1,1,111,0,0.1046401,"\int e^{\tanh ^{-1}(a x)} x^4 \, dx","Int[E^ArcTanh[a*x]*x^4,x]","-\frac{x^4 \sqrt{1-a^2 x^2}}{5 a}-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a^2}-\frac{4 x^2 \sqrt{1-a^2 x^2}}{15 a^3}-\frac{(45 a x+64) \sqrt{1-a^2 x^2}}{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{4 x^2 \sqrt{1-a^2 x^2}}{15 a^3}-\frac{(45 a x+64) \sqrt{1-a^2 x^2}}{120 a^5}+\frac{3 \sin ^{-1}(a x)}{8 a^5}",1,"(-4*x^2*Sqrt[1 - a^2*x^2])/(15*a^3) - (x^3*Sqrt[1 - a^2*x^2])/(4*a^2) - (x^4*Sqrt[1 - a^2*x^2])/(5*a) - ((64 + 45*a*x)*Sqrt[1 - a^2*x^2])/(120*a^5) + (3*ArcSin[a*x])/(8*a^5)","A",6,4,10,0.4000,1,"{6124, 833, 780, 216}"
2,1,87,0,0.0754742,"\int e^{\tanh ^{-1}(a x)} x^3 \, dx","Int[E^ArcTanh[a*x]*x^3,x]","-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2}-\frac{(9 a x+16) \sqrt{1-a^2 x^2}}{24 a^4}+\frac{3 \sin ^{-1}(a x)}{8 a^4}","-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2}-\frac{(9 a x+16) \sqrt{1-a^2 x^2}}{24 a^4}+\frac{3 \sin ^{-1}(a x)}{8 a^4}",1,"-(x^2*Sqrt[1 - a^2*x^2])/(3*a^2) - (x^3*Sqrt[1 - a^2*x^2])/(4*a) - ((16 + 9*a*x)*Sqrt[1 - a^2*x^2])/(24*a^4) + (3*ArcSin[a*x])/(8*a^4)","A",5,4,10,0.4000,1,"{6124, 833, 780, 216}"
3,1,74,0,0.0536717,"\int e^{\tanh ^{-1}(a x)} x^2 \, dx","Int[E^ArcTanh[a*x]*x^2,x]","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3}-\frac{x \sqrt{1-a^2 x^2}}{2 a^2}-\frac{\sqrt{1-a^2 x^2}}{a^3}+\frac{\sin ^{-1}(a x)}{2 a^3}","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3}-\frac{x \sqrt{1-a^2 x^2}}{2 a^2}-\frac{\sqrt{1-a^2 x^2}}{a^3}+\frac{\sin ^{-1}(a x)}{2 a^3}",1,"-(Sqrt[1 - a^2*x^2]/a^3) - (x*Sqrt[1 - a^2*x^2])/(2*a^2) + (1 - a^2*x^2)^(3/2)/(3*a^3) + ArcSin[a*x]/(2*a^3)","A",7,5,10,0.5000,1,"{6124, 797, 641, 195, 216}"
4,1,38,0,0.0217802,"\int e^{\tanh ^{-1}(a x)} x \, dx","Int[E^ArcTanh[a*x]*x,x]","\frac{\sin ^{-1}(a x)}{2 a^2}-\frac{(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])/(2*a^2) + ArcSin[a*x]/(2*a^2)","A",3,3,8,0.3750,1,"{6124, 780, 216}"
5,1,28,0,0.0109539,"\int e^{\tanh ^{-1}(a x)} \, dx","Int[E^ArcTanh[a*x],x]","\frac{\sin ^{-1}(a x)}{a}-\frac{\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]/a) + ArcSin[a*x]/a","A",3,3,6,0.5000,1,"{6123, 641, 216}"
6,1,22,0,0.0423695,"\int \frac{e^{\tanh ^{-1}(a x)}}{x} \, dx","Int[E^ArcTanh[a*x]/x,x]","\sin ^{-1}(a x)-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","\sin ^{-1}(a x)-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"ArcSin[a*x] - ArcTanh[Sqrt[1 - a^2*x^2]]","A",6,6,10,0.6000,1,"{6124, 844, 216, 266, 63, 208}"
7,1,38,0,0.0444022,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^ArcTanh[a*x]/x^2,x]","-\frac{\sqrt{1-a^2 x^2}}{x}-a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\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*ArcTanh[Sqrt[1 - a^2*x^2]]","A",5,5,10,0.5000,1,"{6124, 807, 266, 63, 208}"
8,1,64,0,0.0626748,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^ArcTanh[a*x]/x^3,x]","-\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)","-\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,"-Sqrt[1 - a^2*x^2]/(2*x^2) - (a*Sqrt[1 - a^2*x^2])/x - (a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",6,6,10,0.6000,1,"{6124, 835, 807, 266, 63, 208}"
9,1,90,0,0.0851134,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^ArcTanh[a*x]/x^4,x]","-\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)","-\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]/(3*x^3) - (a*Sqrt[1 - a^2*x^2])/(2*x^2) - (2*a^2*Sqrt[1 - a^2*x^2])/(3*x) - (a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",7,6,10,0.6000,1,"{6124, 835, 807, 266, 63, 208}"
10,1,114,0,0.1074576,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^5} \, dx","Int[E^ArcTanh[a*x]/x^5,x]","-\frac{2 a^3 \sqrt{1-a^2 x^2}}{3 x}-\frac{3 a^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{a \sqrt{1-a^2 x^2}}{3 x^3}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\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}-\frac{3 a^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{a \sqrt{1-a^2 x^2}}{3 x^3}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-Sqrt[1 - a^2*x^2]/(4*x^4) - (a*Sqrt[1 - a^2*x^2])/(3*x^3) - (3*a^2*Sqrt[1 - a^2*x^2])/(8*x^2) - (2*a^3*Sqrt[1 - a^2*x^2])/(3*x) - (3*a^4*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",8,6,10,0.6000,1,"{6124, 835, 807, 266, 63, 208}"
11,1,44,0,0.0423027,"\int e^{2 \tanh ^{-1}(a x)} x^3 \, dx","Int[E^(2*ArcTanh[a*x])*x^3,x]","-\frac{x^2}{a^2}-\frac{2 x}{a^3}-\frac{2 \log (1-a x)}{a^4}-\frac{2 x^3}{3 a}-\frac{x^4}{4}","-\frac{x^2}{a^2}-\frac{2 x}{a^3}-\frac{2 \log (1-a x)}{a^4}-\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",3,2,12,0.1667,1,"{6126, 77}"
12,1,34,0,0.0339557,"\int e^{2 \tanh ^{-1}(a x)} x^2 \, dx","Int[E^(2*ArcTanh[a*x])*x^2,x]","-\frac{2 x}{a^2}-\frac{2 \log (1-a x)}{a^3}-\frac{x^2}{a}-\frac{x^3}{3}","-\frac{2 x}{a^2}-\frac{2 \log (1-a x)}{a^3}-\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",3,2,12,0.1667,1,"{6126, 77}"
13,1,26,0,0.0287868,"\int e^{2 \tanh ^{-1}(a x)} x \, dx","Int[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",3,2,10,0.2000,1,"{6126, 77}"
14,1,16,0,0.0120185,"\int e^{2 \tanh ^{-1}(a x)} \, dx","Int[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",3,2,8,0.2500,1,"{6125, 43}"
15,1,12,0,0.0253327,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x} \, dx","Int[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",3,2,12,0.1667,1,"{6126, 72}"
16,1,21,0,0.0283413,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2} \, dx","Int[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",3,2,12,0.1667,1,"{6126, 77}"
17,1,33,0,0.0322523,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3} \, dx","Int[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*x^2) - (2*a)/x + 2*a^2*Log[x] - 2*a^2*Log[1 - a*x]","A",3,2,12,0.1667,1,"{6126, 77}"
18,1,41,0,0.0356681,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^(2*ArcTanh[a*x])/x^4,x]","-\frac{2 a^2}{x}+2 a^3 \log (x)-2 a^3 \log (1-a x)-\frac{a}{x^2}-\frac{1}{3 x^3}","-\frac{2 a^2}{x}+2 a^3 \log (x)-2 a^3 \log (1-a x)-\frac{a}{x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - a/x^2 - (2*a^2)/x + 2*a^3*Log[x] - 2*a^3*Log[1 - a*x]","A",3,2,12,0.1667,1,"{6126, 77}"
19,1,92,0,0.649267,"\int e^{3 \tanh ^{-1}(a x)} x^2 \, dx","Int[E^(3*ArcTanh[a*x])*x^2,x]","\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}-\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}-\frac{11 \sin ^{-1}(a x)}{2 a^3}",1,"(1 + a*x)^3/(a^3*Sqrt[1 - a^2*x^2]) + ((3 + a*x)^2*Sqrt[1 - a^2*x^2])/(3*a^3) + ((28 + 3*a*x)*Sqrt[1 - a^2*x^2])/(6*a^3) - (11*ArcSin[a*x])/(2*a^3)","A",10,9,12,0.7500,1,"{6124, 1633, 1593, 12, 852, 1635, 1654, 780, 216}"
20,1,88,0,0.3826878,"\int e^{3 \tanh ^{-1}(a x)} x \, dx","Int[E^(3*ArcTanh[a*x])*x,x]","\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}","\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,"(9*Sqrt[1 - a^2*x^2])/(2*a^2) + (3*(1 - a^2*x^2)^(3/2))/(2*a^2*(1 - a*x)) + (1 - a^2*x^2)^(5/2)/(a^2*(1 - a*x)^3) - (9*ArcSin[a*x])/(2*a^2)","A",9,7,10,0.7000,1,"{6124, 1633, 1593, 12, 793, 665, 216}"
21,1,55,0,0.0491881,"\int e^{3 \tanh ^{-1}(a x)} \, dx","Int[E^(3*ArcTanh[a*x]),x]","\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}","\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,"(2*(1 + a*x)^2)/(a*Sqrt[1 - a^2*x^2]) + (3*Sqrt[1 - a^2*x^2])/a - (3*ArcSin[a*x])/a","A",5,5,8,0.6250,1,"{6123, 853, 669, 641, 216}"
22,1,48,0,0.7867467,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x} \, dx","Int[E^(3*ArcTanh[a*x])/x,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)","\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] - ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,7,12,0.5833,1,"{6124, 6742, 216, 266, 63, 208, 651}"
23,1,63,0,0.6965109,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^(3*ArcTanh[a*x])/x^2,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)","\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) + (4*a*Sqrt[1 - a^2*x^2])/(1 - a*x) - 3*a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,7,12,0.5833,1,"{6124, 6742, 264, 266, 63, 208, 651}"
24,1,91,0,0.741374,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^(3*ArcTanh[a*x])/x^3,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)","\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]/(2*x^2) - (3*a*Sqrt[1 - a^2*x^2])/x + (4*a^2*Sqrt[1 - a^2*x^2])/(1 - a*x) - (9*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",12,8,12,0.6667,1,"{6124, 6742, 266, 51, 63, 208, 264, 651}"
25,1,117,0,0.7378762,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^(3*ArcTanh[a*x])/x^4,x]","\frac{4 a^3 \sqrt{1-a^2 x^2}}{1-a x}-\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{11}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","\frac{4 a^3 \sqrt{1-a^2 x^2}}{1-a x}-\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{11}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-Sqrt[1 - a^2*x^2]/(3*x^3) - (3*a*Sqrt[1 - a^2*x^2])/(2*x^2) - (14*a^2*Sqrt[1 - a^2*x^2])/(3*x) + (4*a^3*Sqrt[1 - a^2*x^2])/(1 - a*x) - (11*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",14,9,12,0.7500,1,"{6124, 6742, 271, 264, 266, 51, 63, 208, 651}"
26,1,57,0,0.0495242,"\int e^{4 \tanh ^{-1}(a x)} x^3 \, dx","Int[E^(4*ArcTanh[a*x])*x^3,x]","\frac{4 x^2}{a^2}+\frac{12 x}{a^3}+\frac{4}{a^4 (1-a x)}+\frac{16 \log (1-a x)}{a^4}+\frac{4 x^3}{3 a}+\frac{x^4}{4}","\frac{4 x^2}{a^2}+\frac{12 x}{a^3}+\frac{4}{a^4 (1-a x)}+\frac{16 \log (1-a x)}{a^4}+\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",3,2,12,0.1667,1,"{6126, 88}"
27,1,47,0,0.0437176,"\int e^{4 \tanh ^{-1}(a x)} x^2 \, dx","Int[E^(4*ArcTanh[a*x])*x^2,x]","\frac{8 x}{a^2}+\frac{4}{a^3 (1-a x)}+\frac{12 \log (1-a x)}{a^3}+\frac{2 x^2}{a}+\frac{x^3}{3}","\frac{8 x}{a^2}+\frac{4}{a^3 (1-a x)}+\frac{12 \log (1-a x)}{a^3}+\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",3,2,12,0.1667,1,"{6126, 88}"
28,1,39,0,0.0285469,"\int e^{4 \tanh ^{-1}(a x)} x \, dx","Int[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",3,2,10,0.2000,1,"{6126, 77}"
29,1,27,0,0.0143055,"\int e^{4 \tanh ^{-1}(a x)} \, dx","Int[E^(4*ArcTanh[a*x]),x]","\frac{4}{a (1-a x)}+\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",3,2,8,0.2500,1,"{6125, 43}"
30,1,13,0,0.0251725,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x} \, dx","Int[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",3,2,12,0.1667,1,"{6126, 88}"
31,1,32,0,0.0331429,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x^2} \, dx","Int[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",3,2,12,0.1667,1,"{6126, 88}"
32,1,46,0,0.0371758,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x^3} \, dx","Int[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*x^2) - (4*a)/x + (4*a^2)/(1 - a*x) + 8*a^2*Log[x] - 8*a^2*Log[1 - a*x]","A",3,2,12,0.1667,1,"{6126, 88}"
33,1,54,0,0.0449314,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^(4*ArcTanh[a*x])/x^4,x]","\frac{4 a^3}{1-a x}-\frac{8 a^2}{x}+12 a^3 \log (x)-12 a^3 \log (1-a x)-\frac{2 a}{x^2}-\frac{1}{3 x^3}","\frac{4 a^3}{1-a x}-\frac{8 a^2}{x}+12 a^3 \log (x)-12 a^3 \log (1-a x)-\frac{2 a}{x^2}-\frac{1}{3 x^3}",1,"-1/(3*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",3,2,12,0.1667,1,"{6126, 88}"
34,1,87,0,0.076842,"\int e^{-\tanh ^{-1}(a x)} x^3 \, dx","Int[x^3/E^ArcTanh[a*x],x]","\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2}-\frac{(16-9 a x) \sqrt{1-a^2 x^2}}{24 a^4}-\frac{3 \sin ^{-1}(a x)}{8 a^4}","\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}-\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2}-\frac{(16-9 a x) \sqrt{1-a^2 x^2}}{24 a^4}-\frac{3 \sin ^{-1}(a x)}{8 a^4}",1,"-(x^2*Sqrt[1 - a^2*x^2])/(3*a^2) + (x^3*Sqrt[1 - a^2*x^2])/(4*a) - ((16 - 9*a*x)*Sqrt[1 - a^2*x^2])/(24*a^4) - (3*ArcSin[a*x])/(8*a^4)","A",5,4,12,0.3333,1,"{6124, 833, 780, 216}"
35,1,73,0,0.055245,"\int e^{-\tanh ^{-1}(a x)} x^2 \, dx","Int[x^2/E^ArcTanh[a*x],x]","-\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3}-\frac{x \sqrt{1-a^2 x^2}}{2 a^2}+\frac{\sqrt{1-a^2 x^2}}{a^3}+\frac{\sin ^{-1}(a x)}{2 a^3}","-\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a^3}-\frac{x \sqrt{1-a^2 x^2}}{2 a^2}+\frac{\sqrt{1-a^2 x^2}}{a^3}+\frac{\sin ^{-1}(a x)}{2 a^3}",1,"Sqrt[1 - a^2*x^2]/a^3 - (x*Sqrt[1 - a^2*x^2])/(2*a^2) - (1 - a^2*x^2)^(3/2)/(3*a^3) + ArcSin[a*x]/(2*a^3)","A",7,5,12,0.4167,1,"{6124, 797, 641, 195, 216}"
36,1,39,0,0.0231506,"\int e^{-\tanh ^{-1}(a x)} x \, dx","Int[x/E^ArcTanh[a*x],x]","-\frac{\sqrt{1-a^2 x^2} (2-a x)}{2 a^2}-\frac{\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])/(2*a^2) - ArcSin[a*x]/(2*a^2)","A",3,3,10,0.3000,1,"{6124, 780, 216}"
37,1,27,0,0.0108152,"\int e^{-\tanh ^{-1}(a x)} \, dx","Int[E^(-ArcTanh[a*x]),x]","\frac{\sqrt{1-a^2 x^2}}{a}+\frac{\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]/a + ArcSin[a*x]/a","A",3,3,8,0.3750,1,"{6123, 641, 216}"
38,1,24,0,0.0416582,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x} \, dx","Int[1/(E^ArcTanh[a*x]*x),x]","-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\sin ^{-1}(a x)","-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\sin ^{-1}(a x)",1,"-ArcSin[a*x] - ArcTanh[Sqrt[1 - a^2*x^2]]","A",6,6,12,0.5000,1,"{6124, 844, 216, 266, 63, 208}"
39,1,37,0,0.0420877,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^ArcTanh[a*x]*x^2),x]","a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\sqrt{1-a^2 x^2}}{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*ArcTanh[Sqrt[1 - a^2*x^2]]","A",5,5,12,0.4167,1,"{6124, 807, 266, 63, 208}"
40,1,63,0,0.0604718,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^ArcTanh[a*x]*x^3),x]","\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)","\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,"-Sqrt[1 - a^2*x^2]/(2*x^2) + (a*Sqrt[1 - a^2*x^2])/x - (a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",6,6,12,0.5000,1,"{6124, 835, 807, 266, 63, 208}"
41,1,90,0,0.082619,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^ArcTanh[a*x]*x^4),x]","-\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)","-\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]/(3*x^3) + (a*Sqrt[1 - a^2*x^2])/(2*x^2) - (2*a^2*Sqrt[1 - a^2*x^2])/(3*x) + (a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",7,6,12,0.5000,1,"{6124, 835, 807, 266, 63, 208}"
42,1,114,0,0.103138,"\int \frac{e^{-\tanh ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^ArcTanh[a*x]*x^5),x]","\frac{2 a^3 \sqrt{1-a^2 x^2}}{3 x}-\frac{3 a^2 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{a \sqrt{1-a^2 x^2}}{3 x^3}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\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}-\frac{3 a^2 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{a \sqrt{1-a^2 x^2}}{3 x^3}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\frac{3}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-Sqrt[1 - a^2*x^2]/(4*x^4) + (a*Sqrt[1 - a^2*x^2])/(3*x^3) - (3*a^2*Sqrt[1 - a^2*x^2])/(8*x^2) + (2*a^3*Sqrt[1 - a^2*x^2])/(3*x) - (3*a^4*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",8,6,12,0.5000,1,"{6124, 835, 807, 266, 63, 208}"
43,1,43,0,0.0392676,"\int e^{-2 \tanh ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(2*ArcTanh[a*x]),x]","-\frac{x^2}{a^2}+\frac{2 x}{a^3}-\frac{2 \log (a x+1)}{a^4}+\frac{2 x^3}{3 a}-\frac{x^4}{4}","-\frac{x^2}{a^2}+\frac{2 x}{a^3}-\frac{2 \log (a x+1)}{a^4}+\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",3,2,12,0.1667,1,"{6126, 77}"
44,1,32,0,0.0331909,"\int e^{-2 \tanh ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(2*ArcTanh[a*x]),x]","-\frac{2 x}{a^2}+\frac{2 \log (a x+1)}{a^3}+\frac{x^2}{a}-\frac{x^3}{3}","-\frac{2 x}{a^2}+\frac{2 \log (a x+1)}{a^3}+\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",3,2,12,0.1667,1,"{6126, 77}"
45,1,25,0,0.0239714,"\int e^{-2 \tanh ^{-1}(a x)} x \, dx","Int[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",3,2,10,0.2000,1,"{6126, 77}"
46,1,15,0,0.0095735,"\int e^{-2 \tanh ^{-1}(a x)} \, dx","Int[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",3,2,8,0.2500,1,"{6125, 43}"
47,1,11,0,0.023803,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x} \, dx","Int[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",3,2,12,0.1667,1,"{6126, 72}"
48,1,20,0,0.0270994,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x^2} \, dx","Int[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",3,2,12,0.1667,1,"{6126, 77}"
49,1,32,0,0.0297747,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x^3} \, dx","Int[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*x^2) + (2*a)/x + 2*a^2*Log[x] - 2*a^2*Log[1 + a*x]","A",3,2,12,0.1667,1,"{6126, 77}"
50,1,39,0,0.0317947,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(2*ArcTanh[a*x])*x^4),x]","-\frac{2 a^2}{x}-2 a^3 \log (x)+2 a^3 \log (a x+1)+\frac{a}{x^2}-\frac{1}{3 x^3}","-\frac{2 a^2}{x}-2 a^3 \log (x)+2 a^3 \log (a x+1)+\frac{a}{x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) + a/x^2 - (2*a^2)/x - 2*a^3*Log[x] + 2*a^3*Log[1 + a*x]","A",3,2,12,0.1667,1,"{6126, 77}"
51,1,131,0,0.6894972,"\int e^{-3 \tanh ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(3*ArcTanh[a*x]),x]","-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}+\frac{x^2 \sqrt{1-a^2 x^2}}{a^2}+\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}}+\frac{51 \sin ^{-1}(a x)}{8 a^4}","-\frac{x^3 \sqrt{1-a^2 x^2}}{4 a}+\frac{x^2 \sqrt{1-a^2 x^2}}{a^2}+\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}}+\frac{51 \sin ^{-1}(a x)}{8 a^4}",1,"(1 - a*x)^3/(a^4*Sqrt[1 - a^2*x^2]) + (27*Sqrt[1 - a^2*x^2])/(4*a^4) + (x^2*Sqrt[1 - a^2*x^2])/a^2 - (x^3*Sqrt[1 - a^2*x^2])/(4*a) + (9*(2 - 3*a*x)*Sqrt[1 - a^2*x^2])/(8*a^4) + (51*ArcSin[a*x])/(8*a^4)","A",14,11,12,0.9167,1,"{6124, 1633, 1593, 12, 852, 1635, 1815, 27, 743, 641, 216}"
52,1,95,0,0.6376272,"\int e^{-3 \tanh ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(3*ArcTanh[a*x]),x]","-\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}-\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}-\frac{11 \sin ^{-1}(a x)}{2 a^3}",1,"-((1 - a*x)^3/(a^3*Sqrt[1 - a^2*x^2])) - ((28 - 3*a*x)*Sqrt[1 - a^2*x^2])/(6*a^3) - ((3 - a*x)^2*Sqrt[1 - a^2*x^2])/(3*a^3) - (11*ArcSin[a*x])/(2*a^3)","A",10,9,12,0.7500,1,"{6124, 1633, 1593, 12, 852, 1635, 1654, 780, 216}"
53,1,86,0,0.364178,"\int e^{-3 \tanh ^{-1}(a x)} x \, dx","Int[x/E^(3*ArcTanh[a*x]),x]","\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}","\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,"(9*Sqrt[1 - a^2*x^2])/(2*a^2) + (3*(1 - a^2*x^2)^(3/2))/(2*a^2*(1 + a*x)) + (1 - a^2*x^2)^(5/2)/(a^2*(1 + a*x)^3) + (9*ArcSin[a*x])/(2*a^2)","A",9,7,10,0.7000,1,"{6124, 1633, 1593, 12, 793, 665, 216}"
54,1,56,0,0.0492489,"\int e^{-3 \tanh ^{-1}(a x)} \, dx","Int[E^(-3*ArcTanh[a*x]),x]","-\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}","-\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,"(-2*(1 - a*x)^2)/(a*Sqrt[1 - a^2*x^2]) - (3*Sqrt[1 - a^2*x^2])/a - (3*ArcSin[a*x])/a","A",5,5,8,0.6250,1,"{6123, 853, 669, 641, 216}"
55,1,45,0,0.7081008,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x} \, dx","Int[1/(E^(3*ArcTanh[a*x])*x),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)","\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] - ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,7,12,0.5833,1,"{6124, 6742, 216, 266, 63, 208, 651}"
56,1,62,0,0.6896102,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(3*ArcTanh[a*x])*x^2),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)","-\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) - (4*a*Sqrt[1 - a^2*x^2])/(1 + a*x) + 3*a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,7,12,0.5833,1,"{6124, 6742, 264, 266, 63, 208, 651}"
57,1,90,0,0.7354627,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(3*ArcTanh[a*x])*x^3),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)","\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]/(2*x^2) + (3*a*Sqrt[1 - a^2*x^2])/x + (4*a^2*Sqrt[1 - a^2*x^2])/(1 + a*x) - (9*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",12,8,12,0.6667,1,"{6124, 6742, 266, 51, 63, 208, 264, 651}"
58,1,116,0,0.7478712,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(3*ArcTanh[a*x])*x^4),x]","-\frac{4 a^3 \sqrt{1-a^2 x^2}}{a x+1}-\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{11}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{4 a^3 \sqrt{1-a^2 x^2}}{a x+1}-\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{11}{2} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-Sqrt[1 - a^2*x^2]/(3*x^3) + (3*a*Sqrt[1 - a^2*x^2])/(2*x^2) - (14*a^2*Sqrt[1 - a^2*x^2])/(3*x) - (4*a^3*Sqrt[1 - a^2*x^2])/(1 + a*x) + (11*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",14,9,12,0.7500,1,"{6124, 6742, 271, 264, 266, 51, 63, 208, 651}"
59,1,135,0,0.8224905,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^(3*ArcTanh[a*x])*x^5),x]","\frac{4 a^4 \sqrt{1-a^2 x^2}}{a x+1}+\frac{6 a^3 \sqrt{1-a^2 x^2}}{x}-\frac{19 a^2 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{a \sqrt{1-a^2 x^2}}{x^3}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\frac{51}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","\frac{4 a^4 \sqrt{1-a^2 x^2}}{a x+1}+\frac{6 a^3 \sqrt{1-a^2 x^2}}{x}-\frac{19 a^2 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{a \sqrt{1-a^2 x^2}}{x^3}-\frac{\sqrt{1-a^2 x^2}}{4 x^4}-\frac{51}{8} a^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-Sqrt[1 - a^2*x^2]/(4*x^4) + (a*Sqrt[1 - a^2*x^2])/x^3 - (19*a^2*Sqrt[1 - a^2*x^2])/(8*x^2) + (6*a^3*Sqrt[1 - a^2*x^2])/x + (4*a^4*Sqrt[1 - a^2*x^2])/(1 + a*x) - (51*a^4*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",19,9,12,0.7500,1,"{6124, 6742, 266, 51, 63, 208, 271, 264, 651}"
60,1,31,0,0.0272853,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x^m \, dx","Int[E^(ArcTanh[a*x]/2)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{1}{4},-\frac{1}{4};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, 1/4, -1/4, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
61,1,282,0,0.2140729,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x^2 \, dx","Int[E^(ArcTanh[a*x]/2)*x^2,x]","-\frac{x (1-a x)^{3/4} (a x+1)^{5/4}}{3 a^2}-\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}-\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}",1,"(-3*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(8*a^3) - ((1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(12*a^3) - (x*(1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(3*a^2) + (3*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (3*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3) + (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3)","A",15,12,14,0.8571,1,"{6126, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
62,1,255,0,0.1734925,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} x \, dx","Int[E^(ArcTanh[a*x]/2)*x,x]","-\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}","-\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 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*a^2) - ((1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(2*a^2) + ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(4*Sqrt[2]*a^2) - ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(4*Sqrt[2]*a^2) - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(8*Sqrt[2]*a^2) + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(8*Sqrt[2]*a^2)","A",14,11,12,0.9167,1,"{6126, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
63,1,222,0,0.1462684,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \, dx","Int[E^(ArcTanh[a*x]/2),x]","-\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}","-\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,"-(((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/a) + ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a) - ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a) - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(2*Sqrt[2]*a) + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(2*Sqrt[2]*a)","A",13,10,10,1.000,1,"{6125, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
64,1,227,0,0.163354,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x} \, dx","Int[E^(ArcTanh[a*x]/2)/x,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)","-\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*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - 2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6126, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
65,1,73,0,0.0337581,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^(ArcTanh[a*x]/2)/x^2,x]","-\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)","-\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 - a*x)^(3/4)*(1 + a*x)^(1/4))/x) - a*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - a*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)]","A",6,6,14,0.4286,1,"{6126, 94, 93, 212, 206, 203}"
66,1,110,0,0.0438452,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^(ArcTanh[a*x]/2)/x^3,x]","-\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}","-\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,"-(a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*x) - ((1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(2*x^2) - (a^2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4 - (a^2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4","A",7,7,14,0.5000,1,"{6126, 96, 94, 93, 212, 206, 203}"
67,1,139,0,0.0620214,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^(ArcTanh[a*x]/2)/x^4,x]","-\frac{11 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x}-\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{5 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{12 x^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{3 x^3}","-\frac{11 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x}-\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{5 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{12 x^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{3 x^3}",1,"-((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(3*x^3) - (5*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(12*x^2) - (11*a^2*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(24*x) - (3*a^3*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8 - (3*a^3*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8","A",9,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 212, 206, 203}"
68,1,168,0,0.0794604,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Int[E^(ArcTanh[a*x]/2)/x^5,x]","-\frac{29 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{96 x^2}-\frac{83 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{192 x}-\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{7 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x^3}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x^4}","-\frac{29 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{96 x^2}-\frac{83 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{192 x}-\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{7 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x^3}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x^4}",1,"-((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*x^4) - (7*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(24*x^3) - (29*a^2*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(96*x^2) - (83*a^3*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(192*x) - (11*a^4*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64 - (11*a^4*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64","A",10,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 212, 206, 203}"
69,1,197,0,0.0955458,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^6} \, dx","Int[E^(ArcTanh[a*x]/2)/x^6,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{611 a^4 (1-a x)^{3/4} \sqrt[4]{a x+1}}{1920 x}-\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{9 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{40 x^4}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{5 x^5}","-\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{611 a^4 (1-a x)^{3/4} \sqrt[4]{a x+1}}{1920 x}-\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{9 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{40 x^4}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{5 x^5}",1,"-((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(5*x^5) - (9*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(40*x^4) - (11*a^2*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(48*x^3) - (269*a^3*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(960*x^2) - (611*a^4*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(1920*x) - (31*a^5*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/128 - (31*a^5*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/128","A",11,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 212, 206, 203}"
70,1,31,0,0.0278198,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^m \, dx","Int[E^((3*ArcTanh[a*x])/2)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{3}{4},-\frac{3}{4};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, 3/4, -3/4, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
71,1,290,0,0.2039795,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^3 \, dx","Int[E^((3*ArcTanh[a*x])/2)*x^3,x]","-\frac{x^2 \sqrt[4]{1-a x} (a x+1)^{7/4}}{4 a^2}-\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}-\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}",1,"(-41*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(64*a^4) - (x^2*(1 - a*x)^(1/4)*(1 + a*x)^(7/4))/(4*a^2) - ((1 - a*x)^(1/4)*(1 + a*x)^(7/4)*(11 + 4*a*x))/(32*a^4) + (123*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) - (123*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (123*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (123*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",15,12,14,0.8571,1,"{6126, 100, 147, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
72,1,282,0,0.1997761,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x^2 \, dx","Int[E^((3*ArcTanh[a*x])/2)*x^2,x]","-\frac{x \sqrt[4]{1-a x} (a x+1)^{7/4}}{3 a^2}-\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}-\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}",1,"(-17*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(24*a^3) - ((1 - a*x)^(1/4)*(1 + a*x)^(7/4))/(4*a^3) - (x*(1 - a*x)^(1/4)*(1 + a*x)^(7/4))/(3*a^2) + (17*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (17*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) + (17*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3) - (17*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3)","A",15,12,14,0.8571,1,"{6126, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
73,1,255,0,0.1685389,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} x \, dx","Int[E^((3*ArcTanh[a*x])/2)*x,x]","-\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}","-\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,"(-3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*a^2) - ((1 - a*x)^(1/4)*(1 + a*x)^(7/4))/(2*a^2) + (9*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (9*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (9*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2) - (9*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",14,11,12,0.9167,1,"{6126, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
74,1,223,0,0.1344117,"\int e^{\frac{3}{2} \tanh ^{-1}(a x)} \, dx","Int[E^((3*ArcTanh[a*x])/2),x]","-\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}","-\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,"-(((1 - a*x)^(1/4)*(1 + a*x)^(3/4))/a) + (3*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) - (3*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) + (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a) - (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a)","A",13,10,10,1.000,1,"{6125, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
75,1,227,0,0.1581095,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x} \, dx","Int[E^((3*ArcTanh[a*x])/2)/x,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)","\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*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - 2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6126, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
76,1,73,0,0.0327228,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^((3*ArcTanh[a*x])/2)/x^2,x]","-\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)","-\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)^(3/4))/x) + 3*a*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - 3*a*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)]","A",6,6,14,0.4286,1,"{6126, 94, 93, 298, 203, 206}"
77,1,110,0,0.0435755,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^((3*ArcTanh[a*x])/2)/x^3,x]","\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}","\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,"(-3*a*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*x) - ((1 - a*x)^(1/4)*(1 + a*x)^(7/4))/(2*x^2) + (9*a^2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4 - (9*a^2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4","A",7,7,14,0.5000,1,"{6126, 96, 94, 93, 298, 203, 206}"
78,1,139,0,0.0612806,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^((3*ArcTanh[a*x])/2)/x^4,x]","-\frac{23 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x}+\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{7 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{3 x^3}","-\frac{23 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x}+\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{7 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{3 x^3}",1,"-((1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(3*x^3) - (7*a*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(12*x^2) - (23*a^2*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(24*x) + (17*a^3*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8 - (17*a^3*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8","A",9,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 298, 203, 206}"
79,1,168,0,0.0780924,"\int \frac{e^{\frac{3}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Int[E^((3*ArcTanh[a*x])/2)/x^5,x]","-\frac{15 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{32 x^2}-\frac{63 a^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{64 x}+\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{3 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{8 x^3}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x^4}","-\frac{15 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{32 x^2}-\frac{63 a^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{64 x}+\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{3 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{8 x^3}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x^4}",1,"-((1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*x^4) - (3*a*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(8*x^3) - (15*a^2*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(32*x^2) - (63*a^3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(64*x) + (123*a^4*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64 - (123*a^4*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64","A",10,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 298, 203, 206}"
80,1,31,0,0.025512,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^m \, dx","Int[E^((5*ArcTanh[a*x])/2)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{5}{4},-\frac{5}{4};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, 5/4, -5/4, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
81,1,317,0,0.2413695,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^3 \, dx","Int[E^((5*ArcTanh[a*x])/2)*x^3,x]","\frac{17 x^2 (1-a x)^{3/4} (a x+1)^{5/4}}{4 a^2}+\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{4 x^3 (a x+1)^{5/4}}{a \sqrt[4]{1-a x}}","\frac{17 x^2 (1-a x)^{3/4} (a x+1)^{5/4}}{4 a^2}+\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{4 x^3 (a x+1)^{5/4}}{a \sqrt[4]{1-a x}}",1,"(475*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(64*a^4) + (4*x^3*(1 + a*x)^(5/4))/(a*(1 - a*x)^(1/4)) + (17*x^2*(1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(4*a^2) + ((1 - a*x)^(3/4)*(1 + a*x)^(5/4)*(521 + 452*a*x))/(96*a^4) - (475*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (475*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (475*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (475*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",16,13,14,0.9286,1,"{6126, 97, 153, 147, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
82,1,305,0,0.2259323,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x^2 \, dx","Int[E^((5*ArcTanh[a*x])/2)*x^2,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}","\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,"(55*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(8*a^3) + (11*(1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(4*a^3) + (2*(1 + a*x)^(9/4))/(a^3*(1 - a*x)^(1/4)) + ((1 - a*x)^(3/4)*(1 + a*x)^(9/4))/(3*a^3) - (55*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) + (55*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) + (55*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3) - (55*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3)","A",16,12,14,0.8571,1,"{6126, 89, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
83,1,279,0,0.1937066,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} x \, dx","Int[E^((5*ArcTanh[a*x])/2)*x,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}","\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,"(25*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*a^2) + (5*(1 - a*x)^(3/4)*(1 + a*x)^(5/4))/(2*a^2) + (2*(1 + a*x)^(9/4))/(a^2*(1 - a*x)^(1/4)) - (25*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (25*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (25*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2) - (25*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",15,11,12,0.9167,1,"{6126, 78, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
84,1,247,0,0.1654594,"\int e^{\frac{5}{2} \tanh ^{-1}(a x)} \, dx","Int[E^((5*ArcTanh[a*x])/2),x]","\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}","\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,"(5*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/a + (4*(1 + a*x)^(5/4))/(a*(1 - a*x)^(1/4)) - (5*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) + (5*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) + (5*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a) - (5*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a)","A",14,11,10,1.100,1,"{6125, 47, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
85,1,248,0,0.2054541,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x} \, dx","Int[E^((5*ArcTanh[a*x])/2)/x,x]","\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)","\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,"(8*(1 + a*x)^(1/4))/(1 - a*x)^(1/4) - 2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - 2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2]","A",19,16,14,1.143,1,"{6126, 98, 21, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
86,1,95,0,0.0386483,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^((5*ArcTanh[a*x])/2)/x^2,x]","-\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)","-\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,"(10*a*(1 + a*x)^(1/4))/(1 - a*x)^(1/4) - (1 + a*x)^(5/4)/(x*(1 - a*x)^(1/4)) - 5*a*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - 5*a*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)]","A",7,6,14,0.4286,1,"{6126, 94, 93, 212, 206, 203}"
87,1,136,0,0.0485649,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^((5*ArcTanh[a*x])/2)/x^3,x]","\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}}","\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,"(25*a^2*(1 + a*x)^(1/4))/(2*(1 - a*x)^(1/4)) - (5*a*(1 + a*x)^(5/4))/(4*x*(1 - a*x)^(1/4)) - (1 + a*x)^(9/4)/(2*x^2*(1 - a*x)^(1/4)) - (25*a^2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4 - (25*a^2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4","A",8,7,14,0.5000,1,"{6126, 96, 94, 93, 212, 206, 203}"
88,1,165,0,0.0787501,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^((5*ArcTanh[a*x])/2)/x^4,x]","\frac{287 a^3 \sqrt[4]{a x+1}}{24 \sqrt[4]{1-a x}}-\frac{61 a^2 \sqrt[4]{a x+1}}{24 x \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{13 a \sqrt[4]{a x+1}}{12 x^2 \sqrt[4]{1-a x}}-\frac{\sqrt[4]{a x+1}}{3 x^3 \sqrt[4]{1-a x}}","\frac{287 a^3 \sqrt[4]{a x+1}}{24 \sqrt[4]{1-a x}}-\frac{61 a^2 \sqrt[4]{a x+1}}{24 x \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{13 a \sqrt[4]{a x+1}}{12 x^2 \sqrt[4]{1-a x}}-\frac{\sqrt[4]{a x+1}}{3 x^3 \sqrt[4]{1-a x}}",1,"(287*a^3*(1 + a*x)^(1/4))/(24*(1 - a*x)^(1/4)) - (1 + a*x)^(1/4)/(3*x^3*(1 - a*x)^(1/4)) - (13*a*(1 + a*x)^(1/4))/(12*x^2*(1 - a*x)^(1/4)) - (61*a^2*(1 + a*x)^(1/4))/(24*x*(1 - a*x)^(1/4)) - (55*a^3*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8 - (55*a^3*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8","A",10,9,14,0.6429,1,"{6126, 98, 151, 155, 12, 93, 212, 206, 203}"
89,1,194,0,0.0940809,"\int \frac{e^{\frac{5}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Int[E^((5*ArcTanh[a*x])/2)/x^5,x]","-\frac{113 a^2 \sqrt[4]{a x+1}}{96 x^2 \sqrt[4]{1-a x}}+\frac{2467 a^4 \sqrt[4]{a x+1}}{192 \sqrt[4]{1-a x}}-\frac{521 a^3 \sqrt[4]{a x+1}}{192 x \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{17 a \sqrt[4]{a x+1}}{24 x^3 \sqrt[4]{1-a x}}-\frac{\sqrt[4]{a x+1}}{4 x^4 \sqrt[4]{1-a x}}","-\frac{113 a^2 \sqrt[4]{a x+1}}{96 x^2 \sqrt[4]{1-a x}}+\frac{2467 a^4 \sqrt[4]{a x+1}}{192 \sqrt[4]{1-a x}}-\frac{521 a^3 \sqrt[4]{a x+1}}{192 x \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{17 a \sqrt[4]{a x+1}}{24 x^3 \sqrt[4]{1-a x}}-\frac{\sqrt[4]{a x+1}}{4 x^4 \sqrt[4]{1-a x}}",1,"(2467*a^4*(1 + a*x)^(1/4))/(192*(1 - a*x)^(1/4)) - (1 + a*x)^(1/4)/(4*x^4*(1 - a*x)^(1/4)) - (17*a*(1 + a*x)^(1/4))/(24*x^3*(1 - a*x)^(1/4)) - (113*a^2*(1 + a*x)^(1/4))/(96*x^2*(1 - a*x)^(1/4)) - (521*a^3*(1 + a*x)^(1/4))/(192*x*(1 - a*x)^(1/4)) - (475*a^4*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64 - (475*a^4*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64","A",11,9,14,0.6429,1,"{6126, 98, 151, 155, 12, 93, 212, 206, 203}"
90,1,31,0,0.0247624,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^m \, dx","Int[x^m/E^(ArcTanh[a*x]/2),x]","\frac{x^{m+1} F_1\left(m+1;-\frac{1}{4},\frac{1}{4};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, -1/4, 1/4, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
91,1,290,0,0.2128915,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(ArcTanh[a*x]/2),x]","-\frac{x^2 (1-a x)^{5/4} (a x+1)^{3/4}}{4 a^2}-\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}-\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}",1,"(-11*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(64*a^4) - (x^2*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(4*a^2) - ((25 - 4*a*x)*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(96*a^4) - (11*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (11*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) - (11*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4) + (11*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",15,12,14,0.8571,1,"{6126, 100, 147, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
92,1,282,0,0.1985886,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(ArcTanh[a*x]/2),x]","-\frac{x (a x+1)^{3/4} (1-a x)^{5/4}}{3 a^2}+\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}+\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}",1,"(3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(8*a^3) + ((1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(12*a^3) - (x*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(3*a^2) + (3*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (3*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) + (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3) - (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3)","A",15,12,14,0.8571,1,"{6126, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
93,1,255,0,0.168347,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} x \, dx","Int[x/E^(ArcTanh[a*x]/2),x]","-\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}","-\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)^(1/4)*(1 + a*x)^(3/4))/(4*a^2) - ((1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(2*a^2) - ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(4*Sqrt[2]*a^2) + ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(4*Sqrt[2]*a^2) - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(8*Sqrt[2]*a^2) + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(8*Sqrt[2]*a^2)","A",14,11,12,0.9167,1,"{6126, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
94,1,221,0,0.1381305,"\int e^{-\frac{1}{2} \tanh ^{-1}(a x)} \, dx","Int[E^(-ArcTanh[a*x]/2),x]","\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}","\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,"((1 - a*x)^(1/4)*(1 + a*x)^(3/4))/a + ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a) - ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a) + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(2*Sqrt[2]*a) - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(2*Sqrt[2]*a)","A",13,10,10,1.000,1,"{6125, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
95,1,227,0,0.1612607,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x} \, dx","Int[1/(E^(ArcTanh[a*x]/2)*x),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)","-\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*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - 2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6126, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
96,1,72,0,0.0363453,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(ArcTanh[a*x]/2)*x^2),x]","-\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)","-\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)^(3/4))/x) - a*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + a*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)]","A",6,6,14,0.4286,1,"{6126, 94, 93, 298, 203, 206}"
97,1,110,0,0.0455312,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(ArcTanh[a*x]/2)*x^3),x]","\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}","\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,"(a*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*x) - ((1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(2*x^2) + (a^2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4 - (a^2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4","A",7,7,14,0.5000,1,"{6126, 96, 94, 93, 298, 203, 206}"
98,1,139,0,0.0619941,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(ArcTanh[a*x]/2)*x^4),x]","-\frac{11 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x}-\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{5 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{3 x^3}","-\frac{11 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x}-\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{5 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{12 x^2}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{3 x^3}",1,"-((1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(3*x^3) + (5*a*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(12*x^2) - (11*a^2*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(24*x) - (3*a^3*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8 + (3*a^3*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8","A",9,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 298, 203, 206}"
99,1,168,0,0.0785711,"\int \frac{e^{-\frac{1}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^(ArcTanh[a*x]/2)*x^5),x]","-\frac{29 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{96 x^2}+\frac{83 a^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{192 x}+\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{7 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x^3}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x^4}","-\frac{29 a^2 \sqrt[4]{1-a x} (a x+1)^{3/4}}{96 x^2}+\frac{83 a^3 \sqrt[4]{1-a x} (a x+1)^{3/4}}{192 x}+\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{7 a \sqrt[4]{1-a x} (a x+1)^{3/4}}{24 x^3}-\frac{\sqrt[4]{1-a x} (a x+1)^{3/4}}{4 x^4}",1,"-((1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*x^4) + (7*a*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(24*x^3) - (29*a^2*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(96*x^2) + (83*a^3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(192*x) + (11*a^4*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64 - (11*a^4*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64","A",10,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 298, 203, 206}"
100,1,31,0,0.027221,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^m \, dx","Int[x^m/E^((3*ArcTanh[a*x])/2),x]","\frac{x^{m+1} F_1\left(m+1;-\frac{3}{4},\frac{3}{4};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, -3/4, 3/4, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
101,1,290,0,0.2077102,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((3*ArcTanh[a*x])/2),x]","-\frac{x^2 (1-a x)^{7/4} \sqrt[4]{a x+1}}{4 a^2}-\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}-\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}",1,"(-41*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(64*a^4) - (x^2*(1 - a*x)^(7/4)*(1 + a*x)^(1/4))/(4*a^2) - ((11 - 4*a*x)*(1 - a*x)^(7/4)*(1 + a*x)^(1/4))/(32*a^4) - (123*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (123*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (123*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (123*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",15,12,14,0.8571,1,"{6126, 100, 147, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
102,1,282,0,0.2074091,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((3*ArcTanh[a*x])/2),x]","-\frac{x \sqrt[4]{a x+1} (1-a x)^{7/4}}{3 a^2}+\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}+\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}",1,"(17*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(24*a^3) + ((1 - a*x)^(7/4)*(1 + a*x)^(1/4))/(4*a^3) - (x*(1 - a*x)^(7/4)*(1 + a*x)^(1/4))/(3*a^2) + (17*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (17*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (17*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3) + (17*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3)","A",15,12,14,0.8571,1,"{6126, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
103,1,255,0,0.1698917,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} x \, dx","Int[x/E^((3*ArcTanh[a*x])/2),x]","-\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}","-\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,"(-3*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*a^2) - ((1 - a*x)^(7/4)*(1 + a*x)^(1/4))/(2*a^2) - (9*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (9*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (9*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2) - (9*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",14,11,12,0.9167,1,"{6126, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
104,1,222,0,0.1400965,"\int e^{-\frac{3}{2} \tanh ^{-1}(a x)} \, dx","Int[E^((-3*ArcTanh[a*x])/2),x]","\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}","\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,"((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/a + (3*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) - (3*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) - (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a) + (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a)","A",13,10,10,1.000,1,"{6125, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
105,1,227,0,0.1625505,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x} \, dx","Int[1/(E^((3*ArcTanh[a*x])/2)*x),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)","\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*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - 2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6126, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
106,1,73,0,0.032562,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((3*ArcTanh[a*x])/2)*x^2),x]","-\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)","-\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)^(1/4))/x) + 3*a*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + 3*a*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)]","A",6,6,14,0.4286,1,"{6126, 94, 93, 212, 206, 203}"
107,1,110,0,0.0421458,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((3*ArcTanh[a*x])/2)*x^3),x]","-\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}","-\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,"(3*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*x) - ((1 - a*x)^(7/4)*(1 + a*x)^(1/4))/(2*x^2) - (9*a^2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4 - (9*a^2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4","A",7,7,14,0.5000,1,"{6126, 96, 94, 93, 212, 206, 203}"
108,1,139,0,0.0614669,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((3*ArcTanh[a*x])/2)*x^4),x]","-\frac{23 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x}+\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{7 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{12 x^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{3 x^3}","-\frac{23 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{24 x}+\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{7 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{12 x^2}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{3 x^3}",1,"-((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(3*x^3) + (7*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(12*x^2) - (23*a^2*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(24*x) + (17*a^3*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8 + (17*a^3*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8","A",9,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 212, 206, 203}"
109,1,168,0,0.0790486,"\int \frac{e^{-\frac{3}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^((3*ArcTanh[a*x])/2)*x^5),x]","-\frac{15 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{32 x^2}+\frac{63 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{64 x}-\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{3 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{8 x^3}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x^4}","-\frac{15 a^2 (1-a x)^{3/4} \sqrt[4]{a x+1}}{32 x^2}+\frac{63 a^3 (1-a x)^{3/4} \sqrt[4]{a x+1}}{64 x}-\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{3 a (1-a x)^{3/4} \sqrt[4]{a x+1}}{8 x^3}-\frac{(1-a x)^{3/4} \sqrt[4]{a x+1}}{4 x^4}",1,"-((1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(4*x^4) + (3*a*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(8*x^3) - (15*a^2*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(32*x^2) + (63*a^3*(1 - a*x)^(3/4)*(1 + a*x)^(1/4))/(64*x) - (123*a^4*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64 - (123*a^4*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64","A",10,8,14,0.5714,1,"{6126, 99, 151, 12, 93, 212, 206, 203}"
110,1,31,0,0.026762,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^m \, dx","Int[x^m/E^((5*ArcTanh[a*x])/2),x]","\frac{x^{m+1} F_1\left(m+1;-\frac{5}{4},\frac{5}{4};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, -5/4, 5/4, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
111,1,317,0,0.2378613,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((5*ArcTanh[a*x])/2),x]","\frac{17 x^2 (1-a x)^{5/4} (a x+1)^{3/4}}{4 a^2}+\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{4 x^3 (1-a x)^{5/4}}{a \sqrt[4]{a x+1}}","\frac{17 x^2 (1-a x)^{5/4} (a x+1)^{3/4}}{4 a^2}+\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{4 x^3 (1-a x)^{5/4}}{a \sqrt[4]{a x+1}}",1,"(-4*x^3*(1 - a*x)^(5/4))/(a*(1 + a*x)^(1/4)) + (475*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(64*a^4) + (17*x^2*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(4*a^2) + ((521 - 452*a*x)*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(96*a^4) + (475*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) - (475*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a^4) + (475*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4) - (475*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a^4)","A",16,13,14,0.9286,1,"{6126, 97, 153, 147, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
112,1,305,0,0.2252521,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((5*ArcTanh[a*x])/2),x]","-\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}","-\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,"(-2*(1 - a*x)^(9/4))/(a^3*(1 + a*x)^(1/4)) - (55*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(8*a^3) - (11*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(4*a^3) - ((1 - a*x)^(9/4)*(1 + a*x)^(3/4))/(3*a^3) - (55*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) + (55*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^3) - (55*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3) + (55*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(16*Sqrt[2]*a^3)","A",16,12,14,0.8571,1,"{6126, 89, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
113,1,279,0,0.1926707,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} x \, dx","Int[x/E^((5*ArcTanh[a*x])/2),x]","\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}","\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))/(a^2*(1 + a*x)^(1/4)) + (25*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*a^2) + (5*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(2*a^2) + (25*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) - (25*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a^2) + (25*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2) - (25*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a^2)","A",15,11,12,0.9167,1,"{6126, 78, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
114,1,247,0,0.1577079,"\int e^{-\frac{5}{2} \tanh ^{-1}(a x)} \, dx","Int[E^((-5*ArcTanh[a*x])/2),x]","-\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}","-\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,"(-4*(1 - a*x)^(5/4))/(a*(1 + a*x)^(1/4)) - (5*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/a - (5*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) + (5*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a) - (5*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a) + (5*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(2*Sqrt[2]*a)","A",14,11,10,1.100,1,"{6125, 47, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
115,1,248,0,0.2042063,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x} \, dx","Int[1/(E^((5*ArcTanh[a*x])/2)*x),x]","\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)","\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,"(8*(1 - a*x)^(1/4))/(1 + a*x)^(1/4) + 2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)] - 2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/Sqrt[2]","A",19,16,14,1.143,1,"{6126, 98, 21, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
116,1,95,0,0.039102,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((5*ArcTanh[a*x])/2)*x^2),x]","-\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)","-\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,"(-10*a*(1 - a*x)^(1/4))/(1 + a*x)^(1/4) - (1 - a*x)^(5/4)/(x*(1 + a*x)^(1/4)) - 5*a*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)] + 5*a*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)]","A",7,6,14,0.4286,1,"{6126, 94, 93, 298, 203, 206}"
117,1,136,0,0.0536025,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((5*ArcTanh[a*x])/2)*x^3),x]","\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}}","\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,"(25*a^2*(1 - a*x)^(1/4))/(2*(1 + a*x)^(1/4)) + (5*a*(1 - a*x)^(5/4))/(4*x*(1 + a*x)^(1/4)) - (1 - a*x)^(9/4)/(2*x^2*(1 + a*x)^(1/4)) + (25*a^2*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4 - (25*a^2*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/4","A",8,7,14,0.5000,1,"{6126, 96, 94, 93, 298, 203, 206}"
118,1,165,0,0.0754489,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((5*ArcTanh[a*x])/2)*x^4),x]","-\frac{287 a^3 \sqrt[4]{1-a x}}{24 \sqrt[4]{a x+1}}-\frac{61 a^2 \sqrt[4]{1-a x}}{24 x \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{13 a \sqrt[4]{1-a x}}{12 x^2 \sqrt[4]{a x+1}}-\frac{\sqrt[4]{1-a x}}{3 x^3 \sqrt[4]{a x+1}}","-\frac{287 a^3 \sqrt[4]{1-a x}}{24 \sqrt[4]{a x+1}}-\frac{61 a^2 \sqrt[4]{1-a x}}{24 x \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{13 a \sqrt[4]{1-a x}}{12 x^2 \sqrt[4]{a x+1}}-\frac{\sqrt[4]{1-a x}}{3 x^3 \sqrt[4]{a x+1}}",1,"(-287*a^3*(1 - a*x)^(1/4))/(24*(1 + a*x)^(1/4)) - (1 - a*x)^(1/4)/(3*x^3*(1 + a*x)^(1/4)) + (13*a*(1 - a*x)^(1/4))/(12*x^2*(1 + a*x)^(1/4)) - (61*a^2*(1 - a*x)^(1/4))/(24*x*(1 + a*x)^(1/4)) - (55*a^3*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8 + (55*a^3*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/8","A",10,9,14,0.6429,1,"{6126, 98, 151, 155, 12, 93, 298, 203, 206}"
119,1,194,0,0.0983551,"\int \frac{e^{-\frac{5}{2} \tanh ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^((5*ArcTanh[a*x])/2)*x^5),x]","-\frac{113 a^2 \sqrt[4]{1-a x}}{96 x^2 \sqrt[4]{a x+1}}+\frac{2467 a^4 \sqrt[4]{1-a x}}{192 \sqrt[4]{a x+1}}+\frac{521 a^3 \sqrt[4]{1-a x}}{192 x \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{17 a \sqrt[4]{1-a x}}{24 x^3 \sqrt[4]{a x+1}}-\frac{\sqrt[4]{1-a x}}{4 x^4 \sqrt[4]{a x+1}}","-\frac{113 a^2 \sqrt[4]{1-a x}}{96 x^2 \sqrt[4]{a x+1}}+\frac{2467 a^4 \sqrt[4]{1-a x}}{192 \sqrt[4]{a x+1}}+\frac{521 a^3 \sqrt[4]{1-a x}}{192 x \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{17 a \sqrt[4]{1-a x}}{24 x^3 \sqrt[4]{a x+1}}-\frac{\sqrt[4]{1-a x}}{4 x^4 \sqrt[4]{a x+1}}",1,"(2467*a^4*(1 - a*x)^(1/4))/(192*(1 + a*x)^(1/4)) - (1 - a*x)^(1/4)/(4*x^4*(1 + a*x)^(1/4)) + (17*a*(1 - a*x)^(1/4))/(24*x^3*(1 + a*x)^(1/4)) - (113*a^2*(1 - a*x)^(1/4))/(96*x^2*(1 + a*x)^(1/4)) + (521*a^3*(1 - a*x)^(1/4))/(192*x*(1 + a*x)^(1/4)) + (475*a^4*ArcTan[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64 - (475*a^4*ArcTanh[(1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/64","A",11,9,14,0.6429,1,"{6126, 98, 151, 155, 12, 93, 298, 203, 206}"
120,1,28,0,0.0238578,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} x^m \, dx","Int[E^(ArcTanh[x]/3)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{1}{6},-\frac{1}{6};m+2;x,-x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{1}{6},-\frac{1}{6};m+2;x,-x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, 1/6, -1/6, 2 + m, x, -x])/(1 + m)","A",2,2,12,0.1667,1,"{6126, 133}"
121,1,245,0,0.3854042,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} x^2 \, dx","Int[E^(ArcTanh[x]/3)*x^2,x]","-\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)","-\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,"(-19*(1 - x)^(5/6)*(1 + x)^(1/6))/54 - ((1 - x)^(5/6)*(1 + x)^(7/6))/18 - ((1 - x)^(5/6)*x*(1 + x)^(7/6))/3 - (19*ArcTan[(1 - x)^(1/6)/(1 + x)^(1/6)])/81 + (19*ArcTan[Sqrt[3] - (2*(1 - x)^(1/6))/(1 + x)^(1/6)])/162 - (19*ArcTan[Sqrt[3] + (2*(1 - x)^(1/6))/(1 + x)^(1/6)])/162 - (19*Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) - (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)])/(108*Sqrt[3]) + (19*Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) + (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)])/(108*Sqrt[3])","A",16,12,12,1.000,1,"{6126, 90, 80, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
122,1,224,0,0.3401095,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} x \, dx","Int[E^(ArcTanh[x]/3)*x,x]","-\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)","-\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 - x)^(5/6)*(1 + x)^(1/6))/6 - ((1 - x)^(5/6)*(1 + x)^(7/6))/2 - ArcTan[(1 - x)^(1/6)/(1 + x)^(1/6)]/9 + ArcTan[Sqrt[3] - (2*(1 - x)^(1/6))/(1 + x)^(1/6)]/18 - ArcTan[Sqrt[3] + (2*(1 - x)^(1/6))/(1 + x)^(1/6)]/18 - Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) - (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)]/(12*Sqrt[3]) + Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) + (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)]/(12*Sqrt[3])","A",15,11,10,1.100,1,"{6126, 80, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
123,1,202,0,0.3291099,"\int e^{\frac{1}{3} \tanh ^{-1}(x)} \, dx","Int[E^(ArcTanh[x]/3),x]","-(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-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,"-((1 - x)^(5/6)*(1 + x)^(1/6)) - (2*ArcTan[(1 - x)^(1/6)/(1 + x)^(1/6)])/3 + ArcTan[Sqrt[3] - (2*(1 - x)^(1/6))/(1 + x)^(1/6)]/3 - ArcTan[Sqrt[3] + (2*(1 - x)^(1/6))/(1 + x)^(1/6)]/3 - Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) - (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)]/(2*Sqrt[3]) + Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) + (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)]/(2*Sqrt[3])","A",14,10,8,1.250,1,"{6125, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
124,1,346,0,0.454681,"\int \frac{e^{\frac{1}{3} \tanh ^{-1}(x)}}{x} \, dx","Int[E^(ArcTanh[x]/3)/x,x]","-\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)","-\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,"-2*ArcTan[(1 - x)^(1/6)/(1 + x)^(1/6)] + ArcTan[Sqrt[3] - (2*(1 - x)^(1/6))/(1 + x)^(1/6)] - ArcTan[Sqrt[3] + (2*(1 - x)^(1/6))/(1 + x)^(1/6)] + Sqrt[3]*ArcTan[(1 - (2*(1 + x)^(1/6))/(1 - x)^(1/6))/Sqrt[3]] - Sqrt[3]*ArcTan[(1 + (2*(1 + x)^(1/6))/(1 - x)^(1/6))/Sqrt[3]] - 2*ArcTanh[(1 + x)^(1/6)/(1 - x)^(1/6)] - (Sqrt[3]*Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) - (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)])/2 + (Sqrt[3]*Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3) + (Sqrt[3]*(1 - x)^(1/6))/(1 + x)^(1/6)])/2 + Log[1 - (1 + x)^(1/6)/(1 - x)^(1/6) + (1 + x)^(1/3)/(1 - x)^(1/3)]/2 - Log[1 + (1 + x)^(1/6)/(1 - x)^(1/6) + (1 + x)^(1/3)/(1 - x)^(1/3)]/2","A",25,13,12,1.083,1,"{6126, 105, 63, 331, 295, 634, 618, 204, 628, 203, 93, 210, 206}"
125,1,194,0,0.1572033,"\int \frac{e^{\frac{1}{3} \tanh ^{-1}(x)}}{x^2} \, dx","Int[E^(ArcTanh[x]/3)/x^2,x]","-\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)","-\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 - x)^(5/6)*(1 + x)^(1/6))/x) + ArcTan[(1 - (2*(1 + x)^(1/6))/(1 - x)^(1/6))/Sqrt[3]]/Sqrt[3] - ArcTan[(1 + (2*(1 + x)^(1/6))/(1 - x)^(1/6))/Sqrt[3]]/Sqrt[3] - (2*ArcTanh[(1 + x)^(1/6)/(1 - x)^(1/6)])/3 + Log[1 - (1 + x)^(1/6)/(1 - x)^(1/6) + (1 + x)^(1/3)/(1 - x)^(1/3)]/6 - Log[1 + (1 + x)^(1/6)/(1 - x)^(1/6) + (1 + x)^(1/3)/(1 - x)^(1/3)]/6","A",13,9,12,0.7500,1,"{6126, 94, 93, 210, 634, 618, 204, 628, 206}"
126,1,224,0,0.1750902,"\int \frac{e^{\frac{1}{3} \tanh ^{-1}(x)}}{x^3} \, dx","Int[E^(ArcTanh[x]/3)/x^3,x]","-\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)","-\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 - x)^(5/6)*(1 + x)^(1/6))/(6*x) - ((1 - x)^(5/6)*(1 + x)^(7/6))/(2*x^2) + ArcTan[(1 - (2*(1 + x)^(1/6))/(1 - x)^(1/6))/Sqrt[3]]/(6*Sqrt[3]) - ArcTan[(1 + (2*(1 + x)^(1/6))/(1 - x)^(1/6))/Sqrt[3]]/(6*Sqrt[3]) - ArcTanh[(1 + x)^(1/6)/(1 - x)^(1/6)]/9 + Log[1 - (1 + x)^(1/6)/(1 - x)^(1/6) + (1 + x)^(1/3)/(1 - x)^(1/3)]/36 - Log[1 + (1 + x)^(1/6)/(1 - x)^(1/6) + (1 + x)^(1/3)/(1 - x)^(1/3)]/36","A",14,10,12,0.8333,1,"{6126, 96, 94, 93, 210, 634, 618, 204, 628, 206}"
127,1,28,0,0.0263824,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} x^m \, dx","Int[E^((2*ArcTanh[x])/3)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{1}{3},-\frac{1}{3};m+2;x,-x\right)}{m+1}","\frac{x^{m+1} F_1\left(m+1;\frac{1}{3},-\frac{1}{3};m+2;x,-x\right)}{m+1}",1,"(x^(1 + m)*AppellF1[1 + m, 1/3, -1/3, 2 + m, x, -x])/(1 + m)","A",2,2,12,0.1667,1,"{6126, 133}"
128,1,133,0,0.049726,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} x^2 \, dx","Int[E^((2*ArcTanh[x])/3)*x^2,x]","-\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}}","-\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,"(-11*(1 - x)^(2/3)*(1 + x)^(1/3))/27 - ((1 - x)^(2/3)*(1 + x)^(4/3))/9 - ((1 - x)^(2/3)*x*(1 + x)^(4/3))/3 + (22*ArcTan[1/Sqrt[3] - (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(27*Sqrt[3]) + (11*Log[1 + x])/81 + (11*Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3)])/27","A",5,5,12,0.4167,1,"{6126, 90, 80, 50, 60}"
129,1,112,0,0.0319433,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} x \, dx","Int[E^((2*ArcTanh[x])/3)*x,x]","-\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}}","-\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 - x)^(2/3)*(1 + x)^(1/3))/3 - ((1 - x)^(2/3)*(1 + x)^(4/3))/2 + (2*ArcTan[1/Sqrt[3] - (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(3*Sqrt[3]) + Log[1 + x]/9 + Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3)]/3","A",4,4,10,0.4000,1,"{6126, 80, 50, 60}"
130,1,84,0,0.0171154,"\int e^{\frac{2}{3} \tanh ^{-1}(x)} \, dx","Int[E^((2*ArcTanh[x])/3),x]","-(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-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,"-((1 - x)^(2/3)*(1 + x)^(1/3)) + (2*ArcTan[1/Sqrt[3] - (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/Sqrt[3] + Log[1 + x]/3 + Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3)]","A",3,3,8,0.3750,1,"{6125, 50, 60}"
131,1,135,0,0.0317323,"\int \frac{e^{\frac{2}{3} \tanh ^{-1}(x)}}{x} \, dx","Int[E^((2*ArcTanh[x])/3)/x,x]","-\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)","-\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,"Sqrt[3]*ArcTan[1/Sqrt[3] - (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))] + Sqrt[3]*ArcTan[1/Sqrt[3] + (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))] - Log[x]/2 + Log[1 + x]/2 + (3*Log[1 + (1 - x)^(1/3)/(1 + x)^(1/3)])/2 + (3*Log[(1 - x)^(1/3) - (1 + x)^(1/3)])/2","A",4,4,12,0.3333,1,"{6126, 105, 60, 91}"
132,1,85,0,0.0314888,"\int \frac{e^{\frac{2}{3} \tanh ^{-1}(x)}}{x^2} \, dx","Int[E^((2*ArcTanh[x])/3)/x^2,x]","-\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}}","-\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)^(1/3))/x) + (2*ArcTan[1/Sqrt[3] + (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/Sqrt[3] - Log[x]/3 + Log[(1 - x)^(1/3) - (1 + x)^(1/3)]","A",3,3,12,0.2500,1,"{6126, 94, 91}"
133,1,116,0,0.0377013,"\int \frac{e^{\frac{2}{3} \tanh ^{-1}(x)}}{x^3} \, dx","Int[E^((2*ArcTanh[x])/3)/x^3,x]","-\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}}","-\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 - x)^(2/3)*(1 + x)^(1/3))/(3*x) - ((1 - x)^(2/3)*(1 + x)^(4/3))/(2*x^2) + (2*ArcTan[1/Sqrt[3] + (2*(1 - x)^(1/3))/(Sqrt[3]*(1 + x)^(1/3))])/(3*Sqrt[3]) - Log[x]/9 + Log[(1 - x)^(1/3) - (1 + x)^(1/3)]/3","A",4,4,12,0.3333,1,"{6126, 96, 94, 91}"
134,1,31,0,0.0275486,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x^m \, dx","Int[E^(ArcTanh[a*x]/4)*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{1}{8},-\frac{1}{8};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, 1/8, -1/8, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,14,0.1429,1,"{6126, 133}"
135,1,646,0,0.7018208,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x^2 \, dx","Int[E^(ArcTanh[a*x]/4)*x^2,x]","-\frac{x (1-a x)^{7/8} (a x+1)^{9/8}}{3 a^2}-\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}-\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}",1,"(-11*(1 - a*x)^(7/8)*(1 + a*x)^(1/8))/(32*a^3) - ((1 - a*x)^(7/8)*(1 + a*x)^(9/8))/(24*a^3) - (x*(1 - a*x)^(7/8)*(1 + a*x)^(9/8))/(3*a^2) + (11*Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(128*a^3) + (11*Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(128*a^3) - (11*Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(128*a^3) - (11*Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(128*a^3) - (11*Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(256*a^3) + (11*Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(256*a^3) - (11*Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(256*a^3) + (11*Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(256*a^3)","A",27,13,14,0.9286,1,"{6126, 90, 80, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
136,1,619,0,0.4815024,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} x \, dx","Int[E^(ArcTanh[a*x]/4)*x,x]","-\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}","-\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 - a*x)^(7/8)*(1 + a*x)^(1/8))/(8*a^2) - ((1 - a*x)^(7/8)*(1 + a*x)^(9/8))/(2*a^2) + (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(32*a^2) + (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(32*a^2) - (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(32*a^2) - (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(32*a^2) - (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(64*a^2) + (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(64*a^2) - (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(64*a^2) + (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(64*a^2)","A",26,12,12,1.000,1,"{6126, 80, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
137,1,591,0,0.4366282,"\int e^{\frac{1}{4} \tanh ^{-1}(a x)} \, dx","Int[E^(ArcTanh[a*x]/4),x]","-\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}","-\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,"-(((1 - a*x)^(7/8)*(1 + a*x)^(1/8))/a) + (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(4*a) + (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(4*a) - (Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]])/(4*a) - (Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]])/(4*a) - (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(8*a) + (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(8*a) - (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(8*a) + (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/(8*a)","A",25,11,10,1.100,1,"{6125, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
138,1,759,0,0.5271734,"\int \frac{e^{\frac{1}{4} \tanh ^{-1}(a x)}}{x} \, dx","Int[E^(ArcTanh[a*x]/4)/x,x]","-\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)","-\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,"-2*ArcTan[(1 + a*x)^(1/8)/(1 - a*x)^(1/8)] + Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]] + Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]] - Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 + Sqrt[2]]] - Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - a*x)^(1/8))/(1 + a*x)^(1/8))/Sqrt[2 - Sqrt[2]]] + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8)] - 2*ArcTanh[(1 + a*x)^(1/8)/(1 - a*x)^(1/8)] - (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/2 + (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/2 - (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/2 + (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - a*x)^(1/4)/(1 + a*x)^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - a*x)^(1/8))/(1 + a*x)^(1/8)])/2 + Log[1 - (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8) + (1 + a*x)^(1/4)/(1 - a*x)^(1/4)]/Sqrt[2] - Log[1 + (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8) + (1 + a*x)^(1/4)/(1 - a*x)^(1/4)]/Sqrt[2]","A",39,20,14,1.429,1,"{6126, 105, 63, 331, 299, 1122, 1169, 634, 618, 204, 628, 93, 214, 212, 206, 203, 211, 1165, 1162, 617}"
139,1,271,0,0.1292039,"\int \frac{e^{\frac{1}{4} \tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^(ArcTanh[a*x]/4)/x^2,x]","-\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)","-\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 - a*x)^(7/8)*(1 + a*x)^(1/8))/x) - (a*ArcTan[(1 + a*x)^(1/8)/(1 - a*x)^(1/8)])/2 + (a*ArcTan[1 - (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8)])/(2*Sqrt[2]) - (a*ArcTan[1 + (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8)])/(2*Sqrt[2]) - (a*ArcTanh[(1 + a*x)^(1/8)/(1 - a*x)^(1/8)])/2 + (a*Log[1 - (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8) + (1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/(4*Sqrt[2]) - (a*Log[1 + (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8) + (1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/(4*Sqrt[2])","A",16,13,14,0.9286,1,"{6126, 94, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
140,1,312,0,0.1526555,"\int \frac{e^{\frac{1}{4} \tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^(ArcTanh[a*x]/4)/x^3,x]","\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}","\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,"-(a*(1 - a*x)^(7/8)*(1 + a*x)^(1/8))/(8*x) - ((1 - a*x)^(7/8)*(1 + a*x)^(9/8))/(2*x^2) - (a^2*ArcTan[(1 + a*x)^(1/8)/(1 - a*x)^(1/8)])/16 + (a^2*ArcTan[1 - (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8)])/(16*Sqrt[2]) - (a^2*ArcTan[1 + (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8)])/(16*Sqrt[2]) - (a^2*ArcTanh[(1 + a*x)^(1/8)/(1 - a*x)^(1/8)])/16 + (a^2*Log[1 - (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8) + (1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/(32*Sqrt[2]) - (a^2*Log[1 + (Sqrt[2]*(1 + a*x)^(1/8))/(1 - a*x)^(1/8) + (1 + a*x)^(1/4)/(1 - a*x)^(1/4)])/(32*Sqrt[2])","A",17,14,14,1.000,1,"{6126, 96, 94, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
141,1,45,0,0.0431906,"\int e^{4 \tanh ^{-1}(a x)} x^m \, dx","Int[E^(4*ArcTanh[a*x])*x^m,x]","-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}","-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)/(1 + m) + (4*x^(1 + m))/(1 - a*x) - 4*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x]","A",4,4,12,0.3333,1,"{6126, 89, 80, 64}"
142,1,151,0,0.8810884,"\int e^{3 \tanh ^{-1}(a x)} x^m \, dx","Int[E^(3*ArcTanh[a*x])*x^m,x]","-\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}","-\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,"(-3*x^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) - (a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m) + (4*x^(1 + m)*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (4*a*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",9,5,12,0.4167,1,"{6124, 6742, 364, 850, 808}"
143,1,36,0,0.0245886,"\int e^{2 \tanh ^{-1}(a x)} x^m \, dx","Int[E^(2*ArcTanh[a*x])*x^m,x]","\frac{2 x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{m+1}-\frac{x^{m+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 + m)) + (2*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/(1 + m)","A",3,3,12,0.2500,1,"{6126, 80, 64}"
144,1,74,0,0.0419184,"\int e^{\tanh ^{-1}(a x)} x^m \, dx","Int[E^ArcTanh[a*x]*x^m,x]","\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}","\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)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",4,3,10,0.3000,1,"{6124, 808, 364}"
145,1,75,0,0.0445418,"\int e^{-\tanh ^{-1}(a x)} x^m \, dx","Int[x^m/E^ArcTanh[a*x],x]","\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}","\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)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) - (a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",4,3,12,0.2500,1,"{6124, 808, 364}"
146,1,37,0,0.0249729,"\int e^{-2 \tanh ^{-1}(a x)} x^m \, dx","Int[x^m/E^(2*ArcTanh[a*x]),x]","\frac{2 x^{m+1} \, _2F_1(1,m+1;m+2;-a x)}{m+1}-\frac{x^{m+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 + m)) + (2*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)])/(1 + m)","A",3,3,12,0.2500,1,"{6126, 80, 64}"
147,1,150,0,0.813987,"\int e^{-3 \tanh ^{-1}(a x)} x^m \, dx","Int[x^m/E^(3*ArcTanh[a*x]),x]","-\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}","-\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,"(-3*x^(1 + m)*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m) + (4*x^(1 + m)*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) - (4*a*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",9,5,12,0.4167,1,"{6124, 6742, 364, 850, 808}"
148,1,35,0,0.0295276,"\int e^{n \tanh ^{-1}(a x)} x^m \, dx","Int[E^(n*ArcTanh[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(m+1;\frac{n}{2},-\frac{n}{2};m+2;a x,-a x\right)}{m+1}","\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,"(x^(1 + m)*AppellF1[1 + m, n/2, -n/2, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,12,0.1667,1,"{6126, 133}"
149,1,155,0,0.1175221,"\int e^{n \tanh ^{-1}(a x)} x^3 \, dx","Int[E^(n*ArcTanh[a*x])*x^3,x]","-\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}","-\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,"-(x^2*(1 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2))/(4*a^2) - ((1 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2)*(6 + n^2 + 2*a*n*x))/(24*a^4) - (2^(-2 + n/2)*n*(8 + n^2)*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a*x)/2])/(3*a^4*(2 - n))","A",4,4,12,0.3333,1,"{6126, 100, 147, 69}"
150,1,141,0,0.0948837,"\int e^{n \tanh ^{-1}(a x)} x^2 \, dx","Int[E^(n*ArcTanh[a*x])*x^2,x]","-\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}","-\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,"-(n*(1 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2))/(6*a^3) - (x*(1 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2))/(3*a^2) - (2^(n/2)*(2 + n^2)*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a*x)/2])/(3*a^3*(2 - n))","A",4,4,12,0.3333,1,"{6126, 90, 80, 69}"
151,1,99,0,0.0414173,"\int e^{n \tanh ^{-1}(a x)} x \, dx","Int[E^(n*ArcTanh[a*x])*x,x]","-\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}","-\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 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2))/(2*a^2) - (2^(n/2)*n*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a*x)/2])/(a^2*(2 - n))","A",3,3,10,0.3000,1,"{6126, 80, 69}"
152,1,65,0,0.0116714,"\int e^{n \tanh ^{-1}(a x)} \, dx","Int[E^(n*ArcTanh[a*x]),x]","-\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)}","-\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,"-((2^(1 + n/2)*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a*x)/2])/(a*(2 - n)))","A",2,2,8,0.2500,1,"{6125, 69}"
153,1,111,0,0.0509592,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x} \, dx","Int[E^(n*ArcTanh[a*x])/x,x]","\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}","\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, -n/2, 1 - n/2, (1 - a*x)/(1 + a*x)])/(n*(1 - a*x)^(n/2)) - (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(n*(1 - a*x)^(n/2))","A",4,4,12,0.3333,1,"{6126, 105, 69, 131}"
154,1,67,0,0.0311097,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2} \, dx","Int[E^(n*ArcTanh[a*x])/x^2,x]","-\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}","-\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)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(2 - n)","A",2,2,12,0.1667,1,"{6126, 131}"
155,1,105,0,0.0489941,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3} \, dx","Int[E^(n*ArcTanh[a*x])/x^3,x]","-\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}","-\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)^((2 + n)/2))/(2*x^2) - (2*a^2*n*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(2 - n)","A",3,3,12,0.2500,1,"{6126, 96, 131}"
156,1,147,0,0.0676119,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^4} \, dx","Int[E^(n*ArcTanh[a*x])/x^4,x]","-\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 n (a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{6 x^2}-\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{3 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 n (a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{6 x^2}-\frac{(a x+1)^{\frac{n+2}{2}} (1-a x)^{1-\frac{n}{2}}}{3 x^3}",1,"-((1 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2))/(3*x^3) - (a*n*(1 - a*x)^(1 - n/2)*(1 + a*x)^((2 + n)/2))/(6*x^2) - (2*a^3*(2 + n^2)*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(3*(2 - n))","A",5,5,12,0.4167,1,"{6126, 129, 151, 12, 131}"
157,1,65,0,0.0490697,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^p,x]","-\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}}","-\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]*(c - a*c*x)^(1 + p)*Hypergeometric2F1[-1/2, 1/2 + p, 3/2 + p, (1 - a*x)/2])/(a*c*(1 + 2*p)*Sqrt[1 - a*x])","A",3,3,16,0.1875,1,"{6130, 23, 69}"
158,1,123,0,0.0804764,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^4,x]","\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}","\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,"(7*c^4*x*Sqrt[1 - a^2*x^2])/8 + (7*c^4*(1 - a^2*x^2)^(3/2))/(12*a) + (7*c^4*(1 - a*x)*(1 - a^2*x^2)^(3/2))/(20*a) + (c^4*(1 - a*x)^2*(1 - a^2*x^2)^(3/2))/(5*a) + (7*c^4*ArcSin[a*x])/(8*a)","A",6,5,16,0.3125,1,"{6127, 671, 641, 195, 216}"
159,1,91,0,0.0559282,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^3,x]","\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}","\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,"(5*c^3*x*Sqrt[1 - a^2*x^2])/8 + (5*c^3*(1 - a^2*x^2)^(3/2))/(12*a) + (c^3*(1 - a*x)*(1 - a^2*x^2)^(3/2))/(4*a) + (5*c^3*ArcSin[a*x])/(8*a)","A",5,5,16,0.3125,1,"{6127, 671, 641, 195, 216}"
160,1,61,0,0.0374053,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^2,x]","\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}","\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*x*Sqrt[1 - a^2*x^2])/2 + (c^2*(1 - a^2*x^2)^(3/2))/(3*a) + (c^2*ArcSin[a*x])/(2*a)","A",4,4,16,0.2500,1,"{6127, 641, 195, 216}"
161,1,33,0,0.0191962,"\int e^{\tanh ^{-1}(a x)} (c-a c x) \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x),x]","\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}","\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}",1,"(c*x*Sqrt[1 - a^2*x^2])/2 + (c*ArcSin[a*x])/(2*a)","A",3,3,14,0.2143,1,"{6127, 195, 216}"
162,1,43,0,0.0407308,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x),x]","\frac{2 \sqrt{1-a^2 x^2}}{a c (1-a x)}-\frac{\sin ^{-1}(a x)}{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^2*x^2])/(a*c*(1 - a*x)) - ArcSin[a*x]/(a*c)","A",3,3,16,0.1875,1,"{6127, 663, 216}"
