 (a x+1)}","\frac{11}{16 a^5 c^3 (1-a x)}-\frac{1}{16 a^5 c^3 (a x+1)}-\frac{3}{8 a^5 c^3 (1-a x)^2}+\frac{1}{12 a^5 c^3 (1-a x)^3}-\frac{\tanh ^{-1}(a x)}{4 a^5 c^3}",1,"(-4 + 5*a*x + 6*a^2*x^2 - 9*a^3*x^3 - 3*(-1 + a*x)^3*(1 + a*x)*ArcTanh[a*x])/(12*a^5*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
1069,1,64,86,0.0423217,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^3,x]","\frac{-3 a^3 x^3-6 a^2 x^2+7 a x+3 (a x-1)^3 (a x+1) \tanh ^{-1}(a x)-2}{24 a^4 c^3 (a x-1)^3 (a x+1)}","\frac{3}{16 a^4 c^3 (1-a x)}+\frac{1}{16 a^4 c^3 (a x+1)}-\frac{1}{4 a^4 c^3 (1-a x)^2}+\frac{1}{12 a^4 c^3 (1-a x)^3}+\frac{\tanh ^{-1}(a x)}{8 a^4 c^3}",1,"(-2 + 7*a*x - 6*a^2*x^2 - 3*a^3*x^3 + 3*(-1 + a*x)^3*(1 + a*x)*ArcTanh[a*x])/(24*a^4*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
1070,1,30,31,0.0299783,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^3,x]","\frac{1-2 a x}{6 a^3 c^3 (a x-1)^3 (a x+1)}","-\frac{1-2 a x}{6 a^3 c^3 (1-a x)^3 (a x+1)}",1,"(1 - 2*a*x)/(6*a^3*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
1071,1,60,68,0.0330744,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^3,x]","\frac{-\frac{1}{16 a^2 (1-a x)}+\frac{1}{16 a^2 (a x+1)}+\frac{1}{12 a^2 (1-a x)^3}-\frac{\tanh ^{-1}(a x)}{8 a^2}}{c^3}","-\frac{1}{16 a^2 c^3 (1-a x)}+\frac{1}{16 a^2 c^3 (a x+1)}+\frac{1}{12 a^2 c^3 (1-a x)^3}-\frac{\tanh ^{-1}(a x)}{8 a^2 c^3}",1,"(1/(12*a^2*(1 - a*x)^3) - 1/(16*a^2*(1 - a*x)) + 1/(16*a^2*(1 + a*x)) - ArcTanh[a*x]/(8*a^2))/c^3","A",1
1072,1,63,86,0.032387,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","-\frac{3 a^3 x^3-6 a^2 x^2+a x-3 (a x-1)^3 (a x+1) \tanh ^{-1}(a x)+4}{12 a c^3 (a x-1)^3 (a x+1)}","\frac{3}{16 a c^3 (1-a x)}-\frac{1}{16 a c^3 (a x+1)}+\frac{1}{8 a c^3 (1-a x)^2}+\frac{1}{12 a c^3 (1-a x)^3}+\frac{\tanh ^{-1}(a x)}{4 a c^3}",1,"-1/12*(4 + a*x - 6*a^2*x^2 + 3*a^3*x^3 - 3*(-1 + a*x)^3*(1 + a*x)*ArcTanh[a*x])/(a*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
1073,1,66,93,0.0713462,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^3),x]","\frac{\frac{33}{1-a x}+\frac{3}{a x+1}+\frac{12}{(a x-1)^2}-\frac{4}{(a x-1)^3}-39 \log (1-a x)-9 \log (a x+1)+48 \log (x)}{48 c^3}","\frac{11}{16 c^3 (1-a x)}+\frac{1}{16 c^3 (a x+1)}+\frac{1}{4 c^3 (1-a x)^2}+\frac{1}{12 c^3 (1-a x)^3}-\frac{13 \log (1-a x)}{16 c^3}-\frac{3 \log (a x+1)}{16 c^3}+\frac{\log (x)}{c^3}",1,"(33/(1 - a*x) - 4/(-1 + a*x)^3 + 12/(-1 + a*x)^2 + 3/(1 + a*x) + 48*Log[x] - 39*Log[1 - a*x] - 9*Log[1 + a*x])/(48*c^3)","A",1
1074,1,78,109,0.0865864,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^3),x]","\frac{\frac{69 a}{1-a x}-\frac{3 a}{a x+1}+\frac{18 a}{(a x-1)^2}-\frac{4 a}{(a x-1)^3}+96 a \log (x)-108 a \log (1-a x)+12 a \log (a x+1)-\frac{48}{x}}{48 c^3}","\frac{23 a}{16 c^3 (1-a x)}-\frac{a}{16 c^3 (a x+1)}+\frac{3 a}{8 c^3 (1-a x)^2}+\frac{a}{12 c^3 (1-a x)^3}+\frac{2 a \log (x)}{c^3}-\frac{9 a \log (1-a x)}{4 c^3}+\frac{a \log (a x+1)}{4 c^3}-\frac{1}{c^3 x}",1,"(-48/x + (69*a)/(1 - a*x) - (4*a)/(-1 + a*x)^3 + (18*a)/(-1 + a*x)^2 - (3*a)/(1 + a*x) + 96*a*Log[x] - 108*a*Log[1 - a*x] + 12*a*Log[1 + a*x])/(48*c^3)","A",1
1075,1,98,134,0.1207627,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^3),x]","\frac{\frac{117 a^2}{1-a x}+\frac{3 a^2}{a x+1}+\frac{24 a^2}{(a x-1)^2}-\frac{4 a^2}{(a x-1)^3}+240 a^2 \log (x)-225 a^2 \log (1-a x)-15 a^2 \log (a x+1)-\frac{96 a}{x}-\frac{24}{x^2}}{48 c^3}","\frac{39 a^2}{16 c^3 (1-a x)}+\frac{a^2}{16 c^3 (a x+1)}+\frac{a^2}{2 c^3 (1-a x)^2}+\frac{a^2}{12 c^3 (1-a x)^3}+\frac{5 a^2 \log (x)}{c^3}-\frac{75 a^2 \log (1-a x)}{16 c^3}-\frac{5 a^2 \log (a x+1)}{16 c^3}-\frac{2 a}{c^3 x}-\frac{1}{2 c^3 x^2}",1,"(-24/x^2 - (96*a)/x + (117*a^2)/(1 - a*x) - (4*a^2)/(-1 + a*x)^3 + (24*a^2)/(-1 + a*x)^2 + (3*a^2)/(1 + a*x) + 240*a^2*Log[x] - 225*a^2*Log[1 - a*x] - 15*a^2*Log[1 + a*x])/(48*c^3)","A",1
1076,1,82,121,0.0598504,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","\frac{-15 a^5 x^5+30 a^4 x^4+10 a^3 x^3-50 a^2 x^2+17 a x+15 (a x-1)^4 (a x+1)^2 \tanh ^{-1}(a x)+16}{64 a c^4 (a x-1)^4 (a x+1)^2}","\frac{5}{32 a c^4 (1-a x)}-\frac{5}{64 a c^4 (a x+1)}+\frac{3}{32 a c^4 (1-a x)^2}-\frac{1}{64 a c^4 (a x+1)^2}+\frac{1}{16 a c^4 (1-a x)^3}+\frac{1}{32 a c^4 (1-a x)^4}+\frac{15 \tanh ^{-1}(a x)}{64 a c^4}",1,"(16 + 17*a*x - 50*a^2*x^2 + 10*a^3*x^3 + 30*a^4*x^4 - 15*a^5*x^5 + 15*(-1 + a*x)^4*(1 + a*x)^2*ArcTanh[a*x])/(64*a*c^4*(-1 + a*x)^4*(1 + a*x)^2)","A",1
1077,1,96,137,0.1438074,"\int e^{2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","-\frac{15 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\left(4 a^4 x^4+10 a^3 x^3+12 a^2 x^2+15 a x+24\right) \sqrt{c-a^2 c x^2}}{20 a^4}","-\frac{3 x^2 \sqrt{c-a^2 c x^2}}{5 a^2}-\frac{1}{5} x^4 \sqrt{c-a^2 c x^2}-\frac{x^3 \sqrt{c-a^2 c x^2}}{2 a}-\frac{3 (5 a x+8) \sqrt{c-a^2 c x^2}}{20 a^4}+\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{4 a^4}",1,"-1/20*(Sqrt[c - a^2*c*x^2]*(24 + 15*a*x + 12*a^2*x^2 + 10*a^3*x^3 + 4*a^4*x^4) + 15*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/a^4","A",1
1078,1,88,112,0.1169027,"\int e^{2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","-\frac{21 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\left(6 a^3 x^3+16 a^2 x^2+21 a x+32\right) \sqrt{c-a^2 c x^2}}{24 a^3}","-\frac{2 x^2 \sqrt{c-a^2 c x^2}}{3 a}-\frac{1}{4} x^3 \sqrt{c-a^2 c x^2}-\frac{(21 a x+32) \sqrt{c-a^2 c x^2}}{24 a^3}+\frac{7 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a^3}",1,"-1/24*(Sqrt[c - a^2*c*x^2]*(32 + 21*a*x + 16*a^2*x^2 + 6*a^3*x^3) + 21*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/a^3","A",1
1079,1,79,84,0.0950499,"\int e^{2 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x*Sqrt[c - a^2*c*x^2],x]","-\frac{\left(a^2 x^2+3 a x+5\right) \sqrt{c-a^2 c x^2}+3 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{3 a^2}","-\frac{1}{3} x^2 \sqrt{c-a^2 c x^2}-\frac{(3 a x+5) \sqrt{c-a^2 c x^2}}{3 a^2}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a^2}",1,"-1/3*((5 + 3*a*x + a^2*x^2)*Sqrt[c - a^2*c*x^2] + 3*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/a^2","A",1
1080,1,76,86,0.0553607,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{c-a^2 c x^2} \left(\sqrt{1-a^2 x^2} (a x+4)+6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{2 a \sqrt{1-a^2 x^2}}","-\frac{(a x+1) \sqrt{c-a^2 c x^2}}{2 a}-\frac{3 \sqrt{c-a^2 c x^2}}{2 a}+\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{2 a}",1,"-1/2*(Sqrt[c - a^2*c*x^2]*((4 + a*x)*Sqrt[1 - a^2*x^2] + 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a^2*x^2])","A",0
1081,1,99,78,0.0790911,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x,x]","-\sqrt{c-a^2 c x^2}-\sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)-2 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\sqrt{c} \log (x)","-\sqrt{c-a^2 c x^2}+2 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-Sqrt[c - a^2*c*x^2] - 2*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] + Sqrt[c]*Log[x] - Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1082,1,106,82,0.0934106,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^2,x]","-\frac{\sqrt{c-a^2 c x^2}}{x}-2 a \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)-a \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+2 a \sqrt{c} \log (x)","-\frac{\sqrt{c-a^2 c x^2}}{x}+a \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-2 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-(Sqrt[c - a^2*c*x^2]/x) - a*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] + 2*a*Sqrt[c]*Log[x] - 2*a*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1083,1,79,78,0.1040014,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^3,x]","-\frac{(4 a x+1) \sqrt{c-a^2 c x^2}}{2 x^2}-\frac{3}{2} a^2 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{3}{2} a^2 \sqrt{c} \log (x)","-\frac{2 a \sqrt{c-a^2 c x^2}}{x}-\frac{\sqrt{c-a^2 c x^2}}{2 x^2}-\frac{3}{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-1/2*((1 + 4*a*x)*Sqrt[c - a^2*c*x^2])/x^2 + (3*a^2*Sqrt[c]*Log[x])/2 - (3*a^2*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/2","A",0
1084,1,82,101,0.1197174,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^4,x]","a^3 \sqrt{c} \log (x)-\frac{\left(5 a^2 x^2+3 a x+1\right) \sqrt{c-a^2 c x^2}}{3 x^3}-a^3 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)","-\frac{5 a^2 \sqrt{c-a^2 c x^2}}{3 x}-\frac{a \sqrt{c-a^2 c x^2}}{x^2}-\frac{\sqrt{c-a^2 c x^2}}{3 x^3}+a^3 \left(-\sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-1/3*((1 + 3*a*x + 5*a^2*x^2)*Sqrt[c - a^2*c*x^2])/x^3 + a^3*Sqrt[c]*Log[x] - a^3*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1085,1,95,130,0.1440891,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^5,x]","\frac{7}{8} a^4 \sqrt{c} \log (x)-\frac{7}{8} a^4 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)-\frac{\left(32 a^3 x^3+21 a^2 x^2+16 a x+6\right) \sqrt{c-a^2 c x^2}}{24 x^4}","-\frac{7 a^2 \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4}-\frac{2 a \sqrt{c-a^2 c x^2}}{3 x^3}-\frac{7}{8} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{4 a^3 \sqrt{c-a^2 c x^2}}{3 x}",1,"-1/24*(Sqrt[c - a^2*c*x^2]*(6 + 16*a*x + 21*a^2*x^2 + 32*a^3*x^3))/x^4 + (7*a^4*Sqrt[c]*Log[x])/8 - (7*a^4*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/8","A",0
1086,1,113,161,0.1441099,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^(3/2),x]","\frac{c \left(120 a^6 x^6+280 a^5 x^5+144 a^4 x^4-70 a^3 x^3-88 a^2 x^2-105 a x-176\right) \sqrt{c-a^2 c x^2}-105 c^{3/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{840 a^4}","-\frac{11 x^2 \left(c-a^2 c x^2\right)^{3/2}}{35 a^2}-\frac{1}{7} x^4 \left(c-a^2 c x^2\right)^{3/2}-\frac{x^3 \left(c-a^2 c x^2\right)^{3/2}}{3 a}+\frac{c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a^4}-\frac{(105 a x+88) \left(c-a^2 c x^2\right)^{3/2}}{420 a^4}+\frac{c x \sqrt{c-a^2 c x^2}}{8 a^3}",1,"(c*Sqrt[c - a^2*c*x^2]*(-176 - 105*a*x - 88*a^2*x^2 - 70*a^3*x^3 + 144*a^4*x^4 + 280*a^5*x^5 + 120*a^6*x^6) - 105*c^(3/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(840*a^4)","A",1
1087,1,105,136,0.1255489,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^(3/2),x]","\frac{c \left(40 a^5 x^5+96 a^4 x^4+50 a^3 x^3-32 a^2 x^2-45 a x-64\right) \sqrt{c-a^2 c x^2}-45 c^{3/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{240 a^3}","-\frac{2 x^2 \left(c-a^2 c x^2\right)^{3/2}}{5 a}+\frac{3 c x \sqrt{c-a^2 c x^2}}{16 a^2}-\frac{1}{6} x^3 \left(c-a^2 c x^2\right)^{3/2}+\frac{3 c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{16 a^3}-\frac{(45 a x+32) \left(c-a^2 c x^2\right)^{3/2}}{120 a^3}",1,"(c*Sqrt[c - a^2*c*x^2]*(-64 - 45*a*x - 32*a^2*x^2 + 50*a^3*x^3 + 96*a^4*x^4 + 40*a^5*x^5) - 45*c^(3/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(240*a^3)","A",1
1088,1,97,111,0.105571,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^(3/2),x]","\frac{c \left(12 a^4 x^4+30 a^3 x^3+16 a^2 x^2-15 a x-28\right) \sqrt{c-a^2 c x^2}-15 c^{3/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{60 a^2}","\frac{c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{4 a^2}-\frac{1}{5} x^2 \left(c-a^2 c x^2\right)^{3/2}+\frac{c x \sqrt{c-a^2 c x^2}}{4 a}-\frac{(15 a x+14) \left(c-a^2 c x^2\right)^{3/2}}{30 a^2}",1,"(c*Sqrt[c - a^2*c*x^2]*(-28 - 15*a*x + 16*a^2*x^2 + 30*a^3*x^3 + 12*a^4*x^4) - 15*c^(3/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(60*a^2)","A",1
1089,1,117,107,0.0938393,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2),x]","-\frac{c \sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(6 a^4 x^4+10 a^3 x^3-7 a^2 x^2-25 a x+16\right)+30 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{24 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{5 c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a}+\frac{5}{8} c x \sqrt{c-a^2 c x^2}-\frac{(a x+1) \left(c-a^2 c x^2\right)^{3/2}}{4 a}-\frac{5 \left(c-a^2 c x^2\right)^{3/2}}{12 a}",1,"-1/24*(c*Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(16 - 25*a*x - 7*a^2*x^2 + 10*a^3*x^3 + 6*a^4*x^4) + 30*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1090,1,115,101,0.1107699,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x,x]","-c^{3/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+c^{3/2} \left(-\tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)\right)+\frac{1}{3} c \left(a^2 x^2+3 a x+2\right) \sqrt{c-a^2 c x^2}+c^{3/2} \log (x)","c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)+c (a x+1) \sqrt{c-a^2 c x^2}-\frac{1}{3} \left(c-a^2 c x^2\right)^{3/2}",1,"(c*(2 + 3*a*x + a^2*x^2)*Sqrt[c - a^2*c*x^2])/3 - c^(3/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] + c^(3/2)*Log[x] - c^(3/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1091,1,124,112,0.1525177,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^2,x]","-2 a c^{3/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{1}{2} a c^{3/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\frac{c \left(a^2 x^2+4 a x-2\right) \sqrt{c-a^2 c x^2}}{2 x}+2 a c^{3/2} \log (x)","-\frac{1}{2} a c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-2 a c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)+\frac{1}{2} a c (4-a x) \sqrt{c-a^2 c x^2}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{x}",1,"(c*(-2 + 4*a*x + a^2*x^2)*Sqrt[c - a^2*c*x^2])/(2*x) + (a*c^(3/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/2 + 2*a*c^(3/2)*Log[x] - 2*a*c^(3/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1092,1,129,121,0.21329,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^3,x]","\frac{1}{2} c \left(\frac{\left(2 a^2 x^2-4 a x-1\right) \sqrt{c-a^2 c x^2}}{x^2}-a^2 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+4 a^2 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+a^2 \sqrt{c} \log (x)\right)","-2 a^2 c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-\frac{1}{2} a^2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{a c (4-a x) \sqrt{c-a^2 c x^2}}{2 x}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{2 x^2}",1,"(c*(((-1 - 4*a*x + 2*a^2*x^2)*Sqrt[c - a^2*c*x^2])/x^2 + 4*a^2*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] + a^2*Sqrt[c]*Log[x] - a^2*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]))/2","A",0
1093,1,127,115,0.1517849,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^4,x]","-a^3 c^{3/2} \log (x)-\frac{c \left(2 a^2 x^2+3 a x+1\right) \sqrt{c-a^2 c x^2}}{3 x^3}+a^3 c^{3/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+a^3 c^{3/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)","-\frac{a c (a x+1) \sqrt{c-a^2 c x^2}}{x^2}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{3 x^3}+a^3 \left(-c^{3/2}\right) \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)+a^3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-1/3*(c*(1 + 3*a*x + 2*a^2*x^2)*Sqrt[c - a^2*c*x^2])/x^3 + a^3*c^(3/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] - a^3*c^(3/2)*Log[x] + a^3*c^(3/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1094,1,96,106,0.1527653,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^5,x]","-\frac{5}{8} a^4 c^{3/2} \log (x)+\frac{5}{8} a^4 c^{3/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{c \left(16 a^3 x^3-9 a^2 x^2-16 a x-6\right) \sqrt{c-a^2 c x^2}}{24 x^4}","-\frac{5 a^2 c \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{4 x^4}-\frac{2 a \left(c-a^2 c x^2\right)^{3/2}}{3 x^3}+\frac{5}{8} a^4 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"(c*Sqrt[c - a^2*c*x^2]*(-6 - 16*a*x - 9*a^2*x^2 + 16*a^3*x^3))/(24*x^4) - (5*a^4*c^(3/2)*Log[x])/8 + (5*a^4*c^(3/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/8","A",0
1095,1,104,131,0.1679101,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^6} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^6,x]","-\frac{1}{4} a^5 c^{3/2} \log (x)+\frac{1}{4} a^5 c^{3/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{c \left(28 a^4 x^4+15 a^3 x^3-16 a^2 x^2-30 a x-12\right) \sqrt{c-a^2 c x^2}}{60 x^5}","-\frac{\left(c-a^2 c x^2\right)^{3/2}}{5 x^5}-\frac{a \left(c-a^2 c x^2\right)^{3/2}}{2 x^4}-\frac{7 a^2 \left(c-a^2 c x^2\right)^{3/2}}{15 x^3}+\frac{1}{4} a^5 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{a^3 c \sqrt{c-a^2 c x^2}}{4 x^2}",1,"(c*Sqrt[c - a^2*c*x^2]*(-12 - 30*a*x - 16*a^2*x^2 + 15*a^3*x^3 + 28*a^4*x^4))/(60*x^5) - (a^5*c^(3/2)*Log[x])/4 + (a^5*c^(3/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/4","A",0
1096,1,109,156,0.2411002,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^7} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^7,x]","\frac{1}{240} c \left(-45 a^6 \sqrt{c} \log (x)+45 a^6 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{\left(64 a^5 x^5+45 a^4 x^4+32 a^3 x^3-50 a^2 x^2-96 a x-40\right) \sqrt{c-a^2 c x^2}}{x^6}\right)","-\frac{\left(c-a^2 c x^2\right)^{3/2}}{6 x^6}-\frac{2 a \left(c-a^2 c x^2\right)^{3/2}}{5 x^5}-\frac{3 a^2 \left(c-a^2 c x^2\right)^{3/2}}{8 x^4}+\frac{3}{16} a^6 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{3 a^4 c \sqrt{c-a^2 c x^2}}{16 x^2}-\frac{4 a^3 \left(c-a^2 c x^2\right)^{3/2}}{15 x^3}",1,"(c*((Sqrt[c - a^2*c*x^2]*(-40 - 96*a*x - 50*a^2*x^2 + 32*a^3*x^3 + 45*a^4*x^4 + 64*a^5*x^5))/x^6 - 45*a^6*Sqrt[c]*Log[x] + 45*a^6*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]))/240","A",0
1097,1,120,181,0.189922,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^8} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^8,x]","-\frac{1}{8} a^7 c^{3/2} \log (x)+\frac{1}{8} a^7 c^{3/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{c \left(176 a^6 x^6+105 a^5 x^5+88 a^4 x^4+70 a^3 x^3-144 a^2 x^2-280 a x-120\right) \sqrt{c-a^2 c x^2}}{840 x^7}","-\frac{\left(c-a^2 c x^2\right)^{3/2}}{7 x^7}-\frac{a \left(c-a^2 c x^2\right)^{3/2}}{3 x^6}-\frac{11 a^2 \left(c-a^2 c x^2\right)^{3/2}}{35 x^5}+\frac{1}{8} a^7 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{a^5 c \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{22 a^4 \left(c-a^2 c x^2\right)^{3/2}}{105 x^3}-\frac{a^3 \left(c-a^2 c x^2\right)^{3/2}}{4 x^4}",1,"(c*Sqrt[c - a^2*c*x^2]*(-120 - 280*a*x - 144*a^2*x^2 + 70*a^3*x^3 + 88*a^4*x^4 + 105*a^5*x^5 + 176*a^6*x^6))/(840*x^7) - (a^7*c^(3/2)*Log[x])/8 + (a^7*c^(3/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/8","A",0
1098,1,131,187,0.2213457,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^(5/2),x]","-\frac{c^2 \left(945 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\left(2240 a^8 x^8+5040 a^7 x^7-320 a^6 x^6-7560 a^5 x^5-4416 a^4 x^4+630 a^3 x^3+832 a^2 x^2+945 a x+1664\right) \sqrt{c-a^2 c x^2}\right)}{20160 a^4}","-\frac{13 x^2 \left(c-a^2 c x^2\right)^{5/2}}{63 a^2}-\frac{1}{9} x^4 \left(c-a^2 c x^2\right)^{5/2}-\frac{x^3 \left(c-a^2 c x^2\right)^{5/2}}{4 a}+\frac{3 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{64 a^4}-\frac{(315 a x+208) \left(c-a^2 c x^2\right)^{5/2}}{2520 a^4}+\frac{3 c^2 x \sqrt{c-a^2 c x^2}}{64 a^3}+\frac{c x \left(c-a^2 c x^2\right)^{3/2}}{32 a^3}",1,"-1/20160*(c^2*(Sqrt[c - a^2*c*x^2]*(1664 + 945*a*x + 832*a^2*x^2 + 630*a^3*x^3 - 4416*a^4*x^4 - 7560*a^5*x^5 - 320*a^6*x^6 + 5040*a^7*x^7 + 2240*a^8*x^8) + 945*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))]))/a^4","A",1
1099,1,123,162,0.174568,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^(5/2),x]","-\frac{c^2 \left(1155 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\left(1680 a^7 x^7+3840 a^6 x^6-280 a^5 x^5-6144 a^4 x^4-3710 a^3 x^3+768 a^2 x^2+1155 a x+1536\right) \sqrt{c-a^2 c x^2}\right)}{13440 a^3}","\frac{11 c^2 x \sqrt{c-a^2 c x^2}}{128 a^2}-\frac{2 x^2 \left(c-a^2 c x^2\right)^{5/2}}{7 a}+\frac{11 c x \left(c-a^2 c x^2\right)^{3/2}}{192 a^2}-\frac{1}{8} x^3 \left(c-a^2 c x^2\right)^{5/2}+\frac{11 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a^3}-\frac{(385 a x+192) \left(c-a^2 c x^2\right)^{5/2}}{1680 a^3}",1,"-1/13440*(c^2*(Sqrt[c - a^2*c*x^2]*(1536 + 1155*a*x + 768*a^2*x^2 - 3710*a^3*x^3 - 6144*a^4*x^4 - 280*a^5*x^5 + 3840*a^6*x^6 + 1680*a^7*x^7) + 1155*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))]))/a^3","A",1
1100,1,115,137,0.1545592,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^(5/2),x]","-\frac{c^2 \left(105 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\left(120 a^6 x^6+280 a^5 x^5-24 a^4 x^4-490 a^3 x^3-312 a^2 x^2+105 a x+216\right) \sqrt{c-a^2 c x^2}\right)}{840 a^2}","\frac{c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a^2}+\frac{c^2 x \sqrt{c-a^2 c x^2}}{8 a}+\frac{c x \left(c-a^2 c x^2\right)^{3/2}}{12 a}-\frac{1}{7} x^2 \left(c-a^2 c x^2\right)^{5/2}-\frac{(35 a x+27) \left(c-a^2 c x^2\right)^{5/2}}{105 a^2}",1,"-1/840*(c^2*(Sqrt[c - a^2*c*x^2]*(216 + 105*a*x - 312*a^2*x^2 - 490*a^3*x^3 - 24*a^4*x^4 + 280*a^5*x^5 + 120*a^6*x^6) + 105*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))]))/a^2","A",1
1101,1,135,130,0.144489,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2),x]","\frac{c^2 \sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(40 a^6 x^6+56 a^5 x^5-106 a^4 x^4-182 a^3 x^3+57 a^2 x^2+231 a x-96\right)-210 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{240 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{7 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{16 a}+\frac{7}{16} c^2 x \sqrt{c-a^2 c x^2}+\frac{7}{24} c x \left(c-a^2 c x^2\right)^{3/2}-\frac{(a x+1) \left(c-a^2 c x^2\right)^{5/2}}{6 a}-\frac{7 \left(c-a^2 c x^2\right)^{5/2}}{30 a}",1,"(c^2*Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(-96 + 231*a*x + 57*a^2*x^2 - 182*a^3*x^3 - 106*a^4*x^4 + 56*a^5*x^5 + 40*a^6*x^6) - 210*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(240*a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1102,1,136,136,0.1456564,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x,x]","-c^{5/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)-\frac{3}{4} c^{5/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-\frac{1}{60} c^2 \left(12 a^4 x^4+30 a^3 x^3-4 a^2 x^2-75 a x-68\right) \sqrt{c-a^2 c x^2}+c^{5/2} \log (x)","\frac{3}{4} c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)+\frac{1}{4} c^2 (3 a x+4) \sqrt{c-a^2 c x^2}+\frac{1}{6} c (3 a x+2) \left(c-a^2 c x^2\right)^{3/2}-\frac{1}{5} \left(c-a^2 c x^2\right)^{5/2}",1,"-1/60*(c^2*Sqrt[c - a^2*c*x^2]*(-68 - 75*a*x - 4*a^2*x^2 + 30*a^3*x^3 + 12*a^4*x^4)) - (3*c^(5/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/4 + c^(5/2)*Log[x] - c^(5/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1103,1,143,141,0.236308,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^2,x]","-2 a c^{5/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{9}{8} a c^{5/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-\frac{c^2 \left(6 a^4 x^4+16 a^3 x^3-3 a^2 x^2-64 a x+24\right) \sqrt{c-a^2 c x^2}}{24 x}+2 a c^{5/2} \log (x)","-\frac{9}{8} a c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-2 a c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)+\frac{1}{8} a c^2 (16-9 a x) \sqrt{c-a^2 c x^2}+\frac{1}{12} a c (8-9 a x) \left(c-a^2 c x^2\right)^{3/2}-\frac{\left(c-a^2 c x^2\right)^{5/2}}{x}",1,"-1/24*(c^2*Sqrt[c - a^2*c*x^2]*(24 - 64*a*x - 3*a^2*x^2 + 16*a^3*x^3 + 6*a^4*x^4))/x + (9*a*c^(5/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/8 + 2*a*c^(5/2)*Log[x] - 2*a*c^(5/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1104,1,151,151,0.266071,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^3,x]","\frac{1}{2} a^2 c^{5/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+3 a^2 c^{5/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-\frac{1}{2} a^2 c^{5/2} \log (x)-\frac{c^2 \left(2 a^4 x^4+6 a^3 x^3-2 a^2 x^2+12 a x+3\right) \sqrt{c-a^2 c x^2}}{6 x^2}","-3 a^2 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)+\frac{1}{2} a^2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{1}{2} a^2 c^2 (6 a x+1) \sqrt{c-a^2 c x^2}-\frac{a c (a x+12) \left(c-a^2 c x^2\right)^{3/2}}{6 x}-\frac{\left(c-a^2 c x^2\right)^{5/2}}{2 x^2}",1,"-1/6*(c^2*Sqrt[c - a^2*c*x^2]*(3 + 12*a*x - 2*a^2*x^2 + 6*a^3*x^3 + 2*a^4*x^4))/x^2 + 3*a^2*c^(5/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] - (a^2*c^(5/2)*Log[x])/2 + (a^2*c^(5/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/2","A",0
1105,1,149,155,0.2760623,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^4} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^4,x]","-3 a^3 c^{5/2} \log (x)+3 a^3 c^{5/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{1}{2} a^3 c^{5/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-\frac{c^2 \left(3 a^4 x^4+12 a^3 x^3-2 a^2 x^2+6 a x+2\right) \sqrt{c-a^2 c x^2}}{6 x^3}","-\frac{a^2 c^2 (6 a x+1) \sqrt{c-a^2 c x^2}}{2 x}-\frac{a c (6-a x) \left(c-a^2 c x^2\right)^{3/2}}{6 x^2}-\frac{\left(c-a^2 c x^2\right)^{5/2}}{3 x^3}-\frac{1}{2} a^3 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)+3 a^3 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-1/6*(c^2*Sqrt[c - a^2*c*x^2]*(2 + 6*a*x - 2*a^2*x^2 + 12*a^3*x^3 + 3*a^4*x^4))/x^3 + (a^3*c^(5/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/2 - 3*a^3*c^(5/2)*Log[x] + 3*a^3*c^(5/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1106,1,151,155,0.2748982,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^5} \, dx","Integrate[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^5,x]","-\frac{9}{8} a^4 c^{5/2} \log (x)+\frac{9}{8} a^4 c^{5/2} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)-2 a^4 c^{5/2} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-\frac{c^2 \left(24 a^4 x^4-64 a^3 x^3-3 a^2 x^2+16 a x+6\right) \sqrt{c-a^2 c x^2}}{24 x^4}","-\frac{\left(c-a^2 c x^2\right)^{5/2}}{4 x^4}-\frac{a c (9 a x+16) \left(c-a^2 c x^2\right)^{3/2}}{24 x^3}+2 a^4 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)+\frac{9}{8} a^4 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)+\frac{a^3 c^2 (16-9 a x) \sqrt{c-a^2 c x^2}}{8 x}",1,"-1/24*(c^2*Sqrt[c - a^2*c*x^2]*(6 + 16*a*x - 3*a^2*x^2 - 64*a^3*x^3 + 24*a^4*x^4))/x^4 - 2*a^4*c^(5/2)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] - (9*a^4*c^(5/2)*Log[x])/8 + (9*a^4*c^(5/2)*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/8","A",0
