1,1,114,0,0.1233816,"\int e^{\coth ^{-1}(a x)} x^3 \, dx","Int[E^ArcCoth[a*x]*x^3,x]","\frac{1}{4} x^4 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}+\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a^4}","\frac{1}{4} x^4 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}+\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a^4}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*a^3) + (3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(8*a^2) + (Sqrt[1 - 1/(a^2*x^2)]*x^3)/(3*a) + (Sqrt[1 - 1/(a^2*x^2)]*x^4)/4 + (3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a^4)","A",8,6,10,0.6000,1,"{6169, 835, 807, 266, 63, 208}"
2,1,90,0,0.093424,"\int e^{\coth ^{-1}(a x)} x^2 \, dx","Int[E^ArcCoth[a*x]*x^2,x]","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*a^2) + (Sqrt[1 - 1/(a^2*x^2)]*x^2)/(2*a) + (Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(2*a^3)","A",7,6,10,0.6000,1,"{6169, 835, 807, 266, 63, 208}"
3,1,63,0,0.0644179,"\int e^{\coth ^{-1}(a x)} x \, dx","Int[E^ArcCoth[a*x]*x,x]","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/a + (Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(2*a^2)","A",6,6,8,0.7500,1,"{6169, 835, 807, 266, 63, 208}"
4,1,36,0,0.0358052,"\int e^{\coth ^{-1}(a x)} \, dx","Int[E^ArcCoth[a*x],x]","x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}","x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}",1,"Sqrt[1 - 1/(a^2*x^2)]*x + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/a","A",5,5,6,0.8333,1,"{6168, 807, 266, 63, 208}"
5,1,22,0,0.0434277,"\int \frac{e^{\coth ^{-1}(a x)}}{x} \, dx","Int[E^ArcCoth[a*x]/x,x]","\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)-\csc ^{-1}(a x)","\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)-\csc ^{-1}(a x)",1,"-ArcCsc[a*x] + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]","A",6,6,10,0.6000,1,"{6169, 844, 216, 266, 63, 208}"
6,1,24,0,0.0247176,"\int \frac{e^{\coth ^{-1}(a x)}}{x^2} \, dx","Int[E^ArcCoth[a*x]/x^2,x]","a \sqrt{1-\frac{1}{a^2 x^2}}-a \csc ^{-1}(a x)","a \sqrt{1-\frac{1}{a^2 x^2}}-a \csc ^{-1}(a x)",1,"a*Sqrt[1 - 1/(a^2*x^2)] - a*ArcCsc[a*x]","A",3,3,10,0.3000,1,"{6169, 641, 216}"
7,1,38,0,0.0308692,"\int \frac{e^{\coth ^{-1}(a x)}}{x^3} \, dx","Int[E^ArcCoth[a*x]/x^3,x]","\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a+\frac{1}{x}\right)-\frac{1}{2} a^2 \csc ^{-1}(a x)","\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a+\frac{1}{x}\right)-\frac{1}{2} a^2 \csc ^{-1}(a x)",1,"(a*Sqrt[1 - 1/(a^2*x^2)]*(2*a + x^(-1)))/2 - (a^2*ArcCsc[a*x])/2","A",3,3,10,0.3000,1,"{6169, 780, 216}"
8,1,75,0,0.0618059,"\int \frac{e^{\coth ^{-1}(a x)}}{x^4} \, dx","Int[E^ArcCoth[a*x]/x^4,x]","-\frac{1}{3} a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+a^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 x}-\frac{1}{2} a^3 \csc ^{-1}(a x)","-\frac{1}{3} a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+a^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 x}-\frac{1}{2} a^3 \csc ^{-1}(a x)",1,"a^3*Sqrt[1 - 1/(a^2*x^2)] - (a^3*(1 - 1/(a^2*x^2))^(3/2))/3 + (a^2*Sqrt[1 - 1/(a^2*x^2)])/(2*x) - (a^3*ArcCsc[a*x])/2","A",7,5,10,0.5000,1,"{6169, 797, 641, 195, 216}"