163,1,32,0,0.0333797,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^2,x]","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}",1,"(1 - a^2*x^2)^(3/2)/(3*a*c^2*(1 - a*x)^3)","A",2,2,16,0.1250,1,"{6127, 651}"
164,1,65,0,0.0495264,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^3,x]","\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}","\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,"(1 - a^2*x^2)^(3/2)/(5*a*c^3*(1 - a*x)^4) + (1 - a^2*x^2)^(3/2)/(15*a*c^3*(1 - a*x)^3)","A",3,3,16,0.1875,1,"{6127, 659, 651}"
165,1,97,0,0.0685209,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^4,x]","\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}","\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 - a^2*x^2)^(3/2)/(7*a*c^4*(1 - a*x)^5) + (2*(1 - a^2*x^2)^(3/2))/(35*a*c^4*(1 - a*x)^4) + (2*(1 - a^2*x^2)^(3/2))/(105*a*c^4*(1 - a*x)^3)","A",4,3,16,0.1875,1,"{6127, 659, 651}"
166,1,129,0,0.0910225,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^5,x]","\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}","\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^2*x^2)^(3/2)/(9*a*c^5*(1 - a*x)^6) + (1 - a^2*x^2)^(3/2)/(21*a*c^5*(1 - a*x)^5) + (2*(1 - a^2*x^2)^(3/2))/(105*a*c^5*(1 - a*x)^4) + (2*(1 - a^2*x^2)^(3/2))/(315*a*c^5*(1 - a*x)^3)","A",5,3,16,0.1875,1,"{6127, 659, 651}"
167,1,41,0,0.0441538,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^p,x]","\frac{(c-a c x)^{p+1}}{a c (p+1)}-\frac{2 (c-a c x)^p}{a p}","\frac{(c-a c x)^{p+1}}{a c (p+1)}-\frac{2 (c-a c x)^p}{a p}",1,"(-2*(c - a*c*x)^p)/(a*p) + (c - a*c*x)^(1 + p)/(a*c*(1 + p))","A",4,3,18,0.1667,1,"{6130, 21, 43}"
168,1,37,0,0.0339982,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^5 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^5,x]","\frac{c^5 (1-a x)^6}{6 a}-\frac{2 c^5 (1-a x)^5}{5 a}","\frac{c^5 (1-a x)^6}{6 a}-\frac{2 c^5 (1-a x)^5}{5 a}",1,"(-2*c^5*(1 - a*x)^5)/(5*a) + (c^5*(1 - a*x)^6)/(6*a)","A",3,2,18,0.1111,1,"{6129, 43}"
169,1,37,0,0.0323223,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^4,x]","\frac{c^4 (1-a x)^5}{5 a}-\frac{c^4 (1-a x)^4}{2 a}","\frac{c^4 (1-a x)^5}{5 a}-\frac{c^4 (1-a x)^4}{2 a}",1,"-(c^4*(1 - a*x)^4)/(2*a) + (c^4*(1 - a*x)^5)/(5*a)","A",3,2,18,0.1111,1,"{6129, 43}"
170,1,37,0,0.0347904,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^3,x]","\frac{c^3 (1-a x)^4}{4 a}-\frac{2 c^3 (1-a x)^3}{3 a}","\frac{c^3 (1-a x)^4}{4 a}-\frac{2 c^3 (1-a x)^3}{3 a}",1,"(-2*c^3*(1 - a*x)^3)/(3*a) + (c^3*(1 - a*x)^4)/(4*a)","A",3,2,18,0.1111,1,"{6129, 43}"
171,1,19,0,0.0255281,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^2,x]","c^2 x-\frac{1}{3} a^2 c^2 x^3","c^2 x-\frac{1}{3} a^2 c^2 x^3",1,"c^2*x - (a^2*c^2*x^3)/3","A",3,2,18,0.1111,1,"{6129, 41}"
172,1,26,0,0.011943,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x) \, dx","Int[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",1,1,16,0.06250,1,"{2288}"
173,1,31,0,0.0381136,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x),x]","\frac{2}{a c (1-a x)}+\frac{\log (1-a x)}{a c}","\frac{2}{a c (1-a x)}+\frac{\log (1-a x)}{a c}",1,"2/(a*c*(1 - a*x)) + Log[1 - a*x]/(a*c)","A",3,2,18,0.1111,1,"{6129, 43}"
174,1,13,0,0.0261538,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x)^2,x]","\frac{x}{c^2 (1-a x)^2}","\frac{x}{c^2 (1-a x)^2}",1,"x/(c^2*(1 - a*x)^2)","A",2,2,18,0.1111,1,"{6129, 34}"
175,1,37,0,0.0391528,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x)^3,x]","\frac{2}{3 a c^3 (1-a x)^3}-\frac{1}{2 a c^3 (1-a x)^2}","\frac{2}{3 a c^3 (1-a x)^3}-\frac{1}{2 a c^3 (1-a x)^2}",1,"2/(3*a*c^3*(1 - a*x)^3) - 1/(2*a*c^3*(1 - a*x)^2)","A",3,2,18,0.1111,1,"{6129, 43}"
176,1,37,0,0.0388345,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x)^4,x]","\frac{1}{2 a c^4 (1-a x)^4}-\frac{1}{3 a c^4 (1-a x)^3}","\frac{1}{2 a c^4 (1-a x)^4}-\frac{1}{3 a c^4 (1-a x)^3}",1,"1/(2*a*c^4*(1 - a*x)^4) - 1/(3*a*c^4*(1 - a*x)^3)","A",3,2,18,0.1111,1,"{6129, 43}"
177,1,65,0,0.0518962,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^p,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}}","\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)^(1 + p)*Hypergeometric2F1[-3/2, -1/2 + p, 1/2 + p, (1 - a*x)/2])/(a*c*(1 - 2*p)*(1 - a*x)^(3/2))","A",3,3,18,0.1667,1,"{6130, 23, 69}"
178,1,83,0,0.0485722,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^4,x]","\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}","\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,"(3*c^4*x*Sqrt[1 - a^2*x^2])/8 + (c^4*x*(1 - a^2*x^2)^(3/2))/4 + (c^4*(1 - a^2*x^2)^(5/2))/(5*a) + (3*c^4*ArcSin[a*x])/(8*a)","A",5,4,18,0.2222,1,"{6127, 641, 195, 216}"
179,1,59,0,0.0356936,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^3,x]","\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}","\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,"(3*c^3*x*Sqrt[1 - a^2*x^2])/8 + (c^3*x*(1 - a^2*x^2)^(3/2))/4 + (3*c^3*ArcSin[a*x])/(8*a)","A",4,3,18,0.1667,1,"{6127, 195, 216}"
180,1,61,0,0.0458223,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^2,x]","-\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}","-\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*x*Sqrt[1 - a^2*x^2])/2 - (c^2*(1 - a^2*x^2)^(3/2))/(3*a) + (c^2*ArcSin[a*x])/(2*a)","A",4,4,18,0.2222,1,"{6127, 665, 195, 216}"
181,1,65,0,0.047755,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x) \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x),x]","-\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}","-\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,"(-3*c*Sqrt[1 - a^2*x^2])/(2*a) - (c*(1 - a^2*x^2)^(3/2))/(2*a*(1 - a*x)) + (3*c*ArcSin[a*x])/(2*a)","A",4,3,16,0.1875,1,"{6127, 665, 216}"
182,1,74,0,0.0589498,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x),x]","\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}","\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,"(-2*Sqrt[1 - a^2*x^2])/(a*c*(1 - a*x)) + (2*(1 - a^2*x^2)^(3/2))/(3*a*c*(1 - a*x)^3) + ArcSin[a*x]/(a*c)","A",4,3,18,0.1667,1,"{6127, 663, 216}"
183,1,32,0,0.0367227,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^2,x]","\frac{\left(1-a^2 x^2\right)^{5/2}}{5 a c^2 (1-a x)^5}","\frac{\left(1-a^2 x^2\right)^{5/2}}{5 a c^2 (1-a x)^5}",1,"(1 - a^2*x^2)^(5/2)/(5*a*c^2*(1 - a*x)^5)","A",2,2,18,0.1111,1,"{6127, 651}"
184,1,65,0,0.0514531,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^3,x]","\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}","\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 - a^2*x^2)^(5/2)/(7*a*c^3*(1 - a*x)^6) + (1 - a^2*x^2)^(5/2)/(35*a*c^3*(1 - a*x)^5)","A",3,3,18,0.1667,1,"{6127, 659, 651}"
185,1,97,0,0.069434,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^4,x]","\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}","\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^2*x^2)^(5/2)/(9*a*c^4*(1 - a*x)^7) + (2*(1 - a^2*x^2)^(5/2))/(63*a*c^4*(1 - a*x)^6) + (2*(1 - a^2*x^2)^(5/2))/(315*a*c^4*(1 - a*x)^5)","A",4,3,18,0.1667,1,"{6127, 659, 651}"
186,1,129,0,0.0917504,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^5,x]","\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}","\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 - a^2*x^2)^(5/2)/(11*a*c^5*(1 - a*x)^8) + (1 - a^2*x^2)^(5/2)/(33*a*c^5*(1 - a*x)^7) + (2*(1 - a^2*x^2)^(5/2))/(231*a*c^5*(1 - a*x)^6) + (2*(1 - a^2*x^2)^(5/2))/(1155*a*c^5*(1 - a*x)^5)","A",5,3,18,0.1667,1,"{6127, 659, 651}"
187,1,66,0,0.0583784,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(4*ArcTanh[a*x])*(c - a*c*x)^p,x]","\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)}","\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,"(4*c*(c - a*c*x)^(-1 + p))/(a*(1 - p)) + (4*(c - a*c*x)^p)/(a*p) - (c - a*c*x)^(1 + p)/(a*c*(1 + p))","A",4,3,18,0.1667,1,"{6130, 21, 43}"
188,1,53,0,0.0437818,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^5 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a*c*x)^5,x]","-\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}","-\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,"-((c^5*(1 - a*x)^4)/a) + (4*c^5*(1 - a*x)^5)/(5*a) - (c^5*(1 - a*x)^6)/(6*a)","A",3,2,18,0.1111,1,"{6129, 43}"
189,1,32,0,0.0327282,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a*c*x)^4,x]","\frac{1}{5} a^4 c^4 x^5-\frac{2}{3} a^2 c^4 x^3+c^4 x","\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*c^4*x^3)/3 + (a^4*c^4*x^5)/5","A",4,3,18,0.1667,1,"{6129, 41, 194}"
190,1,35,0,0.0375389,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a*c*x)^3,x]","\frac{2 c^3 (a x+1)^3}{3 a}-\frac{c^3 (a x+1)^4}{4 a}","\frac{2 c^3 (a x+1)^3}{3 a}-\frac{c^3 (a x+1)^4}{4 a}",1,"(2*c^3*(1 + a*x)^3)/(3*a) - (c^3*(1 + a*x)^4)/(4*a)","A",3,2,18,0.1111,1,"{6129, 43}"
191,1,17,0,0.0246137,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a*c*x)^2,x]","\frac{c^2 (a x+1)^3}{3 a}","\frac{c^2 (a x+1)^3}{3 a}",1,"(c^2*(1 + a*x)^3)/(3*a)","A",2,2,18,0.1111,1,"{6129, 32}"
192,1,27,0,0.0225509,"\int e^{4 \tanh ^{-1}(a x)} (c-a c x) \, dx","Int[E^(4*ArcTanh[a*x])*(c - a*c*x),x]","-\frac{1}{2} a c x^2-\frac{4 c \log (1-a x)}{a}-3 c x","-\frac{1}{2} a c x^2-\frac{4 c \log (1-a x)}{a}-3 c x",1,"-3*c*x - (a*c*x^2)/2 - (4*c*Log[1 - a*x])/a","A",3,2,16,0.1250,1,"{6129, 43}"
193,1,48,0,0.0449021,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a*c*x),x]","-\frac{4}{a c (1-a x)}+\frac{2}{a c (1-a x)^2}-\frac{\log (1-a x)}{a c}","-\frac{4}{a c (1-a x)}+\frac{2}{a c (1-a x)^2}-\frac{\log (1-a x)}{a c}",1,"2/(a*c*(1 - a*x)^2) - 4/(a*c*(1 - a*x)) - Log[1 - a*x]/(a*c)","A",3,2,18,0.1111,1,"{6129, 43}"
194,1,25,0,0.0276597,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[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",2,2,18,0.1111,1,"{6129, 37}"
195,1,52,0,0.0431774,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a*c*x)^3,x]","\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}","\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/(a*c^3*(1 - a*x)^4) - 4/(3*a*c^3*(1 - a*x)^3) + 1/(2*a*c^3*(1 - a*x)^2)","A",3,2,18,0.1111,1,"{6129, 43}"
196,1,53,0,0.0420262,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a*c*x)^4,x]","\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}","\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,"4/(5*a*c^4*(1 - a*x)^5) - 1/(a*c^4*(1 - a*x)^4) + 1/(3*a*c^4*(1 - a*x)^3)","A",3,2,18,0.1111,1,"{6129, 43}"
197,1,65,0,0.0493803,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^ArcTanh[a*x],x]","-\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)}","-\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]*Sqrt[1 - a*x]*(c - a*c*x)^(1 + p)*Hypergeometric2F1[1/2, 3/2 + p, 5/2 + p, (1 - a*x)/2])/(a*c*(3 + 2*p)))","A",3,3,18,0.1667,1,"{6130, 23, 69}"
198,1,133,0,0.0955488,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[(c - a*c*x)^3/E^ArcTanh[a*x],x]","\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}","\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,"(35*c^3*Sqrt[1 - a^2*x^2])/(8*a) + (35*c^3*(1 - a*x)*Sqrt[1 - a^2*x^2])/(24*a) + (7*c^3*(1 - a*x)^2*Sqrt[1 - a^2*x^2])/(12*a) + (c^3*(1 - a*x)^3*Sqrt[1 - a^2*x^2])/(4*a) + (35*c^3*ArcSin[a*x])/(8*a)","A",6,4,18,0.2222,1,"{6127, 671, 641, 216}"
199,1,101,0,0.0699396,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[(c - a*c*x)^2/E^ArcTanh[a*x],x]","\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}","\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,"(5*c^2*Sqrt[1 - a^2*x^2])/(2*a) + (5*c^2*(1 - a*x)*Sqrt[1 - a^2*x^2])/(6*a) + (c^2*(1 - a*x)^2*Sqrt[1 - a^2*x^2])/(3*a) + (5*c^2*ArcSin[a*x])/(2*a)","A",5,4,18,0.2222,1,"{6127, 671, 641, 216}"
200,1,63,0,0.0428937,"\int e^{-\tanh ^{-1}(a x)} (c-a c x) \, dx","Int[(c - a*c*x)/E^ArcTanh[a*x],x]","\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}","\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,"(3*c*Sqrt[1 - a^2*x^2])/(2*a) + (c*(1 - a*x)*Sqrt[1 - a^2*x^2])/(2*a) + (3*c*ArcSin[a*x])/(2*a)","A",4,4,16,0.2500,1,"{6127, 671, 641, 216}"
201,1,11,0,0.0279087,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[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",2,2,18,0.1111,1,"{6127, 216}"
202,1,29,0,0.0356859,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^2),x]","\frac{\sqrt{1-a^2 x^2}}{a c^2 (1-a x)}","\frac{\sqrt{1-a^2 x^2}}{a c^2 (1-a x)}",1,"Sqrt[1 - a^2*x^2]/(a*c^2*(1 - a*x))","A",2,2,18,0.1111,1,"{6127, 651}"
203,1,65,0,0.0516709,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^3),x]","\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}","\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,"Sqrt[1 - a^2*x^2]/(3*a*c^3*(1 - a*x)^2) + Sqrt[1 - a^2*x^2]/(3*a*c^3*(1 - a*x))","A",3,3,18,0.1667,1,"{6127, 659, 651}"
204,1,97,0,0.0681872,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^4),x]","\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}","\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^2*x^2]/(5*a*c^4*(1 - a*x)^3) + (2*Sqrt[1 - a^2*x^2])/(15*a*c^4*(1 - a*x)^2) + (2*Sqrt[1 - a^2*x^2])/(15*a*c^4*(1 - a*x))","A",4,3,18,0.1667,1,"{6127, 659, 651}"
205,1,129,0,0.0899088,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^5),x]","\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}","\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,"Sqrt[1 - a^2*x^2]/(7*a*c^5*(1 - a*x)^4) + (3*Sqrt[1 - a^2*x^2])/(35*a*c^5*(1 - a*x)^3) + (2*Sqrt[1 - a^2*x^2])/(35*a*c^5*(1 - a*x)^2) + (2*Sqrt[1 - a^2*x^2])/(35*a*c^5*(1 - a*x))","A",5,3,18,0.1667,1,"{6127, 659, 651}"
206,1,44,0,0.0417842,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^(2*ArcTanh[a*x]),x]","-\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)}","-\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,"-((c - a*c*x)^(2 + p)*Hypergeometric2F1[1, 2 + p, 3 + p, (1 - a*x)/2])/(2*a*c^2*(2 + p))","A",3,3,18,0.1667,1,"{6130, 21, 68}"
207,1,91,0,0.0487565,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Int[(c - a*c*x)^4/E^(2*ArcTanh[a*x]),x]","\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","\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,"-16*c^4*x + (4*c^4*(1 - a*x)^2)/a + (4*c^4*(1 - a*x)^3)/(3*a) + (c^4*(1 - a*x)^4)/(2*a) + (c^4*(1 - a*x)^5)/(5*a) + (32*c^4*Log[1 + a*x])/a","A",3,2,18,0.1111,1,"{6129, 43}"
208,1,73,0,0.0434497,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[(c - a*c*x)^3/E^(2*ArcTanh[a*x]),x]","\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","\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,"-8*c^3*x + (2*c^3*(1 - a*x)^2)/a + (2*c^3*(1 - a*x)^3)/(3*a) + (c^3*(1 - a*x)^4)/(4*a) + (16*c^3*Log[1 + a*x])/a","A",3,2,18,0.1111,1,"{6129, 43}"
209,1,54,0,0.0363179,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[(c - a*c*x)^2/E^(2*ArcTanh[a*x]),x]","\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","\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,"-4*c^2*x + (c^2*(1 - a*x)^2)/a + (c^2*(1 - a*x)^3)/(3*a) + (8*c^2*Log[1 + a*x])/a","A",3,2,18,0.1111,1,"{6129, 43}"
210,1,26,0,0.0230231,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x) \, dx","Int[(c - a*c*x)/E^(2*ArcTanh[a*x]),x]","\frac{1}{2} a c x^2+\frac{4 c \log (a x+1)}{a}-3 c x","\frac{1}{2} a c x^2+\frac{4 c \log (a x+1)}{a}-3 c x",1,"-3*c*x + (a*c*x^2)/2 + (4*c*Log[1 + a*x])/a","A",3,2,16,0.1250,1,"{6129, 43}"
211,1,13,0,0.0256917,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[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",2,2,18,0.1111,1,"{6129, 31}"
212,1,11,0,0.0268221,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[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",3,3,18,0.1667,1,"{6129, 35, 206}"
213,1,33,0,0.0396926,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^3),x]","\frac{1}{2 a c^3 (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*c^3*(1 - a*x)) + ArcTanh[a*x]/(2*a*c^3)","A",4,3,18,0.1667,1,"{6129, 44, 207}"
214,1,51,0,0.0471335,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^4),x]","\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}","\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,"1/(4*a*c^4*(1 - a*x)^2) + 1/(4*a*c^4*(1 - a*x)) + ArcTanh[a*x]/(4*a*c^4)","A",4,3,18,0.1667,1,"{6129, 44, 207}"
215,1,69,0,0.0533353,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^5),x]","\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}","\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,"1/(6*a*c^5*(1 - a*x)^3) + 1/(8*a*c^5*(1 - a*x)^2) + 1/(8*a*c^5*(1 - a*x)) + ArcTanh[a*x]/(8*a*c^5)","A",4,3,18,0.1667,1,"{6129, 44, 207}"
216,1,65,0,0.0521735,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^(3*ArcTanh[a*x]),x]","-\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)}","-\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)^(3/2)*(c - a*c*x)^(1 + p)*Hypergeometric2F1[3/2, 5/2 + p, 7/2 + p, (1 - a*x)/2])/(Sqrt[2]*a*c*(5 + 2*p)))","A",3,3,18,0.1667,1,"{6130, 23, 69}"
217,1,163,0,0.1253408,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[(c - a*c*x)^3/E^(3*ArcTanh[a*x]),x]","-\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}","-\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,"(-2*c^3*(1 - a*x)^5)/(a*Sqrt[1 - a^2*x^2]) - (315*c^3*Sqrt[1 - a^2*x^2])/(8*a) - (105*c^3*(1 - a*x)*Sqrt[1 - a^2*x^2])/(8*a) - (21*c^3*(1 - a*x)^2*Sqrt[1 - a^2*x^2])/(4*a) - (9*c^3*(1 - a*x)^3*Sqrt[1 - a^2*x^2])/(4*a) - (315*c^3*ArcSin[a*x])/(8*a)","A",7,5,18,0.2778,1,"{6127, 669, 671, 641, 216}"
218,1,131,0,0.0941339,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[(c - a*c*x)^2/E^(3*ArcTanh[a*x]),x]","-\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}","-\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,"(-2*c^2*(1 - a*x)^4)/(a*Sqrt[1 - a^2*x^2]) - (35*c^2*Sqrt[1 - a^2*x^2])/(2*a) - (35*c^2*(1 - a*x)*Sqrt[1 - a^2*x^2])/(6*a) - (7*c^2*(1 - a*x)^2*Sqrt[1 - a^2*x^2])/(3*a) - (35*c^2*ArcSin[a*x])/(2*a)","A",6,5,18,0.2778,1,"{6127, 669, 671, 641, 216}"
219,1,91,0,0.0641629,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x) \, dx","Int[(c - a*c*x)/E^(3*ArcTanh[a*x]),x]","-\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}","-\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,"(-2*c*(1 - a*x)^3)/(a*Sqrt[1 - a^2*x^2]) - (15*c*Sqrt[1 - a^2*x^2])/(2*a) - (5*c*(1 - a*x)*Sqrt[1 - a^2*x^2])/(2*a) - (15*c*ArcSin[a*x])/(2*a)","A",5,5,16,0.3125,1,"{6127, 669, 671, 641, 216}"
220,1,41,0,0.04145,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)),x]","-\frac{2 (1-a x)}{a c \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)}{a c}","-\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))/(a*c*Sqrt[1 - a^2*x^2]) - ArcSin[a*x]/(a*c)","A",3,3,18,0.1667,1,"{6127, 653, 216}"
221,1,28,0,0.0329932,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^2),x]","-\frac{1-a x}{a c^2 \sqrt{1-a^2 x^2}}","-\frac{1-a x}{a c^2 \sqrt{1-a^2 x^2}}",1,"-((1 - a*x)/(a*c^2*Sqrt[1 - a^2*x^2]))","A",2,2,18,0.1111,1,"{6127, 637}"
222,1,19,0,0.0278557,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[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",2,2,18,0.1111,1,"{6127, 191}"
223,1,55,0,0.0445643,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^4),x]","\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}}","\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,"(2*x)/(3*c^4*Sqrt[1 - a^2*x^2]) + 1/(3*a*c^4*(1 - a*x)*Sqrt[1 - a^2*x^2])","A",3,3,18,0.1667,1,"{6127, 659, 191}"
224,1,87,0,0.0615994,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^5),x]","\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}}","\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*x)/(5*c^5*Sqrt[1 - a^2*x^2]) + 1/(5*a*c^5*(1 - a*x)^2*Sqrt[1 - a^2*x^2]) + 1/(5*a*c^5*(1 - a*x)*Sqrt[1 - a^2*x^2])","A",4,3,18,0.1667,1,"{6127, 659, 191}"
225,1,119,0,0.0762582,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^6} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^6),x]","\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}}","\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,"(8*x)/(35*c^6*Sqrt[1 - a^2*x^2]) + 1/(7*a*c^6*(1 - a*x)^3*Sqrt[1 - a^2*x^2]) + 4/(35*a*c^6*(1 - a*x)^2*Sqrt[1 - a^2*x^2]) + 4/(35*a*c^6*(1 - a*x)*Sqrt[1 - a^2*x^2])","A",5,3,18,0.1667,1,"{6127, 659, 191}"
226,1,176,0,0.1288845,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^(9/2),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}","\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,"(4096*c^6*(1 - a^2*x^2)^(3/2))/(3465*a*(c - a*c*x)^(3/2)) + (1024*c^5*(1 - a^2*x^2)^(3/2))/(1155*a*Sqrt[c - a*c*x]) + (128*c^4*Sqrt[c - a*c*x]*(1 - a^2*x^2)^(3/2))/(231*a) + (32*c^3*(c - a*c*x)^(3/2)*(1 - a^2*x^2)^(3/2))/(99*a) + (2*c^2*(c - a*c*x)^(5/2)*(1 - a^2*x^2)^(3/2))/(11*a)","A",6,3,18,0.1667,1,"{6127, 657, 649}"
227,1,141,0,0.1042024,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^(7/2),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}","\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,"(256*c^5*(1 - a^2*x^2)^(3/2))/(315*a*(c - a*c*x)^(3/2)) + (64*c^4*(1 - a^2*x^2)^(3/2))/(105*a*Sqrt[c - a*c*x]) + (8*c^3*Sqrt[c - a*c*x]*(1 - a^2*x^2)^(3/2))/(21*a) + (2*c^2*(c - a*c*x)^(3/2)*(1 - a^2*x^2)^(3/2))/(9*a)","A",5,3,18,0.1667,1,"{6127, 657, 649}"
228,1,106,0,0.0817861,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^(5/2),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}","\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,"(64*c^4*(1 - a^2*x^2)^(3/2))/(105*a*(c - a*c*x)^(3/2)) + (16*c^3*(1 - a^2*x^2)^(3/2))/(35*a*Sqrt[c - a*c*x]) + (2*c^2*Sqrt[c - a*c*x]*(1 - a^2*x^2)^(3/2))/(7*a)","A",4,3,18,0.1667,1,"{6127, 657, 649}"
229,1,71,0,0.0607667,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^(3/2),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}}","\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,"(8*c^3*(1 - a^2*x^2)^(3/2))/(15*a*(c - a*c*x)^(3/2)) + (2*c^2*(1 - a^2*x^2)^(3/2))/(5*a*Sqrt[c - a*c*x])","A",3,3,18,0.1667,1,"{6127, 657, 649}"
230,1,35,0,0.0410775,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - a*c*x],x]","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}",1,"(2*c^2*(1 - a^2*x^2)^(3/2))/(3*a*(c - a*c*x)^(3/2))","A",2,2,18,0.1111,1,"{6127, 649}"
231,1,83,0,0.0816572,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^ArcTanh[a*x]/Sqrt[c - a*c*x],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}}","\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[1 - a^2*x^2])/(a*Sqrt[c - a*c*x]) + (2*Sqrt[2]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(a*Sqrt[c])","A",4,4,18,0.2222,1,"{6127, 665, 661, 208}"
232,1,82,0,0.0801186,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^(3/2),x]","\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}}","\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,"Sqrt[1 - a^2*x^2]/(a*(c - a*c*x)^(3/2)) - ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])]/(Sqrt[2]*a*c^(3/2))","A",4,4,18,0.2222,1,"{6127, 663, 661, 208}"
233,1,122,0,0.1063767,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^(5/2),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}}","-\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,"Sqrt[1 - a^2*x^2]/(2*a*(c - a*c*x)^(5/2)) - Sqrt[1 - a^2*x^2]/(8*a*c*(c - a*c*x)^(3/2)) - ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])]/(8*Sqrt[2]*a*c^(5/2))","A",5,5,18,0.2778,1,"{6127, 663, 673, 661, 208}"
234,1,157,0,0.1304794,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^(7/2),x]","-\frac{\sqrt{1-a^2 x^2}}{32 a c^2 (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)}{32 \sqrt{2} a c^{7/2}}-\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}}","-\frac{\sqrt{1-a^2 x^2}}{32 a c^2 (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)}{32 \sqrt{2} a c^{7/2}}-\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,"Sqrt[1 - a^2*x^2]/(3*a*(c - a*c*x)^(7/2)) - Sqrt[1 - a^2*x^2]/(24*a*c*(c - a*c*x)^(5/2)) - Sqrt[1 - a^2*x^2]/(32*a*c^2*(c - a*c*x)^(3/2)) - ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])]/(32*Sqrt[2]*a*c^(7/2))","A",6,5,18,0.2778,1,"{6127, 663, 673, 661, 208}"
235,1,40,0,0.0477566,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^(7/2),x]","\frac{2 (c-a c x)^{9/2}}{9 a c}-\frac{4 (c-a c x)^{7/2}}{7 a}","\frac{2 (c-a c x)^{9/2}}{9 a c}-\frac{4 (c-a c x)^{7/2}}{7 a}",1,"(-4*(c - a*c*x)^(7/2))/(7*a) + (2*(c - a*c*x)^(9/2))/(9*a*c)","A",4,3,20,0.1500,1,"{6130, 21, 43}"
236,1,40,0,0.0472998,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^(5/2),x]","\frac{2 (c-a c x)^{7/2}}{7 a c}-\frac{4 (c-a c x)^{5/2}}{5 a}","\frac{2 (c-a c x)^{7/2}}{7 a c}-\frac{4 (c-a c x)^{5/2}}{5 a}",1,"(-4*(c - a*c*x)^(5/2))/(5*a) + (2*(c - a*c*x)^(7/2))/(7*a*c)","A",4,3,20,0.1500,1,"{6130, 21, 43}"
237,1,40,0,0.0491684,"\int e^{2 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - a*c*x)^(3/2),x]","\frac{2 (c-a c x)^{5/2}}{5 a c}-\frac{4 (c-a c x)^{3/2}}{3 a}","\frac{2 (c-a c x)^{5/2}}{5 a c}-\frac{4 (c-a c x)^{3/2}}{3 a}",1,"(-4*(c - a*c*x)^(3/2))/(3*a) + (2*(c - a*c*x)^(5/2))/(5*a*c)","A",4,3,20,0.1500,1,"{6130, 21, 43}"
238,1,38,0,0.0428272,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","\frac{2 (c-a c x)^{3/2}}{3 a c}-\frac{4 \sqrt{c-a c x}}{a}","\frac{2 (c-a c x)^{3/2}}{3 a c}-\frac{4 \sqrt{c-a c x}}{a}",1,"(-4*Sqrt[c - a*c*x])/a + (2*(c - a*c*x)^(3/2))/(3*a*c)","A",4,3,20,0.1500,1,"{6130, 21, 43}"
239,1,36,0,0.0467426,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^(2*ArcTanh[a*x])/Sqrt[c - a*c*x],x]","\frac{2 \sqrt{c-a c x}}{a c}+\frac{4}{a \sqrt{c-a c x}}","\frac{2 \sqrt{c-a c x}}{a c}+\frac{4}{a \sqrt{c-a c x}}",1,"4/(a*Sqrt[c - a*c*x]) + (2*Sqrt[c - a*c*x])/(a*c)","A",4,3,20,0.1500,1,"{6130, 21, 43}"
240,1,38,0,0.0477366,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x)^(3/2),x]","\frac{4}{3 a (c-a c x)^{3/2}}-\frac{2}{a c \sqrt{c-a c x}}","\frac{4}{3 a (c-a c x)^{3/2}}-\frac{2}{a c \sqrt{c-a c x}}",1,"4/(3*a*(c - a*c*x)^(3/2)) - 2/(a*c*Sqrt[c - a*c*x])","A",4,3,20,0.1500,1,"{6130, 21, 43}"
241,1,40,0,0.0491552,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x)^(5/2),x]","\frac{4}{5 a (c-a c x)^{5/2}}-\frac{2}{3 a c (c-a c x)^{3/2}}","\frac{4}{5 a (c-a c x)^{5/2}}-\frac{2}{3 a c (c-a c x)^{3/2}}",1,"4/(5*a*(c - a*c*x)^(5/2)) - 2/(3*a*c*(c - a*c*x)^(3/2))","A",4,3,20,0.1500,1,"{6130, 21, 43}"
242,1,40,0,0.0517986,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a*c*x)^(7/2),x]","\frac{4}{7 a (c-a c x)^{7/2}}-\frac{2}{5 a c (c-a c x)^{5/2}}","\frac{4}{7 a (c-a c x)^{7/2}}-\frac{2}{5 a c (c-a c x)^{5/2}}",1,"4/(7*a*(c - a*c*x)^(7/2)) - 2/(5*a*c*(c - a*c*x)^(5/2))","A",4,3,20,0.1500,1,"{6130, 21, 43}"
243,1,141,0,0.1089894,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^(9/2),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}","\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,"(256*c^7*(1 - a^2*x^2)^(5/2))/(1155*a*(c - a*c*x)^(5/2)) + (64*c^6*(1 - a^2*x^2)^(5/2))/(231*a*(c - a*c*x)^(3/2)) + (8*c^5*(1 - a^2*x^2)^(5/2))/(33*a*Sqrt[c - a*c*x]) + (2*c^4*Sqrt[c - a*c*x]*(1 - a^2*x^2)^(5/2))/(11*a)","A",5,3,20,0.1500,1,"{6127, 657, 649}"
244,1,106,0,0.087507,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^(7/2),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}}","\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,"(64*c^6*(1 - a^2*x^2)^(5/2))/(315*a*(c - a*c*x)^(5/2)) + (16*c^5*(1 - a^2*x^2)^(5/2))/(63*a*(c - a*c*x)^(3/2)) + (2*c^4*(1 - a^2*x^2)^(5/2))/(9*a*Sqrt[c - a*c*x])","A",4,3,20,0.1500,1,"{6127, 657, 649}"
245,1,71,0,0.0665109,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^(5/2),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}}","\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,"(8*c^5*(1 - a^2*x^2)^(5/2))/(35*a*(c - a*c*x)^(5/2)) + (2*c^4*(1 - a^2*x^2)^(5/2))/(7*a*(c - a*c*x)^(3/2))","A",3,3,20,0.1500,1,"{6127, 657, 649}"
246,1,35,0,0.0498722,"\int e^{3 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a*c*x)^(3/2),x]","\frac{2 c^4 \left(1-a^2 x^2\right)^{5/2}}{5 a (c-a c x)^{5/2}}","\frac{2 c^4 \left(1-a^2 x^2\right)^{5/2}}{5 a (c-a c x)^{5/2}}",1,"(2*c^4*(1 - a^2*x^2)^(5/2))/(5*a*(c - a*c*x)^(5/2))","A",2,2,20,0.1000,1,"{6127, 649}"
247,1,119,0,0.1038446,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x],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}","-\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,"(-4*c*Sqrt[1 - a^2*x^2])/(a*Sqrt[c - a*c*x]) - (2*c^2*(1 - a^2*x^2)^(3/2))/(3*a*(c - a*c*x)^(3/2)) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/a","A",5,4,20,0.2000,1,"{6127, 665, 661, 208}"
248,1,115,0,0.1007174,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^(3*ArcTanh[a*x])/Sqrt[c - a*c*x],x]","\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}}","\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,"(3*Sqrt[1 - a^2*x^2])/(a*Sqrt[c - a*c*x]) + (c^2*(1 - a^2*x^2)^(3/2))/(a*(c - a*c*x)^(5/2)) - (3*Sqrt[2]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(a*Sqrt[c])","A",5,5,20,0.2500,1,"{6127, 663, 665, 661, 208}"
249,1,122,0,0.1047673,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^(3/2),x]","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a (c-a c x)^{7/2}}+\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{3 \sqrt{1-a^2 x^2}}{4 a (c-a c x)^{3/2}}","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a (c-a c x)^{7/2}}+\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{3 \sqrt{1-a^2 x^2}}{4 a (c-a c x)^{3/2}}",1,"(-3*Sqrt[1 - a^2*x^2])/(4*a*(c - a*c*x)^(3/2)) + (c^2*(1 - a^2*x^2)^(3/2))/(2*a*(c - a*c*x)^(7/2)) + (3*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(4*Sqrt[2]*a*c^(3/2))","A",5,4,20,0.2000,1,"{6127, 663, 661, 208}"
250,1,157,0,0.133522,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^(5/2),x]","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{9/2}}+\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{\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}}","\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{9/2}}+\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{\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,"-Sqrt[1 - a^2*x^2]/(4*a*(c - a*c*x)^(5/2)) + Sqrt[1 - a^2*x^2]/(16*a*c*(c - a*c*x)^(3/2)) + (c^2*(1 - a^2*x^2)^(3/2))/(3*a*(c - a*c*x)^(9/2)) + ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])]/(16*Sqrt[2]*a*c^(5/2))","A",6,5,20,0.2500,1,"{6127, 663, 673, 661, 208}"
251,1,192,0,0.1591556,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a*c*x)^(7/2),x]","\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{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{\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}}","\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{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{\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,"-Sqrt[1 - a^2*x^2]/(8*a*(c - a*c*x)^(7/2)) + Sqrt[1 - a^2*x^2]/(64*a*c*(c - a*c*x)^(5/2)) + (3*Sqrt[1 - a^2*x^2])/(256*a*c^2*(c - a*c*x)^(3/2)) + (c^2*(1 - a^2*x^2)^(3/2))/(4*a*(c - a*c*x)^(11/2)) + (3*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(256*Sqrt[2]*a*c^(7/2))","A",7,5,20,0.2500,1,"{6127, 663, 673, 661, 208}"
252,1,206,0,0.1615466,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[(c - a*c*x)^(9/2)/E^ArcTanh[a*x],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}","\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,"(16384*c^5*Sqrt[1 - a^2*x^2])/(693*a*Sqrt[c - a*c*x]) + (4096*c^4*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(693*a) + (512*c^3*(c - a*c*x)^(3/2)*Sqrt[1 - a^2*x^2])/(231*a) + (640*c^2*(c - a*c*x)^(5/2)*Sqrt[1 - a^2*x^2])/(693*a) + (40*c*(c - a*c*x)^(7/2)*Sqrt[1 - a^2*x^2])/(99*a) + (2*(c - a*c*x)^(9/2)*Sqrt[1 - a^2*x^2])/(11*a)","A",7,3,20,0.1500,1,"{6127, 657, 649}"
253,1,171,0,0.1339447,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[(c - a*c*x)^(7/2)/E^ArcTanh[a*x],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}","\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,"(4096*c^4*Sqrt[1 - a^2*x^2])/(315*a*Sqrt[c - a*c*x]) + (1024*c^3*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(315*a) + (128*c^2*(c - a*c*x)^(3/2)*Sqrt[1 - a^2*x^2])/(105*a) + (32*c*(c - a*c*x)^(5/2)*Sqrt[1 - a^2*x^2])/(63*a) + (2*(c - a*c*x)^(7/2)*Sqrt[1 - a^2*x^2])/(9*a)","A",6,3,20,0.1500,1,"{6127, 657, 649}"
254,1,136,0,0.1060378,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[(c - a*c*x)^(5/2)/E^ArcTanh[a*x],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}","\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,"(256*c^3*Sqrt[1 - a^2*x^2])/(35*a*Sqrt[c - a*c*x]) + (64*c^2*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(35*a) + (24*c*(c - a*c*x)^(3/2)*Sqrt[1 - a^2*x^2])/(35*a) + (2*(c - a*c*x)^(5/2)*Sqrt[1 - a^2*x^2])/(7*a)","A",5,3,20,0.1500,1,"{6127, 657, 649}"
255,1,101,0,0.0867293,"\int e^{-\tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[(c - a*c*x)^(3/2)/E^ArcTanh[a*x],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}","\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,"(64*c^2*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[c - a*c*x]) + (16*c*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(15*a) + (2*(c - a*c*x)^(3/2)*Sqrt[1 - a^2*x^2])/(5*a)","A",4,3,20,0.1500,1,"{6127, 657, 649}"
256,1,66,0,0.0622191,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^ArcTanh[a*x],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}","\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,"(8*c*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[c - a*c*x]) + (2*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(3*a)","A",3,3,20,0.1500,1,"{6127, 657, 649}"
257,1,30,0,0.0473599,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[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",2,2,20,0.1000,1,"{6127, 649}"
258,1,51,0,0.0622823,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^(3/2)),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}}","\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]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(a*c^(3/2))","A",3,3,20,0.1500,1,"{6127, 661, 208}"
259,1,90,0,0.0822888,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^(5/2)),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}}","\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,"Sqrt[1 - a^2*x^2]/(2*a*c*(c - a*c*x)^(3/2)) + ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])]/(2*Sqrt[2]*a*c^(5/2))","A",4,4,20,0.2000,1,"{6127, 673, 661, 208}"
260,1,125,0,0.104941,"\int \frac{e^{-\tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a*c*x)^(7/2)),x]","\frac{3 \sqrt{1-a^2 x^2}}{16 a c^2 (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)}{16 \sqrt{2} a c^{7/2}}+\frac{\sqrt{1-a^2 x^2}}{4 a c (c-a c x)^{5/2}}","\frac{3 \sqrt{1-a^2 x^2}}{16 a c^2 (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)}{16 \sqrt{2} a c^{7/2}}+\frac{\sqrt{1-a^2 x^2}}{4 a c (c-a c x)^{5/2}}",1,"Sqrt[1 - a^2*x^2]/(4*a*c*(c - a*c*x)^(5/2)) + (3*Sqrt[1 - a^2*x^2])/(16*a*c^2*(c - a*c*x)^(3/2)) + (3*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(16*Sqrt[2]*a*c^(7/2))","A",5,4,20,0.2000,1,"{6127, 673, 661, 208}"
261,1,137,0,0.1108088,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[(c - a*c*x)^(7/2)/E^(2*ArcTanh[a*x]),x]","\frac{16 c^2 (c-a c x)^{3/2}}{3 a}+\frac{32 c^3 \sqrt{c-a c x}}{a}-\frac{32 \sqrt{2} c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{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}","\frac{16 c^2 (c-a c x)^{3/2}}{3 a}+\frac{32 c^3 \sqrt{c-a c x}}{a}-\frac{32 \sqrt{2} c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{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,"(32*c^3*Sqrt[c - a*c*x])/a + (16*c^2*(c - a*c*x)^(3/2))/(3*a) + (8*c*(c - a*c*x)^(5/2))/(5*a) + (4*(c - a*c*x)^(7/2))/(7*a) + (2*(c - a*c*x)^(9/2))/(9*a*c) - (32*Sqrt[2]*c^(7/2)*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",9,5,20,0.2500,1,"{6130, 21, 50, 63, 206}"
262,1,116,0,0.0983316,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[(c - a*c*x)^(5/2)/E^(2*ArcTanh[a*x]),x]","\frac{16 c^2 \sqrt{c-a c x}}{a}-\frac{16 \sqrt{2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{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}","\frac{16 c^2 \sqrt{c-a c x}}{a}-\frac{16 \sqrt{2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{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,"(16*c^2*Sqrt[c - a*c*x])/a + (8*c*(c - a*c*x)^(3/2))/(3*a) + (4*(c - a*c*x)^(5/2))/(5*a) + (2*(c - a*c*x)^(7/2))/(7*a*c) - (16*Sqrt[2]*c^(5/2)*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",8,5,20,0.2500,1,"{6130, 21, 50, 63, 206}"
263,1,95,0,0.0792074,"\int e^{-2 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[(c - a*c*x)^(3/2)/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"(8*c*Sqrt[c - a*c*x])/a + (4*(c - a*c*x)^(3/2))/(3*a) + (2*(c - a*c*x)^(5/2))/(5*a*c) - (8*Sqrt[2]*c^(3/2)*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",7,5,20,0.2500,1,"{6130, 21, 50, 63, 206}"
264,1,76,0,0.0661381,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(2*ArcTanh[a*x]),x]","\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}","\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,"(4*Sqrt[c - a*c*x])/a + (2*(c - a*c*x)^(3/2))/(3*a*c) - (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",6,5,20,0.2500,1,"{6130, 21, 50, 63, 206}"
265,1,58,0,0.057621,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[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",5,5,20,0.2500,1,"{6130, 21, 50, 63, 206}"
266,1,38,0,0.0511705,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[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",4,4,20,0.2000,1,"{6130, 21, 63, 206}"
267,1,57,0,0.0604231,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(5/2)),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}}","\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,"1/(a*c^2*Sqrt[c - a*c*x]) - ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]/(Sqrt[2]*a*c^(5/2))","A",5,5,20,0.2500,1,"{6130, 21, 51, 63, 206}"
268,1,83,0,0.0696084,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(7/2)),x]","\frac{1}{2 a c^3 \sqrt{c-a c x}}+\frac{1}{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}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a c^{7/2}}",1,"1/(3*a*c^2*(c - a*c*x)^(3/2)) + 1/(2*a*c^3*Sqrt[c - a*c*x]) - ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]/(2*Sqrt[2]*a*c^(7/2))","A",6,5,20,0.2500,1,"{6130, 21, 51, 63, 206}"
269,1,104,0,0.0817663,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{(c-a c x)^{9/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a*c*x)^(9/2)),x]","\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}}-\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}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a c^{9/2}}",1,"1/(5*a*c^2*(c - a*c*x)^(5/2)) + 1/(6*a*c^3*(c - a*c*x)^(3/2)) + 1/(4*a*c^4*Sqrt[c - a*c*x]) - ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])]/(4*Sqrt[2]*a*c^(9/2))","A",7,5,20,0.2500,1,"{6130, 21, 51, 63, 206}"
270,1,171,0,0.1368787,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[(c - a*c*x)^(5/2)/E^(3*ArcTanh[a*x]),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}}","\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,"(-4096*c^2*Sqrt[c - a*c*x])/(35*a*Sqrt[1 - a^2*x^2]) + (1024*c*(c - a*c*x)^(3/2))/(35*a*Sqrt[1 - a^2*x^2]) + (128*(c - a*c*x)^(5/2))/(35*a*Sqrt[1 - a^2*x^2]) + (32*(c - a*c*x)^(7/2))/(35*a*c*Sqrt[1 - a^2*x^2]) + (2*(c - a*c*x)^(9/2))/(7*a*c^2*Sqrt[1 - a^2*x^2])","A",6,3,20,0.1500,1,"{6127, 657, 649}"
271,1,136,0,0.1129876,"\int e^{-3 \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[(c - a*c*x)^(3/2)/E^(3*ArcTanh[a*x]),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}}","\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,"(-256*c*Sqrt[c - a*c*x])/(5*a*Sqrt[1 - a^2*x^2]) + (64*(c - a*c*x)^(3/2))/(5*a*Sqrt[1 - a^2*x^2]) + (8*(c - a*c*x)^(5/2))/(5*a*c*Sqrt[1 - a^2*x^2]) + (2*(c - a*c*x)^(7/2))/(5*a*c^2*Sqrt[1 - a^2*x^2])","A",5,3,20,0.1500,1,"{6127, 657, 649}"
272,1,103,0,0.083532,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(3*ArcTanh[a*x]),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}}","\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,"(-64*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - a^2*x^2]) + (16*(c - a*c*x)^(3/2))/(3*a*c*Sqrt[1 - a^2*x^2]) + (2*(c - a*c*x)^(5/2))/(3*a*c^2*Sqrt[1 - a^2*x^2])","A",4,3,20,0.1500,1,"{6127, 657, 649}"
273,1,67,0,0.0639084,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x]),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}}","\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,"(-8*Sqrt[c - a*c*x])/(a*c*Sqrt[1 - a^2*x^2]) + (2*(c - a*c*x)^(3/2))/(a*c^2*Sqrt[1 - a^2*x^2])","A",3,3,20,0.1500,1,"{6127, 657, 649}"
274,1,33,0,0.0504776,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(3/2)),x]","-\frac{2 \sqrt{c-a c x}}{a c^2 \sqrt{1-a^2 x^2}}","-\frac{2 \sqrt{c-a c x}}{a c^2 \sqrt{1-a^2 x^2}}",1,"(-2*Sqrt[c - a*c*x])/(a*c^2*Sqrt[1 - a^2*x^2])","A",2,2,20,0.1000,1,"{6127, 649}"
275,1,85,0,0.0810259,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(5/2)),x]","\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}}","\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,"-(Sqrt[c - a*c*x]/(a*c^3*Sqrt[1 - a^2*x^2])) + ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])]/(Sqrt[2]*a*c^(5/2))","A",4,4,20,0.2000,1,"{6127, 667, 661, 208}"
276,1,125,0,0.1023015,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(7/2)),x]","-\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}}+\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}}+\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}}",1,"1/(2*a*c^3*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2]) - (3*Sqrt[c - a*c*x])/(4*a*c^4*Sqrt[1 - a^2*x^2]) + (3*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(4*Sqrt[2]*a*c^(7/2))","A",5,5,20,0.2500,1,"{6127, 673, 667, 661, 208}"
277,1,160,0,0.129878,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{(c-a c x)^{9/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a*c*x)^(9/2)),x]","-\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}}+\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}}+\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}}",1,"1/(4*a*c^3*(c - a*c*x)^(3/2)*Sqrt[1 - a^2*x^2]) + 5/(16*a*c^4*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2]) - (15*Sqrt[c - a*c*x])/(32*a*c^5*Sqrt[1 - a^2*x^2]) + (15*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/(32*Sqrt[2]*a*c^(9/2))","A",6,5,20,0.2500,1,"{6127, 673, 667, 661, 208}"
278,1,81,0,0.0667769,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^(n*ArcTanh[a*x])*(c - a*c*x)^(7/2),x]","-\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)}","-\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 - a*c*x)^(9/2)*Hypergeometric2F1[(9 - n)/2, -n/2, (11 - n)/2, (1 - a*x)/2])/(a*c*(9 - n)*(1 - a*x)^(n/2)))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
279,1,81,0,0.0702035,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^(n*ArcTanh[a*x])*(c - a*c*x)^(5/2),x]","-\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)}","-\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 - a*c*x)^(7/2)*Hypergeometric2F1[(7 - n)/2, -n/2, (9 - n)/2, (1 - a*x)/2])/(a*c*(7 - n)*(1 - a*x)^(n/2)))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
280,1,81,0,0.0679431,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^(n*ArcTanh[a*x])*(c - a*c*x)^(3/2),x]","-\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)}","-\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 - a*c*x)^(5/2)*Hypergeometric2F1[(5 - n)/2, -n/2, (7 - n)/2, (1 - a*x)/2])/(a*c*(5 - n)*(1 - a*x)^(n/2)))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
281,1,81,0,0.0633918,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(n*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","-\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)}","-\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)*(c - a*c*x)^(3/2)*Hypergeometric2F1[(3 - n)/2, -n/2, (5 - n)/2, (1 - a*x)/2])/(a*c*(3 - n)*(1 - a*x)^(n/2)))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
282,1,81,0,0.0648541,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[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-n}{2},-\frac{n}{2};\frac{3-n}{2};\frac{1}{2} (1-a x)\right)}{a c (1-n)}","-\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 - n)/2, -n/2, (3 - n)/2, (1 - a*x)/2])/(a*c*(1 - n)*(1 - a*x)^(n/2)))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
283,1,78,0,0.0682523,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[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{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}}","\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 - n)/2, -n/2, (1 - n)/2, (1 - a*x)/2])/(a*c*(1 + n)*(1 - a*x)^(n/2)*Sqrt[c - a*c*x])","A",3,3,20,0.1500,1,"{6130, 23, 69}"
284,1,78,0,0.0671078,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a*c*x)^(5/2),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}}","\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)*Hypergeometric2F1[(-3 - n)/2, -n/2, (-1 - n)/2, (1 - a*x)/2])/(a*c*(3 + n)*(1 - a*x)^(n/2)*(c - a*c*x)^(3/2))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
285,1,78,0,0.0672785,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a*c*x)^(7/2),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}}","\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)*Hypergeometric2F1[(-5 - n)/2, -n/2, (-3 - n)/2, (1 - a*x)/2])/(a*c*(5 + n)*(1 - a*x)^(n/2)*(c - a*c*x)^(5/2))","A",3,3,20,0.1500,1,"{6130, 23, 69}"
286,1,83,0,0.0708394,"\int e^{\tanh ^{-1}(a x)} x^4 (c-a c x) \, dx","Int[E^ArcTanh[a*x]*x^4*(c - a*c*x),x]","\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}+\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}+\frac{c \sin ^{-1}(a x)}{16 a^5}",1,"-(c*x*Sqrt[1 - a^2*x^2])/(16*a^4) - (c*x^3*Sqrt[1 - a^2*x^2])/(24*a^2) + (c*x^5*Sqrt[1 - a^2*x^2])/6 + (c*ArcSin[a*x])/(16*a^5)","A",5,4,17,0.2353,1,"{6128, 279, 321, 216}"
287,1,45,0,0.0649259,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x) \, dx","Int[E^ArcTanh[a*x]*x^3*(c - a*c*x),x]","\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}","\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,"-(c*(1 - a^2*x^2)^(3/2))/(3*a^4) + (c*(1 - a^2*x^2)^(5/2))/(5*a^4)","A",4,3,17,0.1765,1,"{6128, 266, 43}"
288,1,58,0,0.0568359,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x) \, dx","Int[E^ArcTanh[a*x]*x^2*(c - a*c*x),x]","\frac{1}{4} c x^3 \sqrt{1-a^2 x^2}-\frac{c x \sqrt{1-a^2 x^2}}{8 a^2}+\frac{c \sin ^{-1}(a x)}{8 a^3}","\frac{1}{4} c x^3 \sqrt{1-a^2 x^2}-\frac{c x \sqrt{1-a^2 x^2}}{8 a^2}+\frac{c \sin ^{-1}(a x)}{8 a^3}",1,"-(c*x*Sqrt[1 - a^2*x^2])/(8*a^2) + (c*x^3*Sqrt[1 - a^2*x^2])/4 + (c*ArcSin[a*x])/(8*a^3)","A",4,4,17,0.2353,1,"{6128, 279, 321, 216}"
289,1,22,0,0.0282274,"\int e^{\tanh ^{-1}(a x)} x (c-a c x) \, dx","Int[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,"-(c*(1 - a^2*x^2)^(3/2))/(3*a^2)","A",2,2,15,0.1333,1,"{6128, 261}"
290,1,33,0,0.0198065,"\int e^{\tanh ^{-1}(a x)} (c-a c x) \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x),x]","\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}","\frac{1}{2} c x \sqrt{1-a^2 x^2}+\frac{c \sin ^{-1}(a x)}{2 a}",1,"(c*x*Sqrt[1 - a^2*x^2])/2 + (c*ArcSin[a*x])/(2*a)","A",3,3,14,0.2143,1,"{6127, 195, 216}"
291,1,35,0,0.0530402,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x))/x,x]","c \sqrt{1-a^2 x^2}-c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","c \sqrt{1-a^2 x^2}-c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"c*Sqrt[1 - a^2*x^2] - c*ArcTanh[Sqrt[1 - a^2*x^2]]","A",5,5,17,0.2941,1,"{6128, 266, 50, 63, 208}"
292,1,29,0,0.0429045,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x^2} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x))/x^2,x]","-\frac{c \sqrt{1-a^2 x^2}}{x}-a c \sin ^{-1}(a x)","-\frac{c \sqrt{1-a^2 x^2}}{x}-a c \sin ^{-1}(a x)",1,"-((c*Sqrt[1 - a^2*x^2])/x) - a*c*ArcSin[a*x]","A",3,3,17,0.1765,1,"{6128, 277, 216}"
293,1,46,0,0.0578259,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x^3} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x))/x^3,x]","\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}","\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*Sqrt[1 - a^2*x^2])/(2*x^2) + (a^2*c*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",5,5,17,0.2941,1,"{6128, 266, 47, 63, 208}"
294,1,22,0,0.0392372,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)}{x^4} \, dx","Int[(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,"-(c*(1 - a^2*x^2)^(3/2))/(3*x^3)","A",2,2,17,0.1176,1,"{6128, 264}"
295,1,124,0,0.135755,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x)^2 \, dx","Int[E^ArcTanh[a*x]*x^3*(c - a*c*x)^2,x]","\frac{c^2 x^3 \left(1-a^2 x^2\right)^{3/2}}{6 a}-\frac{c^2 x^2 \left(1-a^2 x^2\right)^{3/2}}{5 a^2}-\frac{c^2 x \sqrt{1-a^2 x^2}}{16 a^3}-\frac{c^2 (16-15 a x) \left(1-a^2 x^2\right)^{3/2}}{120 a^4}-\frac{c^2 \sin ^{-1}(a x)}{16 a^4}","\frac{c^2 x^3 \left(1-a^2 x^2\right)^{3/2}}{6 a}-\frac{c^2 x^2 \left(1-a^2 x^2\right)^{3/2}}{5 a^2}-\frac{c^2 x \sqrt{1-a^2 x^2}}{16 a^3}-\frac{c^2 (16-15 a x) \left(1-a^2 x^2\right)^{3/2}}{120 a^4}-\frac{c^2 \sin ^{-1}(a x)}{16 a^4}",1,"-(c^2*x*Sqrt[1 - a^2*x^2])/(16*a^3) - (c^2*x^2*(1 - a^2*x^2)^(3/2))/(5*a^2) + (c^2*x^3*(1 - a^2*x^2)^(3/2))/(6*a) - (c^2*(16 - 15*a*x)*(1 - a^2*x^2)^(3/2))/(120*a^4) - (c^2*ArcSin[a*x])/(16*a^4)","A",6,5,19,0.2632,1,"{6128, 833, 780, 195, 216}"
296,1,113,0,0.1208248,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x)^2 \, dx","Int[E^ArcTanh[a*x]*x^2*(c - a*c*x)^2,x]","-\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}-\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 \sin ^{-1}(a x)}{8 a^3}","-\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}-\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 \sin ^{-1}(a x)}{8 a^3}",1,"(c^2*x*Sqrt[1 - a^2*x^2])/(8*a^2) + (c^2*(1 - a^2*x^2)^(3/2))/(3*a^3) - (c^2*x*(1 - a^2*x^2)^(3/2))/(4*a^2) - (c^2*(1 - a^2*x^2)^(5/2))/(5*a^3) + (c^2*ArcSin[a*x])/(8*a^3)","A",9,5,19,0.2632,1,"{6128, 797, 641, 195, 216}"
297,1,70,0,0.0620288,"\int e^{\tanh ^{-1}(a x)} x (c-a c x)^2 \, dx","Int[E^ArcTanh[a*x]*x*(c - a*c*x)^2,x]","-\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}","-\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,"-(c^2*x*Sqrt[1 - a^2*x^2])/(8*a) - (c^2*(4 - 3*a*x)*(1 - a^2*x^2)^(3/2))/(12*a^2) - (c^2*ArcSin[a*x])/(8*a^2)","A",4,4,17,0.2353,1,"{6128, 780, 195, 216}"
298,1,61,0,0.0372357,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^2,x]","\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}","\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*x*Sqrt[1 - a^2*x^2])/2 + (c^2*(1 - a^2*x^2)^(3/2))/(3*a) + (c^2*ArcSin[a*x])/(2*a)","A",4,4,16,0.2500,1,"{6127, 641, 195, 216}"
299,1,59,0,0.1013814,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x,x]","\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)","\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)*Sqrt[1 - a^2*x^2])/2 - (c^2*ArcSin[a*x])/2 - c^2*ArcTanh[Sqrt[1 - a^2*x^2]]","A",7,7,19,0.3684,1,"{6128, 815, 844, 216, 266, 63, 208}"
300,1,58,0,0.1034976,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^2} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^2,x]","-\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)","-\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*(1 + a*x)*Sqrt[1 - a^2*x^2])/x) - a*c^2*ArcSin[a*x] + a*c^2*ArcTanh[Sqrt[1 - a^2*x^2]]","A",7,7,19,0.3684,1,"{6128, 813, 844, 216, 266, 63, 208}"
301,1,67,0,0.1046051,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^3} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^3,x]","-\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)","-\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,"-(c^2*(1 - 2*a*x)*Sqrt[1 - a^2*x^2])/(2*x^2) + a^2*c^2*ArcSin[a*x] + (a^2*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",7,7,19,0.3684,1,"{6128, 811, 844, 216, 266, 63, 208}"
302,1,75,0,0.0927444,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^4} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^4,x]","\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)","\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,"(a*c^2*Sqrt[1 - a^2*x^2])/(2*x^2) - (c^2*(1 - a^2*x^2)^(3/2))/(3*x^3) - (a^3*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",6,6,19,0.3158,1,"{6128, 807, 266, 47, 63, 208}"
303,1,102,0,0.1187506,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^5} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^5,x]","-\frac{a^2 c^2 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}+\frac{1}{8} a^4 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{a^2 c^2 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}+\frac{1}{8} a^4 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-(a^2*c^2*Sqrt[1 - a^2*x^2])/(8*x^2) - (c^2*(1 - a^2*x^2)^(3/2))/(4*x^4) + (a*c^2*(1 - a^2*x^2)^(3/2))/(3*x^3) + (a^4*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",7,7,19,0.3684,1,"{6128, 835, 807, 266, 47, 63, 208}"
304,1,129,0,0.1404952,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^6} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^6,x]","\frac{a^3 c^2 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{2 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\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}-\frac{2 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{1}{8} a^5 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(a^3*c^2*Sqrt[1 - a^2*x^2])/(8*x^2) - (c^2*(1 - a^2*x^2)^(3/2))/(5*x^5) + (a*c^2*(1 - a^2*x^2)^(3/2))/(4*x^4) - (2*a^2*c^2*(1 - a^2*x^2)^(3/2))/(15*x^3) - (a^5*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",8,7,19,0.3684,1,"{6128, 835, 807, 266, 47, 63, 208}"
305,1,156,0,0.1725938,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^2}{x^7} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^2)/x^7,x]","-\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}-\frac{a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}{8 x^4}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{6 x^6}+\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}-\frac{a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}{8 x^4}+\frac{a c^2 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{6 x^6}+\frac{1}{16} a^6 c^2 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-(a^4*c^2*Sqrt[1 - a^2*x^2])/(16*x^2) - (c^2*(1 - a^2*x^2)^(3/2))/(6*x^6) + (a*c^2*(1 - a^2*x^2)^(3/2))/(5*x^5) - (a^2*c^2*(1 - a^2*x^2)^(3/2))/(8*x^4) + (2*a^3*c^2*(1 - a^2*x^2)^(3/2))/(15*x^3) + (a^6*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/16","A",9,7,19,0.3684,1,"{6128, 835, 807, 266, 47, 63, 208}"
306,1,148,0,0.2375047,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x)^3 \, dx","Int[E^ArcTanh[a*x]*x^3*(c - a*c*x)^3,x]","-\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{11 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}{35 a^2}-\frac{c^3 x \sqrt{1-a^2 x^2}}{8 a^3}-\frac{c^3 (88-105 a x) \left(1-a^2 x^2\right)^{3/2}}{420 a^4}-\frac{c^3 \sin ^{-1}(a x)}{8 a^4}","-\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{11 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}{35 a^2}-\frac{c^3 x \sqrt{1-a^2 x^2}}{8 a^3}-\frac{c^3 (88-105 a x) \left(1-a^2 x^2\right)^{3/2}}{420 a^4}-\frac{c^3 \sin ^{-1}(a x)}{8 a^4}",1,"-(c^3*x*Sqrt[1 - a^2*x^2])/(8*a^3) - (11*c^3*x^2*(1 - a^2*x^2)^(3/2))/(35*a^2) + (c^3*x^3*(1 - a^2*x^2)^(3/2))/(3*a) - (c^3*x^4*(1 - a^2*x^2)^(3/2))/7 - (c^3*(88 - 105*a*x)*(1 - a^2*x^2)^(3/2))/(420*a^4) - (c^3*ArcSin[a*x])/(8*a^4)","A",7,6,19,0.3158,1,"{6128, 1809, 833, 780, 195, 216}"
307,1,121,0,0.2006386,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x)^3 \, dx","Int[E^ArcTanh[a*x]*x^2*(c - a*c*x)^3,x]","-\frac{1}{6} c^3 x^3 \left(1-a^2 x^2\right)^{3/2}+\frac{2 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}+\frac{c^3 (32-45 a x) \left(1-a^2 x^2\right)^{3/2}}{120 a^3}+\frac{3 c^3 x \sqrt{1-a^2 x^2}}{16 a^2}+\frac{3 c^3 \sin ^{-1}(a x)}{16 a^3}","-\frac{1}{6} c^3 x^3 \left(1-a^2 x^2\right)^{3/2}+\frac{2 c^3 x^2 \left(1-a^2 x^2\right)^{3/2}}{5 a}+\frac{c^3 (32-45 a x) \left(1-a^2 x^2\right)^{3/2}}{120 a^3}+\frac{3 c^3 x \sqrt{1-a^2 x^2}}{16 a^2}+\frac{3 c^3 \sin ^{-1}(a x)}{16 a^3}",1,"(3*c^3*x*Sqrt[1 - a^2*x^2])/(16*a^2) + (2*c^3*x^2*(1 - a^2*x^2)^(3/2))/(5*a) - (c^3*x^3*(1 - a^2*x^2)^(3/2))/6 + (c^3*(32 - 45*a*x)*(1 - a^2*x^2)^(3/2))/(120*a^3) + (3*c^3*ArcSin[a*x])/(16*a^3)","A",6,6,19,0.3158,1,"{6128, 1809, 833, 780, 195, 216}"
308,1,94,0,0.1281731,"\int e^{\tanh ^{-1}(a x)} x (c-a c x)^3 \, dx","Int[E^ArcTanh[a*x]*x*(c - a*c*x)^3,x]","-\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}","-\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*x*Sqrt[1 - a^2*x^2])/(4*a) - (c^3*x^2*(1 - a^2*x^2)^(3/2))/5 - (c^3*(14 - 15*a*x)*(1 - a^2*x^2)^(3/2))/(30*a^2) - (c^3*ArcSin[a*x])/(4*a^2)","A",5,5,17,0.2941,1,"{6128, 1809, 780, 195, 216}"
309,1,91,0,0.057276,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^3,x]","\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}","\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,"(5*c^3*x*Sqrt[1 - a^2*x^2])/8 + (5*c^3*(1 - a^2*x^2)^(3/2))/(12*a) + (c^3*(1 - a*x)*(1 - a^2*x^2)^(3/2))/(4*a) + (5*c^3*ArcSin[a*x])/(8*a)","A",5,5,16,0.3125,1,"{6127, 671, 641, 195, 216}"
310,1,75,0,0.1733012,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x,x]","-\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)","-\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*(1 - a*x)*Sqrt[1 - a^2*x^2] - (c^3*(1 - a^2*x^2)^(3/2))/3 - c^3*ArcSin[a*x] - c^3*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,8,19,0.4211,1,"{6128, 1809, 815, 844, 216, 266, 63, 208}"
311,1,83,0,0.1741321,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^2} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^2,x]","-\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)","-\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,"-(a*c^3*(4 + a*x)*Sqrt[1 - a^2*x^2])/2 - (c^3*(1 - a^2*x^2)^(3/2))/x - (a*c^3*ArcSin[a*x])/2 + 2*a*c^3*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,8,19,0.4211,1,"{6128, 1807, 815, 844, 216, 266, 63, 208}"
312,1,92,0,0.179135,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^3} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^3,x]","-\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)","-\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,"(a*c^3*(4 + a*x)*Sqrt[1 - a^2*x^2])/(2*x) - (c^3*(1 - a^2*x^2)^(3/2))/(2*x^2) + 2*a^2*c^3*ArcSin[a*x] - (a^2*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",8,8,19,0.4211,1,"{6128, 1807, 813, 844, 216, 266, 63, 208}"
313,1,88,0,0.178863,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^4} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^4,x]","-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}+\frac{a c^3 (1-a x) \sqrt{1-a^2 x^2}}{x^2}-a^3 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a^3 c^3 \sin ^{-1}(a x)","-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}+\frac{a c^3 (1-a x) \sqrt{1-a^2 x^2}}{x^2}-a^3 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-a^3 c^3 \sin ^{-1}(a x)",1,"(a*c^3*(1 - a*x)*Sqrt[1 - a^2*x^2])/x^2 - (c^3*(1 - a^2*x^2)^(3/2))/(3*x^3) - a^3*c^3*ArcSin[a*x] - a^3*c^3*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,8,19,0.4211,1,"{6128, 1807, 811, 844, 216, 266, 63, 208}"
314,1,102,0,0.1634475,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^5} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^5,x]","-\frac{5 a^2 c^3 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{2 a c^3 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}+\frac{5}{8} a^4 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)","-\frac{5 a^2 c^3 \sqrt{1-a^2 x^2}}{8 x^2}+\frac{2 a c^3 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}+\frac{5}{8} a^4 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-5*a^2*c^3*Sqrt[1 - a^2*x^2])/(8*x^2) - (c^3*(1 - a^2*x^2)^(3/2))/(4*x^4) + (2*a*c^3*(1 - a^2*x^2)^(3/2))/(3*x^3) + (5*a^4*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",7,7,19,0.3684,1,"{6128, 1807, 807, 266, 47, 63, 208}"
315,1,129,0,0.1902514,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^3}{x^6} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^3)/x^6,x]","\frac{a^3 c^3 \sqrt{1-a^2 x^2}}{4 x^2}-\frac{7 a^2 c^3 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}+\frac{a c^3 \left(1-a^2 x^2\right)^{3/2}}{2 x^4}-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\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}-\frac{7 a^2 c^3 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}+\frac{a c^3 \left(1-a^2 x^2\right)^{3/2}}{2 x^4}-\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{1}{4} a^5 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(a^3*c^3*Sqrt[1 - a^2*x^2])/(4*x^2) - (c^3*(1 - a^2*x^2)^(3/2))/(5*x^5) + (a*c^3*(1 - a^2*x^2)^(3/2))/(2*x^4) - (7*a^2*c^3*(1 - a^2*x^2)^(3/2))/(15*x^3) - (a^5*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/4","A",8,8,19,0.4211,1,"{6128, 1807, 835, 807, 266, 47, 63, 208}"
316,1,173,0,0.3331208,"\int e^{\tanh ^{-1}(a x)} x^3 (c-a c x)^4 \, dx","Int[E^ArcTanh[a*x]*x^3*(c - a*c*x)^4,x]","\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{19 c^4 x^2 \left(1-a^2 x^2\right)^{3/2}}{35 a^2}-\frac{29 c^4 x \sqrt{1-a^2 x^2}}{128 a^3}-\frac{c^4 (2432-3045 a x) \left(1-a^2 x^2\right)^{3/2}}{6720 a^4}-\frac{29 c^4 \sin ^{-1}(a x)}{128 a^4}","\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{19 c^4 x^2 \left(1-a^2 x^2\right)^{3/2}}{35 a^2}-\frac{29 c^4 x \sqrt{1-a^2 x^2}}{128 a^3}-\frac{c^4 (2432-3045 a x) \left(1-a^2 x^2\right)^{3/2}}{6720 a^4}-\frac{29 c^4 \sin ^{-1}(a x)}{128 a^4}",1,"(-29*c^4*x*Sqrt[1 - a^2*x^2])/(128*a^3) - (19*c^4*x^2*(1 - a^2*x^2)^(3/2))/(35*a^2) + (29*c^4*x^3*(1 - a^2*x^2)^(3/2))/(48*a) - (3*c^4*x^4*(1 - a^2*x^2)^(3/2))/7 + (a*c^4*x^5*(1 - a^2*x^2)^(3/2))/8 - (c^4*(2432 - 3045*a*x)*(1 - a^2*x^2)^(3/2))/(6720*a^4) - (29*c^4*ArcSin[a*x])/(128*a^4)","A",8,6,19,0.3158,1,"{6128, 1809, 833, 780, 195, 216}"
317,1,146,0,0.3041337,"\int e^{\tanh ^{-1}(a x)} x^2 (c-a c x)^4 \, dx","Int[E^ArcTanh[a*x]*x^2*(c - a*c*x)^4,x]","\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 x^2 \left(1-a^2 x^2\right)^{3/2}}{7 a}+\frac{5 c^4 (16-21 a x) \left(1-a^2 x^2\right)^{3/2}}{168 a^3}+\frac{5 c^4 x \sqrt{1-a^2 x^2}}{16 a^2}+\frac{5 c^4 \sin ^{-1}(a x)}{16 a^3}","\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 x^2 \left(1-a^2 x^2\right)^{3/2}}{7 a}+\frac{5 c^4 (16-21 a x) \left(1-a^2 x^2\right)^{3/2}}{168 a^3}+\frac{5 c^4 x \sqrt{1-a^2 x^2}}{16 a^2}+\frac{5 c^4 \sin ^{-1}(a x)}{16 a^3}",1,"(5*c^4*x*Sqrt[1 - a^2*x^2])/(16*a^2) + (5*c^4*x^2*(1 - a^2*x^2)^(3/2))/(7*a) - (c^4*x^3*(1 - a^2*x^2)^(3/2))/2 + (a*c^4*x^4*(1 - a^2*x^2)^(3/2))/7 + (5*c^4*(16 - 21*a*x)*(1 - a^2*x^2)^(3/2))/(168*a^3) + (5*c^4*ArcSin[a*x])/(16*a^3)","A",7,6,19,0.3158,1,"{6128, 1809, 833, 780, 195, 216}"
318,1,158,0,0.1412188,"\int e^{\tanh ^{-1}(a x)} x (c-a c x)^4 \, dx","Int[E^ArcTanh[a*x]*x*(c - a*c*x)^4,x]","-\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}","-\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,"(-7*c^4*x*Sqrt[1 - a^2*x^2])/(16*a) - (7*c^4*(1 - a^2*x^2)^(3/2))/(24*a^2) - (7*c^4*(1 - a*x)*(1 - a^2*x^2)^(3/2))/(40*a^2) - (c^4*(1 - a*x)^2*(1 - a^2*x^2)^(3/2))/(10*a^2) - (c^4*(1 - a*x)^3*(1 - a^2*x^2)^(3/2))/(6*a^2) - (7*c^4*ArcSin[a*x])/(16*a^2)","A",7,6,17,0.3529,1,"{6128, 795, 671, 641, 195, 216}"
319,1,123,0,0.0812557,"\int e^{\tanh ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^ArcTanh[a*x]*(c - a*c*x)^4,x]","\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}","\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,"(7*c^4*x*Sqrt[1 - a^2*x^2])/8 + (7*c^4*(1 - a^2*x^2)^(3/2))/(12*a) + (7*c^4*(1 - a*x)*(1 - a^2*x^2)^(3/2))/(20*a) + (c^4*(1 - a*x)^2*(1 - a^2*x^2)^(3/2))/(5*a) + (7*c^4*ArcSin[a*x])/(8*a)","A",6,5,16,0.3125,1,"{6127, 671, 641, 195, 216}"
320,1,101,0,0.2464116,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x,x]","\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)","\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*(8 - 13*a*x)*Sqrt[1 - a^2*x^2])/8 - c^4*(1 - a^2*x^2)^(3/2) + (a*c^4*x*(1 - a^2*x^2)^(3/2))/4 - (13*c^4*ArcSin[a*x])/8 - c^4*ArcTanh[Sqrt[1 - a^2*x^2]]","A",9,8,19,0.4211,1,"{6128, 1809, 815, 844, 216, 266, 63, 208}"
321,1,106,0,0.24186,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^2} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^2,x]","\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)","\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,"-(a*c^4*(6 - a*x)*Sqrt[1 - a^2*x^2])/2 + (a*c^4*(1 - a^2*x^2)^(3/2))/3 - (c^4*(1 - a^2*x^2)^(3/2))/x + (a*c^4*ArcSin[a*x])/2 + 3*a*c^4*ArcTanh[Sqrt[1 - a^2*x^2]]","A",9,9,19,0.4737,1,"{6128, 1807, 1809, 815, 844, 216, 266, 63, 208}"
322,1,116,0,0.2469466,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^3} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^3,x]","\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)","\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,"(5*a^2*c^4*(1 + a*x)*Sqrt[1 - a^2*x^2])/2 - (c^4*(1 - a^2*x^2)^(3/2))/(2*x^2) + (3*a*c^4*(1 - a^2*x^2)^(3/2))/x + (5*a^2*c^4*ArcSin[a*x])/2 - (5*a^2*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",9,8,19,0.4211,1,"{6128, 1807, 815, 844, 216, 266, 63, 208}"
323,1,120,0,0.2490443,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^4} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^4,x]","\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{2 x^2}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{a^2 c^4 (6-a x) \sqrt{1-a^2 x^2}}{2 x}-\frac{1}{2} a^3 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-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{c^4 \left(1-a^2 x^2\right)^{3/2}}{3 x^3}-\frac{a^2 c^4 (6-a x) \sqrt{1-a^2 x^2}}{2 x}-\frac{1}{2} a^3 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-3 a^3 c^4 \sin ^{-1}(a x)",1,"-(a^2*c^4*(6 - a*x)*Sqrt[1 - a^2*x^2])/(2*x) - (c^4*(1 - a^2*x^2)^(3/2))/(3*x^3) + (3*a*c^4*(1 - a^2*x^2)^(3/2))/(2*x^2) - 3*a^3*c^4*ArcSin[a*x] - (a^3*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",9,8,19,0.4211,1,"{6128, 1807, 813, 844, 216, 266, 63, 208}"
324,1,116,0,0.2477261,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^5} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^5,x]","\frac{a c^4 \left(1-a^2 x^2\right)^{3/2}}{x^3}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{a^2 c^4 (13-8 a x) \sqrt{1-a^2 x^2}}{8 x^2}+\frac{13}{8} a^4 c^4 \tanh ^{-1}\left(\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{a c^4 \sqrt{1-a^2 x^2}}{x^3}-\frac{c^4 \sqrt{1-a^2 x^2}}{4 x^4}+\frac{13}{8} a^4 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)+a^4 c^4 \sin ^{-1}(a x)",1,"-(a^2*c^4*(13 - 8*a*x)*Sqrt[1 - a^2*x^2])/(8*x^2) - (c^4*(1 - a^2*x^2)^(3/2))/(4*x^4) + (a*c^4*(1 - a^2*x^2)^(3/2))/x^3 + a^4*c^4*ArcSin[a*x] + (13*a^4*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",9,8,19,0.4211,1,"{6128, 1807, 811, 844, 216, 266, 63, 208}"
325,1,129,0,0.245766,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^6} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^6,x]","\frac{7 a^3 c^4 \sqrt{1-a^2 x^2}}{8 x^2}-\frac{17 a^2 c^4 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\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}-\frac{17 a^2 c^4 \left(1-a^2 x^2\right)^{3/2}}{15 x^3}+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{4 x^4}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{7}{8} a^5 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(7*a^3*c^4*Sqrt[1 - a^2*x^2])/(8*x^2) - (c^4*(1 - a^2*x^2)^(3/2))/(5*x^5) + (3*a*c^4*(1 - a^2*x^2)^(3/2))/(4*x^4) - (17*a^2*c^4*(1 - a^2*x^2)^(3/2))/(15*x^3) - (7*a^5*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",8,7,19,0.3684,1,"{6128, 1807, 807, 266, 47, 63, 208}"
326,1,156,0,0.2637335,"\int \frac{e^{\tanh ^{-1}(a x)} (c-a c x)^4}{x^7} \, dx","Int[(E^ArcTanh[a*x]*(c - a*c*x)^4)/x^7,x]","-\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}-\frac{7 a^2 c^4 \left(1-a^2 x^2\right)^{3/2}}{8 x^4}+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{6 x^6}+\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}-\frac{7 a^2 c^4 \left(1-a^2 x^2\right)^{3/2}}{8 x^4}+\frac{3 a c^4 \left(1-a^2 x^2\right)^{3/2}}{5 x^5}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{6 x^6}+\frac{7}{16} a^6 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"(-7*a^4*c^4*Sqrt[1 - a^2*x^2])/(16*x^2) - (c^4*(1 - a^2*x^2)^(3/2))/(6*x^6) + (3*a*c^4*(1 - a^2*x^2)^(3/2))/(5*x^5) - (7*a^2*c^4*(1 - a^2*x^2)^(3/2))/(8*x^4) + (11*a^3*c^4*(1 - a^2*x^2)^(3/2))/(15*x^3) + (7*a^6*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/16","A",9,8,19,0.4211,1,"{6128, 1807, 835, 807, 266, 47, 63, 208}"
327,1,146,0,0.3432827,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{c-a c x} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a*c*x),x]","\frac{x^3 \sqrt{1-a^2 x^2}}{4 a^2 c}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{3 a^3 c}+\frac{11 x \sqrt{1-a^2 x^2}}{8 a^4 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{27 \sin ^{-1}(a x)}{8 a^5 c}","\frac{x^3 \sqrt{1-a^2 x^2}}{4 a^2 c}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{3 a^3 c}+\frac{11 x \sqrt{1-a^2 x^2}}{8 a^4 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{27 \sin ^{-1}(a x)}{8 a^5 c}",1,"(1 + a*x)^2/(a^5*c*Sqrt[1 - a^2*x^2]) + (13*Sqrt[1 - a^2*x^2])/(3*a^5*c) + (11*x*Sqrt[1 - a^2*x^2])/(8*a^4*c) + (2*x^2*Sqrt[1 - a^2*x^2])/(3*a^3*c) + (x^3*Sqrt[1 - a^2*x^2])/(4*a^2*c) - (27*ArcSin[a*x])/(8*a^5*c)","A",8,6,19,0.3158,1,"{6128, 852, 1635, 1815, 641, 216}"
328,1,114,0,0.2857989,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{c-a c x} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a*c*x),x]","\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2 c}+\frac{x \sqrt{1-a^2 x^2}}{a^3 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{3 \sin ^{-1}(a x)}{a^4 c}","\frac{x^2 \sqrt{1-a^2 x^2}}{3 a^2 c}+\frac{x \sqrt{1-a^2 x^2}}{a^3 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{3 \sin ^{-1}(a x)}{a^4 c}",1,"(1 + a*x)^2/(a^4*c*Sqrt[1 - a^2*x^2]) + (11*Sqrt[1 - a^2*x^2])/(3*a^4*c) + (x*Sqrt[1 - a^2*x^2])/(a^3*c) + (x^2*Sqrt[1 - a^2*x^2])/(3*a^2*c) - (3*ArcSin[a*x])/(a^4*c)","A",7,6,19,0.3158,1,"{6128, 852, 1635, 1815, 641, 216}"
329,1,72,0,0.2008764,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{c-a c x} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a*c*x),x]","\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}-\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}-\frac{5 \sin ^{-1}(a x)}{2 a^3 c}",1,"(1 + a*x)^2/(a^3*c*Sqrt[1 - a^2*x^2]) + ((6 + a*x)*Sqrt[1 - a^2*x^2])/(2*a^3*c) - (5*ArcSin[a*x])/(2*a^3*c)","A",5,5,19,0.2632,1,"{6128, 852, 1635, 780, 216}"
330,1,64,0,0.0782248,"\int \frac{e^{\tanh ^{-1}(a x)} x}{c-a c x} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a*c*x),x]","\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}","\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,"(2*Sqrt[1 - a^2*x^2])/(a^2*c) + (1 - a^2*x^2)^(3/2)/(a^2*c*(1 - a*x)^2) - (2*ArcSin[a*x])/(a^2*c)","A",4,4,17,0.2353,1,"{6128, 793, 665, 216}"
331,1,43,0,0.0414235,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x),x]","\frac{2 \sqrt{1-a^2 x^2}}{a c (1-a x)}-\frac{\sin ^{-1}(a x)}{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^2*x^2])/(a*c*(1 - a*x)) - ArcSin[a*x]/(a*c)","A",3,3,16,0.1875,1,"{6127, 663, 216}"
332,1,45,0,0.1677674,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a*c*x)),x]","\frac{2 (a x+1)}{c \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}","\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*(1 + a*x))/(c*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c","A",7,7,19,0.3684,1,"{6128, 852, 1805, 12, 266, 63, 208}"
333,1,69,0,0.193182,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a*c*x)),x]","\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}","\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,"(2*a*(1 + a*x))/(c*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(c*x) - (2*a*ArcTanh[Sqrt[1 - a^2*x^2]])/c","A",7,7,19,0.3684,1,"{6128, 852, 1805, 807, 266, 63, 208}"
334,1,100,0,0.2580565,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a*c*x)),x]","\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}","\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,"(2*a^2*(1 + a*x))/(c*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(2*c*x^2) - (2*a*Sqrt[1 - a^2*x^2])/(c*x) - (5*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c)","A",8,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
335,1,125,0,0.3291865,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 (c-a c x)} \, dx","Int[E^ArcTanh[a*x]/(x^4*(c - a*c*x)),x]","\frac{2 a^3 (a x+1)}{c \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{3 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}","\frac{2 a^3 (a x+1)}{c \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{3 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"(2*a^3*(1 + a*x))/(c*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(3*c*x^3) - (a*Sqrt[1 - a^2*x^2])/(c*x^2) - (8*a^2*Sqrt[1 - a^2*x^2])/(3*c*x) - (3*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/c","A",9,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
336,1,159,0,0.5174022,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{(c-a c x)^2} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a*c*x)^2,x]","-\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}+\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}+\frac{17 \sin ^{-1}(a x)}{2 a^5 c^2}",1,"(1 + a*x)^3/(3*a^5*c^2*(1 - a^2*x^2)^(3/2)) - (2*(1 + a*x)^3)/(a^5*c^2*Sqrt[1 - a^2*x^2]) - (5*Sqrt[1 - a^2*x^2])/(2*a^5*c^2) - ((5 + a*x)*Sqrt[1 - a^2*x^2])/(6*a^5*c^2) - ((5 + a*x)^2*Sqrt[1 - a^2*x^2])/(3*a^5*c^2) + (17*ArcSin[a*x])/(2*a^5*c^2)","A",10,9,19,0.4737,1,"{6128, 852, 1635, 1625, 1654, 21, 743, 641, 216}"
337,1,104,0,0.3041515,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{(c-a c x)^2} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a*c*x)^2,x]","\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}+\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}+\frac{11 \sin ^{-1}(a x)}{2 a^4 c^2}",1,"(1 + a*x)^3/(3*a^4*c^2*(1 - a^2*x^2)^(3/2)) - (3*(1 + a*x)^2)/(a^4*c^2*Sqrt[1 - a^2*x^2]) - ((12 + a*x)*Sqrt[1 - a^2*x^2])/(2*a^4*c^2) + (11*ArcSin[a*x])/(2*a^4*c^2)","A",6,5,19,0.2632,1,"{6128, 852, 1635, 780, 216}"
338,1,104,0,0.1884101,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{(c-a c x)^2} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a*c*x)^2,x]","\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)}+\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)}+\frac{3 \sin ^{-1}(a x)}{a^3 c^2}",1,"(-6*Sqrt[1 - a^2*x^2])/(a^3*c^2*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(3*a^3*c^2*(1 - a*x)^3) + (1 - a^2*x^2)^(3/2)/(a^3*c^2*(1 - a*x)^2) + (3*ArcSin[a*x])/(a^3*c^2)","A",5,5,19,0.2632,1,"{6128, 1639, 793, 663, 216}"
339,1,74,0,0.0803656,"\int \frac{e^{\tanh ^{-1}(a x)} x}{(c-a c x)^2} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a*c*x)^2,x]","\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}","\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,"(-2*Sqrt[1 - a^2*x^2])/(a^2*c^2*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(3*a^2*c^2*(1 - a*x)^3) + ArcSin[a*x]/(a^2*c^2)","A",4,4,17,0.2353,1,"{6128, 793, 663, 216}"
340,1,32,0,0.033848,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^2,x]","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}","\frac{\left(1-a^2 x^2\right)^{3/2}}{3 a c^2 (1-a x)^3}",1,"(1 - a^2*x^2)^(3/2)/(3*a*c^2*(1 - a*x)^3)","A",2,2,16,0.1250,1,"{6127, 651}"
341,1,74,0,0.1995966,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)^2} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a*c*x)^2),x]","\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}","\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,"(4*(1 + a*x))/(3*c^2*(1 - a^2*x^2)^(3/2)) + (3 + 5*a*x)/(3*c^2*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c^2","A",8,8,19,0.4211,1,"{6128, 852, 1805, 823, 12, 266, 63, 208}"
342,1,99,0,0.2668278,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)^2} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a*c*x)^2),x]","\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}","\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,"(4*a*(1 + a*x))/(3*c^2*(1 - a^2*x^2)^(3/2)) + (a*(9 + 11*a*x))/(3*c^2*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(c^2*x) - (3*a*ArcTanh[Sqrt[1 - a^2*x^2]])/c^2","A",8,7,19,0.3684,1,"{6128, 852, 1805, 807, 266, 63, 208}"
343,1,132,0,0.333784,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)^2} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a*c*x)^2),x]","\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}","\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,"(4*a^2*(1 + a*x))/(3*c^2*(1 - a^2*x^2)^(3/2)) + (a^2*(15 + 17*a*x))/(3*c^2*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(2*c^2*x^2) - (3*a*Sqrt[1 - a^2*x^2])/(c^2*x) - (11*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^2)","A",9,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
344,1,161,0,0.4229516,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 (c-a c x)^2} \, dx","Int[E^ArcTanh[a*x]/(x^4*(c - a*c*x)^2),x]","\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^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{17 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^2}","\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^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{17 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 c^2}",1,"(4*a^3*(1 + a*x))/(3*c^2*(1 - a^2*x^2)^(3/2)) + (a^3*(21 + 23*a*x))/(3*c^2*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(3*c^2*x^3) - (3*a*Sqrt[1 - a^2*x^2])/(2*c^2*x^2) - (17*a^2*Sqrt[1 - a^2*x^2])/(3*c^2*x) - (17*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^2)","A",10,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
345,1,135,0,0.4151006,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{(c-a c x)^3} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a*c*x)^3,x]","\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}-\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}-\frac{19 \sin ^{-1}(a x)}{2 a^5 c^3}",1,"(1 + a*x)^4/(5*a^5*c^3*(1 - a^2*x^2)^(5/2)) - (19*(1 + a*x)^3)/(15*a^5*c^3*(1 - a^2*x^2)^(3/2)) + (6*(1 + a*x)^2)/(a^5*c^3*Sqrt[1 - a^2*x^2]) + ((20 + a*x)*Sqrt[1 - a^2*x^2])/(2*a^5*c^3) - (19*ArcSin[a*x])/(2*a^5*c^3)","A",7,5,19,0.2632,1,"{6128, 852, 1635, 780, 216}"
346,1,137,0,0.3328261,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{(c-a c x)^3} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a*c*x)^3,x]","-\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)}-\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)}-\frac{4 \sin ^{-1}(a x)}{a^4 c^3}",1,"(8*Sqrt[1 - a^2*x^2])/(a^4*c^3*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(5*a^4*c^3*(1 - a*x)^4) - (14*(1 - a^2*x^2)^(3/2))/(15*a^4*c^3*(1 - a*x)^3) - (1 - a^2*x^2)^(3/2)/(a^4*c^3*(1 - a*x)^2) - (4*ArcSin[a*x])/(a^4*c^3)","A",9,7,19,0.3684,1,"{6128, 1639, 1637, 659, 651, 663, 216}"
347,1,107,0,0.2200882,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{(c-a c x)^3} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a*c*x)^3,x]","-\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)}-\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)}-\frac{\sin ^{-1}(a x)}{a^3 c^3}",1,"(2*Sqrt[1 - a^2*x^2])/(a^3*c^3*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(5*a^3*c^3*(1 - a*x)^4) - (3*(1 - a^2*x^2)^(3/2))/(5*a^3*c^3*(1 - a*x)^3) - ArcSin[a*x]/(a^3*c^3)","A",8,6,19,0.3158,1,"{6128, 1637, 659, 651, 663, 216}"
348,1,65,0,0.0784652,"\int \frac{e^{\tanh ^{-1}(a x)} x}{(c-a c x)^3} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a*c*x)^3,x]","\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}","\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^2*x^2)^(3/2)/(5*a^2*c^3*(1 - a*x)^4) - (4*(1 - a^2*x^2)^(3/2))/(15*a^2*c^3*(1 - a*x)^3)","A",3,3,17,0.1765,1,"{6128, 793, 651}"
349,1,65,0,0.0516873,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^3,x]","\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}","\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,"(1 - a^2*x^2)^(3/2)/(5*a*c^3*(1 - a*x)^4) + (1 - a^2*x^2)^(3/2)/(15*a*c^3*(1 - a*x)^3)","A",3,3,16,0.1875,1,"{6127, 659, 651}"
350,1,97,0,0.2741376,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)^3} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a*c*x)^3),x]","\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}","\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,"(8*(1 + a*x))/(5*c^3*(1 - a^2*x^2)^(5/2)) + (4*a*x)/(5*c^3*(1 - a^2*x^2)^(3/2)) + (5 + 8*a*x)/(5*c^3*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c^3","A",9,8,19,0.4211,1,"{6128, 852, 1805, 823, 12, 266, 63, 208}"
351,1,127,0,0.3513433,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)^3} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a*c*x)^3),x]","\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}","\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,"(8*a*(1 + a*x))/(5*c^3*(1 - a^2*x^2)^(5/2)) + (4*a*(5 + 8*a*x))/(15*c^3*(1 - a^2*x^2)^(3/2)) + (a*(60 + 79*a*x))/(15*c^3*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(c^3*x) - (4*a*ArcTanh[Sqrt[1 - a^2*x^2]])/c^3","A",9,7,19,0.3684,1,"{6128, 852, 1805, 807, 266, 63, 208}"
352,1,162,0,0.4300187,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)^3} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a*c*x)^3),x]","\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}","\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,"(8*a^2*(1 + a*x))/(5*c^3*(1 - a^2*x^2)^(5/2)) + (4*a^2*(10 + 13*a*x))/(15*c^3*(1 - a^2*x^2)^(3/2)) + (a^2*(135 + 164*a*x))/(15*c^3*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(2*c^3*x^2) - (4*a*Sqrt[1 - a^2*x^2])/(c^3*x) - (19*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^3)","A",10,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
353,1,187,0,0.5248165,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 (c-a c x)^3} \, dx","Int[E^ArcTanh[a*x]/(x^4*(c - a*c*x)^3),x]","\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{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{18 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^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{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{18 a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c^3}",1,"(8*a^3*(1 + a*x))/(5*c^3*(1 - a^2*x^2)^(5/2)) + (4*a^3*(5 + 6*a*x))/(5*c^3*(1 - a^2*x^2)^(3/2)) + (a^3*(80 + 93*a*x))/(5*c^3*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(3*c^3*x^3) - (2*a*Sqrt[1 - a^2*x^2])/(c^3*x^2) - (29*a^2*Sqrt[1 - a^2*x^2])/(3*c^3*x) - (18*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/c^3","A",11,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
354,1,166,0,0.533396,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{(c-a c x)^4} \, dx","Int[(E^ArcTanh[a*x]*x^5)/(c - a*c*x)^4,x]","\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}+\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}+\frac{29 \sin ^{-1}(a x)}{2 a^6 c^4}",1,"(1 + a*x)^5/(7*a^6*c^4*(1 - a^2*x^2)^(7/2)) - (33*(1 + a*x)^4)/(35*a^6*c^4*(1 - a^2*x^2)^(5/2)) + (317*(1 + a*x)^3)/(105*a^6*c^4*(1 - a^2*x^2)^(3/2)) - (10*(1 + a*x)^2)/(a^6*c^4*Sqrt[1 - a^2*x^2]) - ((30 + a*x)*Sqrt[1 - a^2*x^2])/(2*a^6*c^4) + (29*ArcSin[a*x])/(2*a^6*c^4)","A",8,5,19,0.2632,1,"{6128, 852, 1635, 780, 216}"
355,1,168,0,0.4026633,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{(c-a c x)^4} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a*c*x)^4,x]","\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)}+\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)}+\frac{5 \sin ^{-1}(a x)}{a^5 c^4}",1,"(-10*Sqrt[1 - a^2*x^2])/(a^5*c^4*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(7*a^5*c^4*(1 - a*x)^5) - (26*(1 - a^2*x^2)^(3/2))/(35*a^5*c^4*(1 - a*x)^4) + (184*(1 - a^2*x^2)^(3/2))/(105*a^5*c^4*(1 - a*x)^3) + (1 - a^2*x^2)^(3/2)/(a^5*c^4*(1 - a*x)^2) + (5*ArcSin[a*x])/(a^5*c^4)","A",12,7,19,0.3684,1,"{6128, 1639, 1637, 659, 651, 663, 216}"
356,1,138,0,0.2716013,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{(c-a c x)^4} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a*c*x)^4,x]","\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)}+\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)}+\frac{\sin ^{-1}(a x)}{a^4 c^4}",1,"(-2*Sqrt[1 - a^2*x^2])/(a^4*c^4*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(7*a^4*c^4*(1 - a*x)^5) - (19*(1 - a^2*x^2)^(3/2))/(35*a^4*c^4*(1 - a*x)^4) + (86*(1 - a^2*x^2)^(3/2))/(105*a^4*c^4*(1 - a*x)^3) + ArcSin[a*x]/(a^4*c^4)","A",11,6,19,0.3158,1,"{6128, 1637, 659, 651, 663, 216}"
357,1,97,0,0.208041,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{(c-a c x)^4} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a*c*x)^4,x]","\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}","\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 - a^2*x^2)^(3/2)/(7*a^3*c^4*(1 - a*x)^5) - (12*(1 - a^2*x^2)^(3/2))/(35*a^3*c^4*(1 - a*x)^4) + (23*(1 - a^2*x^2)^(3/2))/(105*a^3*c^4*(1 - a*x)^3)","A",5,5,19,0.2632,1,"{6128, 1639, 793, 659, 651}"
358,1,97,0,0.1007738,"\int \frac{e^{\tanh ^{-1}(a x)} x}{(c-a c x)^4} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a*c*x)^4,x]","-\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}","-\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 - a^2*x^2)^(3/2)/(7*a^2*c^4*(1 - a*x)^5) - (1 - a^2*x^2)^(3/2)/(7*a^2*c^4*(1 - a*x)^4) - (1 - a^2*x^2)^(3/2)/(21*a^2*c^4*(1 - a*x)^3)","A",4,4,17,0.2353,1,"{6128, 793, 659, 651}"
359,1,97,0,0.070342,"\int \frac{e^{\tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^ArcTanh[a*x]/(c - a*c*x)^4,x]","\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}","\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 - a^2*x^2)^(3/2)/(7*a*c^4*(1 - a*x)^5) + (2*(1 - a^2*x^2)^(3/2))/(35*a*c^4*(1 - a*x)^4) + (2*(1 - a^2*x^2)^(3/2))/(105*a*c^4*(1 - a*x)^3)","A",4,3,16,0.1875,1,"{6127, 659, 651}"
360,1,128,0,0.3106097,"\int \frac{e^{\tanh ^{-1}(a x)}}{x (c-a c x)^4} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a*c*x)^4),x]","-\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}","-\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,"(16*(1 + a*x))/(7*c^4*(1 - a^2*x^2)^(7/2)) - (4*(7 - 3*a*x))/(35*c^4*(1 - a^2*x^2)^(5/2)) + (35 + 83*a*x)/(105*c^4*(1 - a^2*x^2)^(3/2)) + (105 + 166*a*x)/(105*c^4*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c^4","A",10,8,19,0.4211,1,"{6128, 852, 1805, 823, 12, 266, 63, 208}"