1107,1,151,153,0.1411187,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2),x]","-\frac{c^3 \sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(112 a^8 x^8+144 a^7 x^7-424 a^6 x^6-600 a^5 x^5+558 a^4 x^4+978 a^3 x^3-187 a^2 x^2-837 a x+256\right)+630 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{896 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{45 c^{7/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a}+\frac{45}{128} c^3 x \sqrt{c-a^2 c x^2}+\frac{15}{64} c^2 x \left(c-a^2 c x^2\right)^{3/2}+\frac{3}{16} c x \left(c-a^2 c x^2\right)^{5/2}-\frac{(a x+1) \left(c-a^2 c x^2\right)^{7/2}}{8 a}-\frac{9 \left(c-a^2 c x^2\right)^{7/2}}{56 a}",1,"-1/896*(c^3*Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(256 - 837*a*x - 187*a^2*x^2 + 978*a^3*x^3 + 558*a^4*x^4 - 600*a^5*x^5 - 424*a^6*x^6 + 144*a^7*x^7 + 112*a^8*x^8) + 630*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1108,1,97,137,0.1786668,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^3)/Sqrt[c - a^2*c*x^2],x]","\frac{9 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\frac{\left(a^3 x^3+2 a^2 x^2+5 a x-14\right) \sqrt{c-a^2 c x^2}}{a x-1}}{3 a^4 c}","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 a^2 c}+\frac{11 \sqrt{c-a^2 c x^2}}{3 a^4 c}+\frac{(a x+1)^2}{a^4 \sqrt{c-a^2 c x^2}}-\frac{3 \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a^4 \sqrt{c}}+\frac{x \sqrt{c-a^2 c x^2}}{a^3 c}",1,"((Sqrt[c - a^2*c*x^2]*(-14 + 5*a*x + 2*a^2*x^2 + a^3*x^3))/(-1 + a*x) + 9*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(3*a^4*c)","A",1
1109,1,94,93,0.1071748,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^2)/Sqrt[c - a^2*c*x^2],x]","\frac{\left(a^2 x^2+3 a x-8\right) \sqrt{c-a^2 c x^2}+5 \sqrt{c} (a x-1) \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{2 a^3 c (a x-1)}","\frac{(a x+1)^2}{a^3 \sqrt{c-a^2 c x^2}}+\frac{(a x+6) \sqrt{c-a^2 c x^2}}{2 a^3 c}-\frac{5 \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{2 a^3 \sqrt{c}}",1,"((-8 + 3*a*x + a^2*x^2)*Sqrt[c - a^2*c*x^2] + 5*Sqrt[c]*(-1 + a*x)*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(2*a^3*c*(-1 + a*x))","A",1
1110,1,78,84,0.1120944,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x)/Sqrt[c - a^2*c*x^2],x]","\frac{\frac{(a x-3) \sqrt{c-a^2 c x^2}}{a x-1}+2 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{a^2 c}","\frac{(a x+1)^2}{a^2 \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{c-a^2 c x^2}}{a^2 c}-\frac{2 \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a^2 \sqrt{c}}",1,"(((-3 + a*x)*Sqrt[c - a^2*c*x^2])/(-1 + a*x) + 2*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(a^2*c)","A",1
1111,1,82,60,0.0358451,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{1-a^2 x^2} \left(\sqrt{a x+1}+\sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{a \sqrt{1-a x} \sqrt{c-a^2 c x^2}}","\frac{2 (a x+1)}{a \sqrt{c-a^2 c x^2}}-\frac{\tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a \sqrt{c}}",1,"(2*Sqrt[1 - a^2*x^2]*(Sqrt[1 + a*x] + Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a*x]*Sqrt[c - a^2*c*x^2])","A",0
1112,1,66,52,0.1237862,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x*Sqrt[c - a^2*c*x^2]),x]","\frac{2 \sqrt{c-a^2 c x^2}}{c-a c x}-\frac{\log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)}{\sqrt{c}}+\frac{\log (x)}{\sqrt{c}}","\frac{2 (a x+1)}{\sqrt{c-a^2 c x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{\sqrt{c}}",1,"(2*Sqrt[c - a^2*c*x^2])/(c - a*c*x) + Log[x]/Sqrt[c] - Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]/Sqrt[c]","A",0
1113,1,78,77,0.1374656,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^2*Sqrt[c - a^2*c*x^2]),x]","\frac{(1-3 a x) \sqrt{c-a^2 c x^2}}{c x (a x-1)}-\frac{2 a \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)}{\sqrt{c}}+\frac{2 a \log (x)}{\sqrt{c}}","\frac{2 a (a x+1)}{\sqrt{c-a^2 c x^2}}-\frac{\sqrt{c-a^2 c x^2}}{c x}-\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{\sqrt{c}}",1,"((1 - 3*a*x)*Sqrt[c - a^2*c*x^2])/(c*x*(-1 + a*x)) + (2*a*Log[x])/Sqrt[c] - (2*a*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/Sqrt[c]","A",0
1114,1,94,109,0.1670365,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^3*Sqrt[c - a^2*c*x^2]),x]","\frac{\frac{\left(-8 a^2 x^2+3 a x+1\right) \sqrt{c-a^2 c x^2}}{x^2 (a x-1)}-5 a^2 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+5 a^2 \sqrt{c} \log (x)}{2 c}","\frac{2 a^2 (a x+1)}{\sqrt{c-a^2 c x^2}}-\frac{2 a \sqrt{c-a^2 c x^2}}{c x}-\frac{\sqrt{c-a^2 c x^2}}{2 c x^2}-\frac{5 a^2 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{2 \sqrt{c}}",1,"(((1 + 3*a*x - 8*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(x^2*(-1 + a*x)) + 5*a^2*Sqrt[c]*Log[x] - 5*a^2*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/(2*c)","A",0
1115,1,101,135,0.174676,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^4*Sqrt[c - a^2*c*x^2]),x]","\frac{3 a^3 \log (x)}{\sqrt{c}}-\frac{3 a^3 \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)}{\sqrt{c}}+\frac{\left(-14 a^3 x^3+5 a^2 x^2+2 a x+1\right) \sqrt{c-a^2 c x^2}}{3 c x^3 (a x-1)}","-\frac{8 a^2 \sqrt{c-a^2 c x^2}}{3 c x}-\frac{a \sqrt{c-a^2 c x^2}}{c x^2}-\frac{\sqrt{c-a^2 c x^2}}{3 c x^3}+\frac{2 a^3 (a x+1)}{\sqrt{c-a^2 c x^2}}-\frac{3 a^3 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{\sqrt{c}}",1,"(Sqrt[c - a^2*c*x^2]*(1 + 2*a*x + 5*a^2*x^2 - 14*a^3*x^3))/(3*c*x^3*(-1 + a*x)) + (3*a^3*Log[x])/Sqrt[c] - (3*a^3*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/Sqrt[c]","A",0
1116,1,90,117,0.1713186,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^(3/2),x]","\frac{\frac{\left(-3 a^2 x^2+14 a x-10\right) \sqrt{c-a^2 c x^2}}{(a x-1)^2}-6 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{3 a^4 c^2}","\frac{2 \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a^4 c^{3/2}}-\frac{\sqrt{c-a^2 c x^2}}{a^4 c^2}+\frac{(a x+1)^2}{3 a^4 \left(c-a^2 c x^2\right)^{3/2}}-\frac{8 (a x+1)}{3 a^4 c \sqrt{c-a^2 c x^2}}",1,"(((-10 + 14*a*x - 3*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(-1 + a*x)^2 - 6*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(3*a^4*c^2)","A",1
1117,1,82,93,0.1214861,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(3/2),x]","\frac{\frac{(5 a x-4) \sqrt{c-a^2 c x^2}}{(a x-1)^2}-3 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{3 a^3 c^2}","\frac{\tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a^3 c^{3/2}}+\frac{(a x+1)^2}{3 a^3 \left(c-a^2 c x^2\right)^{3/2}}-\frac{5 (a x+1)}{3 a^3 c \sqrt{c-a^2 c x^2}}",1,"(((-4 + 5*a*x)*Sqrt[c - a^2*c*x^2])/(-1 + a*x)^2 - 3*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(3*a^3*c^2)","A",1
1118,1,38,60,0.061091,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^(3/2),x]","\frac{(2 a x-1) \sqrt{c-a^2 c x^2}}{3 a^2 c^2 (a x-1)^2}","\frac{(a x+1)^2}{3 a^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 (a x+1)}{3 a^2 c \sqrt{c-a^2 c x^2}}",1,"((-1 + 2*a*x)*Sqrt[c - a^2*c*x^2])/(3*a^2*c^2*(-1 + a*x)^2)","A",1
1119,1,63,51,0.0322378,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^(3/2),x]","-\frac{(a x-2) \sqrt{a x+1} \sqrt{1-a^2 x^2}}{3 a c (1-a x)^{3/2} \sqrt{c-a^2 c x^2}}","\frac{x}{3 c \sqrt{c-a^2 c x^2}}+\frac{2 (a x+1)}{3 a \left(c-a^2 c x^2\right)^{3/2}}",1,"-1/3*((-2 + a*x)*Sqrt[1 + a*x]*Sqrt[1 - a^2*x^2])/(a*c*(1 - a*x)^(3/2)*Sqrt[c - a^2*c*x^2])","A",0
1120,1,75,82,0.11831,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^(3/2)),x]","-\frac{\log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)}{c^{3/2}}+\frac{(5-4 a x) \sqrt{c-a^2 c x^2}}{3 c^2 (a x-1)^2}+\frac{\log (x)}{c^{3/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{c^{3/2}}+\frac{2 (a x+1)}{3 \left(c-a^2 c x^2\right)^{3/2}}+\frac{4 a x+3}{3 c \sqrt{c-a^2 c x^2}}",1,"((5 - 4*a*x)*Sqrt[c - a^2*c*x^2])/(3*c^2*(-1 + a*x)^2) + Log[x]/c^(3/2) - Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]/c^(3/2)","A",0
1121,1,89,108,0.1378575,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^(3/2)),x]","-\frac{2 a \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)}{c^{3/2}}+\frac{\left(-10 a^2 x^2+14 a x-3\right) \sqrt{c-a^2 c x^2}}{3 c^2 x (a x-1)^2}+\frac{2 a \log (x)}{c^{3/2}}","-\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{c^{3/2}}-\frac{\sqrt{c-a^2 c x^2}}{c^2 x}+\frac{2 a (a x+1)}{3 \left(c-a^2 c x^2\right)^{3/2}}+\frac{a (7 a x+6)}{3 c \sqrt{c-a^2 c x^2}}",1,"((-3 + 14*a*x - 10*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(3*c^2*x*(-1 + a*x)^2) + (2*a*Log[x])/c^(3/2) - (2*a*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/c^(3/2)","A",0
1122,1,105,142,0.1458477,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^(3/2)),x]","-\frac{7 a^2 \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)}{2 c^{3/2}}+\frac{7 a^2 \log (x)}{2 c^{3/2}}-\frac{\left(32 a^3 x^3-43 a^2 x^2+6 a x+3\right) \sqrt{c-a^2 c x^2}}{6 c^2 x^2 (a x-1)^2}","-\frac{7 a^2 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{2 c^{3/2}}-\frac{2 a \sqrt{c-a^2 c x^2}}{c^2 x}-\frac{\sqrt{c-a^2 c x^2}}{2 c^2 x^2}+\frac{a^2 (10 a x+9)}{3 c \sqrt{c-a^2 c x^2}}+\frac{2 a^2 (a x+1)}{3 \left(c-a^2 c x^2\right)^{3/2}}",1,"-1/6*(Sqrt[c - a^2*c*x^2]*(3 + 6*a*x - 43*a^2*x^2 + 32*a^3*x^3))/(c^2*x^2*(-1 + a*x)^2) + (7*a^2*Log[x])/(2*c^(3/2)) - (7*a^2*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/(2*c^(3/2))","A",0
1123,1,53,74,0.0359714,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^(5/2),x]","\frac{2 a^3 x^3-4 a^2 x^2+a x+2}{5 a c^2 (a x-1)^2 \sqrt{c-a^2 c x^2}}","\frac{2 x}{5 c^2 \sqrt{c-a^2 c x^2}}+\frac{x}{5 c \left(c-a^2 c x^2\right)^{3/2}}+\frac{2 (a x+1)}{5 a \left(c-a^2 c x^2\right)^{5/2}}",1,"(2 + a*x - 4*a^2*x^2 + 2*a^3*x^3)/(5*a*c^2*(-1 + a*x)^2*Sqrt[c - a^2*c*x^2])","A",1
1124,1,96,97,0.0506346,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^(7/2),x]","-\frac{\sqrt{1-a^2 x^2} \left(8 a^5 x^5-16 a^4 x^4-4 a^3 x^3+24 a^2 x^2-9 a x-6\right)}{21 a c^3 (1-a x)^{7/2} (a x+1)^{3/2} \sqrt{c-a^2 c x^2}}","\frac{8 x}{21 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x}{21 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x}{7 c \left(c-a^2 c x^2\right)^{5/2}}+\frac{2 (a x+1)}{7 a \left(c-a^2 c x^2\right)^{7/2}}",1,"-1/21*(Sqrt[1 - a^2*x^2]*(-6 - 9*a*x + 24*a^2*x^2 - 4*a^3*x^3 - 16*a^4*x^4 + 8*a^5*x^5))/(a*c^3*(1 - a*x)^(7/2)*(1 + a*x)^(3/2)*Sqrt[c - a^2*c*x^2])","A",1
1125,1,88,120,0.0684814,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^3,x]","c^3 x^{m+1} \left(\frac{a^6 x^6}{m+7}+\frac{2 a^5 x^5}{m+6}-\frac{a^4 x^4}{m+5}-\frac{4 a^3 x^3}{m+4}-\frac{a^2 x^2}{m+3}+\frac{2 a x}{m+2}+\frac{1}{m+1}\right)","\frac{a^6 c^3 x^{m+7}}{m+7}+\frac{2 a^5 c^3 x^{m+6}}{m+6}-\frac{a^4 c^3 x^{m+5}}{m+5}-\frac{4 a^3 c^3 x^{m+4}}{m+4}-\frac{a^2 c^3 x^{m+3}}{m+3}+\frac{2 a c^3 x^{m+2}}{m+2}+\frac{c^3 x^{m+1}}{m+1}",1,"c^3*x^(1 + m)*((1 + m)^(-1) + (2*a*x)/(2 + m) - (a^2*x^2)/(3 + m) - (4*a^3*x^3)/(4 + m) - (a^4*x^4)/(5 + m) + (2*a^5*x^5)/(6 + m) + (a^6*x^6)/(7 + m))","A",1
1126,1,69,67,0.1097045,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^2,x]","\frac{c^2 x^{m+1} \left(2 (m+3) \left(\frac{a^3 x^3}{m+4}+\frac{3 a^2 x^2}{m+3}+\frac{3 a x}{m+2}+\frac{1}{m+1}\right)-(a x+1)^4\right)}{m+5}","-\frac{a^4 c^2 x^{m+5}}{m+5}-\frac{2 a^3 c^2 x^{m+4}}{m+4}+\frac{2 a c^2 x^{m+2}}{m+2}+\frac{c^2 x^{m+1}}{m+1}",1,"(c^2*x^(1 + m)*(-(1 + a*x)^4 + 2*(3 + m)*((1 + m)^(-1) + (3*a*x)/(2 + m) + (3*a^2*x^2)/(3 + m) + (a^3*x^3)/(4 + m))))/(5 + m)","A",1
1127,1,34,42,0.057916,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2),x]","c x^{m+1} \left(\frac{a^2 x^2}{m+3}+\frac{2 a x}{m+2}+\frac{1}{m+1}\right)","\frac{a^2 c x^{m+3}}{m+3}+\frac{2 a c x^{m+2}}{m+2}+\frac{c x^{m+1}}{m+1}",1,"c*x^(1 + m)*((1 + m)^(-1) + (2*a*x)/(2 + m) + (a^2*x^2)/(3 + m))","A",1
1128,1,25,25,0.0153659,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{c-a^2 c x^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2),x]","\frac{x^{m+1} \, _2F_1(2,m+1;m+2;a x)}{c (m+1)}","\frac{x^{m+1} \, _2F_1(2,m+1;m+2;a x)}{c (m+1)}",1,"(x^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, a*x])/(c*(1 + m))","A",1
1129,1,92,113,0.0709861,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^2,x]","\frac{x^{m+1} \left(\left(2 m^2-4 m+1\right) (a x-1)^2 \, _2F_1(1,m+1;m+2;a x)+(a x-1)^2 \, _2F_1(1,m+1;m+2;-a x)+2 (m+1) (m (a x-1)-2 a x+3)\right)}{8 c^2 (m+1) (a x-1)^2}","\frac{\left(2 m^2-4 m+1\right) x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{8 c^2 (m+1)}+\frac{x^{m+1} \, _2F_1(1,m+1;m+2;-a x)}{8 c^2 (m+1)}+\frac{(2-m) x^{m+1}}{4 c^2 (1-a x)}+\frac{x^{m+1}}{4 c^2 (1-a x)^2}",1,"(x^(1 + m)*(2*(1 + m)*(3 - 2*a*x + m*(-1 + a*x)) + (-1 + a*x)^2*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)] + (1 - 4*m + 2*m^2)*(-1 + a*x)^2*Hypergeometric2F1[1, 1 + m, 2 + m, a*x]))/(8*c^2*(1 + m)*(-1 + a*x)^2)","A",1
1130,1,194,203,0.1572319,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^3,x]","\frac{x^{m+1} \left(-2 \left(m^2 \left(-5 a^3 x^3+6 a^2 x^2+5 a x-6\right)+m \left(2 a^3 x^3-3 a^2 x^2-6 a x+11\right)+2 \left(4 a^3 x^3-5 a^2 x^2-6 a x+9\right)+m^3 (a x-1)^2 (a x+1)\right)-\left(2 m^3-12 m^2+19 m-6\right) (a x+1) (a x-1)^3 \, _2F_1(1,m+1;m+2;a x)-3 (m-2) (a x+1) (a x-1)^3 \, _2F_1(1,m+1;m+2;-a x)\right)}{48 c^3 (m+1) (a x-1)^3 (a x+1)}","\frac{(2-m) \left(2 m^2-8 m+3\right) x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{48 c^3 (m+1)}+\frac{(2-m) x^{m+1} \, _2F_1(1,m+1;m+2;-a x)}{16 c^3 (m+1)}-\frac{(2-m) (4-m) x^{m+1}}{24 c^3 (a x+1)}+\frac{(7-2 m) (2-m) x^{m+1}}{24 c^3 (1-a x) (a x+1)}+\frac{(4-m) x^{m+1}}{12 c^3 (1-a x)^2 (a x+1)}+\frac{x^{m+1}}{6 c^3 (1-a x)^3 (a x+1)}",1,"(x^(1 + m)*(-2*(m^3*(-1 + a*x)^2*(1 + a*x) + m^2*(-6 + 5*a*x + 6*a^2*x^2 - 5*a^3*x^3) + m*(11 - 6*a*x - 3*a^2*x^2 + 2*a^3*x^3) + 2*(9 - 6*a*x - 5*a^2*x^2 + 4*a^3*x^3)) - 3*(-2 + m)*(-1 + a*x)^3*(1 + a*x)*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)] - (-6 + 19*m - 12*m^2 + 2*m^3)*(-1 + a*x)^3*(1 + a*x)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x]))/(48*c^3*(1 + m)*(-1 + a*x)^3*(1 + a*x))","A",1
1131,1,180,176,0.2237859,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^(5/2),x]","\frac{c^2 x^{m+1} \sqrt{c-a^2 c x^2} \left(\frac{2 a x \, _2F_1\left(-\frac{1}{2},\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)}{m+2}+\frac{\, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}-\frac{a^4 x^4 \, _2F_1\left(-\frac{1}{2},\frac{m+5}{2};\frac{m+7}{2};a^2 x^2\right)}{m+5}-\frac{2 a^3 x^3 \, _2F_1\left(-\frac{1}{2},\frac{m}{2}+2;\frac{m}{2}+3;a^2 x^2\right)}{m+4}\right)}{\sqrt{1-a^2 x^2}}","\frac{c^2 (2 m+7) x^{m+1} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{(m+1) (m+6) \sqrt{1-a^2 x^2}}+\frac{2 a c^2 x^{m+2} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{(m+2) \sqrt{1-a^2 x^2}}-\frac{x^{m+1} \left(c-a^2 c x^2\right)^{5/2}}{m+6}",1,"(c^2*x^(1 + m)*Sqrt[c - a^2*c*x^2]*((2*a*x*Hypergeometric2F1[-1/2, 1 + m/2, 2 + m/2, a^2*x^2])/(2 + m) - (2*a^3*x^3*Hypergeometric2F1[-1/2, 2 + m/2, 3 + m/2, a^2*x^2])/(4 + m) + Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2]/(1 + m) - (a^4*x^4*Hypergeometric2F1[-1/2, (5 + m)/2, (7 + m)/2, a^2*x^2])/(5 + m)))/Sqrt[1 - a^2*x^2]","A",0
1132,1,158,172,0.1499178,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^(3/2),x]","\frac{c x^{m+1} \sqrt{c-a^2 c x^2} \left(2 a \left(m^2+4 m+3\right) x \, _2F_1\left(-\frac{1}{2},\frac{m}{2}+1;\frac{m}{2}+2;a^2 x^2\right)+(m+2) \left(a^2 (m+1) x^2 \, _2F_1\left(-\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};a^2 x^2\right)+(m+3) \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)\right)\right)}{(m+1) (m+2) (m+3) \sqrt{1-a^2 x^2}}","\frac{c (2 m+5) x^{m+1} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{(m+1) (m+4) \sqrt{1-a^2 x^2}}+\frac{2 a c x^{m+2} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{(m+2) \sqrt{1-a^2 x^2}}-\frac{x^{m+1} \left(c-a^2 c x^2\right)^{3/2}}{m+4}",1,"(c*x^(1 + m)*Sqrt[c - a^2*c*x^2]*(2*a*(3 + 4*m + m^2)*x*Hypergeometric2F1[-1/2, 1 + m/2, 2 + m/2, a^2*x^2] + (2 + m)*((3 + m)*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2] + a^2*(1 + m)*x^2*Hypergeometric2F1[-1/2, (3 + m)/2, (5 + m)/2, a^2*x^2])))/((1 + m)*(2 + m)*(3 + m)*Sqrt[1 - a^2*x^2])","A",0
1133,1,130,172,0.22696,"\int e^{2 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(2*ArcTanh[a*x])*x^m*Sqrt[c - a^2*c*x^2],x]","\frac{x^{m+1} \left(-\frac{\sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{\sqrt{1-a^2 x^2}}-\frac{2 \sqrt{1-a x} \sqrt{-c (a x+1)} F_1\left(m+1;\frac{1}{2},-\frac{1}{2};m+2;a x,-a x\right)}{\sqrt{a x-1} \sqrt{a x+1}}\right)}{m+1}","\frac{c (2 m+3) \sqrt{1-a^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{(m+1) (m+2) \sqrt{c-a^2 c x^2}}+\frac{2 a c \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{(m+2) \sqrt{c-a^2 c x^2}}-\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{m+2}",1,"(x^(1 + m)*((-2*Sqrt[1 - a*x]*Sqrt[-(c*(1 + a*x))]*AppellF1[1 + m, 1/2, -1/2, 2 + m, a*x, -(a*x)])/(Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/Sqrt[1 - a^2*x^2]))/(1 + m)","C",0
1134,1,66,169,0.1135247,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^m)/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} x^{m+1} F_1\left(m+1;\frac{3}{2},-\frac{1}{2};m+2;a x,-a x\right)}{(m+1) \sqrt{a x-1} \sqrt{-c (a x+1)}}","-\frac{(2 m+1) \sqrt{1-a^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{(m+1) \sqrt{c-a^2 c x^2}}-\frac{2 a (m+1) \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{(m+2) \sqrt{c-a^2 c x^2}}+\frac{2 (a x+1) x^{m+1}}{\sqrt{c-a^2 c x^2}}",1,"(x^(1 + m)*Sqrt[1 - a^2*x^2]*AppellF1[1 + m, 3/2, -1/2, 2 + m, a*x, -(a*x)])/((1 + m)*Sqrt[-1 + a*x]*Sqrt[-(c*(1 + a*x))])","C",0
1135,1,173,183,0.2503797,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^(3/2),x]","\frac{x^{m+1} \left(\sqrt{a x-1} \sqrt{a x+1} \sqrt{c-a c x} F_1\left(m+1;\frac{1}{2},-\frac{1}{2};m+2;-a x,a x\right)+(a x-1) \sqrt{-c (a x+1)} \left(F_1\left(m+1;\frac{1}{2},-\frac{1}{2};m+2;a x,-a x\right)+2 F_1\left(m+1;\frac{3}{2},-\frac{1}{2};m+2;a x,-a x\right)+4 F_1\left(m+1;\frac{5}{2},-\frac{1}{2};m+2;a x,-a x\right)\right)\right)}{8 c^2 (m+1) \sqrt{-(a x-1)^2} \sqrt{a x+1}}","\frac{(1-2 m) \sqrt{1-a^2 x^2} x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{3 c (m+1) \sqrt{c-a^2 c x^2}}+\frac{2 a (1-m) \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{3 c (m+2) \sqrt{c-a^2 c x^2}}+\frac{2 (a x+1) x^{m+1}}{3 \left(c-a^2 c x^2\right)^{3/2}}",1,"(x^(1 + m)*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[c - a*c*x]*AppellF1[1 + m, 1/2, -1/2, 2 + m, -(a*x), a*x] + (-1 + a*x)*Sqrt[-(c*(1 + a*x))]*(AppellF1[1 + m, 1/2, -1/2, 2 + m, a*x, -(a*x)] + 2*AppellF1[1 + m, 3/2, -1/2, 2 + m, a*x, -(a*x)] + 4*AppellF1[1 + m, 5/2, -1/2, 2 + m, a*x, -(a*x)])))/(8*c^2*(1 + m)*Sqrt[-(-1 + a*x)^2]*Sqrt[1 + a*x])","C",0
1136,1,68,55,0.0175747,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","-\frac{2^{p+1} (1-a x)^p \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-1,p;p+1;\frac{1}{2} (1-a x)\right)}{a p}","-\frac{2^{p+1} (a x+1)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-1,p;p+1;\frac{1}{2} (1-a x)\right)}{a p}",1,"-((2^(1 + p)*(1 - a*x)^p*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - p, p, 1 + p, (1 - a*x)/2])/(a*p*(1 - a^2*x^2)^p))","A",1
1137,1,70,136,0.1166817,"\int e^{3 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right) \, dx","Integrate[E^(3*ArcTanh[a*x])*x^3*(c - a^2*c*x^2),x]","\frac{345 c \sin ^{-1}(a x)-c \sqrt{1-a^2 x^2} \left(40 a^5 x^5+144 a^4 x^4+230 a^3 x^3+272 a^2 x^2+345 a x+544\right)}{240 a^4}","\frac{23 c \sin ^{-1}(a x)}{16 a^4}-\frac{17 c x^2 \sqrt{1-a^2 x^2}}{15 a^2}-\frac{1}{6} a c x^5 \sqrt{1-a^2 x^2}-\frac{3}{5} c x^4 \sqrt{1-a^2 x^2}-\frac{23 c x^3 \sqrt{1-a^2 x^2}}{24 a}-\frac{c (345 a x+544) \sqrt{1-a^2 x^2}}{240 a^4}",1,"(-(c*Sqrt[1 - a^2*x^2]*(544 + 345*a*x + 272*a^2*x^2 + 230*a^3*x^3 + 144*a^4*x^4 + 40*a^5*x^5)) + 345*c*ArcSin[a*x])/(240*a^4)","A",1
1138,1,62,111,0.0897952,"\int e^{3 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right) \, dx","Integrate[E^(3*ArcTanh[a*x])*x^2*(c - a^2*c*x^2),x]","\frac{195 c \sin ^{-1}(a x)-c \sqrt{1-a^2 x^2} \left(24 a^4 x^4+90 a^3 x^3+152 a^2 x^2+195 a x+304\right)}{120 a^3}","\frac{13 c \sin ^{-1}(a x)}{8 a^3}-\frac{19 c x^2 \sqrt{1-a^2 x^2}}{15 a}-\frac{1}{5} a c x^4 \sqrt{1-a^2 x^2}-\frac{3}{4} c x^3 \sqrt{1-a^2 x^2}-\frac{c (195 a x+304) \sqrt{1-a^2 x^2}}{120 a^3}",1,"(-(c*Sqrt[1 - a^2*x^2]*(304 + 195*a*x + 152*a^2*x^2 + 90*a^3*x^3 + 24*a^4*x^4)) + 195*c*ArcSin[a*x])/(120*a^3)","A",1
1139,1,54,120,0.0714183,"\int e^{3 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right) \, dx","Integrate[E^(3*ArcTanh[a*x])*x*(c - a^2*c*x^2),x]","\frac{15 c \sin ^{-1}(a x)-c \sqrt{1-a^2 x^2} \left(2 a^3 x^3+8 a^2 x^2+15 a x+24\right)}{8 a^2}","-\frac{c \sqrt{1-a^2 x^2} (a x+1)^3}{4 a^2}-\frac{c \sqrt{1-a^2 x^2} (a x+1)^2}{4 a^2}-\frac{5 c \sqrt{1-a^2 x^2} (a x+1)}{8 a^2}-\frac{15 c \sqrt{1-a^2 x^2}}{8 a^2}+\frac{15 c \sin ^{-1}(a x)}{8 a^2}",1,"(-(c*Sqrt[1 - a^2*x^2]*(24 + 15*a*x + 8*a^2*x^2 + 2*a^3*x^3)) + 15*c*ArcSin[a*x])/(8*a^2)","A",1
1140,1,57,91,0.0524988,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2),x]","-\frac{c \left(\sqrt{1-a^2 x^2} \left(2 a^2 x^2+9 a x+22\right)+30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","-\frac{c \sqrt{1-a^2 x^2} (a x+1)^2}{3 a}-\frac{5 c \sqrt{1-a^2 x^2} (a x+1)}{6 a}-\frac{5 c \sqrt{1-a^2 x^2}}{2 a}+\frac{5 c \sin ^{-1}(a x)}{2 a}",1,"-1/6*(c*(Sqrt[1 - a^2*x^2]*(22 + 9*a*x + 2*a^2*x^2) + 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
1141,1,49,66,0.0486326,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x,x]","-\frac{1}{2} c \left(\sqrt{1-a^2 x^2} (a x+6)+2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-7 \sin ^{-1}(a x)\right)","-\frac{1}{2} a c x \sqrt{1-a^2 x^2}-3 c \sqrt{1-a^2 x^2}-c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+\frac{7}{2} c \sin ^{-1}(a x)",1,"-1/2*(c*((6 + a*x)*Sqrt[1 - a^2*x^2] - 7*ArcSin[a*x] + 2*ArcTanh[Sqrt[1 - a^2*x^2]]))","A",1
1142,1,52,66,0.0692539,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^2,x]","c \left(-\frac{\sqrt{1-a^2 x^2} (a x+1)}{x}-3 a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+3 a \sin ^{-1}(a x)\right)","-a c \sqrt{1-a^2 x^2}-\frac{c \sqrt{1-a^2 x^2}}{x}-3 a c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+3 a c \sin ^{-1}(a x)",1,"c*(-(((1 + a*x)*Sqrt[1 - a^2*x^2])/x) + 3*a*ArcSin[a*x] - 3*a*ArcTanh[Sqrt[1 - a^2*x^2]])","A",1
1143,1,60,76,0.0783597,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^3} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^3,x]","\frac{1}{2} c \left(-\frac{(6 a x+1) \sqrt{1-a^2 x^2}}{x^2}-7 a^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+2 a^2 \sin ^{-1}(a x)\right)","-\frac{3 a c \sqrt{1-a^2 x^2}}{x}-\frac{c \sqrt{1-a^2 x^2}}{2 x^2}-\frac{7}{2} a^2 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a^2 c \sin ^{-1}(a x)",1,"(c*(-(((1 + 6*a*x)*Sqrt[1 - a^2*x^2])/x^2) + 2*a^2*ArcSin[a*x] - 7*a^2*ArcTanh[Sqrt[1 - a^2*x^2]]))/2","A",1
1144,1,60,94,0.063132,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^4} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^4,x]","-\frac{c \sqrt{1-a^2 x^2} \left(22 a^2 x^2+9 a x+2\right)}{6 x^3}-\frac{5}{2} a^3 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{11 a^2 c \sqrt{1-a^2 x^2}}{3 x}-\frac{3 a c \sqrt{1-a^2 x^2}}{2 x^2}-\frac{c \sqrt{1-a^2 x^2}}{3 x^3}-\frac{5}{2} a^3 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-1/6*(c*Sqrt[1 - a^2*x^2]*(2 + 9*a*x + 22*a^2*x^2))/x^3 - (5*a^3*c*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",1
1145,1,97,115,0.117636,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^5} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^5,x]","\frac{1}{2} a c \left(-\frac{\sqrt{1-a^2 x^2} \left(6 a^2 x^2+3 a x+2\right)}{x^3}-2 a^3 \sqrt{1-a^2 x^2} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-a^2 x^2\right)-3 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)\right)","-\frac{15 a^2 c \sqrt{1-a^2 x^2}}{8 x^2}-\frac{c \sqrt{1-a^2 x^2}}{4 x^4}-\frac{a c \sqrt{1-a^2 x^2}}{x^3}-\frac{15}{8} a^4 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{3 a^3 c \sqrt{1-a^2 x^2}}{x}",1,"(a*c*(-((Sqrt[1 - a^2*x^2]*(2 + 3*a*x + 6*a^2*x^2))/x^3) - 3*a^3*ArcTanh[Sqrt[1 - a^2*x^2]] - 2*a^3*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, 3, 3/2, 1 - a^2*x^2]))/2","C",0