9,1,88,0,0.0828003,"\int \frac{e^{\coth ^{-1}(a x)}}{x^5} \, dx","Int[E^ArcCoth[a*x]/x^5,x]","\frac{1}{24} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(16 a+\frac{9}{x}\right)+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{3 x^2}+\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{4 x^3}-\frac{3}{8} a^4 \csc ^{-1}(a x)","\frac{1}{24} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(16 a+\frac{9}{x}\right)+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{3 x^2}+\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{4 x^3}-\frac{3}{8} a^4 \csc ^{-1}(a x)",1,"(a^3*Sqrt[1 - 1/(a^2*x^2)]*(16*a + 9/x))/24 + (a*Sqrt[1 - 1/(a^2*x^2)])/(4*x^3) + (a^2*Sqrt[1 - 1/(a^2*x^2)])/(3*x^2) - (3*a^4*ArcCsc[a*x])/8","A",5,4,10,0.4000,1,"{6169, 833, 780, 216}"
10,1,43,0,0.0526951,"\int e^{2 \coth ^{-1}(a x)} x^3 \, dx","Int[E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
11,1,33,0,0.0493616,"\int e^{2 \coth ^{-1}(a x)} x^2 \, dx","Int[E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
12,1,26,0,0.0327405,"\int e^{2 \coth ^{-1}(a x)} x \, dx","Int[E^(2*ArcCoth[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",4,3,10,0.3000,1,"{6167, 6126, 77}"
13,1,14,0,0.0141243,"\int e^{2 \coth ^{-1}(a x)} \, dx","Int[E^(2*ArcCoth[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",4,3,8,0.3750,1,"{6167, 6125, 43}"
14,1,14,0,0.0396086,"\int \frac{e^{2 \coth ^{-1}(a x)}}{x} \, dx","Int[E^(2*ArcCoth[a*x])/x,x]","2 \log (1-a x)-\log (x)","2 \log (1-a x)-\log (x)",1,"-Log[x] + 2*Log[1 - a*x]","A",4,3,12,0.2500,1,"{6167, 6126, 72}"
15,1,19,0,0.0445641,"\int \frac{e^{2 \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
16,1,33,0,0.0474221,"\int \frac{e^{2 \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
17,1,40,0,0.0514506,"\int \frac{e^{2 \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
18,1,118,0,1.0714083,"\int e^{3 \coth ^{-1}(a x)} x^2 \, dx","Int[E^(3*ArcCoth[a*x])*x^2,x]","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{14 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a^2 \left(a-\frac{1}{x}\right)}+\frac{11 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{14 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a^2 \left(a-\frac{1}{x}\right)}+\frac{11 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}",1,"(-4*Sqrt[1 - 1/(a^2*x^2)])/(a^2*(a - x^(-1))) + (14*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*a^2) + (3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(2*a) + (Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 + (11*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a^3)","A",14,9,12,0.7500,1,"{6169, 6742, 651, 271, 264, 266, 51, 63, 208}"
19,1,92,0,0.8715729,"\int e^{3 \coth ^{-1}(a x)} x \, dx","Int[E^(3*ArcCoth[a*x])*x,x]","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{3 x \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a \left(a-\frac{1}{x}\right)}+\frac{9 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{3 x \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a \left(a-\frac{1}{x}\right)}+\frac{9 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}",1,"(-4*Sqrt[1 - 1/(a^2*x^2)])/(a*(a - x^(-1))) + (3*Sqrt[1 - 1/(a^2*x^2)]*x)/a + (Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (9*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a^2)","A",12,8,10,0.8000,1,"{6169, 6742, 651, 266, 51, 63, 208, 264}"
20,1,62,0,0.8106456,"\int e^{3 \coth ^{-1}(a x)} \, dx","Int[E^(3*ArcCoth[a*x]),x]","x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a-\frac{1}{x}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}","x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a-\frac{1}{x}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}",1,"(-4*Sqrt[1 - 1/(a^2*x^2)])/(a - x^(-1)) + Sqrt[1 - 1/(a^2*x^2)]*x + (3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,7,8,0.8750,1,"{6168, 6742, 651, 264, 266, 63, 208}"