361,1,155,0,0.4494721,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 (c-a c x)^4} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a*c*x)^4),x]","\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}","\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,"(16*a*(1 + a*x))/(7*c^4*(1 - a^2*x^2)^(7/2)) + (4*a*(7 + 17*a*x))/(35*c^4*(1 - a^2*x^2)^(5/2)) + (a*(175 + 307*a*x))/(105*c^4*(1 - a^2*x^2)^(3/2)) + (a*(525 + 719*a*x))/(105*c^4*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(c^4*x) - (5*a*ArcTanh[Sqrt[1 - a^2*x^2]])/c^4","A",10,7,19,0.3684,1,"{6128, 852, 1805, 807, 266, 63, 208}"
362,1,192,0,0.5237591,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 (c-a c x)^4} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a*c*x)^4),x]","\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}","\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,"(16*a^2*(1 + a*x))/(7*c^4*(1 - a^2*x^2)^(7/2)) + (4*a^2*(21 + 31*a*x))/(35*c^4*(1 - a^2*x^2)^(5/2)) + (a^2*(455 + 671*a*x))/(105*c^4*(1 - a^2*x^2)^(3/2)) + (a^2*(1470 + 1867*a*x))/(105*c^4*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(2*c^4*x^2) - (5*a*Sqrt[1 - a^2*x^2])/(c^4*x) - (29*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^4)","A",11,8,19,0.4211,1,"{6128, 852, 1805, 1807, 807, 266, 63, 208}"
363,1,61,0,0.0319597,"\int e^{\tanh ^{-1}(x)} x (1+x) \, dx","Int[E^ArcTanh[x]*x*(1 + x),x]","-\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)","-\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,"-(Sqrt[1 - x]*Sqrt[1 + x]) - (Sqrt[1 - x]*(1 + x)^(3/2))/3 - (Sqrt[1 - x]*(1 + x)^(5/2))/3 + ArcSin[x]","A",6,5,9,0.5556,1,"{6129, 80, 50, 41, 216}"
364,1,47,0,0.0174384,"\int e^{\tanh ^{-1}(x)} (1+x) \, dx","Int[E^ArcTanh[x]*(1 + x),x]","-\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)","-\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,"(-3*Sqrt[1 - x]*Sqrt[1 + x])/2 - (Sqrt[1 - x]*(1 + x)^(3/2))/2 + (3*ArcSin[x])/2","A",5,4,8,0.5000,1,"{6129, 50, 41, 216}"
365,1,87,0,0.0482521,"\int e^{\tanh ^{-1}(x)} x (1+x)^2 \, dx","Int[E^ArcTanh[x]*x*(1 + x)^2,x]","-\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)","-\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,"(-15*Sqrt[1 - x]*Sqrt[1 + x])/8 - (5*Sqrt[1 - x]*(1 + x)^(3/2))/8 - (Sqrt[1 - x]*(1 + x)^(5/2))/4 - (Sqrt[1 - x]*(1 + x)^(7/2))/4 + (15*ArcSin[x])/8","A",7,5,11,0.4545,1,"{6129, 80, 50, 41, 216}"
366,1,67,0,0.0290799,"\int e^{\tanh ^{-1}(x)} (1+x)^2 \, dx","Int[E^ArcTanh[x]*(1 + x)^2,x]","-\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)","-\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,"(-5*Sqrt[1 - x]*Sqrt[1 + x])/2 - (5*Sqrt[1 - x]*(1 + x)^(3/2))/6 - (Sqrt[1 - x]*(1 + x)^(5/2))/3 + (5*ArcSin[x])/2","A",6,4,10,0.4000,1,"{6129, 50, 41, 216}"
367,1,18,0,0.0340615,"\int \frac{e^{\tanh ^{-1}(x)} x}{1+x} \, dx","Int[(E^ArcTanh[x]*x)/(1 + x),x]","-\sqrt{1-x} \sqrt{x+1}","-\sqrt{1-x} \sqrt{x+1}",1,"-(Sqrt[1 - x]*Sqrt[1 + x])","A",2,2,11,0.1818,1,"{6129, 74}"
368,1,2,0,0.0194153,"\int \frac{e^{\tanh ^{-1}(x)}}{1+x} \, dx","Int[E^ArcTanh[x]/(1 + x),x]","\sin ^{-1}(x)","\sin ^{-1}(x)",1,"ArcSin[x]","A",3,3,10,0.3000,1,"{6129, 41, 216}"
369,1,20,0,0.0335342,"\int \frac{e^{\tanh ^{-1}(x)} x}{(1+x)^2} \, dx","Int[(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",4,4,11,0.3636,1,"{6129, 78, 41, 216}"
370,1,18,0,0.0181478,"\int \frac{e^{\tanh ^{-1}(x)}}{(1+x)^2} \, dx","Int[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",2,2,10,0.2000,1,"{6129, 37}"
371,1,49,0,0.0479878,"\int e^{\tanh ^{-1}(x)} x (1+x)^{3/2} \, dx","Int[E^ArcTanh[x]*x*(1 + x)^(3/2),x]","\frac{2}{7} (1-x)^{7/2}-2 (1-x)^{5/2}+\frac{16}{3} (1-x)^{3/2}-8 \sqrt{1-x}","\frac{2}{7} (1-x)^{7/2}-2 (1-x)^{5/2}+\frac{16}{3} (1-x)^{3/2}-8 \sqrt{1-x}",1,"-8*Sqrt[1 - x] + (16*(1 - x)^(3/2))/3 - 2*(1 - x)^(5/2) + (2*(1 - x)^(7/2))/7","A",3,2,13,0.1538,1,"{6129, 77}"
372,1,38,0,0.0288797,"\int e^{\tanh ^{-1}(x)} (1+x)^{3/2} \, dx","Int[E^ArcTanh[x]*(1 + x)^(3/2),x]","-\frac{2}{5} (1-x)^{5/2}+\frac{8}{3} (1-x)^{3/2}-8 \sqrt{1-x}","-\frac{2}{5} (1-x)^{5/2}+\frac{8}{3} (1-x)^{3/2}-8 \sqrt{1-x}",1,"-8*Sqrt[1 - x] + (8*(1 - x)^(3/2))/3 - (2*(1 - x)^(5/2))/5","A",3,2,12,0.1667,1,"{6129, 43}"
373,1,47,0,0.0620389,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} x \, dx","Int[E^ArcTanh[x]*(1 - x)^(3/2)*x,x]","-\frac{2}{7} \sqrt{1-x} \left(1-x^2\right)^{3/2}+\frac{2}{35} (x+1)^{5/2}-\frac{4}{21} (x+1)^{3/2}","-\frac{2}{7} (x+1)^{7/2}+\frac{6}{5} (x+1)^{5/2}-\frac{4}{3} (x+1)^{3/2}",1,"(-4*(1 + x)^(3/2))/21 + (2*(1 + x)^(5/2))/35 - (2*Sqrt[1 - x]*(1 - x^2)^(3/2))/7","A",5,4,15,0.2667,0,"{6128, 795, 627, 43}"
374,1,23,0,0.033876,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} \, dx","Int[E^ArcTanh[x]*(1 - x)^(3/2),x]","\frac{4}{3} (x+1)^{3/2}-\frac{2}{5} (x+1)^{5/2}","\frac{4}{3} (x+1)^{3/2}-\frac{2}{5} (x+1)^{5/2}",1,"(4*(1 + x)^(3/2))/3 - (2*(1 + x)^(5/2))/5","A",4,3,14,0.2143,1,"{6127, 627, 43}"
375,1,36,0,0.0415186,"\int e^{\tanh ^{-1}(x)} x \sqrt{1+x} \, dx","Int[E^ArcTanh[x]*x*Sqrt[1 + x],x]","-\frac{2}{5} (1-x)^{5/2}+2 (1-x)^{3/2}-4 \sqrt{1-x}","-\frac{2}{5} (1-x)^{5/2}+2 (1-x)^{3/2}-4 \sqrt{1-x}",1,"-4*Sqrt[1 - x] + 2*(1 - x)^(3/2) - (2*(1 - x)^(5/2))/5","A",3,2,13,0.1538,1,"{6129, 77}"
376,1,25,0,0.0234036,"\int e^{\tanh ^{-1}(x)} \sqrt{1+x} \, dx","Int[E^ArcTanh[x]*Sqrt[1 + x],x]","\frac{2}{3} (1-x)^{3/2}-4 \sqrt{1-x}","\frac{2}{3} (1-x)^{3/2}-4 \sqrt{1-x}",1,"-4*Sqrt[1 - x] + (2*(1 - x)^(3/2))/3","A",3,2,12,0.1667,1,"{6129, 43}"
377,1,23,0,0.0393961,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} x \, dx","Int[E^ArcTanh[x]*Sqrt[1 - x]*x,x]","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(-2*(1 + x)^(3/2))/3 + (2*(1 + x)^(5/2))/5","A",4,3,15,0.2000,1,"{6128, 26, 43}"
378,1,11,0,0.0200117,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} \, dx","Int[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",3,3,14,0.2143,1,"{6127, 26, 32}"
379,1,25,0,0.0390745,"\int \frac{e^{\tanh ^{-1}(x)} x}{\sqrt{1+x}} \, dx","Int[(E^ArcTanh[x]*x)/Sqrt[1 + x],x]","\frac{2}{3} (1-x)^{3/2}-2 \sqrt{1-x}","\frac{2}{3} (1-x)^{3/2}-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x] + (2*(1 - x)^(3/2))/3","A",3,2,13,0.1538,1,"{6129, 43}"
380,1,11,0,0.0192077,"\int \frac{e^{\tanh ^{-1}(x)}}{\sqrt{1+x}} \, dx","Int[E^ArcTanh[x]/Sqrt[1 + x],x]","-2 \sqrt{1-x}","-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x]","A",2,2,12,0.1667,1,"{6129, 32}"
381,1,42,0,0.0463722,"\int \frac{e^{\tanh ^{-1}(x)} x}{\sqrt{1-x}} \, dx","Int[(E^ArcTanh[x]*x)/Sqrt[1 - x],x]","-\frac{2}{3} (x+1)^{3/2}-2 \sqrt{x+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{2}}\right)","-\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] - (2*(1 + x)^(3/2))/3 + 2*Sqrt[2]*ArcTanh[Sqrt[1 + x]/Sqrt[2]]","A",5,5,15,0.3333,1,"{6129, 80, 50, 63, 206}"
382,1,31,0,0.0336543,"\int \frac{e^{\tanh ^{-1}(x)}}{\sqrt{1-x}} \, dx","Int[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",5,5,14,0.3571,1,"{6127, 627, 50, 63, 206}"
383,1,34,0,0.045287,"\int \frac{e^{\tanh ^{-1}(x)} x}{(1+x)^{3/2}} \, dx","Int[(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",4,4,13,0.3077,1,"{6129, 80, 63, 206}"
384,1,23,0,0.028107,"\int \frac{e^{\tanh ^{-1}(x)}}{(1+x)^{3/2}} \, dx","Int[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",3,3,12,0.2500,1,"{6129, 63, 206}"
385,1,51,0,0.0545211,"\int \frac{e^{\tanh ^{-1}(x)} x}{(1-x)^{3/2}} \, dx","Int[(E^ArcTanh[x]*x)/(1 - x)^(3/2),x]","\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}}","\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,"(5*Sqrt[1 + x])/2 + (1 + x)^(3/2)/(2*(1 - x)) - (5*ArcTanh[Sqrt[1 + x]/Sqrt[2]])/Sqrt[2]","A",5,5,15,0.3333,1,"{6129, 78, 50, 63, 206}"
386,1,37,0,0.0370145,"\int \frac{e^{\tanh ^{-1}(x)}}{(1-x)^{3/2}} \, dx","Int[E^ArcTanh[x]/(1 - x)^(3/2),x]","\frac{\sqrt{x+1}}{1-x}-\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",5,5,14,0.3571,1,"{6127, 627, 47, 63, 206}"
387,1,64,0,0.1240618,"\int e^{\tanh ^{-1}(a x)} x^m \sqrt{c-a c x} \, dx","Int[E^ArcTanh[a*x]*x^m*Sqrt[c - a*c*x],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}}","\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,"(2*c*x^m*(1 + a*x)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[3/2, -m, 5/2, 1 + a*x])/(3*a*(-(a*x))^m*Sqrt[c - a*c*x])","A",4,4,21,0.1905,1,"{6128, 892, 67, 65}"
388,1,107,0,0.1583811,"\int e^{\tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[E^ArcTanh[a*x]*x^2*Sqrt[c - a*c*x],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}}","\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,"(-8*c^2*(1 - a^2*x^2)^(3/2))/(105*a^3*(c - a*c*x)^(3/2)) + (2*c^2*x^2*(1 - a^2*x^2)^(3/2))/(7*a*(c - a*c*x)^(3/2)) + (8*c*(1 - a^2*x^2)^(3/2))/(35*a^3*Sqrt[c - a*c*x])","A",4,4,21,0.1905,1,"{6128, 871, 795, 649}"
389,1,69,0,0.0897471,"\int e^{\tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[E^ArcTanh[a*x]*x*Sqrt[c - a*c*x],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}}","\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*c^2*(1 - a^2*x^2)^(3/2))/(15*a^2*(c - a*c*x)^(3/2)) - (2*c*(1 - a^2*x^2)^(3/2))/(5*a^2*Sqrt[c - a*c*x])","A",3,3,19,0.1579,1,"{6128, 795, 649}"
390,1,35,0,0.0451377,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - a*c*x],x]","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}","\frac{2 c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a (c-a c x)^{3/2}}",1,"(2*c^2*(1 - a^2*x^2)^(3/2))/(3*a*(c - a*c*x)^(3/2))","A",2,2,18,0.1111,1,"{6127, 649}"
391,1,68,0,0.1516217,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - a*c*x])/x,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)","\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^2*x^2])/Sqrt[c - a*c*x] - 2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]]","A",4,4,21,0.1905,1,"{6128, 865, 875, 208}"
392,1,72,0,0.1568015,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - a*c*x])/x^2,x]","-\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)","-\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,"-((c*Sqrt[1 - a^2*x^2])/(x*Sqrt[c - a*c*x])) - a*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]]","A",4,4,21,0.1905,1,"{6128, 863, 875, 208}"
393,1,101,0,0.1322962,"\int e^{2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[E^(2*ArcTanh[a*x])*x^3*Sqrt[c - a*c*x],x]","-\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}","-\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,"(-4*Sqrt[c - a*c*x])/a^4 + (14*(c - a*c*x)^(3/2))/(3*a^4*c) - (18*(c - a*c*x)^(5/2))/(5*a^4*c^2) + (10*(c - a*c*x)^(7/2))/(7*a^4*c^3) - (2*(c - a*c*x)^(9/2))/(9*a^4*c^4)","A",4,3,23,0.1304,1,"{6130, 21, 77}"
394,1,80,0,0.1628926,"\int e^{2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[E^(2*ArcTanh[a*x])*x^2*Sqrt[c - a*c*x],x]","\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}","\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,"(-4*Sqrt[c - a*c*x])/a^3 + (10*(c - a*c*x)^(3/2))/(3*a^3*c) - (8*(c - a*c*x)^(5/2))/(5*a^3*c^2) + (2*(c - a*c*x)^(7/2))/(7*a^3*c^3)","A",4,3,23,0.1304,1,"{6130, 21, 77}"
395,1,57,0,0.0857842,"\int e^{2 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[E^(2*ArcTanh[a*x])*x*Sqrt[c - a*c*x],x]","-\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}","-\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,"(-4*Sqrt[c - a*c*x])/a^2 + (2*(c - a*c*x)^(3/2))/(a^2*c) - (2*(c - a*c*x)^(5/2))/(5*a^2*c^2)","A",4,3,21,0.1429,1,"{6130, 21, 77}"
396,1,38,0,0.0480732,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x],x]","\frac{2 (c-a c x)^{3/2}}{3 a c}-\frac{4 \sqrt{c-a c x}}{a}","\frac{2 (c-a c x)^{3/2}}{3 a c}-\frac{4 \sqrt{c-a c x}}{a}",1,"(-4*Sqrt[c - a*c*x])/a + (2*(c - a*c*x)^(3/2))/(3*a*c)","A",4,3,20,0.1500,1,"{6130, 21, 43}"
397,1,39,0,0.1049197,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[(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",5,5,23,0.2174,1,"{6130, 21, 80, 63, 208}"
398,1,43,0,0.1066193,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[(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",5,5,23,0.2174,1,"{6130, 21, 78, 63, 208}"
399,1,68,0,0.1159611,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[(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{\sqrt{c-a c x}}{2 x^2}-\frac{7 a \sqrt{c-a c x}}{4 x}","-\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,"-Sqrt[c - a*c*x]/(2*x^2) - (7*a*Sqrt[c - a*c*x])/(4*x) - (7*a^2*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/4","A",6,6,23,0.2609,1,"{6130, 21, 78, 51, 63, 208}"
400,1,89,0,0.128482,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^4,x]","-\frac{11 a^2 \sqrt{c-a c x}}{8 x}-\frac{11}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{11 a \sqrt{c-a c x}}{12 x^2}-\frac{\sqrt{c-a c x}}{3 x^3}","-\frac{11 a^2 \sqrt{c-a c x}}{8 x}-\frac{11}{8} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{11 a \sqrt{c-a c x}}{12 x^2}-\frac{\sqrt{c-a c x}}{3 x^3}",1,"-Sqrt[c - a*c*x]/(3*x^3) - (11*a*Sqrt[c - a*c*x])/(12*x^2) - (11*a^2*Sqrt[c - a*c*x])/(8*x) - (11*a^3*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/8","A",7,6,23,0.2609,1,"{6130, 21, 78, 51, 63, 208}"
401,1,110,0,0.1446416,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^5,x]","-\frac{25 a^2 \sqrt{c-a c x}}{32 x^2}-\frac{75 a^3 \sqrt{c-a c x}}{64 x}-\frac{75}{64} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{5 a \sqrt{c-a c x}}{8 x^3}-\frac{\sqrt{c-a c x}}{4 x^4}","-\frac{25 a^2 \sqrt{c-a c x}}{32 x^2}-\frac{75 a^3 \sqrt{c-a c x}}{64 x}-\frac{75}{64} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a c x}}{\sqrt{c}}\right)-\frac{5 a \sqrt{c-a c x}}{8 x^3}-\frac{\sqrt{c-a c x}}{4 x^4}",1,"-Sqrt[c - a*c*x]/(4*x^4) - (5*a*Sqrt[c - a*c*x])/(8*x^3) - (25*a^2*Sqrt[c - a*c*x])/(32*x^2) - (75*a^3*Sqrt[c - a*c*x])/(64*x) - (75*a^4*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/Sqrt[c]])/64","A",8,6,23,0.2609,1,"{6130, 21, 78, 51, 63, 208}"
402,1,249,0,0.1796399,"\int e^{3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[E^(3*ArcTanh[a*x])*x^3*Sqrt[c - a*c*x],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}}","-\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,"(-4*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(a^4*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(3/2)*(c - a*c*x)^(3/2))/(3*a^4*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(5/2)*(c - a*c*x)^(3/2))/(5*a^4*c*(1 - a*x)^(3/2)) + (2*(1 + a*x)^(7/2)*(c - a*c*x)^(3/2))/(7*a^4*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(9/2)*(c - a*c*x)^(3/2))/(9*a^4*c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(a^4*c*(1 - a*x)^(3/2))","A",8,6,23,0.2609,1,"{6130, 23, 88, 50, 63, 208}"
403,1,169,0,0.1597882,"\int e^{3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[E^(3*ArcTanh[a*x])*x^2*Sqrt[c - a*c*x],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}}","-\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,"(-4*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(a^3*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(3/2)*(c - a*c*x)^(3/2))/(3*a^3*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(7/2)*(c - a*c*x)^(3/2))/(7*a^3*c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(a^3*c*(1 - a*x)^(3/2))","A",8,6,23,0.2609,1,"{6130, 23, 88, 50, 63, 208}"
404,1,169,0,0.1144208,"\int e^{3 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[E^(3*ArcTanh[a*x])*x*Sqrt[c - a*c*x],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}}","-\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,"(-4*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(a^2*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(3/2)*(c - a*c*x)^(3/2))/(3*a^2*c*(1 - a*x)^(3/2)) - (2*(1 + a*x)^(5/2)*(c - a*c*x)^(3/2))/(5*a^2*c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(a^2*c*(1 - a*x)^(3/2))","A",7,6,21,0.2857,1,"{6130, 23, 80, 50, 63, 208}"
405,1,119,0,0.1144036,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x],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}","-\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,"(-4*c*Sqrt[1 - a^2*x^2])/(a*Sqrt[c - a*c*x]) - (2*c^2*(1 - a^2*x^2)^(3/2))/(3*a*(c - a*c*x)^(3/2)) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/(Sqrt[2]*Sqrt[c - a*c*x])])/a","A",5,4,20,0.2000,1,"{6127, 665, 661, 208}"
406,1,119,0,0.1360047,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x,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}}","-\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[1 + a*x]*(c - a*c*x)^(3/2))/(c*(1 - a*x)^(3/2)) - (2*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(c*(1 - a*x)^(3/2))","A",8,6,23,0.2609,1,"{6130, 23, 84, 156, 63, 208}"
407,1,124,0,0.1350351,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^2,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}}","-\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[1 + a*x]*(c - a*c*x)^(3/2))/(c*x*(1 - a*x)^(3/2))) - (5*a*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*a*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(c*(1 - a*x)^(3/2))","A",8,6,23,0.2609,1,"{6130, 23, 98, 156, 63, 208}"
408,1,173,0,0.1492171,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^3,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}}","-\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,"-(Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(2*c*x^2*(1 - a*x)^(3/2)) - (9*a*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(4*c*x*(1 - a*x)^(3/2)) - (23*a^2*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(4*c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*a^2*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(c*(1 - a*x)^(3/2))","A",9,7,23,0.3043,1,"{6130, 23, 98, 151, 156, 63, 208}"
409,1,216,0,0.166241,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^4,x]","-\frac{19 a^2 \sqrt{a x+1} (c-a c x)^{3/2}}{8 c x (1-a x)^{3/2}}-\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{13 a \sqrt{a x+1} (c-a c x)^{3/2}}{12 c x^2 (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{19 a^2 \sqrt{a x+1} (c-a c x)^{3/2}}{8 c x (1-a x)^{3/2}}-\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{13 a \sqrt{a x+1} (c-a c x)^{3/2}}{12 c x^2 (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}}",1,"-(Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(3*c*x^3*(1 - a*x)^(3/2)) - (13*a*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(12*c*x^2*(1 - a*x)^(3/2)) - (19*a^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(8*c*x*(1 - a*x)^(3/2)) - (45*a^3*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(8*c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*a^3*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(c*(1 - a*x)^(3/2))","A",10,7,23,0.3043,1,"{6130, 23, 98, 151, 156, 63, 208}"
410,1,259,0,0.1918455,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a*c*x])/x^5,x]","-\frac{107 a^2 \sqrt{a x+1} (c-a c x)^{3/2}}{96 c x^2 (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{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{17 a \sqrt{a x+1} (c-a c x)^{3/2}}{24 c x^3 (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{107 a^2 \sqrt{a x+1} (c-a c x)^{3/2}}{96 c x^2 (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{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{17 a \sqrt{a x+1} (c-a c x)^{3/2}}{24 c x^3 (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}}",1,"-(Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(4*c*x^4*(1 - a*x)^(3/2)) - (17*a*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(24*c*x^3*(1 - a*x)^(3/2)) - (107*a^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(96*c*x^2*(1 - a*x)^(3/2)) - (149*a^3*Sqrt[1 + a*x]*(c - a*c*x)^(3/2))/(64*c*x*(1 - a*x)^(3/2)) - (363*a^4*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(64*c*(1 - a*x)^(3/2)) + (4*Sqrt[2]*a^4*(c - a*c*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]/Sqrt[2]])/(c*(1 - a*x)^(3/2))","A",11,7,23,0.3043,1,"{6130, 23, 98, 151, 156, 63, 208}"
411,1,114,0,0.1848649,"\int e^{-\tanh ^{-1}(a x)} x^m \sqrt{c-a c x} \, dx","Int[(x^m*Sqrt[c - a*c*x])/E^ArcTanh[a*x],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}}","\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,"(-2*c*x^(1 + m)*Sqrt[1 - a^2*x^2])/((3 + 2*m)*Sqrt[c - a*c*x]) + (2*(5 + 4*m)*x^m*(1 + a*x)*Sqrt[c - a*c*x]*Hypergeometric2F1[1/2, -m, 3/2, 1 + a*x])/(a*(3 + 2*m)*(-(a*x))^m*Sqrt[1 - a^2*x^2])","A",5,5,23,0.2174,1,"{6128, 881, 892, 67, 65}"
412,1,135,0,0.2129595,"\int e^{-\tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[(x^2*Sqrt[c - a*c*x])/E^ArcTanh[a*x],x]","-\frac{2 c x^3 \sqrt{1-a^2 x^2}}{7 \sqrt{c-a c x}}+\frac{26 c x^2 \sqrt{1-a^2 x^2}}{35 a \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}}","-\frac{2 c x^3 \sqrt{1-a^2 x^2}}{7 \sqrt{c-a c x}}+\frac{26 c x^2 \sqrt{1-a^2 x^2}}{35 a \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,"(104*c*Sqrt[1 - a^2*x^2])/(105*a^3*Sqrt[c - a*c*x]) + (26*c*x^2*Sqrt[1 - a^2*x^2])/(35*a*Sqrt[c - a*c*x]) - (2*c*x^3*Sqrt[1 - a^2*x^2])/(7*Sqrt[c - a*c*x]) + (104*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(105*a^3)","A",5,5,23,0.2174,1,"{6128, 881, 871, 795, 649}"
413,1,101,0,0.1211453,"\int e^{-\tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[(x*Sqrt[c - a*c*x])/E^ArcTanh[a*x],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}}","-\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,"(-8*c*Sqrt[1 - a^2*x^2])/(5*a^2*Sqrt[c - a*c*x]) - (2*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(5*a^2) - (2*(c - a*c*x)^(3/2)*Sqrt[1 - a^2*x^2])/(5*a^2*c)","A",4,4,21,0.1905,1,"{6128, 795, 657, 649}"
414,1,66,0,0.0652532,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^ArcTanh[a*x],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}","\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,"(8*c*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[c - a*c*x]) + (2*Sqrt[c - a*c*x]*Sqrt[1 - a^2*x^2])/(3*a)","A",3,3,20,0.1500,1,"{6127, 657, 649}"
415,1,68,0,0.1582144,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x),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)","-\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^2*x^2])/Sqrt[c - a*c*x] - 2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]]","A",4,4,23,0.1739,1,"{6128, 881, 875, 208}"
416,1,72,0,0.1606205,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x^2),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}}","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,"-((c*Sqrt[1 - a^2*x^2])/(x*Sqrt[c - a*c*x])) + 3*a*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]]","A",4,4,23,0.1739,1,"{6128, 879, 875, 208}"
417,1,112,0,0.1959977,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x^3),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)","\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,"-(c*Sqrt[1 - a^2*x^2])/(2*x^2*Sqrt[c - a*c*x]) + (7*a*c*Sqrt[1 - a^2*x^2])/(4*x*Sqrt[c - a*c*x]) - (7*a^2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]])/4","A",5,5,23,0.2174,1,"{6128, 879, 873, 875, 208}"
418,1,148,0,0.2366449,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[Sqrt[c - a*c*x]/(E^ArcTanh[a*x]*x^4),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)","-\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])/(3*x^3*Sqrt[c - a*c*x]) + (11*a*c*Sqrt[1 - a^2*x^2])/(12*x^2*Sqrt[c - a*c*x]) - (11*a^2*c*Sqrt[1 - a^2*x^2])/(8*x*Sqrt[c - a*c*x]) + (11*a^3*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - a^2*x^2])/Sqrt[c - a*c*x]])/8","A",6,5,23,0.2174,1,"{6128, 879, 873, 875, 208}"
419,1,139,0,0.1725034,"\int e^{-2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[(x^3*Sqrt[c - a*c*x])/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"(-4*Sqrt[c - a*c*x])/a^4 - (2*(c - a*c*x)^(3/2))/(3*a^4*c) - (2*(c - a*c*x)^(5/2))/(5*a^4*c^2) + (2*(c - a*c*x)^(7/2))/(7*a^4*c^3) - (2*(c - a*c*x)^(9/2))/(9*a^4*c^4) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a^4","A",8,6,23,0.2609,1,"{6130, 21, 88, 50, 63, 206}"
420,1,97,0,0.1577766,"\int e^{-2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[(x^2*Sqrt[c - a*c*x])/E^(2*ArcTanh[a*x]),x]","\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}","\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,"(4*Sqrt[c - a*c*x])/a^3 + (2*(c - a*c*x)^(3/2))/(3*a^3*c) + (2*(c - a*c*x)^(7/2))/(7*a^3*c^3) - (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a^3","A",8,6,23,0.2609,1,"{6130, 21, 88, 50, 63, 206}"
421,1,97,0,0.1068036,"\int e^{-2 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[(x*Sqrt[c - a*c*x])/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"(-4*Sqrt[c - a*c*x])/a^2 - (2*(c - a*c*x)^(3/2))/(3*a^2*c) - (2*(c - a*c*x)^(5/2))/(5*a^2*c^2) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a^2","A",7,6,21,0.2857,1,"{6130, 21, 80, 50, 63, 206}"
422,1,76,0,0.0662254,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(2*ArcTanh[a*x]),x]","\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}","\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,"(4*Sqrt[c - a*c*x])/a + (2*(c - a*c*x)^(3/2))/(3*a*c) - (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - a*c*x]/(Sqrt[2]*Sqrt[c])])/a","A",6,5,20,0.2500,1,"{6130, 21, 50, 63, 206}"
423,1,74,0,0.1375562,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[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",8,7,23,0.3043,1,"{6130, 21, 84, 156, 63, 208, 206}"
424,1,79,0,0.1397174,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[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",8,7,23,0.3043,1,"{6130, 21, 98, 156, 63, 208, 206}"
425,1,106,0,0.1585765,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[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{\sqrt{c-a c x}}{2 x^2}+\frac{9 a \sqrt{c-a c x}}{4 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{\sqrt{c-a c x}}{2 x^2}+\frac{9 a \sqrt{c-a c x}}{4 x}",1,"-Sqrt[c - a*c*x]/(2*x^2) + (9*a*Sqrt[c - a*c*x])/(4*x) - (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",9,8,23,0.3478,1,"{6130, 21, 98, 151, 156, 63, 208, 206}"
426,1,127,0,0.1815126,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x^4),x]","-\frac{19 a^2 \sqrt{c-a c x}}{8 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{13 a \sqrt{c-a c x}}{12 x^2}-\frac{\sqrt{c-a c x}}{3 x^3}","-\frac{19 a^2 \sqrt{c-a c x}}{8 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{13 a \sqrt{c-a c x}}{12 x^2}-\frac{\sqrt{c-a c x}}{3 x^3}",1,"-Sqrt[c - a*c*x]/(3*x^3) + (13*a*Sqrt[c - a*c*x])/(12*x^2) - (19*a^2*Sqrt[c - a*c*x])/(8*x) + (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",10,8,23,0.3478,1,"{6130, 21, 98, 151, 156, 63, 208, 206}"
427,1,148,0,0.2088834,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcTanh[a*x])*x^5),x]","-\frac{107 a^2 \sqrt{c-a c x}}{96 x^2}+\frac{149 a^3 \sqrt{c-a c x}}{64 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{17 a \sqrt{c-a c x}}{24 x^3}-\frac{\sqrt{c-a c x}}{4 x^4}","-\frac{107 a^2 \sqrt{c-a c x}}{96 x^2}+\frac{149 a^3 \sqrt{c-a c x}}{64 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{17 a \sqrt{c-a c x}}{24 x^3}-\frac{\sqrt{c-a c x}}{4 x^4}",1,"-Sqrt[c - a*c*x]/(4*x^4) + (17*a*Sqrt[c - a*c*x])/(24*x^3) - (107*a^2*Sqrt[c - a*c*x])/(96*x^2) + (149*a^3*Sqrt[c - a*c*x])/(64*x) - (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",11,8,23,0.3478,1,"{6130, 21, 98, 151, 156, 63, 208, 206}"
428,1,235,0,0.1536054,"\int e^{-3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[(x^3*Sqrt[c - a*c*x])/E^(3*ArcTanh[a*x]),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}}","\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,"(8*c^2*(1 - a*x)^(3/2))/(a^4*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (32*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(a^4*(c - a*c*x)^(3/2)) - (50*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2))/(3*a^4*(c - a*c*x)^(3/2)) + (38*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(5/2))/(5*a^4*(c - a*c*x)^(3/2)) - (2*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(7/2))/(a^4*(c - a*c*x)^(3/2)) + (2*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(9/2))/(9*a^4*(c - a*c*x)^(3/2))","A",4,3,23,0.1304,1,"{6130, 23, 88}"
429,1,197,0,0.1496034,"\int e^{-3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[(x^2*Sqrt[c - a*c*x])/E^(3*ArcTanh[a*x]),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}}","\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,"(-8*c^2*(1 - a*x)^(3/2))/(a^3*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) - (24*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(a^3*(c - a*c*x)^(3/2)) + (26*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2))/(3*a^3*(c - a*c*x)^(3/2)) - (12*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(5/2))/(5*a^3*(c - a*c*x)^(3/2)) + (2*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(7/2))/(7*a^3*(c - a*c*x)^(3/2))","A",4,3,23,0.1304,1,"{6130, 23, 88}"
430,1,157,0,0.1054916,"\int e^{-3 \tanh ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[(x*Sqrt[c - a*c*x])/E^(3*ArcTanh[a*x]),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}}","\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,"(8*c^2*(1 - a*x)^(3/2))/(a^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (16*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(a^2*(c - a*c*x)^(3/2)) - (10*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2))/(3*a^2*(c - a*c*x)^(3/2)) + (2*c^2*(1 - a*x)^(3/2)*(1 + a*x)^(5/2))/(5*a^2*(c - a*c*x)^(3/2))","A",4,3,21,0.1429,1,"{6130, 23, 77}"
431,1,103,0,0.0961596,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(3*ArcTanh[a*x]),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}}","\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,"(-64*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - a^2*x^2]) + (16*(c - a*c*x)^(3/2))/(3*a*c*Sqrt[1 - a^2*x^2]) + (2*(c - a*c*x)^(5/2))/(3*a*c^2*Sqrt[1 - a^2*x^2])","A",4,3,20,0.1500,1,"{6127, 657, 649}"
432,1,107,0,0.1286151,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x),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}}","\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,"(8*c^2*(1 - a*x)^(3/2))/(Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (2*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(c - a*c*x)^(3/2) - (2*c^2*(1 - a*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(c - a*c*x)^(3/2)","A",6,5,23,0.2174,1,"{6130, 23, 87, 63, 208}"
433,1,112,0,0.1188607,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^2),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}}","-\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,"(-9*a*c^2*(1 - a*x)^(3/2))/(Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) - (c^2*(1 - a*x)^(3/2))/(x*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (7*a*c^2*(1 - a*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(c - a*c*x)^(3/2)","A",6,6,23,0.2609,1,"{6130, 23, 89, 78, 63, 208}"
434,1,163,0,0.1295306,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^3),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}}","\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,"(47*a^2*c^2*(1 - a*x)^(3/2))/(4*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) - (c^2*(1 - a*x)^(3/2))/(2*x^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (13*a*c^2*(1 - a*x)^(3/2))/(4*x*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) - (47*a^2*c^2*(1 - a*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(4*(c - a*c*x)^(3/2))","A",7,7,23,0.3043,1,"{6130, 23, 89, 78, 51, 63, 208}"
435,1,209,0,0.1382609,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^4),x]","-\frac{119 a^2 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{8 x (c-a c x)^{3/2}}+\frac{119 a^2 c^2 (1-a x)^{3/2}}{12 x \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{19 a c^2 (1-a x)^{3/2}}{12 x^2 \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{119 a^3 c^2 (1-a x)^{3/2}}{8 \sqrt{a x+1} (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{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{19 a c^2 (1-a x)^{3/2}}{12 x^2 \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}}",1,"-(c^2*(1 - a*x)^(3/2))/(3*x^3*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (19*a*c^2*(1 - a*x)^(3/2))/(12*x^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (119*a^2*c^2*(1 - a*x)^(3/2))/(12*x*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) - (119*a^2*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(8*x*(c - a*c*x)^(3/2)) + (119*a^3*c^2*(1 - a*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(8*(c - a*c*x)^(3/2))","A",8,7,23,0.3043,1,"{6130, 23, 89, 78, 51, 63, 208}"
436,1,252,0,0.1546558,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcTanh[a*x])*x^5),x]","-\frac{1115 a^2 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{96 x^2 (c-a c x)^{3/2}}+\frac{223 a^2 c^2 (1-a x)^{3/2}}{24 x^2 \sqrt{a x+1} (c-a c x)^{3/2}}+\frac{1115 a^3 c^2 (1-a x)^{3/2} \sqrt{a x+1}}{64 x (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{25 a c^2 (1-a x)^{3/2}}{24 x^3 \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{223 a^2 c^2 (1-a x)^{3/2}}{96 x^2 \sqrt{a x+1} (c-a c x)^{3/2}}+\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^3 c^2 (1-a x)^{3/2}}{192 x \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{25 a c^2 (1-a x)^{3/2}}{24 x^3 \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}}",1,"-(c^2*(1 - a*x)^(3/2))/(4*x^4*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (25*a*c^2*(1 - a*x)^(3/2))/(24*x^3*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) + (223*a^2*c^2*(1 - a*x)^(3/2))/(24*x^2*Sqrt[1 + a*x]*(c - a*c*x)^(3/2)) - (1115*a^2*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(96*x^2*(c - a*c*x)^(3/2)) + (1115*a^3*c^2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(64*x*(c - a*c*x)^(3/2)) - (1115*a^4*c^2*(1 - a*x)^(3/2)*ArcTanh[Sqrt[1 + a*x]])/(64*(c - a*c*x)^(3/2))","A",9,7,23,0.3043,1,"{6130, 23, 89, 78, 51, 63, 208}"
437,1,61,0,0.0587585,"\int e^{-2 p \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^(2*p*ArcTanh[a*x]),x]","-\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)}","-\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)^p*(c - a*c*x)^(1 + p)*Hypergeometric2F1[p, 1 + 2*p, 2*(1 + p), (1 - a*x)/2])/(2^p*a*c*(1 + 2*p)))","A",3,3,19,0.1579,1,"{6130, 23, 69}"
438,1,37,0,0.0346184,"\int e^{2 p \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(2*p*ArcTanh[a*x])*(c - a*c*x)^p,x]","\frac{(1-a x)^{-p} (a x+1)^{p+1} (c-a c x)^p}{a (p+1)}","\frac{(1-a x)^{-p} (a x+1)^{p+1} (c-a c x)^p}{a (p+1)}",1,"((1 + a*x)^(1 + p)*(c - a*c*x)^p)/(a*(1 + p)*(1 - a*x)^p)","A",3,3,19,0.1579,1,"{6130, 23, 32}"
439,1,82,0,0.0623685,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(n*ArcTanh[a*x])*(c - a*c*x)^p,x]","-\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)}","-\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)*(c - a*c*x)^(1 + p)*Hypergeometric2F1[-n/2, 1 - n/2 + p, 2 - n/2 + p, (1 - a*x)/2])/(a*c*(2 - n + 2*p)*(1 - a*x)^(n/2)))","A",3,3,18,0.1667,1,"{6130, 23, 69}"
440,1,68,0,0.0469197,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^3 \, dx","Int[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 (8-n)}","-\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, -n/2, 5 - n/2, (1 - a*x)/2])/(a*(8 - n)))","A",2,2,18,0.1111,1,"{6129, 69}"
441,1,68,0,0.0489045,"\int e^{n \tanh ^{-1}(a x)} (c-a c x)^2 \, dx","Int[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 (6-n)}","-\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, -n/2, 4 - n/2, (1 - a*x)/2])/(a*(6 - n)))","A",2,2,18,0.1111,1,"{6129, 69}"
442,1,66,0,0.0376154,"\int e^{n \tanh ^{-1}(a x)} (c-a c x) \, dx","Int[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 (4-n)}","-\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, -n/2, 3 - n/2, (1 - a*x)/2])/(a*(4 - n)))","A",2,2,16,0.1250,1,"{6129, 69}"
443,1,59,0,0.0430239,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-a c x} \, dx","Int[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[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(a*c*n*(1 - a*x)^(n/2))","A",2,2,18,0.1111,1,"{6129, 69}"
444,1,39,0,0.0389181,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[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}{2}}}{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)^((2 + n)/2))/(a*c^2*(2 + n))","A",2,2,18,0.1111,1,"{6129, 37}"
445,1,84,0,0.0558024,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a*c*x)^3,x]","\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)}","\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)*(1 + a*x)^((2 + n)/2))/(a*c^3*(4 + n)) + ((1 - a*x)^(-1 - n/2)*(1 + a*x)^((2 + n)/2))/(a*c^3*(8 + 6*n + n^2))","A",3,3,18,0.1667,1,"{6129, 45, 37}"
446,1,135,0,0.0807233,"\int \frac{e^{n \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a*c*x)^4,x]","\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)}","\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)^((2 + n)/2))/(a*c^4*(6 + n)) + (2*(1 - a*x)^(-2 - n/2)*(1 + a*x)^((2 + n)/2))/(a*c^4*(4 + n)*(6 + n)) + (2*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((2 + n)/2))/(a*c^4*(6 + n)*(8 + 6*n + n^2))","A",4,3,18,0.1667,1,"{6129, 45, 37}"
447,1,60,0,0.1015067,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^p,x]","\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}","\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,"((c - c/(a*x))^p*x*AppellF1[1 - p, 1/2 - p, -1/2, 2 - p, a*x, -(a*x)])/((1 - p)*(1 - a*x)^p)","A",3,3,20,0.1500,1,"{6134, 6129, 133}"
448,1,125,0,0.2558565,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^4,x]","\frac{3 c^4 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\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{3 c^4 \sin ^{-1}(a x)}{a}","\frac{3 c^4 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{c^4 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\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{3 c^4 \sin ^{-1}(a x)}{a}",1,"-(c^4*(6 - a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) - (c^4*(1 - a^2*x^2)^(3/2))/(3*a^4*x^3) + (3*c^4*(1 - a^2*x^2)^(3/2))/(2*a^3*x^2) - (3*c^4*ArcSin[a*x])/a - (c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",10,9,20,0.4500,1,"{6131, 6128, 1807, 813, 844, 216, 266, 63, 208}"
449,1,97,0,0.1913051,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^3,x]","\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\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{2 c^3 \sin ^{-1}(a x)}{a}","\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\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{2 c^3 \sin ^{-1}(a x)}{a}",1,"-(c^3*(4 + a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) + (c^3*(1 - a^2*x^2)^(3/2))/(2*a^3*x^2) - (2*c^3*ArcSin[a*x])/a + (c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",9,9,20,0.4500,1,"{6131, 6128, 1807, 813, 844, 216, 266, 63, 208}"
450,1,65,0,0.1225471,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^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}","-\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*(1 + a*x)*Sqrt[1 - a^2*x^2])/(a^2*x)) - (c^2*ArcSin[a*x])/a + (c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",8,8,20,0.4000,1,"{6131, 6128, 813, 844, 216, 266, 63, 208}"
451,1,41,0,0.0677943,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x)),x]","\frac{c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\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{c \sqrt{1-a^2 x^2}}{a}",1,"-((c*Sqrt[1 - a^2*x^2])/a) + (c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",6,6,18,0.3333,1,"{6131, 6128, 266, 50, 63, 208}"
452,1,65,0,0.0956761,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a*x)),x]","-\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}","-\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,"(-2*Sqrt[1 - a^2*x^2])/(a*c) - (1 - a^2*x^2)^(3/2)/(a*c*(1 - a*x)^2) + (2*ArcSin[a*x])/(a*c)","A",5,5,20,0.2500,1,"{6131, 6128, 793, 665, 216}"
453,1,104,0,0.1854018,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a*x))^2,x]","\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}","\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,"(-6*Sqrt[1 - a^2*x^2])/(a*c^2*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(3*a*c^2*(1 - a*x)^3) + (1 - a^2*x^2)^(3/2)/(a*c^2*(1 - a*x)^2) + (3*ArcSin[a*x])/(a*c^2)","A",6,6,20,0.3000,1,"{6131, 6128, 1639, 793, 663, 216}"
454,1,136,0,0.2819838,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a*x))^3,x]","\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}","\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,"(-8*Sqrt[1 - a^2*x^2])/(a*c^3*(1 - a*x)) - (1 - a^2*x^2)^(3/2)/(5*a*c^3*(1 - a*x)^4) + (14*(1 - a^2*x^2)^(3/2))/(15*a*c^3*(1 - a*x)^3) + (1 - a^2*x^2)^(3/2)/(a*c^3*(1 - a*x)^2) + (4*ArcSin[a*x])/(a*c^3)","A",10,8,20,0.4000,1,"{6131, 6128, 1639, 1637, 659, 651, 663, 216}"
455,1,168,0,0.3519773,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a*x))^4,x]","\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}","\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,"(-10*Sqrt[1 - a^2*x^2])/(a*c^4*(1 - a*x)) + (1 - a^2*x^2)^(3/2)/(7*a*c^4*(1 - a*x)^5) - (26*(1 - a^2*x^2)^(3/2))/(35*a*c^4*(1 - a*x)^4) + (184*(1 - a^2*x^2)^(3/2))/(105*a*c^4*(1 - a*x)^3) + (1 - a^2*x^2)^(3/2)/(a*c^4*(1 - a*x)^2) + (5*ArcSin[a*x])/(a*c^4)","A",13,8,20,0.4000,1,"{6131, 6128, 1639, 1637, 659, 651, 663, 216}"
456,1,59,0,0.0803001,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^p,x]","-\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","-\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*x) - ((2 - p)*(c - c/(a*x))^p*Hypergeometric2F1[1, p, 1 + p, 1 - 1/(a*x)])/(a*p)","A",6,6,22,0.2727,1,"{6133, 25, 514, 375, 78, 65}"
457,1,62,0,0.1131986,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^5 \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^5,x]","\frac{c^5}{a^3 x^2}-\frac{c^5}{a^4 x^3}+\frac{c^5}{4 a^5 x^4}+\frac{2 c^5}{a^2 x}+\frac{3 c^5 \log (x)}{a}+c^5 (-x)","\frac{c^5}{a^3 x^2}-\frac{c^5}{a^4 x^3}+\frac{c^5}{4 a^5 x^4}+\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[x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 75}"
458,1,40,0,0.1021178,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^4,x]","\frac{c^4}{a^3 x^2}-\frac{c^4}{3 a^4 x^3}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)","\frac{c^4}{a^3 x^2}-\frac{c^4}{3 a^4 x^3}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)",1,"-c^4/(3*a^4*x^3) + c^4/(a^3*x^2) - c^4*x + (2*c^4*Log[x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 75}"
459,1,40,0,0.0984824,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[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 (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[x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 75}"
460,1,18,0,0.089764,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[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",5,4,22,0.1818,1,"{6131, 6129, 73, 14}"
461,1,13,0,0.0541777,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[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",4,3,20,0.1500,1,"{6131, 6129, 43}"
462,1,38,0,0.0878648,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x)),x]","-\frac{2}{a c (1-a x)}-\frac{3 \log (1-a x)}{a c}-\frac{x}{c}","-\frac{2}{a c (1-a x)}-\frac{3 \log (1-a x)}{a c}-\frac{x}{c}",1,"-(x/c) - 2/(a*c*(1 - a*x)) - (3*Log[1 - a*x])/(a*c)","A",4,3,22,0.1364,1,"{6131, 6129, 77}"
463,1,53,0,0.1139056,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x))^2,x]","-\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}","-\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",4,3,22,0.1364,1,"{6131, 6129, 77}"
464,1,74,0,0.1333558,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x))^3,x]","-\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}","-\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,"-(x/c^3) - 2/(3*a*c^3*(1 - a*x)^3) + 7/(2*a*c^3*(1 - a*x)^2) - 9/(a*c^3*(1 - a*x)) - (5*Log[1 - a*x])/(a*c^3)","A",4,3,22,0.1364,1,"{6131, 6129, 77}"
465,1,88,0,0.1385213,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x))^4,x]","-\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}","-\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,"-(x/c^4) + 1/(2*a*c^4*(1 - a*x)^4) - 3/(a*c^4*(1 - a*x)^3) + 8/(a*c^4*(1 - a*x)^2) - 14/(a*c^4*(1 - a*x)) - (6*Log[1 - a*x])/(a*c^4)","A",4,3,22,0.1364,1,"{6131, 6129, 77}"
466,1,103,0,0.1679678,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^4,x]","-\frac{c^4 (2-3 a x) \left(1-a^2 x^2\right)^{3/2}}{6 a^4 x^3}+\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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^4*(2 + 3*a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) - (c^4*(2 - 3*a*x)*(1 - a^2*x^2)^(3/2))/(6*a^4*x^3) + (c^4*ArcSin[a*x])/a - (3*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",9,9,22,0.4091,1,"{6131, 6128, 811, 813, 844, 216, 266, 63, 208}"
467,1,77,0,0.1211254,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^3,x]","\frac{c^3 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}+\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}+\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}",1,"(3*c^3*Sqrt[1 - a^2*x^2])/(2*a) + (c^3*(1 - a^2*x^2)^(3/2))/(2*a^3*x^2) - (3*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",7,7,22,0.3182,1,"{6131, 6128, 266, 47, 50, 63, 208}"
468,1,67,0,0.1583548,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^2,x]","-\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}","-\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*(1 - a*x)*Sqrt[1 - a^2*x^2])/(a^2*x)) - (c^2*ArcSin[a*x])/a - (c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",9,9,22,0.4091,1,"{6131, 6128, 850, 813, 844, 216, 266, 63, 208}"
469,1,50,0,0.1638306,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x)),x]","\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}","\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])/a - (2*c*ArcSin[a*x])/a + (c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",9,9,20,0.4500,1,"{6131, 6128, 852, 1809, 844, 216, 266, 63, 208}"
470,1,99,0,0.1202711,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a*x)),x]","-\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}","-\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,"(4*Sqrt[1 - a^2*x^2])/(a*c) + (8*(1 - a^2*x^2)^(3/2))/(3*a*c*(1 - a*x)^2) - (1 - a^2*x^2)^(5/2)/(3*a*c*(1 - a*x)^4) - (4*ArcSin[a*x])/(a*c)","A",6,6,22,0.2727,1,"{6131, 6128, 793, 663, 665, 216}"
471,1,128,0,0.2572916,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a*x))^2,x]","\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}","\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,"(1 + a*x)^5/(5*a*c^2*(1 - a^2*x^2)^(5/2)) - (2*(1 + a*x)^4)/(3*a*c^2*(1 - a^2*x^2)^(3/2)) + (10*(1 + a*x)^2)/(3*a*c^2*Sqrt[1 - a^2*x^2]) + (5*Sqrt[1 - a^2*x^2])/(a*c^2) - (5*ArcSin[a*x])/(a*c^2)","A",9,8,22,0.3636,1,"{6131, 6128, 852, 1635, 21, 669, 641, 216}"
472,1,155,0,0.3342138,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a*x))^3,x]","-\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}","-\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,"-(1 + a*x)^6/(7*a*c^3*(1 - a^2*x^2)^(7/2)) + (4*(1 + a*x)^5)/(7*a*c^3*(1 - a^2*x^2)^(5/2)) - (1 + a*x)^4/(a*c^3*(1 - a^2*x^2)^(3/2)) + (4*(1 + a*x)^2)/(a*c^3*Sqrt[1 - a^2*x^2]) + (6*Sqrt[1 - a^2*x^2])/(a*c^3) - (6*ArcSin[a*x])/(a*c^3)","A",9,8,22,0.3636,1,"{6131, 6128, 852, 1635, 789, 669, 641, 216}"
473,1,190,0,0.4432568,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a*x))^4,x]","\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}","\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,"(1 + a*x)^7/(9*a*c^4*(1 - a^2*x^2)^(9/2)) - (34*(1 + a*x)^6)/(63*a*c^4*(1 - a^2*x^2)^(7/2)) + (344*(1 + a*x)^5)/(315*a*c^4*(1 - a^2*x^2)^(5/2)) - (4*(1 + a*x)^4)/(3*a*c^4*(1 - a^2*x^2)^(3/2)) + (14*(1 + a*x)^2)/(3*a*c^4*Sqrt[1 - a^2*x^2]) + (7*Sqrt[1 - a^2*x^2])/(a*c^4) - (7*ArcSin[a*x])/(a*c^4)","A",10,8,22,0.3636,1,"{6131, 6128, 852, 1635, 789, 669, 641, 216}"
474,1,93,0,0.1147922,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a*x))^p,x]","\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}","\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*(5 - p)*(c - c/(a*x))^(-1 + p))/(a*(1 - p))) + c*(c - c/(a*x))^(-1 + p)*x + ((4 - p)*(c - c/(a*x))^p*Hypergeometric2F1[1, p, 1 + p, 1 - 1/(a*x)])/(a*p)","A",7,7,22,0.3182,1,"{6133, 25, 514, 375, 89, 79, 65}"
475,1,64,0,0.1106304,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^5 \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a*x))^5,x]","-\frac{c^5}{a^3 x^2}-\frac{c^5}{3 a^4 x^3}+\frac{c^5}{4 a^5 x^4}+\frac{2 c^5}{a^2 x}-\frac{c^5 \log (x)}{a}+c^5 x","-\frac{c^5}{a^3 x^2}-\frac{c^5}{3 a^4 x^3}+\frac{c^5}{4 a^5 x^4}+\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[x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
476,1,30,0,0.0975286,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[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,"-c^4/(3*a^4*x^3) + (2*c^4)/(a^2*x) + c^4*x","A",5,4,22,0.1818,1,"{6131, 6129, 73, 270}"
477,1,38,0,0.1010552,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[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 (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[x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 75}"
478,1,27,0,0.0961591,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a*x))^2,x]","-\frac{c^2}{a^2 x}+\frac{2 c^2 \log (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[x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 43}"
479,1,25,0,0.0654436,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[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",4,3,20,0.1500,1,"{6131, 6129, 72}"
480,1,53,0,0.1015518,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a*x)),x]","\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}","\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,"x/c - 2/(a*c*(1 - a*x)^2) + 8/(a*c*(1 - a*x)) + (5*Log[1 - a*x])/(a*c)","A",4,3,22,0.1364,1,"{6131, 6129, 77}"
481,1,71,0,0.1269464,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a*x))^2,x]","\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}","\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,"x/c^2 + 4/(3*a*c^2*(1 - a*x)^3) - 6/(a*c^2*(1 - a*x)^2) + 13/(a*c^2*(1 - a*x)) + (6*Log[1 - a*x])/(a*c^2)","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
482,1,89,0,0.1450354,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a*x))^3,x]","\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}","\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,"x/c^3 - 1/(a*c^3*(1 - a*x)^4) + 16/(3*a*c^3*(1 - a*x)^3) - 25/(2*a*c^3*(1 - a*x)^2) + 19/(a*c^3*(1 - a*x)) + (7*Log[1 - a*x])/(a*c^3)","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
483,1,105,0,0.1488226,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a*x))^4,x]","\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}","\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,"x/c^4 + 4/(5*a*c^4*(1 - a*x)^5) - 5/(a*c^4*(1 - a*x)^4) + 41/(3*a*c^4*(1 - a*x)^3) - 22/(a*c^4*(1 - a*x)^2) + 26/(a*c^4*(1 - a*x)) + (8*Log[1 - a*x])/(a*c^4)","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
484,1,60,0,0.0952823,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[(c - c/(a*x))^p/E^ArcTanh[a*x],x]","\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}","\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,"((c - c/(a*x))^p*x*AppellF1[1 - p, -1/2 - p, 1/2, 2 - p, a*x, -(a*x)])/((1 - p)*(1 - a*x)^p)","A",3,3,22,0.1364,1,"{6134, 6129, 133}"
485,1,140,0,0.4198236,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[(c - c/(a*x))^4/E^ArcTanh[a*x],x]","\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{5 c^4 \sqrt{1-a^2 x^2}}{2 a^3 x^2}-\frac{c^4 \sqrt{1-a^2 x^2}}{3 a^4 x^3}+\frac{25 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{5 c^4 \sin ^{-1}(a x)}{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{5 c^4 \sqrt{1-a^2 x^2}}{2 a^3 x^2}-\frac{c^4 \sqrt{1-a^2 x^2}}{3 a^4 x^3}+\frac{25 c^4 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{5 c^4 \sin ^{-1}(a x)}{a}",1,"(c^4*Sqrt[1 - a^2*x^2])/a - (c^4*Sqrt[1 - a^2*x^2])/(3*a^4*x^3) + (5*c^4*Sqrt[1 - a^2*x^2])/(2*a^3*x^2) - (32*c^4*Sqrt[1 - a^2*x^2])/(3*a^2*x) + (5*c^4*ArcSin[a*x])/a + (25*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",11,9,22,0.4091,1,"{6131, 6128, 1807, 1809, 844, 216, 266, 63, 208}"
486,1,111,0,0.3119599,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[(c - c/(a*x))^3/E^ArcTanh[a*x],x]","\frac{c^3 \sqrt{1-a^2 x^2}}{a}-\frac{4 c^3 \sqrt{1-a^2 x^2}}{a^2 x}+\frac{c^3 \sqrt{1-a^2 x^2}}{2 a^3 x^2}+\frac{13 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{4 c^3 \sin ^{-1}(a x)}{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{c^3 \sqrt{1-a^2 x^2}}{2 a^3 x^2}+\frac{13 c^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{2 a}+\frac{4 c^3 \sin ^{-1}(a x)}{a}",1,"(c^3*Sqrt[1 - a^2*x^2])/a + (c^3*Sqrt[1 - a^2*x^2])/(2*a^3*x^2) - (4*c^3*Sqrt[1 - a^2*x^2])/(a^2*x) + (4*c^3*ArcSin[a*x])/a + (13*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",10,9,22,0.4091,1,"{6131, 6128, 1807, 1809, 844, 216, 266, 63, 208}"
487,1,82,0,0.2378084,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[(c - c/(a*x))^2/E^ArcTanh[a*x],x]","\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}","\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*Sqrt[1 - a^2*x^2])/a - (c^2*Sqrt[1 - a^2*x^2])/(a^2*x) + (3*c^2*ArcSin[a*x])/a + (3*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",9,9,22,0.4091,1,"{6131, 6128, 1807, 1809, 844, 216, 266, 63, 208}"
488,1,50,0,0.1513841,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[(c - c/(a*x))/E^ArcTanh[a*x],x]","\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}","\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])/a + (2*c*ArcSin[a*x])/a + (c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",8,8,20,0.4000,1,"{6131, 6128, 1809, 844, 216, 266, 63, 208}"
489,1,21,0,0.0738308,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[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",3,3,22,0.1364,1,"{6131, 6128, 261}"
490,1,63,0,0.1792483,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a*x))^2),x]","\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}","\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]/(a*c^2) + Sqrt[1 - a^2*x^2]/(a*c^2*(1 - a*x)) - ArcSin[a*x]/(a*c^2)","A",6,6,22,0.2727,1,"{6131, 6128, 1639, 12, 793, 216}"
491,1,94,0,0.2598974,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a*x))^3),x]","-\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}","-\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,"-(1 + a*x)^2/(3*a*c^3*(1 - a^2*x^2)^(3/2)) + (8*(1 + a*x))/(3*a*c^3*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a*c^3) - (2*ArcSin[a*x])/(a*c^3)","A",7,6,22,0.2727,1,"{6131, 6128, 852, 1635, 641, 216}"
492,1,125,0,0.3537447,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a*x))^4),x]","\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}","\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,"(1 + a*x)^3/(5*a*c^4*(1 - a^2*x^2)^(5/2)) - (6*(1 + a*x)^2)/(5*a*c^4*(1 - a^2*x^2)^(3/2)) + (24*(1 + a*x))/(5*a*c^4*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a*c^4) - (3*ArcSin[a*x])/(a*c^4)","A",8,6,22,0.2727,1,"{6131, 6128, 852, 1635, 641, 216}"
493,1,114,0,0.1300919,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[(c - c/(a*x))^p/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"-(((c - c/(a*x))^(2 + p)*x)/c^2) - ((c - c/(a*x))^(2 + p)*Hypergeometric2F1[1, 2 + p, 3 + p, (a - x^(-1))/(2*a)])/(2*a*c^2*(2 + p)) + ((c - c/(a*x))^(2 + p)*Hypergeometric2F1[1, 2 + p, 3 + p, 1 - 1/(a*x)])/(a*c^2)","A",8,8,22,0.3636,1,"{6133, 25, 514, 375, 103, 156, 65, 68}"
494,1,66,0,0.1175143,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[(c - c/(a*x))^4/E^(2*ArcTanh[a*x]),x]","\frac{3 c^4}{a^3 x^2}-\frac{c^4}{3 a^4 x^3}-\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)","\frac{3 c^4}{a^3 x^2}-\frac{c^4}{3 a^4 x^3}-\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,"-c^4/(3*a^4*x^3) + (3*c^4)/(a^3*x^2) - (16*c^4)/(a^2*x) - c^4*x - (26*c^4*Log[x])/a + (32*c^4*Log[1 + a*x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
495,1,55,0,0.1162944,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[(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 (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[x])/a + (16*c^3*Log[1 + a*x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
496,1,42,0,0.1106251,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[(c - c/(a*x))^2/E^(2*ArcTanh[a*x]),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)","-\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[x])/a + (8*c^2*Log[1 + a*x])/a","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
497,1,25,0,0.0656118,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[(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",4,3,20,0.1500,1,"{6131, 6129, 72}"
498,1,20,0,0.0875015,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))),x]","\frac{\log (a x+1)}{a c}-\frac{x}{c}","\frac{\log (a x+1)}{a c}-\frac{x}{c}",1,"-(x/c) + Log[1 + a*x]/(a*c)","A",4,3,22,0.1364,1,"{6131, 6129, 43}"
499,1,18,0,0.1097265,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^2),x]","\frac{\tanh ^{-1}(a x)}{a c^2}-\frac{x}{c^2}","\frac{\tanh ^{-1}(a x)}{a c^2}-\frac{x}{c^2}",1,"-(x/c^2) + ArcTanh[a*x]/(a*c^2)","A",5,4,22,0.1818,1,"{6131, 6129, 72, 207}"
500,1,58,0,0.1248368,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^3),x]","-\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}","-\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",4,3,22,0.1364,1,"{6131, 6129, 88}"
501,1,76,0,0.1327206,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^4),x]","-\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}","-\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,"-(x/c^4) + 1/(4*a*c^4*(1 - a*x)^2) - 7/(4*a*c^4*(1 - a*x)) - (17*Log[1 - a*x])/(8*a*c^4) + Log[1 + a*x]/(8*a*c^4)","A",4,3,22,0.1364,1,"{6131, 6129, 88}"
502,1,140,0,0.3679225,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[(c - c/(a*x))^3/E^(3*ArcTanh[a*x]),x]","-\frac{c^3 \sqrt{1-a^2 x^2}}{a}-\frac{6 c^3 \sqrt{1-a^2 x^2}}{a^2 x}+\frac{c^3 \sqrt{1-a^2 x^2}}{2 a^3 x^2}-\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{6 c^3 \sin ^{-1}(a x)}{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{c^3 \sqrt{1-a^2 x^2}}{2 a^3 x^2}-\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{6 c^3 \sin ^{-1}(a x)}{a}",1,"(-32*c^3*(1 - a*x))/(a*Sqrt[1 - a^2*x^2]) - (c^3*Sqrt[1 - a^2*x^2])/a + (c^3*Sqrt[1 - a^2*x^2])/(2*a^3*x^2) - (6*c^3*Sqrt[1 - a^2*x^2])/(a^2*x) - (6*c^3*ArcSin[a*x])/a + (33*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",11,10,22,0.4545,1,"{6131, 6128, 1805, 1807, 1809, 844, 216, 266, 63, 208}"
503,1,111,0,0.2954617,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[(c - c/(a*x))^2/E^(3*ArcTanh[a*x]),x]","-\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}","-\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,"(-16*c^2*(1 - a*x))/(a*Sqrt[1 - a^2*x^2]) - (c^2*Sqrt[1 - a^2*x^2])/a - (c^2*Sqrt[1 - a^2*x^2])/(a^2*x) - (5*c^2*ArcSin[a*x])/a + (5*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",10,10,22,0.4545,1,"{6131, 6128, 1805, 1807, 1809, 844, 216, 266, 63, 208}"
504,1,77,0,0.2056723,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[(c - c/(a*x))/E^(3*ArcTanh[a*x]),x]","-\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}","-\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,"(-8*c*(1 - a*x))/(a*Sqrt[1 - a^2*x^2]) - (c*Sqrt[1 - a^2*x^2])/a - (4*c*ArcSin[a*x])/a + (c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",9,9,20,0.4500,1,"{6131, 6128, 1805, 1809, 844, 216, 266, 63, 208}"
505,1,65,0,0.1040939,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))),x]","-\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}","-\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,"-((1 - a*x)^2/(a*c*Sqrt[1 - a^2*x^2])) - (2*Sqrt[1 - a^2*x^2])/(a*c) - (2*ArcSin[a*x])/(a*c)","A",5,5,22,0.2273,1,"{6131, 6128, 789, 641, 216}"
506,1,63,0,0.1249523,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^2),x]","-\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}","-\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,"-((1 - a*x)/(a*c^2*Sqrt[1 - a^2*x^2])) - Sqrt[1 - a^2*x^2]/(a*c^2) - ArcSin[a*x]/(a*c^2)","A",6,6,22,0.2727,1,"{6131, 6128, 797, 641, 216, 637}"
507,1,45,0,0.1189586,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^3),x]","-\frac{\sqrt{1-a^2 x^2}}{a c^3}-\frac{1}{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,"-(1/(a*c^3*Sqrt[1 - a^2*x^2])) - Sqrt[1 - a^2*x^2]/(a*c^3)","A",5,4,22,0.1818,1,"{6131, 6128, 266, 43}"
508,1,96,0,0.1648054,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^4),x]","\frac{a^2 x^3 (a x+1)}{3 c^4 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^4}","\frac{a^2 x^3 (a x+1)}{3 c^4 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^4}",1,"(a^2*x^3*(1 + a*x))/(3*c^4*(1 - a^2*x^2)^(3/2)) - (x*(3 + 4*a*x))/(3*c^4*Sqrt[1 - a^2*x^2]) - (8*Sqrt[1 - a^2*x^2])/(3*a*c^4) + ArcSin[a*x]/(a*c^4)","A",7,6,22,0.2727,1,"{6131, 6128, 850, 819, 641, 216}"
509,1,125,0,0.3177024,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^5} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^5),x]","-\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}","-\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,"-(1 + a*x)^2/(5*a*c^5*(1 - a^2*x^2)^(5/2)) + (22*(1 + a*x))/(15*a*c^5*(1 - a^2*x^2)^(3/2)) - (2*(30 + 23*a*x))/(15*a*c^5*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(a*c^5) + (2*ArcSin[a*x])/(a*c^5)","A",8,7,22,0.3182,1,"{6131, 6128, 852, 1635, 1814, 641, 216}"
510,1,225,0,0.2087673,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^(9/2),x]","-\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{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{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{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}}","-\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{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{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{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,"-(a^3*(c - c/(a*x))^(9/2)*x^4*(54 - 227*a*x)*Sqrt[1 + a*x])/(105*(1 - a*x)^(9/2)) - (10*a^2*(c - c/(a*x))^(9/2)*x^3*Sqrt[1 + a*x])/(21*(1 - a*x)^(5/2)) + (2*a*(c - c/(a*x))^(9/2)*x^2*Sqrt[1 + a*x])/(5*(1 - a*x)^(3/2)) - (2*(c - c/(a*x))^(9/2)*x*Sqrt[1 + a*x])/(7*Sqrt[1 - a*x]) - (7*a^(7/2)*(c - c/(a*x))^(9/2)*x^(9/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(9/2)","A",8,7,22,0.3182,1,"{6134, 6129, 97, 150, 143, 54, 215}"
511,1,181,0,0.1653715,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^(7/2),x]","-\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{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{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}}","-\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{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{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,"(2*a*(c - c/(a*x))^(7/2)*x^2*Sqrt[1 + a*x])/(3*(1 - a*x)^(3/2)) - (2*(c - c/(a*x))^(7/2)*x*Sqrt[1 + a*x])/(5*Sqrt[1 - a*x]) - (a^2*(c - c/(a*x))^(7/2)*x^3*Sqrt[1 + a*x]*(18 + 31*a*x))/(15*(1 - a*x)^(7/2)) + (5*a^(5/2)*(c - c/(a*x))^(7/2)*x^(7/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(7/2)","A",7,7,22,0.3182,1,"{6134, 6129, 97, 150, 143, 54, 215}"
512,1,171,0,0.1578817,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^(5/2),x]","-\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{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{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}}","-\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{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{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,"(-3*a^2*(c - c/(a*x))^(5/2)*x^3*Sqrt[1 + a*x])/(1 - a*x)^(5/2) - (2*(c - c/(a*x))^(5/2)*x*(1 + a*x)^(3/2))/(3*(1 - a*x)^(5/2)) + (4*a*(c - c/(a*x))^(5/2)*x^2*(1 + a*x)^(3/2))/(1 - a*x)^(5/2) - (3*a^(3/2)*(c - c/(a*x))^(5/2)*x^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(5/2)","A",7,7,22,0.3182,1,"{6134, 6129, 89, 78, 50, 54, 215}"
513,1,128,0,0.1920491,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a*x))^(3/2),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{a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}+\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{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{a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}+\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}}",1,"(a*(c - c/(a*x))^(3/2)*x^2*Sqrt[1 + a*x])/(1 - a*x)^(3/2) - (2*(c - c/(a*x))^(3/2)*x*(1 - a^2*x^2)^(3/2))/(1 - a*x)^3 + (Sqrt[a]*(c - c/(a*x))^(3/2)*x^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(3/2)","A",7,7,22,0.3182,1,"{6134, 6128, 879, 848, 50, 54, 215}"
514,1,85,0,0.1440272,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)],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}}","\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)]*x*Sqrt[1 + a*x])/Sqrt[1 - a*x] + (Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",6,6,22,0.2727,1,"{6134, 6128, 848, 50, 54, 215}"
515,1,157,0,0.1577162,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^ArcTanh[a*x]/Sqrt[c - c/(a*x)],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}}}","-\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[1 + a*x])/(a*Sqrt[c - c/(a*x)])) - (3*Sqrt[1 - a*x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x]) + (2*Sqrt[2]*Sqrt[1 - a*x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x])","A",8,8,22,0.3636,1,"{6134, 6129, 101, 157, 54, 215, 93, 206}"
516,1,198,0,0.1867583,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a*x))^(3/2),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}}","\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,"(Sqrt[1 - a*x]*Sqrt[1 + a*x])/(a*(c - c/(a*x))^(3/2)) + (2*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(a^2*(c - c/(a*x))^(3/2)*x) + (5*(1 - a*x)^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2)) - (7*(1 - a*x)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(Sqrt[2]*a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2))","A",9,9,22,0.4091,1,"{6134, 6129, 97, 154, 157, 54, 215, 93, 206}"
517,1,249,0,0.202928,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a*x))^(5/2),x]","-\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{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{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}}","-\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{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{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,"(Sqrt[1 - a*x]*Sqrt[1 + a*x])/(2*a*(c - c/(a*x))^(5/2)) - (11*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(8*a^2*(c - c/(a*x))^(5/2)*x) - (23*(1 - a*x)^(5/2)*Sqrt[1 + a*x])/(8*a^3*(c - c/(a*x))^(5/2)*x^2) - (7*(1 - a*x)^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2)) + (79*(1 - a*x)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(8*Sqrt[2]*a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2))","A",10,10,22,0.4545,1,"{6134, 6129, 97, 149, 154, 157, 54, 215, 93, 206}"
518,1,145,0,0.1850469,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(9/2),x]","-\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^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{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}","-\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^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{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,"(-5*c^4*Sqrt[c - c/(a*x)])/a - (5*c^3*(c - c/(a*x))^(3/2))/(3*a) - (c^2*(c - c/(a*x))^(5/2))/a - (5*c*(c - c/(a*x))^(7/2))/(7*a) - (c - c/(a*x))^(9/2)*x + (5*c^(9/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",11,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 50, 63, 208}"
519,1,120,0,0.1608382,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(7/2),x]","-\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^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{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}","-\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^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{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,"(-3*c^3*Sqrt[c - c/(a*x)])/a - (c^2*(c - c/(a*x))^(3/2))/a - (3*c*(c - c/(a*x))^(5/2))/(5*a) - (c - c/(a*x))^(7/2)*x + (3*c^(7/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",10,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 50, 63, 208}"
520,1,96,0,0.1429079,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(5/2),x]","-\frac{c^2 \sqrt{c-\frac{c}{a x}}}{a}+\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}-\frac{c \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-x \left(c-\frac{c}{a x}\right)^{5/2}","-\frac{c^2 \sqrt{c-\frac{c}{a x}}}{a}+\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{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)])/a) - (c*(c - c/(a*x))^(3/2))/(3*a) - (c - c/(a*x))^(5/2)*x + (c^(5/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",9,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 50, 63, 208}"
521,1,71,0,0.120584,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a*x))^(3/2),x]","-\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}","-\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)])/a - (c - c/(a*x))^(3/2)*x - (c^(3/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a","A",8,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 50, 63, 208}"
522,1,51,0,0.1012608,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[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",7,7,24,0.2917,1,"{6133, 25, 514, 375, 78, 63, 208}"
523,1,71,0,0.1622344,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^(2*ArcTanh[a*x])/Sqrt[c - c/(a*x)],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}}","-\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,"5/(a*Sqrt[c - c/(a*x)]) - x/Sqrt[c - c/(a*x)] - (5*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*Sqrt[c])","A",8,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 51, 63, 208}"
524,1,96,0,0.1502778,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x))^(3/2),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}}","-\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,"7/(3*a*(c - c/(a*x))^(3/2)) + 7/(a*c*Sqrt[c - c/(a*x)]) - x/(c - c/(a*x))^(3/2) - (7*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*c^(3/2))","A",9,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 51, 63, 208}"
525,1,119,0,0.1590881,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x))^(5/2),x]","\frac{9}{a c^2 \sqrt{c-\frac{c}{a x}}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{5/2}}-\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}}","\frac{9}{a c^2 \sqrt{c-\frac{c}{a x}}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{5/2}}-\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,"9/(5*a*(c - c/(a*x))^(5/2)) + 3/(a*c*(c - c/(a*x))^(3/2)) + 9/(a*c^2*Sqrt[c - c/(a*x)]) - x/(c - c/(a*x))^(5/2) - (9*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*c^(5/2))","A",10,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 51, 63, 208}"
526,1,146,0,0.1897253,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a*x))^(7/2),x]","\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{11 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{7/2}}-\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}}","\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{11 \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a c^{7/2}}-\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,"11/(7*a*(c - c/(a*x))^(7/2)) + 11/(5*a*c*(c - c/(a*x))^(5/2)) + 11/(3*a*c^2*(c - c/(a*x))^(3/2)) + 11/(a*c^3*Sqrt[c - c/(a*x)]) - x/(c - c/(a*x))^(7/2) - (11*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*c^(7/2))","A",11,8,24,0.3333,1,"{6133, 25, 514, 375, 78, 51, 63, 208}"
527,1,223,0,0.1839271,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(9/2),x]","\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{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^{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{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}}","\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{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^{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{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,"(-3*a^3*(c - c/(a*x))^(9/2)*x^4*Sqrt[1 + a*x])/(1 - a*x)^(9/2) + (3*a^2*(c - c/(a*x))^(9/2)*x^3*(6 - 17*a*x)*(1 + a*x)^(3/2))/(35*(1 - a*x)^(9/2)) + (6*a*(c - c/(a*x))^(9/2)*x^2*(1 + a*x)^(3/2))/(35*(1 - a*x)^(5/2)) - (2*(c - c/(a*x))^(9/2)*x*(1 + a*x)^(3/2))/(7*(1 - a*x)^(3/2)) + (3*a^(7/2)*(c - c/(a*x))^(9/2)*x^(9/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(9/2)","A",8,8,24,0.3333,1,"{6134, 6129, 97, 150, 143, 47, 54, 215}"
528,1,217,0,0.1692688,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(7/2),x]","-\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{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{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}}","-\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{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{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,"-((a^3*(c - c/(a*x))^(7/2)*x^4*Sqrt[1 + a*x])/(1 - a*x)^(7/2)) + (2*a^2*(c - c/(a*x))^(7/2)*x^3*(1 + a*x)^(3/2))/(3*(1 - a*x)^(7/2)) - (2*(c - c/(a*x))^(7/2)*x*(1 + a*x)^(5/2))/(5*(1 - a*x)^(7/2)) + (4*a*(c - c/(a*x))^(7/2)*x^2*(1 + a*x)^(5/2))/(3*(1 - a*x)^(7/2)) - (a^(5/2)*(c - c/(a*x))^(7/2)*x^(7/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(7/2)","A",8,8,24,0.3333,1,"{6134, 6129, 89, 78, 47, 50, 54, 215}"
529,1,176,0,0.2055234,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(5/2),x]","-\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{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{2 a x^2 (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{5/2}}{3 (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{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{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,"-((a^2*(c - c/(a*x))^(5/2)*x^3*Sqrt[1 + a*x])/(1 - a*x)^(5/2)) + (2*a*(c - c/(a*x))^(5/2)*x^2*(1 + a*x)^(3/2))/(3*(1 - a*x)^(5/2)) - (2*(c - c/(a*x))^(5/2)*x*(1 - a^2*x^2)^(5/2))/(3*(1 - a*x)^5) - (a^(3/2)*(c - c/(a*x))^(5/2)*x^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(5/2)","A",8,8,24,0.3333,1,"{6134, 6128, 879, 848, 47, 50, 54, 215}"
530,1,127,0,0.1725674,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a*x))^(3/2),x]","\frac{3 a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(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{2 x (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}{(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{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{2 x (a x+1)^{3/2} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}",1,"(3*a*(c - c/(a*x))^(3/2)*x^2*Sqrt[1 + a*x])/(1 - a*x)^(3/2) - (2*(c - c/(a*x))^(3/2)*x*(1 + a*x)^(3/2))/(1 - a*x)^(3/2) + (3*Sqrt[a]*(c - c/(a*x))^(3/2)*x^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(3/2)","A",7,7,24,0.2917,1,"{6134, 6128, 848, 47, 50, 54, 215}"
531,1,155,0,0.1544796,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)],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}}","-\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)]*x*Sqrt[1 + a*x])/Sqrt[1 - a*x]) - (5*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x]) + (4*Sqrt[2]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",8,8,24,0.3333,1,"{6134, 6129, 102, 157, 54, 215, 93, 206}"
532,1,195,0,0.1700963,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^(3*ArcTanh[a*x])/Sqrt[c - c/(a*x)],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}}}","\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,"(2*Sqrt[1 - a*x]*Sqrt[1 + a*x])/(a*Sqrt[c - c/(a*x)]) + (1 + a*x)^(3/2)/(a*Sqrt[c - c/(a*x)]*Sqrt[1 - a*x]) + (7*Sqrt[1 - a*x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x]) - (5*Sqrt[2]*Sqrt[1 - a*x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x])","A",9,9,24,0.3750,1,"{6134, 6129, 97, 154, 157, 54, 215, 93, 206}"
533,1,249,0,0.2052659,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a*x))^(3/2),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}}","-\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,"(-21*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(8*a^2*(c - c/(a*x))^(3/2)*x) + (1 + a*x)^(3/2)/(2*a*(c - c/(a*x))^(3/2)*Sqrt[1 - a*x]) - (9*Sqrt[1 - a*x]*(1 + a*x)^(3/2))/(8*a^2*(c - c/(a*x))^(3/2)*x) - (9*(1 - a*x)^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2)) + (51*(1 - a*x)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(4*Sqrt[2]*a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2))","A",10,10,24,0.4167,1,"{6134, 6129, 97, 149, 154, 157, 54, 215, 93, 206}"
534,1,293,0,0.2312213,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a*x))^(5/2),x]","\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{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{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}}","\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{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{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,"(103*(1 - a*x)^(5/2)*Sqrt[1 + a*x])/(32*a^3*(c - c/(a*x))^(5/2)*x^2) + (1 + a*x)^(3/2)/(3*a*(c - c/(a*x))^(5/2)*Sqrt[1 - a*x]) - (13*Sqrt[1 - a*x]*(1 + a*x)^(3/2))/(24*a^2*(c - c/(a*x))^(5/2)*x) + (43*(1 - a*x)^(3/2)*(1 + a*x)^(3/2))/(32*a^3*(c - c/(a*x))^(5/2)*x^2) + (11*(1 - a*x)^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2)) - (249*(1 - a*x)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(16*Sqrt[2]*a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2))","A",11,10,24,0.4167,1,"{6134, 6129, 97, 149, 154, 157, 54, 215, 93, 206}"
535,1,225,0,0.18765,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[(c - c/(a*x))^(9/2)/E^ArcTanh[a*x],x]","\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{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{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}}","\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{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{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,"(-94*a^2*(c - c/(a*x))^(9/2)*x^3*Sqrt[1 + a*x])/(21*(1 - a*x)^(5/2)) + (6*a*(c - c/(a*x))^(9/2)*x^2*Sqrt[1 + a*x])/(5*(1 - a*x)^(3/2)) - (2*(c - c/(a*x))^(9/2)*x*Sqrt[1 + a*x])/(7*Sqrt[1 - a*x]) + (a^3*(c - c/(a*x))^(9/2)*x^4*Sqrt[1 + a*x]*(2718 + 521*a*x))/(105*(1 - a*x)^(9/2)) + (11*a^(7/2)*(c - c/(a*x))^(9/2)*x^(9/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(9/2)","A",8,7,24,0.2917,1,"{6134, 6129, 98, 150, 143, 54, 215}"
536,1,179,0,0.166558,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[(c - c/(a*x))^(7/2)/E^ArcTanh[a*x],x]","-\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{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{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}}","-\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{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{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,"(2*a*(c - c/(a*x))^(7/2)*x^2*Sqrt[1 + a*x])/(1 - a*x)^(3/2) - (2*(c - c/(a*x))^(7/2)*x*Sqrt[1 + a*x])/(5*Sqrt[1 - a*x]) - (a^2*(c - c/(a*x))^(7/2)*x^3*Sqrt[1 + a*x]*(66 + 7*a*x))/(5*(1 - a*x)^(7/2)) - (9*a^(5/2)*(c - c/(a*x))^(7/2)*x^(7/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(7/2)","A",7,7,24,0.2917,1,"{6134, 6129, 98, 150, 143, 54, 215}"
537,1,137,0,0.154269,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[(c - c/(a*x))^(5/2)/E^ArcTanh[a*x],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}}","\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,"(-2*(c - c/(a*x))^(5/2)*x*Sqrt[1 + a*x])/(3*Sqrt[1 - a*x]) + (a*(c - c/(a*x))^(5/2)*x^2*(18 - a*x)*Sqrt[1 + a*x])/(3*(1 - a*x)^(5/2)) + (7*a^(3/2)*(c - c/(a*x))^(5/2)*x^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(5/2)","A",6,6,24,0.2500,1,"{6134, 6129, 98, 143, 54, 215}"
538,1,126,0,0.1511515,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[(c - c/(a*x))^(3/2)/E^ArcTanh[a*x],x]","\frac{a x^2 \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}-\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{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(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{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{2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{3/2}}{(1-a x)^{3/2}}",1,"(-2*(c - c/(a*x))^(3/2)*x*Sqrt[1 + a*x])/(1 - a*x)^(3/2) + (a*(c - c/(a*x))^(3/2)*x^2*Sqrt[1 + a*x])/(1 - a*x)^(3/2) - (5*Sqrt[a]*(c - c/(a*x))^(3/2)*x^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(3/2)","A",6,6,24,0.2500,1,"{6134, 6129, 89, 80, 54, 215}"
539,1,90,0,0.1644072,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^ArcTanh[a*x],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}","\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)]*x*Sqrt[1 - a^2*x^2])/(1 - a*x)) + (3*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",6,6,24,0.2500,1,"{6134, 6128, 881, 848, 54, 215}"
540,1,88,0,0.1458462,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[1/(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]),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}}}","\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[1 + a*x])/(a*Sqrt[c - c/(a*x)]) - (Sqrt[1 - a*x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x])","A",6,6,24,0.2500,1,"{6134, 6128, 848, 50, 54, 215}"
541,1,159,0,0.1795646,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a*x))^(3/2)),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}}","-\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,"-(((1 - a*x)^(3/2)*Sqrt[1 + a*x])/(a^2*(c - c/(a*x))^(3/2)*x)) - ((1 - a*x)^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2)) + (Sqrt[2]*(1 - a*x)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2))","A",9,9,24,0.3750,1,"{6134, 6129, 102, 21, 105, 54, 215, 93, 206}"
542,1,208,0,0.1894357,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a*x))^(5/2)),x]","\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{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{\sqrt{a x+1} (1-a x)^{3/2}}{2 a^2 x \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{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{\sqrt{a x+1} (1-a x)^{3/2}}{2 a^2 x \left(c-\frac{c}{a x}\right)^{5/2}}",1,"((1 - a*x)^(3/2)*Sqrt[1 + a*x])/(2*a^2*(c - c/(a*x))^(5/2)*x) + (3*(1 - a*x)^(5/2)*Sqrt[1 + a*x])/(2*a^3*(c - c/(a*x))^(5/2)*x^2) + (3*(1 - a*x)^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2)) - (9*(1 - a*x)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(2*Sqrt[2]*a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2))","A",9,9,24,0.3750,1,"{6134, 6129, 98, 154, 157, 54, 215, 93, 206}"
543,1,252,0,0.2045629,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a*x))^(7/2)),x]","-\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{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{\sqrt{a x+1} (1-a x)^{3/2}}{4 a^2 x \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{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{\sqrt{a x+1} (1-a x)^{3/2}}{4 a^2 x \left(c-\frac{c}{a x}\right)^{7/2}}",1,"((1 - a*x)^(3/2)*Sqrt[1 + a*x])/(4*a^2*(c - c/(a*x))^(7/2)*x) - (15*(1 - a*x)^(5/2)*Sqrt[1 + a*x])/(16*a^3*(c - c/(a*x))^(7/2)*x^2) - (35*(1 - a*x)^(7/2)*Sqrt[1 + a*x])/(16*a^4*(c - c/(a*x))^(7/2)*x^3) - (5*(1 - a*x)^(7/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(9/2)*(c - c/(a*x))^(7/2)*x^(7/2)) + (115*(1 - a*x)^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(16*Sqrt[2]*a^(9/2)*(c - c/(a*x))^(7/2)*x^(7/2))","A",10,10,24,0.4167,1,"{6134, 6129, 98, 149, 154, 157, 54, 215, 93, 206}"
544,1,189,0,0.2648895,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[(c - c/(a*x))^(9/2)/E^(2*ArcTanh[a*x]),x]","\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{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{5 c \left(c-\frac{c}{a x}\right)^{7/2}}{7 a}-x \left(c-\frac{c}{a x}\right)^{9/2}","\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{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{5 c \left(c-\frac{c}{a x}\right)^{7/2}}{7 a}-x \left(c-\frac{c}{a x}\right)^{9/2}",1,"(51*c^4*Sqrt[c - c/(a*x)])/a + (19*c^3*(c - c/(a*x))^(3/2))/(3*a) + (3*c^2*(c - c/(a*x))^(5/2))/(5*a) - (5*c*(c - c/(a*x))^(7/2))/(7*a) - (c - c/(a*x))^(9/2)*x + (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",14,9,24,0.3750,1,"{6133, 25, 514, 375, 98, 154, 156, 63, 208}"
545,1,164,0,0.2264229,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[(c - c/(a*x))^(7/2)/E^(2*ArcTanh[a*x]),x]","\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{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{3 c \left(c-\frac{c}{a x}\right)^{5/2}}{5 a}-x \left(c-\frac{c}{a x}\right)^{7/2}","\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{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{3 c \left(c-\frac{c}{a x}\right)^{5/2}}{5 a}-x \left(c-\frac{c}{a x}\right)^{7/2}",1,"(21*c^3*Sqrt[c - c/(a*x)])/a + (5*c^2*(c - c/(a*x))^(3/2))/(3*a) - (3*c*(c - c/(a*x))^(5/2))/(5*a) - (c - c/(a*x))^(7/2)*x + (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",13,9,24,0.3750,1,"{6133, 25, 514, 375, 98, 154, 156, 63, 208}"
546,1,139,0,0.1981388,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[(c - c/(a*x))^(5/2)/E^(2*ArcTanh[a*x]),x]","\frac{7 c^2 \sqrt{c-\frac{c}{a x}}}{a}+\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{c \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-x \left(c-\frac{c}{a x}\right)^{5/2}","\frac{7 c^2 \sqrt{c-\frac{c}{a x}}}{a}+\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{c \left(c-\frac{c}{a x}\right)^{3/2}}{3 a}-x \left(c-\frac{c}{a x}\right)^{5/2}",1,"(7*c^2*Sqrt[c - c/(a*x)])/a - (c*(c - c/(a*x))^(3/2))/(3*a) - (c - c/(a*x))^(5/2)*x + (9*c^(5/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a - (16*Sqrt[2]*c^(5/2)*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",12,9,24,0.3750,1,"{6133, 25, 514, 375, 98, 154, 156, 63, 208}"