1146,1,110,144,0.1326312,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^6} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^6,x]","-3 a^5 c \sqrt{1-a^2 x^2} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};1-a^2 x^2\right)-\frac{1}{2} a^5 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{c \sqrt{1-a^2 x^2} \left(76 a^4 x^4+15 a^3 x^3+38 a^2 x^2+6\right)}{30 x^5}","-\frac{c \sqrt{1-a^2 x^2}}{5 x^5}-\frac{3 a c \sqrt{1-a^2 x^2}}{4 x^4}-\frac{19 a^2 c \sqrt{1-a^2 x^2}}{15 x^3}-\frac{13}{8} a^5 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{38 a^4 c \sqrt{1-a^2 x^2}}{15 x}-\frac{13 a^3 c \sqrt{1-a^2 x^2}}{8 x^2}",1,"-1/30*(c*Sqrt[1 - a^2*x^2]*(6 + 38*a^2*x^2 + 15*a^3*x^3 + 76*a^4*x^4))/x^5 - (a^5*c*ArcTanh[Sqrt[1 - a^2*x^2]])/2 - 3*a^5*c*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, 3, 3/2, 1 - a^2*x^2]","C",0
1147,1,75,121,0.1039638,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(24 a^4 x^4+90 a^3 x^3+112 a^2 x^2+15 a x-136\right)-210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{120 a}","-\frac{c^2 (a x+1)^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}-\frac{7 c^2 (a x+1) \left(1-a^2 x^2\right)^{3/2}}{20 a}-\frac{7 c^2 \left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{7}{8} c^2 x \sqrt{1-a^2 x^2}+\frac{7 c^2 \sin ^{-1}(a x)}{8 a}",1,"(c^2*(Sqrt[1 - a^2*x^2]*(-136 + 15*a*x + 112*a^2*x^2 + 90*a^3*x^3 + 24*a^4*x^4) - 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(120*a)","A",0
1148,1,91,143,0.1227294,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","-\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(80 a^6 x^6+280 a^5 x^5+208 a^4 x^4-350 a^3 x^3-656 a^2 x^2-245 a x+368\right)+630 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{560 a}","-\frac{c^3 (a x+1)^2 \left(1-a^2 x^2\right)^{5/2}}{7 a}-\frac{3 c^3 (a x+1) \left(1-a^2 x^2\right)^{5/2}}{14 a}-\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{10 a}+\frac{3}{8} c^3 x \left(1-a^2 x^2\right)^{3/2}+\frac{9}{16} c^3 x \sqrt{1-a^2 x^2}+\frac{9 c^3 \sin ^{-1}(a x)}{16 a}",1,"-1/560*(c^3*(Sqrt[1 - a^2*x^2]*(368 - 245*a*x - 656*a^2*x^2 - 350*a^3*x^3 + 208*a^4*x^4 + 280*a^5*x^5 + 80*a^6*x^6) + 630*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
1149,1,107,165,0.1482181,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^4,x]","\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(896 a^8 x^8+3024 a^7 x^7+1024 a^6 x^6-7224 a^5 x^5-8448 a^4 x^4+3066 a^3 x^3+10240 a^2 x^2+4599 a x-3712\right)-6930 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{8064 a}","-\frac{c^4 (a x+1)^2 \left(1-a^2 x^2\right)^{7/2}}{9 a}-\frac{11 c^4 (a x+1) \left(1-a^2 x^2\right)^{7/2}}{72 a}-\frac{11 c^4 \left(1-a^2 x^2\right)^{7/2}}{56 a}+\frac{11}{48} c^4 x \left(1-a^2 x^2\right)^{5/2}+\frac{55}{192} c^4 x \left(1-a^2 x^2\right)^{3/2}+\frac{55}{128} c^4 x \sqrt{1-a^2 x^2}+\frac{55 c^4 \sin ^{-1}(a x)}{128 a}",1,"(c^4*(Sqrt[1 - a^2*x^2]*(-3712 + 4599*a*x + 10240*a^2*x^2 + 3066*a^3*x^3 - 8448*a^4*x^4 - 7224*a^5*x^5 + 1024*a^6*x^6 + 3024*a^7*x^7 + 896*a^8*x^8) - 6930*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(8064*a)","A",0
1150,1,78,95,0.0855872,"\int \frac{e^{3 \tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2),x]","\frac{3 a^3 x^3-16 a^2 x^2+9 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-5 a x+14}{3 a^3 c (a x-1) \sqrt{1-a^2 x^2}}","\frac{3 \sin ^{-1}(a x)}{a^3 c}+\frac{(a x+1)^3}{3 a^3 c \left(1-a^2 x^2\right)^{3/2}}-\frac{2 (a x+1)^2}{a^3 c \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{1-a^2 x^2}}{a^3 c}",1,"(14 - 5*a*x - 16*a^2*x^2 + 3*a^3*x^3 + 9*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a^3*c*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
1151,1,70,70,0.0625845,"\int \frac{e^{3 \tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*x)/(c - a^2*c*x^2),x]","\frac{-7 a^2 x^2+3 (a x-1) \sqrt{1-a^2 x^2} \sin ^{-1}(a x)-2 a x+5}{3 a^2 c (a x-1) \sqrt{1-a^2 x^2}}","\frac{(a x+1)^3}{3 a^2 c \left(1-a^2 x^2\right)^{3/2}}-\frac{2 (a x+1)}{a^2 c \sqrt{1-a^2 x^2}}+\frac{\sin ^{-1}(a x)}{a^2 c}",1,"(5 - 2*a*x - 7*a^2*x^2 + 3*(-1 + a*x)*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(3*a^2*c*(-1 + a*x)*Sqrt[1 - a^2*x^2])","A",1
1152,1,29,18,0.0115266,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{(a x+1)^{3/2}}{3 a c (1-a x)^{3/2}}","\frac{e^{3 \tanh ^{-1}(a x)}}{3 a c}",1,"(1 + a*x)^(3/2)/(3*a*c*(1 - a*x)^(3/2))","A",0
1153,1,43,97,0.0182323,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","\frac{\sqrt{a x+1} \left(2 a^2 x^2-6 a x+7\right)}{15 a c^2 (1-a x)^{5/2}}","\frac{2 \sqrt{1-a^2 x^2}}{15 a c^2 (1-a x)}+\frac{2 \sqrt{1-a^2 x^2}}{15 a c^2 (1-a x)^2}+\frac{\sqrt{1-a^2 x^2}}{5 a c^2 (1-a x)^3}",1,"(Sqrt[1 + a*x]*(7 - 6*a*x + 2*a^2*x^2))/(15*a*c^2*(1 - a*x)^(5/2))","A",0
1154,1,61,119,0.021476,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","\frac{8 a^4 x^4-24 a^3 x^3+20 a^2 x^2+4 a x-13}{35 a c^3 (a x-1)^3 \sqrt{1-a^2 x^2}}","\frac{8 x}{35 c^3 \sqrt{1-a^2 x^2}}+\frac{4}{35 a c^3 (1-a x) \sqrt{1-a^2 x^2}}+\frac{4}{35 a c^3 (1-a x)^2 \sqrt{1-a^2 x^2}}+\frac{1}{7 a c^3 (1-a x)^3 \sqrt{1-a^2 x^2}}",1,"(-13 + 4*a*x + 20*a^2*x^2 - 24*a^3*x^3 + 8*a^4*x^4)/(35*a*c^3*(-1 + a*x)^3*Sqrt[1 - a^2*x^2])","A",1
1155,1,75,141,0.0295117,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","\frac{16 a^6 x^6-48 a^5 x^5+24 a^4 x^4+56 a^3 x^3-66 a^2 x^2+6 a x+19}{63 a c^4 (1-a x)^{9/2} (a x+1)^{3/2}}","\frac{16 x}{63 c^4 \sqrt{1-a^2 x^2}}+\frac{8 x}{63 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{2}{21 a c^4 (1-a x) \left(1-a^2 x^2\right)^{3/2}}+\frac{2}{21 a c^4 (1-a x)^2 \left(1-a^2 x^2\right)^{3/2}}+\frac{1}{9 a c^4 (1-a x)^3 \left(1-a^2 x^2\right)^{3/2}}",1,"(19 + 6*a*x - 66*a^2*x^2 + 56*a^3*x^3 + 24*a^4*x^4 - 48*a^5*x^5 + 16*a^6*x^6)/(63*a*c^4*(1 - a*x)^(9/2)*(1 + a*x)^(3/2))","A",1
1156,1,79,226,0.0521343,"\int e^{3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","-\frac{\sqrt{c-a^2 c x^2} \left(a x \left(12 a^4 x^4+45 a^3 x^3+80 a^2 x^2+120 a x+240\right)+240 \log (1-a x)\right)}{60 a^4 \sqrt{1-a^2 x^2}}","-\frac{2 x^2 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}-\frac{a x^5 \sqrt{c-a^2 c x^2}}{5 \sqrt{1-a^2 x^2}}-\frac{3 x^4 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-a^2 x^2}}-\frac{4 x^3 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^4 \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-a^2 x^2}}",1,"-1/60*(Sqrt[c - a^2*c*x^2]*(a*x*(240 + 120*a*x + 80*a^2*x^2 + 45*a^3*x^3 + 12*a^4*x^4) + 240*Log[1 - a*x]))/(a^4*Sqrt[1 - a^2*x^2])","A",1
1157,1,70,185,0.0412286,"\int e^{3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{c-a^2 c x^2} \left(-\frac{4 \log (1-a x)}{a^3}-\frac{4 x}{a^2}-\frac{a x^4}{4}-\frac{2 x^2}{a}-x^3\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 x^2 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}-\frac{a x^4 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-a^2 x^2}}-\frac{x^3 \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*((-4*x)/a^2 - (2*x^2)/a - x^3 - (a*x^4)/4 - (4*Log[1 - a*x])/a^3))/Sqrt[1 - a^2*x^2]","A",1
1158,1,64,150,0.0368582,"\int e^{3 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])*x*Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{c-a^2 c x^2} \left(-\frac{4 \log (1-a x)}{a^2}-\frac{a x^3}{3}-\frac{4 x}{a}-\frac{3 x^2}{2}\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^2 \sqrt{1-a^2 x^2}}-\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*((-4*x)/a - (3*x^2)/2 - (a*x^3)/3 - (4*Log[1 - a*x])/a^2))/Sqrt[1 - a^2*x^2]","A",1
1159,1,54,111,0.0221484,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{c-a^2 c x^2} \left(-\frac{a x^2}{2}-\frac{4 \log (1-a x)}{a}-3 x\right)}{\sqrt{1-a^2 x^2}}","-\frac{a x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}-\frac{3 x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-3*x - (a*x^2)/2 - (4*Log[1 - a*x])/a))/Sqrt[1 - a^2*x^2]","A",1
1160,1,46,104,0.029301,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x,x]","\frac{\sqrt{c-a^2 c x^2} (-a x-4 \log (1-a x)+\log (x))}{\sqrt{1-a^2 x^2}}","-\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-(a*x) + Log[x] - 4*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
1161,1,51,108,0.0318336,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^2,x]","\frac{\sqrt{c-a^2 c x^2} \left(3 a \log (x)-4 a \log (1-a x)-\frac{1}{x}\right)}{\sqrt{1-a^2 x^2}}","-\frac{\sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}+\frac{3 a \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 a \sqrt{c-a^2 c x^2} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-x^(-1) + 3*a*Log[x] - 4*a*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
1162,1,63,149,0.0454231,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^3,x]","\frac{\sqrt{c-a^2 c x^2} \left(4 a^2 \log (x)-4 a^2 \log (1-a x)-\frac{3 a}{x}-\frac{1}{2 x^2}\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 a \sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{2 x^2 \sqrt{1-a^2 x^2}}+\frac{4 a^2 \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 a^2 \sqrt{c-a^2 c x^2} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-1/2*1/x^2 - (3*a)/x + 4*a^2*Log[x] - 4*a^2*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
1163,1,73,188,0.0459016,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^4,x]","\frac{\sqrt{c-a^2 c x^2} \left(4 a^3 \log (x)-4 a^3 \log (1-a x)-\frac{4 a^2}{x}-\frac{3 a}{2 x^2}-\frac{1}{3 x^3}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 a^2 \sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}-\frac{3 a \sqrt{c-a^2 c x^2}}{2 x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{3 x^3 \sqrt{1-a^2 x^2}}+\frac{4 a^3 \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 a^3 \sqrt{c-a^2 c x^2} \log (1-a x)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-1/3*1/x^3 - (3*a)/(2*x^2) - (4*a^2)/x + 4*a^3*Log[x] - 4*a^3*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
1164,1,79,223,0.0531129,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Integrate[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^5,x]","\frac{\sqrt{c-a^2 c x^2} \left(4 a^4 \log (x)-4 a^4 \log (1-a x)-\frac{4 a^3}{x}-\frac{2 a^2}{x^2}-\frac{a}{x^3}-\frac{1}{4 x^4}\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4 \sqrt{1-a^2 x^2}}-\frac{a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-a^2 x^2}}+\frac{4 a^4 \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 a^4 \sqrt{c-a^2 c x^2} \log (1-a x)}{\sqrt{1-a^2 x^2}}-\frac{4 a^3 \sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-1/4*1/x^4 - a/x^3 - (2*a^2)/x^2 - (4*a^3)/x + 4*a^4*Log[x] - 4*a^4*Log[1 - a*x]))/Sqrt[1 - a^2*x^2]","A",1
1165,1,58,44,0.0300359,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2),x]","\frac{c \left(\frac{a^3 x^4}{4}+a^2 x^3+\frac{3 a x^2}{2}+x\right) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}","\frac{c (a x+1)^4 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-a^2 x^2}}",1,"(c*Sqrt[c - a^2*c*x^2]*(x + (3*a*x^2)/2 + a^2*x^3 + (a^3*x^4)/4))/Sqrt[1 - a^2*x^2]","A",0
1166,1,52,93,0.0407345,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2),x]","-\frac{c^2 (a x+1)^5 (5 a x-7) \sqrt{c-a^2 c x^2}}{30 a \sqrt{1-a^2 x^2}}","\frac{2 c^2 (a x+1)^5 \sqrt{c-a^2 c x^2}}{5 a \sqrt{1-a^2 x^2}}-\frac{c^2 (a x+1)^6 \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}",1,"-1/30*(c^2*(1 + a*x)^5*(-7 + 5*a*x)*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2])","A",1
1167,1,60,139,0.0491142,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2),x]","\frac{c^3 (a x+1)^6 \left(21 a^2 x^2-54 a x+37\right) \sqrt{c-a^2 c x^2}}{168 a \sqrt{1-a^2 x^2}}","\frac{c^3 (a x+1)^8 \sqrt{c-a^2 c x^2}}{8 a \sqrt{1-a^2 x^2}}-\frac{4 c^3 (a x+1)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}+\frac{2 c^3 (a x+1)^6 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}",1,"(c^3*(1 + a*x)^6*(37 - 54*a*x + 21*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(168*a*Sqrt[1 - a^2*x^2])","A",1
1168,1,68,185,0.0532201,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(9/2),x]","-\frac{c^4 (a x+1)^7 \left(21 a^3 x^3-77 a^2 x^2+98 a x-44\right) \sqrt{c-a^2 c x^2}}{210 a \sqrt{1-a^2 x^2}}","-\frac{c^4 (a x+1)^{10} \sqrt{c-a^2 c x^2}}{10 a \sqrt{1-a^2 x^2}}+\frac{2 c^4 (a x+1)^9 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}-\frac{3 c^4 (a x+1)^8 \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-a^2 x^2}}+\frac{8 c^4 (a x+1)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}",1,"-1/210*(c^4*(1 + a*x)^7*Sqrt[c - a^2*c*x^2]*(-44 + 98*a*x - 77*a^2*x^2 + 21*a^3*x^3))/(a*Sqrt[1 - a^2*x^2])","A",1
1169,1,51,83,0.0349488,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{2}{1-a x}+\log (1-a x)\right)}{a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2}}{a (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{a \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(2/(1 - a*x) + Log[1 - a*x]))/(a*Sqrt[c - a^2*c*x^2])","A",1
1170,1,53,47,0.0408685,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^(3/2),x]","-\frac{\sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}{2 a c^2 (a x-1)^3 (a x+1)}","\frac{\sqrt{1-a^2 x^2}}{2 a c (1-a x)^2 \sqrt{c-a^2 c x^2}}",1,"-1/2*(Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2])/(a*c^2*(-1 + a*x)^3*(1 + a*x))","A",1
1171,1,73,185,0.0542658,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} \left(-3 a^2 x^2+9 a x+3 (a x-1)^3 \tanh ^{-1}(a x)-10\right)}{24 a c^2 (a x-1)^3 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (1-a x) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (1-a x)^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{6 a c^2 (1-a x)^3 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-10 + 9*a*x - 3*a^2*x^2 + 3*(-1 + a*x)^3*ArcTanh[a*x]))/(24*a*c^2*(-1 + a*x)^3*Sqrt[c - a^2*c*x^2])","A",1
1172,1,101,278,0.0775874,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^(7/2),x]","\frac{\sqrt{1-a^2 x^2} \left(-15 a^4 x^4+45 a^3 x^3-35 a^2 x^2-15 a x+15 (a x-1)^4 (a x+1) \tanh ^{-1}(a x)+32\right)}{96 a c^3 (a x-1)^4 (a x+1) \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{8 a c^3 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{32 a c^3 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2}}{32 a c^3 (1-a x)^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{12 a c^3 (1-a x)^3 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{16 a c^3 (1-a x)^4 \sqrt{c-a^2 c x^2}}+\frac{5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{32 a c^3 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(32 - 15*a*x - 35*a^2*x^2 + 45*a^3*x^3 - 15*a^4*x^4 + 15*(-1 + a*x)^4*(1 + a*x)*ArcTanh[a*x]))/(96*a*c^3*(-1 + a*x)^4*(1 + a*x)*Sqrt[c - a^2*c*x^2])","A",1
1173,1,74,136,0.0502955,"\int e^{3 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(3*ArcTanh[a*x])*x^m*Sqrt[c - a^2*c*x^2],x]","-\frac{x^{m+1} \sqrt{c-a^2 c x^2} (-4 (m+2) \, _2F_1(1,m+1;m+2;a x)+m (a x+3)+a x+6)}{(m+1) (m+2) \sqrt{1-a^2 x^2}}","\frac{4 x^{m+1} \sqrt{c-a^2 c x^2} \, _2F_1(1,m+1;m+2;a x)}{(m+1) \sqrt{1-a^2 x^2}}-\frac{3 x^{m+1} \sqrt{c-a^2 c x^2}}{(m+1) \sqrt{1-a^2 x^2}}-\frac{a x^{m+2} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-a^2 x^2}}",1,"-((x^(1 + m)*Sqrt[c - a^2*c*x^2]*(6 + a*x + m*(3 + a*x) - 4*(2 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x]))/((1 + m)*(2 + m)*Sqrt[1 - a^2*x^2]))","A",1
1174,1,186,251,0.1681046,"\int e^{3 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^p,x]","x^{m+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{\, _2F_1\left(\frac{m+1}{2},\frac{3}{2}-p;\frac{m+3}{2};a^2 x^2\right)}{m+1}+a x \left(\frac{3 \, _2F_1\left(\frac{m+2}{2},\frac{3}{2}-p;\frac{m+4}{2};a^2 x^2\right)}{m+2}+a x \left(\frac{3 \, _2F_1\left(\frac{m+3}{2},\frac{3}{2}-p;\frac{m+5}{2};a^2 x^2\right)}{m+3}+\frac{a x \, _2F_1\left(\frac{m+4}{2},\frac{3}{2}-p;\frac{m+6}{2};a^2 x^2\right)}{m+4}\right)\right)\right)","\frac{(4 m+2 p+3) x^{m+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{m+1}{2},\frac{3}{2}-p;\frac{m+3}{2};a^2 x^2\right)}{(m+1) (m+2 p)}+\frac{a (4 m+6 p+5) x^{m+2} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{m+2}{2},\frac{3}{2}-p;\frac{m+4}{2};a^2 x^2\right)}{(m+2) (m+2 p+1)}-\frac{3 x^{m+1} \left(c-a^2 c x^2\right)^p}{\sqrt{1-a^2 x^2} (m+2 p)}-\frac{a x^{m+2} \left(c-a^2 c x^2\right)^p}{\sqrt{1-a^2 x^2} (m+2 p+1)}",1,"(x^(1 + m)*(c - a^2*c*x^2)^p*(Hypergeometric2F1[(1 + m)/2, 3/2 - p, (3 + m)/2, a^2*x^2]/(1 + m) + a*x*((3*Hypergeometric2F1[(2 + m)/2, 3/2 - p, (4 + m)/2, a^2*x^2])/(2 + m) + a*x*((3*Hypergeometric2F1[(3 + m)/2, 3/2 - p, (5 + m)/2, a^2*x^2])/(3 + m) + (a*x*Hypergeometric2F1[(4 + m)/2, 3/2 - p, (6 + m)/2, a^2*x^2])/(4 + m)))))/(1 - a^2*x^2)^p","A",0
1175,1,176,224,0.2049575,"\int e^{3 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^p,x]","\frac{\left(c-a^2 c x^2\right)^p \left(-\frac{105 \left(1-a^2 x^2\right)^{3/2}}{2 p+3}+\frac{245 \sqrt{1-a^2 x^2}}{2 p+1}+\frac{140}{(1-2 p) \sqrt{1-a^2 x^2}}+5 a^7 x^7 \left(1-a^2 x^2\right)^{-p} \, _2F_1\left(\frac{7}{2},\frac{3}{2}-p;\frac{9}{2};a^2 x^2\right)+21 a^5 x^5 \left(1-a^2 x^2\right)^{-p} \, _2F_1\left(\frac{5}{2},\frac{3}{2}-p;\frac{7}{2};a^2 x^2\right)\right)}{35 a^4}","\frac{a (6 p+17) x^5 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{5}{2},\frac{3}{2}-p;\frac{7}{2};a^2 x^2\right)}{10 (p+2)}-\frac{a x^5 \left(c-a^2 c x^2\right)^p}{2 (p+2) \sqrt{1-a^2 x^2}}-\frac{3 \left(1-a^2 x^2\right)^{3/2} \left(c-a^2 c x^2\right)^p}{a^4 (2 p+3)}+\frac{7 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^4 (2 p+1)}+\frac{4 \left(c-a^2 c x^2\right)^p}{a^4 (1-2 p) \sqrt{1-a^2 x^2}}",1,"((c - a^2*c*x^2)^p*(140/((1 - 2*p)*Sqrt[1 - a^2*x^2]) + (245*Sqrt[1 - a^2*x^2])/(1 + 2*p) - (105*(1 - a^2*x^2)^(3/2))/(3 + 2*p) + (21*a^5*x^5*Hypergeometric2F1[5/2, 3/2 - p, 7/2, a^2*x^2])/(1 - a^2*x^2)^p + (5*a^7*x^7*Hypergeometric2F1[7/2, 3/2 - p, 9/2, a^2*x^2])/(1 - a^2*x^2)^p))/(35*a^4)","A",0
1176,1,179,222,0.2398686,"\int e^{3 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^p,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{3}{5} a^2 x^5 \, _2F_1\left(\frac{5}{2},\frac{3}{2}-p;\frac{7}{2};a^2 x^2\right)+\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{2},\frac{3}{2}-p;\frac{5}{2};a^2 x^2\right)+\frac{\left(a^4 x^4-4 a^2 p^2 x^2 \left(a^2 x^2+3\right)-4 p \left(5 a^2 x^2+3\right)+13 a^2 x^2-26\right) \left(1-a^2 x^2\right)^{p-\frac{1}{2}}}{a^3 (2 p-1) (2 p+1) (2 p+3)}\right)","\frac{(2 p+11) x^3 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2},\frac{3}{2}-p;\frac{5}{2};a^2 x^2\right)}{6 (p+1)}-\frac{3 x^3 \left(c-a^2 c x^2\right)^p}{2 (p+1) \sqrt{1-a^2 x^2}}-\frac{\left(1-a^2 x^2\right)^{3/2} \left(c-a^2 c x^2\right)^p}{a^3 (2 p+3)}+\frac{5 \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^3 (2 p+1)}+\frac{4 \left(c-a^2 c x^2\right)^p}{a^3 (1-2 p) \sqrt{1-a^2 x^2}}",1,"((c - a^2*c*x^2)^p*(((1 - a^2*x^2)^(-1/2 + p)*(-26 + 13*a^2*x^2 + a^4*x^4 - 4*a^2*p^2*x^2*(3 + a^2*x^2) - 4*p*(3 + 5*a^2*x^2)))/(a^3*(-1 + 2*p)*(1 + 2*p)*(3 + 2*p)) + (x^3*Hypergeometric2F1[3/2, 3/2 - p, 5/2, a^2*x^2])/3 + (3*a^2*x^5*Hypergeometric2F1[5/2, 3/2 - p, 7/2, a^2*x^2])/5))/(1 - a^2*x^2)^p","A",0
1177,1,134,138,0.3823857,"\int e^{3 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*x*(c - a^2*c*x^2)^p,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(a x^3 \, _2F_1\left(\frac{3}{2},\frac{3}{2}-p;\frac{5}{2};a^2 x^2\right)+\frac{\left(\frac{3-3 a^2 x^2}{2 p+1}+\frac{4}{1-2 p}\right) \left(1-a^2 x^2\right)^{p-\frac{1}{2}}}{a^2}+\frac{1}{5} a^3 x^5 \, _2F_1\left(\frac{5}{2},\frac{3}{2}-p;\frac{7}{2};a^2 x^2\right)\right)","\frac{3\ 2^{p+\frac{3}{2}} (1-a x)^{p-\frac{1}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-\frac{3}{2},p-\frac{1}{2};p+\frac{1}{2};\frac{1}{2} (1-a x)\right)}{a^2 \left(-2 p^2-p+1\right)}-\frac{(a x+1)^3 \left(c-a^2 c x^2\right)^p}{2 a^2 (p+1) \sqrt{1-a^2 x^2}}",1,"((c - a^2*c*x^2)^p*(((1 - a^2*x^2)^(-1/2 + p)*(4/(1 - 2*p) + (3 - 3*a^2*x^2)/(1 + 2*p)))/a^2 + a*x^3*Hypergeometric2F1[3/2, 3/2 - p, 5/2, a^2*x^2] + (a^3*x^5*Hypergeometric2F1[5/2, 3/2 - p, 7/2, a^2*x^2])/5))/(1 - a^2*x^2)^p","A",0
1178,1,83,85,0.0318232,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","\frac{2^{p+\frac{5}{2}} (1-a x)^{p-\frac{1}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-\frac{3}{2},p-\frac{1}{2};p+\frac{1}{2};\frac{1}{2} (1-a x)\right)}{a-2 a p}","\frac{2^{p+\frac{5}{2}} (1-a x)^{p-\frac{1}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-\frac{3}{2},p-\frac{1}{2};p+\frac{1}{2};\frac{1}{2} (1-a x)\right)}{a (1-2 p)}",1,"(2^(5/2 + p)*(1 - a*x)^(-1/2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-3/2 - p, -1/2 + p, 1/2 + p, (1 - a*x)/2])/((a - 2*a*p)*(1 - a^2*x^2)^p)","A",1
1179,1,159,193,0.2248349,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p)/x,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(-\frac{\left(1-a^2 x^2\right)^{p-\frac{1}{2}} \, _2F_1\left(1,p-\frac{1}{2};p+\frac{1}{2};1-a^2 x^2\right)}{2 \left(p-\frac{1}{2}\right)}+3 a x \, _2F_1\left(\frac{1}{2},\frac{3}{2}-p;\frac{3}{2};a^2 x^2\right)+\frac{3 \left(1-a^2 x^2\right)^{p-\frac{1}{2}}}{1-2 p}+\frac{1}{3} a^3 x^3 \, _2F_1\left(\frac{3}{2},\frac{3}{2}-p;\frac{5}{2};a^2 x^2\right)\right)","\frac{a (6 p+1) x \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2},\frac{3}{2}-p;\frac{3}{2};a^2 x^2\right)}{2 p}-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{a x \left(c-a^2 c x^2\right)^p}{2 p \sqrt{1-a^2 x^2}}+\frac{4 \left(c-a^2 c x^2\right)^p}{(1-2 p) \sqrt{1-a^2 x^2}}",1,"((c - a^2*c*x^2)^p*((3*(1 - a^2*x^2)^(-1/2 + p))/(1 - 2*p) + 3*a*x*Hypergeometric2F1[1/2, 3/2 - p, 3/2, a^2*x^2] - ((1 - a^2*x^2)^(-1/2 + p)*Hypergeometric2F1[1, -1/2 + p, 1/2 + p, 1 - a^2*x^2])/(2*(-1/2 + p)) + (a^3*x^3*Hypergeometric2F1[3/2, 3/2 - p, 5/2, a^2*x^2])/3))/(1 - a^2*x^2)^p","A",0
1180,1,133,187,0.2568351,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^2} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p)/x^2,x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(a \left(\frac{\left(1-a^2 x^2\right)^{p-\frac{1}{2}} \left(3 \, _2F_1\left(1,p-\frac{1}{2};p+\frac{1}{2};1-a^2 x^2\right)+1\right)}{1-2 p}+3 a x \, _2F_1\left(\frac{1}{2},\frac{3}{2}-p;\frac{3}{2};a^2 x^2\right)\right)-\frac{\, _2F_1\left(-\frac{1}{2},\frac{3}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}\right)","a^2 (5-2 p) x \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2},\frac{3}{2}-p;\frac{3}{2};a^2 x^2\right)-\frac{3 a \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}+\frac{4 a \left(c-a^2 c x^2\right)^p}{(1-2 p) \sqrt{1-a^2 x^2}}-\frac{\left(c-a^2 c x^2\right)^p}{x \sqrt{1-a^2 x^2}}",1,"((c - a^2*c*x^2)^p*(-(Hypergeometric2F1[-1/2, 3/2 - p, 1/2, a^2*x^2]/x) + a*(3*a*x*Hypergeometric2F1[1/2, 3/2 - p, 3/2, a^2*x^2] + ((1 - a^2*x^2)^(-1/2 + p)*(1 + 3*Hypergeometric2F1[1, -1/2 + p, 1/2 + p, 1 - a^2*x^2]))/(1 - 2*p))))/(1 - a^2*x^2)^p","A",0
1181,1,154,194,0.2975137,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^3} \, dx","Integrate[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p)/x^3,x]","a \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(a \left(\frac{\left(1-a^2 x^2\right)^{p-\frac{1}{2}} \left(3 \, _2F_1\left(1,p-\frac{1}{2};p+\frac{1}{2};1-a^2 x^2\right)+\, _2F_1\left(2,p-\frac{1}{2};p+\frac{1}{2};1-a^2 x^2\right)\right)}{1-2 p}+a x \, _2F_1\left(\frac{1}{2},\frac{3}{2}-p;\frac{3}{2};a^2 x^2\right)\right)-\frac{3 \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}\right)","\frac{a^2 (9-2 p) \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p-\frac{1}{2};p+\frac{1}{2};1-a^2 x^2\right)}{2 (1-2 p) \sqrt{1-a^2 x^2}}-\frac{3 a \left(c-a^2 c x^2\right)^p}{x \sqrt{1-a^2 x^2}}-\frac{\left(c-a^2 c x^2\right)^p}{2 x^2 \sqrt{1-a^2 x^2}}+a^3 (7-6 p) x \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2},\frac{3}{2}-p;\frac{3}{2};a^2 x^2\right)",1,"(a*(c - a^2*c*x^2)^p*((-3*Hypergeometric2F1[-1/2, 3/2 - p, 1/2, a^2*x^2])/x + a*(a*x*Hypergeometric2F1[1/2, 3/2 - p, 3/2, a^2*x^2] + ((1 - a^2*x^2)^(-1/2 + p)*(3*Hypergeometric2F1[1, -1/2 + p, 1/2 + p, 1 - a^2*x^2] + Hypergeometric2F1[2, -1/2 + p, 1/2 + p, 1 - a^2*x^2]))/(1 - 2*p))))/(1 - a^2*x^2)^p","A",0
1182,1,39,66,0.0342577,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^5 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^5,x]","-\frac{c^5 (a x+1)^8 \left(15 a^3 x^3-54 a^2 x^2+67 a x-29\right)}{165 a}","-\frac{c^5 (a x+1)^{11}}{11 a}+\frac{3 c^5 (a x+1)^{10}}{5 a}-\frac{4 c^5 (a x+1)^9}{3 a}+\frac{c^5 (a x+1)^8}{a}",1,"-1/165*(c^5*(1 + a*x)^8*(-29 + 67*a*x - 54*a^2*x^2 + 15*a^3*x^3))/a","A",1
1183,1,31,52,0.026262,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^4,x]","\frac{c^4 (a x+1)^7 \left(14 a^2 x^2-35 a x+23\right)}{126 a}","\frac{c^4 (a x+1)^9}{9 a}-\frac{c^4 (a x+1)^8}{2 a}+\frac{4 c^4 (a x+1)^7}{7 a}",1,"(c^4*(1 + a*x)^7*(23 - 35*a*x + 14*a^2*x^2))/(126*a)","A",1
1184,1,23,35,0.0202839,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","-\frac{c^3 (a x+1)^6 (3 a x-4)}{21 a}","\frac{c^3 (a x+1)^6}{3 a}-\frac{c^3 (a x+1)^7}{7 a}",1,"-1/21*(c^3*(1 + a*x)^6*(-4 + 3*a*x))/a","A",1