21,1,46,0,0.7827562,"\int \frac{e^{3 \coth ^{-1}(a x)}}{x} \, dx","Int[E^(3*ArcCoth[a*x])/x,x]","-\frac{4 a \sqrt{1-\frac{1}{a^2 x^2}}}{a-\frac{1}{x}}+\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)+\csc ^{-1}(a x)","-\frac{4 a \sqrt{1-\frac{1}{a^2 x^2}}}{a-\frac{1}{x}}+\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)+\csc ^{-1}(a x)",1,"(-4*a*Sqrt[1 - 1/(a^2*x^2)])/(a - x^(-1)) + ArcCsc[a*x] + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]","A",8,7,12,0.5833,1,"{6169, 6742, 216, 651, 266, 63, 208}"
22,1,51,0,0.0740333,"\int \frac{e^{3 \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^(3*ArcCoth[a*x])/x^2,x]","-\frac{2 \left(a+\frac{1}{x}\right)^2}{a \sqrt{1-\frac{1}{a^2 x^2}}}-3 a \sqrt{1-\frac{1}{a^2 x^2}}+3 a \csc ^{-1}(a x)","-\frac{2 \left(a+\frac{1}{x}\right)^2}{a \sqrt{1-\frac{1}{a^2 x^2}}}-3 a \sqrt{1-\frac{1}{a^2 x^2}}+3 a \csc ^{-1}(a x)",1,"-3*a*Sqrt[1 - 1/(a^2*x^2)] - (2*(a + x^(-1))^2)/(a*Sqrt[1 - 1/(a^2*x^2)]) + 3*a*ArcCsc[a*x]","A",5,5,12,0.4167,1,"{6169, 853, 669, 641, 216}"
23,1,91,0,0.4532948,"\int \frac{e^{3 \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^(3*ArcCoth[a*x])/x^3,x]","-\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(a-\frac{1}{x}\right)^3}-\frac{3 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(a-\frac{1}{x}\right)}-\frac{9}{2} a^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{9}{2} a^2 \csc ^{-1}(a x)","-\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(a-\frac{1}{x}\right)^3}-\frac{3 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(a-\frac{1}{x}\right)}-\frac{9}{2} a^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{9}{2} a^2 \csc ^{-1}(a x)",1,"(-9*a^2*Sqrt[1 - 1/(a^2*x^2)])/2 - (a^5*(1 - 1/(a^2*x^2))^(5/2))/(a - x^(-1))^3 - (3*a^3*(1 - 1/(a^2*x^2))^(3/2))/(2*(a - x^(-1))) + (9*a^2*ArcCsc[a*x])/2","A",9,7,12,0.5833,1,"{6169, 1633, 1593, 12, 793, 665, 216}"
24,1,93,0,0.7431327,"\int \frac{e^{3 \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^(3*ArcCoth[a*x])/x^4,x]","-\frac{1}{6} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(28 a+\frac{3}{x}\right)-\frac{1}{3} a \sqrt{1-\frac{1}{a^2 x^2}} \left(3 a+\frac{1}{x}\right)^2-\frac{\left(a+\frac{1}{x}\right)^3}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{11}{2} a^3 \csc ^{-1}(a x)","-\frac{1}{6} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(28 a+\frac{3}{x}\right)-\frac{1}{3} a \sqrt{1-\frac{1}{a^2 x^2}} \left(3 a+\frac{1}{x}\right)^2-\frac{\left(a+\frac{1}{x}\right)^3}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{11}{2} a^3 \csc ^{-1}(a x)",1,"-((a + x^(-1))^3/Sqrt[1 - 1/(a^2*x^2)]) - (a*Sqrt[1 - 1/(a^2*x^2)]*(3*a + x^(-1))^2)/3 - (a^2*Sqrt[1 - 1/(a^2*x^2)]*(28*a + 3/x))/6 + (11*a^3*ArcCsc[a*x])/2","A",10,9,12,0.7500,1,"{6169, 1633, 1593, 12, 852, 1635, 1654, 780, 216}"
25,1,57,0,0.0658147,"\int e^{4 \coth ^{-1}(a x)} x^3 \, dx","Int[E^(4*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 88}"
26,1,47,0,0.0595973,"\int e^{4 \coth ^{-1}(a x)} x^2 \, dx","Int[E^(4*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 88}"
27,1,39,0,0.0413822,"\int e^{4 \coth ^{-1}(a x)} x \, dx","Int[E^(4*ArcCoth[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",4,3,10,0.3000,1,"{6167, 6126, 77}"
28,1,27,0,0.0191366,"\int e^{4 \coth ^{-1}(a x)} \, dx","Int[E^(4*ArcCoth[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",4,3,8,0.3750,1,"{6167, 6125, 43}"