547,1,113,0,0.2125018,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[(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)}{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}","\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)])/a - (c - c/(a*x))^(3/2)*x + (7*c^(3/2)*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/a - (8*Sqrt[2]*c^(3/2)*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a","A",11,9,24,0.3750,1,"{6133, 25, 514, 375, 98, 154, 156, 63, 208}"
548,1,93,0,0.1626512,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[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",10,8,24,0.3333,1,"{6133, 25, 514, 375, 98, 156, 63, 208}"
549,1,96,0,0.1611382,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[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",10,8,24,0.3333,1,"{6133, 25, 514, 375, 99, 156, 63, 208}"
550,1,95,0,0.1630081,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(3/2)),x]","-\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}+\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}}",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",11,9,24,0.3750,1,"{6133, 25, 514, 375, 103, 21, 83, 63, 208}"
551,1,119,0,0.1902835,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(5/2)),x]","-\frac{x}{c^2 \sqrt{c-\frac{c}{a x}}}+\frac{2}{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}}}-\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}}",1,"2/(a*c^2*Sqrt[c - c/(a*x)]) - x/(c^2*Sqrt[c - c/(a*x)]) - ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]]/(a*c^(5/2)) - ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]/(Sqrt[2]*a*c^(5/2))","A",11,9,24,0.3750,1,"{6133, 25, 514, 375, 103, 152, 156, 63, 208}"
552,1,148,0,0.2277477,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(7/2)),x]","-\frac{x}{c^2 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{7}{2 a c^3 \sqrt{c-\frac{c}{a x}}}+\frac{4}{3 a c^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\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{x}{c^2 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{7}{2 a c^3 \sqrt{c-\frac{c}{a x}}}+\frac{4}{3 a c^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\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}}",1,"4/(3*a*c^2*(c - c/(a*x))^(3/2)) + 7/(2*a*c^3*Sqrt[c - c/(a*x)]) - x/(c^2*(c - c/(a*x))^(3/2)) - (3*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*c^(7/2)) - ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]/(2*Sqrt[2]*a*c^(7/2))","A",12,9,24,0.3750,1,"{6133, 25, 514, 375, 103, 152, 156, 63, 208}"
553,1,173,0,0.256622,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{9/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a*x))^(9/2)),x]","-\frac{x}{c^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\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{6}{5 a c^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\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{x}{c^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\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{6}{5 a c^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\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}}",1,"6/(5*a*c^2*(c - c/(a*x))^(5/2)) + 11/(6*a*c^3*(c - c/(a*x))^(3/2)) + 21/(4*a*c^4*Sqrt[c - c/(a*x)]) - x/(c^2*(c - c/(a*x))^(5/2)) - (5*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(a*c^(9/2)) - ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]/(4*Sqrt[2]*a*c^(9/2))","A",13,9,24,0.3750,1,"{6133, 25, 514, 375, 103, 152, 156, 63, 208}"
554,1,267,0,0.2429039,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[(c - c/(a*x))^(9/2)/E^(3*ArcTanh[a*x]),x]","\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{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{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}}","\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{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{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,"(5*a^4*(c - c/(a*x))^(9/2)*x^5*(587 - 109*a*x))/(7*(1 - a*x)^(9/2)*Sqrt[1 + a*x]) + (70*a^3*(c - c/(a*x))^(9/2)*x^4)/((1 - a*x)^(5/2)*Sqrt[1 + a*x]) - (50*a^2*(c - c/(a*x))^(9/2)*x^3)/(7*(1 - a*x)^(3/2)*Sqrt[1 + a*x]) + (10*a*(c - c/(a*x))^(9/2)*x^2)/(7*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (2*(c - c/(a*x))^(9/2)*x*Sqrt[1 - a*x])/(7*Sqrt[1 + a*x]) - (15*a^(7/2)*(c - c/(a*x))^(9/2)*x^(9/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(9/2)","A",9,7,24,0.2917,1,"{6134, 6129, 98, 150, 143, 54, 215}"
555,1,225,0,0.2066629,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[(c - c/(a*x))^(7/2)/E^(3*ArcTanh[a*x]),x]","-\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{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{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}}","-\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{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{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,"-(a^3*(c - c/(a*x))^(7/2)*x^4*(2525 - 427*a*x))/(15*(1 - a*x)^(7/2)*Sqrt[1 + a*x]) - (398*a^2*(c - c/(a*x))^(7/2)*x^3)/(15*(1 - a*x)^(3/2)*Sqrt[1 + a*x]) + (38*a*(c - c/(a*x))^(7/2)*x^2)/(15*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (2*(c - c/(a*x))^(7/2)*x*Sqrt[1 - a*x])/(5*Sqrt[1 + a*x]) + (13*a^(5/2)*(c - c/(a*x))^(7/2)*x^(7/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(7/2)","A",8,7,24,0.2917,1,"{6134, 6129, 98, 150, 143, 54, 215}"
556,1,181,0,0.1898981,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[(c - c/(a*x))^(5/2)/E^(3*ArcTanh[a*x]),x]","\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{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{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}}","\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{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{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,"(a^2*(c - c/(a*x))^(5/2)*x^3*(191 - 25*a*x))/(3*(1 - a*x)^(5/2)*Sqrt[1 + a*x]) + (26*a*(c - c/(a*x))^(5/2)*x^2)/(3*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (2*(c - c/(a*x))^(5/2)*x*Sqrt[1 - a*x])/(3*Sqrt[1 + a*x]) - (11*a^(3/2)*(c - c/(a*x))^(5/2)*x^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(5/2)","A",7,7,24,0.2917,1,"{6134, 6129, 98, 150, 143, 54, 215}"
557,1,133,0,0.1753026,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[(c - c/(a*x))^(3/2)/E^(3*ArcTanh[a*x]),x]","-\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{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{2 x \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{3/2}}{\sqrt{a x+1}}","-\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{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{2 x \sqrt{1-a x} \left(c-\frac{c}{a x}\right)^{3/2}}{\sqrt{a x+1}}",1,"(-2*(c - c/(a*x))^(3/2)*x*Sqrt[1 - a*x])/Sqrt[1 + a*x] - (a*(c - c/(a*x))^(3/2)*x^2*(23 - a*x))/((1 - a*x)^(3/2)*Sqrt[1 + a*x]) + (9*Sqrt[a]*(c - c/(a*x))^(3/2)*x^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(1 - a*x)^(3/2)","A",6,6,24,0.2500,1,"{6134, 6129, 98, 143, 54, 215}"
558,1,123,0,0.1589757,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(8*Sqrt[c - c/(a*x)]*x)/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/Sqrt[1 - a*x] - (7*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",6,6,24,0.2500,1,"{6134, 6129, 89, 80, 54, 215}"
559,1,127,0,0.2039857,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]),x]","-\frac{x (1-a x)}{\sqrt{1-a^2 x^2} \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{5 \sqrt{1-a x}}{a \sqrt{a x+1} \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} \sinh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2} \sqrt{x} \sqrt{c-\frac{c}{a x}}}-\frac{5 \sqrt{1-a x}}{a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}",1,"(-5*Sqrt[1 - a*x])/(a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x]) - (x*(1 - a*x))/(Sqrt[c - c/(a*x)]*Sqrt[1 - a^2*x^2]) + (5*Sqrt[1 - a*x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x])","A",7,7,24,0.2917,1,"{6134, 6128, 881, 848, 47, 54, 215}"
560,1,131,0,0.1935462,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^(3/2)),x]","-\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}}","-\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*(1 - a*x)^(3/2))/(a*(c - c/(a*x))^(3/2)*Sqrt[1 + a*x]) + (3*(1 - a*x)^(3/2)*Sqrt[1 + a*x])/(a^2*(c - c/(a*x))^(3/2)*x) - (3*(1 - a*x)^(3/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(5/2)*(c - c/(a*x))^(3/2)*x^(3/2))","A",7,7,24,0.2917,1,"{6134, 6128, 848, 47, 50, 54, 215}"
561,1,199,0,0.2052309,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^(5/2)),x]","-\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} \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{(1-a x)^{5/2}}{a^2 x \sqrt{a x+1} \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} \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{(1-a x)^{5/2}}{a^2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(1 - a*x)^(5/2)/(a^2*(c - c/(a*x))^(5/2)*x*Sqrt[1 + a*x]) - (2*(1 - a*x)^(5/2)*Sqrt[1 + a*x])/(a^3*(c - c/(a*x))^(5/2)*x^2) + ((1 - a*x)^(5/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2)) + ((1 - a*x)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(Sqrt[2]*a^(7/2)*(c - c/(a*x))^(5/2)*x^(5/2))","A",9,9,24,0.3750,1,"{6134, 6129, 98, 154, 157, 54, 215, 93, 206}"
562,1,251,0,0.221361,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a*x))^(7/2)),x]","\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)^{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{(1-a x)^{5/2}}{2 a^2 x \sqrt{a x+1} \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)^{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{(1-a x)^{5/2}}{2 a^2 x \sqrt{a x+1} \left(c-\frac{c}{a x}\right)^{7/2}}",1,"(1 - a*x)^(5/2)/(2*a^2*(c - c/(a*x))^(7/2)*x*Sqrt[1 + a*x]) - (1 - a*x)^(7/2)/(4*a^3*(c - c/(a*x))^(7/2)*x^2*Sqrt[1 + a*x]) + (7*(1 - a*x)^(7/2)*Sqrt[1 + a*x])/(4*a^4*(c - c/(a*x))^(7/2)*x^3) + ((1 - a*x)^(7/2)*ArcSinh[Sqrt[a]*Sqrt[x]])/(a^(9/2)*(c - c/(a*x))^(7/2)*x^(7/2)) - (11*(1 - a*x)^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(4*Sqrt[2]*a^(9/2)*(c - c/(a*x))^(7/2)*x^(7/2))","A",10,10,24,0.4167,1,"{6134, 6129, 98, 150, 154, 157, 54, 215, 93, 206}"
563,1,105,0,0.3218721,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right) x^3} \, dx","Int[E^(3*ArcTanh[a*x])/((c - c/(a*x))*x^3),x]","-\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}","-\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,"(-8*a^2*(1 + a*x))/(3*c*(1 - a^2*x^2)^(3/2)) - (4*a^2*(3 + 4*a*x))/(3*c*Sqrt[1 - a^2*x^2]) + (a*Sqrt[1 - a^2*x^2])/(c*x) + (4*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/c","A",9,8,25,0.3200,1,"{6131, 6128, 852, 1805, 807, 266, 63, 208}"
564,1,57,0,0.2298119,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^m \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]*x^m,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}}","\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,"(2*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",4,4,25,0.1600,1,"{6134, 6128, 848, 64}"
565,1,179,0,0.2508409,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]*x^2,x]","-\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^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^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}}","-\frac{x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^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^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)]*x*Sqrt[1 + a*x])/(8*a^2*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*x^2*Sqrt[1 + a*x])/(12*a*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*x^3*Sqrt[1 + a*x])/(3*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(8*a^(5/2)*Sqrt[1 - a*x])","A",8,6,25,0.2400,1,"{6134, 6128, 848, 50, 54, 215}"
566,1,135,0,0.1885858,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)]*x,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}}","-\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)]*x*Sqrt[1 + a*x])/(4*a*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*x^2*Sqrt[1 + a*x])/(2*Sqrt[1 - a*x]) - (Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(4*a^(3/2)*Sqrt[1 - a*x])","A",7,6,23,0.2609,1,"{6134, 6128, 848, 50, 54, 215}"
567,1,85,0,0.1419547,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a*x)],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}}","\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)]*x*Sqrt[1 + a*x])/Sqrt[1 - a*x] + (Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",6,6,22,0.2727,1,"{6134, 6128, 848, 50, 54, 215}"
568,1,86,0,0.2489216,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x,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}}","\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[1 - a*x] + (2*Sqrt[a]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/Sqrt[1 - a*x]","A",6,6,25,0.2400,1,"{6134, 6128, 848, 47, 54, 215}"
569,1,41,0,0.2268157,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[(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",4,4,25,0.1600,1,"{6134, 6128, 848, 37}"
570,1,84,0,0.2159602,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^3,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}}","\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))/(5*x^2*Sqrt[1 - a*x]) + (4*a*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(15*x*Sqrt[1 - a*x])","A",5,5,25,0.2000,1,"{6134, 6128, 848, 45, 37}"
571,1,128,0,0.2309053,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^4,x]","-\frac{16 a^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{105 x \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}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{7 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{8 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{35 x^2 \sqrt{1-a x}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{7 x^3 \sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(7*x^3*Sqrt[1 - a*x]) + (8*a*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(35*x^2*Sqrt[1 - a*x]) - (16*a^2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(105*x*Sqrt[1 - a*x])","A",6,5,25,0.2000,1,"{6134, 6128, 848, 45, 37}"
572,1,172,0,0.2327871,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - c/(a*x)])/x^5,x]","-\frac{16 a^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{105 x^2 \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{4 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{21 x^3 \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{16 a^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{105 x^2 \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{4 a (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{21 x^3 \sqrt{1-a x}}-\frac{2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{9 x^4 \sqrt{1-a x}}",1,"(-2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(9*x^4*Sqrt[1 - a*x]) + (4*a*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(21*x^3*Sqrt[1 - a*x]) - (16*a^2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(105*x^2*Sqrt[1 - a*x]) + (32*a^3*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(315*x*Sqrt[1 - a*x])","A",7,5,25,0.2000,1,"{6134, 6128, 848, 45, 37}"
573,1,130,0,0.245019,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^3,x]","-\frac{25 x^2 \sqrt{c-\frac{c}{a x}}}{32 a^2}-\frac{75 x \sqrt{c-\frac{c}{a x}}}{64 a^3}-\frac{75 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{64 a^4}-\frac{1}{4} x^4 \sqrt{c-\frac{c}{a x}}-\frac{5 x^3 \sqrt{c-\frac{c}{a x}}}{8 a}","-\frac{25 x^2 \sqrt{c-\frac{c}{a x}}}{32 a^2}-\frac{75 x \sqrt{c-\frac{c}{a x}}}{64 a^3}-\frac{75 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{64 a^4}-\frac{1}{4} x^4 \sqrt{c-\frac{c}{a x}}-\frac{5 x^3 \sqrt{c-\frac{c}{a x}}}{8 a}",1,"(-75*Sqrt[c - c/(a*x)]*x)/(64*a^3) - (25*Sqrt[c - c/(a*x)]*x^2)/(32*a^2) - (5*Sqrt[c - c/(a*x)]*x^3)/(8*a) - (Sqrt[c - c/(a*x)]*x^4)/4 - (75*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(64*a^4)","A",10,8,27,0.2963,1,"{6133, 25, 514, 446, 78, 51, 63, 208}"
574,1,105,0,0.2170479,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^2,x]","-\frac{11 x \sqrt{c-\frac{c}{a x}}}{8 a^2}-\frac{11 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{8 a^3}-\frac{1}{3} x^3 \sqrt{c-\frac{c}{a x}}-\frac{11 x^2 \sqrt{c-\frac{c}{a x}}}{12 a}","-\frac{11 x \sqrt{c-\frac{c}{a x}}}{8 a^2}-\frac{11 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{8 a^3}-\frac{1}{3} x^3 \sqrt{c-\frac{c}{a x}}-\frac{11 x^2 \sqrt{c-\frac{c}{a x}}}{12 a}",1,"(-11*Sqrt[c - c/(a*x)]*x)/(8*a^2) - (11*Sqrt[c - c/(a*x)]*x^2)/(12*a) - (Sqrt[c - c/(a*x)]*x^3)/3 - (11*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(8*a^3)","A",9,8,27,0.2963,1,"{6133, 25, 514, 446, 78, 51, 63, 208}"
575,1,80,0,0.1429792,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x,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}","-\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,"(-7*Sqrt[c - c/(a*x)]*x)/(4*a) - (Sqrt[c - c/(a*x)]*x^2)/2 - (7*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(4*a^2)","A",8,8,25,0.3200,1,"{6133, 25, 434, 446, 78, 51, 63, 208}"
576,1,51,0,0.0962397,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[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",7,7,24,0.2917,1,"{6133, 25, 514, 375, 78, 63, 208}"
577,1,47,0,0.1905768,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[(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",7,7,27,0.2593,1,"{6133, 25, 514, 446, 80, 63, 208}"
578,1,42,0,0.2157321,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^2,x]","\frac{2 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a \sqrt{c-\frac{c}{a x}}","\frac{2 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}-4 a \sqrt{c-\frac{c}{a x}}",1,"-4*a*Sqrt[c - c/(a*x)] + (2*a*(c - c/(a*x))^(3/2))/(3*c)","A",6,5,27,0.1852,1,"{6133, 25, 514, 444, 43}"
579,1,69,0,0.2217028,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^3,x]","-\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}}","-\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,"-4*a^2*Sqrt[c - c/(a*x)] + (2*a^2*(c - c/(a*x))^(3/2))/c - (2*a^2*(c - c/(a*x))^(5/2))/(5*c^2)","A",6,5,27,0.1852,1,"{6133, 25, 514, 446, 77}"
580,1,96,0,0.2244566,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^4,x]","\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}}","\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,"-4*a^3*Sqrt[c - c/(a*x)] + (10*a^3*(c - c/(a*x))^(3/2))/(3*c) - (8*a^3*(c - c/(a*x))^(5/2))/(5*c^2) + (2*a^3*(c - c/(a*x))^(7/2))/(7*c^3)","A",6,5,27,0.1852,1,"{6133, 25, 514, 446, 77}"
581,1,121,0,0.2382457,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^5,x]","-\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}}","-\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,"-4*a^4*Sqrt[c - c/(a*x)] + (14*a^4*(c - c/(a*x))^(3/2))/(3*c) - (18*a^4*(c - c/(a*x))^(5/2))/(5*c^2) + (10*a^4*(c - c/(a*x))^(7/2))/(7*c^3) - (2*a^4*(c - c/(a*x))^(9/2))/(9*c^4)","A",6,5,27,0.1852,1,"{6133, 25, 514, 446, 77}"
582,1,292,0,0.313426,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^3,x]","-\frac{11 x^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{24 a^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{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{x^3 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{4 a \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{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{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{x^3 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"(-107*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(64*a^3*Sqrt[1 - a*x]) - (21*Sqrt[c - c/(a*x)]*x*(1 + a*x)^(3/2))/(32*a^3*Sqrt[1 - a*x]) - (11*Sqrt[c - c/(a*x)]*x^2*(1 + a*x)^(3/2))/(24*a^2*Sqrt[1 - a*x]) - (Sqrt[c - c/(a*x)]*x^3*(1 + a*x)^(3/2))/(4*a*Sqrt[1 - a*x]) - (363*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(64*a^(7/2)*Sqrt[1 - a*x]) + (4*Sqrt[2]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(7/2)*Sqrt[1 - a*x])","A",11,9,27,0.3333,1,"{6134, 6129, 101, 154, 157, 54, 215, 93, 206}"
583,1,248,0,0.2920004,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x^2,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{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{x^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 a \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{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{x^2 (a x+1)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 a \sqrt{1-a x}}",1,"(-13*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(8*a^2*Sqrt[1 - a*x]) - (3*Sqrt[c - c/(a*x)]*x*(1 + a*x)^(3/2))/(4*a^2*Sqrt[1 - a*x]) - (Sqrt[c - c/(a*x)]*x^2*(1 + a*x)^(3/2))/(3*a*Sqrt[1 - a*x]) - (45*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(8*a^(5/2)*Sqrt[1 - a*x]) + (4*Sqrt[2]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(5/2)*Sqrt[1 - a*x])","A",10,9,27,0.3333,1,"{6134, 6129, 101, 154, 157, 54, 215, 93, 206}"
584,1,204,0,0.2279049,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)]*x,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}}","-\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,"(-7*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(4*a*Sqrt[1 - a*x]) - (Sqrt[c - c/(a*x)]*x*(1 + a*x)^(3/2))/(2*a*Sqrt[1 - a*x]) - (23*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(4*a^(3/2)*Sqrt[1 - a*x]) + (4*Sqrt[2]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(a^(3/2)*Sqrt[1 - a*x])","A",9,9,25,0.3600,1,"{6134, 6129, 101, 154, 157, 54, 215, 93, 206}"
585,1,155,0,0.1633086,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)],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}}","-\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)]*x*Sqrt[1 + a*x])/Sqrt[1 - a*x]) - (5*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x]) + (4*Sqrt[2]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",8,8,24,0.3333,1,"{6134, 6129, 102, 157, 54, 215, 93, 206}"
586,1,154,0,0.2514976,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x,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}}","-\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[1 - a*x] - (2*Sqrt[a]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/Sqrt[1 - a*x] + (4*Sqrt[2]*Sqrt[a]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/Sqrt[1 - a*x]","A",8,8,27,0.2963,1,"{6134, 6129, 98, 157, 54, 215, 93, 206}"
587,1,147,0,0.2455729,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^2,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}}","\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,"(-4*a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/Sqrt[1 - a*x] - (2*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(3*x*Sqrt[1 - a*x]) + (4*Sqrt[2]*a^(3/2)*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/Sqrt[1 - a*x]","A",6,5,27,0.1852,1,"{6134, 6129, 94, 93, 206}"
588,1,191,0,0.2794125,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^3,x]","-\frac{4 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\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{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}}","-\frac{4 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{\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{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,"(-4*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/Sqrt[1 - a*x] - (2*a*Sqrt[c - c/(a*x)]*(1 + a*x)^(3/2))/(3*x*Sqrt[1 - a*x]) - (2*Sqrt[c - c/(a*x)]*(1 + a*x)^(5/2))/(5*x^2*Sqrt[1 - a*x]) + (4*Sqrt[2]*a^(5/2)*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/Sqrt[1 - a*x]","A",7,6,27,0.2222,1,"{6134, 6129, 96, 94, 93, 206}"
589,1,237,0,0.2772956,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^4,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{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{6 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{7 x^2 \sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{7 x^3 \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{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{6 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{7 x^2 \sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{7 x^3 \sqrt{1-a x}}",1,"(-104*a^3*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(21*Sqrt[1 - a*x]) - (2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(7*x^3*Sqrt[1 - a*x]) - (6*a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(7*x^2*Sqrt[1 - a*x]) - (32*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(21*x*Sqrt[1 - a*x]) + (4*Sqrt[2]*a^(7/2)*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/Sqrt[1 - a*x]","A",9,7,27,0.2593,1,"{6134, 6129, 98, 152, 12, 93, 206}"
590,1,281,0,0.3067781,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a*x)])/x^5,x]","-\frac{92 a^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 x^2 \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{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{38 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{63 x^3 \sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{9 x^4 \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{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{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{38 a \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{63 x^3 \sqrt{1-a x}}-\frac{2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{9 x^4 \sqrt{1-a x}}",1,"(-1576*a^4*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(315*Sqrt[1 - a*x]) - (2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(9*x^4*Sqrt[1 - a*x]) - (38*a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(63*x^3*Sqrt[1 - a*x]) - (92*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(105*x^2*Sqrt[1 - a*x]) - (472*a^3*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(315*x*Sqrt[1 - a*x]) + (4*Sqrt[2]*a^(9/2)*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[x])/Sqrt[1 + a*x]])/Sqrt[1 - a*x]","A",10,7,27,0.2593,1,"{6134, 6129, 98, 152, 12, 93, 206}"
591,1,116,0,0.2934542,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^m \, dx","Int[(Sqrt[c - c/(a*x)]*x^m)/E^ArcTanh[a*x],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)}","\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,"-((Sqrt[c - c/(a*x)]*x^(1 + m)*Sqrt[1 - a^2*x^2])/((1 + m)*(1 - a*x))) + ((3 + 4*m)*Sqrt[c - c/(a*x)]*x^(1 + m)*Hypergeometric2F1[1/2, 1/2 + m, 3/2 + m, -(a*x)])/((1 + m)*(1 + 2*m)*Sqrt[1 - a*x])","A",5,5,27,0.1852,1,"{6134, 6128, 881, 848, 64}"
592,1,182,0,0.3079731,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[(Sqrt[c - c/(a*x)]*x^2)/E^ArcTanh[a*x],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 \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{11 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{12 a \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 \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{11 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-a x}}",1,"(-11*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(8*a^2*Sqrt[1 - a*x]) + (11*Sqrt[c - c/(a*x)]*x^2*Sqrt[1 + a*x])/(12*a*Sqrt[1 - a*x]) - (Sqrt[c - c/(a*x)]*x^3*Sqrt[1 - a^2*x^2])/(3*(1 - a*x)) + (11*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(8*a^(5/2)*Sqrt[1 - a*x])","A",8,7,27,0.2593,1,"{6134, 6128, 881, 848, 50, 54, 215}"
593,1,138,0,0.2300644,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[(Sqrt[c - c/(a*x)]*x)/E^ArcTanh[a*x],x]","-\frac{x^2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{2 (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{7 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 a \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 \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{7 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-a x}}",1,"(7*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(4*a*Sqrt[1 - a*x]) - (Sqrt[c - c/(a*x)]*x^2*Sqrt[1 - a^2*x^2])/(2*(1 - a*x)) - (7*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(4*a^(3/2)*Sqrt[1 - a*x])","A",7,7,25,0.2800,1,"{6134, 6128, 881, 848, 50, 54, 215}"
594,1,90,0,0.1762043,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^ArcTanh[a*x],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}","\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)]*x*Sqrt[1 - a^2*x^2])/(1 - a*x)) + (3*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",6,6,24,0.2500,1,"{6134, 6128, 881, 848, 54, 215}"
595,1,89,0,0.2661037,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x),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}}","-\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^2*x^2])/(1 - a*x) - (2*Sqrt[a]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/Sqrt[1 - a*x]","A",6,6,27,0.2222,1,"{6134, 6128, 879, 848, 54, 215}"
596,1,84,0,0.2598626,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x^2),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)}","\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,"(10*a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(3*Sqrt[1 - a*x]) - (2*Sqrt[c - c/(a*x)]*Sqrt[1 - a^2*x^2])/(3*x*(1 - a*x))","A",5,5,27,0.1852,1,"{6134, 6128, 879, 848, 37}"
597,1,128,0,0.2671133,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x^3),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}}","-\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,"(-12*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(5*Sqrt[1 - a*x]) + (6*a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(5*x*Sqrt[1 - a*x]) - (2*Sqrt[c - c/(a*x)]*Sqrt[1 - a^2*x^2])/(5*x^2*(1 - a*x))","A",6,6,27,0.2222,1,"{6134, 6128, 879, 848, 45, 37}"
598,1,172,0,0.2634827,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcTanh[a*x]*x^4),x]","-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{7 x^3 (1-a x)}+\frac{208 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 \sqrt{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}}","-\frac{2 \sqrt{1-a^2 x^2} \sqrt{c-\frac{c}{a x}}}{7 x^3 (1-a x)}+\frac{208 a^3 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{105 \sqrt{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,"(208*a^3*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(105*Sqrt[1 - a*x]) + (26*a*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(35*x^2*Sqrt[1 - a*x]) - (104*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(105*x*Sqrt[1 - a*x]) - (2*Sqrt[c - c/(a*x)]*Sqrt[1 - a^2*x^2])/(7*x^3*(1 - a*x))","A",7,6,27,0.2222,1,"{6134, 6128, 879, 848, 45, 37}"
599,1,172,0,0.352306,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[(Sqrt[c - c/(a*x)]*x^3)/E^(2*ArcTanh[a*x]),x]","-\frac{107 x^2 \sqrt{c-\frac{c}{a x}}}{96 a^2}+\frac{149 x \sqrt{c-\frac{c}{a x}}}{64 a^3}-\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{1}{4} x^4 \sqrt{c-\frac{c}{a x}}+\frac{17 x^3 \sqrt{c-\frac{c}{a x}}}{24 a}","-\frac{107 x^2 \sqrt{c-\frac{c}{a x}}}{96 a^2}+\frac{149 x \sqrt{c-\frac{c}{a x}}}{64 a^3}-\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{1}{4} x^4 \sqrt{c-\frac{c}{a x}}+\frac{17 x^3 \sqrt{c-\frac{c}{a x}}}{24 a}",1,"(149*Sqrt[c - c/(a*x)]*x)/(64*a^3) - (107*Sqrt[c - c/(a*x)]*x^2)/(96*a^2) + (17*Sqrt[c - c/(a*x)]*x^3)/(24*a) - (Sqrt[c - c/(a*x)]*x^4)/4 - (363*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(64*a^4) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a^4","A",13,9,27,0.3333,1,"{6133, 25, 514, 446, 98, 151, 156, 63, 208}"
600,1,147,0,0.3144005,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[(Sqrt[c - c/(a*x)]*x^2)/E^(2*ArcTanh[a*x]),x]","-\frac{19 x \sqrt{c-\frac{c}{a x}}}{8 a^2}+\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{1}{3} x^3 \sqrt{c-\frac{c}{a x}}+\frac{13 x^2 \sqrt{c-\frac{c}{a x}}}{12 a}","-\frac{19 x \sqrt{c-\frac{c}{a x}}}{8 a^2}+\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{1}{3} x^3 \sqrt{c-\frac{c}{a x}}+\frac{13 x^2 \sqrt{c-\frac{c}{a x}}}{12 a}",1,"(-19*Sqrt[c - c/(a*x)]*x)/(8*a^2) + (13*Sqrt[c - c/(a*x)]*x^2)/(12*a) - (Sqrt[c - c/(a*x)]*x^3)/3 + (45*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(8*a^3) - (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a^3","A",12,9,27,0.3333,1,"{6133, 25, 514, 446, 98, 151, 156, 63, 208}"
601,1,122,0,0.2403189,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[(Sqrt[c - c/(a*x)]*x)/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"(9*Sqrt[c - c/(a*x)]*x)/(4*a) - (Sqrt[c - c/(a*x)]*x^2)/2 - (23*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/Sqrt[c]])/(4*a^2) + (4*Sqrt[2]*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])])/a^2","A",11,9,25,0.3600,1,"{6133, 25, 514, 446, 98, 151, 156, 63, 208}"
602,1,93,0,0.1578534,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[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",10,8,24,0.3333,1,"{6133, 25, 514, 375, 98, 156, 63, 208}"
603,1,86,0,0.2374228,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[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",10,8,27,0.2963,1,"{6133, 25, 434, 446, 84, 156, 63, 208}"
604,1,82,0,0.235805,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^2),x]","\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)","\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,"4*a*Sqrt[c - c/(a*x)] + (2*a*(c - c/(a*x))^(3/2))/(3*c) - 4*Sqrt[2]*a*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",8,7,27,0.2593,1,"{6133, 25, 514, 444, 50, 63, 208}"
605,1,113,0,0.2531555,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^3),x]","-\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)","-\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,"-4*a^2*Sqrt[c - c/(a*x)] - (2*a^2*(c - c/(a*x))^(3/2))/(3*c) - (2*a^2*(c - c/(a*x))^(5/2))/(5*c^2) + 4*Sqrt[2]*a^2*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",9,8,27,0.2963,1,"{6133, 25, 514, 446, 80, 50, 63, 208}"
606,1,113,0,0.281289,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^4),x]","\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)","\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,"4*a^3*Sqrt[c - c/(a*x)] + (2*a^3*(c - c/(a*x))^(3/2))/(3*c) + (2*a^3*(c - c/(a*x))^(7/2))/(7*c^3) - 4*Sqrt[2]*a^3*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",10,8,27,0.2963,1,"{6133, 25, 514, 446, 88, 50, 63, 208}"
607,1,163,0,0.3026791,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcTanh[a*x])*x^5),x]","-\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)","-\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,"-4*a^4*Sqrt[c - c/(a*x)] - (2*a^4*(c - c/(a*x))^(3/2))/(3*c) - (2*a^4*(c - c/(a*x))^(5/2))/(5*c^2) + (2*a^4*(c - c/(a*x))^(7/2))/(7*c^3) - (2*a^4*(c - c/(a*x))^(9/2))/(9*c^4) + 4*Sqrt[2]*a^4*Sqrt[c]*ArcTanh[Sqrt[c - c/(a*x)]/(Sqrt[2]*Sqrt[c])]","A",10,8,27,0.2963,1,"{6133, 25, 514, 446, 88, 50, 63, 208}"
608,1,262,0,0.2672327,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[(Sqrt[c - c/(a*x)]*x^3)/E^(3*ArcTanh[a*x]),x]","\frac{1115 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{96 a^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 \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{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}}","\frac{1115 x^2 \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{96 a^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 \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{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,"(8*Sqrt[c - c/(a*x)]*x^4)/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (1115*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(64*a^3*Sqrt[1 - a*x]) + (1115*Sqrt[c - c/(a*x)]*x^2*Sqrt[1 + a*x])/(96*a^2*Sqrt[1 - a*x]) - (223*Sqrt[c - c/(a*x)]*x^3*Sqrt[1 + a*x])/(24*a*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*x^4*Sqrt[1 + a*x])/(4*Sqrt[1 - a*x]) + (1115*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(64*a^(7/2)*Sqrt[1 - a*x])","A",9,7,27,0.2593,1,"{6134, 6129, 89, 80, 50, 54, 215}"
609,1,218,0,0.2502082,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[(Sqrt[c - c/(a*x)]*x^2)/E^(3*ArcTanh[a*x]),x]","\frac{119 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-a x}}-\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{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}}","\frac{119 x \sqrt{a x+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-a x}}-\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{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,"(8*Sqrt[c - c/(a*x)]*x^3)/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (119*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(8*a^2*Sqrt[1 - a*x]) - (119*Sqrt[c - c/(a*x)]*x^2*Sqrt[1 + a*x])/(12*a*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*x^3*Sqrt[1 + a*x])/(3*Sqrt[1 - a*x]) - (119*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(8*a^(5/2)*Sqrt[1 - a*x])","A",8,7,27,0.2593,1,"{6134, 6129, 89, 80, 50, 54, 215}"
610,1,174,0,0.1987545,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[(Sqrt[c - c/(a*x)]*x)/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(8*Sqrt[c - c/(a*x)]*x^2)/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (47*Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/(4*a*Sqrt[1 - a*x]) + (Sqrt[c - c/(a*x)]*x^2*Sqrt[1 + a*x])/(2*Sqrt[1 - a*x]) + (47*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(4*a^(3/2)*Sqrt[1 - a*x])","A",7,7,25,0.2800,1,"{6134, 6129, 89, 80, 50, 54, 215}"
611,1,123,0,0.144515,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(8*Sqrt[c - c/(a*x)]*x)/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (Sqrt[c - c/(a*x)]*x*Sqrt[1 + a*x])/Sqrt[1 - a*x] - (7*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[1 - a*x])","A",6,6,24,0.2500,1,"{6134, 6129, 89, 80, 54, 215}"
612,1,124,0,0.2366074,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x),x]","-\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}}","-\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)])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (10*a*Sqrt[c - c/(a*x)]*x)/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (2*Sqrt[a]*Sqrt[c - c/(a*x)]*Sqrt[x]*ArcSinh[Sqrt[a]*Sqrt[x]])/Sqrt[1 - a*x]","A",6,6,27,0.2222,1,"{6134, 6129, 89, 78, 54, 215}"
613,1,123,0,0.2231313,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^2),x]","\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}}","\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,"(20*a*Sqrt[c - c/(a*x)])/(3*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (2*Sqrt[c - c/(a*x)])/(3*x*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (46*a^2*Sqrt[c - c/(a*x)]*x)/(3*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",5,5,27,0.1852,1,"{6134, 6129, 89, 78, 37}"
614,1,166,0,0.2337362,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^3),x]","-\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}}","-\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,"(158*a^2*Sqrt[c - c/(a*x)])/(15*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (2*Sqrt[c - c/(a*x)])/(5*x^2*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (32*a*Sqrt[c - c/(a*x)])/(15*x*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (316*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(15*Sqrt[1 - a*x])","A",6,6,27,0.2222,1,"{6134, 6129, 89, 78, 45, 37}"
615,1,213,0,0.2442914,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^4),x]","\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{44 a \sqrt{c-\frac{c}{a x}}}{35 x^2 \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{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{44 a \sqrt{c-\frac{c}{a x}}}{35 x^2 \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}}",1,"(-2*Sqrt[c - c/(a*x)])/(7*x^3*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (44*a*Sqrt[c - c/(a*x)])/(35*x^2*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (334*a^2*Sqrt[c - c/(a*x)])/(35*x*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (2672*a^3*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(105*Sqrt[1 - a*x]) - (1336*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(105*x*Sqrt[1 - a*x])","A",7,6,27,0.2222,1,"{6134, 6129, 89, 78, 45, 37}"
616,1,257,0,0.2491951,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcTanh[a*x])*x^5),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{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{8 a \sqrt{c-\frac{c}{a x}}}{9 x^3 \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{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{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{8 a \sqrt{c-\frac{c}{a x}}}{9 x^3 \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}}",1,"(-2*Sqrt[c - c/(a*x)])/(9*x^4*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (8*a*Sqrt[c - c/(a*x)])/(9*x^3*Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (82*a^2*Sqrt[c - c/(a*x)])/(9*x^2*Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (1312*a^4*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(45*Sqrt[1 - a*x]) - (164*a^2*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(15*x^2*Sqrt[1 - a*x]) + (656*a^3*Sqrt[c - c/(a*x)]*Sqrt[1 + a*x])/(45*x*Sqrt[1 - a*x])","A",8,6,27,0.2222,1,"{6134, 6129, 89, 78, 45, 37}"
617,1,64,0,0.0993379,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a*x))^p,x]","\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}","\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,"((c - c/(a*x))^p*x*AppellF1[1 - p, (n - 2*p)/2, -n/2, 2 - p, a*x, -(a*x)])/((1 - p)*(1 - a*x)^p)","A",3,3,22,0.1364,1,"{6134, 6129, 133}"
618,1,54,0,0.1071803,"\int e^{-2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[(c - c/(a*x))^p/E^(2*p*ArcTanh[a*x]),x]","\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}","\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,"((c - c/(a*x))^p*x*AppellF1[1 - p, -2*p, p, 2 - p, a*x, -(a*x)])/((1 - p)*(1 - a*x)^p)","A",3,3,23,0.1304,1,"{6134, 6129, 133}"
619,1,50,0,0.0970773,"\int e^{2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[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",3,3,23,0.1304,1,"{6134, 6129, 64}"
620,1,71,0,0.1237301,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a*x))^2,x]","\frac{c^2 2^{3-\frac{n}{2}} (a x+1)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n-4}{2},2;\frac{n+4}{2};\frac{1}{2} (a x+1),a x+1\right)}{a (n+2)}","\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,"(2^(3 - n/2)*c^2*(1 + a*x)^((2 + n)/2)*AppellF1[(2 + n)/2, (-4 + n)/2, 2, (4 + n)/2, (1 + a*x)/2, 1 + a*x])/(a*(2 + n))","C",3,3,22,0.1364,0,"{6131, 6129, 136}"
621,1,184,0,0.1329467,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a*x)),x]","-\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)}-\frac{2 c (a x+1)^{n/2} (1-a x)^{-n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{a n}+\frac{c 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 n}","-\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,"(-2*c*(1 + a*x)^(n/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, (1 - a*x)/(1 + a*x)])/(a*n*(1 - a*x)^(n/2)) - (2^(1 + n/2)*c*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a*x)/2])/(a*(2 - n)) + (2^(1 + n/2)*c*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(a*n*(1 - a*x)^(n/2))","A",7,5,20,0.2500,0,"{6131, 6129, 105, 69, 131}"
622,1,111,0,0.1314418,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a*x)),x]","-\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}","-\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,"-((1 + a*x)^((2 + n)/2)/(a*c*n*(1 - a*x)^(n/2))) - (2^(1 + n/2)*(1 + n)*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a*x)/2])/(a*c*(2 - n)*n)","A",4,4,22,0.1818,1,"{6131, 6129, 79, 69}"
623,1,139,0,0.1723834,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a*x))^2,x]","-\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}","-\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,"((3 + n)*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((2 + n)/2))/(a*c^2*(2 + n)) - (x*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((2 + n)/2))/c^2 - (2^(1 + n/2)*(2 + n)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(a*c^2*n*(1 - a*x)^(n/2))","A",5,5,22,0.2273,1,"{6131, 6129, 90, 79, 69}"
624,1,54,0,0.1689731,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a*x))^(3/2),x]","-\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}}","-\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,"(-2*(c - c/(a*x))^(3/2)*x*AppellF1[-1/2, (-3 + n)/2, -n/2, 1/2, a*x, -(a*x)])/(1 - a*x)^(3/2)","A",3,3,24,0.1250,1,"{6134, 6129, 133}"
625,1,54,0,0.1503968,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(n*ArcTanh[a*x])*Sqrt[c - c/(a*x)],x]","\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}}","\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,"(2*Sqrt[c - c/(a*x)]*x*AppellF1[1/2, (-1 + n)/2, -n/2, 3/2, a*x, -(a*x)])/Sqrt[1 - a*x]","A",3,3,24,0.1250,1,"{6134, 6129, 133}"
626,1,56,0,0.1543027,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^(n*ArcTanh[a*x])/Sqrt[c - c/(a*x)],x]","\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}}}","\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,"(2*x*Sqrt[1 - a*x]*AppellF1[3/2, (1 + n)/2, -n/2, 5/2, a*x, -(a*x)])/(3*Sqrt[c - c/(a*x)])","A",3,3,24,0.1250,1,"{6134, 6129, 133}"
627,1,56,0,0.1703378,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a*x))^(3/2),x]","\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}}","\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,"(2*x*(1 - a*x)^(3/2)*AppellF1[5/2, (3 + n)/2, -n/2, 7/2, a*x, -(a*x)])/(5*(c - c/(a*x))^(3/2))","A",3,3,24,0.1250,1,"{6134, 6129, 133}"
628,1,169,0,0.2193077,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^4,x]","-\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 (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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^4*(16 - 35*a*x)*Sqrt[1 - a^2*x^2])/(16*a^2*x) - (c^4*(16 + 35*a*x)*(1 - a^2*x^2)^(3/2))/(48*a^4*x^3) + (c^4*(24 + 35*a*x)*(1 - a^2*x^2)^(5/2))/(120*a^6*x^5) - (c^4*(6 + 7*a*x)*(1 - a^2*x^2)^(7/2))/(42*a^8*x^7) + (c^4*ArcSin[a*x])/a + (35*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(16*a)","A",11,9,20,0.4500,1,"{6157, 6148, 811, 813, 844, 216, 266, 63, 208}"
629,1,136,0,0.1871809,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^3,x]","\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 (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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^3*(8 - 15*a*x)*Sqrt[1 - a^2*x^2])/(8*a^2*x) - (c^3*(8 + 15*a*x)*(1 - a^2*x^2)^(3/2))/(24*a^4*x^3) + (c^3*(4 + 5*a*x)*(1 - a^2*x^2)^(5/2))/(20*a^6*x^5) + (c^3*ArcSin[a*x])/a + (15*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(8*a)","A",10,9,20,0.4500,1,"{6157, 6148, 811, 813, 844, 216, 266, 63, 208}"
630,1,103,0,0.1580549,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^2,x]","-\frac{c^2 (3 a x+2) \left(1-a^2 x^2\right)^{3/2}}{6 a^4 x^3}+\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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^2*(2 - 3*a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) - (c^2*(2 + 3*a*x)*(1 - a^2*x^2)^(3/2))/(6*a^4*x^3) + (c^2*ArcSin[a*x])/a + (3*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",9,9,20,0.4500,1,"{6157, 6148, 811, 813, 844, 216, 266, 63, 208}"
631,1,58,0,0.1012782,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^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}","\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^2*x) + (c*ArcSin[a*x])/a + (c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",8,8,18,0.4444,1,"{6157, 6148, 813, 844, 216, 266, 63, 208}"
632,1,61,0,0.128842,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2)),x]","-\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}","-\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,"-((1 + a*x)/(a*c*Sqrt[1 - a^2*x^2])) - Sqrt[1 - a^2*x^2]/(a*c) + ArcSin[a*x]/(a*c)","A",6,6,20,0.3000,1,"{6157, 6148, 797, 641, 216, 637}"
633,1,96,0,0.1503247,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^2,x]","\frac{a^2 x^3 (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^2}","\frac{a^2 x^3 (a x+1)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^2}",1,"(a^2*x^3*(1 + a*x))/(3*c^2*(1 - a^2*x^2)^(3/2)) - (x*(3 + 4*a*x))/(3*c^2*Sqrt[1 - a^2*x^2]) - (8*Sqrt[1 - a^2*x^2])/(3*a*c^2) + ArcSin[a*x]/(a*c^2)","A",6,5,20,0.2500,1,"{6157, 6148, 819, 641, 216}"
634,1,129,0,0.1969455,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^3,x]","-\frac{a^4 x^5 (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{a^2 x^3 (6 a x+5)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^3}","-\frac{a^4 x^5 (a x+1)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{a^2 x^3 (6 a x+5)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^3}",1,"-(a^4*x^5*(1 + a*x))/(5*c^3*(1 - a^2*x^2)^(5/2)) + (a^2*x^3*(5 + 6*a*x))/(15*c^3*(1 - a^2*x^2)^(3/2)) - (x*(5 + 8*a*x))/(5*c^3*Sqrt[1 - a^2*x^2]) - (16*Sqrt[1 - a^2*x^2])/(5*a*c^3) + ArcSin[a*x]/(a*c^3)","A",7,5,20,0.2500,1,"{6157, 6148, 819, 641, 216}"
635,1,162,0,0.2231326,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^4,x]","\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{a^2 x^3 (48 a x+35)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^4}","\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{a^2 x^3 (48 a x+35)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^4}",1,"(a^6*x^7*(1 + a*x))/(7*c^4*(1 - a^2*x^2)^(7/2)) - (a^4*x^5*(7 + 8*a*x))/(35*c^4*(1 - a^2*x^2)^(5/2)) + (a^2*x^3*(35 + 48*a*x))/(105*c^4*(1 - a^2*x^2)^(3/2)) - (x*(35 + 64*a*x))/(35*c^4*Sqrt[1 - a^2*x^2]) - (128*Sqrt[1 - a^2*x^2])/(35*a*c^4) + ArcSin[a*x]/(a*c^4)","A",8,5,20,0.2500,1,"{6157, 6148, 819, 641, 216}"
636,1,128,0,0.1502765,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^5 \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^5,x]","-\frac{4 c^5}{a^3 x^2}+\frac{2 c^5}{3 a^4 x^3}+\frac{3 c^5}{a^5 x^4}+\frac{2 c^5}{5 a^6 x^5}-\frac{4 c^5}{3 a^7 x^6}-\frac{3 c^5}{7 a^8 x^7}+\frac{c^5}{4 a^9 x^8}+\frac{c^5}{9 a^{10} x^9}-\frac{3 c^5}{a^2 x}-\frac{2 c^5 \log (x)}{a}+c^5 (-x)","-\frac{4 c^5}{a^3 x^2}+\frac{2 c^5}{3 a^4 x^3}+\frac{3 c^5}{a^5 x^4}+\frac{2 c^5}{5 a^6 x^5}-\frac{4 c^5}{3 a^7 x^6}-\frac{3 c^5}{7 a^8 x^7}+\frac{c^5}{4 a^9 x^8}+\frac{c^5}{9 a^{10} x^9}-\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",4,3,22,0.1364,1,"{6157, 6150, 88}"
637,1,91,0,0.1321132,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^4,x]","-\frac{3 c^4}{a^3 x^2}+\frac{3 c^4}{2 a^5 x^4}+\frac{2 c^4}{5 a^6 x^5}-\frac{c^4}{3 a^7 x^6}-\frac{c^4}{7 a^8 x^7}-\frac{2 c^4}{a^2 x}-\frac{2 c^4 \log (x)}{a}+c^4 (-x)","-\frac{3 c^4}{a^3 x^2}+\frac{3 c^4}{2 a^5 x^4}+\frac{2 c^4}{5 a^6 x^5}-\frac{c^4}{3 a^7 x^6}-\frac{c^4}{7 a^8 x^7}-\frac{2 c^4}{a^2 x}-\frac{2 c^4 \log (x)}{a}+c^4 (-x)",1,"-c^4/(7*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",4,3,22,0.1364,1,"{6157, 6150, 88}"
638,1,78,0,0.1242125,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^3,x]","-\frac{2 c^3}{a^3 x^2}-\frac{c^3}{3 a^4 x^3}+\frac{c^3}{2 a^5 x^4}+\frac{c^3}{5 a^6 x^5}-\frac{c^3}{a^2 x}-\frac{2 c^3 \log (x)}{a}+c^3 (-x)","-\frac{2 c^3}{a^3 x^2}-\frac{c^3}{3 a^4 x^3}+\frac{c^3}{2 a^5 x^4}+\frac{c^3}{5 a^6 x^5}-\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",4,3,22,0.1364,1,"{6157, 6150, 88}"
639,1,41,0,0.1115889,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{c^2}{a^3 x^2}-\frac{c^2}{3 a^4 x^3}-\frac{2 c^2 \log (x)}{a}+c^2 (-x)","-\frac{c^2}{a^3 x^2}-\frac{c^2}{3 a^4 x^3}-\frac{2 c^2 \log (x)}{a}+c^2 (-x)",1,"-c^2/(3*a^4*x^3) - c^2/(a^3*x^2) - c^2*x - (2*c^2*Log[x])/a","A",4,3,22,0.1364,1,"{6157, 6150, 75}"
640,1,21,0,0.0679866,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[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",4,3,20,0.1500,1,"{6157, 6150, 43}"
641,1,38,0,0.1244961,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[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",4,3,22,0.1364,1,"{6157, 6150, 43}"
642,1,76,0,0.1457264,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","-\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}","-\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,"-(x/c^2) + 1/(4*a*c^2*(1 - a*x)^2) - 7/(4*a*c^2*(1 - a*x)) - (17*Log[1 - a*x])/(8*a*c^2) + Log[1 + a*x]/(8*a*c^2)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
643,1,111,0,0.1687016,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^3,x]","-\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}","-\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,"-(x/c^3) - 1/(12*a*c^3*(1 - a*x)^3) + 5/(8*a*c^3*(1 - a*x)^2) - 39/(16*a*c^3*(1 - a*x)) + 1/(16*a*c^3*(1 + a*x)) - (9*Log[1 - a*x])/(4*a*c^3) + Log[1 + a*x]/(4*a*c^3)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
644,1,146,0,0.19897,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^4,x]","-\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}","-\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,"-(x/c^4) + 1/(32*a*c^4*(1 - a*x)^4) - 13/(48*a*c^4*(1 - a*x)^3) + 35/(32*a*c^4*(1 - a*x)^2) - 99/(32*a*c^4*(1 - a*x)) - 1/(64*a*c^4*(1 + a*x)^2) + 11/(64*a*c^4*(1 + a*x)) - (303*Log[1 - a*x])/(128*a*c^4) + (47*Log[1 + a*x])/(128*a*c^4)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
645,1,191,0,0.3662856,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^4,x]","-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{2 a^7 x^6}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{7 a^8 x^7}-\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 (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{3 c^4 \sin ^{-1}(a x)}{a}","-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{2 a^7 x^6}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{7 a^8 x^7}-\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 (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{3 c^4 \sin ^{-1}(a x)}{a}",1,"(-3*c^4*(16 - 5*a*x)*Sqrt[1 - a^2*x^2])/(16*a^2*x) + (c^4*(16 + 5*a*x)*(1 - a^2*x^2)^(3/2))/(16*a^4*x^3) - (c^4*(24 + 5*a*x)*(1 - a^2*x^2)^(5/2))/(40*a^6*x^5) - (c^4*(1 - a^2*x^2)^(7/2))/(7*a^8*x^7) - (c^4*(1 - a^2*x^2)^(7/2))/(2*a^7*x^6) - (3*c^4*ArcSin[a*x])/a - (15*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(16*a)","A",12,10,22,0.4545,1,"{6157, 6148, 1807, 811, 813, 844, 216, 266, 63, 208}"
646,1,157,0,0.3154772,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^3,x]","\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{4 a^5 x^4}+\frac{c^3 \left(1-a^2 x^2\right)^{5/2}}{5 a^6 x^5}+\frac{c^3 (a x+8) \left(1-a^2 x^2\right)^{3/2}}{8 a^4 x^3}-\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{3 c^3 \sin ^{-1}(a x)}{a}","\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{4 a^5 x^4}+\frac{c^3 \left(1-a^2 x^2\right)^{5/2}}{5 a^6 x^5}+\frac{c^3 (a x+8) \left(1-a^2 x^2\right)^{3/2}}{8 a^4 x^3}-\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{3 c^3 \sin ^{-1}(a x)}{a}",1,"(-3*c^3*(8 - a*x)*Sqrt[1 - a^2*x^2])/(8*a^2*x) + (c^3*(8 + a*x)*(1 - a^2*x^2)^(3/2))/(8*a^4*x^3) + (c^3*(1 - a^2*x^2)^(5/2))/(5*a^6*x^5) + (3*c^3*(1 - a^2*x^2)^(5/2))/(4*a^5*x^4) - (3*c^3*ArcSin[a*x])/a - (3*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(8*a)","A",11,10,22,0.4545,1,"{6157, 6148, 1807, 811, 813, 844, 216, 266, 63, 208}"
647,1,124,0,0.2709082,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{3 c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\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{3 c^2 \sin ^{-1}(a x)}{a}","-\frac{3 c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\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{3 c^2 \sin ^{-1}(a x)}{a}",1,"-(c^2*(6 + a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) - (c^2*(1 - a^2*x^2)^(3/2))/(3*a^4*x^3) - (3*c^2*(1 - a^2*x^2)^(3/2))/(2*a^3*x^2) - (3*c^2*ArcSin[a*x])/a + (c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",10,9,22,0.4091,1,"{6157, 6148, 1807, 813, 844, 216, 266, 63, 208}"
648,1,73,0,0.2094112,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^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}","\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*Sqrt[1 - a^2*x^2])/a + (c*Sqrt[1 - a^2*x^2])/(a^2*x) - (3*c*ArcSin[a*x])/a + (3*c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",9,9,20,0.4500,1,"{6157, 6148, 1807, 1809, 844, 216, 266, 63, 208}"
649,1,95,0,0.226167,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2)),x]","-\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}","-\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,"-(1 + a*x)^3/(3*a*c*(1 - a^2*x^2)^(3/2)) + (2*(1 + a*x)^2)/(a*c*Sqrt[1 - a^2*x^2]) + (3*Sqrt[1 - a^2*x^2])/(a*c) - (3*ArcSin[a*x])/(a*c)","A",7,7,22,0.3182,1,"{6157, 6148, 1635, 21, 669, 641, 216}"
650,1,125,0,0.3347669,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","\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}","\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,"(1 + a*x)^3/(5*a*c^2*(1 - a^2*x^2)^(5/2)) - (6*(1 + a*x)^2)/(5*a*c^2*(1 - a^2*x^2)^(3/2)) + (24*(1 + a*x))/(5*a*c^2*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a*c^2) - (3*ArcSin[a*x])/(a*c^2)","A",7,5,22,0.2273,1,"{6157, 6148, 1635, 641, 216}"
651,1,155,0,0.4397828,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^3,x]","-\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}","-\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,"-(1 + a*x)^3/(7*a*c^3*(1 - a^2*x^2)^(7/2)) + (38*(1 + a*x)^2)/(35*a*c^3*(1 - a^2*x^2)^(5/2)) - (137*(1 + a*x))/(35*a*c^3*(1 - a^2*x^2)^(3/2)) + (245 + 181*a*x)/(35*a*c^3*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a*c^3) - (3*ArcSin[a*x])/(a*c^3)","A",8,6,22,0.2727,1,"{6157, 6148, 1635, 1814, 641, 216}"
652,1,185,0,0.5641009,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^4,x]","\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}","\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,"(1 + a*x)^3/(9*a*c^4*(1 - a^2*x^2)^(9/2)) - (22*(1 + a*x)^2)/(21*a*c^4*(1 - a^2*x^2)^(7/2)) + (478*(1 + a*x))/(105*a*c^4*(1 - a^2*x^2)^(5/2)) - (2*(1155 + 829*a*x))/(315*a*c^4*(1 - a^2*x^2)^(3/2)) + (4*(630 + 431*a*x))/(315*a*c^4*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a*c^4) - (3*ArcSin[a*x])/(a*c^4)","A",9,6,22,0.2727,1,"{6157, 6148, 1635, 1814, 641, 216}"
653,1,116,0,0.1431896,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^5 \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^5,x]","\frac{4 c^5}{a^3 x^2}+\frac{14 c^5}{3 a^4 x^3}-\frac{14 c^5}{5 a^6 x^5}-\frac{4 c^5}{3 a^7 x^6}+\frac{3 c^5}{7 a^8 x^7}+\frac{c^5}{2 a^9 x^8}+\frac{c^5}{9 a^{10} x^9}-\frac{3 c^5}{a^2 x}+\frac{4 c^5 \log (x)}{a}+c^5 x","\frac{4 c^5}{a^3 x^2}+\frac{14 c^5}{3 a^4 x^3}-\frac{14 c^5}{5 a^6 x^5}-\frac{4 c^5}{3 a^7 x^6}+\frac{3 c^5}{7 a^8 x^7}+\frac{c^5}{2 a^9 x^8}+\frac{c^5}{9 a^{10} x^9}-\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",4,3,22,0.1364,1,"{6157, 6150, 88}"
654,1,100,0,0.1366989,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^4,x]","\frac{2 c^4}{a^3 x^2}+\frac{10 c^4}{3 a^4 x^3}+\frac{c^4}{a^5 x^4}-\frac{4 c^4}{5 a^6 x^5}-\frac{2 c^4}{3 a^7 x^6}-\frac{c^4}{7 a^8 x^7}-\frac{4 c^4}{a^2 x}+\frac{4 c^4 \log (x)}{a}+c^4 x","\frac{2 c^4}{a^3 x^2}+\frac{10 c^4}{3 a^4 x^3}+\frac{c^4}{a^5 x^4}-\frac{4 c^4}{5 a^6 x^5}-\frac{2 c^4}{3 a^7 x^6}-\frac{c^4}{7 a^8 x^7}-\frac{4 c^4}{a^2 x}+\frac{4 c^4 \log (x)}{a}+c^4 x",1,"-c^4/(7*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",4,3,22,0.1364,1,"{6157, 6150, 88}"
655,1,63,0,0.1230844,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^3,x]","\frac{5 c^3}{3 a^4 x^3}+\frac{c^3}{a^5 x^4}+\frac{c^3}{5 a^6 x^5}-\frac{5 c^3}{a^2 x}+\frac{4 c^3 \log (x)}{a}+c^3 x","\frac{5 c^3}{3 a^4 x^3}+\frac{c^3}{a^5 x^4}+\frac{c^3}{5 a^6 x^5}-\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",4,3,22,0.1364,1,"{6157, 6150, 75}"
656,1,51,0,0.1187803,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","-\frac{2 c^2}{a^3 x^2}-\frac{c^2}{3 a^4 x^3}-\frac{6 c^2}{a^2 x}+\frac{4 c^2 \log (x)}{a}+c^2 x","-\frac{2 c^2}{a^3 x^2}-\frac{c^2}{3 a^4 x^3}-\frac{6 c^2}{a^2 x}+\frac{4 c^2 \log (x)}{a}+c^2 x",1,"-c^2/(3*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",4,3,22,0.1364,1,"{6157, 6150, 43}"
657,1,33,0,0.0768802,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[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",4,3,20,0.1500,1,"{6157, 6150, 88}"
658,1,53,0,0.1335768,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[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",4,3,22,0.1364,1,"{6157, 6150, 77}"
659,1,71,0,0.136199,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","\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}","\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,"x/c^2 + 1/(3*a*c^2*(1 - a*x)^3) - 2/(a*c^2*(1 - a*x)^2) + 6/(a*c^2*(1 - a*x)) + (4*Log[1 - a*x])/(a*c^2)","A",4,3,22,0.1364,1,"{6157, 6150, 43}"
660,1,111,0,0.1661635,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2))^3,x]","\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}","\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,"x/c^3 - 1/(8*a*c^3*(1 - a*x)^4) + 11/(12*a*c^3*(1 - a*x)^3) - 49/(16*a*c^3*(1 - a*x)^2) + 111/(16*a*c^3*(1 - a*x)) + (129*Log[1 - a*x])/(32*a*c^3) - Log[1 + a*x]/(32*a*c^3)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
661,1,146,0,0.1923519,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^(4*ArcTanh[a*x])/(c - c/(a^2*x^2))^4,x]","\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}","\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,"x/c^4 + 1/(20*a*c^4*(1 - a*x)^5) - 7/(16*a*c^4*(1 - a*x)^4) + 83/(48*a*c^4*(1 - a*x)^3) - 67/(16*a*c^4*(1 - a*x)^2) + 501/(64*a*c^4*(1 - a*x)) - 1/(64*a*c^4*(1 + a*x)) + (261*Log[1 - a*x])/(64*a*c^4) - (5*Log[1 + a*x])/(64*a*c^4)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
662,1,169,0,0.2324073,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[(c - c/(a^2*x^2))^4/E^ArcTanh[a*x],x]","-\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 (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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^4*(16 + 35*a*x)*Sqrt[1 - a^2*x^2])/(16*a^2*x) - (c^4*(16 - 35*a*x)*(1 - a^2*x^2)^(3/2))/(48*a^4*x^3) + (c^4*(24 - 35*a*x)*(1 - a^2*x^2)^(5/2))/(120*a^6*x^5) - (c^4*(6 - 7*a*x)*(1 - a^2*x^2)^(7/2))/(42*a^8*x^7) + (c^4*ArcSin[a*x])/a - (35*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(16*a)","A",11,9,22,0.4091,1,"{6157, 6149, 811, 813, 844, 216, 266, 63, 208}"
663,1,136,0,0.2232866,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[(c - c/(a^2*x^2))^3/E^ArcTanh[a*x],x]","\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 (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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^3*(8 + 15*a*x)*Sqrt[1 - a^2*x^2])/(8*a^2*x) - (c^3*(8 - 15*a*x)*(1 - a^2*x^2)^(3/2))/(24*a^4*x^3) + (c^3*(4 - 5*a*x)*(1 - a^2*x^2)^(5/2))/(20*a^6*x^5) + (c^3*ArcSin[a*x])/a - (15*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(8*a)","A",10,9,22,0.4091,1,"{6157, 6149, 811, 813, 844, 216, 266, 63, 208}"
664,1,103,0,0.1695045,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[(c - c/(a^2*x^2))^2/E^ArcTanh[a*x],x]","-\frac{c^2 (2-3 a x) \left(1-a^2 x^2\right)^{3/2}}{6 a^4 x^3}+\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 \sin ^{-1}(a x)}{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 (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 \sin ^{-1}(a x)}{a}",1,"(c^2*(2 + 3*a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) - (c^2*(2 - 3*a*x)*(1 - a^2*x^2)^(3/2))/(6*a^4*x^3) + (c^2*ArcSin[a*x])/a - (3*c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",9,9,22,0.4091,1,"{6157, 6149, 811, 813, 844, 216, 266, 63, 208}"
665,1,58,0,0.1124889,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[(c - c/(a^2*x^2))/E^ArcTanh[a*x],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}","\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^2*x) + (c*ArcSin[a*x])/a - (c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",8,8,20,0.4000,1,"{6157, 6149, 813, 844, 216, 266, 63, 208}"
666,1,60,0,0.1405481,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))),x]","\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}","\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,"(1 - a*x)/(a*c*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a*c) + ArcSin[a*x]/(a*c)","A",6,6,22,0.2727,1,"{6157, 6149, 797, 641, 216, 637}"
667,1,97,0,0.1634241,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^2),x]","\frac{a^2 x^3 (1-a x)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^2}","\frac{a^2 x^3 (1-a x)}{3 c^2 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^2}",1,"(a^2*x^3*(1 - a*x))/(3*c^2*(1 - a^2*x^2)^(3/2)) - (x*(3 - 4*a*x))/(3*c^2*Sqrt[1 - a^2*x^2]) + (8*Sqrt[1 - a^2*x^2])/(3*a*c^2) + ArcSin[a*x]/(a*c^2)","A",6,5,22,0.2273,1,"{6157, 6149, 819, 641, 216}"
668,1,130,0,0.1985604,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^3),x]","-\frac{a^4 x^5 (1-a x)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{a^2 x^3 (5-6 a x)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^3}","-\frac{a^4 x^5 (1-a x)}{5 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{a^2 x^3 (5-6 a x)}{15 c^3 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^3}",1,"-(a^4*x^5*(1 - a*x))/(5*c^3*(1 - a^2*x^2)^(5/2)) + (a^2*x^3*(5 - 6*a*x))/(15*c^3*(1 - a^2*x^2)^(3/2)) - (x*(5 - 8*a*x))/(5*c^3*Sqrt[1 - a^2*x^2]) + (16*Sqrt[1 - a^2*x^2])/(5*a*c^3) + ArcSin[a*x]/(a*c^3)","A",7,5,22,0.2273,1,"{6157, 6149, 819, 641, 216}"
669,1,163,0,0.2407753,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^4),x]","\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{a^2 x^3 (35-48 a x)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^4}","\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{a^2 x^3 (35-48 a x)}{105 c^4 \left(1-a^2 x^2\right)^{3/2}}-\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{\sin ^{-1}(a x)}{a c^4}",1,"(a^6*x^7*(1 - a*x))/(7*c^4*(1 - a^2*x^2)^(7/2)) - (a^4*x^5*(7 - 8*a*x))/(35*c^4*(1 - a^2*x^2)^(5/2)) + (a^2*x^3*(35 - 48*a*x))/(105*c^4*(1 - a^2*x^2)^(3/2)) - (x*(35 - 64*a*x))/(35*c^4*Sqrt[1 - a^2*x^2]) + (128*Sqrt[1 - a^2*x^2])/(35*a*c^4) + ArcSin[a*x]/(a*c^4)","A",8,5,22,0.2273,1,"{6157, 6149, 819, 641, 216}"
670,1,91,0,0.1390249,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[(c - c/(a^2*x^2))^4/E^(2*ArcTanh[a*x]),x]","\frac{3 c^4}{a^3 x^2}-\frac{3 c^4}{2 a^5 x^4}+\frac{2 c^4}{5 a^6 x^5}+\frac{c^4}{3 a^7 x^6}-\frac{c^4}{7 a^8 x^7}-\frac{2 c^4}{a^2 x}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)","\frac{3 c^4}{a^3 x^2}-\frac{3 c^4}{2 a^5 x^4}+\frac{2 c^4}{5 a^6 x^5}+\frac{c^4}{3 a^7 x^6}-\frac{c^4}{7 a^8 x^7}-\frac{2 c^4}{a^2 x}+\frac{2 c^4 \log (x)}{a}+c^4 (-x)",1,"-c^4/(7*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",4,3,22,0.1364,1,"{6157, 6150, 88}"
671,1,78,0,0.1281784,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[(c - c/(a^2*x^2))^3/E^(2*ArcTanh[a*x]),x]","\frac{2 c^3}{a^3 x^2}-\frac{c^3}{3 a^4 x^3}-\frac{c^3}{2 a^5 x^4}+\frac{c^3}{5 a^6 x^5}-\frac{c^3}{a^2 x}+\frac{2 c^3 \log (x)}{a}+c^3 (-x)","\frac{2 c^3}{a^3 x^2}-\frac{c^3}{3 a^4 x^3}-\frac{c^3}{2 a^5 x^4}+\frac{c^3}{5 a^6 x^5}-\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",4,3,22,0.1364,1,"{6157, 6150, 88}"
672,1,40,0,0.1164053,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[(c - c/(a^2*x^2))^2/E^(2*ArcTanh[a*x]),x]","\frac{c^2}{a^3 x^2}-\frac{c^2}{3 a^4 x^3}+\frac{2 c^2 \log (x)}{a}+c^2 (-x)","\frac{c^2}{a^3 x^2}-\frac{c^2}{3 a^4 x^3}+\frac{2 c^2 \log (x)}{a}+c^2 (-x)",1,"-c^2/(3*a^4*x^3) + c^2/(a^3*x^2) - c^2*x + (2*c^2*Log[x])/a","A",4,3,22,0.1364,1,"{6157, 6150, 75}"
673,1,21,0,0.0703377,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[(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",4,3,20,0.1500,1,"{6157, 6150, 43}"
674,1,35,0,0.1323579,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))),x]","\frac{1}{a c (a x+1)}+\frac{2 \log (a x+1)}{a c}-\frac{x}{c}","\frac{1}{a c (a x+1)}+\frac{2 \log (a x+1)}{a c}-\frac{x}{c}",1,"-(x/c) + 1/(a*c*(1 + a*x)) + (2*Log[1 + a*x])/(a*c)","A",4,3,22,0.1364,1,"{6157, 6150, 43}"
675,1,74,0,0.144847,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^2),x]","\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}","\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,"-(x/c^2) - 1/(4*a*c^2*(1 + a*x)^2) + 7/(4*a*c^2*(1 + a*x)) - Log[1 - a*x]/(8*a*c^2) + (17*Log[1 + a*x])/(8*a*c^2)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
676,1,109,0,0.1656495,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^3),x]","-\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}","-\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,"-(x/c^3) - 1/(16*a*c^3*(1 - a*x)) + 1/(12*a*c^3*(1 + a*x)^3) - 5/(8*a*c^3*(1 + a*x)^2) + 39/(16*a*c^3*(1 + a*x)) - Log[1 - a*x]/(4*a*c^3) + (9*Log[1 + a*x])/(4*a*c^3)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
677,1,144,0,0.2009861,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^4),x]","-\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}","-\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,"-(x/c^4) + 1/(64*a*c^4*(1 - a*x)^2) - 11/(64*a*c^4*(1 - a*x)) - 1/(32*a*c^4*(1 + a*x)^4) + 13/(48*a*c^4*(1 + a*x)^3) - 35/(32*a*c^4*(1 + a*x)^2) + 99/(32*a*c^4*(1 + a*x)) - (47*Log[1 - a*x])/(128*a*c^4) + (303*Log[1 + a*x])/(128*a*c^4)","A",4,3,22,0.1364,1,"{6157, 6150, 88}"
678,1,191,0,0.3616918,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[(c - c/(a^2*x^2))^4/E^(3*ArcTanh[a*x]),x]","\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{2 a^7 x^6}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{7 a^8 x^7}-\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 (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{3 c^4 \sin ^{-1}(a x)}{a}","\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{2 a^7 x^6}-\frac{c^4 \left(1-a^2 x^2\right)^{7/2}}{7 a^8 x^7}-\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 (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{3 c^4 \sin ^{-1}(a x)}{a}",1,"(-3*c^4*(16 + 5*a*x)*Sqrt[1 - a^2*x^2])/(16*a^2*x) + (c^4*(16 - 5*a*x)*(1 - a^2*x^2)^(3/2))/(16*a^4*x^3) - (c^4*(24 - 5*a*x)*(1 - a^2*x^2)^(5/2))/(40*a^6*x^5) - (c^4*(1 - a^2*x^2)^(7/2))/(7*a^8*x^7) + (c^4*(1 - a^2*x^2)^(7/2))/(2*a^7*x^6) - (3*c^4*ArcSin[a*x])/a + (15*c^4*ArcTanh[Sqrt[1 - a^2*x^2]])/(16*a)","A",12,10,22,0.4545,1,"{6157, 6149, 1807, 811, 813, 844, 216, 266, 63, 208}"
679,1,157,0,0.3213405,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[(c - c/(a^2*x^2))^3/E^(3*ArcTanh[a*x]),x]","-\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{4 a^5 x^4}+\frac{c^3 \left(1-a^2 x^2\right)^{5/2}}{5 a^6 x^5}+\frac{c^3 (8-a x) \left(1-a^2 x^2\right)^{3/2}}{8 a^4 x^3}-\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{3 c^3 \sin ^{-1}(a x)}{a}","-\frac{3 c^3 \left(1-a^2 x^2\right)^{5/2}}{4 a^5 x^4}+\frac{c^3 \left(1-a^2 x^2\right)^{5/2}}{5 a^6 x^5}+\frac{c^3 (8-a x) \left(1-a^2 x^2\right)^{3/2}}{8 a^4 x^3}-\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{3 c^3 \sin ^{-1}(a x)}{a}",1,"(-3*c^3*(8 + a*x)*Sqrt[1 - a^2*x^2])/(8*a^2*x) + (c^3*(8 - a*x)*(1 - a^2*x^2)^(3/2))/(8*a^4*x^3) + (c^3*(1 - a^2*x^2)^(5/2))/(5*a^6*x^5) - (3*c^3*(1 - a^2*x^2)^(5/2))/(4*a^5*x^4) - (3*c^3*ArcSin[a*x])/a + (3*c^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(8*a)","A",11,10,22,0.4545,1,"{6157, 6149, 1807, 811, 813, 844, 216, 266, 63, 208}"
680,1,125,0,0.275947,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[(c - c/(a^2*x^2))^2/E^(3*ArcTanh[a*x]),x]","\frac{3 c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\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{3 c^2 \sin ^{-1}(a x)}{a}","\frac{3 c^2 \left(1-a^2 x^2\right)^{3/2}}{2 a^3 x^2}-\frac{c^2 \left(1-a^2 x^2\right)^{3/2}}{3 a^4 x^3}-\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{3 c^2 \sin ^{-1}(a x)}{a}",1,"-(c^2*(6 - a*x)*Sqrt[1 - a^2*x^2])/(2*a^2*x) - (c^2*(1 - a^2*x^2)^(3/2))/(3*a^4*x^3) + (3*c^2*(1 - a^2*x^2)^(3/2))/(2*a^3*x^2) - (3*c^2*ArcSin[a*x])/a - (c^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*a)","A",10,9,22,0.4091,1,"{6157, 6149, 1807, 813, 844, 216, 266, 63, 208}"
681,1,74,0,0.2079674,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[(c - c/(a^2*x^2))/E^(3*ArcTanh[a*x]),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}","-\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*Sqrt[1 - a^2*x^2])/a) + (c*Sqrt[1 - a^2*x^2])/(a^2*x) - (3*c*ArcSin[a*x])/a - (3*c*ArcTanh[Sqrt[1 - a^2*x^2]])/a","A",9,9,20,0.4500,1,"{6157, 6149, 1807, 1809, 844, 216, 266, 63, 208}"
682,1,97,0,0.2336861,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))),x]","\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}","\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,"(1 - a*x)^3/(3*a*c*(1 - a^2*x^2)^(3/2)) - (2*(1 - a*x)^2)/(a*c*Sqrt[1 - a^2*x^2]) - (3*Sqrt[1 - a^2*x^2])/(a*c) - (3*ArcSin[a*x])/(a*c)","A",7,7,22,0.3182,1,"{6157, 6149, 1635, 21, 669, 641, 216}"
683,1,129,0,0.3634051,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^2),x]","-\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}","-\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,"-(1 - a*x)^3/(5*a*c^2*(1 - a^2*x^2)^(5/2)) + (6*(1 - a*x)^2)/(5*a*c^2*(1 - a^2*x^2)^(3/2)) - (24*(1 - a*x))/(5*a*c^2*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(a*c^2) - (3*ArcSin[a*x])/(a*c^2)","A",7,5,22,0.2273,1,"{6157, 6149, 1635, 641, 216}"
684,1,159,0,0.450863,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^3),x]","\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}","\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,"(1 - a*x)^3/(7*a*c^3*(1 - a^2*x^2)^(7/2)) - (38*(1 - a*x)^2)/(35*a*c^3*(1 - a^2*x^2)^(5/2)) + (137*(1 - a*x))/(35*a*c^3*(1 - a^2*x^2)^(3/2)) - (245 - 181*a*x)/(35*a*c^3*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(a*c^3) - (3*ArcSin[a*x])/(a*c^3)","A",8,6,22,0.2727,1,"{6157, 6149, 1635, 1814, 641, 216}"
685,1,189,0,0.6362547,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^4),x]","-\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}","-\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,"-(1 - a*x)^3/(9*a*c^4*(1 - a^2*x^2)^(9/2)) + (22*(1 - a*x)^2)/(21*a*c^4*(1 - a^2*x^2)^(7/2)) - (478*(1 - a*x))/(105*a*c^4*(1 - a^2*x^2)^(5/2)) + (2*(1155 - 829*a*x))/(315*a*c^4*(1 - a^2*x^2)^(3/2)) - (4*(630 - 431*a*x))/(315*a*c^4*Sqrt[1 - a^2*x^2]) - Sqrt[1 - a^2*x^2]/(a*c^4) - (3*ArcSin[a*x])/(a*c^4)","A",9,6,22,0.2727,1,"{6157, 6149, 1635, 1814, 641, 216}"
686,1,374,0,0.204493,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(9/2),x]","\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{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}}+\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 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^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{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{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}}+\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 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^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}}",1,"-((c - c/(a^2*x^2))^(9/2)*x)/(8*(1 - a^2*x^2)^(9/2)) - (a*(c - c/(a^2*x^2))^(9/2)*x^2)/(7*(1 - a^2*x^2)^(9/2)) + (2*a^2*(c - c/(a^2*x^2))^(9/2)*x^3)/(3*(1 - a^2*x^2)^(9/2)) + (4*a^3*(c - c/(a^2*x^2))^(9/2)*x^4)/(5*(1 - a^2*x^2)^(9/2)) - (3*a^4*(c - c/(a^2*x^2))^(9/2)*x^5)/(2*(1 - a^2*x^2)^(9/2)) - (2*a^5*(c - c/(a^2*x^2))^(9/2)*x^6)/(1 - a^2*x^2)^(9/2) + (2*a^6*(c - c/(a^2*x^2))^(9/2)*x^7)/(1 - a^2*x^2)^(9/2) + (4*a^7*(c - c/(a^2*x^2))^(9/2)*x^8)/(1 - a^2*x^2)^(9/2) + (a^9*(c - c/(a^2*x^2))^(9/2)*x^10)/(1 - a^2*x^2)^(9/2) + (a^8*(c - c/(a^2*x^2))^(9/2)*x^9*Log[x])/(1 - a^2*x^2)^(9/2)","A",4,3,22,0.1364,1,"{6160, 6150, 88}"
687,1,299,0,0.1903842,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(7/2),x]","-\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^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}}+\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 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^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^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^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}}+\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 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^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}}",1,"-((c - c/(a^2*x^2))^(7/2)*x)/(6*(1 - a^2*x^2)^(7/2)) - (a*(c - c/(a^2*x^2))^(7/2)*x^2)/(5*(1 - a^2*x^2)^(7/2)) + (3*a^2*(c - c/(a^2*x^2))^(7/2)*x^3)/(4*(1 - a^2*x^2)^(7/2)) + (a^3*(c - c/(a^2*x^2))^(7/2)*x^4)/(1 - a^2*x^2)^(7/2) - (3*a^4*(c - c/(a^2*x^2))^(7/2)*x^5)/(2*(1 - a^2*x^2)^(7/2)) - (3*a^5*(c - c/(a^2*x^2))^(7/2)*x^6)/(1 - a^2*x^2)^(7/2) - (a^7*(c - c/(a^2*x^2))^(7/2)*x^8)/(1 - a^2*x^2)^(7/2) - (a^6*(c - c/(a^2*x^2))^(7/2)*x^7*Log[x])/(1 - a^2*x^2)^(7/2)","A",4,3,22,0.1364,1,"{6160, 6150, 88}"
688,1,219,0,0.1785668,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(5/2),x]","\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{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}}+\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 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^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{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{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}}+\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 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^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}}",1,"-((c - c/(a^2*x^2))^(5/2)*x)/(4*(1 - a^2*x^2)^(5/2)) - (a*(c - c/(a^2*x^2))^(5/2)*x^2)/(3*(1 - a^2*x^2)^(5/2)) + (a^2*(c - c/(a^2*x^2))^(5/2)*x^3)/(1 - a^2*x^2)^(5/2) + (2*a^3*(c - c/(a^2*x^2))^(5/2)*x^4)/(1 - a^2*x^2)^(5/2) + (a^5*(c - c/(a^2*x^2))^(5/2)*x^6)/(1 - a^2*x^2)^(5/2) + (a^4*(c - c/(a^2*x^2))^(5/2)*x^5*Log[x])/(1 - a^2*x^2)^(5/2)","A",4,3,22,0.1364,1,"{6160, 6150, 88}"
689,1,146,0,0.1674569,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(3/2),x]","-\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}}-\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}}-\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}}",1,"-((c - c/(a^2*x^2))^(3/2)*x)/(2*(1 - a^2*x^2)^(3/2)) - (a*(c - c/(a^2*x^2))^(3/2)*x^2)/(1 - a^2*x^2)^(3/2) - (a^3*(c - c/(a^2*x^2))^(3/2)*x^4)/(1 - a^2*x^2)^(3/2) - (a^2*(c - c/(a^2*x^2))^(3/2)*x^3*Log[x])/(1 - a^2*x^2)^(3/2)","A",4,3,22,0.1364,1,"{6160, 6150, 75}"
690,1,68,0,0.1435452,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)],x]","\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{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,"(a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2] + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,22,0.1364,1,"{6160, 6150, 43}"
691,1,79,0,0.1228045,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^ArcTanh[a*x]/Sqrt[c - c/(a^2*x^2)],x]","-\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}}}","-\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*Sqrt[c - c/(a^2*x^2)])) - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",4,3,22,0.1364,1,"{6160, 6150, 43}"
692,1,175,0,0.1840583,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^(3/2),x]","\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{\left(1-a^2 x^2\right)^{3/2}}{a^3 x^2 \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}}{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}}{a^3 x^2 \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}}",1,"(1 - a^2*x^2)^(3/2)/(a^3*(c - c/(a^2*x^2))^(3/2)*x^2) + (1 - a^2*x^2)^(3/2)/(2*a^4*(c - c/(a^2*x^2))^(3/2)*x^3*(1 - a*x)) + (5*(1 - a^2*x^2)^(3/2)*Log[1 - a*x])/(4*a^4*(c - c/(a^2*x^2))^(3/2)*x^3) - ((1 - a^2*x^2)^(3/2)*Log[1 + a*x])/(4*a^4*(c - c/(a^2*x^2))^(3/2)*x^3)","A",4,3,22,0.1364,1,"{6160, 6150, 88}"
693,1,267,0,0.204935,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^(5/2),x]","-\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{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \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^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{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \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}}",1,"-((1 - a^2*x^2)^(5/2)/(a^5*(c - c/(a^2*x^2))^(5/2)*x^4)) + (1 - a^2*x^2)^(5/2)/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 - a*x)^2) - (1 - a^2*x^2)^(5/2)/(a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 - a*x)) + (1 - a^2*x^2)^(5/2)/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 + a*x)) - (23*(1 - a^2*x^2)^(5/2)*Log[1 - a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5) + (7*(1 - a^2*x^2)^(5/2)*Log[1 + a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",4,3,22,0.1364,1,"{6160, 6150, 88}"
694,1,361,0,0.297853,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[E^ArcTanh[a*x]/(c - c/(a^2*x^2))^(7/2),x]","\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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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{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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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}}",1,"(1 - a^2*x^2)^(7/2)/(a^7*(c - c/(a^2*x^2))^(7/2)*x^6) + (1 - a^2*x^2)^(7/2)/(24*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)^3) - (11*(1 - a^2*x^2)^(7/2))/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)^2) + (3*(1 - a^2*x^2)^(7/2))/(2*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)) + (1 - a^2*x^2)^(7/2)/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)^2) - (5*(1 - a^2*x^2)^(7/2))/(16*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)) + (51*(1 - a^2*x^2)^(7/2)*Log[1 - a*x])/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7) - (19*(1 - a^2*x^2)^(7/2)*Log[1 + a*x])/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7)","A",4,3,22,0.1364,1,"{6160, 6150, 88}"
695,1,450,0,0.5567702,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(9/2),x]","-\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{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}+\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{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{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{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{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}+\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{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{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}}",1,"(295*a^4*(c - c/(a^2*x^2))^(9/2)*x^5)/(1344*(1 - a*x)^4) - (501*a^8*(c - c/(a^2*x^2))^(9/2)*x^9)/(128*(1 - a*x)^4*(1 + a*x)^4) + (373*a^7*(c - c/(a^2*x^2))^(9/2)*x^8)/(192*(1 - a*x)^4*(1 + a*x)^3) + (501*a^6*(c - c/(a^2*x^2))^(9/2)*x^7)/(640*(1 - a*x)^4*(1 + a*x)^2) + (661*a^5*(c - c/(a^2*x^2))^(9/2)*x^6)/(1680*(1 - a*x)^4*(1 + a*x)) - (127*a^3*(c - c/(a^2*x^2))^(9/2)*x^4*(1 + a*x))/(420*(1 - a*x)^4) + (71*a^2*(c - c/(a^2*x^2))^(9/2)*x^3*(1 + a*x))/(336*(1 - a*x)^3) - (a*(c - c/(a^2*x^2))^(9/2)*x^2*(1 + a*x))/(28*(1 - a*x)^2) - ((c - c/(a^2*x^2))^(9/2)*x*(1 + a*x))/(8*(1 - a*x)) + (2*a^8*(c - c/(a^2*x^2))^(9/2)*x^9*ArcSin[a*x])/((1 - a*x)^(9/2)*(1 + a*x)^(9/2)) + (245*a^8*(c - c/(a^2*x^2))^(9/2)*x^9*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(128*(1 - a*x)^(9/2)*(1 + a*x)^(9/2))","A",16,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
696,1,372,0,0.4968654,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2),x]","\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{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}+\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{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{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{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{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}+\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{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{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}}",1,"(-11*a^3*(c - c/(a^2*x^2))^(7/2)*x^4)/(30*(1 - a*x)^3) + (57*a^6*(c - c/(a^2*x^2))^(7/2)*x^7)/(16*(1 - a*x)^3*(1 + a*x)^3) - (41*a^5*(c - c/(a^2*x^2))^(7/2)*x^6)/(24*(1 - a*x)^3*(1 + a*x)^2) - (57*a^4*(c - c/(a^2*x^2))^(7/2)*x^5)/(80*(1 - a*x)^3*(1 + a*x)) + (13*a^2*(c - c/(a^2*x^2))^(7/2)*x^3*(1 + a*x))/(40*(1 - a*x)^3) - (a*(c - c/(a^2*x^2))^(7/2)*x^2*(1 + a*x))/(15*(1 - a*x)^2) - ((c - c/(a^2*x^2))^(7/2)*x*(1 + a*x))/(6*(1 - a*x)) - (2*a^6*(c - c/(a^2*x^2))^(7/2)*x^7*ArcSin[a*x])/((1 - a*x)^(7/2)*(1 + a*x)^(7/2)) - (25*a^6*(c - c/(a^2*x^2))^(7/2)*x^7*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(16*(1 - a*x)^(7/2)*(1 + a*x)^(7/2))","A",14,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
697,1,294,0,0.4540688,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2),x]","-\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{17 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{12 (1-a x)^2 (a x+1)}+\frac{5 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2}-\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{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{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{17 a^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{12 (1-a x)^2 (a x+1)}+\frac{5 a^2 x^3 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2}-\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{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}}",1,"(5*a^2*(c - c/(a^2*x^2))^(5/2)*x^3)/(8*(1 - a*x)^2) - (25*a^4*(c - c/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(1 + a*x)^2) + (17*a^3*(c - c/(a^2*x^2))^(5/2)*x^4)/(12*(1 - a*x)^2*(1 + a*x)) - (a*(c - c/(a^2*x^2))^(5/2)*x^2*(1 + a*x))/(6*(1 - a*x)^2) - ((c - c/(a^2*x^2))^(5/2)*x*(1 + a*x))/(4*(1 - a*x)) + (2*a^4*(c - c/(a^2*x^2))^(5/2)*x^5*ArcSin[a*x])/((1 - a*x)^(5/2)*(1 + a*x)^(5/2)) + (9*a^4*(c - c/(a^2*x^2))^(5/2)*x^5*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(8*(1 - a*x)^(5/2)*(1 + a*x)^(5/2))","A",12,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
698,1,214,0,0.3947972,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2),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{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{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}}","\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{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{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,"-((a*(c - c/(a^2*x^2))^(3/2)*x^2)/(1 - a*x)) + (5*a^2*(c - c/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(1 + a*x)) - ((c - c/(a^2*x^2))^(3/2)*x*(1 + a*x))/(2*(1 - a*x)) - (2*a^2*(c - c/(a^2*x^2))^(3/2)*x^3*ArcSin[a*x])/((1 - a*x)^(3/2)*(1 + a*x)^(3/2)) - (a^2*(c - c/(a^2*x^2))^(3/2)*x^3*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2))","A",10,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