1185,1,37,17,0.0186077,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","c^2 \left(\frac{a^4 x^5}{5}+a^3 x^4+2 a^2 x^3+2 a x^2+x\right)","\frac{c^2 (a x+1)^5}{5 a}",1,"c^2*(x + 2*a*x^2 + 2*a^2*x^3 + a^3*x^4 + (a^4*x^5)/5)","B",1
1186,1,36,36,0.0108222,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2),x]","-\frac{1}{3} a^2 c x^3-2 a c x^2-\frac{8 c \log (1-a x)}{a}-7 c x","-\frac{1}{3} a^2 c x^3-2 a c x^2-\frac{8 c \log (1-a x)}{a}-7 c x",1,"-7*c*x - 2*a*c*x^2 - (a^2*c*x^3)/3 - (8*c*Log[1 - a*x])/a","A",1
1187,1,25,13,0.0085675,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{(a x+1)^2}{4 a c (1-a x)^2}","\frac{x}{c (1-a x)^2}",1,"(1 + a*x)^2/(4*a*c*(1 - a*x)^2)","A",1
1188,1,17,18,0.0172319,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","-\frac{1}{3 a c^2 (a x-1)^3}","\frac{1}{3 a c^2 (1-a x)^3}",1,"-1/3*1/(a*c^2*(-1 + a*x)^3)","A",1
1189,1,52,87,0.036133,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","\frac{-3 a^3 x^3+12 a^2 x^2-19 a x+3 (a x-1)^4 \tanh ^{-1}(a x)+16}{48 a c^3 (a x-1)^4}","\frac{1}{16 a c^3 (1-a x)}+\frac{1}{16 a c^3 (1-a x)^2}+\frac{1}{12 a c^3 (1-a x)^3}+\frac{1}{8 a c^3 (1-a x)^4}+\frac{\tanh ^{-1}(a x)}{16 a c^3}",1,"(16 - 19*a*x + 12*a^2*x^2 - 3*a^3*x^3 + 3*(-1 + a*x)^4*ArcTanh[a*x])/(48*a*c^3*(-1 + a*x)^4)","A",1
1190,1,80,122,0.0565452,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","\frac{-15 a^5 x^5+60 a^4 x^4-80 a^3 x^3+20 a^2 x^2+47 a x+15 (a x-1)^5 (a x+1) \tanh ^{-1}(a x)-48}{160 a c^4 (a x-1)^5 (a x+1)}","\frac{5}{64 a c^4 (1-a x)}-\frac{1}{64 a c^4 (a x+1)}+\frac{1}{16 a c^4 (1-a x)^2}+\frac{1}{16 a c^4 (1-a x)^3}+\frac{1}{16 a c^4 (1-a x)^4}+\frac{1}{20 a c^4 (1-a x)^5}+\frac{3 \tanh ^{-1}(a x)}{32 a c^4}",1,"(-48 + 47*a*x + 20*a^2*x^2 - 80*a^3*x^3 + 60*a^4*x^4 - 15*a^5*x^5 + 15*(-1 + a*x)^5*(1 + a*x)*ArcTanh[a*x])/(160*a*c^4*(-1 + a*x)^5*(1 + a*x))","A",1
1191,1,72,63,0.0205094,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","-\frac{2^{p+2} (1-a x)^{p-1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-2,p-1;p;\frac{1}{2} (1-a x)\right)}{a (p-1)}","\frac{c 2^{p+2} (a x+1)^{1-p} \left(c-a^2 c x^2\right)^{p-1} \, _2F_1\left(-p-2,p-1;p;\frac{1}{2} (1-a x)\right)}{a (1-p)}",1,"-((2^(2 + p)*(1 - a*x)^(-1 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-2 - p, -1 + p, p, (1 - a*x)/2])/(a*(-1 + p)*(1 - a^2*x^2)^p))","A",1
1192,1,107,127,0.1500923,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[(c - a^2*c*x^2)^4/E^ArcTanh[a*x],x]","\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(128 a^8 x^8-144 a^7 x^7-512 a^6 x^6+600 a^5 x^5+768 a^4 x^4-978 a^3 x^3-512 a^2 x^2+837 a x+128\right)-630 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{1152 a}","\frac{c^4 \left(1-a^2 x^2\right)^{9/2}}{9 a}+\frac{1}{8} c^4 x \left(1-a^2 x^2\right)^{7/2}+\frac{7}{48} c^4 x \left(1-a^2 x^2\right)^{5/2}+\frac{35}{192} c^4 x \left(1-a^2 x^2\right)^{3/2}+\frac{35}{128} c^4 x \sqrt{1-a^2 x^2}+\frac{35 c^4 \sin ^{-1}(a x)}{128 a}",1,"(c^4*(Sqrt[1 - a^2*x^2]*(128 + 837*a*x - 512*a^2*x^2 - 978*a^3*x^3 + 768*a^4*x^4 + 600*a^5*x^5 - 512*a^6*x^6 - 144*a^7*x^7 + 128*a^8*x^8) - 630*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(1152*a)","A",0
1193,1,91,105,0.1252509,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[(c - a^2*c*x^2)^3/E^ArcTanh[a*x],x]","-\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(48 a^6 x^6-56 a^5 x^5-144 a^4 x^4+182 a^3 x^3+144 a^2 x^2-231 a x-48\right)+210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{336 a}","\frac{c^3 \left(1-a^2 x^2\right)^{7/2}}{7 a}+\frac{1}{6} c^3 x \left(1-a^2 x^2\right)^{5/2}+\frac{5}{24} c^3 x \left(1-a^2 x^2\right)^{3/2}+\frac{5}{16} c^3 x \sqrt{1-a^2 x^2}+\frac{5 c^3 \sin ^{-1}(a x)}{16 a}",1,"-1/336*(c^3*(Sqrt[1 - a^2*x^2]*(-48 - 231*a*x + 144*a^2*x^2 + 182*a^3*x^3 - 144*a^4*x^4 - 56*a^5*x^5 + 48*a^6*x^6) + 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
1194,1,75,83,0.0989096,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[(c - a^2*c*x^2)^2/E^ArcTanh[a*x],x]","\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(8 a^4 x^4-10 a^3 x^3-16 a^2 x^2+25 a x+8\right)-30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{40 a}","\frac{c^2 \left(1-a^2 x^2\right)^{5/2}}{5 a}+\frac{1}{4} c^2 x \left(1-a^2 x^2\right)^{3/2}+\frac{3}{8} c^2 x \sqrt{1-a^2 x^2}+\frac{3 c^2 \sin ^{-1}(a x)}{8 a}",1,"(c^2*(Sqrt[1 - a^2*x^2]*(8 + 25*a*x - 16*a^2*x^2 - 10*a^3*x^3 + 8*a^4*x^4) - 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(40*a)","A",0
1195,1,57,55,0.0883773,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[(c - a^2*c*x^2)/E^ArcTanh[a*x],x]","\frac{c \left(\left(-2 a^2 x^2+3 a x+2\right) \sqrt{1-a^2 x^2}-6 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","\frac{c \left(1-a^2 x^2\right)^{3/2}}{3 a}+\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}",1,"(c*((2 + 3*a*x - 2*a^2*x^2)*Sqrt[1 - a^2*x^2] - 6*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(6*a)","A",0
1196,1,27,16,0.0104596,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)),x]","-\frac{\sqrt{1-a x}}{a c \sqrt{a x+1}}","-\frac{e^{-\tanh ^{-1}(a x)}}{a c}",1,"-(Sqrt[1 - a*x]/(a*c*Sqrt[1 + a*x]))","A",0
1197,1,43,53,0.0177386,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^2),x]","\frac{2 a^2 x^2+2 a x-1}{3 a c^2 \sqrt{1-a x} (a x+1)^{3/2}}","\frac{2 x}{3 c^2 \sqrt{1-a^2 x^2}}-\frac{1-a x}{3 a c^2 \left(1-a^2 x^2\right)^{3/2}}",1,"(-1 + 2*a*x + 2*a^2*x^2)/(3*a*c^2*Sqrt[1 - a*x]*(1 + a*x)^(3/2))","A",1
1198,1,59,75,0.0283465,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^3),x]","-\frac{8 a^4 x^4+8 a^3 x^3-12 a^2 x^2-12 a x+3}{15 a c^3 (1-a x)^{3/2} (a x+1)^{5/2}}","\frac{8 x}{15 c^3 \sqrt{1-a^2 x^2}}+\frac{4 x}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\frac{1-a x}{5 a c^3 \left(1-a^2 x^2\right)^{5/2}}",1,"-1/15*(3 - 12*a*x - 12*a^2*x^2 + 8*a^3*x^3 + 8*a^4*x^4)/(a*c^3*(1 - a*x)^(3/2)*(1 + a*x)^(5/2))","A",1
1199,1,75,97,0.0351004,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^4),x]","\frac{16 a^6 x^6+16 a^5 x^5-40 a^4 x^4-40 a^3 x^3+30 a^2 x^2+30 a x-5}{35 a c^4 (1-a x)^{5/2} (a x+1)^{7/2}}","\frac{16 x}{35 c^4 \sqrt{1-a^2 x^2}}+\frac{8 x}{35 c^4 \left(1-a^2 x^2\right)^{3/2}}+\frac{6 x}{35 c^4 \left(1-a^2 x^2\right)^{5/2}}-\frac{1-a x}{7 a c^4 \left(1-a^2 x^2\right)^{7/2}}",1,"(-5 + 30*a*x + 30*a^2*x^2 - 40*a^3*x^3 - 40*a^4*x^4 + 16*a^5*x^5 + 16*a^6*x^6)/(35*a*c^4*(1 - a*x)^(5/2)*(1 + a*x)^(7/2))","A",0
1200,1,91,119,0.0412609,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^5} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^5),x]","-\frac{128 a^8 x^8+128 a^7 x^7-448 a^6 x^6-448 a^5 x^5+560 a^4 x^4+560 a^3 x^3-280 a^2 x^2-280 a x+35}{315 a c^5 (1-a x)^{7/2} (a x+1)^{9/2}}","\frac{128 x}{315 c^5 \sqrt{1-a^2 x^2}}+\frac{64 x}{315 c^5 \left(1-a^2 x^2\right)^{3/2}}+\frac{16 x}{105 c^5 \left(1-a^2 x^2\right)^{5/2}}+\frac{8 x}{63 c^5 \left(1-a^2 x^2\right)^{7/2}}-\frac{1-a x}{9 a c^5 \left(1-a^2 x^2\right)^{9/2}}",1,"-1/315*(35 - 280*a*x - 280*a^2*x^2 + 560*a^3*x^3 + 560*a^4*x^4 - 448*a^5*x^5 - 448*a^6*x^6 + 128*a^7*x^7 + 128*a^8*x^8)/(a*c^5*(1 - a*x)^(7/2)*(1 + a*x)^(9/2))","A",0
1201,1,50,83,0.0583186,"\int e^{-\tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^m*Sqrt[c - a^2*c*x^2])/E^ArcTanh[a*x],x]","\frac{x^{m+1} \sqrt{c-a^2 c x^2} \left(\frac{1}{m+1}-\frac{a x}{m+2}\right)}{\sqrt{1-a^2 x^2}}","\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+1) \sqrt{1-a^2 x^2}}-\frac{a x^{m+2} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-a^2 x^2}}",1,"(x^(1 + m)*((1 + m)^(-1) - (a*x)/(2 + m))*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]","A",1
1202,1,42,74,0.0291594,"\int e^{-\tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^2*Sqrt[c - a^2*c*x^2])/E^ArcTanh[a*x],x]","-\frac{x^3 (3 a x-4) \sqrt{c-a^2 c x^2}}{12 \sqrt{1-a^2 x^2}}","\frac{x^3 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-a^2 x^2}}-\frac{a x^4 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-a^2 x^2}}",1,"-1/12*(x^3*(-4 + 3*a*x)*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]","A",1
1203,1,42,74,0.0279785,"\int e^{-\tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[(x*Sqrt[c - a^2*c*x^2])/E^ArcTanh[a*x],x]","-\frac{x^2 (2 a x-3) \sqrt{c-a^2 c x^2}}{6 \sqrt{1-a^2 x^2}}","\frac{x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}-\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-a^2 x^2}}",1,"-1/6*(x^2*(-3 + 2*a*x)*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]","A",1
1204,1,40,69,0.0202972,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/E^ArcTanh[a*x],x]","\frac{\left(x-\frac{a x^2}{2}\right) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}","\frac{x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{a x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}",1,"((x - (a*x^2)/2)*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]","A",1
1205,1,37,66,0.0271666,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^ArcTanh[a*x]*x),x]","\frac{\sqrt{c-a^2 c x^2} (\log (x)-a x)}{\sqrt{1-a^2 x^2}}","\frac{\log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-(a*x) + Log[x]))/Sqrt[1 - a^2*x^2]","A",1
1206,1,41,69,0.0297847,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^ArcTanh[a*x]*x^2),x]","\frac{\sqrt{c-a^2 c x^2} \left(-a \log (x)-\frac{1}{x}\right)}{\sqrt{1-a^2 x^2}}","-\frac{\sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}-\frac{a \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-x^(-1) - a*Log[x]))/Sqrt[1 - a^2*x^2]","A",1
1207,1,57,91,0.0363713,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[(c - a^2*c*x^2)^(3/2)/E^ArcTanh[a*x],x]","\frac{c x \left(3 a^3 x^3-4 a^2 x^2-6 a x+12\right) \sqrt{c-a^2 c x^2}}{12 \sqrt{1-a^2 x^2}}","\frac{c (1-a x)^4 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-a^2 x^2}}-\frac{2 c (1-a x)^3 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}",1,"(c*x*Sqrt[c - a^2*c*x^2]*(12 - 6*a*x - 4*a^2*x^2 + 3*a^3*x^3))/(12*Sqrt[1 - a^2*x^2])","A",0
1208,1,60,140,0.0518209,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[(c - a^2*c*x^2)^(5/2)/E^ArcTanh[a*x],x]","-\frac{c^2 (a x-1)^4 \left(5 a^2 x^2+14 a x+11\right) \sqrt{c-a^2 c x^2}}{30 a \sqrt{1-a^2 x^2}}","-\frac{c^2 (1-a x)^6 \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}+\frac{4 c^2 (1-a x)^5 \sqrt{c-a^2 c x^2}}{5 a \sqrt{1-a^2 x^2}}-\frac{c^2 (1-a x)^4 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}",1,"-1/30*(c^2*(-1 + a*x)^4*(11 + 14*a*x + 5*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2])","A",1
1209,1,68,187,0.071885,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Integrate[(c - a^2*c*x^2)^(7/2)/E^ArcTanh[a*x],x]","\frac{c^3 (a x-1)^5 \left(35 a^3 x^3+135 a^2 x^2+185 a x+93\right) \sqrt{c-a^2 c x^2}}{280 a \sqrt{1-a^2 x^2}}","\frac{c^3 (1-a x)^8 \sqrt{c-a^2 c x^2}}{8 a \sqrt{1-a^2 x^2}}-\frac{6 c^3 (1-a x)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}+\frac{2 c^3 (1-a x)^6 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}-\frac{8 c^3 (1-a x)^5 \sqrt{c-a^2 c x^2}}{5 a \sqrt{1-a^2 x^2}}",1,"(c^3*(-1 + a*x)^5*Sqrt[c - a^2*c*x^2]*(93 + 185*a*x + 135*a^2*x^2 + 35*a^3*x^3))/(280*a*Sqrt[1 - a^2*x^2])","A",1
1210,1,76,234,0.0834945,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Integrate[(c - a^2*c*x^2)^(9/2)/E^ArcTanh[a*x],x]","-\frac{c^4 (a x-1)^6 \left(63 a^4 x^4+308 a^3 x^3+588 a^2 x^2+528 a x+193\right) \sqrt{c-a^2 c x^2}}{630 a \sqrt{1-a^2 x^2}}","-\frac{c^4 (1-a x)^{10} \sqrt{c-a^2 c x^2}}{10 a \sqrt{1-a^2 x^2}}+\frac{8 c^4 (1-a x)^9 \sqrt{c-a^2 c x^2}}{9 a \sqrt{1-a^2 x^2}}-\frac{3 c^4 (1-a x)^8 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}+\frac{32 c^4 (1-a x)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}-\frac{8 c^4 (1-a x)^6 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}",1,"-1/630*(c^4*(-1 + a*x)^6*Sqrt[c - a^2*c*x^2]*(193 + 528*a*x + 588*a^2*x^2 + 308*a^3*x^3 + 63*a^4*x^4))/(a*Sqrt[1 - a^2*x^2])","A",1
1211,1,39,39,0.0232859,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{a \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{a \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(a*Sqrt[c - a^2*c*x^2])","A",1
1212,1,59,90,0.0587417,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{\tanh ^{-1}(a x)}{2 a}-\frac{1}{2 a (a x+1)}\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{2 a c \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{2 a c (a x+1) \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-1/2*1/(a*(1 + a*x)) + ArcTanh[a*x]/(2*a)))/(c*Sqrt[c - a^2*c*x^2])","A",1
1213,1,83,183,0.0843126,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(-3 a^2 x^2-3 a x+3 (a x-1) (a x+1)^2 \tanh ^{-1}(a x)+2\right)}{8 a (a x-1) (a c x+c)^2 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{4 a c^2 (a x+1) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (a x+1)^2 \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(2 - 3*a*x - 3*a^2*x^2 + 3*(-1 + a*x)*(1 + a*x)^2*ArcTanh[a*x]))/(8*a*(-1 + a*x)*(c + a*c*x)^2*Sqrt[c - a^2*c*x^2])","A",1
1214,1,101,276,0.1207837,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(7/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(-15 a^4 x^4-15 a^3 x^3+25 a^2 x^2+25 a x+15 (a x-1)^2 (a x+1)^3 \tanh ^{-1}(a x)-8\right)}{48 a (a x-1)^2 (a c x+c)^3 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{8 a c^3 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{1-a^2 x^2}}{16 a c^3 (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2}}{32 a c^3 (1-a x)^2 \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{1-a^2 x^2}}{32 a c^3 (a x+1)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{24 a c^3 (a x+1)^3 \sqrt{c-a^2 c x^2}}+\frac{5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{16 a c^3 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-8 + 25*a*x + 25*a^2*x^2 - 15*a^3*x^3 - 15*a^4*x^4 + 15*(-1 + a*x)^2*(1 + a*x)^3*ArcTanh[a*x]))/(48*a*(-1 + a*x)^2*(c + a*c*x)^3*Sqrt[c - a^2*c*x^2])","A",1
1215,1,115,137,0.0608173,"\int e^{-\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Integrate[(x^m*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{x^{m+1} \, _2F_1\left(\frac{m+1}{2},\frac{1}{2}-p;\frac{m+1}{2}+1;a^2 x^2\right)}{m+1}-\frac{a x^{m+2} \, _2F_1\left(\frac{m+2}{2},\frac{1}{2}-p;\frac{m+2}{2}+1;a^2 x^2\right)}{m+2}\right)","\frac{x^{m+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{m+1}{2},\frac{1}{2}-p;\frac{m+3}{2};a^2 x^2\right)}{m+1}-\frac{a x^{m+2} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{m+2}{2},\frac{1}{2}-p;\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"((c - a^2*c*x^2)^p*((x^(1 + m)*Hypergeometric2F1[(1 + m)/2, 1/2 - p, 1 + (1 + m)/2, a^2*x^2])/(1 + m) - (a*x^(2 + m)*Hypergeometric2F1[(2 + m)/2, 1/2 - p, 1 + (2 + m)/2, a^2*x^2])/(2 + m)))/(1 - a^2*x^2)^p","A",1
1216,1,77,85,0.0841007,"\int e^{-\tanh ^{-1}(a x)} x^3 \left(1-a^2 x^2\right)^p \, dx","Integrate[(x^3*(1 - a^2*x^2)^p)/E^ArcTanh[a*x],x]","-\frac{1}{5} a x^5 \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)-\frac{\left(a^2 (2 p+1) x^2+2\right) \left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^4 \left(4 p^2+8 p+3\right)}","-\frac{1}{5} a x^5 \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^4 (2 p+1)}+\frac{\left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^4 (2 p+3)}",1,"-(((1 - a^2*x^2)^(1/2 + p)*(2 + a^2*(1 + 2*p)*x^2))/(a^4*(3 + 8*p + 4*p^2))) - (a*x^5*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/5","A",1
1217,1,75,84,0.07436,"\int e^{-\tanh ^{-1}(a x)} x^2 \left(1-a^2 x^2\right)^p \, dx","Integrate[(x^2*(1 - a^2*x^2)^p)/E^ArcTanh[a*x],x]","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)+\frac{\left(a^2 (2 p+1) x^2+2\right) \left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^3 \left(4 p^2+8 p+3\right)}","\frac{1}{3} x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)+\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^3 (2 p+1)}-\frac{\left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^3 (2 p+3)}",1,"((1 - a^2*x^2)^(1/2 + p)*(2 + a^2*(1 + 2*p)*x^2))/(a^3*(3 + 8*p + 4*p^2)) + (x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3","A",1
1218,1,60,58,0.0296187,"\int e^{-\tanh ^{-1}(a x)} x \left(1-a^2 x^2\right)^p \, dx","Integrate[(x*(1 - a^2*x^2)^p)/E^ArcTanh[a*x],x]","-\frac{1}{3} a x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{2 a^2 \left(p+\frac{1}{2}\right)}","-\frac{1}{3} a x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^2 (2 p+1)}",1,"-1/2*(1 - a^2*x^2)^(1/2 + p)/(a^2*(1/2 + p)) - (a*x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3","A",1
1219,1,56,59,0.0241649,"\int e^{-\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p \, dx","Integrate[(1 - a^2*x^2)^p/E^ArcTanh[a*x],x]","\frac{(a x-1) (2-2 a x)^{p+\frac{1}{2}} \, _2F_1\left(\frac{1}{2}-p,p+\frac{3}{2};p+\frac{5}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+3)}","-\frac{2^{p+\frac{1}{2}} (1-a x)^{p+\frac{3}{2}} \, _2F_1\left(\frac{1}{2}-p,p+\frac{3}{2};p+\frac{5}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+3)}",1,"((2 - 2*a*x)^(1/2 + p)*(-1 + a*x)*Hypergeometric2F1[1/2 - p, 3/2 + p, 5/2 + p, (1 - a*x)/2])/(a*(3 + 2*p))","A",1
1220,1,75,73,0.034463,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x} \, dx","Integrate[(1 - a^2*x^2)^p/(E^ArcTanh[a*x]*x),x]","-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}-a x \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)","-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-a x \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)",1,"-(a*x*Hypergeometric2F1[1/2, 1/2 - p, 3/2, a^2*x^2]) - ((1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))","A",1
1221,1,74,74,0.0346824,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x^2} \, dx","Integrate[(1 - a^2*x^2)^p/(E^ArcTanh[a*x]*x^2),x]","\frac{a \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{\, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}","\frac{a \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{\, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}",1,"-(Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2]/x) + (a*(1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",1
1222,1,119,134,0.0762128,"\int e^{-\tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^p \, dx","Integrate[(x^3*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{1}{2} \left(\frac{2 \left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^4 (2 p+3)}-\frac{2 \left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{a^4 (2 p+1)}\right)-\frac{1}{5} a x^5 \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)\right)","-\frac{1}{5} a x^5 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{5}{2},\frac{1}{2}-p;\frac{7}{2};a^2 x^2\right)+\frac{\left(1-a^2 x^2\right)^{3/2} \left(c-a^2 c x^2\right)^p}{a^4 (2 p+3)}-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^4 (2 p+1)}",1,"((c - a^2*c*x^2)^p*(((-2*(1 - a^2*x^2)^(1/2 + p))/(a^4*(1 + 2*p)) + (2*(1 - a^2*x^2)^(3/2 + p))/(a^4*(3 + 2*p)))/2 - (a*x^5*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/5))/(1 - a^2*x^2)^p","A",1
1223,1,102,133,0.0963301,"\int e^{-\tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^p \, dx","Integrate[(x^2*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","\frac{1}{3} \left(c-a^2 c x^2\right)^p \left(x^3 \left(1-a^2 x^2\right)^{-p} \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)+\frac{3 \sqrt{1-a^2 x^2} \left(a^2 (2 p+1) x^2+2\right)}{a^3 \left(4 p^2+8 p+3\right)}\right)","\frac{1}{3} x^3 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{3/2} \left(c-a^2 c x^2\right)^p}{a^3 (2 p+3)}+\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^3 (2 p+1)}",1,"((c - a^2*c*x^2)^p*((3*Sqrt[1 - a^2*x^2]*(2 + a^2*(1 + 2*p)*x^2))/(a^3*(3 + 8*p + 4*p^2)) + (x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/(1 - a^2*x^2)^p))/3","A",1
1224,1,88,96,0.0367175,"\int e^{-\tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Integrate[(x*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(-\frac{1}{3} a x^3 \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}}}{2 a^2 \left(p+\frac{1}{2}\right)}\right)","-\frac{1}{3} a x^3 \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2},\frac{1}{2}-p;\frac{5}{2};a^2 x^2\right)-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p}{a^2 (2 p+1)}",1,"((c - a^2*c*x^2)^p*(-1/2*(1 - a^2*x^2)^(1/2 + p)/(a^2*(1/2 + p)) - (a*x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3))/(1 - a^2*x^2)^p","A",1
1225,1,83,86,0.0355804,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[(c - a^2*c*x^2)^p/E^ArcTanh[a*x],x]","\frac{(a x-1) (2-2 a x)^{p+\frac{1}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2}-p,p+\frac{3}{2};p+\frac{5}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+3)}","-\frac{2^{p+\frac{1}{2}} (1-a x)^{p+\frac{3}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2}-p,p+\frac{3}{2};p+\frac{5}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+3)}",1,"((2 - 2*a*x)^(1/2 + p)*(-1 + a*x)*(c - a^2*c*x^2)^p*Hypergeometric2F1[1/2 - p, 3/2 + p, 5/2 + p, (1 - a*x)/2])/(a*(3 + 2*p)*(1 - a^2*x^2)^p)","A",1
1226,1,103,111,0.0380058,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x} \, dx","Integrate[(c - a^2*c*x^2)^p/(E^ArcTanh[a*x]*x),x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(-\frac{\left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 \left(p+\frac{1}{2}\right)}-a x \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)\right)","-a x \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{1}{2},\frac{1}{2}-p;\frac{3}{2};a^2 x^2\right)-\frac{\sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}",1,"((c - a^2*c*x^2)^p*(-(a*x*Hypergeometric2F1[1/2, 1/2 - p, 3/2, a^2*x^2]) - ((1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(2*(1/2 + p))))/(1 - a^2*x^2)^p","A",1
1227,1,102,112,0.0395469,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^2} \, dx","Integrate[(c - a^2*c*x^2)^p/(E^ArcTanh[a*x]*x^2),x]","\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{a \left(1-a^2 x^2\right)^{p+\frac{1}{2}} \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{\, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}\right)","\frac{a \sqrt{1-a^2 x^2} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1,p+\frac{1}{2};p+\frac{3}{2};1-a^2 x^2\right)}{2 p+1}-\frac{\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-p;\frac{1}{2};a^2 x^2\right)}{x}",1,"((c - a^2*c*x^2)^p*(-(Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2]/x) + (a*(1 - a^2*x^2)^(1/2 + p)*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)))/(1 - a^2*x^2)^p","A",1
1228,1,39,73,0.0303664,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[(c - a^2*c*x^2)^4/E^(2*ArcTanh[a*x]),x]","-\frac{c^4 (a x-1)^6 \left(28 a^3 x^3+105 a^2 x^2+138 a x+65\right)}{252 a}","\frac{c^4 (1-a x)^9}{9 a}-\frac{3 c^4 (1-a x)^8}{4 a}+\frac{12 c^4 (1-a x)^7}{7 a}-\frac{4 c^4 (1-a x)^6}{3 a}",1,"-1/252*(c^4*(-1 + a*x)^6*(65 + 138*a*x + 105*a^2*x^2 + 28*a^3*x^3))/a","A",1
1229,1,31,55,0.0256195,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[(c - a^2*c*x^2)^3/E^(2*ArcTanh[a*x]),x]","\frac{c^3 (a x-1)^5 \left(15 a^2 x^2+40 a x+29\right)}{105 a}","-\frac{c^3 (1-a x)^7}{7 a}+\frac{2 c^3 (1-a x)^6}{3 a}-\frac{4 c^3 (1-a x)^5}{5 a}",1,"(c^3*(-1 + a*x)^5*(29 + 40*a*x + 15*a^2*x^2))/(105*a)","A",1
1230,1,32,37,0.016945,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[(c - a^2*c*x^2)^2/E^(2*ArcTanh[a*x]),x]","c^2 \left(-\frac{1}{5} a^4 x^5+\frac{a^3 x^4}{2}-a x^2+x\right)","\frac{c^2 (1-a x)^5}{5 a}-\frac{c^2 (1-a x)^4}{2 a}",1,"c^2*(x - a*x^2 + (a^3*x^4)/2 - (a^4*x^5)/5)","A",1
1231,1,20,16,0.0130506,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[(c - a^2*c*x^2)/E^(2*ArcTanh[a*x]),x]","c \left(\frac{a^2 x^3}{3}-a x^2+x\right)","-\frac{c (1-a x)^3}{3 a}",1,"c*(x - a*x^2 + (a^2*x^3)/3)","A",1
1232,1,18,15,0.0152496,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)),x]","-\frac{e^{-2 \tanh ^{-1}(a x)}}{2 a c}","-\frac{1}{a c (a x+1)}",1,"-1/2*1/(a*c*E^(2*ArcTanh[a*x]))","C",1
1233,1,33,49,0.0265258,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2),x]","\frac{-a x+(a x+1)^2 \tanh ^{-1}(a x)-2}{4 a (a c x+c)^2}","-\frac{1}{4 a c^2 (a x+1)}-\frac{1}{4 a c^2 (a x+1)^2}+\frac{\tanh ^{-1}(a x)}{4 a c^2}",1,"(-2 - a*x + (1 + a*x)^2*ArcTanh[a*x])/(4*a*(c + a*c*x)^2)","A",1
1234,1,61,84,0.046615,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3),x]","-\frac{3 a^3 x^3+6 a^2 x^2+a x-3 (a x-1) (a x+1)^3 \tanh ^{-1}(a x)-4}{12 a (a x-1) (a c x+c)^3}","\frac{1}{16 a c^3 (1-a x)}-\frac{3}{16 a c^3 (a x+1)}-\frac{1}{8 a c^3 (a x+1)^2}-\frac{1}{12 a c^3 (a x+1)^3}+\frac{\tanh ^{-1}(a x)}{4 a c^3}",1,"-1/12*(-4 + a*x + 6*a^2*x^2 + 3*a^3*x^3 - 3*(-1 + a*x)*(1 + a*x)^3*ArcTanh[a*x])/(a*(-1 + a*x)*(c + a*c*x)^3)","A",1
1235,1,80,119,0.0662384,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^4),x]","\frac{-15 a^5 x^5-30 a^4 x^4+10 a^3 x^3+50 a^2 x^2+17 a x+15 (a x-1)^2 (a x+1)^4 \tanh ^{-1}(a x)-16}{64 a (a x-1)^2 (a c x+c)^4}","\frac{5}{64 a c^4 (1-a x)}-\frac{5}{32 a c^4 (a x+1)}+\frac{1}{64 a c^4 (1-a x)^2}-\frac{3}{32 a c^4 (a x+1)^2}-\frac{1}{16 a c^4 (a x+1)^3}-\frac{1}{32 a c^4 (a x+1)^4}+\frac{15 \tanh ^{-1}(a x)}{64 a c^4}",1,"(-16 + 17*a*x + 50*a^2*x^2 + 10*a^3*x^3 - 30*a^4*x^4 - 15*a^5*x^5 + 15*(-1 + a*x)^2*(1 + a*x)^4*ArcTanh[a*x])/(64*a*(-1 + a*x)^2*(c + a*c*x)^4)","A",1
1236,1,96,137,0.1535662,"\int e^{-2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^3*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","\frac{15 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\left(-4 a^4 x^4+10 a^3 x^3-12 a^2 x^2+15 a x-24\right) \sqrt{c-a^2 c x^2}}{20 a^4}","-\frac{3 x^2 \sqrt{c-a^2 c x^2}}{5 a^2}-\frac{1}{5} x^4 \sqrt{c-a^2 c x^2}+\frac{x^3 \sqrt{c-a^2 c x^2}}{2 a}-\frac{3 (8-5 a x) \sqrt{c-a^2 c x^2}}{20 a^4}-\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{4 a^4}",1,"(Sqrt[c - a^2*c*x^2]*(-24 + 15*a*x - 12*a^2*x^2 + 10*a^3*x^3 - 4*a^4*x^4) + 15*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(20*a^4)","A",1
1237,1,88,112,0.1112416,"\int e^{-2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^2*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","\frac{\left(-6 a^3 x^3+16 a^2 x^2-21 a x+32\right) \sqrt{c-a^2 c x^2}-21 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)}{24 a^3}","\frac{2 x^2 \sqrt{c-a^2 c x^2}}{3 a}-\frac{1}{4} x^3 \sqrt{c-a^2 c x^2}+\frac{(32-21 a x) \sqrt{c-a^2 c x^2}}{24 a^3}+\frac{7 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a^3}",1,"(Sqrt[c - a^2*c*x^2]*(32 - 21*a*x + 16*a^2*x^2 - 6*a^3*x^3) - 21*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(24*a^3)","A",1
1238,1,80,85,0.0919577,"\int e^{-2 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[(x*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-\left(a^2 x^2-3 a x+5\right) \sqrt{c-a^2 c x^2}}{3 a^2}","-\frac{1}{3} x^2 \sqrt{c-a^2 c x^2}-\frac{(5-3 a x) \sqrt{c-a^2 c x^2}}{3 a^2}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a^2}",1,"(-((5 - 3*a*x + a^2*x^2)*Sqrt[c - a^2*c*x^2]) + 3*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))])/(3*a^2)","A",1
1239,1,99,87,0.0584493,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/E^(2*ArcTanh[a*x]),x]","\frac{\sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(a^2 x^2-5 a x+4\right)-6 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{2 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{(1-a x) \sqrt{c-a^2 c x^2}}{2 a}+\frac{3 \sqrt{c-a^2 c x^2}}{2 a}+\frac{3 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{2 a}",1,"(Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(4 - 5*a*x + a^2*x^2) - 6*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(2*a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1240,1,99,78,0.1035265,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x),x]","-\sqrt{c-a^2 c x^2}-\sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+2 \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)+\sqrt{c} \log (x)","-\sqrt{c-a^2 c x^2}-2 \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)-\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-Sqrt[c - a^2*c*x^2] + 2*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] + Sqrt[c]*Log[x] - Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1241,1,106,82,0.1083831,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^2),x]","-\frac{\sqrt{c-a^2 c x^2}}{x}+2 a \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)-a \sqrt{c} \tan ^{-1}\left(\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{c} \left(a^2 x^2-1\right)}\right)-2 a \sqrt{c} \log (x)","-\frac{\sqrt{c-a^2 c x^2}}{x}+a \sqrt{c} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)+2 a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-(Sqrt[c - a^2*c*x^2]/x) - a*Sqrt[c]*ArcTan[(a*x*Sqrt[c - a^2*c*x^2])/(Sqrt[c]*(-1 + a^2*x^2))] - 2*a*Sqrt[c]*Log[x] + 2*a*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1242,1,76,78,0.1488394,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^3),x]","\frac{1}{2} \left(\frac{(4 a x-1) \sqrt{c-a^2 c x^2}}{x^2}-3 a^2 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+3 a^2 \sqrt{c} \log (x)\right)","\frac{2 a \sqrt{c-a^2 c x^2}}{x}-\frac{\sqrt{c-a^2 c x^2}}{2 x^2}-\frac{3}{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"(((-1 + 4*a*x)*Sqrt[c - a^2*c*x^2])/x^2 + 3*a^2*Sqrt[c]*Log[x] - 3*a^2*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/2","A",0
1243,1,82,99,0.1494097,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^4),x]","a^3 \left(-\sqrt{c}\right) \log (x)+\frac{\left(-5 a^2 x^2+3 a x-1\right) \sqrt{c-a^2 c x^2}}{3 x^3}+a^3 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)","-\frac{5 a^2 \sqrt{c-a^2 c x^2}}{3 x}+\frac{a \sqrt{c-a^2 c x^2}}{x^2}-\frac{\sqrt{c-a^2 c x^2}}{3 x^3}+a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"((-1 + 3*a*x - 5*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(3*x^3) - a^3*Sqrt[c]*Log[x] + a^3*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]]","A",0
1244,1,95,130,0.1630381,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^5),x]","\frac{7}{8} a^4 \sqrt{c} \log (x)-\frac{7}{8} a^4 \sqrt{c} \log \left(\sqrt{c} \sqrt{c-a^2 c x^2}+c\right)+\frac{\left(32 a^3 x^3-21 a^2 x^2+16 a x-6\right) \sqrt{c-a^2 c x^2}}{24 x^4}","-\frac{7 a^2 \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4}+\frac{2 a \sqrt{c-a^2 c x^2}}{3 x^3}-\frac{7}{8} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)+\frac{4 a^3 \sqrt{c-a^2 c x^2}}{3 x}",1,"(Sqrt[c - a^2*c*x^2]*(-6 + 16*a*x - 21*a^2*x^2 + 32*a^3*x^3))/(24*x^4) + (7*a^4*Sqrt[c]*Log[x])/8 - (7*a^4*Sqrt[c]*Log[c + Sqrt[c]*Sqrt[c - a^2*c*x^2]])/8","A",0
1245,1,117,108,0.113945,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[(c - a^2*c*x^2)^(3/2)/E^(2*ArcTanh[a*x]),x]","-\frac{c \sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(6 a^4 x^4-22 a^3 x^3+25 a^2 x^2+7 a x-16\right)+30 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{24 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{5 c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a}+\frac{5}{8} c x \sqrt{c-a^2 c x^2}+\frac{(1-a x) \left(c-a^2 c x^2\right)^{3/2}}{4 a}+\frac{5 \left(c-a^2 c x^2\right)^{3/2}}{12 a}",1,"-1/24*(c*Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(-16 + 7*a*x + 25*a^2*x^2 - 22*a^3*x^3 + 6*a^4*x^4) + 30*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1246,1,135,131,0.17167,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[(c - a^2*c*x^2)^(5/2)/E^(2*ArcTanh[a*x]),x]","\frac{c^2 \sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(40 a^6 x^6-136 a^5 x^5+86 a^4 x^4+202 a^3 x^3-327 a^2 x^2+39 a x+96\right)-210 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{240 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{7 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{16 a}+\frac{7}{16} c^2 x \sqrt{c-a^2 c x^2}+\frac{7}{24} c x \left(c-a^2 c x^2\right)^{3/2}+\frac{(1-a x) \left(c-a^2 c x^2\right)^{5/2}}{6 a}+\frac{7 \left(c-a^2 c x^2\right)^{5/2}}{30 a}",1,"(c^2*Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(96 + 39*a*x - 327*a^2*x^2 + 202*a^3*x^3 + 86*a^4*x^4 - 136*a^5*x^5 + 40*a^6*x^6) - 210*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(240*a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1247,1,151,154,0.1808931,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Integrate[(c - a^2*c*x^2)^(7/2)/E^(2*ArcTanh[a*x]),x]","-\frac{c^3 \sqrt{c-a^2 c x^2} \left(\sqrt{a x+1} \left(112 a^8 x^8-368 a^7 x^7+88 a^6 x^6+936 a^5 x^5-978 a^4 x^4-558 a^3 x^3+1349 a^2 x^2-325 a x-256\right)+630 \sqrt{1-a x} \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{896 a \sqrt{1-a x} \sqrt{1-a^2 x^2}}","\frac{45 c^{7/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a}+\frac{45}{128} c^3 x \sqrt{c-a^2 c x^2}+\frac{15}{64} c^2 x \left(c-a^2 c x^2\right)^{3/2}+\frac{3}{16} c x \left(c-a^2 c x^2\right)^{5/2}+\frac{(1-a x) \left(c-a^2 c x^2\right)^{7/2}}{8 a}+\frac{9 \left(c-a^2 c x^2\right)^{7/2}}{56 a}",1,"-1/896*(c^3*Sqrt[c - a^2*c*x^2]*(Sqrt[1 + a*x]*(-256 - 325*a*x + 1349*a^2*x^2 - 558*a^3*x^3 - 978*a^4*x^4 + 936*a^5*x^5 + 88*a^6*x^6 - 368*a^7*x^7 + 112*a^8*x^8) + 630*Sqrt[1 - a*x]*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a*x]*Sqrt[1 - a^2*x^2])","A",0
1248,1,100,61,0.0795349,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2]),x]","\frac{2 \sqrt{1-a^2 x^2} \left(\sqrt{a x+1} (a x-1)+\sqrt{1-a x} (a x+1) \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{a \sqrt{1-a x} (a x+1) \sqrt{c-a^2 c x^2}}","-\frac{2 (1-a x)}{a \sqrt{c-a^2 c x^2}}-\frac{\tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{a \sqrt{c}}",1,"(2*Sqrt[1 - a^2*x^2]*((-1 + a*x)*Sqrt[1 + a*x] + Sqrt[1 - a*x]*(1 + a*x)*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(a*Sqrt[1 - a*x]*(1 + a*x)*Sqrt[c - a^2*c*x^2])","A",0
1249,1,63,52,0.0427505,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2)),x]","-\frac{\sqrt{1-a x} (a x+2) \sqrt{1-a^2 x^2}}{3 a c (a x+1)^{3/2} \sqrt{c-a^2 c x^2}}","\frac{x}{3 c \sqrt{c-a^2 c x^2}}-\frac{2 (1-a x)}{3 a \left(c-a^2 c x^2\right)^{3/2}}",1,"-1/3*(Sqrt[1 - a*x]*(2 + a*x)*Sqrt[1 - a^2*x^2])/(a*c*(1 + a*x)^(3/2)*Sqrt[c - a^2*c*x^2])","A",0
1250,1,79,75,0.066793,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(2 a^3 x^3+4 a^2 x^2+a x-2\right)}{5 a c^2 \sqrt{1-a x} (a x+1)^{5/2} \sqrt{c-a^2 c x^2}}","\frac{2 x}{5 c^2 \sqrt{c-a^2 c x^2}}+\frac{x}{5 c \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 (1-a x)}{5 a \left(c-a^2 c x^2\right)^{5/2}}",1,"(Sqrt[1 - a^2*x^2]*(-2 + a*x + 4*a^2*x^2 + 2*a^3*x^3))/(5*a*c^2*Sqrt[1 - a*x]*(1 + a*x)^(5/2)*Sqrt[c - a^2*c*x^2])","A",1
1251,1,96,98,0.084558,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2)),x]","-\frac{\sqrt{1-a^2 x^2} \left(8 a^5 x^5+16 a^4 x^4-4 a^3 x^3-24 a^2 x^2-9 a x+6\right)}{21 a c^3 (1-a x)^{3/2} (a x+1)^{7/2} \sqrt{c-a^2 c x^2}}","\frac{8 x}{21 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x}{21 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x}{7 c \left(c-a^2 c x^2\right)^{5/2}}-\frac{2 (1-a x)}{7 a \left(c-a^2 c x^2\right)^{7/2}}",1,"-1/21*(Sqrt[1 - a^2*x^2]*(6 - 9*a*x - 24*a^2*x^2 - 4*a^3*x^3 + 16*a^4*x^4 + 8*a^5*x^5))/(a*c^3*(1 - a*x)^(3/2)*(1 + a*x)^(7/2)*Sqrt[c - a^2*c*x^2])","A",1
1252,1,111,172,0.195872,"\int e^{-2 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^m*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","\frac{x^{m+1} \left(\frac{2 \sqrt{c-a c x} F_1\left(m+1;\frac{1}{2},-\frac{1}{2};m+2;-a x,a x\right)}{\sqrt{1-a x}}-\frac{\sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{\sqrt{1-a^2 x^2}}\right)}{m+1}","\frac{c (2 m+3) \sqrt{1-a^2 x^2} x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{(m+1) (m+2) \sqrt{c-a^2 c x^2}}-\frac{2 a c \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{(m+2) \sqrt{c-a^2 c x^2}}-\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{m+2}",1,"(x^(1 + m)*((2*Sqrt[c - a*c*x]*AppellF1[1 + m, 1/2, -1/2, 2 + m, -(a*x), a*x])/Sqrt[1 - a*x] - (Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/Sqrt[1 - a^2*x^2]))/(1 + m)","C",0
1253,1,74,54,0.0394141,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[(c - a^2*c*x^2)^p/E^(2*ArcTanh[a*x]),x]","-\frac{2^{p-1} (1-a x)^{p+2} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(1-p,p+2;p+3;\frac{1}{2} (1-a x)\right)}{a (p+2)}","\frac{2^{p+1} (1-a x)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-p-1,p;p+1;\frac{1}{2} (a x+1)\right)}{a p}",1,"-((2^(-1 + p)*(1 - a*x)^(2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[1 - p, 2 + p, 3 + p, (1 - a*x)/2])/(a*(2 + p)*(1 - a^2*x^2)^p))","A",0
1254,1,107,167,0.1786858,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Integrate[(c - a^2*c*x^2)^4/E^(3*ArcTanh[a*x]),x]","-\frac{c^4 \left(\sqrt{1-a^2 x^2} \left(896 a^8 x^8-3024 a^7 x^7+1024 a^6 x^6+7224 a^5 x^5-8448 a^4 x^4-3066 a^3 x^3+10240 a^2 x^2-4599 a x-3712\right)+6930 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{8064 a}","\frac{c^4 (1-a x)^2 \left(1-a^2 x^2\right)^{7/2}}{9 a}+\frac{11 c^4 (1-a x) \left(1-a^2 x^2\right)^{7/2}}{72 a}+\frac{11 c^4 \left(1-a^2 x^2\right)^{7/2}}{56 a}+\frac{11}{48} c^4 x \left(1-a^2 x^2\right)^{5/2}+\frac{55}{192} c^4 x \left(1-a^2 x^2\right)^{3/2}+\frac{55}{128} c^4 x \sqrt{1-a^2 x^2}+\frac{55 c^4 \sin ^{-1}(a x)}{128 a}",1,"-1/8064*(c^4*(Sqrt[1 - a^2*x^2]*(-3712 - 4599*a*x + 10240*a^2*x^2 - 3066*a^3*x^3 - 8448*a^4*x^4 + 7224*a^5*x^5 + 1024*a^6*x^6 - 3024*a^7*x^7 + 896*a^8*x^8) + 6930*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
1255,1,91,145,0.1476652,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[(c - a^2*c*x^2)^3/E^(3*ArcTanh[a*x]),x]","\frac{c^3 \left(\sqrt{1-a^2 x^2} \left(80 a^6 x^6-280 a^5 x^5+208 a^4 x^4+350 a^3 x^3-656 a^2 x^2+245 a x+368\right)-630 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{560 a}","\frac{c^3 (1-a x)^2 \left(1-a^2 x^2\right)^{5/2}}{7 a}+\frac{3 c^3 (1-a x) \left(1-a^2 x^2\right)^{5/2}}{14 a}+\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{10 a}+\frac{3}{8} c^3 x \left(1-a^2 x^2\right)^{3/2}+\frac{9}{16} c^3 x \sqrt{1-a^2 x^2}+\frac{9 c^3 \sin ^{-1}(a x)}{16 a}",1,"(c^3*(Sqrt[1 - a^2*x^2]*(368 + 245*a*x - 656*a^2*x^2 + 350*a^3*x^3 + 208*a^4*x^4 - 280*a^5*x^5 + 80*a^6*x^6) - 630*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(560*a)","A",0
1256,1,75,123,0.1211734,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[(c - a^2*c*x^2)^2/E^(3*ArcTanh[a*x]),x]","-\frac{c^2 \left(\sqrt{1-a^2 x^2} \left(24 a^4 x^4-90 a^3 x^3+112 a^2 x^2-15 a x-136\right)+210 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{120 a}","\frac{c^2 (1-a x)^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}+\frac{7 c^2 (1-a x) \left(1-a^2 x^2\right)^{3/2}}{20 a}+\frac{7 c^2 \left(1-a^2 x^2\right)^{3/2}}{12 a}+\frac{7}{8} c^2 x \sqrt{1-a^2 x^2}+\frac{7 c^2 \sin ^{-1}(a x)}{8 a}",1,"-1/120*(c^2*(Sqrt[1 - a^2*x^2]*(-136 - 15*a*x + 112*a^2*x^2 - 90*a^3*x^3 + 24*a^4*x^4) + 210*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/a","A",0
1257,1,70,93,0.1039173,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[(c - a^2*c*x^2)/E^(3*ArcTanh[a*x]),x]","\frac{c \left(\frac{\sqrt{a x+1} \left(-2 a^3 x^3+11 a^2 x^2-31 a x+22\right)}{\sqrt{1-a x}}-30 \sin ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)\right)}{6 a}","\frac{c \sqrt{1-a^2 x^2} (1-a x)^2}{3 a}+\frac{5 c \sqrt{1-a^2 x^2} (1-a x)}{6 a}+\frac{5 c \sqrt{1-a^2 x^2}}{2 a}+\frac{5 c \sin ^{-1}(a x)}{2 a}",1,"(c*((Sqrt[1 + a*x]*(22 - 31*a*x + 11*a^2*x^2 - 2*a^3*x^3))/Sqrt[1 - a*x] - 30*ArcSin[Sqrt[1 - a*x]/Sqrt[2]]))/(6*a)","A",0
1258,1,29,18,0.0146419,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)),x]","-\frac{(1-a x)^{3/2}}{3 a c (a x+1)^{3/2}}","-\frac{e^{-3 \tanh ^{-1}(a x)}}{3 a c}",1,"-1/3*(1 - a*x)^(3/2)/(a*c*(1 + a*x)^(3/2))","A",0
1259,1,43,94,0.0204743,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^2),x]","-\frac{\sqrt{1-a x} \left(2 a^2 x^2+6 a x+7\right)}{15 a c^2 (a x+1)^{5/2}}","-\frac{2 \sqrt{1-a^2 x^2}}{15 a c^2 (a x+1)}-\frac{2 \sqrt{1-a^2 x^2}}{15 a c^2 (a x+1)^2}-\frac{\sqrt{1-a^2 x^2}}{5 a c^2 (a x+1)^3}",1,"-1/15*(Sqrt[1 - a*x]*(7 + 6*a*x + 2*a^2*x^2))/(a*c^2*(1 + a*x)^(5/2))","A",0
1260,1,59,116,0.0280052,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^3),x]","\frac{8 a^4 x^4+24 a^3 x^3+20 a^2 x^2-4 a x-13}{35 a c^3 \sqrt{1-a x} (a x+1)^{7/2}}","\frac{8 x}{35 c^3 \sqrt{1-a^2 x^2}}-\frac{4}{35 a c^3 (a x+1) \sqrt{1-a^2 x^2}}-\frac{4}{35 a c^3 (a x+1)^2 \sqrt{1-a^2 x^2}}-\frac{1}{7 a c^3 (a x+1)^3 \sqrt{1-a^2 x^2}}",1,"(-13 - 4*a*x + 20*a^2*x^2 + 24*a^3*x^3 + 8*a^4*x^4)/(35*a*c^3*Sqrt[1 - a*x]*(1 + a*x)^(7/2))","A",1
1261,1,75,138,0.0367668,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^4),x]","-\frac{16 a^6 x^6+48 a^5 x^5+24 a^4 x^4-56 a^3 x^3-66 a^2 x^2-6 a x+19}{63 a c^4 (1-a x)^{3/2} (a x+1)^{9/2}}","\frac{16 x}{63 c^4 \sqrt{1-a^2 x^2}}+\frac{8 x}{63 c^4 \left(1-a^2 x^2\right)^{3/2}}-\frac{2}{21 a c^4 (a x+1) \left(1-a^2 x^2\right)^{3/2}}-\frac{2}{21 a c^4 (a x+1)^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{1}{9 a c^4 (a x+1)^3 \left(1-a^2 x^2\right)^{3/2}}",1,"-1/63*(19 - 6*a*x - 66*a^2*x^2 - 56*a^3*x^3 + 24*a^4*x^4 + 48*a^5*x^5 + 16*a^6*x^6)/(a*c^4*(1 - a*x)^(3/2)*(1 + a*x)^(9/2))","A",1
1262,1,81,225,0.0670567,"\int e^{-3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^3*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{c-a^2 c x^2} \left(-\frac{4 \log (a x+1)}{a^4}+\frac{4 x}{a^3}-\frac{2 x^2}{a^2}+\frac{a x^5}{5}+\frac{4 x^3}{3 a}-\frac{3 x^4}{4}\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 x^2 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}+\frac{a x^5 \sqrt{c-a^2 c x^2}}{5 \sqrt{1-a^2 x^2}}-\frac{3 x^4 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-a^2 x^2}}+\frac{4 x^3 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^4 \sqrt{1-a^2 x^2}}+\frac{4 x \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*((4*x)/a^3 - (2*x^2)/a^2 + (4*x^3)/(3*a) - (3*x^4)/4 + (a*x^5)/5 - (4*Log[1 + a*x])/a^4))/Sqrt[1 - a^2*x^2]","A",1
1263,1,69,184,0.0543967,"\int e^{-3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^2*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{c-a^2 c x^2} \left(\frac{4 \log (a x+1)}{a^3}-\frac{4 x}{a^2}+\frac{a x^4}{4}+\frac{2 x^2}{a}-x^3\right)}{\sqrt{1-a^2 x^2}}","\frac{2 x^2 \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}+\frac{a x^4 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-a^2 x^2}}-\frac{x^3 \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*((-4*x)/a^2 + (2*x^2)/a - x^3 + (a*x^4)/4 + (4*Log[1 + a*x])/a^3))/Sqrt[1 - a^2*x^2]","A",1
1264,1,63,149,0.05025,"\int e^{-3 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[(x*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{c-a^2 c x^2} \left(-\frac{4 \log (a x+1)}{a^2}+\frac{a x^3}{3}+\frac{4 x}{a}-\frac{3 x^2}{2}\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}+\frac{4 x \sqrt{c-a^2 c x^2}}{a \sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^2 \sqrt{1-a^2 x^2}}+\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*((4*x)/a - (3*x^2)/2 + (a*x^3)/3 - (4*Log[1 + a*x])/a^2))/Sqrt[1 - a^2*x^2]","A",1
1265,1,53,110,0.0283971,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/E^(3*ArcTanh[a*x]),x]","\frac{\sqrt{c-a^2 c x^2} \left(\frac{a x^2}{2}+\frac{4 \log (a x+1)}{a}-3 x\right)}{\sqrt{1-a^2 x^2}}","\frac{a x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}-\frac{3 x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-3*x + (a*x^2)/2 + (4*Log[1 + a*x])/a))/Sqrt[1 - a^2*x^2]","A",1
1266,1,44,102,0.0284175,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x),x]","\frac{\sqrt{c-a^2 c x^2} (a x-4 \log (a x+1)+\log (x))}{\sqrt{1-a^2 x^2}}","\frac{a x \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(a*x + Log[x] - 4*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
1267,1,50,107,0.0345365,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^2),x]","\frac{\sqrt{c-a^2 c x^2} \left(-3 a \log (x)+4 a \log (a x+1)-\frac{1}{x}\right)}{\sqrt{1-a^2 x^2}}","-\frac{\sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}-\frac{3 a \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{4 a \sqrt{c-a^2 c x^2} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-x^(-1) - 3*a*Log[x] + 4*a*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
1268,1,62,148,0.0453448,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^3),x]","\frac{\sqrt{c-a^2 c x^2} \left(4 a^2 \log (x)-4 a^2 \log (a x+1)+\frac{3 a}{x}-\frac{1}{2 x^2}\right)}{\sqrt{1-a^2 x^2}}","\frac{3 a \sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{2 x^2 \sqrt{1-a^2 x^2}}+\frac{4 a^2 \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 a^2 \sqrt{c-a^2 c x^2} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-1/2*1/x^2 + (3*a)/x + 4*a^2*Log[x] - 4*a^2*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
1269,1,72,187,0.0468267,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^4),x]","\frac{\sqrt{c-a^2 c x^2} \left(-4 a^3 \log (x)+4 a^3 \log (a x+1)-\frac{4 a^2}{x}+\frac{3 a}{2 x^2}-\frac{1}{3 x^3}\right)}{\sqrt{1-a^2 x^2}}","-\frac{4 a^2 \sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}+\frac{3 a \sqrt{c-a^2 c x^2}}{2 x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{3 x^3 \sqrt{1-a^2 x^2}}-\frac{4 a^3 \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}+\frac{4 a^3 \sqrt{c-a^2 c x^2} \log (a x+1)}{\sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-1/3*1/x^3 + (3*a)/(2*x^2) - (4*a^2)/x - 4*a^3*Log[x] + 4*a^3*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
1270,1,77,221,0.0580184,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Integrate[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^5),x]","\frac{\sqrt{c-a^2 c x^2} \left(4 a^4 \log (x)-4 a^4 \log (a x+1)+\frac{4 a^3}{x}-\frac{2 a^2}{x^2}+\frac{a}{x^3}-\frac{1}{4 x^4}\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4 \sqrt{1-a^2 x^2}}+\frac{a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-a^2 x^2}}+\frac{4 a^4 \log (x) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}-\frac{4 a^4 \sqrt{c-a^2 c x^2} \log (a x+1)}{\sqrt{1-a^2 x^2}}+\frac{4 a^3 \sqrt{c-a^2 c x^2}}{x \sqrt{1-a^2 x^2}}",1,"(Sqrt[c - a^2*c*x^2]*(-1/4*1/x^4 + a/x^3 - (2*a^2)/x^2 + (4*a^3)/x + 4*a^4*Log[x] - 4*a^4*Log[1 + a*x]))/Sqrt[1 - a^2*x^2]","A",1
1271,1,68,189,0.0580375,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Integrate[(c - a^2*c*x^2)^(9/2)/E^(3*ArcTanh[a*x]),x]","\frac{c^4 (a x-1)^7 \left(21 a^3 x^3+77 a^2 x^2+98 a x+44\right) \sqrt{c-a^2 c x^2}}{210 a \sqrt{1-a^2 x^2}}","\frac{c^4 (1-a x)^{10} \sqrt{c-a^2 c x^2}}{10 a \sqrt{1-a^2 x^2}}-\frac{2 c^4 (1-a x)^9 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}+\frac{3 c^4 (1-a x)^8 \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-a^2 x^2}}-\frac{8 c^4 (1-a x)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}",1,"(c^4*(-1 + a*x)^7*Sqrt[c - a^2*c*x^2]*(44 + 98*a*x + 77*a^2*x^2 + 21*a^3*x^3))/(210*a*Sqrt[1 - a^2*x^2])","A",1
1272,1,60,142,0.0536739,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Integrate[(c - a^2*c*x^2)^(7/2)/E^(3*ArcTanh[a*x]),x]","-\frac{c^3 (a x-1)^6 \left(21 a^2 x^2+54 a x+37\right) \sqrt{c-a^2 c x^2}}{168 a \sqrt{1-a^2 x^2}}","-\frac{c^3 (1-a x)^8 \sqrt{c-a^2 c x^2}}{8 a \sqrt{1-a^2 x^2}}+\frac{4 c^3 (1-a x)^7 \sqrt{c-a^2 c x^2}}{7 a \sqrt{1-a^2 x^2}}-\frac{2 c^3 (1-a x)^6 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-a^2 x^2}}",1,"-1/168*(c^3*(-1 + a*x)^6*(37 + 54*a*x + 21*a^2*x^2)*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2])","A",1
1273,1,52,95,0.0426315,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[(c - a^2*c*x^2)^(5/2)/E^(3*ArcTanh[a*x]),x]","\frac{c^2 (a x-1)^5 (5 a x+7) \sqrt{c-a^2 c x^2}}{30 a \sqrt{1-a^2 x^2}}","\frac{c^2 (1-a x)^6 \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{2 c^2 (1-a x)^5 \sqrt{c-a^2 c x^2}}{5 a \sqrt{1-a^2 x^2}}",1,"(c^2*(-1 + a*x)^5*(7 + 5*a*x)*Sqrt[c - a^2*c*x^2])/(30*a*Sqrt[1 - a^2*x^2])","A",1
1274,1,58,45,0.0357817,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[(c - a^2*c*x^2)^(3/2)/E^(3*ArcTanh[a*x]),x]","\frac{c \left(-\frac{1}{4} a^3 x^4+a^2 x^3-\frac{3 a x^2}{2}+x\right) \sqrt{c-a^2 c x^2}}{\sqrt{1-a^2 x^2}}","-\frac{c (1-a x)^4 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-a^2 x^2}}",1,"(c*Sqrt[c - a^2*c*x^2]*(x - (3*a*x^2)/2 + a^2*x^3 - (a^3*x^4)/4))/Sqrt[1 - a^2*x^2]","A",0
1275,1,54,82,0.036676,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} \left(-\frac{2}{a (a x+1)}-\frac{\log (a x+1)}{a}\right)}{\sqrt{c-a^2 c x^2}}","-\frac{2 \sqrt{1-a^2 x^2}}{a (a x+1) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{a \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-2/(a*(1 + a*x)) - Log[1 + a*x]/a))/Sqrt[c - a^2*c*x^2]","A",1
1276,1,53,46,0.0500199,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} \sqrt{c-a^2 c x^2}}{2 a c^2 (a x-1) (a x+1)^3}","-\frac{\sqrt{1-a^2 x^2}}{2 a c (a x+1)^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*Sqrt[c - a^2*c*x^2])/(2*a*c^2*(-1 + a*x)*(1 + a*x)^3)","A",1
1277,1,73,182,0.0622414,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(-3 a^2 x^2-9 a x+3 (a x+1)^3 \tanh ^{-1}(a x)-10\right)}{24 a c^2 (a x+1)^3 \sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (a x+1) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a c^2 (a x+1)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{6 a c^2 (a x+1)^3 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{8 a c^2 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(-10 - 9*a*x - 3*a^2*x^2 + 3*(1 + a*x)^3*ArcTanh[a*x]))/(24*a*c^2*(1 + a*x)^3*Sqrt[c - a^2*c*x^2])","A",1
1278,1,101,275,0.0964147,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2)),x]","\frac{\sqrt{1-a^2 x^2} \left(-15 a^4 x^4-45 a^3 x^3-35 a^2 x^2+15 a x+15 (a x-1) (a x+1)^4 \tanh ^{-1}(a x)+32\right)}{96 a c^3 (a x-1) (a x+1)^4 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{32 a c^3 (1-a x) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{8 a c^3 (a x+1) \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{1-a^2 x^2}}{32 a c^3 (a x+1)^2 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{12 a c^3 (a x+1)^3 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2}}{16 a c^3 (a x+1)^4 \sqrt{c-a^2 c x^2}}+\frac{5 \sqrt{1-a^2 x^2} \tanh ^{-1}(a x)}{32 a c^3 \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(32 + 15*a*x - 35*a^2*x^2 - 45*a^3*x^3 - 15*a^4*x^4 + 15*(-1 + a*x)*(1 + a*x)^4*ArcTanh[a*x]))/(96*a*c^3*(-1 + a*x)*(1 + a*x)^4*Sqrt[c - a^2*c*x^2])","A",1