699,1,118,0,0.3053553,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-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}}","-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) + (2*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,8,24,0.3333,1,"{6159, 6129, 102, 157, 41, 216, 92, 208}"
700,1,110,0,0.244246,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^(2*ArcTanh[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\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}}}","\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,"(2*(1 - a*x)*(1 + a*x))/(a^2*Sqrt[c - c/(a^2*x^2)]*x) + (1 + a*x)^2/(a^2*Sqrt[c - c/(a^2*x^2)]*x) - (2*Sqrt[1 - a*x]*Sqrt[1 + a*x]*ArcSin[a*x])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",6,6,24,0.2500,1,"{6159, 6129, 78, 50, 41, 216}"
701,1,123,0,0.3732122,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(3/2),x]","-\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{(a x+1)^2}{3 a^2 x \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}}","-\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{(a x+1)^2}{3 a^2 x \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,"(1 + a*x)^2/(3*a^2*(c - c/(a^2*x^2))^(3/2)*x) - (2*(5 - 2*a*x)*(1 - a*x)*(1 + a*x)^2)/(3*a^4*(c - c/(a^2*x^2))^(3/2)*x^3) + (2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2)*ArcSin[a*x])/(a^4*(c - c/(a^2*x^2))^(3/2)*x^3)","A",6,6,24,0.2500,1,"{6159, 6129, 98, 143, 41, 216}"
702,1,203,0,0.4053633,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(5/2),x]","\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{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}}+\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)^{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)^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{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}}+\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)^{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}}",1,"(1 + a*x)^2/(5*a^2*(c - c/(a^2*x^2))^(5/2)*x) - (2*(1 - a*x)*(1 + a*x)^2)/(3*a^3*(c - c/(a^2*x^2))^(5/2)*x^2) + (58*(1 - a*x)^2*(1 + a*x)^2)/(15*a^4*(c - c/(a^2*x^2))^(5/2)*x^3) + (2*(1 - a*x)^3*(1 + a*x)^2*(28 + 43*a*x))/(15*a^6*(c - c/(a^2*x^2))^(5/2)*x^5) - (2*(1 - a*x)^(5/2)*(1 + a*x)^(5/2)*ArcSin[a*x])/(a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",8,7,24,0.2917,1,"{6159, 6129, 98, 150, 143, 41, 216}"
703,1,283,0,0.4274047,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(7/2),x]","-\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{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{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}}+\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)^{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{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{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}}+\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)^{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}}",1,"(1 + a*x)^2/(7*a^2*(c - c/(a^2*x^2))^(7/2)*x) - (2*(1 - a*x)*(1 + a*x)^2)/(5*a^3*(c - c/(a^2*x^2))^(7/2)*x^2) + (124*(1 - a*x)^2*(1 + a*x)^2)/(105*a^4*(c - c/(a^2*x^2))^(7/2)*x^3) - (782*(1 - a*x)^3*(1 + a*x)^2)/(105*a^5*(c - c/(a^2*x^2))^(7/2)*x^4) - (142*(1 - a*x)^4*(1 + a*x)^2)/(35*a^6*(c - c/(a^2*x^2))^(7/2)*x^5) - (2*(1 - a*x)^4*(1 + a*x)^3*(72 + 107*a*x))/(35*a^8*(c - c/(a^2*x^2))^(7/2)*x^7) + (2*(1 - a*x)^(7/2)*(1 + a*x)^(7/2)*ArcSin[a*x])/(a^8*(c - c/(a^2*x^2))^(7/2)*x^7)","A",10,7,24,0.2917,1,"{6159, 6129, 98, 150, 143, 41, 216}"
704,1,363,0,0.4754017,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{9/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - c/(a^2*x^2))^(9/2),x]","\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{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{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}}+\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)^{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{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{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}}+\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)^{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}}",1,"(1 + a*x)^2/(9*a^2*(c - c/(a^2*x^2))^(9/2)*x) - (2*(1 - a*x)*(1 + a*x)^2)/(7*a^3*(c - c/(a^2*x^2))^(9/2)*x^2) + (214*(1 - a*x)^2*(1 + a*x)^2)/(315*a^4*(c - c/(a^2*x^2))^(9/2)*x^3) - (646*(1 - a*x)^3*(1 + a*x)^2)/(315*a^5*(c - c/(a^2*x^2))^(9/2)*x^4) + (302*(1 - a*x)^4*(1 + a*x)^2)/(21*a^6*(c - c/(a^2*x^2))^(9/2)*x^5) + (2458*(1 - a*x)^5*(1 + a*x)^2)/(315*a^7*(c - c/(a^2*x^2))^(9/2)*x^6) + (1334*(1 - a*x)^5*(1 + a*x)^3)/(315*a^8*(c - c/(a^2*x^2))^(9/2)*x^7) + (2*(1 - a*x)^5*(1 + a*x)^4*(704 + 1019*a*x))/(315*a^10*(c - c/(a^2*x^2))^(9/2)*x^9) - (2*(1 - a*x)^(9/2)*(1 + a*x)^(9/2)*ArcSin[a*x])/(a^10*(c - c/(a^2*x^2))^(9/2)*x^9)","A",12,7,24,0.2917,1,"{6159, 6129, 98, 150, 143, 41, 216}"
705,1,300,0,0.1941417,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(9/2),x]","-\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{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}}-\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{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{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{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}}-\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{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}}",1,"-((c - c/(a^2*x^2))^(9/2)*x)/(8*(1 - a^2*x^2)^(9/2)) - (3*a*(c - c/(a^2*x^2))^(9/2)*x^2)/(7*(1 - a^2*x^2)^(9/2)) + (8*a^3*(c - c/(a^2*x^2))^(9/2)*x^4)/(5*(1 - a^2*x^2)^(9/2)) + (3*a^4*(c - c/(a^2*x^2))^(9/2)*x^5)/(2*(1 - a^2*x^2)^(9/2)) - (2*a^5*(c - c/(a^2*x^2))^(9/2)*x^6)/(1 - a^2*x^2)^(9/2) - (4*a^6*(c - c/(a^2*x^2))^(9/2)*x^7)/(1 - a^2*x^2)^(9/2) - (a^9*(c - c/(a^2*x^2))^(9/2)*x^10)/(1 - a^2*x^2)^(9/2) - (3*a^8*(c - c/(a^2*x^2))^(9/2)*x^9*Log[x])/(1 - a^2*x^2)^(9/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
706,1,301,0,0.196597,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2),x]","\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^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}}-\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{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{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^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^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}}-\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{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{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}}",1,"-((c - c/(a^2*x^2))^(7/2)*x)/(6*(1 - a^2*x^2)^(7/2)) - (3*a*(c - c/(a^2*x^2))^(7/2)*x^2)/(5*(1 - a^2*x^2)^(7/2)) - (a^2*(c - c/(a^2*x^2))^(7/2)*x^3)/(4*(1 - a^2*x^2)^(7/2)) + (5*a^3*(c - c/(a^2*x^2))^(7/2)*x^4)/(3*(1 - a^2*x^2)^(7/2)) + (5*a^4*(c - c/(a^2*x^2))^(7/2)*x^5)/(2*(1 - a^2*x^2)^(7/2)) - (a^5*(c - c/(a^2*x^2))^(7/2)*x^6)/(1 - a^2*x^2)^(7/2) + (a^7*(c - c/(a^2*x^2))^(7/2)*x^8)/(1 - a^2*x^2)^(7/2) + (3*a^6*(c - c/(a^2*x^2))^(7/2)*x^7*Log[x])/(1 - a^2*x^2)^(7/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
707,1,220,0,0.1848503,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2),x]","-\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{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}}-\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 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{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{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{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}}-\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 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{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}}",1,"-((c - c/(a^2*x^2))^(5/2)*x)/(4*(1 - a^2*x^2)^(5/2)) - (a*(c - c/(a^2*x^2))^(5/2)*x^2)/(1 - a^2*x^2)^(5/2) - (a^2*(c - c/(a^2*x^2))^(5/2)*x^3)/(1 - a^2*x^2)^(5/2) + (2*a^3*(c - c/(a^2*x^2))^(5/2)*x^4)/(1 - a^2*x^2)^(5/2) - (a^5*(c - c/(a^2*x^2))^(5/2)*x^6)/(1 - a^2*x^2)^(5/2) - (3*a^4*(c - c/(a^2*x^2))^(5/2)*x^5*Log[x])/(1 - a^2*x^2)^(5/2)","A",4,3,24,0.1250,1,"{6160, 6150, 75}"
708,1,145,0,0.1700075,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2),x]","\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}}-\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}}-\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}}",1,"-((c - c/(a^2*x^2))^(3/2)*x)/(2*(1 - a^2*x^2)^(3/2)) - (3*a*(c - c/(a^2*x^2))^(3/2)*x^2)/(1 - a^2*x^2)^(3/2) + (a^3*(c - c/(a^2*x^2))^(3/2)*x^4)/(1 - a^2*x^2)^(3/2) + (3*a^2*(c - c/(a^2*x^2))^(3/2)*x^3*Log[x])/(1 - a^2*x^2)^(3/2)","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
709,1,108,0,0.1517778,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-\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}}","-\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,"-((a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2]) + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,24,0.1250,1,"{6160, 6150, 72}"
710,1,123,0,0.1395212,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^(3*ArcTanh[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\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}}}","\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*Sqrt[c - c/(a^2*x^2)]) + (2*Sqrt[1 - a^2*x^2])/(a^2*Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x)) + (3*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6160, 6150, 77}"
711,1,174,0,0.1916014,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^(3/2),x]","-\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}}{a^3 x^2 \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{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}}{a^3 x^2 \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}}",1,"-((1 - a^2*x^2)^(3/2)/(a^3*(c - c/(a^2*x^2))^(3/2)*x^2)) + (1 - a^2*x^2)^(3/2)/(2*a^4*(c - c/(a^2*x^2))^(3/2)*x^3*(1 - a*x)^2) - (3*(1 - a^2*x^2)^(3/2))/(a^4*(c - c/(a^2*x^2))^(3/2)*x^3*(1 - a*x)) - (3*(1 - a^2*x^2)^(3/2)*Log[1 - a*x])/(a^4*(c - c/(a^2*x^2))^(3/2)*x^3)","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
712,1,269,0,0.2186083,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^(5/2),x]","\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{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \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{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{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \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}}",1,"(1 - a^2*x^2)^(5/2)/(a^5*(c - c/(a^2*x^2))^(5/2)*x^4) + (1 - a^2*x^2)^(5/2)/(6*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 - a*x)^3) - (9*(1 - a^2*x^2)^(5/2))/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 - a*x)^2) + (31*(1 - a^2*x^2)^(5/2))/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 - a*x)) + (49*(1 - a^2*x^2)^(5/2)*Log[1 - a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5) - ((1 - a^2*x^2)^(5/2)*Log[1 + a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
713,1,363,0,0.2468,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - c/(a^2*x^2))^(7/2),x]","-\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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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{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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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}}",1,"-((1 - a^2*x^2)^(7/2)/(a^7*(c - c/(a^2*x^2))^(7/2)*x^6)) + (1 - a^2*x^2)^(7/2)/(16*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)^4) - (1 - a^2*x^2)^(7/2)/(2*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)^3) + (59*(1 - a^2*x^2)^(7/2))/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)^2) - (75*(1 - a^2*x^2)^(7/2))/(16*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)) + (1 - a^2*x^2)^(7/2)/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)) - (201*(1 - a^2*x^2)^(7/2)*Log[1 - a*x])/(64*a^8*(c - c/(a^2*x^2))^(7/2)*x^7) + (9*(1 - a^2*x^2)^(7/2)*Log[1 + a*x])/(64*a^8*(c - c/(a^2*x^2))^(7/2)*x^7)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
714,1,375,0,0.2073941,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[(c - c/(a^2*x^2))^(9/2)/E^ArcTanh[a*x],x]","-\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{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}}+\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 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^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{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{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}}+\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 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^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}}",1,"-((c - c/(a^2*x^2))^(9/2)*x)/(8*(1 - a^2*x^2)^(9/2)) + (a*(c - c/(a^2*x^2))^(9/2)*x^2)/(7*(1 - a^2*x^2)^(9/2)) + (2*a^2*(c - c/(a^2*x^2))^(9/2)*x^3)/(3*(1 - a^2*x^2)^(9/2)) - (4*a^3*(c - c/(a^2*x^2))^(9/2)*x^4)/(5*(1 - a^2*x^2)^(9/2)) - (3*a^4*(c - c/(a^2*x^2))^(9/2)*x^5)/(2*(1 - a^2*x^2)^(9/2)) + (2*a^5*(c - c/(a^2*x^2))^(9/2)*x^6)/(1 - a^2*x^2)^(9/2) + (2*a^6*(c - c/(a^2*x^2))^(9/2)*x^7)/(1 - a^2*x^2)^(9/2) - (4*a^7*(c - c/(a^2*x^2))^(9/2)*x^8)/(1 - a^2*x^2)^(9/2) - (a^9*(c - c/(a^2*x^2))^(9/2)*x^10)/(1 - a^2*x^2)^(9/2) + (a^8*(c - c/(a^2*x^2))^(9/2)*x^9*Log[x])/(1 - a^2*x^2)^(9/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
715,1,299,0,0.1920871,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[(c - c/(a^2*x^2))^(7/2)/E^ArcTanh[a*x],x]","\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^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}}+\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 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^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^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^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}}+\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 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^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}}",1,"-((c - c/(a^2*x^2))^(7/2)*x)/(6*(1 - a^2*x^2)^(7/2)) + (a*(c - c/(a^2*x^2))^(7/2)*x^2)/(5*(1 - a^2*x^2)^(7/2)) + (3*a^2*(c - c/(a^2*x^2))^(7/2)*x^3)/(4*(1 - a^2*x^2)^(7/2)) - (a^3*(c - c/(a^2*x^2))^(7/2)*x^4)/(1 - a^2*x^2)^(7/2) - (3*a^4*(c - c/(a^2*x^2))^(7/2)*x^5)/(2*(1 - a^2*x^2)^(7/2)) + (3*a^5*(c - c/(a^2*x^2))^(7/2)*x^6)/(1 - a^2*x^2)^(7/2) + (a^7*(c - c/(a^2*x^2))^(7/2)*x^8)/(1 - a^2*x^2)^(7/2) - (a^6*(c - c/(a^2*x^2))^(7/2)*x^7*Log[x])/(1 - a^2*x^2)^(7/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
716,1,220,0,0.1789439,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[(c - c/(a^2*x^2))^(5/2)/E^ArcTanh[a*x],x]","-\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{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}}+\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 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^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{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{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}}+\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 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^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}}",1,"-((c - c/(a^2*x^2))^(5/2)*x)/(4*(1 - a^2*x^2)^(5/2)) + (a*(c - c/(a^2*x^2))^(5/2)*x^2)/(3*(1 - a^2*x^2)^(5/2)) + (a^2*(c - c/(a^2*x^2))^(5/2)*x^3)/(1 - a^2*x^2)^(5/2) - (2*a^3*(c - c/(a^2*x^2))^(5/2)*x^4)/(1 - a^2*x^2)^(5/2) - (a^5*(c - c/(a^2*x^2))^(5/2)*x^6)/(1 - a^2*x^2)^(5/2) + (a^4*(c - c/(a^2*x^2))^(5/2)*x^5*Log[x])/(1 - a^2*x^2)^(5/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
717,1,144,0,0.1673498,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[(c - c/(a^2*x^2))^(3/2)/E^ArcTanh[a*x],x]","\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}}+\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}}+\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}}",1,"-((c - c/(a^2*x^2))^(3/2)*x)/(2*(1 - a^2*x^2)^(3/2)) + (a*(c - c/(a^2*x^2))^(3/2)*x^2)/(1 - a^2*x^2)^(3/2) + (a^3*(c - c/(a^2*x^2))^(3/2)*x^4)/(1 - a^2*x^2)^(3/2) - (a^2*(c - c/(a^2*x^2))^(3/2)*x^3*Log[x])/(1 - a^2*x^2)^(3/2)","A",4,3,24,0.1250,1,"{6160, 6150, 75}"
718,1,69,0,0.1433448,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^ArcTanh[a*x],x]","\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}}","\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,"-((a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2]) + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
719,1,77,0,0.1279992,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[1/(E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]),x]","\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}}}","\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]/(a*Sqrt[c - c/(a^2*x^2)]) - (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
720,1,175,0,0.1859514,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(3/2)),x]","\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}}{a^3 x^2 \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}}{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}}{a^3 x^2 \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}}",1,"-((1 - a^2*x^2)^(3/2)/(a^3*(c - c/(a^2*x^2))^(3/2)*x^2)) + (1 - a^2*x^2)^(3/2)/(2*a^4*(c - c/(a^2*x^2))^(3/2)*x^3*(1 + a*x)) - ((1 - a^2*x^2)^(3/2)*Log[1 - a*x])/(4*a^4*(c - c/(a^2*x^2))^(3/2)*x^3) + (5*(1 - a^2*x^2)^(3/2)*Log[1 + a*x])/(4*a^4*(c - c/(a^2*x^2))^(3/2)*x^3)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
721,1,265,0,0.2111013,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(5/2)),x]","\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{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \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}}{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{\left(1-a^2 x^2\right)^{5/2}}{a^5 x^4 \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}}",1,"(1 - a^2*x^2)^(5/2)/(a^5*(c - c/(a^2*x^2))^(5/2)*x^4) + (1 - a^2*x^2)^(5/2)/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 - a*x)) + (1 - a^2*x^2)^(5/2)/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 + a*x)^2) - (1 - a^2*x^2)^(5/2)/(a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 + a*x)) + (7*(1 - a^2*x^2)^(5/2)*Log[1 - a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5) - (23*(1 - a^2*x^2)^(5/2)*Log[1 + a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
722,1,361,0,0.2403285,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - c/(a^2*x^2))^(7/2)),x]","-\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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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{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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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}}",1,"-((1 - a^2*x^2)^(7/2)/(a^7*(c - c/(a^2*x^2))^(7/2)*x^6)) + (1 - a^2*x^2)^(7/2)/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)^2) - (5*(1 - a^2*x^2)^(7/2))/(16*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)) + (1 - a^2*x^2)^(7/2)/(24*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)^3) - (11*(1 - a^2*x^2)^(7/2))/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)^2) + (3*(1 - a^2*x^2)^(7/2))/(2*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)) - (19*(1 - a^2*x^2)^(7/2)*Log[1 - a*x])/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7) + (51*(1 - a^2*x^2)^(7/2)*Log[1 + a*x])/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
723,1,455,0,0.5371512,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[(c - c/(a^2*x^2))^(9/2)/E^(2*ArcTanh[a*x]),x]","\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{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)}+\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{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{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{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{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)}+\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{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{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}}",1,"(11*a^8*(c - c/(a^2*x^2))^(9/2)*x^9)/(128*(1 - a*x)^4*(1 + a*x)^4) + (39*a^7*(c - c/(a^2*x^2))^(9/2)*x^8)/(64*(1 - a*x)^4*(1 + a*x)^3) - (11*a^6*(c - c/(a^2*x^2))^(9/2)*x^7)/(640*(1 - a*x)^4*(1 + a*x)^2) + (a*(c - c/(a^2*x^2))^(9/2)*x^2)/(28*(1 + a*x)) - (103*a^5*(c - c/(a^2*x^2))^(9/2)*x^6)/(160*(1 - a*x)^4*(1 + a*x)) + (629*a^4*(c - c/(a^2*x^2))^(9/2)*x^5)/(960*(1 - a*x)^3*(1 + a*x)) - (2*a^3*(c - c/(a^2*x^2))^(9/2)*x^4)/(5*(1 - a*x)^2*(1 + a*x)) + (47*a^2*(c - c/(a^2*x^2))^(9/2)*x^3)/(336*(1 - a*x)*(1 + a*x)) - ((c - c/(a^2*x^2))^(9/2)*x*(1 - a*x))/(8*(1 + a*x)) - (2*a^8*(c - c/(a^2*x^2))^(9/2)*x^9*ArcSin[a*x])/((1 - a*x)^(9/2)*(1 + a*x)^(9/2)) + (245*a^8*(c - c/(a^2*x^2))^(9/2)*x^9*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(128*(1 - a*x)^(9/2)*(1 + a*x)^(9/2))","A",16,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
724,1,375,0,0.4670532,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[(c - c/(a^2*x^2))^(7/2)/E^(2*ArcTanh[a*x]),x]","-\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{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)}+\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{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{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{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{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)}+\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{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{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}}",1,"(-7*a^6*(c - c/(a^2*x^2))^(7/2)*x^7)/(16*(1 - a*x)^3*(1 + a*x)^3) - (3*a^5*(c - c/(a^2*x^2))^(7/2)*x^6)/(8*(1 - a*x)^3*(1 + a*x)^2) + (a*(c - c/(a^2*x^2))^(7/2)*x^2)/(15*(1 + a*x)) + (19*a^4*(c - c/(a^2*x^2))^(7/2)*x^5)/(16*(1 - a*x)^3*(1 + a*x)) - (2*a^3*(c - c/(a^2*x^2))^(7/2)*x^4)/(3*(1 - a*x)^2*(1 + a*x)) + (23*a^2*(c - c/(a^2*x^2))^(7/2)*x^3)/(120*(1 - a*x)*(1 + a*x)) - ((c - c/(a^2*x^2))^(7/2)*x*(1 - a*x))/(6*(1 + a*x)) + (2*a^6*(c - c/(a^2*x^2))^(7/2)*x^7*ArcSin[a*x])/((1 - a*x)^(7/2)*(1 + a*x)^(7/2)) - (25*a^6*(c - c/(a^2*x^2))^(7/2)*x^7*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(16*(1 - a*x)^(7/2)*(1 + a*x)^(7/2))","A",14,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
725,1,293,0,0.4267567,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[(c - c/(a^2*x^2))^(5/2)/E^(2*ArcTanh[a*x]),x]","\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^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{(1-a x)^2 (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{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{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{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^3 x^4 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}{(1-a x)^2 (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{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{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}}",1,"(7*a^4*(c - c/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(1 + a*x)^2) + (a*(c - c/(a^2*x^2))^(5/2)*x^2)/(6*(1 + a*x)) - (2*a^3*(c - c/(a^2*x^2))^(5/2)*x^4)/((1 - a*x)^2*(1 + a*x)) + (7*a^2*(c - c/(a^2*x^2))^(5/2)*x^3)/(24*(1 - a*x)*(1 + a*x)) - ((c - c/(a^2*x^2))^(5/2)*x*(1 - a*x))/(4*(1 + a*x)) - (2*a^4*(c - c/(a^2*x^2))^(5/2)*x^5*ArcSin[a*x])/((1 - a*x)^(5/2)*(1 + a*x)^(5/2)) + (9*a^4*(c - c/(a^2*x^2))^(5/2)*x^5*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(8*(1 - a*x)^(5/2)*(1 + a*x)^(5/2))","A",12,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
726,1,212,0,0.3835817,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[(c - c/(a^2*x^2))^(3/2)/E^(2*ArcTanh[a*x]),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{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{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}}","\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{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{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,"(a*(c - c/(a^2*x^2))^(3/2)*x^2)/(1 + a*x) + (5*a^2*(c - c/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(1 + a*x)) - ((c - c/(a^2*x^2))^(3/2)*x*(1 - a*x))/(2*(1 + a*x)) + (2*a^2*(c - c/(a^2*x^2))^(3/2)*x^3*ArcSin[a*x])/((1 - a*x)^(3/2)*(1 + a*x)^(3/2)) - (a^2*(c - c/(a^2*x^2))^(3/2)*x^3*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2))","A",10,10,24,0.4167,1,"{6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
727,1,118,0,0.2957435,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(2*ArcTanh[a*x]),x]","-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}}","-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) - (2*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,8,24,0.3333,1,"{6159, 6129, 102, 157, 41, 216, 92, 208}"
728,1,111,0,0.2411502,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]),x]","\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}}}","\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,"(1 - a*x)^2/(a^2*Sqrt[c - c/(a^2*x^2)]*x) + (2*(1 - a*x)*(1 + a*x))/(a^2*Sqrt[c - c/(a^2*x^2)]*x) + (2*Sqrt[1 - a*x]*Sqrt[1 + a*x]*ArcSin[a*x])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",6,6,24,0.2500,1,"{6159, 6129, 78, 50, 41, 216}"
729,1,124,0,0.3661432,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2)),x]","-\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{(1-a x)^2}{3 a^2 x \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}}","-\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{(1-a x)^2}{3 a^2 x \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,"(1 - a*x)^2/(3*a^2*(c - c/(a^2*x^2))^(3/2)*x) - (2*(1 - a*x)^2*(1 + a*x)*(5 + 2*a*x))/(3*a^4*(c - c/(a^2*x^2))^(3/2)*x^3) - (2*(1 - a*x)^(3/2)*(1 + a*x)^(3/2)*ArcSin[a*x])/(a^4*(c - c/(a^2*x^2))^(3/2)*x^3)","A",6,6,24,0.2500,1,"{6159, 6129, 98, 143, 41, 216}"
730,1,194,0,0.3980652,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2)),x]","-\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 (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 (1-a x)^3}{5 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{(1-a x)^2}{a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{2 (a x+1)^{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 (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 (1-a x)^3}{5 a^3 x^2 \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{(1-a x)^2}{a^2 x \left(c-\frac{c}{a^2 x^2}\right)^{5/2}}+\frac{2 (a x+1)^{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}}",1,"(1 - a*x)^2/(a^2*(c - c/(a^2*x^2))^(5/2)*x) + (2*(1 - a*x)^3)/(5*a^3*(c - c/(a^2*x^2))^(5/2)*x^2) - (2*(1 - a*x)^3*(1 + a*x))/(15*a^4*(c - c/(a^2*x^2))^(5/2)*x^3) + (2*(1 - a*x)^3*(1 + a*x)^2*(28 + 13*a*x))/(15*a^6*(c - c/(a^2*x^2))^(5/2)*x^5) + (2*(1 - a*x)^(5/2)*(1 + a*x)^(5/2)*ArcSin[a*x])/(a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",8,7,24,0.2917,1,"{6159, 6129, 98, 150, 143, 41, 216}"
731,1,270,0,0.4270297,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2)),x]","-\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{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{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}}+\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)^{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{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{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}}+\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)^{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}}",1,"(1 - a*x)^2/(3*a^2*(c - c/(a^2*x^2))^(7/2)*x) - (10*(1 - a*x)^3)/(3*a^3*(c - c/(a^2*x^2))^(7/2)*x^2) - (12*(1 - a*x)^4)/(7*a^4*(c - c/(a^2*x^2))^(7/2)*x^3) - (82*(1 - a*x)^4*(1 + a*x))/(105*a^5*(c - c/(a^2*x^2))^(7/2)*x^4) - (2*(1 - a*x)^4*(1 + a*x)^2)/(35*a^6*(c - c/(a^2*x^2))^(7/2)*x^5) - (2*(1 - a*x)^4*(1 + a*x)^3*(72 + 37*a*x))/(35*a^8*(c - c/(a^2*x^2))^(7/2)*x^7) - (2*(1 - a*x)^(7/2)*(1 + a*x)^(7/2)*ArcSin[a*x])/(a^8*(c - c/(a^2*x^2))^(7/2)*x^7)","A",10,7,24,0.2917,1,"{6159, 6129, 98, 150, 143, 41, 216}"
732,1,299,0,0.2010242,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[(c - c/(a^2*x^2))^(9/2)/E^(3*ArcTanh[a*x]),x]","\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{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}}+\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{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{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{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}}+\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{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}}",1,"-((c - c/(a^2*x^2))^(9/2)*x)/(8*(1 - a^2*x^2)^(9/2)) + (3*a*(c - c/(a^2*x^2))^(9/2)*x^2)/(7*(1 - a^2*x^2)^(9/2)) - (8*a^3*(c - c/(a^2*x^2))^(9/2)*x^4)/(5*(1 - a^2*x^2)^(9/2)) + (3*a^4*(c - c/(a^2*x^2))^(9/2)*x^5)/(2*(1 - a^2*x^2)^(9/2)) + (2*a^5*(c - c/(a^2*x^2))^(9/2)*x^6)/(1 - a^2*x^2)^(9/2) - (4*a^6*(c - c/(a^2*x^2))^(9/2)*x^7)/(1 - a^2*x^2)^(9/2) + (a^9*(c - c/(a^2*x^2))^(9/2)*x^10)/(1 - a^2*x^2)^(9/2) - (3*a^8*(c - c/(a^2*x^2))^(9/2)*x^9*Log[x])/(1 - a^2*x^2)^(9/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
733,1,301,0,0.1895914,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[(c - c/(a^2*x^2))^(7/2)/E^(3*ArcTanh[a*x]),x]","-\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^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}}-\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{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{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^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^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}}-\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{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{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}}",1,"-((c - c/(a^2*x^2))^(7/2)*x)/(6*(1 - a^2*x^2)^(7/2)) + (3*a*(c - c/(a^2*x^2))^(7/2)*x^2)/(5*(1 - a^2*x^2)^(7/2)) - (a^2*(c - c/(a^2*x^2))^(7/2)*x^3)/(4*(1 - a^2*x^2)^(7/2)) - (5*a^3*(c - c/(a^2*x^2))^(7/2)*x^4)/(3*(1 - a^2*x^2)^(7/2)) + (5*a^4*(c - c/(a^2*x^2))^(7/2)*x^5)/(2*(1 - a^2*x^2)^(7/2)) + (a^5*(c - c/(a^2*x^2))^(7/2)*x^6)/(1 - a^2*x^2)^(7/2) - (a^7*(c - c/(a^2*x^2))^(7/2)*x^8)/(1 - a^2*x^2)^(7/2) + (3*a^6*(c - c/(a^2*x^2))^(7/2)*x^7*Log[x])/(1 - a^2*x^2)^(7/2)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
734,1,218,0,0.1847155,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[(c - c/(a^2*x^2))^(5/2)/E^(3*ArcTanh[a*x]),x]","\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{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}}-\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 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{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{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{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}}-\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 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{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}}",1,"-((c - c/(a^2*x^2))^(5/2)*x)/(4*(1 - a^2*x^2)^(5/2)) + (a*(c - c/(a^2*x^2))^(5/2)*x^2)/(1 - a^2*x^2)^(5/2) - (a^2*(c - c/(a^2*x^2))^(5/2)*x^3)/(1 - a^2*x^2)^(5/2) - (2*a^3*(c - c/(a^2*x^2))^(5/2)*x^4)/(1 - a^2*x^2)^(5/2) + (a^5*(c - c/(a^2*x^2))^(5/2)*x^6)/(1 - a^2*x^2)^(5/2) - (3*a^4*(c - c/(a^2*x^2))^(5/2)*x^5*Log[x])/(1 - a^2*x^2)^(5/2)","A",4,3,24,0.1250,1,"{6160, 6150, 75}"
735,1,146,0,0.1671821,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[(c - c/(a^2*x^2))^(3/2)/E^(3*ArcTanh[a*x]),x]","-\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}}+\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}}+\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}}",1,"-((c - c/(a^2*x^2))^(3/2)*x)/(2*(1 - a^2*x^2)^(3/2)) + (3*a*(c - c/(a^2*x^2))^(3/2)*x^2)/(1 - a^2*x^2)^(3/2) - (a^3*(c - c/(a^2*x^2))^(3/2)*x^4)/(1 - a^2*x^2)^(3/2) + (3*a^2*(c - c/(a^2*x^2))^(3/2)*x^3*Log[x])/(1 - a^2*x^2)^(3/2)","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
736,1,106,0,0.1472556,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2] + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,24,0.1250,1,"{6160, 6150, 72}"
737,1,122,0,0.1367767,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]),x]","-\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}}}","-\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*Sqrt[c - c/(a^2*x^2)])) + (2*Sqrt[1 - a^2*x^2])/(a^2*Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x)) + (3*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(a^2*Sqrt[c - c/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6160, 6150, 77}"
738,1,170,0,0.197348,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2)),x]","-\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}}{a^3 x^2 \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{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}}{a^3 x^2 \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}}",1,"(1 - a^2*x^2)^(3/2)/(a^3*(c - c/(a^2*x^2))^(3/2)*x^2) + (1 - a^2*x^2)^(3/2)/(2*a^4*(c - c/(a^2*x^2))^(3/2)*x^3*(1 + a*x)^2) - (3*(1 - a^2*x^2)^(3/2))/(a^4*(c - c/(a^2*x^2))^(3/2)*x^3*(1 + a*x)) - (3*(1 - a^2*x^2)^(3/2)*Log[1 + a*x])/(a^4*(c - c/(a^2*x^2))^(3/2)*x^3)","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
739,1,267,0,0.2204544,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(5/2)),x]","\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}}{a^5 x^4 \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{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}}{a^5 x^4 \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}}",1,"-((1 - a^2*x^2)^(5/2)/(a^5*(c - c/(a^2*x^2))^(5/2)*x^4)) + (1 - a^2*x^2)^(5/2)/(6*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 + a*x)^3) - (9*(1 - a^2*x^2)^(5/2))/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 + a*x)^2) + (31*(1 - a^2*x^2)^(5/2))/(8*a^6*(c - c/(a^2*x^2))^(5/2)*x^5*(1 + a*x)) - ((1 - a^2*x^2)^(5/2)*Log[1 - a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5) + (49*(1 - a^2*x^2)^(5/2)*Log[1 + a*x])/(16*a^6*(c - c/(a^2*x^2))^(5/2)*x^5)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
740,1,359,0,0.2512013,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^(7/2)),x]","\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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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}}{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{\left(1-a^2 x^2\right)^{7/2}}{a^7 x^6 \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}}",1,"(1 - a^2*x^2)^(7/2)/(a^7*(c - c/(a^2*x^2))^(7/2)*x^6) + (1 - a^2*x^2)^(7/2)/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 - a*x)) + (1 - a^2*x^2)^(7/2)/(16*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)^4) - (1 - a^2*x^2)^(7/2)/(2*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)^3) + (59*(1 - a^2*x^2)^(7/2))/(32*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)^2) - (75*(1 - a^2*x^2)^(7/2))/(16*a^8*(c - c/(a^2*x^2))^(7/2)*x^7*(1 + a*x)) + (9*(1 - a^2*x^2)^(7/2)*Log[1 - a*x])/(64*a^8*(c - c/(a^2*x^2))^(7/2)*x^7) - (201*(1 - a^2*x^2)^(7/2)*Log[1 + a*x])/(64*a^8*(c - c/(a^2*x^2))^(7/2)*x^7)","A",4,3,24,0.1250,1,"{6160, 6150, 88}"
741,1,80,0,0.2200954,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^m \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]*x^m,x]","\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}}","\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^(1 + m))/(m*Sqrt[1 - a^2*x^2]) + (a*Sqrt[c - c/(a^2*x^2)]*x^(2 + m))/((1 + m)*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6160, 6150, 43}"
742,1,74,0,0.2121679,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]*x^2,x]","\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}}","\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)/(2*Sqrt[1 - a^2*x^2]) + (a*Sqrt[c - c/(a^2*x^2)]*x^4)/(3*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6160, 6150, 43}"
743,1,71,0,0.127907,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)]*x,x]","\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{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}}+\frac{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^2)/Sqrt[1 - a^2*x^2] + (a*Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2])","A",3,2,23,0.08696,1,"{6160, 6140}"
744,1,68,0,0.129959,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)],x]","\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{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,"(a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2] + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,22,0.1364,1,"{6160, 6150, 43}"
745,1,66,0,0.2229968,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)])/x,x]","\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}}","\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)]/Sqrt[1 - a^2*x^2]) + (a*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,25,0.1200,1,"{6160, 6150, 43}"
746,1,43,0,0.2123504,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - c/(a^2*x^2)])/x^2,x]","-\frac{(a x+1)^2 \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,"-(Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2)/(2*x*Sqrt[1 - a^2*x^2])","A",3,3,25,0.1200,1,"{6160, 6150, 37}"
747,1,160,0,0.4081552,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^3,x]","-\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}}","-\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,"(-7*Sqrt[c - c/(a^2*x^2)]*x)/(8*a^3) - (7*Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x))/(24*a^3) - (Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x)^2)/(6*a^3) - (Sqrt[c - c/(a^2*x^2)]*x^2*(1 + a*x)^2)/(4*a^2) + (7*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(8*a^3*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,7,27,0.2593,1,"{6159, 6129, 90, 80, 50, 41, 216}"
748,1,123,0,0.3306857,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^2,x]","-\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}}","-\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,"-((Sqrt[c - c/(a^2*x^2)]*x)/a^2) - (Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x))/(3*a^2) - (Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x)^2)/(3*a^2) + (Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(a^2*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",7,6,27,0.2222,1,"{6159, 6129, 80, 50, 41, 216}"
749,1,98,0,0.2102406,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x,x]","-\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}}","-\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,"(-3*Sqrt[c - c/(a^2*x^2)]*x)/(2*a) - (Sqrt[c - c/(a^2*x^2)]*x*(1 + a*x))/(2*a) + (3*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(2*a*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",6,5,25,0.2000,1,"{6159, 6129, 50, 41, 216}"
750,1,118,0,0.287734,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-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}}","-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) + (2*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,8,24,0.3333,1,"{6159, 6129, 102, 157, 41, 216, 92, 208}"
751,1,118,0,0.3833065,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x,x]","-\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}}","-\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)] + (a*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (2*a*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,8,27,0.2963,1,"{6159, 6129, 98, 157, 41, 216, 92, 208}"
752,1,111,0,0.3817353,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^2,x]","-\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}}","-\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,"(-3*a*Sqrt[c - c/(a^2*x^2)])/2 - (Sqrt[c - c/(a^2*x^2)]*(1 + a*x))/(2*x) - (3*a^2*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(2*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",6,5,27,0.1852,1,"{6159, 6129, 94, 92, 208}"
753,1,139,0,0.3882389,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^3,x]","-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}}","-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,"-(a^2*Sqrt[c - c/(a^2*x^2)]) - (a*Sqrt[c - c/(a^2*x^2)]*(1 + a*x))/(3*x) - (Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2)/(3*x^2) - (a^3*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",7,6,27,0.2222,1,"{6159, 6129, 96, 94, 92, 208}"
754,1,156,0,0.4109494,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^4,x]","-\frac{4}{3} a^3 \sqrt{c-\frac{c}{a^2 x^2}}-\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}}-\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}}",1,"(-4*a^3*Sqrt[c - c/(a^2*x^2)])/3 - Sqrt[c - c/(a^2*x^2)]/(4*x^3) - (2*a*Sqrt[c - c/(a^2*x^2)])/(3*x^2) - (7*a^2*Sqrt[c - c/(a^2*x^2)])/(8*x) - (7*a^4*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(8*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",9,7,27,0.2593,1,"{6159, 6129, 98, 151, 12, 92, 208}"
755,1,181,0,0.4303332,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^5,x]","-\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}-\frac{3 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{5 x^2}-\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^3}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4}-\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}-\frac{3 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{5 x^2}-\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^3}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4}-\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}}",1,"(-6*a^4*Sqrt[c - c/(a^2*x^2)])/5 - Sqrt[c - c/(a^2*x^2)]/(5*x^4) - (a*Sqrt[c - c/(a^2*x^2)])/(2*x^3) - (3*a^2*Sqrt[c - c/(a^2*x^2)])/(5*x^2) - (3*a^3*Sqrt[c - c/(a^2*x^2)])/(4*x) - (3*a^5*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(4*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",10,7,27,0.2593,1,"{6159, 6129, 98, 151, 12, 92, 208}"
756,1,188,0,0.2647483,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^3,x]","-\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^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \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}}","-\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^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \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,"(-4*Sqrt[c - c/(a^2*x^2)]*x^2)/(a^2*Sqrt[1 - a^2*x^2]) - (2*Sqrt[c - c/(a^2*x^2)]*x^3)/(a*Sqrt[1 - a^2*x^2]) - (Sqrt[c - c/(a^2*x^2)]*x^4)/Sqrt[1 - a^2*x^2] - (a*Sqrt[c - c/(a^2*x^2)]*x^5)/(4*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/(a^3*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
757,1,153,0,0.2322995,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x^2,x]","-\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}}-\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}}-\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}}",1,"(-4*Sqrt[c - c/(a^2*x^2)]*x^2)/(a*Sqrt[1 - a^2*x^2]) - (3*Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2]) - (a*Sqrt[c - c/(a^2*x^2)]*x^4)/(3*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/(a^2*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6160, 6150, 77}"
758,1,114,0,0.1477054,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)]*x,x]","-\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \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}}-\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}}",1,"(-3*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2] - (a*Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/(a*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6160, 6140, 43}"
759,1,108,0,0.1473062,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-\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}}","-\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,"-((a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2]) + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,24,0.1250,1,"{6160, 6150, 72}"
760,1,107,0,0.2448184,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x,x]","-\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}}","-\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)]/Sqrt[1 - a^2*x^2]) + (3*a*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
761,1,148,0,0.2495102,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^2,x]","-\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}}","-\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,"(-3*a*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(2*x*Sqrt[1 - a^2*x^2]) + (4*a^2*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^2*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
762,1,187,0,0.2571469,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^3,x]","-\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}}","-\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,"(-4*a^2*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(3*x^2*Sqrt[1 - a^2*x^2]) - (3*a*Sqrt[c - c/(a^2*x^2)])/(2*x*Sqrt[1 - a^2*x^2]) + (4*a^3*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^3*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
763,1,222,0,0.2671874,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^4,x]","-\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{\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}}-\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}}",1,"(-4*a^3*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(4*x^3*Sqrt[1 - a^2*x^2]) - (a*Sqrt[c - c/(a^2*x^2)])/(x^2*Sqrt[1 - a^2*x^2]) - (2*a^2*Sqrt[c - c/(a^2*x^2)])/(x*Sqrt[1 - a^2*x^2]) + (4*a^4*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
764,1,263,0,0.2735881,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)])/x^5,x]","-\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}}-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \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{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4 \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}}-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \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{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4 \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}}",1,"(-4*a^4*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(5*x^4*Sqrt[1 - a^2*x^2]) - (3*a*Sqrt[c - c/(a^2*x^2)])/(4*x^3*Sqrt[1 - a^2*x^2]) - (4*a^2*Sqrt[c - c/(a^2*x^2)])/(3*x^2*Sqrt[1 - a^2*x^2]) - (2*a^3*Sqrt[c - c/(a^2*x^2)])/(x*Sqrt[1 - a^2*x^2]) + (4*a^5*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^5*Sqrt[c - c/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
765,1,81,0,0.2340889,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^m \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x^m)/E^ArcTanh[a*x],x]","\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}}","\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^(1 + m))/(m*Sqrt[1 - a^2*x^2]) - (a*Sqrt[c - c/(a^2*x^2)]*x^(2 + m))/((1 + m)*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6160, 6150, 43}"
766,1,74,0,0.2085402,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x^2)/E^ArcTanh[a*x],x]","\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}}","\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,"(Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2]) - (a*Sqrt[c - c/(a^2*x^2)]*x^4)/(3*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6160, 6150, 43}"
767,1,71,0,0.1313133,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x)/E^ArcTanh[a*x],x]","\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}}","\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^2)/Sqrt[1 - a^2*x^2] - (a*Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2])","A",3,2,25,0.08000,1,"{6160, 6140}"
768,1,69,0,0.136392,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^ArcTanh[a*x],x]","\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}}","\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,"-((a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2]) + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,24,0.1250,1,"{6160, 6150, 43}"
769,1,67,0,0.2306614,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^ArcTanh[a*x]*x),x]","-\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}}","-\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)]/Sqrt[1 - a^2*x^2]) - (a*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 43}"
770,1,44,0,0.2219659,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^ArcTanh[a*x]*x^2),x]","-\frac{(1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x \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 - a*x)^2)/(2*x*Sqrt[1 - a^2*x^2])","A",3,3,27,0.1111,1,"{6160, 6150, 37}"
771,1,163,0,0.4031139,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x^3)/E^(2*ArcTanh[a*x]),x]","-\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}}","-\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,"(7*Sqrt[c - c/(a^2*x^2)]*x)/(8*a^3) + (7*Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x))/(24*a^3) + (Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x)^2)/(6*a^3) - (Sqrt[c - c/(a^2*x^2)]*x^2*(1 - a*x)^2)/(4*a^2) + (7*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(8*a^3*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,7,27,0.2593,1,"{6159, 6129, 90, 80, 50, 41, 216}"
772,1,126,0,0.3268632,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x^2)/E^(2*ArcTanh[a*x]),x]","-\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}}","-\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,"-((Sqrt[c - c/(a^2*x^2)]*x)/a^2) - (Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x))/(3*a^2) - (Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x)^2)/(3*a^2) - (Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(a^2*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",7,6,27,0.2222,1,"{6159, 6129, 80, 50, 41, 216}"
773,1,99,0,0.2134156,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x)/E^(2*ArcTanh[a*x]),x]","\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}}","\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,"(3*Sqrt[c - c/(a^2*x^2)]*x)/(2*a) + (Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x))/(2*a) + (3*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(2*a*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",6,5,25,0.2000,1,"{6159, 6129, 50, 41, 216}"
774,1,118,0,0.2900683,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(2*ArcTanh[a*x]),x]","-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}}","-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) - (2*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) - (Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,8,24,0.3333,1,"{6159, 6129, 102, 157, 41, 216, 92, 208}"
775,1,118,0,0.4178121,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x),x]","-\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}}","-\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)] + (a*Sqrt[c - c/(a^2*x^2)]*x*ArcSin[a*x])/(Sqrt[1 - a*x]*Sqrt[1 + a*x]) + (2*a*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",8,8,27,0.2963,1,"{6159, 6129, 98, 157, 41, 216, 92, 208}"
776,1,112,0,0.3908929,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^2),x]","\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}}","\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,"(3*a*Sqrt[c - c/(a^2*x^2)])/2 - (Sqrt[c - c/(a^2*x^2)]*(1 - a*x))/(2*x) - (3*a^2*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(2*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",6,5,27,0.1852,1,"{6159, 6129, 94, 92, 208}"
777,1,140,0,0.3934284,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^3),x]","-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}}","-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,"-(a^2*Sqrt[c - c/(a^2*x^2)]) + (a*Sqrt[c - c/(a^2*x^2)]*(1 - a*x))/(3*x) - (Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2)/(3*x^2) + (a^3*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",7,6,27,0.2222,1,"{6159, 6129, 96, 94, 92, 208}"
778,1,156,0,0.4153109,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^4),x]","\frac{4}{3} a^3 \sqrt{c-\frac{c}{a^2 x^2}}-\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}}-\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}}",1,"(4*a^3*Sqrt[c - c/(a^2*x^2)])/3 - Sqrt[c - c/(a^2*x^2)]/(4*x^3) + (2*a*Sqrt[c - c/(a^2*x^2)])/(3*x^2) - (7*a^2*Sqrt[c - c/(a^2*x^2)])/(8*x) - (7*a^4*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(8*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",9,7,27,0.2593,1,"{6159, 6129, 98, 151, 12, 92, 208}"
779,1,181,0,0.4401282,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcTanh[a*x])*x^5),x]","-\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}-\frac{3 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{5 x^2}+\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^3}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4}+\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}-\frac{3 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{5 x^2}+\frac{a \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^3}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4}+\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}}",1,"(-6*a^4*Sqrt[c - c/(a^2*x^2)])/5 - Sqrt[c - c/(a^2*x^2)]/(5*x^4) + (a*Sqrt[c - c/(a^2*x^2)])/(2*x^3) - (3*a^2*Sqrt[c - c/(a^2*x^2)])/(5*x^2) + (3*a^3*Sqrt[c - c/(a^2*x^2)])/(4*x) + (3*a^5*Sqrt[c - c/(a^2*x^2)]*x*ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]])/(4*Sqrt[1 - a*x]*Sqrt[1 + a*x])","A",10,7,27,0.2593,1,"{6159, 6129, 98, 151, 12, 92, 208}"
780,1,187,0,0.2659325,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x^3)/E^(3*ArcTanh[a*x]),x]","\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^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \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}}","\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^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \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,"(-4*Sqrt[c - c/(a^2*x^2)]*x^2)/(a^2*Sqrt[1 - a^2*x^2]) + (2*Sqrt[c - c/(a^2*x^2)]*x^3)/(a*Sqrt[1 - a^2*x^2]) - (Sqrt[c - c/(a^2*x^2)]*x^4)/Sqrt[1 - a^2*x^2] + (a*Sqrt[c - c/(a^2*x^2)]*x^5)/(4*Sqrt[1 - a^2*x^2]) + (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/(a^3*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
781,1,152,0,0.2401858,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x^2)/E^(3*ArcTanh[a*x]),x]","\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}}+\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}}+\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}}",1,"(4*Sqrt[c - c/(a^2*x^2)]*x^2)/(a*Sqrt[1 - a^2*x^2]) - (3*Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2]) + (a*Sqrt[c - c/(a^2*x^2)]*x^4)/(3*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/(a^2*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6160, 6150, 77}"
782,1,113,0,0.1756693,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x)/E^(3*ArcTanh[a*x]),x]","\frac{a x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \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}}-\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}}",1,"(-3*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2] + (a*Sqrt[c - c/(a^2*x^2)]*x^3)/(2*Sqrt[1 - a^2*x^2]) + (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/(a*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6160, 6140, 43}"
783,1,106,0,0.1691826,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(a*Sqrt[c - c/(a^2*x^2)]*x^2)/Sqrt[1 - a^2*x^2] + (Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,24,0.1250,1,"{6160, 6150, 72}"
784,1,106,0,0.2612296,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x),x]","-\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}}","-\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)]/Sqrt[1 - a^2*x^2]) - (3*a*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] + (4*a*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
785,1,147,0,0.2686983,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^2),x]","\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}}","\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,"(3*a*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(2*x*Sqrt[1 - a^2*x^2]) + (4*a^2*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^2*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
786,1,186,0,0.2813784,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^3),x]","-\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}}","-\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,"(-4*a^2*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(3*x^2*Sqrt[1 - a^2*x^2]) + (3*a*Sqrt[c - c/(a^2*x^2)])/(2*x*Sqrt[1 - a^2*x^2]) - (4*a^3*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] + (4*a^3*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
787,1,220,0,0.258756,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^4),x]","\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{\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}}-\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}}",1,"(4*a^3*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(4*x^3*Sqrt[1 - a^2*x^2]) + (a*Sqrt[c - c/(a^2*x^2)])/(x^2*Sqrt[1 - a^2*x^2]) - (2*a^2*Sqrt[c - c/(a^2*x^2)])/(x*Sqrt[1 - a^2*x^2]) + (4*a^4*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^4*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
788,1,262,0,0.2622669,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcTanh[a*x])*x^5),x]","-\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}}-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \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{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4 \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}}-\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^2 \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{\sqrt{c-\frac{c}{a^2 x^2}}}{5 x^4 \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}}",1,"(-4*a^4*Sqrt[c - c/(a^2*x^2)])/Sqrt[1 - a^2*x^2] - Sqrt[c - c/(a^2*x^2)]/(5*x^4*Sqrt[1 - a^2*x^2]) + (3*a*Sqrt[c - c/(a^2*x^2)])/(4*x^3*Sqrt[1 - a^2*x^2]) - (4*a^2*Sqrt[c - c/(a^2*x^2)])/(3*x^2*Sqrt[1 - a^2*x^2]) + (2*a^3*Sqrt[c - c/(a^2*x^2)])/(x*Sqrt[1 - a^2*x^2]) - (4*a^5*Sqrt[c - c/(a^2*x^2)]*x*Log[x])/Sqrt[1 - a^2*x^2] + (4*a^5*Sqrt[c - c/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6160, 6150, 88}"
789,1,53,0,0.1158954,"\int e^{-2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[(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",3,3,23,0.1304,1,"{6160, 6150, 64}"
790,1,54,0,0.1162213,"\int e^{2 p \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[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",3,3,23,0.1304,1,"{6160, 6150, 64}"
791,1,71,0,0.1333268,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2))^2,x]","\frac{c^2 2^{3-\frac{n}{2}} (a x+1)^{\frac{n+6}{2}} F_1\left(\frac{n+6}{2};\frac{n-4}{2},4;\frac{n+8}{2};\frac{1}{2} (a x+1),a x+1\right)}{a (n+6)}","-\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+10) (a x+1)^{\frac{n-4}{2}} (1-a x)^{3-\frac{n}{2}}}{6 a^3 x^2}-\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 \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,"(2^(3 - n/2)*c^2*(1 + a*x)^((6 + n)/2)*AppellF1[(6 + n)/2, (-4 + n)/2, 4, (8 + n)/2, (1 + a*x)/2, 1 + a*x])/(a*(6 + n))","C",3,3,22,0.1364,0,"{6157, 6150, 136}"
792,1,70,0,0.0968612,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2)),x]","-\frac{c 2^{2-\frac{n}{2}} (a x+1)^{\frac{n+4}{2}} F_1\left(\frac{n+4}{2};\frac{n-2}{2},2;\frac{n+6}{2};\frac{1}{2} (a x+1),a x+1\right)}{a (n+4)}","\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,"-((2^(2 - n/2)*c*(1 + a*x)^((4 + n)/2)*AppellF1[(4 + n)/2, (-2 + n)/2, 2, (6 + n)/2, (1 + a*x)/2, 1 + a*x])/(a*(4 + n)))","C",3,3,20,0.1500,0,"{6157, 6150, 136}"
793,1,125,0,0.1713886,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2)),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}+\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}","-\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 - n)*(1 + a*x)^(n/2))/(a*c*n*(1 - a*x)^(n/2))) + (x*(1 + a*x)^(n/2))/(c*(1 - a*x)^(n/2)) - (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(a*c*(1 - a*x)^(n/2))","A",5,5,22,0.2273,1,"{6157, 6150, 90, 79, 69}"
794,1,373,0,0.4230048,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2))^2,x]","-\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}","-\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 - n)*(3 + n)*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a*c^2*(2 - n)) + ((3 + n)*x*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/c^2 - (a^2*x^3*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/c^2 + ((1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a*c^2*(2 - n)) - (1 + a*x)^((-2 + n)/2)/(a*c^2*(1 - a*x)^(n/2)) - ((3 + n)*(2 - n^2)*(1 - a*x)^(-1 - n/2)*(1 + a*x)^(n/2))/(a*c^2*(4 - n^2)) - ((3 + n)*(2 - n^2)*(1 + a*x)^(n/2))/(a*c^2*n*(4 - n^2)*(1 - a*x)^(n/2)) - (2^(n/2)*n*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[(2 - n)/2, 1 - n/2, 2 - n/2, (1 - a*x)/2])/(a*c^2*(2 - n))","A",11,10,22,0.4545,1,"{6157, 6150, 100, 159, 89, 79, 69, 90, 45, 37}"
795,1,103,0,0.2060549,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^(n*ArcTanh[a*x])*(c - c/(a^2*x^2))^(3/2),x]","-\frac{a^2 2^{\frac{5}{2}-\frac{n}{2}} x^3 \left(c-\frac{c}{a^2 x^2}\right)^{3/2} (a x+1)^{\frac{n+5}{2}} F_1\left(\frac{n+5}{2};\frac{n-3}{2},3;\frac{n+7}{2};\frac{1}{2} (a x+1),a x+1\right)}{(n+5) \left(1-a^2 x^2\right)^{3/2}}","-\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{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}}-\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}}",1,"-((2^(5/2 - n/2)*a^2*(c - c/(a^2*x^2))^(3/2)*x^3*(1 + a*x)^((5 + n)/2)*AppellF1[(5 + n)/2, (-3 + n)/2, 3, (7 + n)/2, (1 + a*x)/2, 1 + a*x])/((5 + n)*(1 - a^2*x^2)^(3/2)))","C",3,3,24,0.1250,0,"{6160, 6150, 136}"
796,1,302,0,0.259879,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(n*ArcTanh[a*x])*Sqrt[c - c/(a^2*x^2)],x]","\frac{2 x \sqrt{c-\frac{c}{a^2 x^2}} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1}{2} (-n-1)} \, _2F_1\left(1,\frac{1}{2} (-n-1);\frac{1-n}{2};\frac{1-a x}{a x+1}\right)}{(n+1) \sqrt{1-a^2 x^2}}-\frac{2^{\frac{n+3}{2}} x \sqrt{c-\frac{c}{a^2 x^2}} (1-a x)^{\frac{1}{2} (-n-1)} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{1}{2} (-n-1);\frac{1-n}{2};\frac{1}{2} (1-a x)\right)}{(n+1) \sqrt{1-a^2 x^2}}+\frac{2^{\frac{n+3}{2}} x \sqrt{c-\frac{c}{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)}{(1-n) \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 + a*x)^((1 + n)/2)*Hypergeometric2F1[1, (-1 - n)/2, (1 - n)/2, (1 - a*x)/(1 + a*x)])/((1 + n)*Sqrt[1 - a^2*x^2]) - (2^((3 + n)/2)*Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x)^((-1 - n)/2)*Hypergeometric2F1[(-1 - n)/2, (-1 - n)/2, (1 - n)/2, (1 - a*x)/2])/((1 + n)*Sqrt[1 - a^2*x^2]) + (2^((3 + n)/2)*Sqrt[c - c/(a^2*x^2)]*x*(1 - a*x)^((1 - n)/2)*Hypergeometric2F1[(-1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/((1 - n)*Sqrt[1 - a^2*x^2])","A",7,5,24,0.2083,0,"{6160, 6150, 105, 69, 131}"
797,1,182,0,0.1895588,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^(n*ArcTanh[a*x])/Sqrt[c - c/(a^2*x^2)],x]","-\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}}}","-\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 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(a^2*(1 + n)*Sqrt[c - c/(a^2*x^2)]*x)) - (2^((3 + n)/2)*n*(1 - a*x)^((1 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(-1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/(a^2*(1 - n^2)*Sqrt[c - c/(a^2*x^2)]*x)","A",4,4,24,0.1667,1,"{6160, 6150, 79, 69}"
798,1,267,0,0.2911791,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2))^(3/2),x]","-\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}}-\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}}-\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}}",1,"-(((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(1 - a^2*x^2)^(3/2))/(a^2*(c - c/(a^2*x^2))^(3/2)*x)) + ((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(2 + 2*n + n^2 - a*n*(3 + 2*n)*x)*(1 - a^2*x^2)^(3/2))/(a^4*(1 - n^2)*(c - c/(a^2*x^2))^(3/2)*x^3) - (2^((-1 + n)/2)*n*(1 - a*x)^((3 - n)/2)*(1 - a^2*x^2)^(3/2)*Hypergeometric2F1[(3 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2])/(a^4*(3 - n)*(c - c/(a^2*x^2))^(3/2)*x^3)","A",5,5,24,0.2083,1,"{6160, 6150, 100, 145, 69}"
799,1,1039,0,0.7703485,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - c/(a^2*x^2))^(5/2),x]","-\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}","-\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,"((4 + n)*(1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^3*(3 + n)*(c - c/(a^2*x^2))^(5/2)*x^2) - ((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^2*(c - c/(a^2*x^2))^(5/2)*x) + (n*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(1 + n)*(c - c/(a^2*x^2))^(5/2)*x^5) - (3*(2 - n)*(4 + n)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(9 - n^2)*(c - c/(a^2*x^2))^(5/2)*x^5) - (3*(4 + n)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^5*(3 + n)*(c - c/(a^2*x^2))^(5/2)*x^4) - (2*n*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(1 - n^2)*(c - c/(a^2*x^2))^(5/2)*x^5) + (2*n*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(1 + n)*(3 - 4*n + n^2)*(c - c/(a^2*x^2))^(5/2)*x^5) - (3*n*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(1 + n)*(c - c/(a^2*x^2))^(5/2)*x^5) + (3*(4 + n)*(1 + 2*n - n^2)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(3 - n)*(1 + n)*(3 + n)*(c - c/(a^2*x^2))^(5/2)*x^5) + (3*n*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(1 - n^2)*(c - c/(a^2*x^2))^(5/2)*x^5) - (3*(4 + n)*(1 + 2*n - n^2)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(9 - 10*n^2 + n^4)*(c - c/(a^2*x^2))^(5/2)*x^5) + (3*n*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((1 + n)/2)*(1 - a^2*x^2)^(5/2))/(a^6*(1 + n)*(c - c/(a^2*x^2))^(5/2)*x^5) - (2^((3 + n)/2)*n*(1 - a*x)^((-1 - n)/2)*(1 - a^2*x^2)^(5/2)*Hypergeometric2F1[(-1 - n)/2, (-1 - n)/2, (1 - n)/2, (1 - a*x)/2])/(a^6*(1 + n)*(c - c/(a^2*x^2))^(5/2)*x^5)","A",18,11,24,0.4583,1,"{6160, 6150, 100, 159, 128, 45, 37, 69, 94, 90, 79}"
800,1,72,0,0.1283112,"\int e^{n \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[E^(n*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 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}","\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,"((c - c/(a^2*x^2))^p*x*AppellF1[1 - 2*p, (n - 2*p)/2, -n/2 - p, 2 - 2*p, a*x, -(a*x)])/((1 - 2*p)*(1 - a^2*x^2)^p)","A",3,3,22,0.1364,1,"{6160, 6150, 133}"
801,1,339,0,0.3427466,"\int e^{4 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[E^(4*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\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{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}+\frac{2 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^p}{(1-p) (1-a x) (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{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}+\frac{2 a x^2 \left(c-\frac{c}{a^2 x^2}\right)^p}{(1-p) (1-a x) (a x+1)}",1,"(2*a*(c - c/(a^2*x^2))^p*x^2)/((1 - p)*(1 - a*x)*(1 + a*x)) + ((c - c/(a^2*x^2))^p*x*Hypergeometric2F1[(1 - 2*p)/2, 2 - p, (3 - 2*p)/2, a^2*x^2])/((1 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) + (6*a^2*(c - c/(a^2*x^2))^p*x^3*Hypergeometric2F1[(3 - 2*p)/2, 2 - p, (5 - 2*p)/2, a^2*x^2])/((3 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) + (a^4*(c - c/(a^2*x^2))^p*x^5*Hypergeometric2F1[(5 - 2*p)/2, 2 - p, (7 - 2*p)/2, a^2*x^2])/((5 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) + (2*a^3*(c - c/(a^2*x^2))^p*x^4*Hypergeometric2F1[2 - p, 2 - p, 3 - p, a^2*x^2])/((2 - p)*(1 - a*x)^p*(1 + a*x)^p)","A",13,6,22,0.2727,1,"{6159, 6129, 127, 95, 125, 364}"
802,1,217,0,0.3300869,"\int e^{3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[E^(3*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\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 (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{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}}","\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 (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{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)/((1 - 2*p)*Sqrt[1 - a^2*x^2]) - (a*(c - c/(a^2*x^2))^p*x^2)/Sqrt[1 - a^2*x^2] + (3*a^2*(c - c/(a^2*x^2))^p*x^3*Hypergeometric2F1[(3 - 2*p)/2, 3/2 - p, (5 - 2*p)/2, a^2*x^2])/((3 - 2*p)*(1 - a^2*x^2)^p) + (a*(5 - 2*p)*(c - c/(a^2*x^2))^p*x^2*Hypergeometric2F1[1 - p, 3/2 - p, 2 - p, a^2*x^2])/(2*(1 - p)*(1 - a^2*x^2)^p)","A",7,6,22,0.2727,1,"{6160, 6148, 1809, 1808, 364, 807}"
803,1,217,0,0.2605791,"\int e^{2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[E^(2*ArcTanh[a*x])*(c - c/(a^2*x^2))^p,x]","\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^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}+\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{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^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}+\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}",1,"((c - c/(a^2*x^2))^p*x*Hypergeometric2F1[(1 - 2*p)/2, 1 - p, (3 - 2*p)/2, a^2*x^2])/((1 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) + (a^2*(c - c/(a^2*x^2))^p*x^3*Hypergeometric2F1[(3 - 2*p)/2, 1 - p, (5 - 2*p)/2, a^2*x^2])/((3 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) + (a*(c - c/(a^2*x^2))^p*x^2*Hypergeometric2F1[1 - p, 1 - p, 2 - p, a^2*x^2])/((1 - p)*(1 - a*x)^p*(1 + a*x)^p)","A",10,5,22,0.2273,1,"{6159, 6129, 127, 125, 364}"
804,1,137,0,0.1329281,"\int e^{\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[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 \, _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)}","\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*Hypergeometric2F1[(1 - 2*p)/2, 1/2 - p, (3 - 2*p)/2, a^2*x^2])/((1 - 2*p)*(1 - a^2*x^2)^p) + (a*(c - c/(a^2*x^2))^p*x^2*Hypergeometric2F1[1/2 - p, 1 - p, 2 - p, a^2*x^2])/(2*(1 - p)*(1 - a^2*x^2)^p)","A",5,4,20,0.2000,1,"{6160, 6148, 808, 364}"
805,1,137,0,0.13672,"\int e^{-\tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[(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 \, _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)}","\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*Hypergeometric2F1[(1 - 2*p)/2, 1/2 - p, (3 - 2*p)/2, a^2*x^2])/((1 - 2*p)*(1 - a^2*x^2)^p) - (a*(c - c/(a^2*x^2))^p*x^2*Hypergeometric2F1[1/2 - p, 1 - p, 2 - p, a^2*x^2])/(2*(1 - p)*(1 - a^2*x^2)^p)","A",5,4,22,0.1818,1,"{6160, 6149, 808, 364}"
806,1,218,0,0.2636545,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[(c - c/(a^2*x^2))^p/E^(2*ArcTanh[a*x]),x]","\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^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}-\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{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^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}-\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}",1,"((c - c/(a^2*x^2))^p*x*Hypergeometric2F1[(1 - 2*p)/2, 1 - p, (3 - 2*p)/2, a^2*x^2])/((1 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) + (a^2*(c - c/(a^2*x^2))^p*x^3*Hypergeometric2F1[(3 - 2*p)/2, 1 - p, (5 - 2*p)/2, a^2*x^2])/((3 - 2*p)*(1 - a*x)^p*(1 + a*x)^p) - (a*(c - c/(a^2*x^2))^p*x^2*Hypergeometric2F1[1 - p, 1 - p, 2 - p, a^2*x^2])/((1 - p)*(1 - a*x)^p*(1 + a*x)^p)","A",10,5,22,0.2273,1,"{6159, 6129, 127, 125, 364}"
807,1,216,0,0.3217886,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[(c - c/(a^2*x^2))^p/E^(3*ArcTanh[a*x]),x]","\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 (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{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}}","\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 (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{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)/((1 - 2*p)*Sqrt[1 - a^2*x^2]) + (a*(c - c/(a^2*x^2))^p*x^2)/Sqrt[1 - a^2*x^2] + (3*a^2*(c - c/(a^2*x^2))^p*x^3*Hypergeometric2F1[(3 - 2*p)/2, 3/2 - p, (5 - 2*p)/2, a^2*x^2])/((3 - 2*p)*(1 - a^2*x^2)^p) - (a*(5 - 2*p)*(c - c/(a^2*x^2))^p*x^2*Hypergeometric2F1[1 - p, 3/2 - p, 2 - p, a^2*x^2])/(2*(1 - p)*(1 - a^2*x^2)^p)","A",7,6,22,0.2727,1,"{6160, 6149, 1809, 1808, 364, 807}"
808,1,240,0,0.3967525,"\int e^{\tanh ^{-1}(x)} x \sqrt{1+x} \sin (x) \, dx","Int[E^ArcTanh[x]*x*Sqrt[1 + x]*Sin[x],x]","-2 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-3 \sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","-2 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-3 \sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"3*Sqrt[1 - x]*Cos[x] - (1 - x)^(3/2)*Cos[x] - 3*Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]] - (3*Sqrt[Pi/2]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]])/2 + 2*Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]] + (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1])/2 - 2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - 3*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - (3*Sqrt[1 - x]*Sin[x])/2","A",16,8,15,0.5333,1,"{6129, 6742, 3353, 3352, 3351, 3385, 3354, 3386}"
809,1,141,0,0.1700364,"\int e^{\tanh ^{-1}(x)} \sqrt{1+x} \sin (x) \, dx","Int[E^ArcTanh[x]*Sqrt[1 + x]*Sin[x],x]","-2 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","-2 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"Sqrt[1 - x]*Cos[x] - Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]] + 2*Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]] - 2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1]","A",11,7,14,0.5000,1,"{6129, 6742, 3353, 3352, 3351, 3385, 3354}"
810,1,163,0,0.2979273,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} x \sin (x) \, dx","Int[E^ArcTanh[x]*Sqrt[1 - x]*x*Sin[x],x]","\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)-\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"Sqrt[1 + x]*Cos[x] - (1 + x)^(3/2)*Cos[x] - Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]] - (3*Sqrt[Pi/2]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]])/2 + (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1])/2 - Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1] + (3*Sqrt[1 + x]*Sin[x])/2","A",13,8,17,0.4706,1,"{6129, 6742, 3385, 3354, 3352, 3351, 3386, 3353}"
811,1,72,0,0.122283,"\int e^{\tanh ^{-1}(x)} \sqrt{1-x} \sin (x) \, dx","Int[E^ArcTanh[x]*Sqrt[1 - x]*Sin[x],x]","\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"-(Sqrt[1 + x]*Cos[x]) + Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]] + Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1]","A",7,7,16,0.4375,1,"{6129, 3296, 3306, 3305, 3351, 3304, 3352}"
812,1,335,0,0.4756614,"\int e^{\tanh ^{-1}(x)} x (1+x)^{3/2} \sin (x) \, dx","Int[E^ArcTanh[x]*x*(1 + x)^(3/2)*Sin[x],x]","-4 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-4 \sqrt{2 \pi } \cos (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{4} \sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","-4 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-4 \sqrt{2 \pi } \cos (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{15}{4} \sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"(17*Sqrt[1 - x]*Cos[x])/4 - 5*(1 - x)^(3/2)*Cos[x] + (1 - x)^(5/2)*Cos[x] + (15*Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]])/4 - 4*Sqrt[2*Pi]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]] - (15*Sqrt[Pi/2]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]])/2 + 4*Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]] + (15*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1])/2 - 4*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] + (15*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1])/4 - 4*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - (15*Sqrt[1 - x]*Sin[x])/2 + (5*(1 - x)^(3/2)*Sin[x])/2","A",22,8,15,0.5333,1,"{6129, 6742, 3353, 3352, 3351, 3385, 3354, 3386}"
813,1,236,0,0.262805,"\int e^{\tanh ^{-1}(x)} (1+x)^{3/2} \sin (x) \, dx","Int[E^ArcTanh[x]*(1 + x)^(3/2)*Sin[x],x]","-4 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-2 \sqrt{2 \pi } \cos (1) \text{FresnelC}\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)","-4 \sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)+\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-2 \sqrt{2 \pi } \cos (1) \text{FresnelC}\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,"4*Sqrt[1 - x]*Cos[x] - (1 - x)^(3/2)*Cos[x] - 2*Sqrt[2*Pi]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]] - (3*Sqrt[Pi/2]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]])/2 + 4*Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]] + (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1])/2 - 4*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - 2*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - (3*Sqrt[1 - x]*Sin[x])/2","A",16,8,14,0.5714,1,"{6129, 6742, 3353, 3352, 3351, 3385, 3354, 3386}"
814,1,193,0,0.4012797,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} x \sin (x) \, dx","Int[E^ArcTanh[x]*(1 - x)^(3/2)*x*Sin[x],x]","\frac{9}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\frac{7}{4} \sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","\frac{9}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\frac{7}{4} \sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"(-7*Sqrt[1 + x]*Cos[x])/4 - 3*(1 + x)^(3/2)*Cos[x] + (1 + x)^(5/2)*Cos[x] + (7*Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]])/4 - (9*Sqrt[Pi/2]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]])/2 + (9*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1])/2 + (7*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1])/4 + (9*Sqrt[1 + x]*Sin[x])/2 - (5*(1 + x)^(3/2)*Sin[x])/2","A",19,8,17,0.4706,1,"{6129, 6742, 3385, 3354, 3352, 3351, 3386, 3353}"
815,1,157,0,0.2325285,"\int e^{\tanh ^{-1}(x)} (1-x)^{3/2} \sin (x) \, dx","Int[E^ArcTanh[x]*(1 - x)^(3/2)*Sin[x],x]","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\sqrt{2 \pi } \cos (1) \text{FresnelC}\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)","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x+1}\right)+\sqrt{2 \pi } \cos (1) \text{FresnelC}\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,"-2*Sqrt[1 + x]*Cos[x] + (1 + x)^(3/2)*Cos[x] + Sqrt[2*Pi]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]] + (3*Sqrt[Pi/2]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]])/2 - (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1])/2 + Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[1 + x]]*Sin[1] - (3*Sqrt[1 + x]*Sin[x])/2","A",13,8,16,0.5000,1,"{6129, 6742, 3385, 3354, 3352, 3351, 3386, 3353}"
816,1,140,0,0.187591,"\int \frac{e^{\tanh ^{-1}(x)} x \sin (x)}{\sqrt{1+x}} \, dx","Int[(E^ArcTanh[x]*x*Sin[x])/Sqrt[1 + x],x]","-\sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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)","-\sqrt{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{\frac{\pi }{2}} \cos (1) \text{FresnelC}\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,"Sqrt[1 - x]*Cos[x] - Sqrt[Pi/2]*Cos[1]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]] + Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]] - Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1] - Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1]","A",11,7,15,0.4667,1,"{6129, 6742, 3353, 3352, 3351, 3385, 3354}"
817,1,62,0,0.1101646,"\int \frac{e^{\tanh ^{-1}(x)} \sin (x)}{\sqrt{1+x}} \, dx","Int[(E^ArcTanh[x]*Sin[x])/Sqrt[1 + x],x]","\sqrt{2 \pi } \cos (1) S\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)-\sqrt{2 \pi } \sin (1) \text{FresnelC}\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{2 \pi } \sin (1) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{1-x}\right)",1,"Sqrt[2*Pi]*Cos[1]*FresnelS[Sqrt[2/Pi]*Sqrt[1 - x]] - Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[1 - x]]*Sin[1]","A",6,6,14,0.4286,1,"{6129, 3306, 3305, 3351, 3304, 3352}"
818,1,156,0,0.1597056,"\int e^{\tanh ^{-1}(a+b x)} x^3 \, dx","Int[E^ArcTanh[a + b*x]*x^3,x]","-\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}","-\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,"-((3 - 12*a + 12*a^2 - 8*a^3)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(8*b^4) - (x^2*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(4*b^2) - (Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2)*(7 - 10*a + 18*a^2 + 2*(1 - 6*a)*b*x))/(24*b^4) + ((3 - 12*a + 12*a^2 - 8*a^3)*ArcSin[a + b*x])/(8*b^4)","A",7,7,12,0.5833,1,"{6163, 100, 147, 50, 53, 619, 216}"
819,1,130,0,0.1667572,"\int e^{\tanh ^{-1}(a+b x)} x^2 \, dx","Int[E^ArcTanh[a + b*x]*x^2,x]","-\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{x \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{3 b^2}-\frac{(1-4 a) \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{6 b^3}","-\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{x \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{3 b^2}-\frac{(1-4 a) \sqrt{-a-b x+1} (a+b x+1)^{3/2}}{6 b^3}",1,"-((1 - 2*a + 2*a^2)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^3) - ((1 - 4*a)*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(6*b^3) - (x*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(3*b^2) + ((1 - 2*a + 2*a^2)*ArcSin[a + b*x])/(2*b^3)","A",7,7,12,0.5833,1,"{6163, 90, 80, 50, 53, 619, 216}"
820,1,84,0,0.0639097,"\int e^{\tanh ^{-1}(a+b x)} x \, dx","Int[E^ArcTanh[a + b*x]*x,x]","-\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}","-\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,"-((1 - 2*a)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^2) - (Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(2*b^2) + ((1 - 2*a)*ArcSin[a + b*x])/(2*b^2)","A",6,6,10,0.6000,1,"{6163, 80, 50, 53, 619, 216}"
821,1,39,0,0.0264667,"\int e^{\tanh ^{-1}(a+b x)} \, dx","Int[E^ArcTanh[a + b*x],x]","\frac{\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}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{b}",1,"-((Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/b) + ArcSin[a + b*x]/b","A",5,5,8,0.6250,1,"{6161, 50, 53, 619, 216}"
822,1,64,0,0.0754015,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x} \, dx","Int[E^ArcTanh[a + b*x]/x,x]","\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}}","\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,"ArcSin[a + b*x] - (2*(1 + a)*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/Sqrt[1 - a^2]","A",7,7,12,0.5833,1,"{6163, 105, 53, 619, 216, 93, 208}"
823,1,98,0,0.0559057,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[E^ArcTanh[a + b*x]/x^2,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)}{(1-a) \sqrt{1-a^2}}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{(1-a) 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)}{(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]*Sqrt[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)*Sqrt[1 - a^2])","A",4,4,12,0.3333,1,"{6163, 94, 93, 208}"
824,1,162,0,0.1083953,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[E^ArcTanh[a + b*x]/x^3,x]","-\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}","-\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 + 2*a)*b*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*(1 - a)^2*(1 + a)*x) - (Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(2*(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)^2*(1 + a)*Sqrt[1 - a^2])","A",5,5,12,0.4167,1,"{6163, 96, 94, 93, 208}"
825,1,213,0,0.1826271,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^4} \, dx","Int[E^ArcTanh[a + b*x]/x^4,x]","-\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{(2 a+3) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a)^2 (a+1) x^2}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{3 (1-a) 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{(2 a+3) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a)^2 (a+1) x^2}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{3 (1-a) x^3}",1,"-(Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(3*(1 - a)*x^3) - ((3 + 2*a)*b*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(6*(1 - a)^2*(1 + a)*x^2) - ((4 + a)*(1 + 2*a)*b^2*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(6*(1 - a)^3*(1 + a)^2*x) - ((1 + 2*a + 2*a^2)*b^3*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)*(1 - a^2)^(5/2))","A",7,6,12,0.5000,1,"{6163, 99, 151, 12, 93, 208}"
826,1,83,0,0.0834926,"\int e^{2 \tanh ^{-1}(a+b x)} x^4 \, dx","Int[E^(2*ArcTanh[a + b*x])*x^4,x]","-\frac{2 (1-a) x^3}{3 b^2}-\frac{(1-a)^2 x^2}{b^3}-\frac{2 (1-a)^3 x}{b^4}-\frac{2 (1-a)^4 \log (-a-b x+1)}{b^5}-\frac{x^4}{2 b}-\frac{x^5}{5}","-\frac{2 (1-a) x^3}{3 b^2}-\frac{(1-a)^2 x^2}{b^3}-\frac{2 (1-a)^3 x}{b^4}-\frac{2 (1-a)^4 \log (-a-b x+1)}{b^5}-\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",3,2,14,0.1429,1,"{6163, 77}"
827,1,66,0,0.0600754,"\int e^{2 \tanh ^{-1}(a+b x)} x^3 \, dx","Int[E^(2*ArcTanh[a + b*x])*x^3,x]","-\frac{(1-a) x^2}{b^2}-\frac{2 (1-a)^2 x}{b^3}-\frac{2 (1-a)^3 \log (-a-b x+1)}{b^4}-\frac{2 x^3}{3 b}-\frac{x^4}{4}","-\frac{(1-a) x^2}{b^2}-\frac{2 (1-a)^2 x}{b^3}-\frac{2 (1-a)^3 \log (-a-b x+1)}{b^4}-\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",3,2,14,0.1429,1,"{6163, 77}"
828,1,49,0,0.0506131,"\int e^{2 \tanh ^{-1}(a+b x)} x^2 \, dx","Int[E^(2*ArcTanh[a + b*x])*x^2,x]","-\frac{2 (1-a) x}{b^2}-\frac{2 (1-a)^2 \log (-a-b x+1)}{b^3}-\frac{x^2}{b}-\frac{x^3}{3}","-\frac{2 (1-a) x}{b^2}-\frac{2 (1-a)^2 \log (-a-b x+1)}{b^3}-\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",3,2,14,0.1429,1,"{6163, 77}"
829,1,34,0,0.0306465,"\int e^{2 \tanh ^{-1}(a+b x)} x \, dx","Int[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",3,2,12,0.1667,1,"{6163, 77}"
830,1,19,0,0.0124833,"\int e^{2 \tanh ^{-1}(a+b x)} \, dx","Int[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",3,2,10,0.2000,1,"{6161, 43}"