1279,1,74,136,0.0557567,"\int e^{-3 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Integrate[(x^m*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\frac{x^{m+1} \sqrt{c-a^2 c x^2} (4 (m+2) \, _2F_1(1,m+1;m+2;-a x)+m (a x-3)+a x-6)}{(m+1) (m+2) \sqrt{1-a^2 x^2}}","\frac{4 x^{m+1} \sqrt{c-a^2 c x^2} \, _2F_1(1,m+1;m+2;-a x)}{(m+1) \sqrt{1-a^2 x^2}}-\frac{3 x^{m+1} \sqrt{c-a^2 c x^2}}{(m+1) \sqrt{1-a^2 x^2}}+\frac{a x^{m+2} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-a^2 x^2}}",1,"(x^(1 + m)*Sqrt[c - a^2*c*x^2]*(-6 + a*x + m*(-3 + a*x) + 4*(2 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)]))/((1 + m)*(2 + m)*Sqrt[1 - a^2*x^2])","A",1
1280,1,86,86,0.0338558,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[(c - a^2*c*x^2)^p/E^(3*ArcTanh[a*x]),x]","-\frac{2^{p-\frac{3}{2}} (1-a x)^{p+\frac{5}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2}-p,p+\frac{5}{2};p+\frac{7}{2};\frac{1}{2} (1-a x)\right)}{a \left(p+\frac{5}{2}\right)}","-\frac{2^{p-\frac{1}{2}} (1-a x)^{p+\frac{5}{2}} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p \, _2F_1\left(\frac{3}{2}-p,p+\frac{5}{2};p+\frac{7}{2};\frac{1}{2} (1-a x)\right)}{a (2 p+5)}",1,"-((2^(-3/2 + p)*(1 - a*x)^(5/2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[3/2 - p, 5/2 + p, 7/2 + p, (1 - a*x)/2])/(a*(5/2 + p)*(1 - a^2*x^2)^p))","A",1
1281,1,42,359,0.0207858,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^{5/2} \, dx","Integrate[E^(ArcTanh[a*x]/2)*(1 - a^2*x^2)^(5/2),x]","-\frac{16\ 2^{3/4} (1-a x)^{13/4} \, _2F_1\left(-\frac{11}{4},\frac{13}{4};\frac{17}{4};\frac{1}{2} (1-a x)\right)}{13 a}","-\frac{(a x+1)^{11/4} (1-a x)^{13/4}}{6 a}-\frac{11 (a x+1)^{7/4} (1-a x)^{13/4}}{60 a}-\frac{77 (a x+1)^{3/4} (1-a x)^{13/4}}{480 a}+\frac{77 (a x+1)^{3/4} (1-a x)^{9/4}}{960 a}+\frac{231 (a x+1)^{3/4} (1-a x)^{5/4}}{1280 a}+\frac{231 (a x+1)^{3/4} \sqrt[4]{1-a x}}{512 a}+\frac{231 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{1024 \sqrt{2} a}-\frac{231 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{1024 \sqrt{2} a}+\frac{231 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{512 \sqrt{2} a}-\frac{231 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{512 \sqrt{2} a}",1,"(-16*2^(3/4)*(1 - a*x)^(13/4)*Hypergeometric2F1[-11/4, 13/4, 17/4, (1 - a*x)/2])/(13*a)","C",0
1282,1,42,307,0.0168884,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^{3/2} \, dx","Integrate[E^(ArcTanh[a*x]/2)*(1 - a^2*x^2)^(3/2),x]","-\frac{8\ 2^{3/4} (1-a x)^{9/4} \, _2F_1\left(-\frac{7}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2} (1-a x)\right)}{9 a}","-\frac{(a x+1)^{7/4} (1-a x)^{9/4}}{4 a}-\frac{7 (a x+1)^{3/4} (1-a x)^{9/4}}{24 a}+\frac{7 (a x+1)^{3/4} (1-a x)^{5/4}}{32 a}+\frac{35 (a x+1)^{3/4} \sqrt[4]{1-a x}}{64 a}+\frac{35 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a}-\frac{35 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a}+\frac{35 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a}-\frac{35 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a}",1,"(-8*2^(3/4)*(1 - a*x)^(9/4)*Hypergeometric2F1[-7/4, 9/4, 13/4, (1 - a*x)/2])/(9*a)","C",0
1283,1,42,255,0.0141668,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \sqrt{1-a^2 x^2} \, dx","Integrate[E^(ArcTanh[a*x]/2)*Sqrt[1 - a^2*x^2],x]","-\frac{4\ 2^{3/4} (1-a x)^{5/4} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)}{5 a}","-\frac{(a x+1)^{3/4} (1-a x)^{5/4}}{2 a}+\frac{3 (a x+1)^{3/4} \sqrt[4]{1-a x}}{4 a}+\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a}-\frac{3 \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a}+\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a}",1,"(-4*2^(3/4)*(1 - a*x)^(5/4)*Hypergeometric2F1[-3/4, 5/4, 9/4, (1 - a*x)/2])/(5*a)","C",0
1284,1,40,193,0.0109547,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\sqrt{1-a^2 x^2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/Sqrt[1 - a^2*x^2],x]","-\frac{2\ 2^{3/4} \sqrt[4]{1-a x} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)}{a}","\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a}+\frac{\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{a}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{a}",1,"(-2*2^(3/4)*(1 - a*x)^(1/4)*Hypergeometric2F1[1/4, 1/4, 5/4, (1 - a*x)/2])/a","C",0
1285,1,32,37,0.0139345,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(3/2),x]","\frac{2 (2 a x-1)}{3 a (1-a x)^{3/4} \sqrt[4]{a x+1}}","-\frac{2 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{3 a \sqrt{1-a^2 x^2}}",1,"(2*(-1 + 2*a*x))/(3*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))","A",0
1286,1,48,75,0.0225532,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(5/2),x]","-\frac{2 \left(16 a^3 x^3-8 a^2 x^2-22 a x+9\right)}{35 a (1-a x)^{7/4} (a x+1)^{5/4}}","-\frac{2 (1-6 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{35 a \left(1-a^2 x^2\right)^{3/2}}-\frac{16 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{35 a \sqrt{1-a^2 x^2}}",1,"(-2*(9 - 22*a*x - 8*a^2*x^2 + 16*a^3*x^3))/(35*a*(1 - a*x)^(7/4)*(1 + a*x)^(5/4))","A",0
1287,1,64,112,0.0331699,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{7/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(7/2),x]","\frac{2 \left(256 a^5 x^5-128 a^4 x^4-608 a^3 x^3+272 a^2 x^2+422 a x-151\right)}{693 a (1-a x)^{11/4} (a x+1)^{9/4}}","-\frac{2 (1-10 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{99 a \left(1-a^2 x^2\right)^{5/2}}-\frac{256 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{693 a \sqrt{1-a^2 x^2}}-\frac{32 (1-6 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{693 a \left(1-a^2 x^2\right)^{3/2}}",1,"(2*(-151 + 422*a*x + 272*a^2*x^2 - 608*a^3*x^3 - 128*a^4*x^4 + 256*a^5*x^5))/(693*a*(1 - a*x)^(11/4)*(1 + a*x)^(9/4))","A",0
1288,1,80,149,0.0351893,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{9/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(9/2),x]","-\frac{2 \left(2048 a^7 x^7-1024 a^6 x^6-6912 a^5 x^5+3200 a^4 x^4+8240 a^3 x^3-3384 a^2 x^2-3838 a x+1241\right)}{6435 a (1-a x)^{15/4} (a x+1)^{13/4}}","-\frac{2 (1-14 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{195 a \left(1-a^2 x^2\right)^{7/2}}-\frac{2048 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{6435 a \sqrt{1-a^2 x^2}}-\frac{256 (1-6 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{6435 a \left(1-a^2 x^2\right)^{3/2}}-\frac{112 (1-10 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{6435 a \left(1-a^2 x^2\right)^{5/2}}",1,"(-2*(1241 - 3838*a*x - 3384*a^2*x^2 + 8240*a^3*x^3 + 3200*a^4*x^4 - 6912*a^5*x^5 - 1024*a^6*x^6 + 2048*a^7*x^7))/(6435*a*(1 - a*x)^(15/4)*(1 + a*x)^(13/4))","A",0
1289,1,74,679,0.04271,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Integrate[E^(ArcTanh[a*x]/2)*(c - a^2*c*x^2)^(5/2),x]","-\frac{16\ 2^{3/4} c^2 (1-a x)^{13/4} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{11}{4},\frac{13}{4};\frac{17}{4};\frac{1}{2} (1-a x)\right)}{13 a \sqrt{1-a^2 x^2}}","-\frac{c^2 (a x+1)^{11/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{6 a \sqrt{1-a^2 x^2}}-\frac{11 c^2 (a x+1)^{7/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{60 a \sqrt{1-a^2 x^2}}-\frac{77 c^2 (a x+1)^{3/4} (1-a x)^{13/4} \sqrt{c-a^2 c x^2}}{480 a \sqrt{1-a^2 x^2}}+\frac{77 c^2 (a x+1)^{3/4} (1-a x)^{9/4} \sqrt{c-a^2 c x^2}}{960 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (a x+1)^{3/4} (1-a x)^{5/4} \sqrt{c-a^2 c x^2}}{1280 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 (a x+1)^{3/4} \sqrt[4]{1-a x} \sqrt{c-a^2 c x^2}}{512 a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{1024 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{231 c^2 \sqrt{c-a^2 c x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{512 \sqrt{2} a \sqrt{1-a^2 x^2}}",1,"(-16*2^(3/4)*c^2*(1 - a*x)^(13/4)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-11/4, 13/4, 17/4, (1 - a*x)/2])/(13*a*Sqrt[1 - a^2*x^2])","C",0
1290,1,72,547,0.0330728,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(ArcTanh[a*x]/2)*(c - a^2*c*x^2)^(3/2),x]","-\frac{8\ 2^{3/4} c (1-a x)^{9/4} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{7}{4},\frac{9}{4};\frac{13}{4};\frac{1}{2} (1-a x)\right)}{9 a \sqrt{1-a^2 x^2}}","-\frac{c (a x+1)^{7/4} (1-a x)^{9/4} \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-a^2 x^2}}-\frac{7 c (a x+1)^{3/4} (1-a x)^{9/4} \sqrt{c-a^2 c x^2}}{24 a \sqrt{1-a^2 x^2}}+\frac{7 c (a x+1)^{3/4} (1-a x)^{5/4} \sqrt{c-a^2 c x^2}}{32 a \sqrt{1-a^2 x^2}}+\frac{35 c (a x+1)^{3/4} \sqrt[4]{1-a x} \sqrt{c-a^2 c x^2}}{64 a \sqrt{1-a^2 x^2}}+\frac{35 c \sqrt{c-a^2 c x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{35 c \sqrt{c-a^2 c x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{128 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{35 c \sqrt{c-a^2 c x^2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{64 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{35 c \sqrt{c-a^2 c x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{64 \sqrt{2} a \sqrt{1-a^2 x^2}}",1,"(-8*2^(3/4)*c*(1 - a*x)^(9/4)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-7/4, 9/4, 13/4, (1 - a*x)/2])/(9*a*Sqrt[1 - a^2*x^2])","C",0
1291,1,71,429,0.0271522,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(ArcTanh[a*x]/2)*Sqrt[c - a^2*c*x^2],x]","-\frac{4\ 2^{3/4} (1-a x)^{5/4} \sqrt{c-a^2 c x^2} \, _2F_1\left(-\frac{3}{4},\frac{5}{4};\frac{9}{4};\frac{1}{2} (1-a x)\right)}{5 a \sqrt{1-a^2 x^2}}","-\frac{(a x+1)^{3/4} (1-a x)^{5/4} \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-a^2 x^2}}+\frac{3 (a x+1)^{3/4} \sqrt[4]{1-a x} \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{c-a^2 c x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{c-a^2 c x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{8 \sqrt{2} a \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{c-a^2 c x^2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{4 \sqrt{2} a \sqrt{1-a^2 x^2}}-\frac{3 \sqrt{c-a^2 c x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{4 \sqrt{2} a \sqrt{1-a^2 x^2}}",1,"(-4*2^(3/4)*(1 - a*x)^(5/4)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-3/4, 5/4, 9/4, (1 - a*x)/2])/(5*a*Sqrt[1 - a^2*x^2])","C",0
1292,1,69,309,0.0231876,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/Sqrt[c - a^2*c*x^2],x]","-\frac{2\ 2^{3/4} \sqrt[4]{1-a x} \sqrt{1-a^2 x^2} \, _2F_1\left(\frac{1}{4},\frac{1}{4};\frac{5}{4};\frac{1}{2} (1-a x)\right)}{a \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}+\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{\sqrt{2} a \sqrt{c-a^2 c x^2}}+\frac{\sqrt{2} \sqrt{1-a^2 x^2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}\right)}{a \sqrt{c-a^2 c x^2}}-\frac{\sqrt{2} \sqrt{1-a^2 x^2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-a x}}{\sqrt[4]{a x+1}}+1\right)}{a \sqrt{c-a^2 c x^2}}",1,"(-2*2^(3/4)*(1 - a*x)^(1/4)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/4, 1/4, 5/4, (1 - a*x)/2])/(a*Sqrt[c - a^2*c*x^2])","C",0
1293,1,64,41,0.0286051,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(3/2),x]","\frac{2 (2 a x-1) \sqrt{1-a^2 x^2}}{3 a c (1-a x)^{3/4} \sqrt[4]{a x+1} \sqrt{c-a^2 c x^2}}","-\frac{2 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{3 a c \sqrt{c-a^2 c x^2}}",1,"(2*(-1 + 2*a*x)*Sqrt[1 - a^2*x^2])/(3*a*c*(1 - a*x)^(3/4)*(1 + a*x)^(1/4)*Sqrt[c - a^2*c*x^2])","A",0
1294,1,80,83,0.0430083,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(5/2),x]","-\frac{2 \sqrt{1-a^2 x^2} \left(16 a^3 x^3-8 a^2 x^2-22 a x+9\right)}{35 a c^2 (1-a x)^{7/4} (a x+1)^{5/4} \sqrt{c-a^2 c x^2}}","-\frac{16 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{35 a c^2 \sqrt{c-a^2 c x^2}}-\frac{2 (1-6 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{35 a c \left(c-a^2 c x^2\right)^{3/2}}",1,"(-2*Sqrt[1 - a^2*x^2]*(9 - 22*a*x - 8*a^2*x^2 + 16*a^3*x^3))/(35*a*c^2*(1 - a*x)^(7/4)*(1 + a*x)^(5/4)*Sqrt[c - a^2*c*x^2])","A",0
1295,1,96,124,0.0558434,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(7/2),x]","\frac{2 \sqrt{1-a^2 x^2} \left(256 a^5 x^5-128 a^4 x^4-608 a^3 x^3+272 a^2 x^2+422 a x-151\right)}{693 a c^3 (1-a x)^{11/4} (a x+1)^{9/4} \sqrt{c-a^2 c x^2}}","-\frac{256 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{693 a c^3 \sqrt{c-a^2 c x^2}}-\frac{32 (1-6 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{693 a c^2 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 (1-10 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{99 a c \left(c-a^2 c x^2\right)^{5/2}}",1,"(2*Sqrt[1 - a^2*x^2]*(-151 + 422*a*x + 272*a^2*x^2 - 608*a^3*x^3 - 128*a^4*x^4 + 256*a^5*x^5))/(693*a*c^3*(1 - a*x)^(11/4)*(1 + a*x)^(9/4)*Sqrt[c - a^2*c*x^2])","A",0
1296,1,112,165,0.0577399,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/2}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(9/2),x]","-\frac{2 \sqrt{1-a^2 x^2} \left(2048 a^7 x^7-1024 a^6 x^6-6912 a^5 x^5+3200 a^4 x^4+8240 a^3 x^3-3384 a^2 x^2-3838 a x+1241\right)}{6435 a c^4 (1-a x)^{15/4} (a x+1)^{13/4} \sqrt{c-a^2 c x^2}}","-\frac{2048 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{6435 a c^4 \sqrt{c-a^2 c x^2}}-\frac{256 (1-6 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{6435 a c^3 \left(c-a^2 c x^2\right)^{3/2}}-\frac{112 (1-10 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{6435 a c^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{2 (1-14 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{195 a c \left(c-a^2 c x^2\right)^{7/2}}",1,"(-2*Sqrt[1 - a^2*x^2]*(1241 - 3838*a*x - 3384*a^2*x^2 + 8240*a^3*x^3 + 3200*a^4*x^4 - 6912*a^5*x^5 - 1024*a^6*x^6 + 2048*a^7*x^7))/(6435*a*c^4*(1 - a*x)^(15/4)*(1 + a*x)^(13/4)*Sqrt[c - a^2*c*x^2])","A",0
1297,1,84,201,0.0629007,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Integrate[(E^(ArcTanh[a*x]/2)*x^3)/(c - a^2*c*x^2)^(5/4),x]","-\frac{\sqrt[4]{1-a^2 x^2} \left(2 \left(a^2 x^2+a x-5\right)+3 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (1-a x)\right)\right)}{3 a^4 c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}","-\frac{2 \sqrt[4]{1-a^2 x^2} (1-a x)^{3/2}}{3 a^4 c \sqrt[4]{c-a^2 c x^2}}+\frac{2 \sqrt[4]{1-a^2 x^2} \sqrt{1-a x}}{a^4 c \sqrt[4]{c-a^2 c x^2}}+\frac{\sqrt[4]{1-a^2 x^2}}{a^4 c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}+\frac{\sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} a^4 c \sqrt[4]{c-a^2 c x^2}}",1,"-1/3*((1 - a^2*x^2)^(1/4)*(2*(-5 + a*x + a^2*x^2) + 3*Hypergeometric2F1[-1/2, 1, 1/2, (1 - a*x)/2]))/(a^4*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4))","C",0
1298,1,70,153,0.0461428,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Integrate[(E^(ArcTanh[a*x]/2)*x^2)/(c - a^2*c*x^2)^(5/4),x]","\frac{\sqrt[4]{1-a^2 x^2} \left(\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (1-a x)\right)-2 a x+2\right)}{a^3 c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}","\frac{2 \sqrt{1-a x} \sqrt[4]{1-a^2 x^2}}{a^3 c \sqrt[4]{c-a^2 c x^2}}+\frac{\sqrt[4]{1-a^2 x^2}}{a^3 c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}-\frac{\sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} a^3 c \sqrt[4]{c-a^2 c x^2}}",1,"((1 - a^2*x^2)^(1/4)*(2 - 2*a*x + Hypergeometric2F1[-1/2, 1, 1/2, (1 - a*x)/2]))/(a^3*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4))","C",0
1299,1,74,105,0.0604662,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Integrate[(E^(ArcTanh[a*x]/2)*x)/(c - a^2*c*x^2)^(5/4),x]","\frac{\sqrt[4]{1-a^2 x^2} \left(\frac{1}{a^2 \sqrt{1-a x}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} a^2}\right)}{c \sqrt[4]{c-a^2 c x^2}}","\frac{\sqrt[4]{1-a^2 x^2}}{a^2 c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}+\frac{\sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} a^2 c \sqrt[4]{c-a^2 c x^2}}",1,"((1 - a^2*x^2)^(1/4)*(1/(a^2*Sqrt[1 - a*x]) + ArcTanh[Sqrt[1 - a*x]/Sqrt[2]]/(Sqrt[2]*a^2)))/(c*(c - a^2*c*x^2)^(1/4))","A",1
1300,1,64,106,0.0195943,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(5/4),x]","\frac{\sqrt[4]{1-a^2 x^2} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (1-a x)\right)}{a c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}","\frac{\sqrt[4]{1-a^2 x^2}}{a c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}-\frac{\sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} a c \sqrt[4]{c-a^2 c x^2}}",1,"((1 - a^2*x^2)^(1/4)*Hypergeometric2F1[-1/2, 1, 1/2, (1 - a*x)/2])/(a*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4))","C",0
1301,1,79,144,0.0372984,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/4}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(x*(c - a^2*c*x^2)^(5/4)),x]","-\frac{\sqrt[4]{1-a^2 x^2} \left(\, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (1-a x)\right)-2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-a x\right)\right)}{c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}","\frac{\sqrt[4]{1-a^2 x^2}}{c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}-\frac{2 \sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a x}\right)}{c \sqrt[4]{c-a^2 c x^2}}+\frac{\sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} c \sqrt[4]{c-a^2 c x^2}}",1,"-(((1 - a^2*x^2)^(1/4)*(Hypergeometric2F1[-1/2, 1, 1/2, (1 - a*x)/2] - 2*Hypergeometric2F1[-1/2, 1, 1/2, 1 - a*x]))/(c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)))","C",0
1302,1,86,196,0.0395648,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/4}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(x^2*(c - a^2*c*x^2)^(5/4)),x]","\frac{\sqrt[4]{1-a^2 x^2} \left(a x \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\frac{1}{2} (1-a x)\right)+a x \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};1-a x\right)-1\right)}{c x \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}","\frac{2 a \sqrt[4]{1-a^2 x^2}}{c \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}-\frac{\sqrt[4]{1-a^2 x^2}}{c x \sqrt{1-a x} \sqrt[4]{c-a^2 c x^2}}-\frac{a \sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\sqrt{1-a x}\right)}{c \sqrt[4]{c-a^2 c x^2}}-\frac{a \sqrt[4]{1-a^2 x^2} \tanh ^{-1}\left(\frac{\sqrt{1-a x}}{\sqrt{2}}\right)}{\sqrt{2} c \sqrt[4]{c-a^2 c x^2}}",1,"((1 - a^2*x^2)^(1/4)*(-1 + a*x*Hypergeometric2F1[-1/2, 1, 1/2, (1 - a*x)/2] + a*x*Hypergeometric2F1[-1/2, 1, 1/2, 1 - a*x]))/(c*x*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4))","C",0
1303,1,107,200,0.0721236,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Integrate[(E^(ArcTanh[a*x]/2)*x^3)/(c - a^2*c*x^2)^(9/8),x]","-\frac{4 \sqrt[8]{1-a^2 x^2} \left(5 \sqrt[8]{a x+1} \left(3 a^2 x^2+2 a x-12\right)+16 \sqrt[8]{2} (a x-1) \, _2F_1\left(\frac{5}{8},\frac{7}{8};\frac{13}{8};\frac{1}{2} (1-a x)\right)\right)}{105 a^4 c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}","-\frac{4 x^2 \sqrt[8]{a x+1} \sqrt[8]{1-a^2 x^2}}{7 a^2 c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}+\frac{64 \sqrt[8]{2} (1-a x)^{5/8} \sqrt[8]{1-a^2 x^2} \, _2F_1\left(\frac{5}{8},\frac{7}{8};\frac{13}{8};\frac{1}{2} (1-a x)\right)}{105 a^4 c \sqrt[8]{c-a^2 c x^2}}+\frac{8 (6-a x) \sqrt[8]{a x+1} \sqrt[8]{1-a^2 x^2}}{21 a^4 c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}",1,"(-4*(1 - a^2*x^2)^(1/8)*(5*(1 + a*x)^(1/8)*(-12 + 2*a*x + 3*a^2*x^2) + 16*2^(1/8)*(-1 + a*x)*Hypergeometric2F1[5/8, 7/8, 13/8, (1 - a*x)/2]))/(105*a^4*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8))","A",1
1304,1,63,41,0.0346108,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Integrate[(E^(ArcTanh[a*x]/2)*x^2)/(c - a^2*c*x^2)^(9/8),x]","-\frac{4 (a x-2) \sqrt[8]{a x+1} \sqrt[8]{1-a^2 x^2}}{3 a^3 c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}","\frac{4 (2-a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{3 a^3 c \sqrt[8]{c-a^2 c x^2}}",1,"(-4*(-2 + a*x)*(1 + a*x)^(1/8)*(1 - a^2*x^2)^(1/8))/(3*a^3*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8))","A",0
1305,1,93,133,0.0432842,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Integrate[(E^(ArcTanh[a*x]/2)*x)/(c - a^2*c*x^2)^(9/8),x]","-\frac{4 \sqrt[8]{1-a^2 x^2} \left(2 \sqrt[8]{2} (a x-1) \, _2F_1\left(\frac{5}{8},\frac{7}{8};\frac{13}{8};\frac{1}{2} (1-a x)\right)-5 \sqrt[8]{a x+1}\right)}{15 a^2 c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}","\frac{8 \sqrt[8]{2} (1-a x)^{5/8} \sqrt[8]{1-a^2 x^2} \, _2F_1\left(\frac{5}{8},\frac{7}{8};\frac{13}{8};\frac{1}{2} (1-a x)\right)}{15 a^2 c \sqrt[8]{c-a^2 c x^2}}+\frac{4 \sqrt[8]{a x+1} \sqrt[8]{1-a^2 x^2}}{3 a^2 c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}",1,"(-4*(1 - a^2*x^2)^(1/8)*(-5*(1 + a*x)^(1/8) + 2*2^(1/8)*(-1 + a*x)*Hypergeometric2F1[5/8, 7/8, 13/8, (1 - a*x)/2]))/(15*a^2*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8))","A",1
1306,1,69,74,0.0252878,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(9/8),x]","\frac{4 \sqrt[8]{2-2 a^2 x^2} \, _2F_1\left(-\frac{3}{8},\frac{7}{8};\frac{5}{8};\frac{1}{2} (1-a x)\right)}{3 a c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}","\frac{4 \sqrt[8]{2} \sqrt[8]{1-a^2 x^2} \, _2F_1\left(-\frac{3}{8},\frac{7}{8};\frac{5}{8};\frac{1}{2} (1-a x)\right)}{3 a c (1-a x)^{3/8} \sqrt[8]{c-a^2 c x^2}}",1,"(4*(2 - 2*a^2*x^2)^(1/8)*Hypergeometric2F1[-3/8, 7/8, 5/8, (1 - a*x)/2])/(3*a*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8))","A",1
1307,0,0,73,0.6225949,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{9/8}} \, dx","Integrate[E^(ArcTanh[a*x]/2)/(x*(c - a^2*c*x^2)^(9/8)),x]","\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{9/8}} \, dx","-\frac{2\ 2^{5/8} \sqrt[8]{a x+1} \sqrt[8]{1-a^2 x^2} F_1\left(\frac{1}{8};\frac{11}{8},1;\frac{9}{8};\frac{1}{2} (a x+1),a x+1\right)}{c \sqrt[8]{c-a^2 c x^2}}",1,"Integrate[E^(ArcTanh[a*x]/2)/(x*(c - a^2*c*x^2)^(9/8)), x]","F",-1
1308,1,65,68,0.0251291,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a^2*c*x^2),x]","\frac{c 2^{\frac{n}{2}+2} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-1,2-\frac{n}{2};3-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (n-4)}","-\frac{c 2^{\frac{n}{2}+2} (1-a x)^{2-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-1,2-\frac{n}{2};3-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (4-n)}",1,"(2^(2 + n/2)*c*(1 - a*x)^(2 - n/2)*Hypergeometric2F1[-1 - n/2, 2 - n/2, 3 - n/2, (1 - a*x)/2])/(a*(-4 + n))","A",1
1309,1,67,70,0.0245713,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","\frac{c^2 2^{\frac{n}{2}+3} (1-a x)^{3-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-2,3-\frac{n}{2};4-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (n-6)}","-\frac{c^2 2^{\frac{n}{2}+3} (1-a x)^{3-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-2,3-\frac{n}{2};4-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (6-n)}",1,"(2^(3 + n/2)*c^2*(1 - a*x)^(3 - n/2)*Hypergeometric2F1[-2 - n/2, 3 - n/2, 4 - n/2, (1 - a*x)/2])/(a*(-6 + n))","A",1
1310,1,67,70,0.0244714,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","\frac{c^3 2^{\frac{n}{2}+4} (1-a x)^{4-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-3,4-\frac{n}{2};5-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (n-8)}","-\frac{c^3 2^{\frac{n}{2}+4} (1-a x)^{4-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-3,4-\frac{n}{2};5-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a (8-n)}",1,"(2^(4 + n/2)*c^3*(1 - a*x)^(4 - n/2)*Hypergeometric2F1[-3 - n/2, 4 - n/2, 5 - n/2, (1 - a*x)/2])/(a*(-8 + n))","A",1
1311,1,172,209,0.2315244,"\int \frac{e^{n \tanh ^{-1}(a x)} x^4}{c-a^2 c x^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2),x]","\frac{(1-a x)^{-n/2} \left(2^{\frac{n}{2}+1} n \left(n^2-2 n+2\right) (a x-1) \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)-(n-2) \left((a x+1)^{n/2} \left(2 n \left(a^3 x^3+2 a x+3\right)+(a n x+n)^2-6\right)-2^{\frac{n}{2}+2} n (n+3) \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)\right)}{6 a^5 c (n-2) n}","\frac{2^{\frac{n}{2}-1} n \left(n^2+8\right) (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{3 a^5 c (2-n)}+\frac{(a x+1)^{n/2} \left(-a \left(n^2+6\right) n x+n^3+n^2+8 n+6\right) (1-a x)^{-n/2}}{6 a^5 c n}-\frac{n x^2 (a x+1)^{n/2} (1-a x)^{-n/2}}{6 a^3 c}-\frac{x^3 (a x+1)^{n/2} (1-a x)^{-n/2}}{3 a^2 c}",1,"(2^(1 + n/2)*n*(2 - 2*n + n^2)*(-1 + a*x)*Hypergeometric2F1[1 - n/2, -1/2*n, 2 - n/2, (1 - a*x)/2] - (-2 + n)*((1 + a*x)^(n/2)*(-6 + (n + a*n*x)^2 + 2*n*(3 + 2*a*x + a^3*x^3)) - 2^(2 + n/2)*n*(3 + n)*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a*x)/2]))/(6*a^5*c*(-2 + n)*n*(1 - a*x)^(n/2))","A",0
1312,1,120,160,0.0730675,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{c-a^2 c x^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2),x]","\frac{(1-a x)^{-n/2} \left(2^{n/2} n \left(n^2+2\right) (a x-1) \, _2F_1\left(1-\frac{n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)-(n-2) (a x+1)^{n/2} \left(n \left(a^2 x^2-1\right)+n^2 (a x-1)-2\right)\right)}{2 a^4 c (n-2) n}","\frac{2^{\frac{n}{2}-1} \left(n^2+2\right) (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a^4 c (2-n)}+\frac{(a x+1)^{n/2} \left(-a n^2 x+n^2+n+2\right) (1-a x)^{-n/2}}{2 a^4 c n}-\frac{x^2 (a x+1)^{n/2} (1-a x)^{-n/2}}{2 a^2 c}",1,"(-((-2 + n)*(1 + a*x)^(n/2)*(-2 + n^2*(-1 + a*x) + n*(-1 + a^2*x^2))) + 2^(n/2)*n*(2 + n^2)*(-1 + a*x)*Hypergeometric2F1[1 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2])/(2*a^4*c*(-2 + n)*n*(1 - a*x)^(n/2))","A",1