831,1,33,0,0.0377747,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x} \, dx","Int[E^(2*ArcTanh[a + b*x])/x,x]","\frac{(a+1) \log (x)}{1-a}-\frac{2 \log (-a-b x+1)}{1-a}","\frac{(a+1) \log (x)}{1-a}-\frac{2 \log (-a-b x+1)}{1-a}",1,"((1 + a)*Log[x])/(1 - a) - (2*Log[1 - a - b*x])/(1 - a)","A",3,2,14,0.1429,1,"{6163, 72}"
832,1,48,0,0.0408594,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[E^(2*ArcTanh[a + b*x])/x^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}","\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)/((1 - a)*x)) + (2*b*Log[x])/(1 - a)^2 - (2*b*Log[1 - a - b*x])/(1 - a)^2","A",3,2,14,0.1429,1,"{6163, 77}"
833,1,67,0,0.050526,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[E^(2*ArcTanh[a + b*x])/x^3,x]","\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}","\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)/(2*(1 - a)*x^2) - (2*b)/((1 - a)^2*x) + (2*b^2*Log[x])/(1 - a)^3 - (2*b^2*Log[1 - a - b*x])/(1 - a)^3","A",3,2,14,0.1429,1,"{6163, 77}"
834,1,82,0,0.0616321,"\int \frac{e^{2 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Int[E^(2*ArcTanh[a + b*x])/x^4,x]","-\frac{2 b^2}{(1-a)^3 x}+\frac{2 b^3 \log (x)}{(1-a)^4}-\frac{2 b^3 \log (-a-b x+1)}{(1-a)^4}-\frac{b}{(1-a)^2 x^2}-\frac{a+1}{3 (1-a) x^3}","-\frac{2 b^2}{(1-a)^3 x}+\frac{2 b^3 \log (x)}{(1-a)^4}-\frac{2 b^3 \log (-a-b x+1)}{(1-a)^4}-\frac{b}{(1-a)^2 x^2}-\frac{a+1}{3 (1-a) x^3}",1,"-(1 + a)/(3*(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",3,2,14,0.1429,1,"{6163, 77}"
835,1,187,0,0.1822046,"\int e^{3 \tanh ^{-1}(a+b x)} x^3 \, dx","Int[E^(3*ArcTanh[a + b*x])*x^3,x]","\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}}","\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,"(3*(17 - 44*a + 36*a^2 - 8*a^3)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(8*b^4) + (2*x^3*(1 + a + b*x)^(3/2))/(b*Sqrt[1 - a - b*x]) + (9*x^2*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(4*b^2) + (Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2)*(29 - 54*a + 22*a^2 + 2*(11 - 10*a)*b*x))/(8*b^4) - (3*(17 - 44*a + 36*a^2 - 8*a^3)*ArcSin[a + b*x])/(8*b^4)","A",8,8,14,0.5714,1,"{6163, 97, 153, 147, 50, 53, 619, 216}"
836,1,168,0,0.1913077,"\int e^{3 \tanh ^{-1}(a+b x)} x^2 \, dx","Int[E^(3*ArcTanh[a + b*x])*x^2,x]","\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}}","\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,"((11 - 18*a + 6*a^2)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^3) + ((11 - 18*a + 6*a^2)*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(6*b^3) + ((1 - a)^2*(1 + a + b*x)^(5/2))/(b^3*Sqrt[1 - a - b*x]) + (Sqrt[1 - a - b*x]*(1 + a + b*x)^(5/2))/(3*b^3) - ((11 - 18*a + 6*a^2)*ArcSin[a + b*x])/(2*b^3)","A",8,7,14,0.5000,1,"{6163, 89, 80, 50, 53, 619, 216}"
837,1,121,0,0.0955477,"\int e^{3 \tanh ^{-1}(a+b x)} x \, dx","Int[E^(3*ArcTanh[a + b*x])*x,x]","\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}","\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,"(3*(3 - 2*a)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^2) + ((3 - 2*a)*Sqrt[1 - a - b*x]*(1 + a + b*x)^(3/2))/(2*b^2) + ((1 - a)*(1 + a + b*x)^(5/2))/(b^2*Sqrt[1 - a - b*x]) - (3*(3 - 2*a)*ArcSin[a + b*x])/(2*b^2)","A",7,6,12,0.5000,1,"{6163, 78, 50, 53, 619, 216}"
838,1,68,0,0.0343045,"\int e^{3 \tanh ^{-1}(a+b x)} \, dx","Int[E^(3*ArcTanh[a + b*x]),x]","\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}","\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,"(3*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/b + (2*(1 + a + b*x)^(3/2))/(b*Sqrt[1 - a - b*x]) - (3*ArcSin[a + b*x])/b","A",6,6,10,0.6000,1,"{6161, 47, 50, 53, 619, 216}"
839,1,107,0,0.0908619,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x} \, dx","Int[E^(3*ArcTanh[a + b*x])/x,x]","-\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)","-\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,"(4*Sqrt[1 + a + b*x])/((1 - a)*Sqrt[1 - a - b*x]) - ArcSin[a + b*x] - (2*(1 + a)^2*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)*Sqrt[1 - a^2])","A",8,8,14,0.5714,1,"{6163, 98, 157, 53, 619, 216, 93, 208}"
840,1,134,0,0.0753951,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[E^(3*ArcTanh[a + b*x])/x^2,x]","-\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}}","-\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,"(6*b*Sqrt[1 + a + b*x])/((1 - a)^2*Sqrt[1 - a - b*x]) - (1 + a + b*x)^(3/2)/((1 - a)*x*Sqrt[1 - a - b*x]) - (6*(1 + a)*b*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)^2*Sqrt[1 - a^2])","A",5,4,14,0.2857,1,"{6163, 94, 93, 208}"
841,1,202,0,0.1221699,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[E^(3*ArcTanh[a + b*x])/x^3,x]","-\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}}","-\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,"(3*(3 + 2*a)*b^2*Sqrt[1 + a + b*x])/((1 - a)^3*(1 + a)*Sqrt[1 - a - b*x]) - ((3 + 2*a)*b*(1 + a + b*x)^(3/2))/(2*(1 - a)^2*(1 + a)*x*Sqrt[1 - a - b*x]) - (1 + a + b*x)^(5/2)/(2*(1 - a^2)*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)^3*Sqrt[1 - a^2])","A",6,5,14,0.3571,1,"{6163, 96, 94, 93, 208}"
842,1,260,0,0.2095205,"\int \frac{e^{3 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Int[E^(3*ArcTanh[a + b*x])/x^4,x]","\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{7 b \sqrt{a+b x+1}}{6 (1-a)^2 x^2 \sqrt{-a-b x+1}}-\frac{(a+1) \sqrt{a+b x+1}}{3 (1-a) 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{7 b \sqrt{a+b x+1}}{6 (1-a)^2 x^2 \sqrt{-a-b x+1}}-\frac{(a+1) \sqrt{a+b x+1}}{3 (1-a) x^3 \sqrt{-a-b x+1}}",1,"((52 + 51*a + 2*a^2)*b^3*Sqrt[1 + a + b*x])/(6*(1 - a)^4*(1 + a)*Sqrt[1 - a - b*x]) - ((1 + a)*Sqrt[1 + a + b*x])/(3*(1 - a)*x^3*Sqrt[1 - a - b*x]) - (7*b*Sqrt[1 + a + b*x])/(6*(1 - a)^2*x^2*Sqrt[1 - a - b*x]) - ((19 + 16*a)*b^2*Sqrt[1 + a + b*x])/(6*(1 - a)^3*(1 + a)*x*Sqrt[1 - a - b*x]) - ((11 + 18*a + 6*a^2)*b^3*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)^4*(1 + a)*Sqrt[1 - a^2])","A",8,7,14,0.5000,1,"{6163, 98, 151, 152, 12, 93, 208}"
843,1,156,0,0.1660454,"\int e^{-\tanh ^{-1}(a+b x)} x^3 \, dx","Int[x^3/E^ArcTanh[a + b*x],x]","-\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}","-\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,"-((3 + 12*a + 12*a^2 + 8*a^3)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(8*b^4) - (x^2*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(4*b^2) - ((1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x]*(7 + 10*a + 18*a^2 - 2*(1 + 6*a)*b*x))/(24*b^4) - ((3 + 12*a + 12*a^2 + 8*a^3)*ArcSin[a + b*x])/(8*b^4)","A",7,7,14,0.5000,1,"{6163, 100, 147, 50, 53, 619, 216}"
844,1,130,0,0.1457556,"\int e^{-\tanh ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^ArcTanh[a + b*x],x]","\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{x \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{3 b^2}+\frac{(4 a+1) \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{6 b^3}","\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{x \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{3 b^2}+\frac{(4 a+1) \sqrt{a+b x+1} (-a-b x+1)^{3/2}}{6 b^3}",1,"((1 + 2*a + 2*a^2)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^3) + ((1 + 4*a)*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(6*b^3) - (x*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(3*b^2) + ((1 + 2*a + 2*a^2)*ArcSin[a + b*x])/(2*b^3)","A",7,7,14,0.5000,1,"{6163, 90, 80, 50, 53, 619, 216}"
845,1,84,0,0.0631693,"\int e^{-\tanh ^{-1}(a+b x)} x \, dx","Int[x/E^ArcTanh[a + b*x],x]","-\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}","-\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,"-((1 + 2*a)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^2) - ((1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(2*b^2) - ((1 + 2*a)*ArcSin[a + b*x])/(2*b^2)","A",6,6,12,0.5000,1,"{6163, 80, 50, 53, 619, 216}"
846,1,38,0,0.0281589,"\int e^{-\tanh ^{-1}(a+b x)} \, dx","Int[E^(-ArcTanh[a + b*x]),x]","\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{b}+\frac{\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]*Sqrt[1 + a + b*x])/b + ArcSin[a + b*x]/b","A",5,5,10,0.5000,1,"{6161, 50, 53, 619, 216}"
847,1,68,0,0.0601839,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^ArcTanh[a + b*x]*x),x]","-\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)","-\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,"-ArcSin[a + b*x] - (2*(1 - a)*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/Sqrt[1 - a^2]","A",7,7,14,0.5000,1,"{6163, 105, 53, 619, 216, 93, 208}"
848,1,94,0,0.0567481,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^ArcTanh[a + b*x]*x^2),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}","\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]*Sqrt[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)*Sqrt[1 - a^2])","A",4,4,14,0.2857,1,"{6163, 94, 93, 208}"
849,1,162,0,0.0979128,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[1/(E^ArcTanh[a + b*x]*x^3),x]","-\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}","-\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*a)*b*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*(1 - a)*(1 + a)^2*x) - ((1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(2*(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)*(1 + a)^2*Sqrt[1 - a^2])","A",5,5,14,0.3571,1,"{6163, 96, 94, 93, 208}"
850,1,210,0,0.1679322,"\int \frac{e^{-\tanh ^{-1}(a+b x)}}{x^4} \, dx","Int[1/(E^ArcTanh[a + b*x]*x^4),x]","\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{(3-2 a) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a) (a+1)^2 x^2}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{3 (a+1) 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{(3-2 a) b \sqrt{-a-b x+1} \sqrt{a+b x+1}}{6 (1-a) (a+1)^2 x^2}-\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1}}{3 (a+1) x^3}",1,"-(Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(3*(1 + a)*x^3) + ((3 - 2*a)*b*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(6*(1 - a)*(1 + a)^2*x^2) - ((1 - 2*a)*(4 - a)*b^2*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(6*(1 - a)^2*(1 + a)^3*x) + ((1 - 2*a + 2*a^2)*b^3*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 + a)*(1 - a^2)^(5/2))","A",7,6,14,0.4286,1,"{6163, 99, 151, 12, 93, 208}"
851,1,71,0,0.0785129,"\int e^{-2 \tanh ^{-1}(a+b x)} x^4 \, dx","Int[x^4/E^(2*ArcTanh[a + b*x]),x]","-\frac{2 (a+1) x^3}{3 b^2}+\frac{(a+1)^2 x^2}{b^3}-\frac{2 (a+1)^3 x}{b^4}+\frac{2 (a+1)^4 \log (a+b x+1)}{b^5}+\frac{x^4}{2 b}-\frac{x^5}{5}","-\frac{2 (a+1) x^3}{3 b^2}+\frac{(a+1)^2 x^2}{b^3}-\frac{2 (a+1)^3 x}{b^4}+\frac{2 (a+1)^4 \log (a+b x+1)}{b^5}+\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",3,2,14,0.1429,1,"{6163, 77}"
852,1,57,0,0.0559445,"\int e^{-2 \tanh ^{-1}(a+b x)} x^3 \, dx","Int[x^3/E^(2*ArcTanh[a + b*x]),x]","-\frac{(a+1) x^2}{b^2}+\frac{2 (a+1)^2 x}{b^3}-\frac{2 (a+1)^3 \log (a+b x+1)}{b^4}+\frac{2 x^3}{3 b}-\frac{x^4}{4}","-\frac{(a+1) x^2}{b^2}+\frac{2 (a+1)^2 x}{b^3}-\frac{2 (a+1)^3 \log (a+b x+1)}{b^4}+\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",3,2,14,0.1429,1,"{6163, 77}"
853,1,41,0,0.0456562,"\int e^{-2 \tanh ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^(2*ArcTanh[a + b*x]),x]","-\frac{2 (a+1) x}{b^2}+\frac{2 (a+1)^2 \log (a+b x+1)}{b^3}+\frac{x^2}{b}-\frac{x^3}{3}","-\frac{2 (a+1) x}{b^2}+\frac{2 (a+1)^2 \log (a+b x+1)}{b^3}+\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",3,2,14,0.1429,1,"{6163, 77}"
854,1,29,0,0.0317985,"\int e^{-2 \tanh ^{-1}(a+b x)} x \, dx","Int[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",3,2,12,0.1667,1,"{6163, 77}"
855,1,16,0,0.0121516,"\int e^{-2 \tanh ^{-1}(a+b x)} \, dx","Int[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",3,2,10,0.2000,1,"{6161, 43}"
856,1,28,0,0.0346215,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^(2*ArcTanh[a + b*x])*x),x]","\frac{(1-a) \log (x)}{a+1}-\frac{2 \log (a+b x+1)}{a+1}","\frac{(1-a) \log (x)}{a+1}-\frac{2 \log (a+b x+1)}{a+1}",1,"((1 - a)*Log[x])/(1 + a) - (2*Log[1 + a + b*x])/(1 + a)","A",3,2,14,0.1429,1,"{6163, 72}"
857,1,41,0,0.043266,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^(2*ArcTanh[a + b*x])*x^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}","-\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)/((1 + a)*x)) - (2*b*Log[x])/(1 + a)^2 + (2*b*Log[1 + a + b*x])/(1 + a)^2","A",3,2,14,0.1429,1,"{6163, 77}"
858,1,58,0,0.0498517,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[1/(E^(2*ArcTanh[a + b*x])*x^3),x]","\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}","\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)/(2*(1 + a)*x^2) + (2*b)/((1 + a)^2*x) + (2*b^2*Log[x])/(1 + a)^3 - (2*b^2*Log[1 + a + b*x])/(1 + a)^3","A",3,2,14,0.1429,1,"{6163, 77}"
859,1,70,0,0.0582411,"\int \frac{e^{-2 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Int[1/(E^(2*ArcTanh[a + b*x])*x^4),x]","-\frac{2 b^2}{(a+1)^3 x}-\frac{2 b^3 \log (x)}{(a+1)^4}+\frac{2 b^3 \log (a+b x+1)}{(a+1)^4}+\frac{b}{(a+1)^2 x^2}-\frac{1-a}{3 (a+1) x^3}","-\frac{2 b^2}{(a+1)^3 x}-\frac{2 b^3 \log (x)}{(a+1)^4}+\frac{2 b^3 \log (a+b x+1)}{(a+1)^4}+\frac{b}{(a+1)^2 x^2}-\frac{1-a}{3 (a+1) x^3}",1,"-(1 - a)/(3*(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",3,2,14,0.1429,1,"{6163, 77}"
860,1,187,0,0.1877654,"\int e^{-3 \tanh ^{-1}(a+b x)} x^3 \, dx","Int[x^3/E^(3*ArcTanh[a + b*x]),x]","\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}}","\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,"(-2*x^3*(1 - a - b*x)^(3/2))/(b*Sqrt[1 + a + b*x]) + (3*(17 + 44*a + 36*a^2 + 8*a^3)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(8*b^4) + (9*x^2*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(4*b^2) + ((1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x]*(29 + 54*a + 22*a^2 - 2*(11 + 10*a)*b*x))/(8*b^4) + (3*(17 + 44*a + 36*a^2 + 8*a^3)*ArcSin[a + b*x])/(8*b^4)","A",8,8,14,0.5714,1,"{6163, 97, 153, 147, 50, 53, 619, 216}"
861,1,167,0,0.2006239,"\int e^{-3 \tanh ^{-1}(a+b x)} x^2 \, dx","Int[x^2/E^(3*ArcTanh[a + b*x]),x]","-\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}}","-\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 + a)^2*(1 - a - b*x)^(5/2))/(b^3*Sqrt[1 + a + b*x])) - ((11 + 18*a + 6*a^2)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^3) - ((11 + 18*a + 6*a^2)*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(6*b^3) - ((1 - a - b*x)^(5/2)*Sqrt[1 + a + b*x])/(3*b^3) - ((11 + 18*a + 6*a^2)*ArcSin[a + b*x])/(2*b^3)","A",8,7,14,0.5000,1,"{6163, 89, 80, 50, 53, 619, 216}"
862,1,119,0,0.0921294,"\int e^{-3 \tanh ^{-1}(a+b x)} x \, dx","Int[x/E^(3*ArcTanh[a + b*x]),x]","\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}","\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,"((1 + a)*(1 - a - b*x)^(5/2))/(b^2*Sqrt[1 + a + b*x]) + (3*(3 + 2*a)*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/(2*b^2) + ((3 + 2*a)*(1 - a - b*x)^(3/2)*Sqrt[1 + a + b*x])/(2*b^2) + (3*(3 + 2*a)*ArcSin[a + b*x])/(2*b^2)","A",7,6,12,0.5000,1,"{6163, 78, 50, 53, 619, 216}"
863,1,68,0,0.0337114,"\int e^{-3 \tanh ^{-1}(a+b x)} \, dx","Int[E^(-3*ArcTanh[a + b*x]),x]","-\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}","-\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,"(-2*(1 - a - b*x)^(3/2))/(b*Sqrt[1 + a + b*x]) - (3*Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/b - (3*ArcSin[a + b*x])/b","A",6,6,10,0.6000,1,"{6161, 47, 50, 53, 619, 216}"
864,1,103,0,0.0853212,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x} \, dx","Int[1/(E^(3*ArcTanh[a + b*x])*x),x]","-\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)","-\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*Sqrt[1 - a - b*x])/((1 + a)*Sqrt[1 + a + b*x]) + ArcSin[a + b*x] - (2*(1 - a)^2*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 + a)*Sqrt[1 - a^2])","A",8,8,14,0.5714,1,"{6163, 98, 157, 53, 619, 216, 93, 208}"
865,1,130,0,0.0768065,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[1/(E^(3*ArcTanh[a + b*x])*x^2),x]","\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}}","\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,"(-6*b*Sqrt[1 - a - b*x])/((1 + a)^2*Sqrt[1 + a + b*x]) - (1 - a - b*x)^(3/2)/((1 + a)*x*Sqrt[1 + a + b*x]) + (6*(1 - a)*b*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 + a)^2*Sqrt[1 - a^2])","A",5,4,14,0.2857,1,"{6163, 94, 93, 208}"
866,1,200,0,0.1294985,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[1/(E^(3*ArcTanh[a + b*x])*x^3),x]","-\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}}","-\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,"(3*(3 - 2*a)*b^2*Sqrt[1 - a - b*x])/((1 - a)*(1 + a)^3*Sqrt[1 + a + b*x]) + ((3 - 2*a)*b*(1 - a - b*x)^(3/2))/(2*(1 - a)*(1 + a)^2*x*Sqrt[1 + a + b*x]) - (1 - a - b*x)^(5/2)/(2*(1 - a^2)*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)^3*Sqrt[1 - a^2])","A",6,5,14,0.3571,1,"{6163, 96, 94, 93, 208}"
867,1,257,0,0.2163357,"\int \frac{e^{-3 \tanh ^{-1}(a+b x)}}{x^4} \, dx","Int[1/(E^(3*ArcTanh[a + b*x])*x^4),x]","-\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{7 b \sqrt{-a-b x+1}}{6 (a+1)^2 x^2 \sqrt{a+b x+1}}-\frac{(1-a) \sqrt{-a-b x+1}}{3 (a+1) 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{7 b \sqrt{-a-b x+1}}{6 (a+1)^2 x^2 \sqrt{a+b x+1}}-\frac{(1-a) \sqrt{-a-b x+1}}{3 (a+1) x^3 \sqrt{a+b x+1}}",1,"-((52 - 51*a + 2*a^2)*b^3*Sqrt[1 - a - b*x])/(6*(1 - a)*(1 + a)^4*Sqrt[1 + a + b*x]) - ((1 - a)*Sqrt[1 - a - b*x])/(3*(1 + a)*x^3*Sqrt[1 + a + b*x]) + (7*b*Sqrt[1 - a - b*x])/(6*(1 + a)^2*x^2*Sqrt[1 + a + b*x]) - ((19 - 16*a)*b^2*Sqrt[1 - a - b*x])/(6*(1 - a)*(1 + a)^3*x*Sqrt[1 + a + b*x]) + ((11 - 18*a + 6*a^2)*b^3*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)*(1 + a)^4*Sqrt[1 - a^2])","A",8,7,14,0.5000,1,"{6163, 98, 151, 152, 12, 93, 208}"
868,1,10,0,0.0353483,"\int \frac{e^{\tanh ^{-1}(1+b x)}}{2+b x} \, dx","Int[E^ArcTanh[1 + b*x]/(2 + b*x),x]","\frac{\sin ^{-1}(b x+1)}{b}","\frac{\sin ^{-1}(b x+1)}{b}",1,"ArcSin[1 + b*x]/b","A",4,4,16,0.2500,1,"{6163, 53, 619, 216}"
869,1,109,0,0.1685881,"\int \frac{e^{\tanh ^{-1}(a+b x)} x^3}{1-a^2-2 a b x-b^2 x^2} \, dx","Int[(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)}{2 b^4}+\frac{(1-a) x^2 \sqrt{a+b x+1}}{b^2 \sqrt{-a-b x+1}}+\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{3 \left(2 a^2-2 a+1\right) \sin ^{-1}(a+b x)}{2 b^4}+\frac{(1-a) x^2 \sqrt{a+b x+1}}{b^2 \sqrt{-a-b x+1}}+\frac{\sqrt{-a-b x+1} \sqrt{a+b x+1} ((3-2 a) b x+(1-2 a) (4-a))}{2 b^4}",1,"((1 - a)*x^2*Sqrt[1 + a + b*x])/(b^2*Sqrt[1 - a - b*x]) + (Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x]*((1 - 2*a)*(4 - a) + (3 - 2*a)*b*x))/(2*b^4) - (3*(1 - 2*a + 2*a^2)*ArcSin[a + b*x])/(2*b^4)","A",6,6,34,0.1765,1,"{6164, 98, 147, 53, 619, 216}"
870,1,78,0,0.1370058,"\int \frac{e^{\tanh ^{-1}(a+b x)} x^2}{1-a^2-2 a b x-b^2 x^2} \, dx","Int[(E^ArcTanh[a + b*x]*x^2)/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","\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}","\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,"((1 - a)^2*Sqrt[1 + a + b*x])/(b^3*Sqrt[1 - a - b*x]) + (Sqrt[1 - a - b*x]*Sqrt[1 + a + b*x])/b^3 - ((1 - 2*a)*ArcSin[a + b*x])/b^3","A",6,6,34,0.1765,1,"{6164, 89, 80, 53, 619, 216}"
871,1,44,0,0.0822346,"\int \frac{e^{\tanh ^{-1}(a+b x)} x}{1-a^2-2 a b x-b^2 x^2} \, dx","Int[(E^ArcTanh[a + b*x]*x)/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","\frac{(1-a) \sqrt{a+b x+1}}{b^2 \sqrt{-a-b x+1}}-\frac{\sin ^{-1}(a+b x)}{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 + b*x])/(b^2*Sqrt[1 - a - b*x]) - ArcSin[a + b*x]/b^2","A",5,5,32,0.1562,1,"{6164, 78, 53, 619, 216}"
872,1,27,0,0.0371005,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{1-a^2-2 a b x-b^2 x^2} \, dx","Int[E^ArcTanh[a + b*x]/(1 - a^2 - 2*a*b*x - b^2*x^2),x]","\frac{\sqrt{a+b x+1}}{b \sqrt{-a-b x+1}}","\frac{\sqrt{a+b x+1}}{b \sqrt{-a-b x+1}}",1,"Sqrt[1 + a + b*x]/(b*Sqrt[1 - a - b*x])","A",2,2,31,0.06452,1,"{6164, 37}"
873,1,93,0,0.131745,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x \left(1-a^2-2 a b x-b^2 x^2\right)} \, dx","Int[E^ArcTanh[a + b*x]/(x*(1 - a^2 - 2*a*b*x - b^2*x^2)),x]","\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}}","\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 + b*x]/((1 - a)*Sqrt[1 - a - b*x]) - (2*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)*Sqrt[1 - a^2])","A",4,4,34,0.1176,1,"{6164, 96, 93, 208}"
874,1,150,0,0.1591943,"\int \frac{e^{\tanh ^{-1}(a+b x)}}{x^2 \left(1-a^2-2 a b x-b^2 x^2\right)} \, dx","Int[E^ArcTanh[a + b*x]/(x^2*(1 - a^2 - 2*a*b*x - b^2*x^2)),x]","-\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}}","-\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,"((2 + a)*b*Sqrt[1 + a + b*x])/((1 - a)^2*(1 + a)*Sqrt[1 - a - b*x]) - Sqrt[1 + a + b*x]/((1 - a^2)*x*Sqrt[1 - a - b*x]) - (2*(1 + 2*a)*b*ArcTanh[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[1 - a - b*x])])/((1 - a)^2*(1 + a)*Sqrt[1 - a^2])","A",6,6,34,0.1765,1,"{6164, 103, 152, 12, 93, 208}"
875,1,109,0,0.0759803,"\int e^{n \tanh ^{-1}(a+b x)} x^m \, dx","Int[E^(n*ArcTanh[a + b*x])*x^m,x]","\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}","\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,"(x^(1 + m)*(1 + a + b*x)^(n/2)*(1 - (b*x)/(1 - a))^(n/2)*AppellF1[1 + m, n/2, -n/2, 2 + m, (b*x)/(1 - a), -((b*x)/(1 + a))])/((1 + m)*(1 - a - b*x)^(n/2)*(1 + (b*x)/(1 + a))^(n/2))","A",4,3,14,0.2143,1,"{6163, 135, 133}"
876,1,206,0,0.182662,"\int e^{n \tanh ^{-1}(a+b x)} x^3 \, dx","Int[E^(n*ArcTanh[a + b*x])*x^3,x]","\frac{2^{\frac{n}{2}-2} \left(-36 a^2 n+24 a^3+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{(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{x^2 (a+b x+1)^{\frac{n+2}{2}} (-a-b x+1)^{1-\frac{n}{2}}}{4 b^2}","\frac{2^{\frac{n}{2}-2} \left(-36 a^2 n+24 a^3+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{(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{x^2 (a+b x+1)^{\frac{n+2}{2}} (-a-b x+1)^{1-\frac{n}{2}}}{4 b^2}",1,"-(x^2*(1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^((2 + n)/2))/(4*b^2) - ((1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^((2 + n)/2)*(6 + 18*a^2 - 10*a*n + n^2 - 2*b*(6*a - n)*x))/(24*b^4) + (2^(-2 + n/2)*(24*a^3 - 36*a^2*n + 12*a*(2 + n^2) - n*(8 + n^2))*(1 - a - b*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a - b*x)/2])/(3*b^4*(2 - n))","A",4,4,14,0.2857,1,"{6163, 100, 147, 69}"
877,1,170,0,0.158488,"\int e^{n \tanh ^{-1}(a+b x)} x^2 \, dx","Int[E^(n*ArcTanh[a + b*x])*x^2,x]","-\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}","-\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,"((4*a - n)*(1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^((2 + n)/2))/(6*b^3) - (x*(1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^((2 + n)/2))/(3*b^2) - (2^(n/2)*(2 + 6*a^2 - 6*a*n + n^2)*(1 - a - b*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a - b*x)/2])/(3*b^3*(2 - n))","A",4,4,14,0.2857,1,"{6163, 90, 80, 69}"
878,1,114,0,0.0687108,"\int e^{n \tanh ^{-1}(a+b x)} x \, dx","Int[E^(n*ArcTanh[a + b*x])*x,x]","\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}","\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)*(1 + a + b*x)^((2 + n)/2))/(2*b^2) + (2^(n/2)*(2*a - n)*(1 - a - b*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a - b*x)/2])/(b^2*(2 - n))","A",3,3,12,0.2500,1,"{6163, 80, 69}"
879,1,71,0,0.0141212,"\int e^{n \tanh ^{-1}(a+b x)} \, dx","Int[E^(n*ArcTanh[a + b*x]),x]","-\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)}","-\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,"-((2^(1 + n/2)*(1 - a - b*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (1 - a - b*x)/2])/(b*(2 - n)))","A",2,2,10,0.2000,1,"{6161, 69}"
880,1,135,0,0.0704511,"\int \frac{e^{n \tanh ^{-1}(a+b x)}}{x} \, dx","Int[E^(n*ArcTanh[a + b*x])/x,x]","\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}","\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, -n/2, 1 - n/2, ((1 + a)*(1 - a - b*x))/((1 - a)*(1 + a + b*x))])/(n*(1 - a - b*x)^(n/2)) - (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a - b*x)/2])/(n*(1 - a - b*x)^(n/2))","A",4,4,14,0.2857,1,"{6163, 105, 69, 131}"
881,1,92,0,0.0415899,"\int \frac{e^{n \tanh ^{-1}(a+b x)}}{x^2} \, dx","Int[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}{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)}","-\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)^((-2 + 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",2,2,14,0.1429,1,"{6163, 131}"
882,1,152,0,0.092375,"\int \frac{e^{n \tanh ^{-1}(a+b x)}}{x^3} \, dx","Int[E^(n*ArcTanh[a + b*x])/x^3,x]","-\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)}","-\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)^((2 + n)/2))/(2*(1 - a^2)*x^2) - (2*b^2*(2*a + n)*(1 - a - b*x)^(1 - n/2)*(1 + a + b*x)^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, ((1 + a)*(1 - a - b*x))/((1 - a)*(1 + a + b*x))])/((1 - a)^3*(1 + a)*(2 - n))","A",3,3,14,0.2143,1,"{6163, 96, 131}"
883,1,127,0,0.0640731,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^4,x]","-\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}","-\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,"(35*c^4*x*Sqrt[1 - a^2*x^2])/128 + (35*c^4*x*(1 - a^2*x^2)^(3/2))/192 + (7*c^4*x*(1 - a^2*x^2)^(5/2))/48 + (c^4*x*(1 - a^2*x^2)^(7/2))/8 - (c^4*(1 - a^2*x^2)^(9/2))/(9*a) + (35*c^4*ArcSin[a*x])/(128*a)","A",7,4,20,0.2000,1,"{6138, 641, 195, 216}"
884,1,105,0,0.0560546,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^3,x]","-\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}","-\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,"(5*c^3*x*Sqrt[1 - a^2*x^2])/16 + (5*c^3*x*(1 - a^2*x^2)^(3/2))/24 + (c^3*x*(1 - a^2*x^2)^(5/2))/6 - (c^3*(1 - a^2*x^2)^(7/2))/(7*a) + (5*c^3*ArcSin[a*x])/(16*a)","A",6,4,20,0.2000,1,"{6138, 641, 195, 216}"
885,1,83,0,0.0463788,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^2,x]","-\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}","-\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,"(3*c^2*x*Sqrt[1 - a^2*x^2])/8 + (c^2*x*(1 - a^2*x^2)^(3/2))/4 - (c^2*(1 - a^2*x^2)^(5/2))/(5*a) + (3*c^2*ArcSin[a*x])/(8*a)","A",5,4,20,0.2000,1,"{6138, 641, 195, 216}"
886,1,55,0,0.029047,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2),x]","-\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}","-\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*x*Sqrt[1 - a^2*x^2])/2 - (c*(1 - a^2*x^2)^(3/2))/(3*a) + (c*ArcSin[a*x])/(2*a)","A",4,4,18,0.2222,1,"{6138, 641, 195, 216}"
887,1,101,0,0.132048,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{c-a^2 c x^2} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2),x]","\frac{x^3 (a x+1)}{a^2 c \sqrt{1-a^2 x^2}}+\frac{4 x^2 \sqrt{1-a^2 x^2}}{3 a^3 c}+\frac{(9 a x+16) \sqrt{1-a^2 x^2}}{6 a^5 c}-\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{4 x^2 \sqrt{1-a^2 x^2}}{3 a^3 c}+\frac{(9 a x+16) \sqrt{1-a^2 x^2}}{6 a^5 c}-\frac{3 \sin ^{-1}(a x)}{2 a^5 c}",1,"(x^3*(1 + a*x))/(a^2*c*Sqrt[1 - a^2*x^2]) + (4*x^2*Sqrt[1 - a^2*x^2])/(3*a^3*c) + ((16 + 9*a*x)*Sqrt[1 - a^2*x^2])/(6*a^5*c) - (3*ArcSin[a*x])/(2*a^5*c)","A",5,5,23,0.2174,1,"{6148, 819, 833, 780, 216}"
888,1,74,0,0.1078343,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{c-a^2 c x^2} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2),x]","\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}-\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}-\frac{3 \sin ^{-1}(a x)}{2 a^4 c}",1,"(x^2*(1 + a*x))/(a^2*c*Sqrt[1 - a^2*x^2]) + ((4 + 3*a*x)*Sqrt[1 - a^2*x^2])/(2*a^4*c) - (3*ArcSin[a*x])/(2*a^4*c)","A",4,4,23,0.1739,1,"{6148, 819, 780, 216}"
889,1,60,0,0.1073998,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2),x]","\frac{a x+1}{a^3 c \sqrt{1-a^2 x^2}}+\frac{\sqrt{1-a^2 x^2}}{a^3 c}-\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}-\frac{\sin ^{-1}(a x)}{a^3 c}",1,"(1 + a*x)/(a^3*c*Sqrt[1 - a^2*x^2]) + Sqrt[1 - a^2*x^2]/(a^3*c) - ArcSin[a*x]/(a^3*c)","A",5,5,23,0.2174,1,"{6148, 797, 641, 216, 637}"
890,1,39,0,0.0639509,"\int \frac{e^{\tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2),x]","\frac{a x+1}{a^2 c \sqrt{1-a^2 x^2}}-\frac{\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 + a*x)/(a^2*c*Sqrt[1 - a^2*x^2]) - ArcSin[a*x]/(a^2*c)","A",3,3,21,0.1429,1,"{6148, 778, 216}"
891,1,13,0,0.0287232,"\int \frac{e^{\tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2),x]","\frac{e^{\tanh ^{-1}(a x)}}{a c}","\frac{e^{\tanh ^{-1}(a x)}}{a c}",1,"E^ArcTanh[a*x]/(a*c)","A",1,1,20,0.05000,1,"{6137}"
892,1,44,0,0.0993619,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)),x]","\frac{a x+1}{c \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}","\frac{a x+1}{c \sqrt{1-a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{c}",1,"(1 + a*x)/(c*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c","A",6,6,23,0.2609,1,"{6148, 823, 12, 266, 63, 208}"
893,1,70,0,0.1167462,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)),x]","\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}","\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)/(c*x*Sqrt[1 - a^2*x^2]) - (2*Sqrt[1 - a^2*x^2])/(c*x) - (a*ArcTanh[Sqrt[1 - a^2*x^2]])/c","A",6,6,23,0.2609,1,"{6148, 823, 807, 266, 63, 208}"
894,1,99,0,0.1388673,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)),x]","-\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}","-\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 + a*x)/(c*x^2*Sqrt[1 - a^2*x^2]) - (3*Sqrt[1 - a^2*x^2])/(2*c*x^2) - (2*a*Sqrt[1 - a^2*x^2])/(c*x) - (3*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c)","A",7,7,23,0.3043,1,"{6148, 823, 835, 807, 266, 63, 208}"
895,1,128,0,0.1661537,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)} \, dx","Int[E^ArcTanh[a*x]/(x^4*(c - a^2*c*x^2)),x]","-\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}","-\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 + a*x)/(c*x^3*Sqrt[1 - a^2*x^2]) - (4*Sqrt[1 - a^2*x^2])/(3*c*x^3) - (3*a*Sqrt[1 - a^2*x^2])/(2*c*x^2) - (8*a^2*Sqrt[1 - a^2*x^2])/(3*c*x) - (3*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c)","A",8,7,23,0.3043,1,"{6148, 823, 835, 807, 266, 63, 208}"
896,1,137,0,0.1543149,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x^6)/(c - a^2*c*x^2)^2,x]","\frac{x^5 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{x^3 (6 a x+5)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{8 x^2 \sqrt{1-a^2 x^2}}{3 a^5 c^2}-\frac{(15 a x+32) \sqrt{1-a^2 x^2}}{6 a^7 c^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{x^3 (6 a x+5)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{8 x^2 \sqrt{1-a^2 x^2}}{3 a^5 c^2}-\frac{(15 a x+32) \sqrt{1-a^2 x^2}}{6 a^7 c^2}+\frac{5 \sin ^{-1}(a x)}{2 a^7 c^2}",1,"(x^5*(1 + a*x))/(3*a^2*c^2*(1 - a^2*x^2)^(3/2)) - (x^3*(5 + 6*a*x))/(3*a^4*c^2*Sqrt[1 - a^2*x^2]) - (8*x^2*Sqrt[1 - a^2*x^2])/(3*a^5*c^2) - ((32 + 15*a*x)*Sqrt[1 - a^2*x^2])/(6*a^7*c^2) + (5*ArcSin[a*x])/(2*a^7*c^2)","A",6,5,23,0.2174,1,"{6148, 819, 833, 780, 216}"
897,1,110,0,0.1359653,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^2,x]","\frac{x^4 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{x^2 (5 a x+4)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{(15 a x+16) \sqrt{1-a^2 x^2}}{6 a^6 c^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{x^2 (5 a x+4)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{(15 a x+16) \sqrt{1-a^2 x^2}}{6 a^6 c^2}+\frac{5 \sin ^{-1}(a x)}{2 a^6 c^2}",1,"(x^4*(1 + a*x))/(3*a^2*c^2*(1 - a^2*x^2)^(3/2)) - (x^2*(4 + 5*a*x))/(3*a^4*c^2*Sqrt[1 - a^2*x^2]) - ((16 + 15*a*x)*Sqrt[1 - a^2*x^2])/(6*a^6*c^2) + (5*ArcSin[a*x])/(2*a^6*c^2)","A",5,4,23,0.1739,1,"{6148, 819, 780, 216}"
898,1,99,0,0.1224054,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^2,x]","\frac{x^3 (a x+1)}{3 a^2 c^2 \left(1-a^2 x^2\right)^{3/2}}-\frac{x (4 a x+3)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{1-a^2 x^2}}{3 a^5 c^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{x (4 a x+3)}{3 a^4 c^2 \sqrt{1-a^2 x^2}}-\frac{8 \sqrt{1-a^2 x^2}}{3 a^5 c^2}+\frac{\sin ^{-1}(a x)}{a^5 c^2}",1,"(x^3*(1 + a*x))/(3*a^2*c^2*(1 - a^2*x^2)^(3/2)) - (x*(3 + 4*a*x))/(3*a^4*c^2*Sqrt[1 - a^2*x^2]) - (8*Sqrt[1 - a^2*x^2])/(3*a^5*c^2) + ArcSin[a*x]/(a^5*c^2)","A",5,4,23,0.1739,1,"{6148, 819, 641, 216}"
899,1,74,0,0.1039282,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^2,x]","\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}}+\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}}+\frac{\sin ^{-1}(a x)}{a^4 c^2}",1,"(x^2*(1 + a*x))/(3*a^2*c^2*(1 - a^2*x^2)^(3/2)) - (2 + 3*a*x)/(3*a^4*c^2*Sqrt[1 - a^2*x^2]) + ArcSin[a*x]/(a^4*c^2)","A",4,4,23,0.1739,1,"{6148, 819, 778, 216}"
900,1,57,0,0.093813,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^2,x]","\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}}","\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,"(x^2*(1 + a*x))/(3*a*c^2*(1 - a^2*x^2)^(3/2)) - 2/(3*a^3*c^2*Sqrt[1 - a^2*x^2])","A",4,4,23,0.1739,1,"{6148, 796, 12, 261}"
901,1,55,0,0.0637577,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^2,x]","\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}}","\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)/(3*a^2*c^2*(1 - a^2*x^2)^(3/2)) - x/(3*a*c^2*Sqrt[1 - a^2*x^2])","A",3,3,21,0.1429,1,"{6148, 778, 191}"
902,1,52,0,0.0396439,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^2,x]","\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}}","\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 + a*x)/(3*a*c^2*(1 - a^2*x^2)^(3/2)) + (2*x)/(3*c^2*Sqrt[1 - a^2*x^2])","A",3,3,20,0.1500,1,"{6138, 639, 191}"
903,1,74,0,0.1164989,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^2} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^2),x]","\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}","\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,"(1 + a*x)/(3*c^2*(1 - a^2*x^2)^(3/2)) + (3 + 2*a*x)/(3*c^2*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c^2","A",7,6,23,0.2609,1,"{6148, 823, 12, 266, 63, 208}"
904,1,105,0,0.1416862,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^2),x]","\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}","\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,"(1 + a*x)/(3*c^2*x*(1 - a^2*x^2)^(3/2)) + (4 + 3*a*x)/(3*c^2*x*Sqrt[1 - a^2*x^2]) - (8*Sqrt[1 - a^2*x^2])/(3*c^2*x) - (a*ArcTanh[Sqrt[1 - a^2*x^2]])/c^2","A",7,6,23,0.2609,1,"{6148, 823, 807, 266, 63, 208}"
905,1,134,0,0.1592171,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^2),x]","-\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}","-\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,"(1 + a*x)/(3*c^2*x^2*(1 - a^2*x^2)^(3/2)) + (5 + 4*a*x)/(3*c^2*x^2*Sqrt[1 - a^2*x^2]) - (5*Sqrt[1 - a^2*x^2])/(2*c^2*x^2) - (8*a*Sqrt[1 - a^2*x^2])/(3*c^2*x) - (5*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^2)","A",8,7,23,0.3043,1,"{6148, 823, 835, 807, 266, 63, 208}"
906,1,161,0,0.1885168,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^ArcTanh[a*x]/(x^4*(c - a^2*c*x^2)^2),x]","-\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}","-\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,"(1 + a*x)/(3*c^2*x^3*(1 - a^2*x^2)^(3/2)) + (6 + 5*a*x)/(3*c^2*x^3*Sqrt[1 - a^2*x^2]) - (8*Sqrt[1 - a^2*x^2])/(3*c^2*x^3) - (5*a*Sqrt[1 - a^2*x^2])/(2*c^2*x^2) - (16*a^2*Sqrt[1 - a^2*x^2])/(3*c^2*x) - (5*a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^2)","A",9,7,23,0.3043,1,"{6148, 823, 835, 807, 266, 63, 208}"
907,1,143,0,0.1809898,"\int \frac{e^{\tanh ^{-1}(a x)} x^7}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^7)/(c - a^2*c*x^2)^3,x]","\frac{x^6 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{x^4 (7 a x+6)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{x^2 (35 a x+24)}{15 a^6 c^3 \sqrt{1-a^2 x^2}}+\frac{(35 a x+32) \sqrt{1-a^2 x^2}}{10 a^8 c^3}-\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{x^4 (7 a x+6)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{x^2 (35 a x+24)}{15 a^6 c^3 \sqrt{1-a^2 x^2}}+\frac{(35 a x+32) \sqrt{1-a^2 x^2}}{10 a^8 c^3}-\frac{7 \sin ^{-1}(a x)}{2 a^8 c^3}",1,"(x^6*(1 + a*x))/(5*a^2*c^3*(1 - a^2*x^2)^(5/2)) - (x^4*(6 + 7*a*x))/(15*a^4*c^3*(1 - a^2*x^2)^(3/2)) + (x^2*(24 + 35*a*x))/(15*a^6*c^3*Sqrt[1 - a^2*x^2]) + ((32 + 35*a*x)*Sqrt[1 - a^2*x^2])/(10*a^8*c^3) - (7*ArcSin[a*x])/(2*a^8*c^3)","A",6,4,23,0.1739,1,"{6148, 819, 780, 216}"
908,1,133,0,0.1544964,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^6)/(c - a^2*c*x^2)^3,x]","\frac{x^5 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{x^3 (6 a x+5)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{x (8 a x+5)}{5 a^6 c^3 \sqrt{1-a^2 x^2}}+\frac{16 \sqrt{1-a^2 x^2}}{5 a^7 c^3}-\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{x^3 (6 a x+5)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{x (8 a x+5)}{5 a^6 c^3 \sqrt{1-a^2 x^2}}+\frac{16 \sqrt{1-a^2 x^2}}{5 a^7 c^3}-\frac{\sin ^{-1}(a x)}{a^7 c^3}",1,"(x^5*(1 + a*x))/(5*a^2*c^3*(1 - a^2*x^2)^(5/2)) - (x^3*(5 + 6*a*x))/(15*a^4*c^3*(1 - a^2*x^2)^(3/2)) + (x*(5 + 8*a*x))/(5*a^6*c^3*Sqrt[1 - a^2*x^2]) + (16*Sqrt[1 - a^2*x^2])/(5*a^7*c^3) - ArcSin[a*x]/(a^7*c^3)","A",6,4,23,0.1739,1,"{6148, 819, 641, 216}"
909,1,108,0,0.129224,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^3,x]","\frac{x^4 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}-\frac{x^2 (5 a x+4)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{15 a x+8}{15 a^6 c^3 \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{x^2 (5 a x+4)}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}+\frac{15 a x+8}{15 a^6 c^3 \sqrt{1-a^2 x^2}}-\frac{\sin ^{-1}(a x)}{a^6 c^3}",1,"(x^4*(1 + a*x))/(5*a^2*c^3*(1 - a^2*x^2)^(5/2)) - (x^2*(4 + 5*a*x))/(15*a^4*c^3*(1 - a^2*x^2)^(3/2)) + (8 + 15*a*x)/(15*a^6*c^3*Sqrt[1 - a^2*x^2]) - ArcSin[a*x]/(a^6*c^3)","A",5,4,23,0.1739,1,"{6148, 819, 778, 216}"
910,1,81,0,0.1161958,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^3,x]","\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}}","\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,"(x^4*(1 + a*x))/(5*a*c^3*(1 - a^2*x^2)^(5/2)) - 4/(15*a^5*c^3*(1 - a^2*x^2)^(3/2)) + 4/(5*a^5*c^3*Sqrt[1 - a^2*x^2])","A",5,4,23,0.1739,1,"{6148, 805, 266, 43}"
911,1,88,0,0.1056761,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^3,x]","\frac{x^2 (a x+1)}{5 a^2 c^3 \left(1-a^2 x^2\right)^{5/2}}+\frac{x}{5 a^3 c^3 \sqrt{1-a^2 x^2}}-\frac{3 a x+2}{15 a^4 c^3 \left(1-a^2 x^2\right)^{3/2}}","\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,"(x^2*(1 + a*x))/(5*a^2*c^3*(1 - a^2*x^2)^(5/2)) - (2 + 3*a*x)/(15*a^4*c^3*(1 - a^2*x^2)^(3/2)) + x/(5*a^3*c^3*Sqrt[1 - a^2*x^2])","A",4,4,23,0.1739,1,"{6148, 819, 778, 191}"
912,1,88,0,0.1075325,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^3,x]","\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}}","\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,"(x^2*(1 + a*x))/(5*a*c^3*(1 - a^2*x^2)^(5/2)) - (2*(1 - a*x))/(15*a^3*c^3*(1 - a^2*x^2)^(3/2)) - (2*x)/(15*a^2*c^3*Sqrt[1 - a^2*x^2])","A",4,4,23,0.1739,1,"{6148, 796, 778, 191}"
913,1,80,0,0.0690854,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^3,x]","-\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}}","-\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,"(1 + a*x)/(5*a^2*c^3*(1 - a^2*x^2)^(5/2)) - x/(15*a*c^3*(1 - a^2*x^2)^(3/2)) - (2*x)/(15*a*c^3*Sqrt[1 - a^2*x^2])","A",4,4,21,0.1905,1,"{6148, 778, 192, 191}"
914,1,74,0,0.0453206,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^3,x]","\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}}","\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,"(1 + a*x)/(5*a*c^3*(1 - a^2*x^2)^(5/2)) + (4*x)/(15*c^3*(1 - a^2*x^2)^(3/2)) + (8*x)/(15*c^3*Sqrt[1 - a^2*x^2])","A",4,4,20,0.2000,1,"{6138, 639, 192, 191}"
915,1,101,0,0.1397884,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^3} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^3),x]","\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}","\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,"(1 + a*x)/(5*c^3*(1 - a^2*x^2)^(5/2)) + (5 + 4*a*x)/(15*c^3*(1 - a^2*x^2)^(3/2)) + (15 + 8*a*x)/(15*c^3*Sqrt[1 - a^2*x^2]) - ArcTanh[Sqrt[1 - a^2*x^2]]/c^3","A",8,6,23,0.2609,1,"{6148, 823, 12, 266, 63, 208}"
916,1,135,0,0.1709987,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^3} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^3),x]","\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}","\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,"(1 + a*x)/(5*c^3*x*(1 - a^2*x^2)^(5/2)) + (6 + 5*a*x)/(15*c^3*x*(1 - a^2*x^2)^(3/2)) + (8 + 5*a*x)/(5*c^3*x*Sqrt[1 - a^2*x^2]) - (16*Sqrt[1 - a^2*x^2])/(5*c^3*x) - (a*ArcTanh[Sqrt[1 - a^2*x^2]])/c^3","A",8,6,23,0.2609,1,"{6148, 823, 807, 266, 63, 208}"
917,1,164,0,0.1943323,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^3} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^3),x]","-\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}","-\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,"(1 + a*x)/(5*c^3*x^2*(1 - a^2*x^2)^(5/2)) + (7 + 6*a*x)/(15*c^3*x^2*(1 - a^2*x^2)^(3/2)) + (35 + 24*a*x)/(15*c^3*x^2*Sqrt[1 - a^2*x^2]) - (7*Sqrt[1 - a^2*x^2])/(2*c^3*x^2) - (16*a*Sqrt[1 - a^2*x^2])/(5*c^3*x) - (7*a^2*ArcTanh[Sqrt[1 - a^2*x^2]])/(2*c^3)","A",9,7,23,0.3043,1,"{6148, 823, 835, 807, 266, 63, 208}"
918,1,96,0,0.053146,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^4,x]","\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}}","\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,"(1 + a*x)/(7*a*c^4*(1 - a^2*x^2)^(7/2)) + (6*x)/(35*c^4*(1 - a^2*x^2)^(5/2)) + (8*x)/(35*c^4*(1 - a^2*x^2)^(3/2)) + (16*x)/(35*c^4*Sqrt[1 - a^2*x^2])","A",5,4,20,0.2000,1,"{6138, 639, 192, 191}"
919,1,118,0,0.0641603,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^5} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^5,x]","\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}}","\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,"(1 + a*x)/(9*a*c^5*(1 - a^2*x^2)^(9/2)) + (8*x)/(63*c^5*(1 - a^2*x^2)^(7/2)) + (16*x)/(105*c^5*(1 - a^2*x^2)^(5/2)) + (64*x)/(315*c^5*(1 - a^2*x^2)^(3/2)) + (128*x)/(315*c^5*Sqrt[1 - a^2*x^2])","A",6,4,20,0.2000,1,"{6138, 639, 192, 191}"
920,1,49,0,0.0999109,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\sqrt{1-a^2 x^2}} \, dx","Int[(E^ArcTanh[a*x]*x^4)/Sqrt[1 - a^2*x^2],x]","-\frac{x^3}{3 a^2}-\frac{x^2}{2 a^3}-\frac{x}{a^4}-\frac{\log (1-a x)}{a^5}-\frac{x^4}{4 a}","-\frac{x^3}{3 a^2}-\frac{x^2}{2 a^3}-\frac{x}{a^4}-\frac{\log (1-a x)}{a^5}-\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",3,2,24,0.08333,1,"{6150, 43}"
921,1,39,0,0.0960698,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(E^ArcTanh[a*x]*x^3)/Sqrt[1 - a^2*x^2],x]","-\frac{x^2}{2 a^2}-\frac{x}{a^3}-\frac{\log (1-a x)}{a^4}-\frac{x^3}{3 a}","-\frac{x^2}{2 a^2}-\frac{x}{a^3}-\frac{\log (1-a x)}{a^4}-\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",3,2,24,0.08333,1,"{6150, 43}"
922,1,29,0,0.0906503,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/Sqrt[1 - a^2*x^2],x]","-\frac{x}{a^2}-\frac{\log (1-a x)}{a^3}-\frac{x^2}{2 a}","-\frac{x}{a^2}-\frac{\log (1-a x)}{a^3}-\frac{x^2}{2 a}",1,"-(x/a^2) - x^2/(2*a) - Log[1 - a*x]/a^3","A",3,2,24,0.08333,1,"{6150, 43}"
923,1,19,0,0.0622626,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\sqrt{1-a^2 x^2}} \, dx","Int[(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",3,2,22,0.09091,1,"{6150, 43}"
924,1,12,0,0.0341307,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{1-a^2 x^2}} \, dx","Int[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",2,2,21,0.09524,1,"{6140, 31}"
925,1,12,0,0.0795024,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \sqrt{1-a^2 x^2}} \, dx","Int[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",4,4,24,0.1667,1,"{6150, 36, 29, 31}"
926,1,20,0,0.0874084,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[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",3,2,24,0.08333,1,"{6150, 44}"
927,1,32,0,0.090373,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[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*x^2) - a/x + a^2*Log[x] - a^2*Log[1 - a*x]","A",3,2,24,0.08333,1,"{6150, 44}"
928,1,42,0,0.090742,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \sqrt{1-a^2 x^2}} \, dx","Int[E^ArcTanh[a*x]/(x^4*Sqrt[1 - a^2*x^2]),x]","-\frac{a^2}{x}+a^3 \log (x)-a^3 \log (1-a x)-\frac{a}{2 x^2}-\frac{1}{3 x^3}","-\frac{a^2}{x}+a^3 \log (x)-a^3 \log (1-a x)-\frac{a}{2 x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - a/(2*x^2) - a^2/x + a^3*Log[x] - a^3*Log[1 - a*x]","A",3,2,24,0.08333,1,"{6150, 44}"
929,1,58,0,0.1150726,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(1 - a^2*x^2)^(3/2),x]","\frac{x^2}{2 a^3}+\frac{x}{a^4}+\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^2}{2 a^3}+\frac{x}{a^4}+\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}",1,"x/a^4 + x^2/(2*a^3) + 1/(2*a^5*(1 - a*x)) + (7*Log[1 - a*x])/(4*a^5) + Log[1 + a*x]/(4*a^5)","A",3,2,24,0.08333,1,"{6150, 88}"
930,1,48,0,0.113325,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(1 - a^2*x^2)^(3/2),x]","\frac{x}{a^3}+\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}+\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}",1,"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)","A",3,2,24,0.08333,1,"{6150, 88}"
931,1,43,0,0.1133376,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(1 - a^2*x^2)^(3/2),x]","\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}","\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,"1/(2*a^3*(1 - a*x)) + (3*Log[1 - a*x])/(4*a^3) + Log[1 + a*x]/(4*a^3)","A",3,2,24,0.08333,1,"{6150, 88}"
932,1,27,0,0.0775094,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x)/(1 - a^2*x^2)^(3/2),x]","\frac{1}{2 a^2 (1-a x)}-\frac{\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/(2*a^2*(1 - a*x)) - ArcTanh[a*x]/(2*a^2)","A",4,3,22,0.1364,1,"{6150, 77, 207}"
933,1,27,0,0.0484609,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(1 - a^2*x^2)^(3/2),x]","\frac{1}{2 a (1-a x)}+\frac{\tanh ^{-1}(a x)}{2 a}","\frac{1}{2 a (1-a x)}+\frac{\tanh ^{-1}(a x)}{2 a}",1,"1/(2*a*(1 - a*x)) + ArcTanh[a*x]/(2*a)","A",4,3,21,0.1429,1,"{6140, 44, 207}"
934,1,36,0,0.1088675,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x*(1 - a^2*x^2)^(3/2)),x]","\frac{1}{2 (1-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,"1/(2*(1 - a*x)) + Log[x] - (3*Log[1 - a*x])/4 - Log[1 + a*x]/4","A",3,2,24,0.08333,1,"{6150, 72}"
935,1,46,0,0.1098483,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[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",3,2,24,0.08333,1,"{6150, 88}"
936,1,63,0,0.1182391,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x^3*(1 - a^2*x^2)^(3/2)),x]","\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}","\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,"-1/(2*x^2) - a/x + a^2/(2*(1 - a*x)) + 2*a^2*Log[x] - (7*a^2*Log[1 - a*x])/4 - (a^2*Log[1 + a*x])/4","A",3,2,24,0.08333,1,"{6150, 88}"
937,1,73,0,0.1216734,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x^4*(1 - a^2*x^2)^(3/2)),x]","\frac{a^3}{2 (1-a x)}-\frac{2 a^2}{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{a}{2 x^2}-\frac{1}{3 x^3}","\frac{a^3}{2 (1-a x)}-\frac{2 a^2}{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{a}{2 x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - a/(2*x^2) - (2*a^2)/x + a^3/(2*(1 - a*x)) + 2*a^3*Log[x] - (9*a^3*Log[1 - a*x])/4 + (a^3*Log[1 + a*x])/4","A",3,2,24,0.08333,1,"{6150, 88}"
938,1,88,0,0.1401048,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^6)/(1 - a^2*x^2)^(5/2),x]","-\frac{x^2}{2 a^5}-\frac{x}{a^6}-\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^2}{2 a^5}-\frac{x}{a^6}-\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}",1,"-(x/a^6) - x^2/(2*a^5) + 1/(8*a^7*(1 - a*x)^2) - 5/(4*a^7*(1 - a*x)) - 1/(8*a^7*(1 + a*x)) - (39*Log[1 - a*x])/(16*a^7) - (9*Log[1 + a*x])/(16*a^7)","A",3,2,24,0.08333,1,"{6150, 88}"
939,1,76,0,0.1268244,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^5)/(1 - a^2*x^2)^(5/2),x]","-\frac{x}{a^5}-\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}-\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}",1,"-(x/a^5) + 1/(8*a^6*(1 - a*x)^2) - 1/(a^6*(1 - a*x)) + 1/(8*a^6*(1 + a*x)) - (23*Log[1 - a*x])/(16*a^6) + (7*Log[1 + a*x])/(16*a^6)","A",3,2,24,0.08333,1,"{6150, 88}"
940,1,72,0,0.124757,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(1 - a^2*x^2)^(5/2),x]","-\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}","-\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,"1/(8*a^5*(1 - a*x)^2) - 3/(4*a^5*(1 - a*x)) - 1/(8*a^5*(1 + a*x)) - (11*Log[1 - a*x])/(16*a^5) - (5*Log[1 + a*x])/(16*a^5)","A",3,2,24,0.08333,1,"{6150, 88}"
941,1,56,0,0.1236667,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(1 - a^2*x^2)^(5/2),x]","-\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}","-\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,"1/(8*a^4*(1 - a*x)^2) - 1/(2*a^4*(1 - a*x)) + 1/(8*a^4*(1 + a*x)) + (3*ArcTanh[a*x])/(8*a^4)","A",4,3,24,0.1250,1,"{6150, 88, 207}"
942,1,56,0,0.1225885,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(1 - a^2*x^2)^(5/2),x]","-\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}","-\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,"1/(8*a^3*(1 - a*x)^2) - 1/(4*a^3*(1 - a*x)) - 1/(8*a^3*(1 + a*x)) - ArcTanh[a*x]/(8*a^3)","A",4,3,24,0.1250,1,"{6150, 88, 207}"
943,1,41,0,0.0841084,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x)/(1 - a^2*x^2)^(5/2),x]","\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}","\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/(8*a^2*(1 - a*x)^2) + 1/(8*a^2*(1 + a*x)) - ArcTanh[a*x]/(8*a^2)","A",4,3,22,0.1364,1,"{6150, 77, 207}"
944,1,56,0,0.0571836,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(1 - a^2*x^2)^(5/2),x]","\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}","\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,"1/(8*a*(1 - a*x)^2) + 1/(4*a*(1 - a*x)) - 1/(8*a*(1 + a*x)) + (3*ArcTanh[a*x])/(8*a)","A",4,3,21,0.1429,1,"{6140, 44, 207}"
945,1,59,0,0.1179074,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x*(1 - a^2*x^2)^(5/2)),x]","\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)","\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,"1/(8*(1 - a*x)^2) + 1/(2*(1 - a*x)) + 1/(8*(1 + a*x)) + Log[x] - (11*Log[1 - a*x])/16 - (5*Log[1 + a*x])/16","A",3,2,24,0.08333,1,"{6150, 88}"
946,1,71,0,0.1268464,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x^2*(1 - a^2*x^2)^(5/2)),x]","\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}","\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,"-x^(-1) + a/(8*(1 - a*x)^2) + (3*a)/(4*(1 - a*x)) - a/(8*(1 + a*x)) + a*Log[x] - (23*a*Log[1 - a*x])/16 + (7*a*Log[1 + a*x])/16","A",3,2,24,0.08333,1,"{6150, 88}"
947,1,89,0,0.1354701,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x^3*(1 - a^2*x^2)^(5/2)),x]","\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}","\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,"-1/(2*x^2) - a/x + a^2/(8*(1 - a*x)^2) + a^2/(1 - a*x) + a^2/(8*(1 + a*x)) + 3*a^2*Log[x] - (39*a^2*Log[1 - a*x])/16 - (9*a^2*Log[1 + a*x])/16","A",3,2,24,0.08333,1,"{6150, 88}"
948,1,102,0,0.1451361,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x^4*(1 - a^2*x^2)^(5/2)),x]","\frac{5 a^3}{4 (1-a x)}-\frac{a^3}{8 (a x+1)}+\frac{a^3}{8 (1-a x)^2}-\frac{3 a^2}{x}+3 a^3 \log (x)-\frac{59}{16} a^3 \log (1-a x)+\frac{11}{16} a^3 \log (a x+1)-\frac{a}{2 x^2}-\frac{1}{3 x^3}","\frac{5 a^3}{4 (1-a x)}-\frac{a^3}{8 (a x+1)}+\frac{a^3}{8 (1-a x)^2}-\frac{3 a^2}{x}+3 a^3 \log (x)-\frac{59}{16} a^3 \log (1-a x)+\frac{11}{16} a^3 \log (a x+1)-\frac{a}{2 x^2}-\frac{1}{3 x^3}",1,"-1/(3*x^3) - a/(2*x^2) - (3*a^2)/x + a^3/(8*(1 - a*x)^2) + (5*a^3)/(4*(1 - a*x)) - a^3/(8*(1 + a*x)) + 3*a^3*Log[x] - (59*a^3*Log[1 - a*x])/16 + (11*a^3*Log[1 + a*x])/16","A",3,2,24,0.08333,1,"{6150, 88}"
949,1,74,0,0.1844289,"\int e^{\tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcTanh[a*x]*x^2*Sqrt[c - a^2*c*x^2],x]","\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}}","\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*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - a^2*x^2]) + (a*x^4*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
950,1,74,0,0.1277941,"\int e^{\tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcTanh[a*x]*x*Sqrt[c - a^2*c*x^2],x]","\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \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}}+\frac{x^2 \sqrt{c-a^2 c x^2}}{2 \sqrt{1-a^2 x^2}}",1,"(x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2]) + (a*x^3*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - a^2*x^2])","A",4,3,23,0.1304,1,"{6153, 6150, 43}"
951,1,69,0,0.0720662,"\int e^{\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2],x]","\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}}","\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*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] + (a*x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2])","A",3,2,22,0.09091,1,"{6143, 6140}"
952,1,65,0,0.1758346,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2])/x,x]","\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{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,"(a*x*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] + (Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
953,1,68,0,0.178264,"\int \frac{e^{\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^ArcTanh[a*x]*Sqrt[c - a^2*c*x^2])/x^2,x]","\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}}","\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*Sqrt[1 - a^2*x^2])) + (a*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
954,1,89,0,0.0872342,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"(2*c*(1 + a*x)^3*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) - (c*(1 + a*x)^4*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - a^2*x^2])","A",4,3,22,0.1364,1,"{6143, 6140, 43}"
955,1,136,0,0.0949734,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^(5/2),x]","\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}}","\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*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) - (4*c^2*(1 + a*x)^5*Sqrt[c - a^2*c*x^2])/(5*a*Sqrt[1 - a^2*x^2]) + (c^2*(1 + a*x)^6*Sqrt[c - a^2*c*x^2])/(6*a*Sqrt[1 - a^2*x^2])","A",4,3,22,0.1364,1,"{6143, 6140, 43}"
956,1,183,0,0.1050445,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^(7/2),x]","-\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}}","-\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,"(8*c^3*(1 + a*x)^5*Sqrt[c - a^2*c*x^2])/(5*a*Sqrt[1 - a^2*x^2]) - (2*c^3*(1 + a*x)^6*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) + (6*c^3*(1 + a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) - (c^3*(1 + a*x)^8*Sqrt[c - a^2*c*x^2])/(8*a*Sqrt[1 - a^2*x^2])","A",4,3,22,0.1364,1,"{6143, 6140, 43}"
957,1,194,0,0.2129406,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^ArcTanh[a*x]*x^4)/Sqrt[c - a^2*c*x^2],x]","-\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{x^2 \sqrt{1-a^2 x^2}}{2 a^3 \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{\sqrt{1-a^2 x^2} \log (1-a x)}{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{x^2 \sqrt{1-a^2 x^2}}{2 a^3 \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{\sqrt{1-a^2 x^2} \log (1-a x)}{a^5 \sqrt{c-a^2 c x^2}}",1,"-((x*Sqrt[1 - a^2*x^2])/(a^4*Sqrt[c - a^2*c*x^2])) - (x^2*Sqrt[1 - a^2*x^2])/(2*a^3*Sqrt[c - a^2*c*x^2]) - (x^3*Sqrt[1 - a^2*x^2])/(3*a^2*Sqrt[c - a^2*c*x^2]) - (x^4*Sqrt[1 - a^2*x^2])/(4*a*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a^5*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
958,1,155,0,0.2096873,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^ArcTanh[a*x]*x^3)/Sqrt[c - a^2*c*x^2],x]","-\frac{x^3 \sqrt{1-a^2 x^2}}{3 a \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 \sqrt{1-a^2 x^2}}{a^3 \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^3 \sqrt{1-a^2 x^2}}{3 a \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 \sqrt{1-a^2 x^2}}{a^3 \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}}",1,"-((x*Sqrt[1 - a^2*x^2])/(a^3*Sqrt[c - a^2*c*x^2])) - (x^2*Sqrt[1 - a^2*x^2])/(2*a^2*Sqrt[c - a^2*c*x^2]) - (x^3*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a^4*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
959,1,116,0,0.2012076,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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,"-((x*Sqrt[1 - a^2*x^2])/(a^2*Sqrt[c - a^2*c*x^2])) - (x^2*Sqrt[1 - a^2*x^2])/(2*a*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a^3*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
960,1,77,0,0.1343778,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^ArcTanh[a*x]*x)/Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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,"-((x*Sqrt[1 - a^2*x^2])/(a*Sqrt[c - a^2*c*x^2])) - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a^2*Sqrt[c - a^2*c*x^2])","A",4,3,23,0.1304,1,"{6153, 6150, 43}"
961,1,41,0,0.0711826,"\int \frac{e^{\tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[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",3,3,22,0.1364,1,"{6143, 6140, 31}"
962,1,71,0,0.1816529,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \sqrt{c-a^2 c x^2}} \, dx","Int[E^ArcTanh[a*x]/(x*Sqrt[c - a^2*c*x^2]),x]","\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}}","\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])/Sqrt[c - a^2*c*x^2] - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/Sqrt[c - a^2*c*x^2]","A",5,5,25,0.2000,1,"{6153, 6150, 36, 29, 31}"
963,1,107,0,0.1904735,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \sqrt{c-a^2 c x^2}} \, dx","Int[E^ArcTanh[a*x]/(x^2*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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*Sqrt[c - a^2*c*x^2])) + (a*Sqrt[1 - a^2*x^2]*Log[x])/Sqrt[c - a^2*c*x^2] - (a*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/Sqrt[c - a^2*c*x^2]","A",4,3,25,0.1200,1,"{6153, 6150, 44}"
964,1,148,0,0.1971699,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \sqrt{c-a^2 c x^2}} \, dx","Int[E^ArcTanh[a*x]/(x^3*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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]/(2*x^2*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2])/(x*Sqrt[c - a^2*c*x^2]) + (a^2*Sqrt[1 - a^2*x^2]*Log[x])/Sqrt[c - a^2*c*x^2] - (a^2*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/Sqrt[c - a^2*c*x^2]","A",4,3,25,0.1200,1,"{6153, 6150, 44}"
965,1,187,0,0.1994297,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \sqrt{c-a^2 c x^2}} \, dx","Int[E^ArcTanh[a*x]/(x^4*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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]/(3*x^3*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2])/(2*x^2*Sqrt[c - a^2*c*x^2]) - (a^2*Sqrt[1 - a^2*x^2])/(x*Sqrt[c - a^2*c*x^2]) + (a^3*Sqrt[1 - a^2*x^2]*Log[x])/Sqrt[c - a^2*c*x^2] - (a^3*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/Sqrt[c - a^2*c*x^2]","A",4,3,25,0.1200,1,"{6153, 6150, 44}"
966,1,261,0,0.2455914,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^(3/2),x]","\frac{x^3 \sqrt{1-a^2 x^2}}{3 a^3 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{2 x \sqrt{1-a^2 x^2}}{a^5 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{x^3 \sqrt{1-a^2 x^2}}{3 a^3 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{2 x \sqrt{1-a^2 x^2}}{a^5 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}}",1,"(2*x*Sqrt[1 - a^2*x^2])/(a^5*c*Sqrt[c - a^2*c*x^2]) + (x^2*Sqrt[1 - a^2*x^2])/(2*a^4*c*Sqrt[c - a^2*c*x^2]) + (x^3*Sqrt[1 - a^2*x^2])/(3*a^3*c*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(2*a^6*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (9*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*a^6*c*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*a^6*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
967,1,218,0,0.2357649,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^(3/2),x]","\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^3 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{\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^2 \sqrt{1-a^2 x^2}}{2 a^3 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{\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}}",1,"(x*Sqrt[1 - a^2*x^2])/(a^4*c*Sqrt[c - a^2*c*x^2]) + (x^2*Sqrt[1 - a^2*x^2])/(2*a^3*c*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(2*a^5*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (7*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*a^5*c*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*a^5*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
968,1,176,0,0.2315714,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^(3/2),x]","\frac{x \sqrt{1-a^2 x^2}}{a^3 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}}+\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}}",1,"(x*Sqrt[1 - a^2*x^2])/(a^3*c*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(2*a^4*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (5*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*a^4*c*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*a^4*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
969,1,139,0,0.2216005,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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]/(2*a^3*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*a^3*c*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*a^3*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
970,1,91,0,0.1511326,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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]/(2*a^2*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*a^2*c*Sqrt[c - a^2*c*x^2])","A",5,4,23,0.1739,1,"{6153, 6150, 77, 207}"
971,1,91,0,0.0928384,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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]/(2*a*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*a*c*Sqrt[c - a^2*c*x^2])","A",5,4,22,0.1818,1,"{6143, 6140, 44, 207}"
972,1,165,0,0.219334,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^(3/2)),x]","\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}}","\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*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[x])/(c*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*c*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 72}"
973,1,206,0,0.2263953,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^(3/2)),x]","\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}}","\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]/(c*x*Sqrt[c - a^2*c*x^2])) + (a*Sqrt[1 - a^2*x^2])/(2*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (a*Sqrt[1 - a^2*x^2]*Log[x])/(c*Sqrt[c - a^2*c*x^2]) - (5*a*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*c*Sqrt[c - a^2*c*x^2]) + (a*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
974,1,255,0,0.2384129,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^(3/2)),x]","\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}}","\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*c*x^2*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2])/(c*x*Sqrt[c - a^2*c*x^2]) + (a^2*Sqrt[1 - a^2*x^2])/(2*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (2*a^2*Sqrt[1 - a^2*x^2]*Log[x])/(c*Sqrt[c - a^2*c*x^2]) - (7*a^2*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*c*Sqrt[c - a^2*c*x^2]) - (a^2*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
975,1,297,0,0.2412168,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcTanh[a*x]/(x^4*(c - a^2*c*x^2)^(3/2)),x]","\frac{a^3 \sqrt{1-a^2 x^2}}{2 c (1-a x) \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{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}}","\frac{a^3 \sqrt{1-a^2 x^2}}{2 c (1-a x) \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{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]/(3*c*x^3*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2])/(2*c*x^2*Sqrt[c - a^2*c*x^2]) - (2*a^2*Sqrt[1 - a^2*x^2])/(c*x*Sqrt[c - a^2*c*x^2]) + (a^3*Sqrt[1 - a^2*x^2])/(2*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (2*a^3*Sqrt[1 - a^2*x^2]*Log[x])/(c*Sqrt[c - a^2*c*x^2]) - (9*a^3*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*c*Sqrt[c - a^2*c*x^2]) + (a^3*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
976,1,312,0,0.2548433,"\int \frac{e^{\tanh ^{-1}(a x)} x^6}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^6)/(c - a^2*c*x^2)^(5/2),x]","-\frac{x^2 \sqrt{1-a^2 x^2}}{2 a^5 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{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^2 \sqrt{1-a^2 x^2}}{2 a^5 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{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}}",1,"-((x*Sqrt[1 - a^2*x^2])/(a^6*c^2*Sqrt[c - a^2*c*x^2])) - (x^2*Sqrt[1 - a^2*x^2])/(2*a^5*c^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a^7*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) - (5*Sqrt[1 - a^2*x^2])/(4*a^7*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a^7*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (39*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(16*a^7*c^2*Sqrt[c - a^2*c*x^2]) - (9*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(16*a^7*c^2*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
977,1,268,0,0.2460309,"\int \frac{e^{\tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^5)/(c - a^2*c*x^2)^(5/2),x]","-\frac{x \sqrt{1-a^2 x^2}}{a^5 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}}-\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}}",1,"-((x*Sqrt[1 - a^2*x^2])/(a^5*c^2*Sqrt[c - a^2*c*x^2])) + Sqrt[1 - a^2*x^2]/(8*a^6*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(a^6*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a^6*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (23*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(16*a^6*c^2*Sqrt[c - a^2*c*x^2]) + (7*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(16*a^6*c^2*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
978,1,232,0,0.237612,"\int \frac{e^{\tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^4)/(c - a^2*c*x^2)^(5/2),x]","-\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}}","-\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]/(8*a^5*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[1 - a^2*x^2])/(4*a^5*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a^5*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (11*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(16*a^5*c^2*Sqrt[c - a^2*c*x^2]) - (5*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(16*a^5*c^2*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
979,1,184,0,0.2353897,"\int \frac{e^{\tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^3)/(c - a^2*c*x^2)^(5/2),x]","-\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}}","-\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]/(8*a^4*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(2*a^4*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a^4*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a^4*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,25,0.1600,1,"{6153, 6150, 88, 207}"
980,1,184,0,0.2367008,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^(5/2),x]","-\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}}","-\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]/(8*a^3*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(4*a^3*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a^3*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a^3*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,25,0.1600,1,"{6153, 6150, 88, 207}"
981,1,137,0,0.1651095,"\int \frac{e^{\tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x)/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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]/(8*a^2*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a^2*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a^2*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,23,0.1739,1,"{6153, 6150, 77, 207}"
982,1,184,0,0.112075,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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]/(8*a*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(4*a*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,22,0.1818,1,"{6143, 6140, 44, 207}"
983,1,252,0,0.2437179,"\int \frac{e^{\tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x*(c - a^2*c*x^2)^(5/2)),x]","\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}}","\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*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(2*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[x])/(c^2*Sqrt[c - a^2*c*x^2]) - (11*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(16*c^2*Sqrt[c - a^2*c*x^2]) - (5*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(16*c^2*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
984,1,295,0,0.2450479,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x^2*(c - a^2*c*x^2)^(5/2)),x]","\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}}","\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]/(c^2*x*Sqrt[c - a^2*c*x^2])) + (a*Sqrt[1 - a^2*x^2])/(8*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + (3*a*Sqrt[1 - a^2*x^2])/(4*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2])/(8*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (a*Sqrt[1 - a^2*x^2]*Log[x])/(c^2*Sqrt[c - a^2*c*x^2]) - (23*a*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(16*c^2*Sqrt[c - a^2*c*x^2]) + (7*a*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(16*c^2*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
985,1,345,0,0.2566934,"\int \frac{e^{\tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcTanh[a*x]/(x^3*(c - a^2*c*x^2)^(5/2)),x]","\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}}","\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]/(2*c^2*x^2*Sqrt[c - a^2*c*x^2]) - (a*Sqrt[1 - a^2*x^2])/(c^2*x*Sqrt[c - a^2*c*x^2]) + (a^2*Sqrt[1 - a^2*x^2])/(8*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + (a^2*Sqrt[1 - a^2*x^2])/(c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (a^2*Sqrt[1 - a^2*x^2])/(8*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (3*a^2*Sqrt[1 - a^2*x^2]*Log[x])/(c^2*Sqrt[c - a^2*c*x^2]) - (39*a^2*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(16*c^2*Sqrt[c - a^2*c*x^2]) - (9*a^2*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(16*c^2*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
986,1,277,0,0.1320343,"\int \frac{e^{\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^ArcTanh[a*x]/(c - a^2*c*x^2)^(7/2),x]","\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}}","\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]/(24*a*c^3*(1 - a*x)^3*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2])/(32*a*c^3*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2])/(16*a*c^3*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(32*a*c^3*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a*c^3*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(16*a*c^3*Sqrt[c - a^2*c*x^2])","A",5,4,22,0.1818,1,"{6143, 6140, 44, 207}"
987,1,80,0,0.095878,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","Int[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2)^2,x]","\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}","\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, (3 + m)/2, a^2*x^2])/(1 + m) + (a*c^2*x^(2 + m)*Hypergeometric2F1[-3/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",4,3,23,0.1304,1,"{6148, 808, 364}"
988,1,76,0,0.0789355,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","Int[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2),x]","\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}","\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)*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*c*x^(2 + m)*Hypergeometric2F1[-1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",4,3,21,0.1429,1,"{6148, 808, 364}"
989,1,80,0,0.1064103,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{c-a^2 c x^2} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2),x]","\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)}","\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, (3 + m)/2, a^2*x^2])/(c*(1 + m)) + (a*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(c*(2 + m))","A",4,3,23,0.1304,1,"{6148, 808, 364}"
990,1,80,0,0.1058536,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^2,x]","\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)}","\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, (3 + m)/2, a^2*x^2])/(c^2*(1 + m)) + (a*x^(2 + m)*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(c^2*(2 + m))","A",4,3,23,0.1304,1,"{6148, 808, 364}"
991,1,80,0,0.1092853,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^3,x]","\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)}","\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, (3 + m)/2, a^2*x^2])/(c^3*(1 + m)) + (a*x^(2 + m)*Hypergeometric2F1[7/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(c^3*(2 + m))","A",4,3,23,0.1304,1,"{6148, 808, 364}"
992,1,82,0,0.1176994,"\int e^{\tanh ^{-1}(a x)} x^m \left(1-a^2 x^2\right)^{5/2} \, dx","Int[E^ArcTanh[a*x]*x^m*(1 - a^2*x^2)^(5/2),x]","-\frac{2 a^2 x^{m+3}}{m+3}-\frac{2 a^3 x^{m+4}}{m+4}+\frac{a^4 x^{m+5}}{m+5}+\frac{a^5 x^{m+6}}{m+6}+\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}","-\frac{2 a^2 x^{m+3}}{m+3}-\frac{2 a^3 x^{m+4}}{m+4}+\frac{a^4 x^{m+5}}{m+5}+\frac{a^5 x^{m+6}}{m+6}+\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)/(1 + m) + (a*x^(2 + m))/(2 + m) - (2*a^2*x^(3 + m))/(3 + m) - (2*a^3*x^(4 + m))/(4 + m) + (a^4*x^(5 + m))/(5 + m) + (a^5*x^(6 + m))/(6 + m)","A",3,2,24,0.08333,1,"{6150, 88}"
993,1,54,0,0.0987892,"\int e^{\tanh ^{-1}(a x)} x^m \left(1-a^2 x^2\right)^{3/2} \, dx","Int[E^ArcTanh[a*x]*x^m*(1 - a^2*x^2)^(3/2),x]","-\frac{a^2 x^{m+3}}{m+3}-\frac{a^3 x^{m+4}}{m+4}+\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}","-\frac{a^2 x^{m+3}}{m+3}-\frac{a^3 x^{m+4}}{m+4}+\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)/(1 + m) + (a*x^(2 + m))/(2 + m) - (a^2*x^(3 + m))/(3 + m) - (a^3*x^(4 + m))/(4 + m)","A",3,2,24,0.08333,1,"{6150, 75}"
994,1,24,0,0.0799803,"\int e^{\tanh ^{-1}(a x)} x^m \sqrt{1-a^2 x^2} \, dx","Int[E^ArcTanh[a*x]*x^m*Sqrt[1 - a^2*x^2],x]","\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}","\frac{a x^{m+2}}{m+2}+\frac{x^{m+1}}{m+1}",1,"x^(1 + m)/(1 + m) + (a*x^(2 + m))/(2 + m)","A",3,2,24,0.08333,1,"{6150, 43}"
995,1,22,0,0.081731,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\sqrt{1-a^2 x^2}} \, dx","Int[(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",2,2,24,0.08333,1,"{6150, 64}"
996,1,70,0,0.1040095,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(1 - a^2*x^2)^(3/2),x]","\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}","\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)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",6,4,24,0.1667,1,"{6150, 82, 73, 364}"
997,1,70,0,0.1163481,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(1 - a^2*x^2)^(5/2),x]","\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}","\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)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[3, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",6,4,24,0.1667,1,"{6150, 82, 73, 364}"
998,1,274,0,0.2298394,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[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}}{(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{2 a^3 c^2 x^{m+4} \sqrt{c-a^2 c x^2}}{(m+4) \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{a^5 c^2 x^{m+6} \sqrt{c-a^2 c x^2}}{(m+6) \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{2 a^3 c^2 x^{m+4} \sqrt{c-a^2 c x^2}}{(m+4) \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{a^5 c^2 x^{m+6} \sqrt{c-a^2 c x^2}}{(m+6) \sqrt{1-a^2 x^2}}",1,"(c^2*x^(1 + m)*Sqrt[c - a^2*c*x^2])/((1 + m)*Sqrt[1 - a^2*x^2]) + (a*c^2*x^(2 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - a^2*x^2]) - (2*a^2*c^2*x^(3 + m)*Sqrt[c - a^2*c*x^2])/((3 + m)*Sqrt[1 - a^2*x^2]) - (2*a^3*c^2*x^(4 + m)*Sqrt[c - a^2*c*x^2])/((4 + m)*Sqrt[1 - a^2*x^2]) + (a^4*c^2*x^(5 + m)*Sqrt[c - a^2*c*x^2])/((5 + m)*Sqrt[1 - a^2*x^2]) + (a^5*c^2*x^(6 + m)*Sqrt[c - a^2*c*x^2])/((6 + m)*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
999,1,174,0,0.2033003,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[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}}{(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}}","\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 + m)*Sqrt[1 - a^2*x^2]) + (a*c*x^(2 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - a^2*x^2]) - (a^2*c*x^(3 + m)*Sqrt[c - a^2*c*x^2])/((3 + m)*Sqrt[1 - a^2*x^2]) - (a^3*c*x^(4 + m)*Sqrt[c - a^2*c*x^2])/((4 + m)*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 75}"
1000,1,82,0,0.1737536,"\int e^{\tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[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}}{(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}}","\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)*Sqrt[c - a^2*c*x^2])/((1 + m)*Sqrt[1 - a^2*x^2]) + (a*x^(2 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
1001,1,51,0,0.1832271,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\sqrt{c-a^2 c x^2}} \, dx","Int[(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",3,3,25,0.1200,1,"{6153, 6150, 64}"
1002,1,134,0,0.2155301,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"(x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(c*(1 + m)*Sqrt[c - a^2*c*x^2]) + (a*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(c*(2 + m)*Sqrt[c - a^2*c*x^2])","A",7,5,25,0.2000,1,"{6153, 6150, 82, 73, 364}"
1003,1,134,0,0.2118231,"\int \frac{e^{\tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcTanh[a*x]*x^m)/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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,"(x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, a^2*x^2])/(c^2*(1 + m)*Sqrt[c - a^2*c*x^2]) + (a*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[3, (2 + m)/2, (4 + m)/2, a^2*x^2])/(c^2*(2 + m)*Sqrt[c - a^2*c*x^2])","A",7,5,25,0.2000,1,"{6153, 6150, 82, 73, 364}"
1004,1,136,0,0.1494912,"\int e^{\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Int[E^ArcTanh[a*x]*x^m*(c - a^2*c*x^2)^p,x]","\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}","\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,"(x^(1 + m)*(c - a^2*c*x^2)^p*Hypergeometric2F1[(1 + m)/2, 1/2 - p, (3 + m)/2, a^2*x^2])/((1 + m)*(1 - a^2*x^2)^p) + (a*x^(2 + m)*(c - a^2*c*x^2)^p*Hypergeometric2F1[(2 + m)/2, 1/2 - p, (4 + m)/2, a^2*x^2])/((2 + m)*(1 - a^2*x^2)^p)","A",5,4,23,0.1739,1,"{6153, 6148, 808, 364}"
1005,1,85,0,0.1137114,"\int e^{\tanh ^{-1}(a x)} x^3 \left(1-a^2 x^2\right)^p \, dx","Int[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}}}{a^4 (2 p+1)}+\frac{\left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^4 (2 p+3)}","\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)/(a^4*(1 + 2*p))) + (1 - a^2*x^2)^(3/2 + p)/(a^4*(3 + 2*p)) + (a*x^5*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/5","A",6,5,22,0.2273,1,"{6148, 764, 266, 43, 364}"
1006,1,84,0,0.1151288,"\int e^{\tanh ^{-1}(a x)} x^2 \left(1-a^2 x^2\right)^p \, dx","Int[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}}}{a^3 (2 p+1)}+\frac{\left(1-a^2 x^2\right)^{p+\frac{3}{2}}}{a^3 (2 p+3)}","\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)/(a^3*(1 + 2*p))) + (1 - a^2*x^2)^(3/2 + p)/(a^3*(3 + 2*p)) + (x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3","A",6,5,22,0.2273,1,"{6148, 764, 364, 266, 43}"
1007,1,58,0,0.0613426,"\int e^{\tanh ^{-1}(a x)} x \left(1-a^2 x^2\right)^p \, dx","Int[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}}}{a^2 (2 p+1)}","\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 - 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",4,4,20,0.2000,1,"{6148, 764, 261, 364}"
1008,1,59,0,0.0388424,"\int e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p \, dx","Int[E^ArcTanh[a*x]*(1 - a^2*x^2)^p,x]","-\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)}","-\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^(3/2 + 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",2,2,19,0.1053,1,"{6140, 69}"
1009,1,72,0,0.0927399,"\int \frac{e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x} \, dx","Int[(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 p+1}","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])/(1 + 2*p)","A",5,5,22,0.2273,1,"{6148, 764, 266, 65, 245}"
1010,1,75,0,0.1001962,"\int \frac{e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x^2} \, dx","Int[(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 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",5,5,22,0.2273,1,"{6148, 764, 364, 266, 65}"
1011,1,78,0,0.0988352,"\int \frac{e^{\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x^3} \, dx","Int[(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 p+1}-\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])/(1 + 2*p)","A",5,5,22,0.2273,1,"{6148, 764, 266, 65, 364}"
1012,1,134,0,0.1806439,"\int e^{\tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^p \, dx","Int[E^ArcTanh[a*x]*x^3*(c - a^2*c*x^2)^p,x]","\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)}","\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,"-((Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^4*(1 + 2*p))) + ((1 - a^2*x^2)^(3/2)*(c - a^2*c*x^2)^p)/(a^4*(3 + 2*p)) + (a*x^5*(c - a^2*c*x^2)^p*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/(5*(1 - a^2*x^2)^p)","A",7,6,23,0.2609,1,"{6153, 6148, 764, 266, 43, 364}"
1013,1,133,0,0.1813602,"\int e^{\tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^p \, dx","Int[E^ArcTanh[a*x]*x^2*(c - a^2*c*x^2)^p,x]","\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)}","\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,"-((Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^3*(1 + 2*p))) + ((1 - a^2*x^2)^(3/2)*(c - a^2*c*x^2)^p)/(a^3*(3 + 2*p)) + (x^3*(c - a^2*c*x^2)^p*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/(3*(1 - a^2*x^2)^p)","A",7,6,23,0.2609,1,"{6153, 6148, 764, 364, 266, 43}"
1014,1,96,0,0.1093446,"\int e^{\tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Int[E^ArcTanh[a*x]*x*(c - a^2*c*x^2)^p,x]","\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)}","\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,"-((Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^2*(1 + 2*p))) + (a*x^3*(c - a^2*c*x^2)^p*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/(3*(1 - a^2*x^2)^p)","A",5,5,21,0.2381,1,"{6153, 6148, 764, 261, 364}"
1015,1,86,0,0.0644312,"\int e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^ArcTanh[a*x]*(c - a^2*c*x^2)^p,x]","-\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)}","-\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^(3/2 + 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",3,3,20,0.1500,1,"{6143, 6140, 69}"
1016,1,110,0,0.1596835,"\int \frac{e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x} \, dx","Int[(E^ArcTanh[a*x]*(c - a^2*c*x^2)^p)/x,x]","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}","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,"(a*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[1/2, 1/2 - p, 3/2, a^2*x^2])/(1 - a^2*x^2)^p - (Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",6,6,23,0.2609,1,"{6153, 6148, 764, 266, 65, 245}"
1017,1,113,0,0.1665985,"\int \frac{e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^2} \, dx","Int[(E^ArcTanh[a*x]*(c - a^2*c*x^2)^p)/x^2,x]","-\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}","-\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*(1 - a^2*x^2)^p)) - (a*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",6,6,23,0.2609,1,"{6153, 6148, 764, 364, 266, 65}"
1018,1,116,0,0.1606757,"\int \frac{e^{\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^3} \, dx","Int[(E^ArcTanh[a*x]*(c - a^2*c*x^2)^p)/x^3,x]","-\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}","-\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,"-((a*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1/2, 1/2 - p, 1/2, a^2*x^2])/(x*(1 - a^2*x^2)^p)) - (a^2*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[2, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",6,6,23,0.2609,1,"{6153, 6148, 764, 266, 65, 364}"
1019,1,29,0,0.0546501,"\int e^{2 \tanh ^{-1}(a x)} x^4 \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcTanh[a*x])*x^4*(c - a^2*c*x^2),x]","\frac{1}{7} a^2 c x^7+\frac{1}{3} a c x^6+\frac{c x^5}{5}","\frac{1}{7} a^2 c x^7+\frac{1}{3} a c x^6+\frac{c x^5}{5}",1,"(c*x^5)/5 + (a*c*x^6)/3 + (a^2*c*x^7)/7","A",3,2,23,0.08696,1,"{6150, 43}"
1020,1,29,0,0.0546217,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2),x]","\frac{1}{6} a^2 c x^6+\frac{2}{5} a c x^5+\frac{c x^4}{4}","\frac{1}{6} a^2 c x^6+\frac{2}{5} a c x^5+\frac{c x^4}{4}",1,"(c*x^4)/4 + (2*a*c*x^5)/5 + (a^2*c*x^6)/6","A",3,2,23,0.08696,1,"{6150, 43}"
1021,1,29,0,0.0534224,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2),x]","\frac{1}{5} a^2 c x^5+\frac{1}{2} a c x^4+\frac{c x^3}{3}","\frac{1}{5} a^2 c x^5+\frac{1}{2} a c x^4+\frac{c x^3}{3}",1,"(c*x^3)/3 + (a*c*x^4)/2 + (a^2*c*x^5)/5","A",3,2,23,0.08696,1,"{6150, 43}"
1022,1,29,0,0.040211,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2),x]","\frac{1}{4} a^2 c x^4+\frac{2}{3} a c x^3+\frac{c x^2}{2}","\frac{1}{4} a^2 c x^4+\frac{2}{3} a c x^3+\frac{c x^2}{2}",1,"(c*x^2)/2 + (2*a*c*x^3)/3 + (a^2*c*x^4)/4","A",3,2,21,0.09524,1,"{6150, 43}"
1023,1,15,0,0.0190191,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2),x]","\frac{c (a x+1)^3}{3 a}","\frac{c (a x+1)^3}{3 a}",1,"(c*(1 + a*x)^3)/(3*a)","A",2,2,20,0.1000,1,"{6140, 32}"
1024,1,21,0,0.0493203,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x,x]","\frac{1}{2} a^2 c x^2+2 a c x+c \log (x)","\frac{1}{2} a^2 c x^2+2 a c x+c \log (x)",1,"2*a*c*x + (a^2*c*x^2)/2 + c*Log[x]","A",3,2,23,0.08696,1,"{6150, 43}"
1025,1,19,0,0.0494398,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x^2,x]","a^2 c x+2 a c \log (x)-\frac{c}{x}","a^2 c x+2 a c \log (x)-\frac{c}{x}",1,"-(c/x) + a^2*c*x + 2*a*c*Log[x]","A",3,2,23,0.08696,1,"{6150, 43}"
1026,1,23,0,0.0521579,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2))/x^3,x]","a^2 c \log (x)-\frac{2 a c}{x}-\frac{c}{2 x^2}","a^2 c \log (x)-\frac{2 a c}{x}-\frac{c}{2 x^2}",1,"-c/(2*x^2) - (2*a*c)/x + a^2*c*Log[x]","A",3,2,23,0.08696,1,"{6150, 43}"
1027,1,15,0,0.0448639,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^4} \, dx","Int[(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,"-(c*(1 + a*x)^3)/(3*x^3)","A",2,2,23,0.08696,1,"{6150, 37}"
1028,1,48,0,0.0881659,"\int e^{2 \tanh ^{-1}(a x)} x^4 \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*x^4*(c - a^2*c*x^2)^2,x]","-\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}","-\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,"(c^2*x^5)/5 + (a*c^2*x^6)/3 - (a^3*c^2*x^8)/4 - (a^4*c^2*x^9)/9","A",3,2,25,0.08000,1,"{6150, 75}"
1029,1,48,0,0.0892372,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^2,x]","-\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}","-\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*c^2*x^5)/5 - (2*a^3*c^2*x^7)/7 - (a^4*c^2*x^8)/8","A",3,2,25,0.08000,1,"{6150, 75}"
1030,1,48,0,0.0896065,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^2,x]","-\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}","-\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,"(c^2*x^3)/3 + (a*c^2*x^4)/2 - (a^3*c^2*x^6)/3 - (a^4*c^2*x^7)/7","A",3,2,25,0.08000,1,"{6150, 75}"
1031,1,48,0,0.066772,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^2,x]","-\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}","-\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,"(c^2*x^2)/2 + (2*a*c^2*x^3)/3 - (2*a^3*c^2*x^5)/5 - (a^4*c^2*x^6)/6","A",3,2,23,0.08696,1,"{6150, 75}"
1032,1,35,0,0.0370518,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","\frac{c^2 (a x+1)^4}{2 a}-\frac{c^2 (a x+1)^5}{5 a}","\frac{c^2 (a x+1)^4}{2 a}-\frac{c^2 (a x+1)^5}{5 a}",1,"(c^2*(1 + a*x)^4)/(2*a) - (c^2*(1 + a*x)^5)/(5*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1033,1,40,0,0.0746111,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x,x]","-\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)","-\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,"2*a*c^2*x - (2*a^3*c^2*x^3)/3 - (a^4*c^2*x^4)/4 + c^2*Log[x]","A",3,2,25,0.08000,1,"{6150, 75}"
1034,1,41,0,0.0818491,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^2} \, dx","Int[(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",3,2,25,0.08000,1,"{6150, 75}"
1035,1,17,0,0.0692598,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^3} \, dx","Int[(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,"-(c^2*(1 + a*x)^4)/(2*x^2)","A",2,2,25,0.08000,1,"{6150, 74}"
1036,1,39,0,0.0802476,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^4} \, dx","Int[(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,"-c^2/(3*x^3) - (a*c^2)/x^2 - a^4*c^2*x - 2*a^3*c^2*Log[x]","A",3,2,25,0.08000,1,"{6150, 75}"
1037,1,43,0,0.0791424,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^5,x]","\frac{2 a^3 c^2}{x}+a^4 \left(-c^2\right) \log (x)-\frac{2 a c^2}{3 x^3}-\frac{c^2}{4 x^4}","\frac{2 a^3 c^2}{x}+a^4 \left(-c^2\right) \log (x)-\frac{2 a c^2}{3 x^3}-\frac{c^2}{4 x^4}",1,"-c^2/(4*x^4) - (2*a*c^2)/(3*x^3) + (2*a^3*c^2)/x - a^4*c^2*Log[x]","A",3,2,25,0.08000,1,"{6150, 75}"
1038,1,42,0,0.080575,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2}{x^6} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2)/x^6,x]","\frac{a^3 c^2}{x^2}+\frac{a^4 c^2}{x}-\frac{a c^2}{2 x^4}-\frac{c^2}{5 x^5}","\frac{a^3 c^2}{x^2}+\frac{a^4 c^2}{x}-\frac{a c^2}{2 x^4}-\frac{c^2}{5 x^5}",1,"-c^2/(5*x^5) - (a*c^2)/(2*x^4) + (a^3*c^2)/x^2 + (a^4*c^2)/x","A",3,2,25,0.08000,1,"{6150, 75}"
1039,1,87,0,0.1018498,"\int e^{2 \tanh ^{-1}(a x)} x^4 \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*x^4*(c - a^2*c*x^2)^3,x]","\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}","\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*c^3*x^6)/3 - (a^2*c^3*x^7)/7 - (a^3*c^3*x^8)/2 - (a^4*c^3*x^9)/9 + (a^5*c^3*x^10)/5 + (a^6*c^3*x^11)/11","A",3,2,25,0.08000,1,"{6150, 88}"
1040,1,87,0,0.0989541,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^3,x]","\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}","\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*c^3*x^5)/5 - (a^2*c^3*x^6)/6 - (4*a^3*c^3*x^7)/7 - (a^4*c^3*x^8)/8 + (2*a^5*c^3*x^9)/9 + (a^6*c^3*x^10)/10","A",3,2,25,0.08000,1,"{6150, 88}"
1041,1,84,0,0.1028099,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^3,x]","\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}","\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,"(4*c^3*(1 + a*x)^5)/(5*a^3) - (2*c^3*(1 + a*x)^6)/a^3 + (13*c^3*(1 + a*x)^7)/(7*a^3) - (3*c^3*(1 + a*x)^8)/(4*a^3) + (c^3*(1 + a*x)^9)/(9*a^3)","A",3,2,25,0.08000,1,"{6150, 88}"
1042,1,69,0,0.0799643,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^3,x]","\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}","\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,"(-4*c^3*(1 + a*x)^5)/(5*a^2) + (4*c^3*(1 + a*x)^6)/(3*a^2) - (5*c^3*(1 + a*x)^7)/(7*a^2) + (c^3*(1 + a*x)^8)/(8*a^2)","A",3,2,23,0.08696,1,"{6150, 77}"
1043,1,52,0,0.0499648,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","\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}","\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,"(4*c^3*(1 + a*x)^5)/(5*a) - (2*c^3*(1 + a*x)^6)/(3*a) + (c^3*(1 + a*x)^7)/(7*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1044,1,79,0,0.0856803,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x,x]","\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)","\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,"2*a*c^3*x - (a^2*c^3*x^2)/2 - (4*a^3*c^3*x^3)/3 - (a^4*c^3*x^4)/4 + (2*a^5*c^3*x^5)/5 + (a^6*c^3*x^6)/6 + c^3*Log[x]","A",3,2,25,0.08000,1,"{6150, 88}"
1045,1,76,0,0.0908948,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x^2,x]","\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}","\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) - a^2*c^3*x - 2*a^3*c^3*x^2 - (a^4*c^3*x^3)/3 + (a^5*c^3*x^4)/2 + (a^6*c^3*x^5)/5 + 2*a*c^3*Log[x]","A",3,2,25,0.08000,1,"{6150, 88}"
1046,1,78,0,0.095062,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x^3,x]","\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}","\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/(2*x^2) - (2*a*c^3)/x - 4*a^3*c^3*x - (a^4*c^3*x^2)/2 + (2*a^5*c^3*x^3)/3 + (a^6*c^3*x^4)/4 - a^2*c^3*Log[x]","A",3,2,25,0.08000,1,"{6150, 88}"
1047,1,72,0,0.0929093,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3)/x^4,x]","\frac{1}{3} a^6 c^3 x^3+a^5 c^3 x^2-a^4 c^3 x+\frac{a^2 c^3}{x}-4 a^3 c^3 \log (x)-\frac{a c^3}{x^2}-\frac{c^3}{3 x^3}","\frac{1}{3} a^6 c^3 x^3+a^5 c^3 x^2-a^4 c^3 x+\frac{a^2 c^3}{x}-4 a^3 c^3 \log (x)-\frac{a c^3}{x^2}-\frac{c^3}{3 x^3}",1,"-c^3/(3*x^3) - (a*c^3)/x^2 + (a^2*c^3)/x - a^4*c^3*x + a^5*c^3*x^2 + (a^6*c^3*x^3)/3 - 4*a^3*c^3*Log[x]","A",3,2,25,0.08000,1,"{6150, 88}"
1048,1,69,0,0.056424,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^4,x]","-\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}","-\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,"(4*c^4*(1 + a*x)^6)/(3*a) - (12*c^4*(1 + a*x)^7)/(7*a) + (3*c^4*(1 + a*x)^8)/(4*a) - (c^4*(1 + a*x)^9)/(9*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1049,1,63,0,0.111975,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^4}{c-a^2 c x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2),x]","\frac{x^3}{3 a^2 c}+\frac{x^2}{a^3 c}+\frac{3 x}{a^4 c}+\frac{1}{a^5 c (1-a x)}+\frac{4 \log (1-a x)}{a^5 c}","\frac{x^3}{3 a^2 c}+\frac{x^2}{a^3 c}+\frac{3 x}{a^4 c}+\frac{1}{a^5 c (1-a x)}+\frac{4 \log (1-a x)}{a^5 c}",1,"(3*x)/(a^4*c) + x^2/(a^3*c) + x^3/(3*a^2*c) + 1/(a^5*c*(1 - a*x)) + (4*Log[1 - a*x])/(a^5*c)","A",3,2,25,0.08000,1,"{6150, 43}"
1050,1,53,0,0.1040902,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{c-a^2 c x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2),x]","\frac{x^2}{2 a^2 c}+\frac{2 x}{a^3 c}+\frac{1}{a^4 c (1-a x)}+\frac{3 \log (1-a x)}{a^4 c}","\frac{x^2}{2 a^2 c}+\frac{2 x}{a^3 c}+\frac{1}{a^4 c (1-a x)}+\frac{3 \log (1-a x)}{a^4 c}",1,"(2*x)/(a^3*c) + x^2/(2*a^2*c) + 1/(a^4*c*(1 - a*x)) + (3*Log[1 - a*x])/(a^4*c)","A",3,2,25,0.08000,1,"{6150, 43}"
1051,1,39,0,0.0955794,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2),x]","\frac{x}{a^2 c}+\frac{1}{a^3 c (1-a x)}+\frac{2 \log (1-a x)}{a^3 c}","\frac{x}{a^2 c}+\frac{1}{a^3 c (1-a x)}+\frac{2 \log (1-a x)}{a^3 c}",1,"x/(a^2*c) + 1/(a^3*c*(1 - a*x)) + (2*Log[1 - a*x])/(a^3*c)","A",3,2,25,0.08000,1,"{6150, 43}"
1052,1,30,0,0.06539,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2),x]","\frac{1}{a^2 c (1-a x)}+\frac{\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^2*c*(1 - a*x)) + Log[1 - a*x]/(a^2*c)","A",3,2,23,0.08696,1,"{6150, 43}"
1053,1,15,0,0.0331008,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{1}{a c (1-a x)}","\frac{1}{a c (1-a x)}",1,"1/(a*c*(1 - a*x))","A",2,2,22,0.09091,1,"{6140, 32}"
1054,1,31,0,0.0866635,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)} \, dx","Int[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)),x]","\frac{1}{c (1-a x)}-\frac{\log (1-a x)}{c}+\frac{\log (x)}{c}","\frac{1}{c (1-a x)}-\frac{\log (1-a x)}{c}+\frac{\log (x)}{c}",1,"1/(c*(1 - a*x)) + Log[x]/c - Log[1 - a*x]/c","A",3,2,25,0.08000,1,"{6150, 44}"
1055,1,43,0,0.0938533,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)} \, dx","Int[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)),x]","\frac{a}{c (1-a x)}+\frac{2 a \log (x)}{c}-\frac{2 a \log (1-a x)}{c}-\frac{1}{c x}","\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,"-(1/(c*x)) + a/(c*(1 - a*x)) + (2*a*Log[x])/c - (2*a*Log[1 - a*x])/c","A",3,2,25,0.08000,1,"{6150, 44}"
1056,1,60,0,0.1014992,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)} \, dx","Int[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)),x]","\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}","\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/(2*c*x^2) - (2*a)/(c*x) + a^2/(c*(1 - a*x)) + (3*a^2*Log[x])/c - (3*a^2*Log[1 - a*x])/c","A",3,2,25,0.08000,1,"{6150, 44}"
1057,1,71,0,0.1098466,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)} \, dx","Int[E^(2*ArcTanh[a*x])/(x^4*(c - a^2*c*x^2)),x]","\frac{a^3}{c (1-a x)}-\frac{3 a^2}{c x}+\frac{4 a^3 \log (x)}{c}-\frac{4 a^3 \log (1-a x)}{c}-\frac{a}{c x^2}-\frac{1}{3 c x^3}","\frac{a^3}{c (1-a x)}-\frac{3 a^2}{c x}+\frac{4 a^3 \log (x)}{c}-\frac{4 a^3 \log (1-a x)}{c}-\frac{a}{c x^2}-\frac{1}{3 c x^3}",1,"-1/(3*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",3,2,25,0.08000,1,"{6150, 44}"
1058,1,79,0,0.1186915,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2)^2,x]","-\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}-\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}",1,"-(x/(a^4*c^2)) + 1/(4*a^5*c^2*(1 - a*x)^2) - 7/(4*a^5*c^2*(1 - a*x)) - (17*Log[1 - a*x])/(8*a^5*c^2) + Log[1 + a*x]/(8*a^5*c^2)","A",3,2,25,0.08000,1,"{6150, 88}"
1059,1,70,0,0.1067007,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^2,x]","-\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}","-\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/(4*a^4*c^2*(1 - a*x)^2) - 5/(4*a^4*c^2*(1 - a*x)) - (7*Log[1 - a*x])/(8*a^4*c^2) - Log[1 + a*x]/(8*a^4*c^2)","A",3,2,25,0.08000,1,"{6150, 88}"
1060,1,51,0,0.105425,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^2,x]","-\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}","-\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,"1/(4*a^3*c^2*(1 - a*x)^2) - 3/(4*a^3*c^2*(1 - a*x)) + ArcTanh[a*x]/(4*a^3*c^2)","A",4,3,25,0.1200,1,"{6150, 88, 207}"
1061,1,51,0,0.0795022,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^2,x]","-\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}","-\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,"1/(4*a^2*c^2*(1 - a*x)^2) - 1/(4*a^2*c^2*(1 - a*x)) - ArcTanh[a*x]/(4*a^2*c^2)","A",4,3,23,0.1304,1,"{6150, 77, 207}"
1062,1,51,0,0.052897,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","\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}","\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,"1/(4*a*c^2*(1 - a*x)^2) + 1/(4*a*c^2*(1 - a*x)) + ArcTanh[a*x]/(4*a*c^2)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1063,1,64,0,0.0992315,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^2),x]","\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}","\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,"1/(4*c^2*(1 - a*x)^2) + 3/(4*c^2*(1 - a*x)) + Log[x]/c^2 - (7*Log[1 - a*x])/(8*c^2) - Log[1 + a*x]/(8*c^2)","A",3,2,25,0.08000,1,"{6150, 72}"
1064,1,78,0,0.1115471,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^2),x]","\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}","\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,"-(1/(c^2*x)) + a/(4*c^2*(1 - a*x)^2) + (5*a)/(4*c^2*(1 - a*x)) + (2*a*Log[x])/c^2 - (17*a*Log[1 - a*x])/(8*c^2) + (a*Log[1 + a*x])/(8*c^2)","A",3,2,25,0.08000,1,"{6150, 88}"
1065,1,99,0,0.1223505,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^2),x]","\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}","\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/(2*c^2*x^2) - (2*a)/(c^2*x) + a^2/(4*c^2*(1 - a*x)^2) + (7*a^2)/(4*c^2*(1 - a*x)) + (4*a^2*Log[x])/c^2 - (31*a^2*Log[1 - a*x])/(8*c^2) - (a^2*Log[1 + a*x])/(8*c^2)","A",3,2,25,0.08000,1,"{6150, 88}"
1066,1,110,0,0.1337707,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcTanh[a*x])/(x^4*(c - a^2*c*x^2)^2),x]","\frac{9 a^3}{4 c^2 (1-a x)}+\frac{a^3}{4 c^2 (1-a x)^2}-\frac{4 a^2}{c^2 x}+\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{a}{c^2 x^2}-\frac{1}{3 c^2 x^3}","\frac{9 a^3}{4 c^2 (1-a x)}+\frac{a^3}{4 c^2 (1-a x)^2}-\frac{4 a^2}{c^2 x}+\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{a}{c^2 x^2}-\frac{1}{3 c^2 x^3}",1,"-1/(3*c^2*x^3) - a/(c^2*x^2) - (4*a^2)/(c^2*x) + a^3/(4*c^2*(1 - a*x)^2) + (9*a^3)/(4*c^2*(1 - a*x)) + (6*a^3*Log[x])/c^2 - (49*a^3*Log[1 - a*x])/(8*c^2) + (a^3*Log[1 + a*x])/(8*c^2)","A",3,2,25,0.08000,1,"{6150, 88}"
1067,1,105,0,0.1332587,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^(2*ArcTanh[a*x])*x^5)/(c - a^2*c*x^2)^3,x]","\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}","\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,"1/(12*a^6*c^3*(1 - a*x)^3) - 1/(2*a^6*c^3*(1 - a*x)^2) + 23/(16*a^6*c^3*(1 - a*x)) + 1/(16*a^6*c^3*(1 + a*x)) + (13*Log[1 - a*x])/(16*a^6*c^3) + (3*Log[1 + a*x])/(16*a^6*c^3)","A",3,2,25,0.08000,1,"{6150, 88}"
1068,1,86,0,0.1375533,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^(2*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2)^3,x]","\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}","\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,"1/(12*a^5*c^3*(1 - a*x)^3) - 3/(8*a^5*c^3*(1 - a*x)^2) + 11/(16*a^5*c^3*(1 - a*x)) - 1/(16*a^5*c^3*(1 + a*x)) - ArcTanh[a*x]/(4*a^5*c^3)","A",4,3,25,0.1200,1,"{6150, 88, 207}"
1069,1,86,0,0.1233702,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^3,x]","\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}","\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,"1/(12*a^4*c^3*(1 - a*x)^3) - 1/(4*a^4*c^3*(1 - a*x)^2) + 3/(16*a^4*c^3*(1 - a*x)) + 1/(16*a^4*c^3*(1 + a*x)) + ArcTanh[a*x]/(8*a^4*c^3)","A",4,3,25,0.1200,1,"{6150, 88, 207}"
1070,1,31,0,0.0889472,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(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 (1-a x)^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",2,2,25,0.08000,1,"{6150, 81}"
1071,1,68,0,0.0880824,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^3,x]","-\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}","-\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*c^3*(1 - a*x)^3) - 1/(16*a^2*c^3*(1 - a*x)) + 1/(16*a^2*c^3*(1 + a*x)) - ArcTanh[a*x]/(8*a^2*c^3)","A",4,3,23,0.1304,1,"{6150, 77, 207}"
1072,1,86,0,0.0676645,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","\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}","\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*a*c^3*(1 - a*x)^3) + 1/(8*a*c^3*(1 - a*x)^2) + 3/(16*a*c^3*(1 - a*x)) - 1/(16*a*c^3*(1 + a*x)) + ArcTanh[a*x]/(4*a*c^3)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1073,1,93,0,0.1186718,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^3),x]","\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}","\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,"1/(12*c^3*(1 - a*x)^3) + 1/(4*c^3*(1 - a*x)^2) + 11/(16*c^3*(1 - a*x)) + 1/(16*c^3*(1 + a*x)) + Log[x]/c^3 - (13*Log[1 - a*x])/(16*c^3) - (3*Log[1 + a*x])/(16*c^3)","A",3,2,25,0.08000,1,"{6150, 88}"
1074,1,109,0,0.1352687,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^3),x]","\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}","\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,"-(1/(c^3*x)) + a/(12*c^3*(1 - a*x)^3) + (3*a)/(8*c^3*(1 - a*x)^2) + (23*a)/(16*c^3*(1 - a*x)) - a/(16*c^3*(1 + a*x)) + (2*a*Log[x])/c^3 - (9*a*Log[1 - a*x])/(4*c^3) + (a*Log[1 + a*x])/(4*c^3)","A",3,2,25,0.08000,1,"{6150, 88}"
1075,1,134,0,0.1513267,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^3} \, dx","Int[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^3),x]","\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}","\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,"-1/(2*c^3*x^2) - (2*a)/(c^3*x) + a^2/(12*c^3*(1 - a*x)^3) + a^2/(2*c^3*(1 - a*x)^2) + (39*a^2)/(16*c^3*(1 - a*x)) + a^2/(16*c^3*(1 + a*x)) + (5*a^2*Log[x])/c^3 - (75*a^2*Log[1 - a*x])/(16*c^3) - (5*a^2*Log[1 + a*x])/(16*c^3)","A",3,2,25,0.08000,1,"{6150, 88}"
1076,1,121,0,0.0910009,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","\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}","\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,"1/(32*a*c^4*(1 - a*x)^4) + 1/(16*a*c^4*(1 - a*x)^3) + 3/(32*a*c^4*(1 - a*x)^2) + 5/(32*a*c^4*(1 - a*x)) - 1/(64*a*c^4*(1 + a*x)^2) - 5/(64*a*c^4*(1 + a*x)) + (15*ArcTanh[a*x])/(64*a*c^4)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1077,1,137,0,0.329491,"\int e^{2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcTanh[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","-\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 x^2 \sqrt{c-a^2 c x^2}}{5 a^2}-\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}","-\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 x^2 \sqrt{c-a^2 c x^2}}{5 a^2}-\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,"(-3*x^2*Sqrt[c - a^2*c*x^2])/(5*a^2) - (x^3*Sqrt[c - a^2*c*x^2])/(2*a) - (x^4*Sqrt[c - a^2*c*x^2])/5 - (3*(8 + 5*a*x)*Sqrt[c - a^2*c*x^2])/(20*a^4) + (3*Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(4*a^4)","A",7,6,27,0.2222,1,"{6151, 1809, 833, 780, 217, 203}"
1078,1,112,0,0.2873305,"\int e^{2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcTanh[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","-\frac{1}{4} x^3 \sqrt{c-a^2 c x^2}-\frac{2 x^2 \sqrt{c-a^2 c x^2}}{3 a}-\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}","-\frac{1}{4} x^3 \sqrt{c-a^2 c x^2}-\frac{2 x^2 \sqrt{c-a^2 c x^2}}{3 a}-\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,"(-2*x^2*Sqrt[c - a^2*c*x^2])/(3*a) - (x^3*Sqrt[c - a^2*c*x^2])/4 - ((32 + 21*a*x)*Sqrt[c - a^2*c*x^2])/(24*a^3) + (7*Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(8*a^3)","A",6,6,27,0.2222,1,"{6151, 1809, 833, 780, 217, 203}"
1079,1,84,0,0.1822435,"\int e^{2 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcTanh[a*x])*x*Sqrt[c - a^2*c*x^2],x]","-\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}","-\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,"-(x^2*Sqrt[c - a^2*c*x^2])/3 - ((5 + 3*a*x)*Sqrt[c - a^2*c*x^2])/(3*a^2) + (Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/a^2","A",5,5,25,0.2000,1,"{6151, 1809, 780, 217, 203}"
1080,1,86,0,0.0784366,"\int e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2],x]","-\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}","-\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,"(-3*Sqrt[c - a^2*c*x^2])/(2*a) - ((1 + a*x)*Sqrt[c - a^2*c*x^2])/(2*a) + (3*Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(2*a)","A",5,5,24,0.2083,1,"{6141, 671, 641, 217, 203}"
1081,1,78,0,0.24485,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x,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)","-\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*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] - Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",8,8,27,0.2963,1,"{6151, 1809, 844, 217, 203, 266, 63, 208}"
1082,1,82,0,0.2473747,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^2,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)","-\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*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] - 2*a*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",8,8,27,0.2963,1,"{6151, 1807, 844, 217, 203, 266, 63, 208}"
1083,1,78,0,0.2464927,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^3,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)","-\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,"-Sqrt[c - a^2*c*x^2]/(2*x^2) - (2*a*Sqrt[c - a^2*c*x^2])/x - (3*a^2*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/2","A",6,6,27,0.2222,1,"{6151, 1807, 807, 266, 63, 208}"
1084,1,101,0,0.2719938,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^4,x]","-\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)","-\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,"-Sqrt[c - a^2*c*x^2]/(3*x^3) - (a*Sqrt[c - a^2*c*x^2])/x^2 - (5*a^2*Sqrt[c - a^2*c*x^2])/(3*x) - a^3*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",7,7,27,0.2593,1,"{6151, 1807, 835, 807, 266, 63, 208}"
1085,1,130,0,0.3092712,"\int \frac{e^{2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^5,x]","-\frac{4 a^3 \sqrt{c-a^2 c x^2}}{3 x}-\frac{7 a^2 \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{2 a \sqrt{c-a^2 c x^2}}{3 x^3}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4}-\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}-\frac{7 a^2 \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{2 a \sqrt{c-a^2 c x^2}}{3 x^3}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4}-\frac{7}{8} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-Sqrt[c - a^2*c*x^2]/(4*x^4) - (2*a*Sqrt[c - a^2*c*x^2])/(3*x^3) - (7*a^2*Sqrt[c - a^2*c*x^2])/(8*x^2) - (4*a^3*Sqrt[c - a^2*c*x^2])/(3*x) - (7*a^4*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/8","A",8,7,27,0.2593,1,"{6151, 1807, 835, 807, 266, 63, 208}"
1086,1,161,0,0.3358745,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^(3/2),x]","\frac{c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a^4}-\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{11 x^2 \left(c-a^2 c x^2\right)^{3/2}}{35 a^2}+\frac{c x \sqrt{c-a^2 c x^2}}{8 a^3}-\frac{(105 a x+88) \left(c-a^2 c x^2\right)^{3/2}}{420 a^4}","\frac{c^{3/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{8 a^4}-\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{11 x^2 \left(c-a^2 c x^2\right)^{3/2}}{35 a^2}+\frac{c x \sqrt{c-a^2 c x^2}}{8 a^3}-\frac{(105 a x+88) \left(c-a^2 c x^2\right)^{3/2}}{420 a^4}",1,"(c*x*Sqrt[c - a^2*c*x^2])/(8*a^3) - (11*x^2*(c - a^2*c*x^2)^(3/2))/(35*a^2) - (x^3*(c - a^2*c*x^2)^(3/2))/(3*a) - (x^4*(c - a^2*c*x^2)^(3/2))/7 - ((88 + 105*a*x)*(c - a^2*c*x^2)^(3/2))/(420*a^4) + (c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(8*a^4)","A",8,7,27,0.2593,1,"{6151, 1809, 833, 780, 195, 217, 203}"
1087,1,136,0,0.3083533,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^(3/2),x]","\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{1}{6} x^3 \left(c-a^2 c x^2\right)^{3/2}-\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{(45 a x+32) \left(c-a^2 c x^2\right)^{3/2}}{120 a^3}","\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{1}{6} x^3 \left(c-a^2 c x^2\right)^{3/2}-\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{(45 a x+32) \left(c-a^2 c x^2\right)^{3/2}}{120 a^3}",1,"(3*c*x*Sqrt[c - a^2*c*x^2])/(16*a^2) - (2*x^2*(c - a^2*c*x^2)^(3/2))/(5*a) - (x^3*(c - a^2*c*x^2)^(3/2))/6 - ((32 + 45*a*x)*(c - a^2*c*x^2)^(3/2))/(120*a^3) + (3*c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(16*a^3)","A",7,7,27,0.2593,1,"{6151, 1809, 833, 780, 195, 217, 203}"
1088,1,111,0,0.1949929,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^(3/2),x]","\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}","\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*x*Sqrt[c - a^2*c*x^2])/(4*a) - (x^2*(c - a^2*c*x^2)^(3/2))/5 - ((14 + 15*a*x)*(c - a^2*c*x^2)^(3/2))/(30*a^2) + (c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(4*a^2)","A",6,6,25,0.2400,1,"{6151, 1809, 780, 195, 217, 203}"
1089,1,107,0,0.0855183,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2),x]","\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}","\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,"(5*c*x*Sqrt[c - a^2*c*x^2])/8 - (5*(c - a^2*c*x^2)^(3/2))/(12*a) - ((1 + a*x)*(c - a^2*c*x^2)^(3/2))/(4*a) + (5*c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(8*a)","A",6,6,24,0.2500,1,"{6141, 671, 641, 195, 217, 203}"
1090,1,101,0,0.2863733,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x,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}","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*(1 + a*x)*Sqrt[c - a^2*c*x^2] - (c - a^2*c*x^2)^(3/2)/3 + c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] - c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",9,9,27,0.3333,1,"{6151, 1809, 815, 844, 217, 203, 266, 63, 208}"
1091,1,112,0,0.2854761,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^2,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}","-\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,"(a*c*(4 - a*x)*Sqrt[c - a^2*c*x^2])/2 - (c - a^2*c*x^2)^(3/2)/x - (a*c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/2 - 2*a*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",9,9,27,0.3333,1,"{6151, 1807, 815, 844, 217, 203, 266, 63, 208}"
1092,1,121,0,0.2892298,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^3,x]","-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}","-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,"-(a*c*(4 - a*x)*Sqrt[c - a^2*c*x^2])/(2*x) - (c - a^2*c*x^2)^(3/2)/(2*x^2) - 2*a^2*c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] - (a^2*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/2","A",9,9,27,0.3333,1,"{6151, 1807, 813, 844, 217, 203, 266, 63, 208}"
1093,1,115,0,0.2823995,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^4,x]","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)-\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)-\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}",1,"-((a*c*(1 + a*x)*Sqrt[c - a^2*c*x^2])/x^2) - (c - a^2*c*x^2)^(3/2)/(3*x^3) - a^3*c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] + a^3*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",9,9,27,0.3333,1,"{6151, 1807, 811, 844, 217, 203, 266, 63, 208}"
1094,1,106,0,0.2567827,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^5,x]","\frac{5}{8} a^4 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{5 a^2 c \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{2 a \left(c-a^2 c x^2\right)^{3/2}}{3 x^3}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{4 x^4}","\frac{5}{8} a^4 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)-\frac{5 a^2 c \sqrt{c-a^2 c x^2}}{8 x^2}-\frac{2 a \left(c-a^2 c x^2\right)^{3/2}}{3 x^3}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{4 x^4}",1,"(-5*a^2*c*Sqrt[c - a^2*c*x^2])/(8*x^2) - (c - a^2*c*x^2)^(3/2)/(4*x^4) - (2*a*(c - a^2*c*x^2)^(3/2))/(3*x^3) + (5*a^4*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/8","A",7,7,27,0.2593,1,"{6151, 1807, 807, 266, 47, 63, 208}"
1095,1,131,0,0.2927196,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^6} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^6,x]","\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}-\frac{7 a^2 \left(c-a^2 c x^2\right)^{3/2}}{15 x^3}-\frac{a \left(c-a^2 c x^2\right)^{3/2}}{2 x^4}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{5 x^5}","\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}-\frac{7 a^2 \left(c-a^2 c x^2\right)^{3/2}}{15 x^3}-\frac{a \left(c-a^2 c x^2\right)^{3/2}}{2 x^4}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{5 x^5}",1,"-(a^3*c*Sqrt[c - a^2*c*x^2])/(4*x^2) - (c - a^2*c*x^2)^(3/2)/(5*x^5) - (a*(c - a^2*c*x^2)^(3/2))/(2*x^4) - (7*a^2*(c - a^2*c*x^2)^(3/2))/(15*x^3) + (a^5*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/4","A",8,8,27,0.2963,1,"{6151, 1807, 835, 807, 266, 47, 63, 208}"
1096,1,156,0,0.3301165,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^7} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^7,x]","\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}-\frac{3 a^2 \left(c-a^2 c x^2\right)^{3/2}}{8 x^4}-\frac{2 a \left(c-a^2 c x^2\right)^{3/2}}{5 x^5}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{6 x^6}","\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}-\frac{3 a^2 \left(c-a^2 c x^2\right)^{3/2}}{8 x^4}-\frac{2 a \left(c-a^2 c x^2\right)^{3/2}}{5 x^5}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{6 x^6}",1,"(-3*a^4*c*Sqrt[c - a^2*c*x^2])/(16*x^2) - (c - a^2*c*x^2)^(3/2)/(6*x^6) - (2*a*(c - a^2*c*x^2)^(3/2))/(5*x^5) - (3*a^2*(c - a^2*c*x^2)^(3/2))/(8*x^4) - (4*a^3*(c - a^2*c*x^2)^(3/2))/(15*x^3) + (3*a^6*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/16","A",9,8,27,0.2963,1,"{6151, 1807, 835, 807, 266, 47, 63, 208}"
1097,1,181,0,0.3714032,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2}}{x^8} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2))/x^8,x]","\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}-\frac{11 a^2 \left(c-a^2 c x^2\right)^{3/2}}{35 x^5}-\frac{a \left(c-a^2 c x^2\right)^{3/2}}{3 x^6}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{7 x^7}","\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}-\frac{11 a^2 \left(c-a^2 c x^2\right)^{3/2}}{35 x^5}-\frac{a \left(c-a^2 c x^2\right)^{3/2}}{3 x^6}-\frac{\left(c-a^2 c x^2\right)^{3/2}}{7 x^7}",1,"-(a^5*c*Sqrt[c - a^2*c*x^2])/(8*x^2) - (c - a^2*c*x^2)^(3/2)/(7*x^7) - (a*(c - a^2*c*x^2)^(3/2))/(3*x^6) - (11*a^2*(c - a^2*c*x^2)^(3/2))/(35*x^5) - (a^3*(c - a^2*c*x^2)^(3/2))/(4*x^4) - (22*a^4*(c - a^2*c*x^2)^(3/2))/(105*x^3) + (a^7*c^(3/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/8","A",10,8,27,0.2963,1,"{6151, 1807, 835, 807, 266, 47, 63, 208}"
1098,1,187,0,0.3700204,"\int e^{2 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^(5/2),x]","\frac{3 c^2 x \sqrt{c-a^2 c x^2}}{64 a^3}+\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{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{13 x^2 \left(c-a^2 c x^2\right)^{5/2}}{63 a^2}+\frac{c x \left(c-a^2 c x^2\right)^{3/2}}{32 a^3}-\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{3 c^{5/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{64 a^4}-\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{13 x^2 \left(c-a^2 c x^2\right)^{5/2}}{63 a^2}+\frac{c x \left(c-a^2 c x^2\right)^{3/2}}{32 a^3}-\frac{(315 a x+208) \left(c-a^2 c x^2\right)^{5/2}}{2520 a^4}",1,"(3*c^2*x*Sqrt[c - a^2*c*x^2])/(64*a^3) + (c*x*(c - a^2*c*x^2)^(3/2))/(32*a^3) - (13*x^2*(c - a^2*c*x^2)^(5/2))/(63*a^2) - (x^3*(c - a^2*c*x^2)^(5/2))/(4*a) - (x^4*(c - a^2*c*x^2)^(5/2))/9 - ((208 + 315*a*x)*(c - a^2*c*x^2)^(5/2))/(2520*a^4) + (3*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(64*a^4)","A",9,7,27,0.2593,1,"{6151, 1809, 833, 780, 195, 217, 203}"
1099,1,162,0,0.3252937,"\int e^{2 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^(5/2),x]","\frac{11 c^2 x \sqrt{c-a^2 c x^2}}{128 a^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{1}{8} x^3 \left(c-a^2 c x^2\right)^{5/2}-\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{(385 a x+192) \left(c-a^2 c x^2\right)^{5/2}}{1680 a^3}","\frac{11 c^2 x \sqrt{c-a^2 c x^2}}{128 a^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{1}{8} x^3 \left(c-a^2 c x^2\right)^{5/2}-\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{(385 a x+192) \left(c-a^2 c x^2\right)^{5/2}}{1680 a^3}",1,"(11*c^2*x*Sqrt[c - a^2*c*x^2])/(128*a^2) + (11*c*x*(c - a^2*c*x^2)^(3/2))/(192*a^2) - (2*x^2*(c - a^2*c*x^2)^(5/2))/(7*a) - (x^3*(c - a^2*c*x^2)^(5/2))/8 - ((192 + 385*a*x)*(c - a^2*c*x^2)^(5/2))/(1680*a^3) + (11*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(128*a^3)","A",8,7,27,0.2593,1,"{6151, 1809, 833, 780, 195, 217, 203}"
1100,1,137,0,0.2157496,"\int e^{2 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*x*(c - a^2*c*x^2)^(5/2),x]","\frac{c^2 x \sqrt{c-a^2 c x^2}}{8 a}+\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 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}","\frac{c^2 x \sqrt{c-a^2 c x^2}}{8 a}+\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 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,"(c^2*x*Sqrt[c - a^2*c*x^2])/(8*a) + (c*x*(c - a^2*c*x^2)^(3/2))/(12*a) - (x^2*(c - a^2*c*x^2)^(5/2))/7 - ((27 + 35*a*x)*(c - a^2*c*x^2)^(5/2))/(105*a^2) + (c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(8*a^2)","A",7,6,25,0.2400,1,"{6151, 1809, 780, 195, 217, 203}"
1101,1,130,0,0.0983591,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2),x]","\frac{7}{16} c^2 x \sqrt{c-a^2 c 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}{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}","\frac{7}{16} c^2 x \sqrt{c-a^2 c 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}{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,"(7*c^2*x*Sqrt[c - a^2*c*x^2])/16 + (7*c*x*(c - a^2*c*x^2)^(3/2))/24 - (7*(c - a^2*c*x^2)^(5/2))/(30*a) - ((1 + a*x)*(c - a^2*c*x^2)^(5/2))/(6*a) + (7*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(16*a)","A",7,6,24,0.2500,1,"{6141, 671, 641, 195, 217, 203}"
1102,1,136,0,0.3338717,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x,x]","\frac{1}{4} c^2 (3 a x+4) \sqrt{c-a^2 c x^2}+\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}{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}","\frac{1}{4} c^2 (3 a x+4) \sqrt{c-a^2 c x^2}+\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}{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,"(c^2*(4 + 3*a*x)*Sqrt[c - a^2*c*x^2])/4 + (c*(2 + 3*a*x)*(c - a^2*c*x^2)^(3/2))/6 - (c - a^2*c*x^2)^(5/2)/5 + (3*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/4 - c^(5/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",10,9,27,0.3333,1,"{6151, 1809, 815, 844, 217, 203, 266, 63, 208}"
1103,1,141,0,0.3348672,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^2} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^2,x]","\frac{1}{8} a c^2 (16-9 a x) \sqrt{c-a^2 c x^2}-\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}{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}","\frac{1}{8} a c^2 (16-9 a x) \sqrt{c-a^2 c x^2}-\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}{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,"(a*c^2*(16 - 9*a*x)*Sqrt[c - a^2*c*x^2])/8 + (a*c*(8 - 9*a*x)*(c - a^2*c*x^2)^(3/2))/12 - (c - a^2*c*x^2)^(5/2)/x - (9*a*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/8 - 2*a*c^(5/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",10,9,27,0.3333,1,"{6151, 1807, 815, 844, 217, 203, 266, 63, 208}"
1104,1,151,0,0.3316364,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^3} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^3,x]","-\frac{1}{2} a^2 c^2 (6 a x+1) \sqrt{c-a^2 c 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{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}","-\frac{1}{2} a^2 c^2 (6 a x+1) \sqrt{c-a^2 c 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{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,"-(a^2*c^2*(1 + 6*a*x)*Sqrt[c - a^2*c*x^2])/2 - (a*c*(12 + a*x)*(c - a^2*c*x^2)^(3/2))/(6*x) - (c - a^2*c*x^2)^(5/2)/(2*x^2) - 3*a^2*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] + (a^2*c^(5/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/2","A",10,10,27,0.3704,1,"{6151, 1807, 813, 815, 844, 217, 203, 266, 63, 208}"
1105,1,155,0,0.3421399,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^4} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^4,x]","-\frac{a^2 c^2 (6 a x+1) \sqrt{c-a^2 c x^2}}{2 x}-\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)-\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{a^2 c^2 (6 a x+1) \sqrt{c-a^2 c x^2}}{2 x}-\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)-\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}",1,"-(a^2*c^2*(1 + 6*a*x)*Sqrt[c - a^2*c*x^2])/(2*x) - (a*c*(6 - a*x)*(c - a^2*c*x^2)^(3/2))/(6*x^2) - (c - a^2*c*x^2)^(5/2)/(3*x^3) - (a^3*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/2 + 3*a^3*c^(5/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",10,9,27,0.3333,1,"{6151, 1807, 813, 844, 217, 203, 266, 63, 208}"
1106,1,155,0,0.333742,"\int \frac{e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2}}{x^5} \, dx","Int[(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2))/x^5,x]","\frac{a^3 c^2 (16-9 a x) \sqrt{c-a^2 c x^2}}{8 x}+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 c (9 a x+16) \left(c-a^2 c x^2\right)^{3/2}}{24 x^3}-\frac{\left(c-a^2 c x^2\right)^{5/2}}{4 x^4}","\frac{a^3 c^2 (16-9 a x) \sqrt{c-a^2 c x^2}}{8 x}+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 c (9 a x+16) \left(c-a^2 c x^2\right)^{3/2}}{24 x^3}-\frac{\left(c-a^2 c x^2\right)^{5/2}}{4 x^4}",1,"(a^3*c^2*(16 - 9*a*x)*Sqrt[c - a^2*c*x^2])/(8*x) - (a*c*(16 + 9*a*x)*(c - a^2*c*x^2)^(3/2))/(24*x^3) - (c - a^2*c*x^2)^(5/2)/(4*x^4) + 2*a^4*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] + (9*a^4*c^(5/2)*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/8","A",10,10,27,0.3704,1,"{6151, 1807, 811, 813, 844, 217, 203, 266, 63, 208}"
1107,1,153,0,0.1097017,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2),x]","\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{45 c^{7/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a}+\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}","\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{45 c^{7/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a}+\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,"(45*c^3*x*Sqrt[c - a^2*c*x^2])/128 + (15*c^2*x*(c - a^2*c*x^2)^(3/2))/64 + (3*c*x*(c - a^2*c*x^2)^(5/2))/16 - (9*(c - a^2*c*x^2)^(7/2))/(56*a) - ((1 + a*x)*(c - a^2*c*x^2)^(7/2))/(8*a) + (45*c^(7/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(128*a)","A",8,6,24,0.2500,1,"{6141, 671, 641, 195, 217, 203}"
1108,1,137,0,0.355805,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x^3)/Sqrt[c - a^2*c*x^2],x]","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 a^2 c}+\frac{x \sqrt{c-a^2 c x^2}}{a^3 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^2 \sqrt{c-a^2 c x^2}}{3 a^2 c}+\frac{x \sqrt{c-a^2 c x^2}}{a^3 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}}",1,"(1 + a*x)^2/(a^4*Sqrt[c - a^2*c*x^2]) + (11*Sqrt[c - a^2*c*x^2])/(3*a^4*c) + (x*Sqrt[c - a^2*c*x^2])/(a^3*c) + (x^2*Sqrt[c - a^2*c*x^2])/(3*a^2*c) - (3*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(a^4*Sqrt[c])","A",7,6,27,0.2222,1,"{6151, 1635, 1815, 641, 217, 203}"
1109,1,93,0,0.2489506,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x^2)/Sqrt[c - a^2*c*x^2],x]","\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}}","\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,"(1 + a*x)^2/(a^3*Sqrt[c - a^2*c*x^2]) + ((6 + a*x)*Sqrt[c - a^2*c*x^2])/(2*a^3*c) - (5*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(2*a^3*Sqrt[c])","A",5,5,27,0.1852,1,"{6151, 1635, 780, 217, 203}"
1110,1,84,0,0.1194625,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x)/Sqrt[c - a^2*c*x^2],x]","\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}}","\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,"(1 + a*x)^2/(a^2*Sqrt[c - a^2*c*x^2]) + (2*Sqrt[c - a^2*c*x^2])/(a^2*c) - (2*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(a^2*Sqrt[c])","A",5,5,25,0.2000,1,"{6151, 789, 641, 217, 203}"
1111,1,60,0,0.0660823,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^(2*ArcTanh[a*x])/Sqrt[c - a^2*c*x^2],x]","\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}}","\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*(1 + a*x))/(a*Sqrt[c - a^2*c*x^2]) - ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]]/(a*Sqrt[c])","A",4,4,24,0.1667,1,"{6141, 653, 217, 203}"
1112,1,52,0,0.2281301,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \sqrt{c-a^2 c x^2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x*Sqrt[c - a^2*c*x^2]),x]","\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}}","\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*(1 + a*x))/Sqrt[c - a^2*c*x^2] - ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]/Sqrt[c]","A",5,5,27,0.1852,1,"{6151, 1805, 266, 63, 208}"
1113,1,77,0,0.2495834,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \sqrt{c-a^2 c x^2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x^2*Sqrt[c - a^2*c*x^2]),x]","\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}}","\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,"(2*a*(1 + a*x))/Sqrt[c - a^2*c*x^2] - Sqrt[c - a^2*c*x^2]/(c*x) - (2*a*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/Sqrt[c]","A",6,6,27,0.2222,1,"{6151, 1805, 807, 266, 63, 208}"
1114,1,109,0,0.3233693,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \sqrt{c-a^2 c x^2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x^3*Sqrt[c - a^2*c*x^2]),x]","\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}}","\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,"(2*a^2*(1 + a*x))/Sqrt[c - a^2*c*x^2] - Sqrt[c - a^2*c*x^2]/(2*c*x^2) - (2*a*Sqrt[c - a^2*c*x^2])/(c*x) - (5*a^2*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/(2*Sqrt[c])","A",7,7,27,0.2593,1,"{6151, 1805, 1807, 807, 266, 63, 208}"
1115,1,135,0,0.4065313,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^4 \sqrt{c-a^2 c x^2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x^4*Sqrt[c - a^2*c*x^2]),x]","\frac{2 a^3 (a x+1)}{\sqrt{c-a^2 c x^2}}-\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{3 a^3 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{\sqrt{c}}","\frac{2 a^3 (a x+1)}{\sqrt{c-a^2 c x^2}}-\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{3 a^3 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{\sqrt{c}}",1,"(2*a^3*(1 + a*x))/Sqrt[c - a^2*c*x^2] - Sqrt[c - a^2*c*x^2]/(3*c*x^3) - (a*Sqrt[c - a^2*c*x^2])/(c*x^2) - (8*a^2*Sqrt[c - a^2*c*x^2])/(3*c*x) - (3*a^3*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/Sqrt[c]","A",8,7,27,0.2593,1,"{6151, 1805, 1807, 807, 266, 63, 208}"
1116,1,117,0,0.3206846,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^(3/2),x]","-\frac{\sqrt{c-a^2 c x^2}}{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{(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}}","-\frac{\sqrt{c-a^2 c x^2}}{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{(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,"(1 + a*x)^2/(3*a^4*(c - a^2*c*x^2)^(3/2)) - (8*(1 + a*x))/(3*a^4*c*Sqrt[c - a^2*c*x^2]) - Sqrt[c - a^2*c*x^2]/(a^4*c^2) + (2*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(a^4*c^(3/2))","A",6,5,27,0.1852,1,"{6151, 1635, 641, 217, 203}"
1117,1,93,0,0.2626825,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"(1 + a*x)^2/(3*a^3*(c - a^2*c*x^2)^(3/2)) - (5*(1 + a*x))/(3*a^3*c*Sqrt[c - a^2*c*x^2]) + ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]]/(a^3*c^(3/2))","A",5,5,27,0.1852,1,"{6151, 1635, 778, 217, 203}"
1118,1,60,0,0.1174169,"\int \frac{e^{2 \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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 + a*x)^2/(3*a^2*(c - a^2*c*x^2)^(3/2)) - (2*(1 + a*x))/(3*a^2*c*Sqrt[c - a^2*c*x^2])","A",3,3,25,0.1200,1,"{6151, 789, 637}"
1119,1,51,0,0.0636296,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"(2*(1 + a*x))/(3*a*(c - a^2*c*x^2)^(3/2)) + x/(3*c*Sqrt[c - a^2*c*x^2])","A",3,3,24,0.1250,1,"{6141, 653, 191}"
1120,1,82,0,0.2680805,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^(3/2)),x]","-\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}}","-\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,"(2*(1 + a*x))/(3*(c - a^2*c*x^2)^(3/2)) + (3 + 4*a*x)/(3*c*Sqrt[c - a^2*c*x^2]) - ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]/c^(3/2)","A",7,7,27,0.2593,1,"{6151, 1805, 823, 12, 266, 63, 208}"
1121,1,108,0,0.3370468,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^(3/2)),x]","-\frac{\sqrt{c-a^2 c x^2}}{c^2 x}-\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{c^{3/2}}+\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}}","-\frac{\sqrt{c-a^2 c x^2}}{c^2 x}-\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{c^{3/2}}+\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,"(2*a*(1 + a*x))/(3*(c - a^2*c*x^2)^(3/2)) + (a*(6 + 7*a*x))/(3*c*Sqrt[c - a^2*c*x^2]) - Sqrt[c - a^2*c*x^2]/(c^2*x) - (2*a*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/c^(3/2)","A",7,6,27,0.2222,1,"{6151, 1805, 807, 266, 63, 208}"
1122,1,142,0,0.4199056,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^(3/2)),x]","-\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{7 a^2 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{2 c^{3/2}}+\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}}","-\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{7 a^2 \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)}{2 c^{3/2}}+\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,"(2*a^2*(1 + a*x))/(3*(c - a^2*c*x^2)^(3/2)) + (a^2*(9 + 10*a*x))/(3*c*Sqrt[c - a^2*c*x^2]) - Sqrt[c - a^2*c*x^2]/(2*c^2*x^2) - (2*a*Sqrt[c - a^2*c*x^2])/(c^2*x) - (7*a^2*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/(2*c^(3/2))","A",8,7,27,0.2593,1,"{6151, 1805, 1807, 807, 266, 63, 208}"
1123,1,74,0,0.0715208,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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*(1 + a*x))/(5*a*(c - a^2*c*x^2)^(5/2)) + x/(5*c*(c - a^2*c*x^2)^(3/2)) + (2*x)/(5*c^2*Sqrt[c - a^2*c*x^2])","A",4,4,24,0.1667,1,"{6141, 653, 192, 191}"
1124,1,97,0,0.0800799,"\int \frac{e^{2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(2*ArcTanh[a*x])/(c - a^2*c*x^2)^(7/2),x]","\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}}","\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,"(2*(1 + a*x))/(7*a*(c - a^2*c*x^2)^(7/2)) + x/(7*c*(c - a^2*c*x^2)^(5/2)) + (4*x)/(21*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x)/(21*c^3*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6141, 653, 192, 191}"
1125,1,120,0,0.1126997,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^3,x]","-\frac{a^2 c^3 x^{m+3}}{m+3}-\frac{4 a^3 c^3 x^{m+4}}{m+4}-\frac{a^4 c^3 x^{m+5}}{m+5}+\frac{2 a^5 c^3 x^{m+6}}{m+6}+\frac{a^6 c^3 x^{m+7}}{m+7}+\frac{2 a c^3 x^{m+2}}{m+2}+\frac{c^3 x^{m+1}}{m+1}","-\frac{a^2 c^3 x^{m+3}}{m+3}-\frac{4 a^3 c^3 x^{m+4}}{m+4}-\frac{a^4 c^3 x^{m+5}}{m+5}+\frac{2 a^5 c^3 x^{m+6}}{m+6}+\frac{a^6 c^3 x^{m+7}}{m+7}+\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) + (2*a*c^3*x^(2 + m))/(2 + m) - (a^2*c^3*x^(3 + m))/(3 + m) - (4*a^3*c^3*x^(4 + m))/(4 + m) - (a^4*c^3*x^(5 + m))/(5 + m) + (2*a^5*c^3*x^(6 + m))/(6 + m) + (a^6*c^3*x^(7 + m))/(7 + m)","A",3,2,25,0.08000,1,"{6150, 88}"
1126,1,67,0,0.0872407,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^2,x]","-\frac{2 a^3 c^2 x^{m+4}}{m+4}-\frac{a^4 c^2 x^{m+5}}{m+5}+\frac{2 a c^2 x^{m+2}}{m+2}+\frac{c^2 x^{m+1}}{m+1}","-\frac{2 a^3 c^2 x^{m+4}}{m+4}-\frac{a^4 c^2 x^{m+5}}{m+5}+\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 + m) + (2*a*c^2*x^(2 + m))/(2 + m) - (2*a^3*c^2*x^(4 + m))/(4 + m) - (a^4*c^2*x^(5 + m))/(5 + m)","A",3,2,25,0.08000,1,"{6150, 75}"
1127,1,42,0,0.0628355,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2),x]","\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}","\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) + (2*a*c*x^(2 + m))/(2 + m) + (a^2*c*x^(3 + m))/(3 + m)","A",3,2,23,0.08696,1,"{6150, 43}"
1128,1,25,0,0.0812267,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{c-a^2 c x^2} \, dx","Int[(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",2,2,25,0.08000,1,"{6150, 64}"
1129,1,113,0,0.1780445,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^2,x]","\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}","\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)/(4*c^2*(1 - a*x)^2) + ((2 - m)*x^(1 + m))/(4*c^2*(1 - a*x)) + (x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)])/(8*c^2*(1 + m)) + ((1 - 4*m + 2*m^2)*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/(8*c^2*(1 + m))","A",6,5,25,0.2000,1,"{6150, 103, 151, 156, 64}"
1130,1,203,0,0.3487739,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^3,x]","\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)}","\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,"-((2 - m)*(4 - m)*x^(1 + m))/(24*c^3*(1 + a*x)) + x^(1 + m)/(6*c^3*(1 - a*x)^3*(1 + a*x)) + ((4 - m)*x^(1 + m))/(12*c^3*(1 - a*x)^2*(1 + a*x)) + ((7 - 2*m)*(2 - m)*x^(1 + m))/(24*c^3*(1 - a*x)*(1 + a*x)) + ((2 - m)*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)])/(16*c^3*(1 + m)) + ((2 - m)*(3 - 8*m + 2*m^2)*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/(48*c^3*(1 + m))","A",8,5,25,0.2000,1,"{6150, 103, 151, 156, 64}"
1131,1,176,0,0.3141567,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^(5/2),x]","\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}","\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,"-((x^(1 + m)*(c - a^2*c*x^2)^(5/2))/(6 + m)) + (c^2*(7 + 2*m)*x^(1 + m)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/((1 + m)*(6 + m)*Sqrt[1 - a^2*x^2]) + (2*a*c^2*x^(2 + m)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-3/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + m)*Sqrt[1 - a^2*x^2])","A",7,5,27,0.1852,1,"{6151, 1809, 808, 365, 364}"
1132,1,172,0,0.2999372,"\int e^{2 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^(3/2),x]","\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}","\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,"-((x^(1 + m)*(c - a^2*c*x^2)^(3/2))/(4 + m)) + (c*(5 + 2*m)*x^(1 + m)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/((1 + m)*(4 + m)*Sqrt[1 - a^2*x^2]) + (2*a*c*x^(2 + m)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[-1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + m)*Sqrt[1 - a^2*x^2])","A",7,5,27,0.1852,1,"{6151, 1809, 808, 365, 364}"
1133,1,172,0,0.2913899,"\int e^{2 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcTanh[a*x])*x^m*Sqrt[c - a^2*c*x^2],x]","\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}","\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)*Sqrt[c - a^2*c*x^2])/(2 + m)) + (c*(3 + 2*m)*x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/((1 + m)*(2 + m)*Sqrt[c - a^2*c*x^2]) + (2*a*c*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + m)*Sqrt[c - a^2*c*x^2])","A",7,5,27,0.1852,1,"{6151, 1809, 808, 365, 364}"
1134,1,169,0,0.2930244,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x^m)/Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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,"(2*x^(1 + m)*(1 + a*x))/Sqrt[c - a^2*c*x^2] - ((1 + 2*m)*x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/((1 + m)*Sqrt[c - a^2*c*x^2]) - (2*a*(1 + m)*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + m)*Sqrt[c - a^2*c*x^2])","A",7,5,27,0.1852,1,"{6151, 1806, 808, 365, 364}"
1135,1,183,0,0.319657,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(2*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"(2*x^(1 + m)*(1 + a*x))/(3*(c - a^2*c*x^2)^(3/2)) + ((1 - 2*m)*x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(3*c*(1 + m)*Sqrt[c - a^2*c*x^2]) + (2*a*(1 - m)*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(3*c*(2 + m)*Sqrt[c - a^2*c*x^2])","A",7,5,27,0.1852,1,"{6151, 1806, 808, 365, 364}"
1136,1,55,0,0.0629494,"\int e^{2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","-\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}","-\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)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - p, p, 1 + p, (1 - a*x)/2])/(a*p*(1 + a*x)^p))","A",3,3,22,0.1364,1,"{6141, 678, 69}"
1137,1,136,0,0.2761703,"\int e^{3 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right) \, dx","Int[E^(3*ArcTanh[a*x])*x^3*(c - a^2*c*x^2),x]","-\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{17 c x^2 \sqrt{1-a^2 x^2}}{15 a^2}-\frac{c (345 a x+544) \sqrt{1-a^2 x^2}}{240 a^4}+\frac{23 c \sin ^{-1}(a x)}{16 a^4}","-\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{17 c x^2 \sqrt{1-a^2 x^2}}{15 a^2}-\frac{c (345 a x+544) \sqrt{1-a^2 x^2}}{240 a^4}+\frac{23 c \sin ^{-1}(a x)}{16 a^4}",1,"(-17*c*x^2*Sqrt[1 - a^2*x^2])/(15*a^2) - (23*c*x^3*Sqrt[1 - a^2*x^2])/(24*a) - (3*c*x^4*Sqrt[1 - a^2*x^2])/5 - (a*c*x^5*Sqrt[1 - a^2*x^2])/6 - (c*(544 + 345*a*x)*Sqrt[1 - a^2*x^2])/(240*a^4) + (23*c*ArcSin[a*x])/(16*a^4)","A",7,5,23,0.2174,1,"{6148, 1809, 833, 780, 216}"
1138,1,111,0,0.2466097,"\int e^{3 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right) \, dx","Int[E^(3*ArcTanh[a*x])*x^2*(c - a^2*c*x^2),x]","-\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{19 c x^2 \sqrt{1-a^2 x^2}}{15 a}-\frac{c (195 a x+304) \sqrt{1-a^2 x^2}}{120 a^3}+\frac{13 c \sin ^{-1}(a x)}{8 a^3}","-\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{19 c x^2 \sqrt{1-a^2 x^2}}{15 a}-\frac{c (195 a x+304) \sqrt{1-a^2 x^2}}{120 a^3}+\frac{13 c \sin ^{-1}(a x)}{8 a^3}",1,"(-19*c*x^2*Sqrt[1 - a^2*x^2])/(15*a) - (3*c*x^3*Sqrt[1 - a^2*x^2])/4 - (a*c*x^4*Sqrt[1 - a^2*x^2])/5 - (c*(304 + 195*a*x)*Sqrt[1 - a^2*x^2])/(120*a^3) + (13*c*ArcSin[a*x])/(8*a^3)","A",6,5,23,0.2174,1,"{6148, 1809, 833, 780, 216}"
1139,1,120,0,0.095905,"\int e^{3 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right) \, dx","Int[E^(3*ArcTanh[a*x])*x*(c - a^2*c*x^2),x]","-\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}","-\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,"(-15*c*Sqrt[1 - a^2*x^2])/(8*a^2) - (5*c*(1 + a*x)*Sqrt[1 - a^2*x^2])/(8*a^2) - (c*(1 + a*x)^2*Sqrt[1 - a^2*x^2])/(4*a^2) - (c*(1 + a*x)^3*Sqrt[1 - a^2*x^2])/(4*a^2) + (15*c*ArcSin[a*x])/(8*a^2)","A",6,5,21,0.2381,1,"{6148, 795, 671, 641, 216}"
1140,1,91,0,0.0568851,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2),x]","-\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}","-\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,"(-5*c*Sqrt[1 - a^2*x^2])/(2*a) - (5*c*(1 + a*x)*Sqrt[1 - a^2*x^2])/(6*a) - (c*(1 + a*x)^2*Sqrt[1 - a^2*x^2])/(3*a) + (5*c*ArcSin[a*x])/(2*a)","A",5,4,20,0.2000,1,"{6138, 671, 641, 216}"
1141,1,66,0,0.19502,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x,x]","-\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)","-\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,"-3*c*Sqrt[1 - a^2*x^2] - (a*c*x*Sqrt[1 - a^2*x^2])/2 + (7*c*ArcSin[a*x])/2 - c*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,7,23,0.3043,1,"{6148, 1809, 844, 216, 266, 63, 208}"
1142,1,66,0,0.1914893,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^2,x]","-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)","-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,"-(a*c*Sqrt[1 - a^2*x^2]) - (c*Sqrt[1 - a^2*x^2])/x + 3*a*c*ArcSin[a*x] - 3*a*c*ArcTanh[Sqrt[1 - a^2*x^2]]","A",8,8,23,0.3478,1,"{6148, 1807, 1809, 844, 216, 266, 63, 208}"
1143,1,76,0,0.1941837,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^3} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^3,x]","-\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)","-\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*Sqrt[1 - a^2*x^2])/(2*x^2) - (3*a*c*Sqrt[1 - a^2*x^2])/x + a^2*c*ArcSin[a*x] - (7*a^2*c*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",8,7,23,0.3043,1,"{6148, 1807, 844, 216, 266, 63, 208}"
1144,1,94,0,0.2003597,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^4} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^4,x]","-\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)","-\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,"-(c*Sqrt[1 - a^2*x^2])/(3*x^3) - (3*a*c*Sqrt[1 - a^2*x^2])/(2*x^2) - (11*a^2*c*Sqrt[1 - a^2*x^2])/(3*x) - (5*a^3*c*ArcTanh[Sqrt[1 - a^2*x^2]])/2","A",7,6,23,0.2609,1,"{6148, 1807, 807, 266, 63, 208}"
1145,1,115,0,0.2233785,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^5} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^5,x]","-\frac{3 a^3 c \sqrt{1-a^2 x^2}}{x}-\frac{15 a^2 c \sqrt{1-a^2 x^2}}{8 x^2}-\frac{a c \sqrt{1-a^2 x^2}}{x^3}-\frac{c \sqrt{1-a^2 x^2}}{4 x^4}-\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}-\frac{15 a^2 c \sqrt{1-a^2 x^2}}{8 x^2}-\frac{a c \sqrt{1-a^2 x^2}}{x^3}-\frac{c \sqrt{1-a^2 x^2}}{4 x^4}-\frac{15}{8} a^4 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-(c*Sqrt[1 - a^2*x^2])/(4*x^4) - (a*c*Sqrt[1 - a^2*x^2])/x^3 - (15*a^2*c*Sqrt[1 - a^2*x^2])/(8*x^2) - (3*a^3*c*Sqrt[1 - a^2*x^2])/x - (15*a^4*c*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",8,7,23,0.3043,1,"{6148, 1807, 835, 807, 266, 63, 208}"
1146,1,144,0,0.2502304,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)}{x^6} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2))/x^6,x]","-\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}-\frac{19 a^2 c \sqrt{1-a^2 x^2}}{15 x^3}-\frac{3 a c \sqrt{1-a^2 x^2}}{4 x^4}-\frac{c \sqrt{1-a^2 x^2}}{5 x^5}-\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}-\frac{19 a^2 c \sqrt{1-a^2 x^2}}{15 x^3}-\frac{3 a c \sqrt{1-a^2 x^2}}{4 x^4}-\frac{c \sqrt{1-a^2 x^2}}{5 x^5}-\frac{13}{8} a^5 c \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)",1,"-(c*Sqrt[1 - a^2*x^2])/(5*x^5) - (3*a*c*Sqrt[1 - a^2*x^2])/(4*x^4) - (19*a^2*c*Sqrt[1 - a^2*x^2])/(15*x^3) - (13*a^3*c*Sqrt[1 - a^2*x^2])/(8*x^2) - (38*a^4*c*Sqrt[1 - a^2*x^2])/(15*x) - (13*a^5*c*ArcTanh[Sqrt[1 - a^2*x^2]])/8","A",9,7,23,0.3043,1,"{6148, 1807, 835, 807, 266, 63, 208}"
1147,1,121,0,0.0715503,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","-\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}","-\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,"(7*c^2*x*Sqrt[1 - a^2*x^2])/8 - (7*c^2*(1 - a^2*x^2)^(3/2))/(12*a) - (7*c^2*(1 + a*x)*(1 - a^2*x^2)^(3/2))/(20*a) - (c^2*(1 + a*x)^2*(1 - a^2*x^2)^(3/2))/(5*a) + (7*c^2*ArcSin[a*x])/(8*a)","A",6,5,22,0.2273,1,"{6138, 671, 641, 195, 216}"
1148,1,143,0,0.081671,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","-\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}","-\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,"(9*c^3*x*Sqrt[1 - a^2*x^2])/16 + (3*c^3*x*(1 - a^2*x^2)^(3/2))/8 - (3*c^3*(1 - a^2*x^2)^(5/2))/(10*a) - (3*c^3*(1 + a*x)*(1 - a^2*x^2)^(5/2))/(14*a) - (c^3*(1 + a*x)^2*(1 - a^2*x^2)^(5/2))/(7*a) + (9*c^3*ArcSin[a*x])/(16*a)","A",7,5,22,0.2273,1,"{6138, 671, 641, 195, 216}"
1149,1,165,0,0.0903055,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^4,x]","-\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}","-\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,"(55*c^4*x*Sqrt[1 - a^2*x^2])/128 + (55*c^4*x*(1 - a^2*x^2)^(3/2))/192 + (11*c^4*x*(1 - a^2*x^2)^(5/2))/48 - (11*c^4*(1 - a^2*x^2)^(7/2))/(56*a) - (11*c^4*(1 + a*x)*(1 - a^2*x^2)^(7/2))/(72*a) - (c^4*(1 + a*x)^2*(1 - a^2*x^2)^(7/2))/(9*a) + (55*c^4*ArcSin[a*x])/(128*a)","A",8,5,22,0.2273,1,"{6138, 671, 641, 195, 216}"
1150,1,95,0,0.1866492,"\int \frac{e^{3 \tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2),x]","\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}+\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}+\frac{3 \sin ^{-1}(a x)}{a^3 c}",1,"(1 + a*x)^3/(3*a^3*c*(1 - a^2*x^2)^(3/2)) - (2*(1 + a*x)^2)/(a^3*c*Sqrt[1 - a^2*x^2]) - (3*Sqrt[1 - a^2*x^2])/(a^3*c) + (3*ArcSin[a*x])/(a^3*c)","A",6,6,25,0.2400,1,"{6148, 1635, 21, 669, 641, 216}"
1151,1,70,0,0.0860757,"\int \frac{e^{3 \tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*x)/(c - a^2*c*x^2),x]","\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}","\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,"(1 + a*x)^3/(3*a^2*c*(1 - a^2*x^2)^(3/2)) - (2*(1 + a*x))/(a^2*c*Sqrt[1 - a^2*x^2]) + ArcSin[a*x]/(a^2*c)","A",4,4,23,0.1739,1,"{6148, 789, 653, 216}"
1152,1,18,0,0.0305452,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{e^{3 \tanh ^{-1}(a x)}}{3 a c}","\frac{e^{3 \tanh ^{-1}(a x)}}{3 a c}",1,"E^(3*ArcTanh[a*x])/(3*a*c)","A",1,1,22,0.04545,1,"{6137}"
1153,1,97,0,0.0742634,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","\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}","\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^2*x^2]/(5*a*c^2*(1 - a*x)^3) + (2*Sqrt[1 - a^2*x^2])/(15*a*c^2*(1 - a*x)^2) + (2*Sqrt[1 - a^2*x^2])/(15*a*c^2*(1 - a*x))","A",5,4,22,0.1818,1,"{6138, 655, 659, 651}"
1154,1,119,0,0.0885734,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","\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}}","\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,"(8*x)/(35*c^3*Sqrt[1 - a^2*x^2]) + 1/(7*a*c^3*(1 - a*x)^3*Sqrt[1 - a^2*x^2]) + 4/(35*a*c^3*(1 - a*x)^2*Sqrt[1 - a^2*x^2]) + 4/(35*a*c^3*(1 - a*x)*Sqrt[1 - a^2*x^2])","A",6,4,22,0.1818,1,"{6138, 655, 659, 191}"
1155,1,141,0,0.0907069,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","\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}}","\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,"(8*x)/(63*c^4*(1 - a^2*x^2)^(3/2)) + 1/(9*a*c^4*(1 - a*x)^3*(1 - a^2*x^2)^(3/2)) + 2/(21*a*c^4*(1 - a*x)^2*(1 - a^2*x^2)^(3/2)) + 2/(21*a*c^4*(1 - a*x)*(1 - a^2*x^2)^(3/2)) + (16*x)/(63*c^4*Sqrt[1 - a^2*x^2])","A",7,5,22,0.2273,1,"{6138, 655, 659, 192, 191}"
1156,1,226,0,0.2211664,"\int e^{3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcTanh[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","-\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{2 x^2 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-a^2 c x^2}}{a^3 \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{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{2 x^2 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{c-a^2 c x^2}}{a^3 \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}}",1,"(-4*x*Sqrt[c - a^2*c*x^2])/(a^3*Sqrt[1 - a^2*x^2]) - (2*x^2*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - a^2*x^2]) - (4*x^3*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) - (3*x^4*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - a^2*x^2]) - (a*x^5*Sqrt[c - a^2*c*x^2])/(5*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^4*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1157,1,185,0,0.2107949,"\int e^{3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcTanh[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","-\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{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{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^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}}-\frac{x^3 \sqrt{c-a^2 c x^2}}{\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{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^3 \sqrt{1-a^2 x^2}}",1,"(-4*x*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - a^2*x^2]) - (2*x^2*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) - (x^3*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] - (a*x^4*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^3*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1158,1,150,0,0.1515829,"\int e^{3 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcTanh[a*x])*x*Sqrt[c - a^2*c*x^2],x]","-\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \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}}-\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}}",1,"(-4*x*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) - (3*x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2]) - (a*x^3*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^2*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 77}"
1159,1,111,0,0.0845421,"\int e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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,"(-3*x*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] - (a*x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1160,1,104,0,0.1939951,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x,x]","-\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}}","-\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,"-((a*x*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]) + (Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 72}"
1161,1,108,0,0.2003321,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^2,x]","-\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}}","-\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*Sqrt[1 - a^2*x^2])) + (3*a*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*a*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1162,1,149,0,0.2063855,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^3,x]","-\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}}","-\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]/(2*x^2*Sqrt[1 - a^2*x^2]) - (3*a*Sqrt[c - a^2*c*x^2])/(x*Sqrt[1 - a^2*x^2]) + (4*a^2*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^2*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1163,1,188,0,0.2096115,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^4,x]","-\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}}","-\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]/(3*x^3*Sqrt[1 - a^2*x^2]) - (3*a*Sqrt[c - a^2*c*x^2])/(2*x^2*Sqrt[1 - a^2*x^2]) - (4*a^2*Sqrt[c - a^2*c*x^2])/(x*Sqrt[1 - a^2*x^2]) + (4*a^3*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^3*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1164,1,223,0,0.2203759,"\int \frac{e^{3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^5,x]","-\frac{4 a^3 \sqrt{c-a^2 c x^2}}{x \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{a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4 \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}}-\frac{2 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-a^2 x^2}}-\frac{a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4 \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}}",1,"-Sqrt[c - a^2*c*x^2]/(4*x^4*Sqrt[1 - a^2*x^2]) - (a*Sqrt[c - a^2*c*x^2])/(x^3*Sqrt[1 - a^2*x^2]) - (2*a^2*Sqrt[c - a^2*c*x^2])/(x^2*Sqrt[1 - a^2*x^2]) - (4*a^3*Sqrt[c - a^2*c*x^2])/(x*Sqrt[1 - a^2*x^2]) + (4*a^4*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1165,1,44,0,0.0824788,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2),x]","\frac{c (a x+1)^4 \sqrt{c-a^2 c x^2}}{4 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,"(c*(1 + a*x)^4*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - a^2*x^2])","A",3,3,24,0.1250,1,"{6143, 6140, 32}"
1166,1,93,0,0.0911275,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2),x]","\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}}","\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,"(2*c^2*(1 + a*x)^5*Sqrt[c - a^2*c*x^2])/(5*a*Sqrt[1 - a^2*x^2]) - (c^2*(1 + a*x)^6*Sqrt[c - a^2*c*x^2])/(6*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1167,1,139,0,0.1039553,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2),x]","\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}}","\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,"(2*c^3*(1 + a*x)^6*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) - (4*c^3*(1 + a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) + (c^3*(1 + a*x)^8*Sqrt[c - a^2*c*x^2])/(8*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1168,1,185,0,0.1151922,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(9/2),x]","-\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}}","-\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,"(8*c^4*(1 + a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) - (3*c^4*(1 + a*x)^8*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - a^2*x^2]) + (2*c^4*(1 + a*x)^9*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) - (c^4*(1 + a*x)^10*Sqrt[c - a^2*c*x^2])/(10*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1169,1,83,0,0.0885614,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^(3*ArcTanh[a*x])/Sqrt[c - a^2*c*x^2],x]","\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}}","\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,"(2*Sqrt[1 - a^2*x^2])/(a*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(a*Sqrt[c - a^2*c*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1170,1,47,0,0.084061,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^(3/2),x]","\frac{\sqrt{1-a^2 x^2}}{2 a c (1-a x)^2 \sqrt{c-a^2 c x^2}}","\frac{\sqrt{1-a^2 x^2}}{2 a c (1-a x)^2 \sqrt{c-a^2 c x^2}}",1,"Sqrt[1 - a^2*x^2]/(2*a*c*(1 - a*x)^2*Sqrt[c - a^2*c*x^2])","A",3,3,24,0.1250,1,"{6143, 6140, 32}"
1171,1,185,0,0.1164301,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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]/(6*a*c^2*(1 - a*x)^3*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a*c^2*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1172,1,278,0,0.1386234,"\int \frac{e^{3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(3*ArcTanh[a*x])/(c - a^2*c*x^2)^(7/2),x]","\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}}","\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]/(16*a*c^3*(1 - a*x)^4*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(12*a*c^3*(1 - a*x)^3*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2])/(32*a*c^3*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a*c^3*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(32*a*c^3*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(32*a*c^3*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1173,1,136,0,0.2069277,"\int e^{3 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcTanh[a*x])*x^m*Sqrt[c - a^2*c*x^2],x]","\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}}","\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,"(-3*x^(1 + m)*Sqrt[c - a^2*c*x^2])/((1 + m)*Sqrt[1 - a^2*x^2]) - (a*x^(2 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - a^2*x^2]) + (4*x^(1 + m)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/((1 + m)*Sqrt[1 - a^2*x^2])","A",5,4,27,0.1481,1,"{6153, 6150, 88, 64}"
1174,1,251,0,0.4160176,"\int e^{3 \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Int[E^(3*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^p,x]","\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)}","\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,"(-3*x^(1 + m)*(c - a^2*c*x^2)^p)/((m + 2*p)*Sqrt[1 - a^2*x^2]) - (a*x^(2 + m)*(c - a^2*c*x^2)^p)/((1 + m + 2*p)*Sqrt[1 - a^2*x^2]) + ((3 + 4*m + 2*p)*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)*(m + 2*p)*(1 - a^2*x^2)^p) + (a*(5 + 4*m + 6*p)*x^(2 + m)*(c - a^2*c*x^2)^p*Hypergeometric2F1[(2 + m)/2, 3/2 - p, (4 + m)/2, a^2*x^2])/((2 + m)*(1 + m + 2*p)*(1 - a^2*x^2)^p)","A",7,5,25,0.2000,1,"{6153, 6148, 1809, 808, 364}"
1175,1,224,0,0.355352,"\int e^{3 \tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^p \, dx","Int[E^(3*ArcTanh[a*x])*x^3*(c - a^2*c*x^2)^p,x]","\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{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{a x^5 \left(c-a^2 c x^2\right)^p}{2 (p+2) \sqrt{1-a^2 x^2}}+\frac{4 \left(c-a^2 c x^2\right)^p}{a^4 (1-2 p) \sqrt{1-a^2 x^2}}","\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{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{a x^5 \left(c-a^2 c x^2\right)^p}{2 (p+2) \sqrt{1-a^2 x^2}}+\frac{4 \left(c-a^2 c x^2\right)^p}{a^4 (1-2 p) \sqrt{1-a^2 x^2}}",1,"(4*(c - a^2*c*x^2)^p)/(a^4*(1 - 2*p)*Sqrt[1 - a^2*x^2]) - (a*x^5*(c - a^2*c*x^2)^p)/(2*(2 + p)*Sqrt[1 - a^2*x^2]) + (7*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^4*(1 + 2*p)) - (3*(1 - a^2*x^2)^(3/2)*(c - a^2*c*x^2)^p)/(a^4*(3 + 2*p)) + (a*(17 + 6*p)*x^5*(c - a^2*c*x^2)^p*Hypergeometric2F1[5/2, 3/2 - p, 7/2, a^2*x^2])/(10*(2 + p)*(1 - a^2*x^2)^p)","A",8,7,25,0.2800,1,"{6153, 6148, 1652, 446, 77, 459, 364}"
1176,1,222,0,0.3390211,"\int e^{3 \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^p \, dx","Int[E^(3*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^p,x]","\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{\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{3 x^3 \left(c-a^2 c x^2\right)^p}{2 (p+1) \sqrt{1-a^2 x^2}}+\frac{4 \left(c-a^2 c x^2\right)^p}{a^3 (1-2 p) \sqrt{1-a^2 x^2}}","\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{\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{3 x^3 \left(c-a^2 c x^2\right)^p}{2 (p+1) \sqrt{1-a^2 x^2}}+\frac{4 \left(c-a^2 c x^2\right)^p}{a^3 (1-2 p) \sqrt{1-a^2 x^2}}",1,"(4*(c - a^2*c*x^2)^p)/(a^3*(1 - 2*p)*Sqrt[1 - a^2*x^2]) - (3*x^3*(c - a^2*c*x^2)^p)/(2*(1 + p)*Sqrt[1 - a^2*x^2]) + (5*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^3*(1 + 2*p)) - ((1 - a^2*x^2)^(3/2)*(c - a^2*c*x^2)^p)/(a^3*(3 + 2*p)) + ((11 + 2*p)*x^3*(c - a^2*c*x^2)^p*Hypergeometric2F1[3/2, 3/2 - p, 5/2, a^2*x^2])/(6*(1 + p)*(1 - a^2*x^2)^p)","A",8,7,25,0.2800,1,"{6153, 6148, 1652, 459, 364, 446, 77}"
1177,1,138,0,0.1694206,"\int e^{3 \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Int[E^(3*ArcTanh[a*x])*x*(c - a^2*c*x^2)^p,x]","\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}}","\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,"-((1 + a*x)^3*(c - a^2*c*x^2)^p)/(2*a^2*(1 + p)*Sqrt[1 - a^2*x^2]) + (3*2^(3/2 + 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*(1 - p - 2*p^2)*(1 - a^2*x^2)^p)","A",5,5,23,0.2174,1,"{6153, 6148, 795, 676, 69}"
1178,1,85,0,0.0740719,"\int e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[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 (1-2 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*(1 - 2*p)*(1 - a^2*x^2)^p)","A",3,3,22,0.1364,1,"{6143, 6140, 69}"
1179,1,193,0,0.2918261,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p)/x,x]","\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}}","\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,"(4*(c - a^2*c*x^2)^p)/((1 - 2*p)*Sqrt[1 - a^2*x^2]) - (a*x*(c - a^2*c*x^2)^p)/(2*p*Sqrt[1 - a^2*x^2]) + (a*(1 + 6*p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[1/2, 3/2 - p, 3/2, a^2*x^2])/(2*p*(1 - a^2*x^2)^p) - (Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",8,8,25,0.3200,1,"{6153, 6148, 1652, 446, 79, 65, 388, 245}"
1180,1,187,0,0.3313958,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^2} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p)/x^2,x]","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}}","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,"(4*a*(c - a^2*c*x^2)^p)/((1 - 2*p)*Sqrt[1 - a^2*x^2]) - (c - a^2*c*x^2)^p/(x*Sqrt[1 - a^2*x^2]) + (a^2*(5 - 2*p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[1/2, 3/2 - p, 3/2, a^2*x^2])/(1 - a^2*x^2)^p - (3*a*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",9,9,25,0.3600,1,"{6153, 6148, 1807, 1652, 446, 79, 65, 12, 245}"
1181,1,194,0,0.3673725,"\int \frac{e^{3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^3} \, dx","Int[(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^p)/x^3,x]","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)+\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)+\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}}",1,"-(c - a^2*c*x^2)^p/(2*x^2*Sqrt[1 - a^2*x^2]) - (3*a*(c - a^2*c*x^2)^p)/(x*Sqrt[1 - a^2*x^2]) + (a^3*(7 - 6*p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[1/2, 3/2 - p, 3/2, a^2*x^2])/(1 - a^2*x^2)^p + (a^2*(9 - 2*p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, -1/2 + p, 1/2 + p, 1 - a^2*x^2])/(2*(1 - 2*p)*Sqrt[1 - a^2*x^2])","A",8,7,25,0.2800,1,"{6153, 6148, 1807, 764, 266, 65, 245}"
1182,1,66,0,0.0643129,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^5 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^5,x]","-\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}","-\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,"(c^5*(1 + a*x)^8)/a - (4*c^5*(1 + a*x)^9)/(3*a) + (3*c^5*(1 + a*x)^10)/(5*a) - (c^5*(1 + a*x)^11)/(11*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1183,1,52,0,0.0565974,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^4,x]","\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}","\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,"(4*c^4*(1 + a*x)^7)/(7*a) - (c^4*(1 + a*x)^8)/(2*a) + (c^4*(1 + a*x)^9)/(9*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1184,1,35,0,0.0392315,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^3,x]","\frac{c^3 (a x+1)^6}{3 a}-\frac{c^3 (a x+1)^7}{7 a}","\frac{c^3 (a x+1)^6}{3 a}-\frac{c^3 (a x+1)^7}{7 a}",1,"(c^3*(1 + a*x)^6)/(3*a) - (c^3*(1 + a*x)^7)/(7*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1185,1,17,0,0.0303655,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^2,x]","\frac{c^2 (a x+1)^5}{5 a}","\frac{c^2 (a x+1)^5}{5 a}",1,"(c^2*(1 + a*x)^5)/(5*a)","A",2,2,22,0.09091,1,"{6140, 32}"
1186,1,46,0,0.0321805,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2),x]","-\frac{c (a x+1)^3}{3 a}-\frac{c (a x+1)^2}{a}-\frac{8 c \log (1-a x)}{a}-4 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,"-4*c*x - (c*(1 + a*x)^2)/a - (c*(1 + a*x)^3)/(3*a) - (8*c*Log[1 - a*x])/a","A",3,2,20,0.1000,1,"{6140, 43}"
1187,1,13,0,0.0339631,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{x}{c (1-a x)^2}","\frac{x}{c (1-a x)^2}",1,"x/(c*(1 - a*x)^2)","A",2,2,22,0.09091,1,"{6140, 34}"
1188,1,18,0,0.035483,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","\frac{1}{3 a c^2 (1-a x)^3}","\frac{1}{3 a c^2 (1-a x)^3}",1,"1/(3*a*c^2*(1 - a*x)^3)","A",2,2,22,0.09091,1,"{6140, 32}"
1189,1,87,0,0.0677188,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","\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}","\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,"1/(8*a*c^3*(1 - a*x)^4) + 1/(12*a*c^3*(1 - a*x)^3) + 1/(16*a*c^3*(1 - a*x)^2) + 1/(16*a*c^3*(1 - a*x)) + ArcTanh[a*x]/(16*a*c^3)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1190,1,122,0,0.0893913,"\int \frac{e^{4 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(4*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","\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}","\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,"1/(20*a*c^4*(1 - a*x)^5) + 1/(16*a*c^4*(1 - a*x)^4) + 1/(16*a*c^4*(1 - a*x)^3) + 1/(16*a*c^4*(1 - a*x)^2) + 5/(64*a*c^4*(1 - a*x)) - 1/(64*a*c^4*(1 + a*x)) + (3*ArcTanh[a*x])/(32*a*c^4)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1191,1,63,0,0.0797909,"\int e^{4 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(4*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","\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)}","\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)*c*(1 + a*x)^(1 - p)*(c - a^2*c*x^2)^(-1 + p)*Hypergeometric2F1[-2 - p, -1 + p, p, (1 - a*x)/2])/(a*(1 - p))","A",3,3,22,0.1364,1,"{6141, 678, 69}"
1192,1,127,0,0.0682698,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[(c - a^2*c*x^2)^4/E^ArcTanh[a*x],x]","\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}","\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,"(35*c^4*x*Sqrt[1 - a^2*x^2])/128 + (35*c^4*x*(1 - a^2*x^2)^(3/2))/192 + (7*c^4*x*(1 - a^2*x^2)^(5/2))/48 + (c^4*x*(1 - a^2*x^2)^(7/2))/8 + (c^4*(1 - a^2*x^2)^(9/2))/(9*a) + (35*c^4*ArcSin[a*x])/(128*a)","A",7,4,22,0.1818,1,"{6139, 641, 195, 216}"
1193,1,105,0,0.0590107,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[(c - a^2*c*x^2)^3/E^ArcTanh[a*x],x]","\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}","\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,"(5*c^3*x*Sqrt[1 - a^2*x^2])/16 + (5*c^3*x*(1 - a^2*x^2)^(3/2))/24 + (c^3*x*(1 - a^2*x^2)^(5/2))/6 + (c^3*(1 - a^2*x^2)^(7/2))/(7*a) + (5*c^3*ArcSin[a*x])/(16*a)","A",6,4,22,0.1818,1,"{6139, 641, 195, 216}"
1194,1,83,0,0.0507057,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[(c - a^2*c*x^2)^2/E^ArcTanh[a*x],x]","\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}","\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,"(3*c^2*x*Sqrt[1 - a^2*x^2])/8 + (c^2*x*(1 - a^2*x^2)^(3/2))/4 + (c^2*(1 - a^2*x^2)^(5/2))/(5*a) + (3*c^2*ArcSin[a*x])/(8*a)","A",5,4,22,0.1818,1,"{6139, 641, 195, 216}"
1195,1,55,0,0.0299767,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[(c - a^2*c*x^2)/E^ArcTanh[a*x],x]","\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}","\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*x*Sqrt[1 - a^2*x^2])/2 + (c*(1 - a^2*x^2)^(3/2))/(3*a) + (c*ArcSin[a*x])/(2*a)","A",4,4,20,0.2000,1,"{6139, 641, 195, 216}"
1196,1,16,0,0.0311933,"\int \frac{e^{-\tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)),x]","-\frac{e^{-\tanh ^{-1}(a x)}}{a c}","-\frac{e^{-\tanh ^{-1}(a x)}}{a c}",1,"-(1/(a*c*E^ArcTanh[a*x]))","A",1,1,22,0.04545,1,"{6137}"
1197,1,53,0,0.0431805,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^2),x]","\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}}","\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 - a*x)/(3*a*c^2*(1 - a^2*x^2)^(3/2)) + (2*x)/(3*c^2*Sqrt[1 - a^2*x^2])","A",3,3,22,0.1364,1,"{6139, 639, 191}"
1198,1,75,0,0.0499653,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^3),x]","\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}}","\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 - a*x)/(5*a*c^3*(1 - a^2*x^2)^(5/2)) + (4*x)/(15*c^3*(1 - a^2*x^2)^(3/2)) + (8*x)/(15*c^3*Sqrt[1 - a^2*x^2])","A",4,4,22,0.1818,1,"{6139, 639, 192, 191}"
1199,1,97,0,0.0566229,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^4),x]","\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}}","\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,"-(1 - a*x)/(7*a*c^4*(1 - a^2*x^2)^(7/2)) + (6*x)/(35*c^4*(1 - a^2*x^2)^(5/2)) + (8*x)/(35*c^4*(1 - a^2*x^2)^(3/2)) + (16*x)/(35*c^4*Sqrt[1 - a^2*x^2])","A",5,4,22,0.1818,1,"{6139, 639, 192, 191}"
1200,1,119,0,0.0659426,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^5} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^5),x]","\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}}","\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 - a*x)/(9*a*c^5*(1 - a^2*x^2)^(9/2)) + (8*x)/(63*c^5*(1 - a^2*x^2)^(7/2)) + (16*x)/(105*c^5*(1 - a^2*x^2)^(5/2)) + (64*x)/(315*c^5*(1 - a^2*x^2)^(3/2)) + (128*x)/(315*c^5*Sqrt[1 - a^2*x^2])","A",6,4,22,0.1818,1,"{6139, 639, 192, 191}"
1201,1,83,0,0.177692,"\int e^{-\tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[(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}}{(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}}","\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)*Sqrt[c - a^2*c*x^2])/((1 + m)*Sqrt[1 - a^2*x^2]) - (a*x^(2 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 43}"
1202,1,74,0,0.1887236,"\int e^{-\tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[(x^2*Sqrt[c - a^2*c*x^2])/E^ArcTanh[a*x],x]","\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}}","\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,"(x^3*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - a^2*x^2]) - (a*x^4*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 43}"
1203,1,74,0,0.1301588,"\int e^{-\tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[(x*Sqrt[c - a^2*c*x^2])/E^ArcTanh[a*x],x]","\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}}","\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*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2]) - (a*x^3*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 43}"
1204,1,69,0,0.0713259,"\int e^{-\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^ArcTanh[a*x],x]","\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}}","\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*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] - (a*x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2])","A",3,2,24,0.08333,1,"{6143, 6140}"
1205,1,66,0,0.1768127,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^ArcTanh[a*x]*x),x]","\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}}","\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,"-((a*x*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2]) + (Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 43}"
1206,1,69,0,0.1788843,"\int \frac{e^{-\tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^ArcTanh[a*x]*x^2),x]","-\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}}","-\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*Sqrt[1 - a^2*x^2])) - (a*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 43}"
1207,1,91,0,0.0882952,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)/E^ArcTanh[a*x],x]","\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}}","\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,"(-2*c*(1 - a*x)^3*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) + (c*(1 - a*x)^4*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1208,1,140,0,0.0974888,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[(c - a^2*c*x^2)^(5/2)/E^ArcTanh[a*x],x]","-\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}}","-\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,"-((c^2*(1 - a*x)^4*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2])) + (4*c^2*(1 - a*x)^5*Sqrt[c - a^2*c*x^2])/(5*a*Sqrt[1 - a^2*x^2]) - (c^2*(1 - a*x)^6*Sqrt[c - a^2*c*x^2])/(6*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1209,1,187,0,0.1160111,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[(c - a^2*c*x^2)^(7/2)/E^ArcTanh[a*x],x]","\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}}","\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,"(-8*c^3*(1 - a*x)^5*Sqrt[c - a^2*c*x^2])/(5*a*Sqrt[1 - a^2*x^2]) + (2*c^3*(1 - a*x)^6*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) - (6*c^3*(1 - a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) + (c^3*(1 - a*x)^8*Sqrt[c - a^2*c*x^2])/(8*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1210,1,234,0,0.1192745,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[(c - a^2*c*x^2)^(9/2)/E^ArcTanh[a*x],x]","-\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}}","-\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,"(-8*c^4*(1 - a*x)^6*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) + (32*c^4*(1 - a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) - (3*c^4*(1 - a*x)^8*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) + (8*c^4*(1 - a*x)^9*Sqrt[c - a^2*c*x^2])/(9*a*Sqrt[1 - a^2*x^2]) - (c^4*(1 - a*x)^10*Sqrt[c - a^2*c*x^2])/(10*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1211,1,39,0,0.0746729,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[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",3,3,24,0.1250,1,"{6143, 6140, 31}"