1313,1,82,86,0.0660169,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2),x]","\frac{(1-a x)^{-n/2} \left(2^{\frac{n}{2}+1} n \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)-(a x+1)^{n/2} (a n x+n-1)\right)}{a^3 c n}","\frac{2^{\frac{n}{2}+1} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a^3 c (2-n)}+\frac{e^{n \tanh ^{-1}(a x)}}{a^3 c n}",1,"(-((1 + a*x)^(n/2)*(-1 + n + a*n*x)) + 2^(1 + n/2)*n*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a*x)/2])/(a^3*c*n*(1 - a*x)^(n/2))","A",0
1314,1,74,94,0.0608397,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2),x]","\frac{(1-a x)^{-n/2} \left(2^{\frac{n}{2}+1} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)-(a x+1)^{n/2}\right)}{a^2 c n}","\frac{2^{\frac{n}{2}+1} (1-a x)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a^2 c n}-\frac{(1-a x)^{-n/2} (a x+1)^{n/2}}{a^2 c n}",1,"(-(1 + a*x)^(n/2) + 2^(1 + n/2)*Hypergeometric2F1[-1/2*n, -1/2*n, 1 - n/2, (1 - a*x)/2])/(a^2*c*n*(1 - a*x)^(n/2))","A",1
1315,1,33,18,0.0075016,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{(1-a x)^{-n/2} (a x+1)^{n/2}}{a c n}","\frac{e^{n \tanh ^{-1}(a x)}}{a c n}",1,"(1 + a*x)^(n/2)/(a*c*n*(1 - a*x)^(n/2))","A",0
1316,1,85,90,0.0390863,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)),x]","\frac{(1-a x)^{-n/2} (a x+1)^{\frac{n}{2}-1} \left((n-2) (a x+1)-2 n (a x-1) \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)\right)}{c (n-2) n}","\frac{(1-a x)^{-n/2} (a x+1)^{n/2}}{c n}-\frac{2 (1-a x)^{-n/2} (a x+1)^{n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a x+1}{1-a x}\right)}{c n}",1,"((1 + a*x)^(-1 + n/2)*((-2 + n)*(1 + a*x) - 2*n*(-1 + a*x)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)]))/(c*(-2 + n)*n*(1 - a*x)^(n/2))","A",0
1317,1,103,123,0.0577925,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)),x]","\frac{(1-a x)^{-n/2} (a x+1)^{\frac{n}{2}-1} \left((n-2) (a x+1) (n (a x-1)+a x)-2 a n^2 x (a x-1) \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)\right)}{c (n-2) n x}","-\frac{2 a (a x+1)^{n/2} (1-a x)^{-n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a x+1}{1-a x}\right)}{c}+\frac{a (n+1) (a x+1)^{n/2} (1-a x)^{-n/2}}{c n}-\frac{(a x+1)^{n/2} (1-a x)^{-n/2}}{c x}",1,"((1 + a*x)^(-1 + n/2)*((-2 + n)*(1 + a*x)*(a*x + n*(-1 + a*x)) - 2*a*n^2*x*(-1 + a*x)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)]))/(c*(-2 + n)*n*x*(1 - a*x)^(n/2))","A",0
1318,1,178,376,0.1717643,"\int \frac{e^{n \tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2)^2,x]","-\frac{(1-a x)^{-\frac{n}{2}-1} \left((a x+1)^{n/2} \left(n^2 \left(1-2 a^2 x^2\right)+6 a^2 x^2+n \left(-4 a^3 x^3+4 a^2 x^2+6 a x-4\right)+n^3 (a x-1)^2 (a x+1)-6\right)-2^{n/2} n^2 (n+2) (a x-1)^2 (a x+1) \, _2F_1\left(1-\frac{n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)\right)}{a^5 c^2 (n-2) n (n+2) (a x+1)}","-\frac{2^{n/2} n (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(\frac{2-n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a^5 c^2 (2-n)}-\frac{(n+3) \left(2-n^2\right) (a x+1)^{n/2} (1-a x)^{-\frac{n}{2}-1}}{a^5 c^2 \left(4-n^2\right)}-\frac{(n+3) \left(2-n^2\right) (a x+1)^{n/2} (1-a x)^{-n/2}}{a^5 c^2 n \left(4-n^2\right)}+\frac{(1-n) (n+3) (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^5 c^2 (2-n)}+\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}}}{a^5 c^2 (2-n)}-\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{-n/2}}{a^5 c^2}+\frac{(n+3) x (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^4 c^2}-\frac{x^3 (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^2 c^2}",1,"-(((1 - a*x)^(-1 - n/2)*((1 + a*x)^(n/2)*(-6 + 6*a^2*x^2 + n^3*(-1 + a*x)^2*(1 + a*x) + n^2*(1 - 2*a^2*x^2) + n*(-4 + 6*a*x + 4*a^2*x^2 - 4*a^3*x^3)) - 2^(n/2)*n^2*(2 + n)*(-1 + a*x)^2*(1 + a*x)*Hypergeometric2F1[1 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2]))/(a^5*c^2*(-2 + n)*n*(2 + n)*(1 + a*x)))","A",1
1319,1,145,311,5.3987455,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^2,x]","-\frac{e^{n \tanh ^{-1}(a x)} \left(-\left(n^2-4\right) \left(a^2 x^2-1\right) \, _2F_1\left(1,\frac{n}{2};\frac{n}{2}+1;-e^{2 \tanh ^{-1}(a x)}\right)+(n-2) n \left(a^2 x^2-1\right) e^{2 \tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n}{2}+1;\frac{n}{2}+2;-e^{2 \tanh ^{-1}(a x)}\right)+n \left(-a^2 x^2+a n x-1\right)\right)}{a^4 c^2 (n-2) n (n+2) \left(a^2 x^2-1\right)}","\frac{2^{\frac{n}{2}+2} (1-a x)^{-\frac{n}{2}-1} \, _2F_1\left(-\frac{n}{2}-1,-\frac{n}{2}-1;-\frac{n}{2};\frac{1}{2} (1-a x)\right)}{a^4 c^2 (n+2)}+\frac{2 (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}}}{a^4 c^2 n \left(4-n^2\right)}-\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^4 c^2 (n+2)}+\frac{3 (a x+1)^{n/2} (1-a x)^{-\frac{n}{2}-1}}{a^4 c^2 (n+2)}-\frac{3 (a x+1)^{\frac{n+2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^4 c^2 (n+2)}-\frac{2 (a x+1)^{\frac{n-2}{2}} (1-a x)^{-n/2}}{a^4 c^2 n (n+2)}+\frac{3 (a x+1)^{n/2} (1-a x)^{-n/2}}{a^4 c^2 n (n+2)}",1,"-((E^(n*ArcTanh[a*x])*(n*(-1 + a*n*x - a^2*x^2) + E^(2*ArcTanh[a*x])*(-2 + n)*n*(-1 + a^2*x^2)*Hypergeometric2F1[1, 1 + n/2, 2 + n/2, -E^(2*ArcTanh[a*x])] - (-4 + n^2)*(-1 + a^2*x^2)*Hypergeometric2F1[1, n/2, 1 + n/2, -E^(2*ArcTanh[a*x])]))/(a^4*c^2*(-2 + n)*n*(2 + n)*(-1 + a^2*x^2)))","A",0
1320,1,65,79,0.0562679,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^2,x]","-\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n}{2}-1} \left(-a^2 \left(n^2-2\right) x^2+2 a n x-2\right)}{a^3 c^2 n \left(n^2-4\right)}","-\frac{\left(2-n^2\right) e^{n \tanh ^{-1}(a x)}}{a^3 c^2 n \left(4-n^2\right)}-\frac{(n-2 a x) e^{n \tanh ^{-1}(a x)}}{a^3 c^2 \left(4-n^2\right) \left(1-a^2 x^2\right)}",1,"-(((1 - a*x)^(-1 - n/2)*(1 + a*x)^(-1 + n/2)*(-2 + 2*a*n*x - a^2*(-2 + n^2)*x^2))/(a^3*c^2*n*(-4 + n^2)))","A",0
1321,1,56,69,0.0363111,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^2,x]","-\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n}{2}-1} \left(a^2 x^2-a n x+1\right)}{a^2 c^2 \left(n^2-4\right)}","\frac{(2-a n x) e^{n \tanh ^{-1}(a x)}}{a^2 c^2 \left(4-n^2\right) \left(1-a^2 x^2\right)}-\frac{e^{n \tanh ^{-1}(a x)}}{a^2 c^2 \left(4-n^2\right)}",1,"-(((1 - a*x)^(-1 - n/2)*(1 + a*x)^(-1 + n/2)*(1 - a*n*x + a^2*x^2))/(a^2*c^2*(-4 + n^2)))","A",0
1322,1,68,72,0.0302147,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","-\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n}{2}-1} \left(-2 a^2 x^2+2 a n x-n^2+2\right)}{a c^2 (n-2) n (n+2)}","\frac{2 e^{n \tanh ^{-1}(a x)}}{a c^2 n \left(4-n^2\right)}-\frac{(n-2 a x) e^{n \tanh ^{-1}(a x)}}{a c^2 \left(4-n^2\right) \left(1-a^2 x^2\right)}",1,"-(((1 - a*x)^(-1 - n/2)*(1 + a*x)^(-1 + n/2)*(2 - n^2 + 2*a*n*x - 2*a^2*x^2))/(a*c^2*(-2 + n)*n*(2 + n)))","A",0
1323,1,121,190,0.0700892,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^2),x]","-\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n}{2}-1} \left(n^2 \left(a^2 x^2-a x-1\right)+a^2 n x^2-4 a^2 x^2-2 (n+2) n (a x-1)^2 \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)+n+4\right)}{c^2 n \left(n^2-4\right)}","-\frac{2 (a x+1)^{n/2} (1-a x)^{-n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a x+1}{1-a x}\right)}{c^2 n}-\frac{\left(-n^2-n+4\right) (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}}}{c^2 n \left(4-n^2\right)}+\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{c^2 (n+2)}+\frac{(n+4) (a x+1)^{\frac{n-2}{2}} (1-a x)^{-n/2}}{c^2 n (n+2)}",1,"-(((1 - a*x)^(-1 - n/2)*(1 + a*x)^(-1 + n/2)*(4 + n - 4*a^2*x^2 + a^2*n*x^2 + n^2*(-1 - a*x + a^2*x^2) - 2*n*(2 + n)*(-1 + a*x)^2*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)]))/(c^2*n*(-4 + n^2)))","A",0
1324,1,163,239,0.1004922,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^2} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^2),x]","-\frac{(1-a x)^{-\frac{n}{2}-1} (a x+1)^{\frac{n}{2}-1} \left(-6 a^3 x^3+a n^2 x \left(a^2 x^2-2\right)+n \left(-4 a^3 x^3+6 a^2 x^2+4 a x-4\right)-2 a (n+2) n^2 x (a x-1)^2 \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)+n^3 (a x-1)^2 (a x+1)+6 a x\right)}{c^2 (n-2) n (n+2) x}","-\frac{2 a (a x+1)^{n/2} (1-a x)^{-n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a x+1}{1-a x}\right)}{c^2}+\frac{a \left(n^2+4 n+6\right) (a x+1)^{\frac{n-2}{2}} (1-a x)^{-n/2}}{c^2 n (n+2)}-\frac{a \left(-n^3-n^2+4 n+6\right) (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}}}{c^2 n \left(4-n^2\right)}+\frac{a (n+3) (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{c^2 (n+2)}-\frac{(a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{c^2 x}",1,"-(((1 - a*x)^(-1 - n/2)*(1 + a*x)^(-1 + n/2)*(6*a*x - 6*a^3*x^3 + n^3*(-1 + a*x)^2*(1 + a*x) + a*n^2*x*(-2 + a^2*x^2) + n*(-4 + 4*a*x + 6*a^2*x^2 - 4*a^3*x^3) - 2*a*n^2*(2 + n)*x*(-1 + a*x)^2*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)]))/(c^2*(-2 + n)*n*(2 + n)*x))","A",0
1325,1,111,127,0.0760963,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","\frac{(1-a x)^{-\frac{n}{2}-2} (a x+1)^{\frac{n}{2}-2} \left(4 n^2 \left(3 a^2 x^2-4\right)-8 a n x \left(3 a^2 x^2-5\right)+24 \left(a^2 x^2-1\right)^2-4 a n^3 x+n^4\right)}{a c^3 (n-4) (n-2) n (n+2) (n+4)}","-\frac{(n-4 a x) e^{n \tanh ^{-1}(a x)}}{a c^3 \left(16-n^2\right) \left(1-a^2 x^2\right)^2}-\frac{12 (n-2 a x) e^{n \tanh ^{-1}(a x)}}{a c^3 \left(4-n^2\right) \left(16-n^2\right) \left(1-a^2 x^2\right)}+\frac{24 e^{n \tanh ^{-1}(a x)}}{a c^3 n \left(n^4-20 n^2+64\right)}",1,"((1 - a*x)^(-2 - n/2)*(1 + a*x)^(-2 + n/2)*(n^4 - 4*a*n^3*x + 24*(-1 + a^2*x^2)^2 - 8*a*n*x*(-5 + 3*a^2*x^2) + 4*n^2*(-4 + 3*a^2*x^2)))/(a*c^3*(-4 + n)*(-2 + n)*n*(2 + n)*(4 + n))","A",0
1326,1,170,197,0.1315014,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","-\frac{(1-a x)^{-\frac{n}{2}-3} (a x+1)^{\frac{n}{2}-3} \left(n^4 \left(50-30 a^2 x^2\right)+120 a n^3 x \left(a^2 x^2-2\right)-720 \left(a^2 x^2-1\right)^3-8 n^2 \left(45 a^4 x^4-105 a^2 x^2+68\right)+48 a n x \left(15 a^4 x^4-40 a^2 x^2+33\right)+6 a n^5 x-n^6\right)}{a c^4 (n-6) (n-4) (n-2) n (n+2) (n+4) (n+6)}","-\frac{(n-6 a x) e^{n \tanh ^{-1}(a x)}}{a c^4 \left(36-n^2\right) \left(1-a^2 x^2\right)^3}-\frac{360 (n-2 a x) e^{n \tanh ^{-1}(a x)}}{a c^4 \left(4-n^2\right) \left(16-n^2\right) \left(36-n^2\right) \left(1-a^2 x^2\right)}-\frac{30 (n-4 a x) e^{n \tanh ^{-1}(a x)}}{a c^4 \left(16-n^2\right) \left(36-n^2\right) \left(1-a^2 x^2\right)^2}+\frac{720 e^{n \tanh ^{-1}(a x)}}{a c^4 n \left(36-n^2\right) \left(n^4-20 n^2+64\right)}",1,"-(((1 - a*x)^(-3 - n/2)*(1 + a*x)^(-3 + n/2)*(-n^6 + 6*a*n^5*x + n^4*(50 - 30*a^2*x^2) + 120*a*n^3*x*(-2 + a^2*x^2) - 720*(-1 + a^2*x^2)^3 + 48*a*n*x*(33 - 40*a^2*x^2 + 15*a^4*x^4) - 8*n^2*(68 - 105*a^2*x^2 + 45*a^4*x^4)))/(a*c^4*(-6 + n)*(-4 + n)*(-2 + n)*n*(2 + n)*(4 + n)*(6 + n)))","A",0
1327,1,236,256,0.5571943,"\int e^{n \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(n*ArcTanh[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{c-a^2 c x^2} (1-a x)^{\frac{3}{2}-\frac{n}{2}} \left(a^2 (n-3) x^2 (a x+1)^{\frac{n+3}{2}}-2^{\frac{n+7}{2}} n \, _2F_1\left(\frac{1}{2} (-n-5),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)+2^{\frac{n+7}{2}} (n-1) \, _2F_1\left(\frac{1}{2} (-n-3),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)-2^{\frac{n+3}{2}} (n-2) \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)\right)}{5 a^4 (3-n) \sqrt{1-a^2 x^2}}","-\frac{x^2 \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+3}{2}} (1-a x)^{\frac{3-n}{2}}}{5 a^2 \sqrt{1-a^2 x^2}}-\frac{2^{\frac{n-1}{2}} n \left(n^2+11\right) \sqrt{c-a^2 c x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{15 a^4 (3-n) \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+3}{2}} \left(3 a n x+n^2+8\right) (1-a x)^{\frac{3-n}{2}}}{60 a^4 \sqrt{1-a^2 x^2}}",1,"((1 - a*x)^(3/2 - n/2)*Sqrt[c - a^2*c*x^2]*(a^2*(-3 + n)*x^2*(1 + a*x)^((3 + n)/2) - 2^((7 + n)/2)*n*Hypergeometric2F1[(-5 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2] + 2^((7 + n)/2)*(-1 + n)*Hypergeometric2F1[(-3 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2] - 2^((3 + n)/2)*(-2 + n)*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2]))/(5*a^4*(3 - n)*Sqrt[1 - a^2*x^2])","A",0
1328,1,135,244,0.2074554,"\int e^{n \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(n*ArcTanh[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{c-a^2 c x^2} (1-a x)^{\frac{3}{2}-\frac{n}{2}} \left(2^{\frac{n+3}{2}} \left(n^2+3\right) \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)-(n-3) (a x+1)^{\frac{n+3}{2}} (3 a x+n)\right)}{12 a^3 (n-3) \sqrt{1-a^2 x^2}}","-\frac{x \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+3}{2}} (1-a x)^{\frac{3-n}{2}}}{4 a^2 \sqrt{1-a^2 x^2}}-\frac{2^{\frac{n-1}{2}} \left(n^2+3\right) \sqrt{c-a^2 c x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{3 a^3 (3-n) \sqrt{1-a^2 x^2}}-\frac{n \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+3}{2}} (1-a x)^{\frac{3-n}{2}}}{12 a^3 \sqrt{1-a^2 x^2}}",1,"((1 - a*x)^(3/2 - n/2)*Sqrt[c - a^2*c*x^2]*(-((-3 + n)*(1 + a*x)^((3 + n)/2)*(n + 3*a*x)) + 2^((3 + n)/2)*(3 + n^2)*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2]))/(12*a^3*(-3 + n)*Sqrt[1 - a^2*x^2])","A",1
1329,1,125,173,0.1371291,"\int e^{n \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(n*ArcTanh[a*x])*x*Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{c-a^2 c x^2} (1-a x)^{\frac{3}{2}-\frac{n}{2}} \left(2^{\frac{n+3}{2}} n \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)-(n-3) (a x+1)^{\frac{n+3}{2}}\right)}{3 a^2 (n-3) \sqrt{1-a^2 x^2}}","-\frac{2^{\frac{n+3}{2}} n \sqrt{c-a^2 c x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{3 a^2 (3-n) \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+3}{2}} (1-a x)^{\frac{3-n}{2}}}{3 a^2 \sqrt{1-a^2 x^2}}",1,"((1 - a*x)^(3/2 - n/2)*Sqrt[c - a^2*c*x^2]*(-((-3 + n)*(1 + a*x)^((3 + n)/2)) + 2^((3 + n)/2)*n*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2]))/(3*a^2*(-3 + n)*Sqrt[1 - a^2*x^2])","A",1
1330,1,101,104,0.0547274,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Integrate[E^(n*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2],x]","\frac{2^{\frac{n+3}{2}} \sqrt{c-a^2 c x^2} (1-a x)^{\frac{3}{2}-\frac{n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{a (n-3) \sqrt{1-a^2 x^2}}","-\frac{2^{\frac{n+3}{2}} \sqrt{c-a^2 c x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{a (3-n) \sqrt{1-a^2 x^2}}",1,"(2^((3 + n)/2)*(1 - a*x)^(3/2 - n/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2])/(a*(-3 + n)*Sqrt[1 - a^2*x^2])","A",1
1331,1,207,269,0.1706169,"\int \frac{e^{n \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Integrate[(E^(n*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x,x]","\frac{2 \sqrt{c-a^2 c x^2} (1-a x)^{\frac{1}{2} (-n-1)} \left((n-1) (a x+1)^{\frac{n+1}{2}} \, _2F_1\left(1,-\frac{n}{2}-\frac{1}{2};\frac{1}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)+2^{\frac{n+1}{2}} \left((n+1) (a x-1) \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)-(n-1) \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},-\frac{n}{2}-\frac{1}{2};\frac{1}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)\right)\right)}{\left(n^2-1\right) \sqrt{1-a^2 x^2}}","\frac{2^{\frac{n+1}{2}} n \sqrt{c-a^2 c x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{\left(n^2-4 n+3\right) \sqrt{1-a^2 x^2}}+\frac{2 \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{(1-n) \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{3-n}{2}}}{(1-n) \sqrt{1-a^2 x^2}}",1,"(2*(1 - a*x)^((-1 - n)/2)*Sqrt[c - a^2*c*x^2]*((-1 + n)*(1 + a*x)^((1 + n)/2)*Hypergeometric2F1[1, -1/2 - n/2, 1/2 - n/2, (1 - a*x)/(1 + a*x)] + 2^((1 + n)/2)*(-((-1 + n)*Hypergeometric2F1[-1/2 - n/2, -1/2 - n/2, 1/2 - n/2, 1/2 - (a*x)/2]) + (1 + n)*(-1 + a*x)*Hypergeometric2F1[-1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2])))/((-1 + n^2)*Sqrt[1 - a^2*x^2])","A",0
1332,1,138,268,0.4705977,"\int \frac{e^{n \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^2,x]","-\frac{c \sqrt{1-a^2 x^2} e^{n \tanh ^{-1}(a x)} \left((n+1) \sqrt{1-a^2 x^2}+2 a x e^{\tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-e^{2 \tanh ^{-1}(a x)}\right)+2 a n x e^{\tanh ^{-1}(a x)} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};e^{2 \tanh ^{-1}(a x)}\right)\right)}{(n+1) x \sqrt{c-a^2 c x^2}}","-\frac{2 a n \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{1-a x}{a x+1}\right)}{(1-n) \sqrt{1-a^2 x^2}}+\frac{a 2^{\frac{n+1}{2}} \sqrt{c-a^2 c x^2} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{1-n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{(1-n) \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{x \sqrt{1-a^2 x^2}}",1,"-((c*E^(n*ArcTanh[a*x])*Sqrt[1 - a^2*x^2]*((1 + n)*Sqrt[1 - a^2*x^2] + 2*a*E^ArcTanh[a*x]*x*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -E^(2*ArcTanh[a*x])] + 2*a*E^ArcTanh[a*x]*n*x*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, E^(2*ArcTanh[a*x])]))/((1 + n)*x*Sqrt[c - a^2*c*x^2]))","A",0
1333,1,102,105,0.0867951,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2),x]","\frac{c 2^{\frac{n+5}{2}} \sqrt{c-a^2 c x^2} (1-a x)^{\frac{5}{2}-\frac{n}{2}} \, _2F_1\left(-\frac{n}{2}-\frac{3}{2},\frac{5}{2}-\frac{n}{2};\frac{7}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (n-5) \sqrt{1-a^2 x^2}}","-\frac{c 2^{\frac{n+5}{2}} \sqrt{c-a^2 c x^2} (1-a x)^{\frac{5-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-3),\frac{5-n}{2};\frac{7-n}{2};\frac{1}{2} (1-a x)\right)}{a (5-n) \sqrt{1-a^2 x^2}}",1,"(2^((5 + n)/2)*c*(1 - a*x)^(5/2 - n/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-3/2 - n/2, 5/2 - n/2, 7/2 - n/2, 1/2 - (a*x)/2])/(a*(-5 + n)*Sqrt[1 - a^2*x^2])","A",1
1334,1,187,275,0.2914082,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^3)/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} \left(2^{\frac{n}{2}+1} n \left(n^2+5\right) (a x-1) \, _2F_1\left(\frac{1}{2}-\frac{n}{2},\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)-\sqrt{2} (n-3) (a x+1)^{\frac{n+1}{2}} \left(n \left(2 a^2 x^2-a x-1\right)-2 \left(a^2 x^2+2\right)+n^2 (a x-1)\right)\right)}{6 \sqrt{2} a^4 (n-3) (n-1) \sqrt{c-a^2 c x^2}}","-\frac{x^2 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{3 a^2 \sqrt{c-a^2 c x^2}}-\frac{2^{\frac{n-1}{2}} n \left(n^2+5\right) \sqrt{1-a^2 x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{3 a^4 (1-n) (3-n) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} \left(a (1-n) n x+n^2+n+4\right) (1-a x)^{\frac{1-n}{2}}}{6 a^4 (1-n) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(1/2 - n/2)*Sqrt[1 - a^2*x^2]*(-(Sqrt[2]*(-3 + n)*(1 + a*x)^((1 + n)/2)*(n^2*(-1 + a*x) - 2*(2 + a^2*x^2) + n*(-1 - a*x + 2*a^2*x^2))) + 2^(1 + n/2)*n*(5 + n^2)*(-1 + a*x)*Hypergeometric2F1[1/2 - n/2, 3/2 - n/2, 5/2 - n/2, 1/2 - (a*x)/2]))/(6*Sqrt[2]*a^4*(-3 + n)*(-1 + n)*Sqrt[c - a^2*c*x^2])","A",1
1335,1,141,253,0.1847268,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^2)/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} \left(2^{\frac{n+3}{2}} \left(n^2+1\right) \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)-(n-1) (a x+1)^{\frac{n+1}{2}} (a n x+a x+n-1)\right)}{2 a^3 \left(n^2-1\right) \sqrt{c-a^2 c x^2}}","-\frac{x \sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{2 a^2 \sqrt{c-a^2 c x^2}}-\frac{2^{\frac{n+1}{2}} \left(n^2+1\right) \sqrt{1-a^2 x^2} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{1-n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a^3 \left(1-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{(1-n) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{2 a^3 (n+1) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(1/2 - n/2)*Sqrt[1 - a^2*x^2]*(-((-1 + n)*(1 + a*x)^((1 + n)/2)*(-1 + n + a*x + a*n*x)) + 2^((3 + n)/2)*(1 + n^2)*Hypergeometric2F1[-1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2]))/(2*a^3*(-1 + n^2)*Sqrt[c - a^2*c*x^2])","A",1
1336,1,124,176,0.1036592,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x)/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} \left(2^{\frac{n+3}{2}} n \, _2F_1\left(-\frac{n}{2}-\frac{1}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)-(n-1) (a x+1)^{\frac{n+1}{2}}\right)}{a^2 \left(n^2-1\right) \sqrt{c-a^2 c x^2}}","-\frac{2^{\frac{n+3}{2}} n \sqrt{1-a^2 x^2} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{1-n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a^2 \left(1-n^2\right) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{a^2 (n+1) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(1/2 - n/2)*Sqrt[1 - a^2*x^2]*(-((-1 + n)*(1 + a*x)^((1 + n)/2)) + 2^((3 + n)/2)*n*Hypergeometric2F1[-1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2]))/(a^2*(-1 + n^2)*Sqrt[c - a^2*c*x^2])","A",1
1337,1,101,104,0.0387577,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/Sqrt[c - a^2*c*x^2],x]","\frac{2^{\frac{n+1}{2}} \sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} \, _2F_1\left(\frac{1}{2}-\frac{n}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{a (n-1) \sqrt{c-a^2 c x^2}}","-\frac{2^{\frac{n+1}{2}} \sqrt{1-a^2 x^2} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{1-n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a (1-n) \sqrt{c-a^2 c x^2}}",1,"(2^((1 + n)/2)*(1 - a*x)^(1/2 - n/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2])/(a*(-1 + n)*Sqrt[c - a^2*c*x^2])","A",1
1338,1,99,101,0.0535408,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x*Sqrt[c - a^2*c*x^2]),x]","\frac{2 \sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} (a x+1)^{\frac{n-1}{2}} \, _2F_1\left(1,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{(n-1) \sqrt{c-a^2 c x^2}}","-\frac{2 \sqrt{1-a^2 x^2} (1-a x)^{\frac{1-n}{2}} (a x+1)^{\frac{n-1}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{1-a x}{a x+1}\right)}{(1-n) \sqrt{c-a^2 c x^2}}",1,"(2*(1 - a*x)^(1/2 - n/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, 1/2 - n/2, 3/2 - n/2, (1 - a*x)/(1 + a*x)])/((-1 + n)*Sqrt[c - a^2*c*x^2])","A",1
1339,1,117,167,0.0783185,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^2*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} (a x+1)^{\frac{n-1}{2}} \left(2 a n x \, _2F_1\left(1,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-1) (a x+1)\right)}{(n-1) x \sqrt{c-a^2 c x^2}}","-\frac{2 a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{1-a x}{a x+1}\right)}{(1-n) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{x \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(1/2 - n/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2]*(-((-1 + n)*(1 + a*x)) + 2*a*n*x*Hypergeometric2F1[1, 1/2 - n/2, 3/2 - n/2, (1 - a*x)/(1 + a*x)]))/((-1 + n)*x*Sqrt[c - a^2*c*x^2])","A",1
1340,1,134,242,0.1355114,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3 \sqrt{c-a^2 c x^2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^3*Sqrt[c - a^2*c*x^2]),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2}-\frac{n}{2}} (a x+1)^{\frac{n-1}{2}} \left(2 a^2 \left(n^2+1\right) x^2 \, _2F_1\left(1,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-1) (a x+1) (a n x+1)\right)}{2 (n-1) x^2 \sqrt{c-a^2 c x^2}}","-\frac{a^2 \left(n^2+1\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{1-a x}{a x+1}\right)}{(1-n) \sqrt{c-a^2 c x^2}}-\frac{a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{2 x \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1-n}{2}}}{2 x^2 \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(1/2 - n/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2]*(-((-1 + n)*(1 + a*x)*(1 + a*n*x)) + 2*a^2*(1 + n^2)*x^2*Hypergeometric2F1[1, 1/2 - n/2, 3/2 - n/2, (1 - a*x)/(1 + a*x)]))/(2*(-1 + n)*x^2*Sqrt[c - a^2*c*x^2])","A",1
1341,1,186,270,0.2932569,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{-\frac{n}{2}-\frac{1}{2}} \left(-4 a^4 x^2 (a x+1)^{\frac{n-1}{2}}+\frac{a^2 2^{\frac{n+3}{2}} n (a x-1)^2 \, _2F_1\left(\frac{3}{2}-\frac{n}{2},\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)}{n-3}+\frac{4 a^2 \left(n^2 (2 a x-1)+n (3 a x-2)-2\right) (a x+1)^{\frac{n-1}{2}}}{n^2-1}\right)}{4 a^6 c \sqrt{c-a^2 c x^2}}","-\frac{x^2 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{a^2 c \sqrt{c-a^2 c x^2}}-\frac{2^{\frac{n-1}{2}} n \sqrt{1-a^2 x^2} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(\frac{3-n}{2},\frac{3-n}{2};\frac{5-n}{2};\frac{1}{2} (1-a x)\right)}{a^4 c (3-n) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} \left(-a (2 n+3) n x+n^2+2 n+2\right) (1-a x)^{\frac{1}{2} (-n-1)}}{a^4 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(-1/2 - n/2)*Sqrt[1 - a^2*x^2]*(-4*a^4*x^2*(1 + a*x)^((-1 + n)/2) + (4*a^2*(1 + a*x)^((-1 + n)/2)*(-2 + n^2*(-1 + 2*a*x) + n*(-2 + 3*a*x)))/(-1 + n^2) + (2^((3 + n)/2)*a^2*n*(-1 + a*x)^2*Hypergeometric2F1[3/2 - n/2, 3/2 - n/2, 5/2 - n/2, 1/2 - (a*x)/2])/(-3 + n)))/(4*a^6*c*Sqrt[c - a^2*c*x^2])","A",1