1212,1,90,0,0.0991248,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(3/2)),x]","\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}}","\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]/(2*a*c*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(2*a*c*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1213,1,183,0,0.1150714,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(5/2)),x]","\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}}","\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]/(8*a*c^2*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a*c^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(4*a*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1214,1,276,0,0.1382082,"\int \frac{e^{-\tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(7/2)),x]","\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}}","\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]/(32*a*c^3*(1 - a*x)^2*Sqrt[c - a^2*c*x^2]) + Sqrt[1 - a^2*x^2]/(8*a*c^3*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(24*a*c^3*(1 + a*x)^3*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[1 - a^2*x^2])/(32*a*c^3*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[1 - a^2*x^2])/(16*a*c^3*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(16*a*c^3*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1215,1,137,0,0.1636961,"\int e^{-\tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Int[(x^m*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","\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}","\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,"(x^(1 + m)*(c - a^2*c*x^2)^p*Hypergeometric2F1[(1 + m)/2, 1/2 - p, (3 + m)/2, a^2*x^2])/((1 + m)*(1 - a^2*x^2)^p) - (a*x^(2 + m)*(c - a^2*c*x^2)^p*Hypergeometric2F1[(2 + m)/2, 1/2 - p, (4 + m)/2, a^2*x^2])/((2 + m)*(1 - a^2*x^2)^p)","A",5,4,25,0.1600,1,"{6153, 6149, 808, 364}"
1216,1,85,0,0.1171799,"\int e^{-\tanh ^{-1}(a x)} x^3 \left(1-a^2 x^2\right)^p \, dx","Int[(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(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)}","-\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)/(a^4*(1 + 2*p))) + (1 - a^2*x^2)^(3/2 + p)/(a^4*(3 + 2*p)) - (a*x^5*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/5","A",6,5,24,0.2083,1,"{6149, 764, 266, 43, 364}"
1217,1,84,0,0.120778,"\int e^{-\tanh ^{-1}(a x)} x^2 \left(1-a^2 x^2\right)^p \, dx","Int[(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(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)}","\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)/(a^3*(1 + 2*p)) - (1 - a^2*x^2)^(3/2 + p)/(a^3*(3 + 2*p)) + (x^3*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/3","A",6,5,24,0.2083,1,"{6149, 764, 364, 266, 43}"
1218,1,58,0,0.0648003,"\int e^{-\tanh ^{-1}(a x)} x \left(1-a^2 x^2\right)^p \, dx","Int[(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}}}{a^2 (2 p+1)}","-\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 - 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",4,4,22,0.1818,1,"{6149, 764, 261, 364}"
1219,1,59,0,0.0412697,"\int e^{-\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p \, dx","Int[(1 - a^2*x^2)^p/E^ArcTanh[a*x],x]","-\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)}","-\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^(1/2 + p)*(1 - a*x)^(3/2 + p)*Hypergeometric2F1[1/2 - p, 3/2 + p, 5/2 + p, (1 - a*x)/2])/(a*(3 + 2*p)))","A",2,2,21,0.09524,1,"{6140, 69}"
1220,1,73,0,0.0949322,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x} \, dx","Int[(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 p+1}-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])/(1 + 2*p)","A",5,5,24,0.2083,1,"{6149, 764, 266, 65, 245}"
1221,1,74,0,0.1056482,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^p}{x^2} \, dx","Int[(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",5,5,24,0.2083,1,"{6149, 764, 364, 266, 65}"
1222,1,134,0,0.1883894,"\int e^{-\tanh ^{-1}(a x)} x^3 \left(c-a^2 c x^2\right)^p \, dx","Int[(x^3*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","-\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)}","-\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,"-((Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^4*(1 + 2*p))) + ((1 - a^2*x^2)^(3/2)*(c - a^2*c*x^2)^p)/(a^4*(3 + 2*p)) - (a*x^5*(c - a^2*c*x^2)^p*Hypergeometric2F1[5/2, 1/2 - p, 7/2, a^2*x^2])/(5*(1 - a^2*x^2)^p)","A",7,6,25,0.2400,1,"{6153, 6149, 764, 266, 43, 364}"
1223,1,133,0,0.1866434,"\int e^{-\tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^p \, dx","Int[(x^2*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","\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)}","\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,"(Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^3*(1 + 2*p)) - ((1 - a^2*x^2)^(3/2)*(c - a^2*c*x^2)^p)/(a^3*(3 + 2*p)) + (x^3*(c - a^2*c*x^2)^p*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/(3*(1 - a^2*x^2)^p)","A",7,6,25,0.2400,1,"{6153, 6149, 764, 364, 266, 43}"
1224,1,96,0,0.1126225,"\int e^{-\tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Int[(x*(c - a^2*c*x^2)^p)/E^ArcTanh[a*x],x]","-\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)}","-\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,"-((Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p)/(a^2*(1 + 2*p))) - (a*x^3*(c - a^2*c*x^2)^p*Hypergeometric2F1[3/2, 1/2 - p, 5/2, a^2*x^2])/(3*(1 - a^2*x^2)^p)","A",5,5,23,0.2174,1,"{6153, 6149, 764, 261, 364}"
1225,1,86,0,0.0664606,"\int e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^ArcTanh[a*x],x]","-\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)}","-\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^(1/2 + p)*(1 - a*x)^(3/2 + p)*(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",3,3,22,0.1364,1,"{6143, 6140, 69}"
1226,1,111,0,0.1583804,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x} \, dx","Int[(c - a^2*c*x^2)^p/(E^ArcTanh[a*x]*x),x]","-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}","-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,"-((a*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[1/2, 1/2 - p, 3/2, a^2*x^2])/(1 - a^2*x^2)^p) - (Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",6,6,25,0.2400,1,"{6153, 6149, 764, 266, 65, 245}"
1227,1,112,0,0.1740161,"\int \frac{e^{-\tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p}{x^2} \, dx","Int[(c - a^2*c*x^2)^p/(E^ArcTanh[a*x]*x^2),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}-\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}-\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*(1 - a^2*x^2)^p)) + (a*Sqrt[1 - a^2*x^2]*(c - a^2*c*x^2)^p*Hypergeometric2F1[1, 1/2 + p, 3/2 + p, 1 - a^2*x^2])/(1 + 2*p)","A",6,6,25,0.2400,1,"{6153, 6149, 764, 364, 266, 65}"
1228,1,73,0,0.0553365,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[(c - a^2*c*x^2)^4/E^(2*ArcTanh[a*x]),x]","\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}","\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,"(-4*c^4*(1 - a*x)^6)/(3*a) + (12*c^4*(1 - a*x)^7)/(7*a) - (3*c^4*(1 - a*x)^8)/(4*a) + (c^4*(1 - a*x)^9)/(9*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1229,1,55,0,0.0467867,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[(c - a^2*c*x^2)^3/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"(-4*c^3*(1 - a*x)^5)/(5*a) + (2*c^3*(1 - a*x)^6)/(3*a) - (c^3*(1 - a*x)^7)/(7*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1230,1,37,0,0.0367321,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[(c - a^2*c*x^2)^2/E^(2*ArcTanh[a*x]),x]","\frac{c^2 (1-a x)^5}{5 a}-\frac{c^2 (1-a x)^4}{2 a}","\frac{c^2 (1-a x)^5}{5 a}-\frac{c^2 (1-a x)^4}{2 a}",1,"-(c^2*(1 - a*x)^4)/(2*a) + (c^2*(1 - a*x)^5)/(5*a)","A",3,2,22,0.09091,1,"{6140, 43}"
1231,1,16,0,0.0189674,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[(c - a^2*c*x^2)/E^(2*ArcTanh[a*x]),x]","-\frac{c (1-a x)^3}{3 a}","-\frac{c (1-a x)^3}{3 a}",1,"-(c*(1 - a*x)^3)/(3*a)","A",2,2,20,0.1000,1,"{6140, 32}"
1232,1,15,0,0.0325568,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)),x]","-\frac{1}{a c (a x+1)}","-\frac{1}{a c (a x+1)}",1,"-(1/(a*c*(1 + a*x)))","A",2,2,22,0.09091,1,"{6140, 32}"
1233,1,49,0,0.0501079,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^2),x]","-\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}","-\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,"-1/(4*a*c^2*(1 + a*x)^2) - 1/(4*a*c^2*(1 + a*x)) + ArcTanh[a*x]/(4*a*c^2)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1234,1,84,0,0.0677399,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^3),x]","\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}","\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/(16*a*c^3*(1 - a*x)) - 1/(12*a*c^3*(1 + a*x)^3) - 1/(8*a*c^3*(1 + a*x)^2) - 3/(16*a*c^3*(1 + a*x)) + ArcTanh[a*x]/(4*a*c^3)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1235,1,119,0,0.0868269,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^4),x]","\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}","\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,"1/(64*a*c^4*(1 - a*x)^2) + 5/(64*a*c^4*(1 - a*x)) - 1/(32*a*c^4*(1 + a*x)^4) - 1/(16*a*c^4*(1 + a*x)^3) - 3/(32*a*c^4*(1 + a*x)^2) - 5/(32*a*c^4*(1 + a*x)) + (15*ArcTanh[a*x])/(64*a*c^4)","A",4,3,22,0.1364,1,"{6140, 44, 207}"
1236,1,137,0,0.327147,"\int e^{-2 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[(x^3*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","-\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 x^2 \sqrt{c-a^2 c x^2}}{5 a^2}-\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}","-\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 x^2 \sqrt{c-a^2 c x^2}}{5 a^2}-\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,"(-3*x^2*Sqrt[c - a^2*c*x^2])/(5*a^2) + (x^3*Sqrt[c - a^2*c*x^2])/(2*a) - (x^4*Sqrt[c - a^2*c*x^2])/5 - (3*(8 - 5*a*x)*Sqrt[c - a^2*c*x^2])/(20*a^4) - (3*Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(4*a^4)","A",7,6,27,0.2222,1,"{6152, 1809, 833, 780, 217, 203}"
1237,1,112,0,0.2842499,"\int e^{-2 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[(x^2*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","-\frac{1}{4} x^3 \sqrt{c-a^2 c x^2}+\frac{2 x^2 \sqrt{c-a^2 c x^2}}{3 a}+\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}","-\frac{1}{4} x^3 \sqrt{c-a^2 c x^2}+\frac{2 x^2 \sqrt{c-a^2 c x^2}}{3 a}+\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,"(2*x^2*Sqrt[c - a^2*c*x^2])/(3*a) - (x^3*Sqrt[c - a^2*c*x^2])/4 + ((32 - 21*a*x)*Sqrt[c - a^2*c*x^2])/(24*a^3) + (7*Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(8*a^3)","A",6,6,27,0.2222,1,"{6152, 1809, 833, 780, 217, 203}"
1238,1,85,0,0.1830818,"\int e^{-2 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[(x*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","-\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}","-\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,"-(x^2*Sqrt[c - a^2*c*x^2])/3 - ((5 - 3*a*x)*Sqrt[c - a^2*c*x^2])/(3*a^2) - (Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/a^2","A",5,5,25,0.2000,1,"{6152, 1809, 780, 217, 203}"
1239,1,87,0,0.0753709,"\int e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^(2*ArcTanh[a*x]),x]","\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}","\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,"(3*Sqrt[c - a^2*c*x^2])/(2*a) + ((1 - a*x)*Sqrt[c - a^2*c*x^2])/(2*a) + (3*Sqrt[c]*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(2*a)","A",5,5,24,0.2083,1,"{6142, 671, 641, 217, 203}"
1240,1,78,0,0.2447619,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x),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)","-\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*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] - Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",8,8,27,0.2963,1,"{6152, 1809, 844, 217, 203, 266, 63, 208}"
1241,1,82,0,0.2483156,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^2),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)","-\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*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]] + 2*a*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",8,8,27,0.2963,1,"{6152, 1807, 844, 217, 203, 266, 63, 208}"
1242,1,78,0,0.2372611,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^3),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)","\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,"-Sqrt[c - a^2*c*x^2]/(2*x^2) + (2*a*Sqrt[c - a^2*c*x^2])/x - (3*a^2*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/2","A",6,6,27,0.2222,1,"{6152, 1807, 807, 266, 63, 208}"
1243,1,99,0,0.2748343,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^4),x]","-\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)","-\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,"-Sqrt[c - a^2*c*x^2]/(3*x^3) + (a*Sqrt[c - a^2*c*x^2])/x^2 - (5*a^2*Sqrt[c - a^2*c*x^2])/(3*x) + a^3*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]]","A",7,7,27,0.2593,1,"{6152, 1807, 835, 807, 266, 63, 208}"
1244,1,130,0,0.3080093,"\int \frac{e^{-2 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcTanh[a*x])*x^5),x]","\frac{4 a^3 \sqrt{c-a^2 c x^2}}{3 x}-\frac{7 a^2 \sqrt{c-a^2 c x^2}}{8 x^2}+\frac{2 a \sqrt{c-a^2 c x^2}}{3 x^3}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4}-\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}-\frac{7 a^2 \sqrt{c-a^2 c x^2}}{8 x^2}+\frac{2 a \sqrt{c-a^2 c x^2}}{3 x^3}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4}-\frac{7}{8} a^4 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-a^2 c x^2}}{\sqrt{c}}\right)",1,"-Sqrt[c - a^2*c*x^2]/(4*x^4) + (2*a*Sqrt[c - a^2*c*x^2])/(3*x^3) - (7*a^2*Sqrt[c - a^2*c*x^2])/(8*x^2) + (4*a^3*Sqrt[c - a^2*c*x^2])/(3*x) - (7*a^4*Sqrt[c]*ArcTanh[Sqrt[c - a^2*c*x^2]/Sqrt[c]])/8","A",8,7,27,0.2593,1,"{6152, 1807, 835, 807, 266, 63, 208}"
1245,1,108,0,0.0865184,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)/E^(2*ArcTanh[a*x]),x]","\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}","\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,"(5*c*x*Sqrt[c - a^2*c*x^2])/8 + (5*(c - a^2*c*x^2)^(3/2))/(12*a) + ((1 - a*x)*(c - a^2*c*x^2)^(3/2))/(4*a) + (5*c^(3/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(8*a)","A",6,6,24,0.2500,1,"{6142, 671, 641, 195, 217, 203}"
1246,1,131,0,0.0968,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[(c - a^2*c*x^2)^(5/2)/E^(2*ArcTanh[a*x]),x]","\frac{7}{16} c^2 x \sqrt{c-a^2 c 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}{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}","\frac{7}{16} c^2 x \sqrt{c-a^2 c 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}{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,"(7*c^2*x*Sqrt[c - a^2*c*x^2])/16 + (7*c*x*(c - a^2*c*x^2)^(3/2))/24 + (7*(c - a^2*c*x^2)^(5/2))/(30*a) + ((1 - a*x)*(c - a^2*c*x^2)^(5/2))/(6*a) + (7*c^(5/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(16*a)","A",7,6,24,0.2500,1,"{6142, 671, 641, 195, 217, 203}"
1247,1,154,0,0.116381,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[(c - a^2*c*x^2)^(7/2)/E^(2*ArcTanh[a*x]),x]","\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{45 c^{7/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a}+\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}","\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{45 c^{7/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{128 a}+\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,"(45*c^3*x*Sqrt[c - a^2*c*x^2])/128 + (15*c^2*x*(c - a^2*c*x^2)^(3/2))/64 + (3*c*x*(c - a^2*c*x^2)^(5/2))/16 + (9*(c - a^2*c*x^2)^(7/2))/(56*a) + ((1 - a*x)*(c - a^2*c*x^2)^(7/2))/(8*a) + (45*c^(7/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(128*a)","A",8,6,24,0.2500,1,"{6142, 671, 641, 195, 217, 203}"
1248,1,61,0,0.0669253,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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*(1 - a*x))/(a*Sqrt[c - a^2*c*x^2]) - ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]]/(a*Sqrt[c])","A",4,4,24,0.1667,1,"{6142, 653, 217, 203}"
1249,1,52,0,0.0642532,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2)),x]","\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}}","\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,"(-2*(1 - a*x))/(3*a*(c - a^2*c*x^2)^(3/2)) + x/(3*c*Sqrt[c - a^2*c*x^2])","A",3,3,24,0.1250,1,"{6142, 653, 191}"
1250,1,75,0,0.0705397,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2)),x]","\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}}","\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,"(-2*(1 - a*x))/(5*a*(c - a^2*c*x^2)^(5/2)) + x/(5*c*(c - a^2*c*x^2)^(3/2)) + (2*x)/(5*c^2*Sqrt[c - a^2*c*x^2])","A",4,4,24,0.1667,1,"{6142, 653, 192, 191}"
1251,1,98,0,0.08145,"\int \frac{e^{-2 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^(2*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2)),x]","\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}}","\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,"(-2*(1 - a*x))/(7*a*(c - a^2*c*x^2)^(7/2)) + x/(7*c*(c - a^2*c*x^2)^(5/2)) + (4*x)/(21*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x)/(21*c^3*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6142, 653, 192, 191}"
1252,1,172,0,0.2761896,"\int e^{-2 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[(x^m*Sqrt[c - a^2*c*x^2])/E^(2*ArcTanh[a*x]),x]","\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}","\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)*Sqrt[c - a^2*c*x^2])/(2 + m)) + (c*(3 + 2*m)*x^(1 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/((1 + m)*(2 + m)*Sqrt[c - a^2*c*x^2]) - (2*a*c*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + m)*Sqrt[c - a^2*c*x^2])","A",7,5,27,0.1852,1,"{6152, 1809, 808, 365, 364}"
1253,1,54,0,0.0585352,"\int e^{-2 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^(2*ArcTanh[a*x]),x]","\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}","\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)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - p, p, 1 + p, (1 + a*x)/2])/(a*p*(1 - a*x)^p)","A",3,3,22,0.1364,1,"{6142, 678, 69}"
1254,1,167,0,0.0943462,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[(c - a^2*c*x^2)^4/E^(3*ArcTanh[a*x]),x]","\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}","\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,"(55*c^4*x*Sqrt[1 - a^2*x^2])/128 + (55*c^4*x*(1 - a^2*x^2)^(3/2))/192 + (11*c^4*x*(1 - a^2*x^2)^(5/2))/48 + (11*c^4*(1 - a^2*x^2)^(7/2))/(56*a) + (11*c^4*(1 - a*x)*(1 - a^2*x^2)^(7/2))/(72*a) + (c^4*(1 - a*x)^2*(1 - a^2*x^2)^(7/2))/(9*a) + (55*c^4*ArcSin[a*x])/(128*a)","A",8,5,22,0.2273,1,"{6139, 671, 641, 195, 216}"
1255,1,145,0,0.0866331,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[(c - a^2*c*x^2)^3/E^(3*ArcTanh[a*x]),x]","\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}","\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,"(9*c^3*x*Sqrt[1 - a^2*x^2])/16 + (3*c^3*x*(1 - a^2*x^2)^(3/2))/8 + (3*c^3*(1 - a^2*x^2)^(5/2))/(10*a) + (3*c^3*(1 - a*x)*(1 - a^2*x^2)^(5/2))/(14*a) + (c^3*(1 - a*x)^2*(1 - a^2*x^2)^(5/2))/(7*a) + (9*c^3*ArcSin[a*x])/(16*a)","A",7,5,22,0.2273,1,"{6139, 671, 641, 195, 216}"
1256,1,123,0,0.0745975,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[(c - a^2*c*x^2)^2/E^(3*ArcTanh[a*x]),x]","\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}","\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,"(7*c^2*x*Sqrt[1 - a^2*x^2])/8 + (7*c^2*(1 - a^2*x^2)^(3/2))/(12*a) + (7*c^2*(1 - a*x)*(1 - a^2*x^2)^(3/2))/(20*a) + (c^2*(1 - a*x)^2*(1 - a^2*x^2)^(3/2))/(5*a) + (7*c^2*ArcSin[a*x])/(8*a)","A",6,5,22,0.2273,1,"{6139, 671, 641, 195, 216}"
1257,1,93,0,0.0567689,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[(c - a^2*c*x^2)/E^(3*ArcTanh[a*x]),x]","\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}","\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,"(5*c*Sqrt[1 - a^2*x^2])/(2*a) + (5*c*(1 - a*x)*Sqrt[1 - a^2*x^2])/(6*a) + (c*(1 - a*x)^2*Sqrt[1 - a^2*x^2])/(3*a) + (5*c*ArcSin[a*x])/(2*a)","A",5,4,20,0.2000,1,"{6139, 671, 641, 216}"
1258,1,18,0,0.0332538,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)),x]","-\frac{e^{-3 \tanh ^{-1}(a x)}}{3 a c}","-\frac{e^{-3 \tanh ^{-1}(a x)}}{3 a c}",1,"-1/(3*a*c*E^(3*ArcTanh[a*x]))","A",1,1,22,0.04545,1,"{6137}"
1259,1,94,0,0.0797878,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^2),x]","-\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}","-\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,"-Sqrt[1 - a^2*x^2]/(5*a*c^2*(1 + a*x)^3) - (2*Sqrt[1 - a^2*x^2])/(15*a*c^2*(1 + a*x)^2) - (2*Sqrt[1 - a^2*x^2])/(15*a*c^2*(1 + a*x))","A",5,4,22,0.1818,1,"{6139, 655, 659, 651}"
1260,1,116,0,0.084844,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^3),x]","\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}}","\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,"(8*x)/(35*c^3*Sqrt[1 - a^2*x^2]) - 1/(7*a*c^3*(1 + a*x)^3*Sqrt[1 - a^2*x^2]) - 4/(35*a*c^3*(1 + a*x)^2*Sqrt[1 - a^2*x^2]) - 4/(35*a*c^3*(1 + a*x)*Sqrt[1 - a^2*x^2])","A",6,4,22,0.1818,1,"{6139, 655, 659, 191}"
1261,1,138,0,0.0930441,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^4),x]","\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}}","\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,"(8*x)/(63*c^4*(1 - a^2*x^2)^(3/2)) - 1/(9*a*c^4*(1 + a*x)^3*(1 - a^2*x^2)^(3/2)) - 2/(21*a*c^4*(1 + a*x)^2*(1 - a^2*x^2)^(3/2)) - 2/(21*a*c^4*(1 + a*x)*(1 - a^2*x^2)^(3/2)) + (16*x)/(63*c^4*Sqrt[1 - a^2*x^2])","A",7,5,22,0.2273,1,"{6139, 655, 659, 192, 191}"
1262,1,225,0,0.2248536,"\int e^{-3 \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[(x^3*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\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{2 x^2 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}+\frac{4 x \sqrt{c-a^2 c x^2}}{a^3 \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{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{2 x^2 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-a^2 x^2}}+\frac{4 x \sqrt{c-a^2 c x^2}}{a^3 \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}}",1,"(4*x*Sqrt[c - a^2*c*x^2])/(a^3*Sqrt[1 - a^2*x^2]) - (2*x^2*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - a^2*x^2]) + (4*x^3*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) - (3*x^4*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - a^2*x^2]) + (a*x^5*Sqrt[c - a^2*c*x^2])/(5*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^4*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1263,1,184,0,0.218766,"\int e^{-3 \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[(x^2*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\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{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{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^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}}-\frac{x^3 \sqrt{c-a^2 c x^2}}{\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{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^3 \sqrt{1-a^2 x^2}}",1,"(-4*x*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - a^2*x^2]) + (2*x^2*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) - (x^3*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] + (a*x^4*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - a^2*x^2]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^3*Sqrt[1 - a^2*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1264,1,149,0,0.1485443,"\int e^{-3 \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[(x*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\frac{a x^3 \sqrt{c-a^2 c x^2}}{3 \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}}-\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}}",1,"(4*x*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - a^2*x^2]) - (3*x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2]) + (a*x^3*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - a^2*x^2]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^2*Sqrt[1 - a^2*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 77}"
1265,1,110,0,0.0833562,"\int e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(-3*x*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] + (a*x^2*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - a^2*x^2]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1266,1,102,0,0.1966041,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x),x]","\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}}","\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,"(a*x*Sqrt[c - a^2*c*x^2])/Sqrt[1 - a^2*x^2] + (Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 72}"
1267,1,107,0,0.2024436,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^2),x]","-\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}}","-\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*Sqrt[1 - a^2*x^2])) - (3*a*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] + (4*a*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1268,1,148,0,0.2057704,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^3),x]","\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}}","\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]/(2*x^2*Sqrt[1 - a^2*x^2]) + (3*a*Sqrt[c - a^2*c*x^2])/(x*Sqrt[1 - a^2*x^2]) + (4*a^2*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^2*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1269,1,187,0,0.2076407,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^4),x]","-\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}}","-\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]/(3*x^3*Sqrt[1 - a^2*x^2]) + (3*a*Sqrt[c - a^2*c*x^2])/(2*x^2*Sqrt[1 - a^2*x^2]) - (4*a^2*Sqrt[c - a^2*c*x^2])/(x*Sqrt[1 - a^2*x^2]) - (4*a^3*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] + (4*a^3*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1270,1,221,0,0.2118212,"\int \frac{e^{-3 \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcTanh[a*x])*x^5),x]","\frac{4 a^3 \sqrt{c-a^2 c x^2}}{x \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{a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4 \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}}-\frac{2 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-a^2 x^2}}+\frac{a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-a^2 x^2}}-\frac{\sqrt{c-a^2 c x^2}}{4 x^4 \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}}",1,"-Sqrt[c - a^2*c*x^2]/(4*x^4*Sqrt[1 - a^2*x^2]) + (a*Sqrt[c - a^2*c*x^2])/(x^3*Sqrt[1 - a^2*x^2]) - (2*a^2*Sqrt[c - a^2*c*x^2])/(x^2*Sqrt[1 - a^2*x^2]) + (4*a^3*Sqrt[c - a^2*c*x^2])/(x*Sqrt[1 - a^2*x^2]) + (4*a^4*Sqrt[c - a^2*c*x^2]*Log[x])/Sqrt[1 - a^2*x^2] - (4*a^4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/Sqrt[1 - a^2*x^2]","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1271,1,189,0,0.1093912,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[(c - a^2*c*x^2)^(9/2)/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(-8*c^4*(1 - a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) + (3*c^4*(1 - a*x)^8*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - a^2*x^2]) - (2*c^4*(1 - a*x)^9*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) + (c^4*(1 - a*x)^10*Sqrt[c - a^2*c*x^2])/(10*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1272,1,142,0,0.1037359,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[(c - a^2*c*x^2)^(7/2)/E^(3*ArcTanh[a*x]),x]","-\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}}","-\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,"(-2*c^3*(1 - a*x)^6*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - a^2*x^2]) + (4*c^3*(1 - a*x)^7*Sqrt[c - a^2*c*x^2])/(7*a*Sqrt[1 - a^2*x^2]) - (c^3*(1 - a*x)^8*Sqrt[c - a^2*c*x^2])/(8*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1273,1,95,0,0.0888439,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[(c - a^2*c*x^2)^(5/2)/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(-2*c^2*(1 - a*x)^5*Sqrt[c - a^2*c*x^2])/(5*a*Sqrt[1 - a^2*x^2]) + (c^2*(1 - a*x)^6*Sqrt[c - a^2*c*x^2])/(6*a*Sqrt[1 - a^2*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1274,1,45,0,0.0801597,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)/E^(3*ArcTanh[a*x]),x]","-\frac{c (1-a x)^4 \sqrt{c-a^2 c x^2}}{4 a \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*(1 - a*x)^4*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - a^2*x^2])","A",3,3,24,0.1250,1,"{6143, 6140, 32}"
1275,1,82,0,0.0875578,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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,"(-2*Sqrt[1 - a^2*x^2])/(a*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(a*Sqrt[c - a^2*c*x^2])","A",4,3,24,0.1250,1,"{6143, 6140, 43}"
1276,1,46,0,0.0812225,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(3/2)),x]","-\frac{\sqrt{1-a^2 x^2}}{2 a c (a x+1)^2 \sqrt{c-a^2 c x^2}}","-\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]/(2*a*c*(1 + a*x)^2*Sqrt[c - a^2*c*x^2])","A",3,3,24,0.1250,1,"{6143, 6140, 32}"
1277,1,182,0,0.1107915,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(5/2)),x]","-\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}}","-\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]/(6*a*c^2*(1 + a*x)^3*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a*c^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a*c^2*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(8*a*c^2*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1278,1,275,0,0.1400193,"\int \frac{e^{-3 \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^(3*ArcTanh[a*x])*(c - a^2*c*x^2)^(7/2)),x]","\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}}","\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*a*c^3*(1 - a*x)*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(16*a*c^3*(1 + a*x)^4*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(12*a*c^3*(1 + a*x)^3*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[1 - a^2*x^2])/(32*a*c^3*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) - Sqrt[1 - a^2*x^2]/(8*a*c^3*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (5*Sqrt[1 - a^2*x^2]*ArcTanh[a*x])/(32*a*c^3*Sqrt[c - a^2*c*x^2])","A",5,4,24,0.1667,1,"{6143, 6140, 44, 207}"
1279,1,136,0,0.2015177,"\int e^{-3 \tanh ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[(x^m*Sqrt[c - a^2*c*x^2])/E^(3*ArcTanh[a*x]),x]","\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}}","\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,"(-3*x^(1 + m)*Sqrt[c - a^2*c*x^2])/((1 + m)*Sqrt[1 - a^2*x^2]) + (a*x^(2 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - a^2*x^2]) + (4*x^(1 + m)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)])/((1 + m)*Sqrt[1 - a^2*x^2])","A",5,4,27,0.1481,1,"{6153, 6150, 88, 64}"
1280,1,86,0,0.0867313,"\int e^{-3 \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^(3*ArcTanh[a*x]),x]","-\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)}","-\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^(-1/2 + 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",3,3,22,0.1364,1,"{6143, 6140, 69}"
1281,1,359,0,0.3063474,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^{5/2} \, dx","Int[E^(ArcTanh[a*x]/2)*(1 - a^2*x^2)^(5/2),x]","-\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}","-\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,"(231*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(512*a) + (231*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(1280*a) + (77*(1 - a*x)^(9/4)*(1 + a*x)^(3/4))/(960*a) - (77*(1 - a*x)^(13/4)*(1 + a*x)^(3/4))/(480*a) - (11*(1 - a*x)^(13/4)*(1 + a*x)^(7/4))/(60*a) - ((1 - a*x)^(13/4)*(1 + a*x)^(11/4))/(6*a) + (231*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(512*Sqrt[2]*a) - (231*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(512*Sqrt[2]*a) + (231*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(1024*Sqrt[2]*a) - (231*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(1024*Sqrt[2]*a)","A",18,10,25,0.4000,1,"{6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1282,1,307,0,0.2398898,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^{3/2} \, dx","Int[E^(ArcTanh[a*x]/2)*(1 - a^2*x^2)^(3/2),x]","-\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}","-\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,"(35*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(64*a) + (7*(1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(32*a) - (7*(1 - a*x)^(9/4)*(1 + a*x)^(3/4))/(24*a) - ((1 - a*x)^(9/4)*(1 + a*x)^(7/4))/(4*a) + (35*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a) - (35*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a) + (35*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a) - (35*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a)","A",16,10,25,0.4000,1,"{6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1283,1,255,0,0.1875669,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \sqrt{1-a^2 x^2} \, dx","Int[E^(ArcTanh[a*x]/2)*Sqrt[1 - a^2*x^2],x]","-\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}","-\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,"(3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4))/(4*a) - ((1 - a*x)^(5/4)*(1 + a*x)^(3/4))/(2*a) + (3*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a) - (3*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a) + (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a) - (3*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a)","A",14,10,25,0.4000,1,"{6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1284,1,193,0,0.1422579,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\sqrt{1-a^2 x^2}} \, dx","Int[E^(ArcTanh[a*x]/2)/Sqrt[1 - a^2*x^2],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} 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}","\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,"(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/a - (Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/a + Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a) - Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)]/(Sqrt[2]*a)","A",12,9,25,0.3600,1,"{6140, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1285,1,37,0,0.0399511,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{3/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(3/2),x]","-\frac{2 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{3 a \sqrt{1-a^2 x^2}}","-\frac{2 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{3 a \sqrt{1-a^2 x^2}}",1,"(-2*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(3*a*Sqrt[1 - a^2*x^2])","A",1,1,25,0.04000,1,"{6135}"
1286,1,75,0,0.0793326,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{5/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(5/2),x]","-\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}}","-\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*E^(ArcTanh[a*x]/2)*(1 - 6*a*x))/(35*a*(1 - a^2*x^2)^(3/2)) - (16*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(35*a*Sqrt[1 - a^2*x^2])","A",2,2,25,0.08000,1,"{6136, 6135}"
1287,1,112,0,0.1171846,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{7/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(7/2),x]","-\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}}","-\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*E^(ArcTanh[a*x]/2)*(1 - 10*a*x))/(99*a*(1 - a^2*x^2)^(5/2)) - (32*E^(ArcTanh[a*x]/2)*(1 - 6*a*x))/(693*a*(1 - a^2*x^2)^(3/2)) - (256*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(693*a*Sqrt[1 - a^2*x^2])","A",3,2,25,0.08000,1,"{6136, 6135}"
1288,1,149,0,0.1680219,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(1-a^2 x^2\right)^{9/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(1 - a^2*x^2)^(9/2),x]","-\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}}","-\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*E^(ArcTanh[a*x]/2)*(1 - 14*a*x))/(195*a*(1 - a^2*x^2)^(7/2)) - (112*E^(ArcTanh[a*x]/2)*(1 - 10*a*x))/(6435*a*(1 - a^2*x^2)^(5/2)) - (256*E^(ArcTanh[a*x]/2)*(1 - 6*a*x))/(6435*a*(1 - a^2*x^2)^(3/2)) - (2048*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(6435*a*Sqrt[1 - a^2*x^2])","A",4,2,25,0.08000,1,"{6136, 6135}"
1289,1,679,0,0.3923667,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(ArcTanh[a*x]/2)*(c - a^2*c*x^2)^(5/2),x]","-\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}}","-\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,"(231*c^2*(1 - a*x)^(1/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(512*a*Sqrt[1 - a^2*x^2]) + (231*c^2*(1 - a*x)^(5/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(1280*a*Sqrt[1 - a^2*x^2]) + (77*c^2*(1 - a*x)^(9/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(960*a*Sqrt[1 - a^2*x^2]) - (77*c^2*(1 - a*x)^(13/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(480*a*Sqrt[1 - a^2*x^2]) - (11*c^2*(1 - a*x)^(13/4)*(1 + a*x)^(7/4)*Sqrt[c - a^2*c*x^2])/(60*a*Sqrt[1 - a^2*x^2]) - (c^2*(1 - a*x)^(13/4)*(1 + a*x)^(11/4)*Sqrt[c - a^2*c*x^2])/(6*a*Sqrt[1 - a^2*x^2]) + (231*c^2*Sqrt[c - a^2*c*x^2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(512*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) - (231*c^2*Sqrt[c - a^2*c*x^2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(512*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) + (231*c^2*Sqrt[c - a^2*c*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(1024*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) - (231*c^2*Sqrt[c - a^2*c*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(1024*Sqrt[2]*a*Sqrt[1 - a^2*x^2])","A",19,11,26,0.4231,1,"{6143, 6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1290,1,547,0,0.3153045,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(ArcTanh[a*x]/2)*(c - a^2*c*x^2)^(3/2),x]","-\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}}","-\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,"(35*c*(1 - a*x)^(1/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(64*a*Sqrt[1 - a^2*x^2]) + (7*c*(1 - a*x)^(5/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(32*a*Sqrt[1 - a^2*x^2]) - (7*c*(1 - a*x)^(9/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(24*a*Sqrt[1 - a^2*x^2]) - (c*(1 - a*x)^(9/4)*(1 + a*x)^(7/4)*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - a^2*x^2]) + (35*c*Sqrt[c - a^2*c*x^2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) - (35*c*Sqrt[c - a^2*c*x^2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(64*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) + (35*c*Sqrt[c - a^2*c*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) - (35*c*Sqrt[c - a^2*c*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(128*Sqrt[2]*a*Sqrt[1 - a^2*x^2])","A",17,11,26,0.4231,1,"{6143, 6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1291,1,429,0,0.2571946,"\int e^{\frac{1}{2} \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(ArcTanh[a*x]/2)*Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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,"(3*(1 - a*x)^(1/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - a^2*x^2]) - ((1 - a*x)^(5/4)*(1 + a*x)^(3/4)*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - a^2*x^2]) + (3*Sqrt[c - a^2*c*x^2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) - (3*Sqrt[c - a^2*c*x^2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(4*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) + (3*Sqrt[c - a^2*c*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a*Sqrt[1 - a^2*x^2]) - (3*Sqrt[c - a^2*c*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(8*Sqrt[2]*a*Sqrt[1 - a^2*x^2])","A",15,11,26,0.4231,1,"{6143, 6140, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1292,1,309,0,0.2047987,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^(ArcTanh[a*x]/2)/Sqrt[c - a^2*c*x^2],x]","\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}}","\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,"(Sqrt[2]*Sqrt[1 - a^2*x^2]*ArcTan[1 - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(a*Sqrt[c - a^2*c*x^2]) - (Sqrt[2]*Sqrt[1 - a^2*x^2]*ArcTan[1 + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(a*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] - (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 + Sqrt[1 - a*x]/Sqrt[1 + a*x] + (Sqrt[2]*(1 - a*x)^(1/4))/(1 + a*x)^(1/4)])/(Sqrt[2]*a*Sqrt[c - a^2*c*x^2])","A",13,10,26,0.3846,1,"{6143, 6140, 63, 240, 211, 1165, 628, 1162, 617, 204}"
1293,1,41,0,0.0452908,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(3/2),x]","-\frac{2 (1-2 a x) e^{\frac{1}{2} \tanh ^{-1}(a x)}}{3 a c \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*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(3*a*c*Sqrt[c - a^2*c*x^2])","A",1,1,26,0.03846,1,"{6135}"
1294,1,83,0,0.093848,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(5/2),x]","-\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}}","-\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*E^(ArcTanh[a*x]/2)*(1 - 6*a*x))/(35*a*c*(c - a^2*c*x^2)^(3/2)) - (16*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(35*a*c^2*Sqrt[c - a^2*c*x^2])","A",2,2,26,0.07692,1,"{6136, 6135}"
1295,1,124,0,0.1432833,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(7/2),x]","-\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}}","-\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*E^(ArcTanh[a*x]/2)*(1 - 10*a*x))/(99*a*c*(c - a^2*c*x^2)^(5/2)) - (32*E^(ArcTanh[a*x]/2)*(1 - 6*a*x))/(693*a*c^2*(c - a^2*c*x^2)^(3/2)) - (256*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(693*a*c^3*Sqrt[c - a^2*c*x^2])","A",3,2,26,0.07692,1,"{6136, 6135}"
1296,1,165,0,0.1970333,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/2}} \, dx","Int[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(9/2),x]","-\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}}","-\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*E^(ArcTanh[a*x]/2)*(1 - 14*a*x))/(195*a*c*(c - a^2*c*x^2)^(7/2)) - (112*E^(ArcTanh[a*x]/2)*(1 - 10*a*x))/(6435*a*c^2*(c - a^2*c*x^2)^(5/2)) - (256*E^(ArcTanh[a*x]/2)*(1 - 6*a*x))/(6435*a*c^3*(c - a^2*c*x^2)^(3/2)) - (2048*E^(ArcTanh[a*x]/2)*(1 - 2*a*x))/(6435*a*c^4*Sqrt[c - a^2*c*x^2])","A",4,2,26,0.07692,1,"{6136, 6135}"
1297,1,201,0,0.2993293,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Int[(E^(ArcTanh[a*x]/2)*x^3)/(c - a^2*c*x^2)^(5/4),x]","-\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}}","-\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 - a^2*x^2)^(1/4)/(a^4*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) + (2*Sqrt[1 - a*x]*(1 - a^2*x^2)^(1/4))/(a^4*c*(c - a^2*c*x^2)^(1/4)) - (2*(1 - a*x)^(3/2)*(1 - a^2*x^2)^(1/4))/(3*a^4*c*(c - a^2*c*x^2)^(1/4)) + ((1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/(Sqrt[2]*a^4*c*(c - a^2*c*x^2)^(1/4))","A",10,8,29,0.2759,1,"{6153, 6150, 87, 43, 783, 78, 63, 207}"
1298,1,153,0,0.2599155,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Int[(E^(ArcTanh[a*x]/2)*x^2)/(c - a^2*c*x^2)^(5/4),x]","\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}}","\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)/(a^3*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) + (2*Sqrt[1 - a*x]*(1 - a^2*x^2)^(1/4))/(a^3*c*(c - a^2*c*x^2)^(1/4)) - ((1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/(Sqrt[2]*a^3*c*(c - a^2*c*x^2)^(1/4))","A",8,7,29,0.2414,1,"{6153, 6150, 87, 627, 51, 63, 207}"
1299,1,105,0,0.1622561,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Int[(E^(ArcTanh[a*x]/2)*x)/(c - a^2*c*x^2)^(5/4),x]","\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}}","\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)/(a^2*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) + ((1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/(Sqrt[2]*a^2*c*(c - a^2*c*x^2)^(1/4))","A",5,5,27,0.1852,1,"{6153, 6150, 78, 63, 206}"
1300,1,106,0,0.0978393,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/4}} \, dx","Int[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(5/4),x]","\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}}","\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)/(a*c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) - ((1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/(Sqrt[2]*a*c*(c - a^2*c*x^2)^(1/4))","A",5,5,26,0.1923,1,"{6143, 6140, 51, 63, 206}"
1301,1,144,0,0.2350618,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/4}} \, dx","Int[E^(ArcTanh[a*x]/2)/(x*(c - a^2*c*x^2)^(5/4)),x]","\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}}","\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)/(c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) - (2*(1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]])/(c*(c - a^2*c*x^2)^(1/4)) + ((1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/(Sqrt[2]*c*(c - a^2*c*x^2)^(1/4))","A",8,7,29,0.2414,1,"{6153, 6150, 85, 156, 63, 208, 206}"
1302,1,196,0,0.2490276,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/4}} \, dx","Int[E^(ArcTanh[a*x]/2)/(x^2*(c - a^2*c*x^2)^(5/4)),x]","\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}}","\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,"(2*a*(1 - a^2*x^2)^(1/4))/(c*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) - (1 - a^2*x^2)^(1/4)/(c*x*Sqrt[1 - a*x]*(c - a^2*c*x^2)^(1/4)) - (a*(1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]])/(c*(c - a^2*c*x^2)^(1/4)) - (a*(1 - a^2*x^2)^(1/4)*ArcTanh[Sqrt[1 - a*x]/Sqrt[2]])/(Sqrt[2]*c*(c - a^2*c*x^2)^(1/4))","A",9,8,29,0.2759,1,"{6153, 6150, 103, 152, 156, 63, 208, 206}"
1303,1,200,0,0.2539501,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Int[(E^(ArcTanh[a*x]/2)*x^3)/(c - a^2*c*x^2)^(9/8),x]","\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{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{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}}","\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{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{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*x^2*(1 + a*x)^(1/8)*(1 - a^2*x^2)^(1/8))/(7*a^2*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8)) + (8*(6 - a*x)*(1 + a*x)^(1/8)*(1 - a^2*x^2)^(1/8))/(21*a^4*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8)) + (64*2^(1/8)*(1 - a*x)^(5/8)*(1 - a^2*x^2)^(1/8)*Hypergeometric2F1[5/8, 7/8, 13/8, (1 - a*x)/2])/(105*a^4*c*(c - a^2*c*x^2)^(1/8))","A",5,5,29,0.1724,1,"{6153, 6150, 100, 146, 69}"
1304,1,41,0,0.1194127,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Int[(E^(ArcTanh[a*x]/2)*x^2)/(c - a^2*c*x^2)^(9/8),x]","\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}}","\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*E^(ArcTanh[a*x]/2)*(2 - a*x))/(3*a^3*c*(c - a^2*c*x^2)^(1/8))","A",1,1,29,0.03448,1,"{6146}"
1305,1,133,0,0.1687611,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Int[(E^(ArcTanh[a*x]/2)*x)/(c - a^2*c*x^2)^(9/8),x]","\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}}","\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*x)^(1/8)*(1 - a^2*x^2)^(1/8))/(3*a^2*c*(1 - a*x)^(3/8)*(c - a^2*c*x^2)^(1/8)) + (8*2^(1/8)*(1 - a*x)^(5/8)*(1 - a^2*x^2)^(1/8)*Hypergeometric2F1[5/8, 7/8, 13/8, (1 - a*x)/2])/(15*a^2*c*(c - a^2*c*x^2)^(1/8))","A",4,4,27,0.1481,1,"{6153, 6150, 78, 69}"
1306,1,74,0,0.0903437,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/8}} \, dx","Int[E^(ArcTanh[a*x]/2)/(c - a^2*c*x^2)^(9/8),x]","\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}}","\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^(1/8)*(1 - 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",3,3,26,0.1154,1,"{6143, 6140, 69}"
1307,1,73,0,0.2246303,"\int \frac{e^{\frac{1}{2} \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{9/8}} \, dx","Int[E^(ArcTanh[a*x]/2)/(x*(c - a^2*c*x^2)^(9/8)),x]","-\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}}","-\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,"(-2*2^(5/8)*(1 + a*x)^(1/8)*(1 - a^2*x^2)^(1/8)*AppellF1[1/8, 11/8, 1, 9/8, (1 + a*x)/2, 1 + a*x])/(c*(c - a^2*c*x^2)^(1/8))","A",3,3,29,0.1034,1,"{6153, 6150, 136}"
1308,1,68,0,0.0441174,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[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 (4-n)}","-\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",2,2,20,0.1000,1,"{6140, 69}"
1309,1,70,0,0.0536608,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[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 (6-n)}","-\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",2,2,22,0.09091,1,"{6140, 69}"
1310,1,70,0,0.0563535,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[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 (8-n)}","-\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",2,2,22,0.09091,1,"{6140, 69}"
1311,1,209,0,0.2572939,"\int \frac{e^{n \tanh ^{-1}(a x)} x^4}{c-a^2 c x^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2),x]","\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{x^3 (a x+1)^{n/2} (1-a x)^{-n/2}}{3 a^2 c}-\frac{n x^2 (a x+1)^{n/2} (1-a x)^{-n/2}}{6 a^3 c}","\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{x^3 (a x+1)^{n/2} (1-a x)^{-n/2}}{3 a^2 c}-\frac{n x^2 (a x+1)^{n/2} (1-a x)^{-n/2}}{6 a^3 c}",1,"-(n*x^2*(1 + a*x)^(n/2))/(6*a^3*c*(1 - a*x)^(n/2)) - (x^3*(1 + a*x)^(n/2))/(3*a^2*c*(1 - a*x)^(n/2)) + ((1 + a*x)^(n/2)*(6 + 8*n + n^2 + n^3 - a*n*(6 + n^2)*x))/(6*a^5*c*n*(1 - a*x)^(n/2)) + (2^(-1 + n/2)*n*(8 + n^2)*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2])/(3*a^5*c*(2 - n))","A",5,5,25,0.2000,1,"{6150, 100, 153, 143, 69}"
1312,1,160,0,0.2050223,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{c-a^2 c x^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2),x]","\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}","\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,"-(x^2*(1 + a*x)^(n/2))/(2*a^2*c*(1 - a*x)^(n/2)) + ((1 + a*x)^(n/2)*(2 + n + n^2 - a*n^2*x))/(2*a^4*c*n*(1 - a*x)^(n/2)) + (2^(-1 + n/2)*(2 + n^2)*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[1 - n/2, 1 - n/2, 2 - n/2, (1 - a*x)/2])/(a^4*c*(2 - n))","A",4,4,25,0.1600,1,"{6150, 100, 143, 69}"
1313,1,127,0,0.135161,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{c-a^2 c x^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2),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^3 c}-\frac{x (a x+1)^{n/2} (1-a x)^{-n/2}}{a^2 c}+\frac{(1-n) (a x+1)^{n/2} (1-a x)^{-n/2}}{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 - n)*(1 + a*x)^(n/2))/(a^3*c*n*(1 - a*x)^(n/2)) - (x*(1 + a*x)^(n/2))/(a^2*c*(1 - a*x)^(n/2)) + (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(a^3*c*(1 - a*x)^(n/2))","A",4,4,25,0.1600,0,"{6150, 90, 79, 69}"
1314,1,94,0,0.0828106,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{c-a^2 c x^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2),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^2 c n}-\frac{(1-a x)^{-n/2} (a x+1)^{n/2}}{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)/(a^2*c*n*(1 - a*x)^(n/2))) + (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (1 - a*x)/2])/(a^2*c*n*(1 - a*x)^(n/2))","A",3,3,23,0.1304,1,"{6150, 79, 69}"
1315,1,18,0,0.0343823,"\int \frac{e^{n \tanh ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2),x]","\frac{e^{n \tanh ^{-1}(a x)}}{a c n}","\frac{e^{n \tanh ^{-1}(a x)}}{a c n}",1,"E^(n*ArcTanh[a*x])/(a*c*n)","A",1,1,22,0.04545,1,"{6137}"
1316,1,100,0,0.1054929,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)} \, dx","Int[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)),x]","\frac{(1-a x)^{-n/2} (a x+1)^{n/2}}{c n}-\frac{2 (1-a x)^{1-\frac{n}{2}} (a x+1)^{\frac{n-2}{2}} \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{c (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)^(n/2)/(c*n*(1 - a*x)^(n/2)) - (2*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(c*(2 - n))","A",3,3,25,0.1200,0,"{6150, 96, 131}"
1317,1,137,0,0.1435684,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)} \, dx","Int[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)),x]","-\frac{2 a n (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{c (2-n)}+\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}","-\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,"(a*(1 + n)*(1 + a*x)^(n/2))/(c*n*(1 - a*x)^(n/2)) - (1 + a*x)^(n/2)/(c*x*(1 - a*x)^(n/2)) - (2*a*n*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(c*(2 - n))","A",5,5,25,0.2000,0,"{6150, 129, 155, 12, 131}"
1318,1,376,0,0.3881703,"\int \frac{e^{n \tanh ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^4)/(c - a^2*c*x^2)^2,x]","-\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{x^3 (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^2 c^2}+\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{(n+3) x (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^4 c^2}+\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{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{x^3 (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^2 c^2}+\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{(n+3) x (a x+1)^{\frac{n-2}{2}} (1-a x)^{-\frac{n}{2}-1}}{a^4 c^2}+\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}",1,"((1 - n)*(3 + n)*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a^5*c^2*(2 - n)) + ((3 + n)*x*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a^4*c^2) - (x^3*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a^2*c^2) + ((1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a^5*c^2*(2 - n)) - (1 + a*x)^((-2 + n)/2)/(a^5*c^2*(1 - a*x)^(n/2)) - ((3 + n)*(2 - n^2)*(1 - a*x)^(-1 - n/2)*(1 + a*x)^(n/2))/(a^5*c^2*(4 - n^2)) - ((3 + n)*(2 - n^2)*(1 + a*x)^(n/2))/(a^5*c^2*n*(4 - n^2)*(1 - a*x)^(n/2)) - (2^(n/2)*n*(1 - a*x)^(1 - n/2)*Hypergeometric2F1[(2 - n)/2, 1 - n/2, 2 - n/2, (1 - a*x)/2])/(a^5*c^2*(2 - n))","A",10,9,25,0.3600,1,"{6150, 100, 159, 89, 79, 69, 90, 45, 37}"
1319,1,311,0,0.2521914,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^2,x]","\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)}","\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,"-(((1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a^4*c^2*(2 + n))) + (2*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2))/(a^4*c^2*n*(4 - n^2)) - (2*(1 + a*x)^((-2 + n)/2))/(a^4*c^2*n*(2 + n)*(1 - a*x)^(n/2)) + (3*(1 - a*x)^(-1 - n/2)*(1 + a*x)^(n/2))/(a^4*c^2*(2 + n)) + (3*(1 + a*x)^(n/2))/(a^4*c^2*n*(2 + n)*(1 - a*x)^(n/2)) - (3*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((2 + n)/2))/(a^4*c^2*(2 + n)) + (2^(2 + n/2)*(1 - a*x)^(-1 - n/2)*Hypergeometric2F1[-1 - n/2, -1 - n/2, -n/2, (1 - a*x)/2])/(a^4*c^2*(2 + n))","A",10,5,25,0.2000,1,"{6150, 128, 45, 37, 69}"
1320,1,79,0,0.1274412,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^2,x]","-\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)}-\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)}-\frac{\left(2-n^2\right) e^{n \tanh ^{-1}(a x)}}{a^3 c^2 n \left(4-n^2\right)}",1,"-((E^(n*ArcTanh[a*x])*(2 - n^2))/(a^3*c^2*n*(4 - n^2))) - (E^(n*ArcTanh[a*x])*(n - 2*a*x))/(a^3*c^2*(4 - n^2)*(1 - a^2*x^2))","A",2,2,25,0.08000,1,"{6147, 6137}"
1321,1,102,0,0.1492314,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^2,x]","\frac{n (n-2 a x) e^{n \tanh ^{-1}(a x)}}{2 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)}+\frac{e^{n \tanh ^{-1}(a x)}}{2 a^2 c^2 \left(1-a^2 x^2\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,"-(E^(n*ArcTanh[a*x])/(a^2*c^2*(4 - n^2))) + E^(n*ArcTanh[a*x])/(2*a^2*c^2*(1 - a^2*x^2)) + (E^(n*ArcTanh[a*x])*n*(n - 2*a*x))/(2*a^2*c^2*(4 - n^2)*(1 - a^2*x^2))","A",3,3,23,0.1304,1,"{6145, 6136, 6137}"
1322,1,72,0,0.074394,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^2,x]","\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)}","\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,"(2*E^(n*ArcTanh[a*x]))/(a*c^2*n*(4 - n^2)) - (E^(n*ArcTanh[a*x])*(n - 2*a*x))/(a*c^2*(4 - n^2)*(1 - a^2*x^2))","A",2,2,22,0.09091,1,"{6136, 6137}"
1323,1,200,0,0.2022661,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^2} \, dx","Int[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^2),x]","-\frac{2 (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{c^2 (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)}","-\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)^((-2 + n)/2))/(c^2*(2 + n)) - ((4 - n - n^2)*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2))/(c^2*n*(4 - n^2)) + ((4 + n)*(1 + a*x)^((-2 + n)/2))/(c^2*n*(2 + n)*(1 - a*x)^(n/2)) - (2*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(c^2*(2 - n))","A",6,5,25,0.2000,0,"{6150, 129, 155, 12, 131}"
1324,1,253,0,0.2514094,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^2} \, dx","Int[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^2),x]","-\frac{2 a n (a x+1)^{\frac{n-2}{2}} (1-a x)^{1-\frac{n}{2}} \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{1-a x}{a x+1}\right)}{c^2 (2-n)}-\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 \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 (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}","-\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^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 \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 (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,"(a*(3 + n)*(1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(c^2*(2 + n)) - ((1 - a*x)^(-1 - n/2)*(1 + a*x)^((-2 + n)/2))/(c^2*x) - (a*(6 + 4*n - n^2 - n^3)*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2))/(c^2*n*(4 - n^2)) + (a*(6 + 4*n + n^2)*(1 + a*x)^((-2 + n)/2))/(c^2*n*(2 + n)*(1 - a*x)^(n/2)) - (2*a*n*(1 - a*x)^(1 - n/2)*(1 + a*x)^((-2 + n)/2)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (1 - a*x)/(1 + a*x)])/(c^2*(2 - n))","A",7,5,25,0.2000,0,"{6150, 129, 155, 12, 131}"
1325,1,127,0,0.1344258,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^3,x]","-\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)}","-\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,"(24*E^(n*ArcTanh[a*x]))/(a*c^3*n*(64 - 20*n^2 + n^4)) - (E^(n*ArcTanh[a*x])*(n - 4*a*x))/(a*c^3*(16 - n^2)*(1 - a^2*x^2)^2) - (12*E^(n*ArcTanh[a*x])*(n - 2*a*x))/(a*c^3*(4 - n^2)*(16 - n^2)*(1 - a^2*x^2))","A",3,2,22,0.09091,1,"{6136, 6137}"
1326,1,197,0,0.1859158,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^4,x]","-\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)}","-\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,"(720*E^(n*ArcTanh[a*x]))/(a*c^4*n*(36 - n^2)*(64 - 20*n^2 + n^4)) - (E^(n*ArcTanh[a*x])*(n - 6*a*x))/(a*c^4*(36 - n^2)*(1 - a^2*x^2)^3) - (30*E^(n*ArcTanh[a*x])*(n - 4*a*x))/(a*c^4*(16 - n^2)*(36 - n^2)*(1 - a^2*x^2)^2) - (360*E^(n*ArcTanh[a*x])*(n - 2*a*x))/(a*c^4*(4 - n^2)*(16 - n^2)*(36 - n^2)*(1 - a^2*x^2))","A",4,2,22,0.09091,1,"{6136, 6137}"
1327,1,256,0,0.3395601,"\int e^{n \tanh ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[E^(n*ArcTanh[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","-\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}}-\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}}-\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}}",1,"-(x^2*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((3 + n)/2)*Sqrt[c - a^2*c*x^2])/(5*a^2*Sqrt[1 - a^2*x^2]) - ((1 - a*x)^((3 - n)/2)*(1 + a*x)^((3 + n)/2)*(8 + n^2 + 3*a*n*x)*Sqrt[c - a^2*c*x^2])/(60*a^4*Sqrt[1 - a^2*x^2]) - (2^((-1 + n)/2)*n*(11 + n^2)*(1 - a*x)^((3 - n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2])/(15*a^4*(3 - n)*Sqrt[1 - a^2*x^2])","A",5,5,27,0.1852,1,"{6153, 6150, 100, 147, 69}"
1328,1,244,0,0.312724,"\int e^{n \tanh ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^(n*ArcTanh[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","-\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}}-\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}}-\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}}",1,"-(n*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((3 + n)/2)*Sqrt[c - a^2*c*x^2])/(12*a^3*Sqrt[1 - a^2*x^2]) - (x*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((3 + n)/2)*Sqrt[c - a^2*c*x^2])/(4*a^2*Sqrt[1 - a^2*x^2]) - (2^((-1 + n)/2)*(3 + n^2)*(1 - a*x)^((3 - n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[(-1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2])/(3*a^3*(3 - n)*Sqrt[1 - a^2*x^2])","A",5,5,27,0.1852,1,"{6153, 6150, 90, 80, 69}"
1329,1,173,0,0.1871529,"\int e^{n \tanh ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^(n*ArcTanh[a*x])*x*Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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 - n)/2)*(1 + a*x)^((3 + n)/2)*Sqrt[c - a^2*c*x^2])/(3*a^2*Sqrt[1 - a^2*x^2]) - (2^((3 + n)/2)*n*(1 - a*x)^((3 - n)/2)*Sqrt[c - a^2*c*x^2]*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",4,4,25,0.1600,1,"{6153, 6150, 80, 69}"
1330,1,104,0,0.096049,"\int e^{n \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[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-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}}","-\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 - 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",3,3,24,0.1250,1,"{6143, 6140, 69}"
1331,1,299,0,0.2930152,"\int \frac{e^{n \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^(n*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x,x]","\frac{2 \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+1}{2}} (1-a x)^{\frac{1}{2} (-n-1)} \, _2F_1\left(1,\frac{1}{2} (-n-1);\frac{1-n}{2};\frac{1-a x}{a x+1}\right)}{(n+1) \sqrt{1-a^2 x^2}}-\frac{2^{\frac{n+3}{2}} \sqrt{c-a^2 c x^2} (1-a x)^{\frac{1}{2} (-n-1)} \, _2F_1\left(\frac{1}{2} (-n-1),\frac{1}{2} (-n-1);\frac{1-n}{2};\frac{1}{2} (1-a x)\right)}{(n+1) \sqrt{1-a^2 x^2}}+\frac{2^{\frac{n+3}{2}} \sqrt{c-a^2 c 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)}{(1-n) \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)*(1 + a*x)^((1 + n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[1, (-1 - n)/2, (1 - n)/2, (1 - a*x)/(1 + a*x)])/((1 + n)*Sqrt[1 - a^2*x^2]) - (2^((3 + n)/2)*(1 - a*x)^((-1 - n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[(-1 - n)/2, (-1 - n)/2, (1 - n)/2, (1 - a*x)/2])/((1 + n)*Sqrt[1 - a^2*x^2]) + (2^((3 + n)/2)*(1 - a*x)^((1 - n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[(-1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/((1 - n)*Sqrt[1 - a^2*x^2])","A",7,5,27,0.1852,0,"{6153, 6150, 105, 69, 131}"
1332,1,97,0,0.2335368,"\int \frac{e^{n \tanh ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^(n*ArcTanh[a*x])*Sqrt[c - a^2*c*x^2])/x^2,x]","\frac{a 2^{\frac{3}{2}-\frac{n}{2}} \sqrt{c-a^2 c x^2} (a x+1)^{\frac{n+3}{2}} F_1\left(\frac{n+3}{2};\frac{n-1}{2},2;\frac{n+5}{2};\frac{1}{2} (a x+1),a x+1\right)}{(n+3) \sqrt{1-a^2 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,"(2^(3/2 - n/2)*a*(1 + a*x)^((3 + n)/2)*Sqrt[c - a^2*c*x^2]*AppellF1[(3 + n)/2, (-1 + n)/2, 2, (5 + n)/2, (1 + a*x)/2, 1 + a*x])/((3 + n)*Sqrt[1 - a^2*x^2])","C",3,3,27,0.1111,0,"{6153, 6150, 136}"
1333,1,105,0,0.1129705,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[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-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}}","-\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 - n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[(-3 - n)/2, (5 - n)/2, (7 - n)/2, (1 - a*x)/2])/(a*(5 - n)*Sqrt[1 - a^2*x^2]))","A",3,3,24,0.1250,1,"{6143, 6140, 69}"
1334,1,275,0,0.3809187,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x^3)/Sqrt[c - a^2*c*x^2],x]","-\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}}-\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}}-\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}}",1,"-(x^2*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(3*a^2*Sqrt[c - a^2*c*x^2]) - ((1 - a*x)^((1 - n)/2)*(1 + a*x)^((1 + n)/2)*(4 + n + n^2 + a*(1 - n)*n*x)*Sqrt[1 - a^2*x^2])/(6*a^4*(1 - n)*Sqrt[c - a^2*c*x^2]) - (2^((-1 + n)/2)*n*(5 + n^2)*(1 - a*x)^((3 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(1 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2])/(3*a^4*(1 - n)*(3 - n)*Sqrt[c - a^2*c*x^2])","A",5,5,27,0.1852,1,"{6153, 6150, 100, 146, 69}"
1335,1,253,0,0.3292194,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x^2)/Sqrt[c - a^2*c*x^2],x]","-\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{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{(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}}","-\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{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{(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 - n)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*a^3*(1 + n)*Sqrt[c - a^2*c*x^2]) - (x*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*a^2*Sqrt[c - a^2*c*x^2]) - (2^((1 + n)/2)*(1 + n^2)*(1 - a*x)^((1 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(-1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/(a^3*(1 - n^2)*Sqrt[c - a^2*c*x^2])","A",5,5,27,0.1852,1,"{6153, 6150, 90, 79, 69}"
1336,1,176,0,0.2015624,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\sqrt{c-a^2 c x^2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x)/Sqrt[c - a^2*c*x^2],x]","-\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}}","-\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 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(a^2*(1 + n)*Sqrt[c - a^2*c*x^2])) - (2^((3 + n)/2)*n*(1 - a*x)^((1 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(-1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/(a^2*(1 - n^2)*Sqrt[c - a^2*c*x^2])","A",4,4,25,0.1600,1,"{6153, 6150, 79, 69}"
1337,1,104,0,0.1055078,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[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-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}}","-\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 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/(a*(1 - n)*Sqrt[c - a^2*c*x^2]))","A",3,3,24,0.1250,1,"{6143, 6140, 69}"
1338,1,101,0,0.2309843,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \sqrt{c-a^2 c x^2}} \, dx","Int[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-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}}","-\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 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, (1 - a*x)/(1 + a*x)])/((1 - n)*Sqrt[c - a^2*c*x^2])","A",3,3,27,0.1111,1,"{6153, 6150, 131}"
1339,1,167,0,0.2492471,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \sqrt{c-a^2 c x^2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x^2*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(x*Sqrt[c - a^2*c*x^2])) - (2*a*n*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, (1 - a*x)/(1 + a*x)])/((1 - n)*Sqrt[c - a^2*c*x^2])","A",4,4,27,0.1481,1,"{6153, 6150, 96, 131}"
1340,1,242,0,0.2735935,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3 \sqrt{c-a^2 c x^2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x^3*Sqrt[c - a^2*c*x^2]),x]","-\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}}","-\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 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*x^2*Sqrt[c - a^2*c*x^2]) - (a*n*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*x*Sqrt[c - a^2*c*x^2]) - (a^2*(1 + n^2)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, (1 - a*x)/(1 + a*x)])/((1 - n)*Sqrt[c - a^2*c*x^2])","A",6,6,27,0.2222,1,"{6153, 6150, 129, 151, 12, 131}"
1341,1,270,0,0.3631322,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^(3/2),x]","-\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}}-\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}}-\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}}",1,"-((x^2*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(a^2*c*Sqrt[c - a^2*c*x^2])) + ((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*(2 + 2*n + n^2 - a*n*(3 + 2*n)*x)*Sqrt[1 - a^2*x^2])/(a^4*c*(1 - n^2)*Sqrt[c - a^2*c*x^2]) - (2^((-1 + n)/2)*n*(1 - a*x)^((3 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(3 - n)/2, (3 - n)/2, (5 - n)/2, (1 - a*x)/2])/(a^4*c*(3 - n)*Sqrt[c - a^2*c*x^2])","A",5,5,27,0.1852,1,"{6153, 6150, 100, 145, 69}"
1342,1,153,0,0.2463334,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"-((E^(n*ArcTanh[a*x])*(n - a*x))/(a^3*c*(1 - n^2)*Sqrt[c - a^2*c*x^2])) + (2^((1 + n)/2)*(1 - a*x)^((1 - n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[(1 - n)/2, (1 - n)/2, (3 - n)/2, (1 - a*x)/2])/(a^3*c*(1 - n)*Sqrt[c - a^2*c*x^2])","A",4,4,27,0.1481,1,"{6147, 6143, 6140, 69}"
1343,1,46,0,0.0932925,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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,"(E^(n*ArcTanh[a*x])*(1 - a*n*x))/(a^2*c*(1 - n^2)*Sqrt[c - a^2*c*x^2])","A",1,1,25,0.04000,1,"{6144}"
1344,1,46,0,0.0526932,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^(3/2),x]","-\frac{(n-a x) e^{n \tanh ^{-1}(a x)}}{a c \left(1-n^2\right) \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,"-((E^(n*ArcTanh[a*x])*(n - a*x))/(a*c*(1 - n^2)*Sqrt[c - a^2*c*x^2]))","A",1,1,24,0.04167,1,"{6135}"
1345,1,247,0,0.3242488,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^(3/2)),x]","-\frac{2 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{1-a x}{a x+1}\right)}{c (3-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}}","\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)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(c*(1 + n)*Sqrt[c - a^2*c*x^2]) - ((2 + n)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(c*(1 - n^2)*Sqrt[c - a^2*c*x^2]) - (2*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (1 - a*x)/(1 + a*x)])/(c*(3 - n)*Sqrt[c - a^2*c*x^2])","A",6,6,27,0.2222,0,"{6153, 6150, 129, 155, 12, 131}"
1346,1,325,0,0.3511417,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^(3/2)),x]","-\frac{2 a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{1-a x}{a x+1}\right)}{c (3-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}}","\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,"(a*(2 + n)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(c*(1 + n)*Sqrt[c - a^2*c*x^2]) - ((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(c*x*Sqrt[c - a^2*c*x^2]) - (a*(2 + 2*n + n^2)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(c*(1 - n^2)*Sqrt[c - a^2*c*x^2]) - (2*a*n*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (1 - a*x)/(1 + a*x)])/(c*(3 - n)*Sqrt[c - a^2*c*x^2])","A",7,6,27,0.2222,0,"{6153, 6150, 129, 155, 12, 131}"
1347,1,422,0,0.420699,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^(3/2)),x]","-\frac{a^2 \left(n^2+3\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{1-a x}{a x+1}\right)}{c (3-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}}","\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,"(a^2*(3 + 2*n + n^2)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c*(1 + n)*Sqrt[c - a^2*c*x^2]) - ((1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c*x^2*Sqrt[c - a^2*c*x^2]) - (a*n*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c*x*Sqrt[c - a^2*c*x^2]) - (a^2*(6 + 5*n + 2*n^2 + n^3)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c*(1 - n^2)*Sqrt[c - a^2*c*x^2]) - (a^2*(3 + n^2)*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (1 - a*x)/(1 + a*x)])/(c*(3 - n)*Sqrt[c - a^2*c*x^2])","A",8,7,27,0.2593,0,"{6153, 6150, 129, 151, 155, 12, 131}"
1348,1,407,0,0.4864616,"\int \frac{e^{n \tanh ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x^3)/(c - a^2*c*x^2)^(5/2),x]","-\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{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 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}}","-\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{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 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,"(x^3*(1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(a*c^2*(3 + n)*Sqrt[c - a^2*c*x^2]) - (3*(2 - n)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(a^4*c^2*(9 - n^2)*Sqrt[c - a^2*c*x^2]) - (3*x*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(a^3*c^2*(3 + n)*Sqrt[c - a^2*c*x^2]) + (3*(1 + 2*n - n^2)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(a^4*c^2*(3 - n)*(1 + n)*(3 + n)*Sqrt[c - a^2*c*x^2]) - (3*(1 + 2*n - n^2)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-1 + n)/2)*Sqrt[1 - a^2*x^2])/(a^4*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2])","A",7,7,27,0.2593,1,"{6153, 6150, 94, 90, 79, 45, 37}"
1349,1,102,0,0.1990661,"\int \frac{e^{n \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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,"-((E^(n*ArcTanh[a*x])*(n - 3*a*x))/(a^3*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2))) + (E^(n*ArcTanh[a*x])*(3 - n^2)*(n - a*x))/(a^3*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2])","A",2,2,27,0.07407,1,"{6147, 6135}"
1350,1,133,0,0.2138213,"\int \frac{e^{n \tanh ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcTanh[a*x])*x)/(c - a^2*c*x^2)^(5/2),x]","\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}}","\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,"E^(n*ArcTanh[a*x])/(3*a^2*c*(c - a^2*c*x^2)^(3/2)) + (E^(n*ArcTanh[a*x])*n*(n - 3*a*x))/(3*a^2*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2)) + (2*E^(n*ArcTanh[a*x])*n*(n - a*x))/(a^2*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2])","A",3,3,25,0.1200,1,"{6145, 6136, 6135}"
1351,1,102,0,0.1063489,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^(5/2),x]","-\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}}","-\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,"-((E^(n*ArcTanh[a*x])*(n - 3*a*x))/(a*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2))) - (6*E^(n*ArcTanh[a*x])*(n - a*x))/(a*c^2*(1 - n^2)*(9 - n^2)*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{6136, 6135}"
1352,1,421,0,0.4575031,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x*(c - a^2*c*x^2)^(5/2)),x]","-\frac{2 \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{1-a x}{a x+1}\right)}{c^2 (3-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}}","\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])/(c^2*(3 + n)*Sqrt[c - a^2*c*x^2]) + ((6 + n)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(1 + n)*(3 + n)*Sqrt[c - a^2*c*x^2]) - ((15 + 6*n + n^2)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(3 + n)*(1 - n^2)*Sqrt[c - a^2*c*x^2]) + ((18 + 7*n - 2*n^2 - n^3)*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2]) - (2*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (1 - a*x)/(1 + a*x)])/(c^2*(3 - n)*Sqrt[c - a^2*c*x^2])","A",8,6,27,0.2222,0,"{6153, 6150, 129, 155, 12, 131}"
1353,1,511,0,0.5354739,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x^2*(c - a^2*c*x^2)^(5/2)),x]","-\frac{2 a n \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{1-a x}{a x+1}\right)}{c^2 (3-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}}","\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,"(a*(4 + n)*(1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(3 + n)*Sqrt[c - a^2*c*x^2]) - ((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*x*Sqrt[c - a^2*c*x^2]) + (a*(12 + 6*n + n^2)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(1 + n)*(3 + n)*Sqrt[c - a^2*c*x^2]) - (a*(24 + 15*n + 6*n^2 + n^3)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(3 + n)*(1 - n^2)*Sqrt[c - a^2*c*x^2]) + (a*(24 + 18*n + 7*n^2 - 2*n^3 - n^4)*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2]) - (2*a*n*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (1 - a*x)/(1 + a*x)])/(c^2*(3 - n)*Sqrt[c - a^2*c*x^2])","A",9,6,27,0.2222,0,"{6153, 6150, 129, 155, 12, 131}"
1354,1,628,0,0.6467277,"\int \frac{e^{n \tanh ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(x^3*(c - a^2*c*x^2)^(5/2)),x]","-\frac{a^2 \left(n^2+5\right) \sqrt{1-a^2 x^2} (a x+1)^{\frac{n-3}{2}} (1-a x)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{1-a x}{a x+1}\right)}{c^2 (3-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}}","\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,"(a^2*(5 + 4*n + n^2)*(1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c^2*(3 + n)*Sqrt[c - a^2*c*x^2]) - ((1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c^2*x^2*Sqrt[c - a^2*c*x^2]) - (a*n*(1 - a*x)^((-3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c^2*x*Sqrt[c - a^2*c*x^2]) + (a^2*(30 + 17*n + 6*n^2 + n^3)*(1 - a*x)^((-1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c^2*(1 + n)*(3 + n)*Sqrt[c - a^2*c*x^2]) - (a^2*(75 + 54*n + 20*n^2 + 6*n^3 + n^4)*(1 - a*x)^((1 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c^2*(3 + n)*(1 - n^2)*Sqrt[c - a^2*c*x^2]) + (a^2*(90 + 59*n + 8*n^2 + 2*n^3 - 2*n^4 - n^5)*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2])/(2*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2]) - (a^2*(5 + n^2)*(1 - a*x)^((3 - n)/2)*(1 + a*x)^((-3 + n)/2)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (1 - a*x)/(1 + a*x)])/(c^2*(3 - n)*Sqrt[c - a^2*c*x^2])","A",10,7,27,0.2593,0,"{6153, 6150, 129, 151, 155, 12, 131}"
1355,1,166,0,0.1863632,"\int \frac{e^{n \tanh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(n*ArcTanh[a*x])/(c - a^2*c*x^2)^(7/2),x]","-\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}}","-\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,"-((E^(n*ArcTanh[a*x])*(n - 5*a*x))/(a*c*(25 - n^2)*(c - a^2*c*x^2)^(5/2))) - (20*E^(n*ArcTanh[a*x])*(n - 3*a*x))/(a*c^2*(9 - n^2)*(25 - n^2)*(c - a^2*c*x^2)^(3/2)) - (120*E^(n*ArcTanh[a*x])*(n - a*x))/(a*c^3*(1 - n^2)*(9 - n^2)*(25 - n^2)*Sqrt[c - a^2*c*x^2])","A",3,2,24,0.08333,1,"{6136, 6135}"
1356,1,42,0,0.0911683,"\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^2,x]","\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}","\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,"(c^2*x^(1 + m)*AppellF1[1 + m, (-4 + n)/2, -2 - n/2, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,25,0.08000,1,"{6150, 133}"
1357,1,40,0,0.0738821,"\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right) \, dx","Int[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2),x]","\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}","\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,"(c*x^(1 + m)*AppellF1[1 + m, (-2 + n)/2, -1 - n/2, 2 + m, a*x, -(a*x)])/(1 + m)","A",2,2,23,0.08696,1,"{6150, 133}"
1358,1,42,0,0.1022888,"\int \frac{e^{n \tanh ^{-1}(a x)} x^m}{c-a^2 c x^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2),x]","\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)}","\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,"(x^(1 + m)*AppellF1[1 + m, (2 + n)/2, 1 - n/2, 2 + m, a*x, -(a*x)])/(c*(1 + m))","A",2,2,25,0.08000,1,"{6150, 133}"
1359,1,42,0,0.098707,"\int \frac{e^{n \tanh ^{-1}(a x)} x^m}{\left(c-a^2 c x^2\right)^2} \, dx","Int[(E^(n*ArcTanh[a*x])*x^m)/(c - a^2*c*x^2)^2,x]","\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)}","\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,"(x^(1 + m)*AppellF1[1 + m, (4 + n)/2, 2 - n/2, 2 + m, a*x, -(a*x)])/(c^2*(1 + m))","A",2,2,25,0.08000,1,"{6150, 133}"
1360,1,70,0,0.1614119,"\int e^{n \tanh ^{-1}(a x)} x^m \left(c-a^2 c x^2\right)^p \, dx","Int[E^(n*ArcTanh[a*x])*x^m*(c - a^2*c*x^2)^p,x]","\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}","\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,"(x^(1 + m)*(c - a^2*c*x^2)^p*AppellF1[1 + m, (n - 2*p)/2, -n/2 - p, 2 + m, a*x, -(a*x)])/((1 + m)*(1 - a^2*x^2)^p)","A",3,3,25,0.1200,1,"{6153, 6150, 133}"
1361,1,177,0,0.183648,"\int e^{n \tanh ^{-1}(a x)} x \left(c-a^2 c x^2\right)^p \, dx","Int[E^(n*ArcTanh[a*x])*x*(c - a^2*c*x^2)^p,x]","-\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)}","-\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 - a*x)^(1 - n/2 + p)*(1 + a*x)^(1 + n/2 + p)*(c - a^2*c*x^2)^p)/(2*a^2*(1 + p)*(1 - a^2*x^2)^p) - (2^(n/2 + p)*n*(1 - a*x)^(1 - n/2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-n/2 - 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",4,4,23,0.1739,1,"{6153, 6150, 80, 69}"
1362,1,103,0,0.085118,"\int e^{n \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(n*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","-\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)}","-\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^(1 + n/2 + p)*(1 - a*x)^(1 - n/2 + p)*(c - a^2*c*x^2)^p*Hypergeometric2F1[-n/2 - p, 1 - n/2 + p, 2 - n/2 + p, (1 - a*x)/2])/(a*(2 - n + 2*p)*(1 - a^2*x^2)^p))","A",3,3,22,0.1364,1,"{6143, 6140, 69}"
1363,1,41,0,0.0478388,"\int e^{2 (1+p) \tanh ^{-1}(a x)} \left(1-a^2 x^2\right)^{-p} \, dx","Int[E^(2*(1 + p)*ArcTanh[a*x])/(1 - a^2*x^2)^p,x]","\frac{(1-a x)^{1-2 p}}{a (1-2 p)}+\frac{(1-a x)^{-2 p}}{a p}","\frac{(1-a x)^{1-2 p}}{a (1-2 p)}+\frac{(1-a x)^{-2 p}}{a p}",1,"(1 - a*x)^(1 - 2*p)/(a*(1 - 2*p)) + 1/(a*p*(1 - a*x)^(2*p))","A",3,2,26,0.07692,1,"{6140, 43}"
1364,1,95,0,0.0903334,"\int e^{2 (1+p) \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^{-p} \, dx","Int[E^(2*(1 + p)*ArcTanh[a*x])/(c - a^2*c*x^2)^p,x]","\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}","\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 - a*x)^(1 - 2*p)*(1 - a^2*x^2)^p)/(a*(1 - 2*p)*(c - a^2*c*x^2)^p) + (1 - a^2*x^2)^p/(a*p*(1 - a*x)^(2*p)*(c - a^2*c*x^2)^p)","A",4,3,27,0.1111,1,"{6143, 6140, 43}"
1365,1,49,0,0.0728544,"\int e^{2 p \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(2*p*ArcTanh[a*x])*(c - a^2*c*x^2)^p,x]","\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)}","\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,"((1 + a*x)^(1 + 2*p)*(c - a^2*c*x^2)^p)/(a*(1 + 2*p)*(1 - a^2*x^2)^p)","A",3,3,23,0.1304,1,"{6143, 6140, 32}"
1366,1,51,0,0.0705453,"\int e^{-2 p \tanh ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^(2*p*ArcTanh[a*x]),x]","-\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)}","-\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)^(1 + 2*p)*(c - a^2*c*x^2)^p)/(a*(1 + 2*p)*(1 - a^2*x^2)^p))","A",3,3,23,0.1304,1,"{6143, 6140, 32}"
1367,1,53,0,0.109377,"\int e^{n \tanh ^{-1}(a x)} x^2 \left(c-a^2 c x^2\right)^{-1-\frac{n^2}{2}} \, dx","Int[E^(n*ArcTanh[a*x])*x^2*(c - a^2*c*x^2)^(-1 - n^2/2),x]","\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)}","\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,"(E^(n*ArcTanh[a*x])*(1 - a*n*x))/(a^3*c*n*(1 - n^2)*(c - a^2*c*x^2)^(n^2/2))","A",1,1,33,0.03030,1,"{6146}"
1368,1,31,0,0.0914841,"\int \frac{e^{6 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{19}} \, dx","Int[(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} (1-a x)^{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",2,2,25,0.08000,1,"{6150, 81}"
1369,1,31,0,0.0890639,"\int \frac{e^{4 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^9} \, dx","Int[(E^(4*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^9,x]","-\frac{1-4 a x}{60 a^3 c^9 (1-a x)^{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",2,2,25,0.08000,1,"{6150, 81}"
1370,1,31,0,0.0879717,"\int \frac{e^{2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Int[(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 (1-a x)^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",2,2,25,0.08000,1,"{6150, 81}"
1371,1,31,0,0.0893645,"\int \frac{e^{-2 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^3} \, dx","Int[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 (1-a x) (a x+1)^3}","\frac{2 a x+1}{6 a^3 c^3 (1-a x) (a x+1)^3}",1,"(1 + 2*a*x)/(6*a^3*c^3*(1 - a*x)*(1 + a*x)^3)","A",2,2,25,0.08000,1,"{6150, 81}"
1372,1,31,0,0.0868716,"\int \frac{e^{-4 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^9} \, dx","Int[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 (1-a x)^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",2,2,25,0.08000,1,"{6150, 81}"
1373,1,60,0,0.2308334,"\int \frac{e^{5 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{27/2}} \, dx","Int[(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} (1-a x)^{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",3,3,27,0.1111,1,"{6153, 6150, 81}"
1374,1,60,0,0.2395698,"\int \frac{e^{3 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{11/2}} \, dx","Int[(E^(3*ArcTanh[a*x])*x^2)/(c - a^2*c*x^2)^(11/2),x]","-\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}}","-\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",3,3,27,0.1111,1,"{6153, 6150, 81}"
1375,1,139,0,0.240193,"\int \frac{e^{\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcTanh[a*x]*x^2)/(c - a^2*c*x^2)^(3/2),x]","\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}}","\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]/(2*a^3*c*(1 - a*x)*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*a^3*c*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*a^3*c*Sqrt[c - a^2*c*x^2])","A",4,3,25,0.1200,1,"{6153, 6150, 88}"
1376,1,138,0,0.2574347,"\int \frac{e^{-\tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[x^2/(E^ArcTanh[a*x]*(c - a^2*c*x^2)^(3/2)),x]","-\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}}","-\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,"-Sqrt[1 - a^2*x^2]/(2*a^3*c*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (Sqrt[1 - a^2*x^2]*Log[1 - a*x])/(4*a^3*c*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[1 - a^2*x^2]*Log[1 + a*x])/(4*a^3*c*Sqrt[c - a^2*c*x^2])","A",4,3,27,0.1111,1,"{6153, 6150, 88}"
1377,1,60,0,0.2366345,"\int \frac{e^{-3 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{11/2}} \, dx","Int[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 (1-a x)^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 + 3*a*x)*Sqrt[1 - a^2*x^2])/(24*a^3*c^5*(1 - a*x)^3*(1 + a*x)^6*Sqrt[c - a^2*c*x^2])","A",3,3,27,0.1111,1,"{6153, 6150, 81}"
1378,1,60,0,0.237762,"\int \frac{e^{-5 \tanh ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{27/2}} \, dx","Int[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} (1-a x)^{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",3,3,27,0.1111,1,"{6153, 6150, 81}"