1342,1,155,153,0.2758941,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{-\frac{n}{2}-\frac{1}{2}} \left(2^{\frac{n+1}{2}} (n+1) (a x-1) \sqrt{a x+1} \, _2F_1\left(\frac{1}{2}-\frac{n}{2},\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};\frac{1}{2}-\frac{a x}{2}\right)+(n-a x) (a x+1)^{n/2}\right)}{a^3 c (n-1) (n+1) \sqrt{a x+1} \sqrt{c-a^2 c x^2}}","\frac{2^{\frac{n+1}{2}} \sqrt{1-a^2 x^2} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{1-n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a^3 c (1-n) \sqrt{c-a^2 c x^2}}-\frac{(n-a x) e^{n \tanh ^{-1}(a x)}}{a^3 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(-1/2 - n/2)*Sqrt[1 - a^2*x^2]*((n - a*x)*(1 + a*x)^(n/2) + 2^((1 + n)/2)*(1 + n)*(-1 + a*x)*Sqrt[1 + a*x]*Hypergeometric2F1[1/2 - n/2, 1/2 - n/2, 3/2 - n/2, 1/2 - (a*x)/2]))/(a^3*c*(-1 + n)*(1 + n)*Sqrt[1 + a*x]*Sqrt[c - a^2*c*x^2])","A",0
1343,1,81,46,0.0625309,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{-\frac{n}{2}-\frac{1}{2}} (a x+1)^{\frac{n-1}{2}} (a n x-1)}{a^2 c (n-1) (n+1) \sqrt{c-a^2 c x^2}}","\frac{(1-a n x) e^{n \tanh ^{-1}(a x)}}{a^2 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^(-1/2 - n/2)*(1 + a*x)^((-1 + n)/2)*(-1 + a*n*x)*Sqrt[1 - a^2*x^2])/(a^2*c*(-1 + n)*(1 + n)*Sqrt[c - a^2*c*x^2])","A",0
1344,1,81,46,0.0550696,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-1)} (n-a x) (a x+1)^{\frac{n-1}{2}}}{a c (n-1) (n+1) \sqrt{c-a^2 c x^2}}","-\frac{(n-a x) e^{n \tanh ^{-1}(a x)}}{a c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^((-1 - n)/2)*(n - a*x)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(a*c*(-1 + n)*(1 + n)*Sqrt[c - a^2*c*x^2])","A",0
1345,1,149,243,0.1636886,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-1)} (a x+1)^{\frac{n-3}{2}} \left(2 \left(n^2-1\right) (a x-1)^2 \, _2F_1\left(1,\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-3) (a x+1) (n (a x-2)+2 a x-1)\right)}{c (n-3) (n-1) (n+1) \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{c (1-n) \sqrt{c-a^2 c x^2}}-\frac{(n+2) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}}}{c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{c (n+1) \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(-((-3 + n)*(1 + a*x)*(-1 + 2*a*x + n*(-2 + a*x))) + 2*(-1 + n^2)*(-1 + a*x)^2*Hypergeometric2F1[1, 3/2 - n/2, 5/2 - n/2, (1 - a*x)/(1 + a*x)]))/(c*(-3 + n)*(-1 + n)*(1 + n)*Sqrt[c - a^2*c*x^2])","A",0
1346,1,173,321,0.1954671,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-1)} (a x+1)^{\frac{n-3}{2}} \left(2 a n \left(n^2-1\right) x (a x-1)^2 \, _2F_1\left(1,\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-3) (a x+1) \left(2 a^2 x^2+n^2 (a x-1)^2+a n x (2 a x-3)-1\right)\right)}{c (n-3) (n-1) (n+1) x \sqrt{c-a^2 c x^2}}","\frac{2 a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{c (1-n) \sqrt{c-a^2 c x^2}}-\frac{a \left(n^2+2 n+2\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}}}{c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{a (n+2) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{c (n+1) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{c x \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(-((-3 + n)*(1 + a*x)*(-1 + 2*a^2*x^2 + n^2*(-1 + a*x)^2 + a*n*x*(-3 + 2*a*x))) + 2*a*n*(-1 + n^2)*x*(-1 + a*x)^2*Hypergeometric2F1[1, 3/2 - n/2, 5/2 - n/2, (1 - a*x)/(1 + a*x)]))/(c*(-3 + n)*(-1 + n)*(1 + n)*x*Sqrt[c - a^2*c*x^2])","A",0
1347,1,219,417,0.2544311,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^(3/2)),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-1)} (a x+1)^{\frac{n-3}{2}} \left(2 a^2 \left(n^4+2 n^2-3\right) x^2 (a x-1)^2 \, _2F_1\left(1,\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)-(n-3) (a x+1) \left(6 a^3 x^3+a n x \left(5 a^2 x^2-6 a x-1\right)-3 a^2 x^2+a n^3 x (a x-1)^2+n^2 (a x-1)^2 (2 a x+1)-1\right)\right)}{2 c (n-3) (n-1) (n+1) x^2 \sqrt{c-a^2 c x^2}}","\frac{a^2 \left(n^2+3\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{c (1-n) \sqrt{c-a^2 c x^2}}+\frac{a^2 \left(n^2+2 n+3\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{2 c (n+1) \sqrt{c-a^2 c x^2}}-\frac{a^2 \left(n^3+2 n^2+5 n+6\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}}}{2 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}-\frac{a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{2 c x \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{2 c x^2 \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(-((-3 + n)*(1 + a*x)*(-1 - 3*a^2*x^2 + 6*a^3*x^3 + a*n^3*x*(-1 + a*x)^2 + n^2*(-1 + a*x)^2*(1 + 2*a*x) + a*n*x*(-1 - 6*a*x + 5*a^2*x^2))) + 2*a^2*(-3 + 2*n^2 + n^4)*x^2*(-1 + a*x)^2*Hypergeometric2F1[1, 3/2 - n/2, 5/2 - n/2, (1 - a*x)/(1 + a*x)]))/(2*c*(-3 + n)*(-1 + n)*(1 + n)*x^2*Sqrt[c - a^2*c*x^2])","A",0
1348,1,112,407,0.2179684,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^(5/2),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(-a^3 n \left(n^2-7\right) x^3+3 a^2 \left(n^2-3\right) x^2-6 a n x+6\right)}{a^4 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}","\frac{x^3 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{a c^2 (n+3) \sqrt{c-a^2 c x^2}}-\frac{3 (2-n) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{a^4 c^2 \left(9-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{3 \left(-n^2+2 n+1\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{a^4 c^2 (3-n) (n+1) (n+3) \sqrt{c-a^2 c x^2}}-\frac{3 \left(-n^2+2 n+1\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}}}{a^4 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}-\frac{3 x \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{a^3 c^2 (n+3) \sqrt{c-a^2 c x^2}}",1,"-(((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(6 - 6*a*n*x + 3*a^2*(-3 + n^2)*x^2 - a^3*n*(-7 + n^2)*x^3))/(a^4*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2]))","A",1
1349,1,125,102,0.2185257,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(5/2),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(-3 a^3 x^3-a^2 n^3 x^2+a n^2 x \left(a^2 x^2+2\right)+n \left(3 a^2 x^2-2\right)\right)}{a^3 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}","\frac{\left(3-n^2\right) (n-a x) e^{n \tanh ^{-1}(a x)}}{a^3 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}-\frac{(n-3 a x) e^{n \tanh ^{-1}(a x)}}{a^3 c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}",1,"-(((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(-(a^2*n^3*x^2) - 3*a^3*x^3 + a*n^2*x*(2 + a^2*x^2) + n*(-2 + 3*a^2*x^2)))/(a^3*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2]))","A",0
1350,1,114,133,0.1928333,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^(5/2),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(-n^2 \left(2 a^2 x^2+1\right)+a n x \left(2 a^2 x^2-3\right)+a n^3 x+3\right)}{a^2 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}","\frac{2 n (n-a x) e^{n \tanh ^{-1}(a x)}}{a^2 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}+\frac{n (n-3 a x) e^{n \tanh ^{-1}(a x)}}{3 a^2 c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}+\frac{e^{n \tanh ^{-1}(a x)}}{3 a^2 c \left(c-a^2 c x^2\right)^{3/2}}",1,"((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(3 + a*n^3*x + a*n*x*(-3 + 2*a^2*x^2) - n^2*(1 + 2*a^2*x^2)))/(a^2*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2])","A",0
1351,1,123,102,0.1613875,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^(5/2),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(6 a^3 x^3+n \left(7-6 a^2 x^2\right)+3 a n^2 x-9 a x-n^3\right)}{a c^2 (n-3) (n-1) (n+1) (n+3) \sqrt{c-a^2 c x^2}}","-\frac{6 (n-a x) e^{n \tanh ^{-1}(a x)}}{a c^2 \left(1-n^2\right) \left(9-n^2\right) \sqrt{c-a^2 c x^2}}-\frac{(n-3 a x) e^{n \tanh ^{-1}(a x)}}{a c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}",1,"-(((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(-n^3 - 9*a*x + 3*a*n^2*x + 6*a^3*x^3 + n*(7 - 6*a^2*x^2)))/(a*c^2*(-3 + n)*(-1 + n)*(1 + n)*(3 + n)*Sqrt[c - a^2*c*x^2]))","A",0
1352,1,222,417,0.3025169,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^(5/2)),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(a n^2 x \left(-2 a^2 x^2+3 a x+2\right)-\left(n^3 \left(a^3 x^3-2 a^2 x^2+2\right)\right)+n \left(7 a^3 x^3-18 a^2 x^2-6 a x+18\right)+3 \left(6 a^3 x^3-3 a^2 x^2-6 a x+2\right)+2 \left(n^3+3 n^2-n-3\right) (a x-1)^3 \, _2F_1\left(1,\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)\right)}{c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{c^2 (1-n) \sqrt{c-a^2 c x^2}}-\frac{\left(n^2+6 n+15\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1-n}{2}}}{c^2 (n+3) \left(1-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{\left(-n^3-2 n^2+7 n+18\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}}}{c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{c^2 (n+3) \sqrt{c-a^2 c x^2}}+\frac{(n+6) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{c^2 (n+1) (n+3) \sqrt{c-a^2 c x^2}}",1,"-(((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(a*n^2*x*(2 + 3*a*x - 2*a^2*x^2) - n^3*(2 - 2*a^2*x^2 + a^3*x^3) + 3*(2 - 6*a*x - 3*a^2*x^2 + 6*a^3*x^3) + n*(18 - 6*a*x - 18*a^2*x^2 + 7*a^3*x^3) + 2*(-3 - n + 3*n^2 + n^3)*(-1 + a*x)^3*Hypergeometric2F1[1, 3/2 - n/2, 5/2 - n/2, (1 - a*x)/(1 + a*x)]))/(c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2]))","A",0
1353,1,268,507,0.3618822,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^(5/2)),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(24 a^4 x^4-36 a^2 x^2+a n^3 x \left(-2 a^3 x^3+3 a^2 x^2+2 a x-4\right)+a n x \left(18 a^3 x^3-33 a^2 x^2-18 a x+34\right)+n^2 \left(7 a^4 x^4-18 a^3 x^3+6 a^2 x^2+18 a x-10\right)+2 a \left(n^3+3 n^2-n-3\right) n x (a x-1)^3 \, _2F_1\left(1,\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)+n^4 \left(-(a x-1)^3\right) (a x+1)+9\right)}{c^2 (n-3) (n-1) (n+1) (n+3) x \sqrt{c-a^2 c x^2}}","\frac{2 a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{c^2 (1-n) \sqrt{c-a^2 c x^2}}+\frac{a \left(n^2+6 n+12\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{c^2 (n+1) (n+3) \sqrt{c-a^2 c x^2}}-\frac{a \left(n^3+6 n^2+15 n+24\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1-n}{2}}}{c^2 (n+3) \left(1-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{a \left(-n^4-2 n^3+7 n^2+18 n+24\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}}}{c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}+\frac{a (n+4) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{c^2 (n+3) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{c^2 x \sqrt{c-a^2 c x^2}}",1,"-(((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*(9 - 36*a^2*x^2 + 24*a^4*x^4 - n^4*(-1 + a*x)^3*(1 + a*x) + a*n^3*x*(-4 + 2*a*x + 3*a^2*x^2 - 2*a^3*x^3) + a*n*x*(34 - 18*a*x - 33*a^2*x^2 + 18*a^3*x^3) + n^2*(-10 + 18*a*x + 6*a^2*x^2 - 18*a^3*x^3 + 7*a^4*x^4) + 2*a*n*(-3 - n + 3*n^2 + n^3)*x*(-1 + a*x)^3*Hypergeometric2F1[1, 3/2 - n/2, 5/2 - n/2, (1 - a*x)/(1 + a*x)]))/(c^2*(-3 + n)*(-1 + n)*(1 + n)*(3 + n)*x*Sqrt[c - a^2*c*x^2]))","A",0
1354,1,267,623,0.8332077,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^(5/2)),x]","\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-3)} (a x+1)^{\frac{n-3}{2}} \left(-\frac{a^2 (1-a x) \left(-(a x-1)^2 \left(2 \left(n^6-5 n^4-41 n^2+45\right) \, _2F_1\left(1,\frac{3}{2}-\frac{n}{2};\frac{5}{2}-\frac{n}{2};\frac{1-a x}{a x+1}\right)-n^6+n^5+8 n^4+2 n^3+35 n^2-87 n-270\right)+\left(n^4+6 n^3+20 n^2+54 n+75\right) (n-3)^2 (a x-1)-\left((n-1) \left(n^3+6 n^2+17 n+30\right) (n-3)^2\right)\right)}{(n-3)^2 (n-1) (n+1) (n+3)}+\frac{a^2 \left(n^2+4 n+5\right)}{n+3}-\frac{a n}{x}-\frac{1}{x^2}\right)}{2 c^2 \sqrt{c-a^2 c x^2}}","\frac{a^2 \left(n^2+5\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-1}{2}} (1-a x)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a x+1}{1-a x}\right)}{c^2 (1-n) \sqrt{c-a^2 c x^2}}+\frac{a^2 \left(n^2+4 n+5\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{2 c^2 (n+3) \sqrt{c-a^2 c x^2}}+\frac{a^2 \left(n^3+6 n^2+17 n+30\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-1)}}{2 c^2 (n+1) (n+3) \sqrt{c-a^2 c x^2}}-\frac{a^2 \left(n^4+6 n^3+20 n^2+54 n+75\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1-n}{2}}}{2 c^2 (n+3) \left(1-n^2\right) \sqrt{c-a^2 c x^2}}+\frac{a^2 \left(-n^5-2 n^4+2 n^3+8 n^2+59 n+90\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}}}{2 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}-\frac{a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{2 c^2 x \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{1}{2} (-n-3)}}{2 c^2 x^2 \sqrt{c-a^2 c x^2}}",1,"((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*((a^2*(5 + 4*n + n^2))/(3 + n) - x^(-2) - (a*n)/x - (a^2*(1 - a*x)*(-((-3 + n)^2*(-1 + n)*(30 + 17*n + 6*n^2 + n^3)) + (-3 + n)^2*(75 + 54*n + 20*n^2 + 6*n^3 + n^4)*(-1 + a*x) - (-1 + a*x)^2*(-270 - 87*n + 35*n^2 + 2*n^3 + 8*n^4 + n^5 - n^6 + 2*(45 - 41*n^2 - 5*n^4 + n^6)*Hypergeometric2F1[1, 3/2 - n/2, 5/2 - n/2, (1 - a*x)/(1 + a*x)])))/((-3 + n)^2*(-1 + n)*(1 + n)*(3 + n))))/(2*c^2*Sqrt[c - a^2*c*x^2])","A",0
1355,1,182,166,0.2603945,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Integrate[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^(7/2),x]","-\frac{\sqrt{1-a^2 x^2} (1-a x)^{\frac{1}{2} (-n-5)} (a x+1)^{\frac{n-5}{2}} \left(n^3 \left(30-20 a^2 x^2\right)+10 a n^2 x \left(6 a^2 x^2-11\right)+n \left(-120 a^4 x^4+260 a^2 x^2-149\right)+15 a x \left(8 a^4 x^4-20 a^2 x^2+15\right)+5 a n^4 x-n^5\right)}{a c^3 (n-5) (n-3) (n-1) (n+1) (n+3) (n+5) \sqrt{c-a^2 c x^2}}","-\frac{120 (n-a x) e^{n \tanh ^{-1}(a x)}}{a c^3 \left(1-n^2\right) \left(9-n^2\right) \left(25-n^2\right) \sqrt{c-a^2 c x^2}}-\frac{20 (n-3 a x) e^{n \tanh ^{-1}(a x)}}{a c^2 \left(9-n^2\right) \left(25-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}-\frac{(n-5 a x) e^{n \tanh ^{-1}(a x)}}{a c \left(25-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}",1,"-(((1 - a*x)^((-5 - n)/2)*(1 + a*x)^((-5 + n)/2)*Sqrt[1 - a^2*x^2]*(-n^5 + 5*a*n^4*x + n^3*(30 - 20*a^2*x^2) + 10*a*n^2*x*(-11 + 6*a^2*x^2) + n*(-149 + 260*a^2*x^2 - 120*a^4*x^4) + 15*a*x*(15 - 20*a^2*x^2 + 8*a^4*x^4)))/(a*c^3*(-5 + n)*(-3 + n)*(-1 + n)*(1 + n)*(3 + n)*(5 + n)*Sqrt[c - a^2*c*x^2]))","A",0
1356,0,0,42,0.3635307,"\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","Integrate[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^2,x]","\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","\frac{c^2 x^{m+1} F_1\left(m+1;\frac{n-4}{2},-\frac{n}{2}-2;m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^2, x]","F",-1
1357,0,0,40,0.3174591,"\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","Integrate[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2),x]","\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","\frac{c x^{m+1} F_1\left(m+1;\frac{n-2}{2},-\frac{n}{2}-1;m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2), x]","F",-1
1358,1,106,42,0.2378704,"\int \frac{e^{n \tanh ^{-1}(a x)} x^m}{c-a^2 c x^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2),x]","\frac{x^m \left(e^{-2 \tanh ^{-1}(a x)}-1\right)^m \left(e^{-2 \tanh ^{-1}(a x)}+1\right)^m \left(-e^{-4 \tanh ^{-1}(a x)} \left(e^{2 \tanh ^{-1}(a x)}-1\right)^2\right)^{-m} e^{n \tanh ^{-1}(a x)} F_1\left(-\frac{n}{2};m,-m;1-\frac{n}{2};-e^{-2 \tanh ^{-1}(a x)},e^{-2 \tanh ^{-1}(a x)}\right)}{a c n}","\frac{x^{m+1} F_1\left(m+1;\frac{n+2}{2},1-\frac{n}{2};m+2;a x,-a x\right)}{c (m+1)}",1,"(E^(n*ArcTanh[a*x])*(-1 + E^(-2*ArcTanh[a*x]))^m*(1 + E^(-2*ArcTanh[a*x]))^m*x^m*AppellF1[-1/2*n, m, -m, 1 - n/2, -E^(-2*ArcTanh[a*x]), E^(-2*ArcTanh[a*x])])/(a*c*(-((-1 + E^(2*ArcTanh[a*x]))^2/E^(4*ArcTanh[a*x])))^m*n)","B",0
1359,0,0,42,0.5337035,"\int \frac{e^{n \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","Integrate[(E^(n*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^2,x]","\int \frac{e^{n \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","\frac{x^{m+1} F_1\left(m+1;\frac{n+4}{2},2-\frac{n}{2};m+2;a x,-a x\right)}{c^2 (m+1)}",1,"Integrate[(E^(n*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^2, x]","F",-1
1360,0,0,70,0.5764057,"\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^p,x]","\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","\frac{x^{m+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p F_1\left(m+1;\frac{1}{2} (n-2 p),-\frac{n}{2}-p;m+2;a x,-a x\right)}{m+1}",1,"Integrate[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^p, x]","F",-1
1361,1,136,177,0.123666,"\int e^{n \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(n*ArcTanh[a*x])*x*(c - a^2*c*x^2)^p,x]","-\frac{\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p (1-a x)^{-\frac{n}{2}+p+1} \left(n 2^{\frac{n}{2}+p+1} \, _2F_1\left(-\frac{n}{2}-p,-\frac{n}{2}+p+1;-\frac{n}{2}+p+2;\frac{1}{2} (1-a x)\right)-(n-2 (p+1)) (a x+1)^{\frac{n}{2}+p+1}\right)}{2 a^2 (p+1) (-n+2 p+2)}","-\frac{n 2^{\frac{n}{2}+p} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p (1-a x)^{-\frac{n}{2}+p+1} \, _2F_1\left(-\frac{n}{2}-p,-\frac{n}{2}+p+1;-\frac{n}{2}+p+2;\frac{1}{2} (1-a x)\right)}{a^2 (p+1) (-n+2 p+2)}-\frac{\left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p (1-a x)^{-\frac{n}{2}+p+1} (a x+1)^{\frac{n}{2}+p+1}}{2 a^2 (p+1)}",1,"-1/2*((1 - a*x)^(1 - n/2 + p)*(c - a^2*c*x^2)^p*(-((n - 2*(1 + p))*(1 + a*x)^(1 + n/2 + p)) + 2^(1 + n/2 + p)*n*Hypergeometric2F1[-1/2*n - p, 1 - n/2 + p, 2 - n/2 + p, (1 - a*x)/2]))/(a^2*(1 + p)*(2 - n + 2*p)*(1 - a^2*x^2)^p)","A",1
1362,1,102,103,0.0364889,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(n*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","-\frac{2^{\frac{n}{2}+p} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p (1-a x)^{-\frac{n}{2}+p+1} \, _2F_1\left(-\frac{n}{2}-p,-\frac{n}{2}+p+1;-\frac{n}{2}+p+2;\frac{1}{2} (1-a x)\right)}{a \left(-\frac{n}{2}+p+1\right)}","-\frac{2^{\frac{n}{2}+p+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p (1-a x)^{-\frac{n}{2}+p+1} \, _2F_1\left(-\frac{n}{2}-p,-\frac{n}{2}+p+1;-\frac{n}{2}+p+2;\frac{1}{2} (1-a x)\right)}{a (-n+2 p+2)}",1,"-((2^(n/2 + p)*(1 - a*x)^(1 - n/2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1/2*n - p, 1 - n/2 + p, 2 - n/2 + p, (1 - a*x)/2])/(a*(1 - n/2 + p)*(1 - a^2*x^2)^p))","A",1
1363,1,31,41,0.0237705,"\int e^{2 (1+p) \tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^{-p} \, dx","Integrate[E^(2*(1 + p)*ArcTanh[a*x])/(1 - a^2*x^2)^p,x]","\frac{(1-a x)^{-2 p} (a p x+p-1)}{a p (2 p-1)}","\frac{(1-a x)^{1-2 p}}{a (1-2 p)}+\frac{(1-a x)^{-2 p}}{a p}",1,"(-1 + p + a*p*x)/(a*p*(-1 + 2*p)*(1 - a*x)^(2*p))","A",1
1364,1,58,95,0.0278148,"\int e^{2 (1+p) \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{-p} \, dx","Integrate[E^(2*(1 + p)*ArcTanh[a*x])/(c - a^2*c*x^2)^p,x]","\frac{(1-a x)^{-2 p} (a p x+p-1) \left(1-a^2 x^2\right)^p \left(c-a^2 c x^2\right)^{-p}}{a p (2 p-1)}","\frac{\left(1-a^2 x^2\right)^p (1-a x)^{1-2 p} \left(c-a^2 c x^2\right)^{-p}}{a (1-2 p)}+\frac{\left(1-a^2 x^2\right)^p (1-a x)^{-2 p} \left(c-a^2 c x^2\right)^{-p}}{a p}",1,"((-1 + p + a*p*x)*(1 - a^2*x^2)^p)/(a*p*(-1 + 2*p)*(1 - a*x)^(2*p)*(c - a^2*c*x^2)^p)","A",1
1365,1,36,49,0.0339825,"\int e^{2 p \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[E^(2*p*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","\frac{(a x+1) \left(c-a^2 c x^2\right)^p e^{2 p \tanh ^{-1}(a x)}}{2 a p+a}","\frac{(a x+1)^{2 p+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p}{a (2 p+1)}",1,"(E^(2*p*ArcTanh[a*x])*(1 + a*x)*(c - a^2*c*x^2)^p)/(a + 2*a*p)","A",1
1366,1,36,51,0.0371218,"\int e^{-2 p \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Integrate[(c - a^2*c*x^2)^p/E^(2*p*ArcTanh[a*x]),x]","\frac{(a x-1) \left(c-a^2 c x^2\right)^p e^{-2 p \tanh ^{-1}(a x)}}{2 a p+a}","-\frac{(1-a x)^{2 p+1} \left(1-a^2 x^2\right)^{-p} \left(c-a^2 c x^2\right)^p}{a (2 p+1)}",1,"((-1 + a*x)*(c - a^2*c*x^2)^p)/(E^(2*p*ArcTanh[a*x])*(a + 2*a*p))","A",1
1367,1,92,53,0.0902232,"\int e^{n \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^{-1-\frac{n^2}{2}} \, dx","Integrate[E^(n*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^(-1 - n^2/2),x]","\frac{(1-a x)^{-\frac{1}{2} n (n+1)} (a x+1)^{-\frac{1}{2} (n-1) n} (a n x-1) \left(1-a^2 x^2\right)^{\frac{n^2}{2}} \left(c-a^2 c x^2\right)^{-\frac{n^2}{2}}}{a^3 c (n-1) n (n+1)}","\frac{(1-a n x) \left(c-a^2 c x^2\right)^{-\frac{n^2}{2}} e^{n \tanh ^{-1}(a x)}}{a^3 c n \left(1-n^2\right)}",1,"((-1 + a*n*x)*(1 - a^2*x^2)^(n^2/2))/(a^3*c*(-1 + n)*n*(1 + n)*(1 - a*x)^((n*(1 + n))/2)*(1 + a*x)^(((-1 + n)*n)/2)*(c - a^2*c*x^2)^(n^2/2))","A",0
1368,1,30,31,1.2706361,"\int \frac{e^{6 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{19}} \, dx","Integrate[(E^(6*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^19,x]","\frac{1-6 a x}{210 a^3 c^{19} (a x-1)^{21} (a x+1)^{15}}","-\frac{1-6 a x}{210 a^3 c^{19} (1-a x)^{21} (a x+1)^{15}}",1,"(1 - 6*a*x)/(210*a^3*c^19*(-1 + a*x)^21*(1 + a*x)^15)","A",1
1369,1,30,31,0.2548977,"\int \frac{e^{4 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^9} \, dx","Integrate[(E^(4*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^9,x]","\frac{4 a x-1}{60 a^3 c^9 (a x-1)^{10} (a x+1)^6}","-\frac{1-4 a x}{60 a^3 c^9 (1-a x)^{10} (a x+1)^6}",1,"(-1 + 4*a*x)/(60*a^3*c^9*(-1 + a*x)^10*(1 + a*x)^6)","A",1
1370,1,30,31,0.0363097,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^3,x]","\frac{1-2 a x}{6 a^3 c^3 (a x-1)^3 (a x+1)}","-\frac{1-2 a x}{6 a^3 c^3 (1-a x)^3 (a x+1)}",1,"(1 - 2*a*x)/(6*a^3*c^3*(-1 + a*x)^3*(1 + a*x))","A",1
1371,1,30,31,0.0388625,"\int \frac{e^{-2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Integrate[x^2/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3),x]","-\frac{2 a x+1}{6 a^3 c^3 (a x-1) (a x+1)^3}","\frac{2 a x+1}{6 a^3 c^3 (1-a x) (a x+1)^3}",1,"-1/6*(1 + 2*a*x)/(a^3*c^3*(-1 + a*x)*(1 + a*x)^3)","A",1
1372,1,30,31,0.2133665,"\int \frac{e^{-4 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^9} \, dx","Integrate[x^2/(E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^9),x]","\frac{4 a x+1}{60 a^3 c^9 (a x-1)^6 (a x+1)^{10}}","\frac{4 a x+1}{60 a^3 c^9 (1-a x)^6 (a x+1)^{10}}",1,"(1 + 4*a*x)/(60*a^3*c^9*(-1 + a*x)^6*(1 + a*x)^10)","A",1
1373,1,59,60,0.5940201,"\int \frac{e^{5 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{27/2}} \, dx","Integrate[(E^(5*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(27/2),x]","\frac{(1-5 a x) \sqrt{1-a^2 x^2}}{120 a^3 c^{13} (a x-1)^{15} (a x+1)^{10} \sqrt{c-a^2 c x^2}}","-\frac{(1-5 a x) \sqrt{1-a^2 x^2}}{120 a^3 c^{13} (1-a x)^{15} (a x+1)^{10} \sqrt{c-a^2 c x^2}}",1,"((1 - 5*a*x)*Sqrt[1 - a^2*x^2])/(120*a^3*c^13*(-1 + a*x)^15*(1 + a*x)^10*Sqrt[c - a^2*c*x^2])","A",1
1374,1,59,60,0.1155463,"\int \frac{e^{3 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{11/2}} \, dx","Integrate[(E^(3*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(11/2),x]","\frac{(3 a x-1) \sqrt{1-a^2 x^2}}{24 a^3 c^5 (a x-1)^6 (a x+1)^3 \sqrt{c-a^2 c x^2}}","-\frac{(1-3 a x) \sqrt{1-a^2 x^2}}{24 a^3 c^5 (1-a x)^6 (a x+1)^3 \sqrt{c-a^2 c x^2}}",1,"((-1 + 3*a*x)*Sqrt[1 - a^2*x^2])/(24*a^3*c^5*(-1 + a*x)^6*(1 + a*x)^3*Sqrt[c - a^2*c*x^2])","A",1
1375,1,76,139,0.0752262,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2} \left(\frac{1}{2 a^3 (1-a x)}+\frac{3 \log (1-a x)}{4 a^3}+\frac{\log (a x+1)}{4 a^3}\right)}{c \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a^3 c (1-a x) \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{1-a^2 x^2} \log (1-a x)}{4 a^3 c \sqrt{c-a^2 c x^2}}+\frac{\sqrt{1-a^2 x^2} \log (a x+1)}{4 a^3 c \sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - a^2*x^2]*(1/(2*a^3*(1 - a*x)) + (3*Log[1 - a*x])/(4*a^3) + Log[1 + a*x]/(4*a^3)))/(c*Sqrt[c - a^2*c*x^2])","A",1
1376,1,72,138,0.0595026,"\int \frac{e^{-\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Integrate[x^2/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(3/2)),x]","-\frac{\sqrt{1-a^2 x^2} ((a x+1) \log (1-a x)+3 (a x+1) \log (a x+1)+2)}{4 a^3 (a c x+c) \sqrt{c-a^2 c x^2}}","-\frac{\sqrt{1-a^2 x^2}}{2 a^3 c (a x+1) \sqrt{c-a^2 c x^2}}-\frac{\sqrt{1-a^2 x^2} \log (1-a x)}{4 a^3 c \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{1-a^2 x^2} \log (a x+1)}{4 a^3 c \sqrt{c-a^2 c x^2}}",1,"-1/4*(Sqrt[1 - a^2*x^2]*(2 + (1 + a*x)*Log[1 - a*x] + 3*(1 + a*x)*Log[1 + a*x]))/(a^3*(c + a*c*x)*Sqrt[c - a^2*c*x^2])","A",1
1377,1,59,60,0.1032816,"\int \frac{e^{-3 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{11/2}} \, dx","Integrate[x^2/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(11/2)),x]","-\frac{(3 a x+1) \sqrt{1-a^2 x^2}}{24 a^3 c^5 (a x-1)^3 (a x+1)^6 \sqrt{c-a^2 c x^2}}","\frac{(3 a x+1) \sqrt{1-a^2 x^2}}{24 a^3 c^5 (1-a x)^3 (a x+1)^6 \sqrt{c-a^2 c x^2}}",1,"-1/24*((1 + 3*a*x)*Sqrt[1 - a^2*x^2])/(a^3*c^5*(-1 + a*x)^3*(1 + a*x)^6*Sqrt[c - a^2*c*x^2])","A",1
1378,1,59,60,0.5219074,"\int \frac{e^{-5 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{27/2}} \, dx","Integrate[x^2/(E^(5*ArcTanh[a*x])*(c - a^2*c*x^2)^(27/2)),x]","\frac{(5 a x+1) \sqrt{1-a^2 x^2}}{120 a^3 c^{13} (a x-1)^{10} (a x+1)^{15} \sqrt{c-a^2 c x^2}}","\frac{(5 a x+1) \sqrt{1-a^2 x^2}}{120 a^3 c^{13} (1-a x)^{10} (a x+1)^{15} \sqrt{c-a^2 c x^2}}",1,"((1 + 5*a*x)*Sqrt[1 - a^2*x^2])/(120*a^3*c^13*(-1 + a*x)^10*(1 + a*x)^15*Sqrt[c - a^2*c*x^2])","A",1