29,1,13,0,0.0392385,"\int \frac{e^{4 \coth ^{-1}(a x)}}{x} \, dx","Int[E^(4*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 88}"
30,1,32,0,0.0505939,"\int \frac{e^{4 \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^(4*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 88}"
31,1,46,0,0.054295,"\int \frac{e^{4 \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^(4*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 88}"
32,1,54,0,0.0612882,"\int \frac{e^{4 \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^(4*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 88}"
33,1,114,0,0.1272824,"\int e^{-\coth ^{-1}(a x)} x^3 \, dx","Int[x^3/E^ArcCoth[a*x],x]","\frac{1}{4} x^4 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}+\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2}-\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a^4}","\frac{1}{4} x^4 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}+\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2}-\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a^4}",1,"(-2*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*a^3) + (3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(8*a^2) - (Sqrt[1 - 1/(a^2*x^2)]*x^3)/(3*a) + (Sqrt[1 - 1/(a^2*x^2)]*x^4)/4 + (3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a^4)","A",8,6,12,0.5000,1,"{6169, 835, 807, 266, 63, 208}"
34,1,90,0,0.100033,"\int e^{-\coth ^{-1}(a x)} x^2 \, dx","Int[x^2/E^ArcCoth[a*x],x]","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*a^2) - (Sqrt[1 - 1/(a^2*x^2)]*x^2)/(2*a) + (Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 - ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(2*a^3)","A",7,6,12,0.5000,1,"{6169, 835, 807, 266, 63, 208}"
35,1,64,0,0.0677775,"\int e^{-\coth ^{-1}(a x)} x \, dx","Int[x/E^ArcCoth[a*x],x]","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}",1,"-((Sqrt[1 - 1/(a^2*x^2)]*x)/a) + (Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(2*a^2)","A",6,6,10,0.6000,1,"{6169, 835, 807, 266, 63, 208}"
36,1,37,0,0.0385505,"\int e^{-\coth ^{-1}(a x)} \, dx","Int[E^(-ArcCoth[a*x]),x]","x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}","x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}",1,"Sqrt[1 - 1/(a^2*x^2)]*x - ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/a","A",5,5,8,0.6250,1,"{6168, 807, 266, 63, 208}"
37,1,20,0,0.0475338,"\int \frac{e^{-\coth ^{-1}(a x)}}{x} \, dx","Int[1/(E^ArcCoth[a*x]*x),x]","\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)+\csc ^{-1}(a x)","\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)+\csc ^{-1}(a x)",1,"ArcCsc[a*x] + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]","A",6,6,12,0.5000,1,"{6169, 844, 216, 266, 63, 208}"
38,1,25,0,0.0267834,"\int \frac{e^{-\coth ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^ArcCoth[a*x]*x^2),x]","a \left(-\csc ^{-1}(a x)\right)-a \sqrt{1-\frac{1}{a^2 x^2}}","a \left(-\csc ^{-1}(a x)\right)-a \sqrt{1-\frac{1}{a^2 x^2}}",1,"-(a*Sqrt[1 - 1/(a^2*x^2)]) - a*ArcCsc[a*x]","A",3,3,12,0.2500,1,"{6169, 641, 216}"
39,1,40,0,0.036613,"\int \frac{e^{-\coth ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^ArcCoth[a*x]*x^3),x]","\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a-\frac{1}{x}\right)+\frac{1}{2} a^2 \csc ^{-1}(a x)","\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a-\frac{1}{x}\right)+\frac{1}{2} a^2 \csc ^{-1}(a x)",1,"(a*Sqrt[1 - 1/(a^2*x^2)]*(2*a - x^(-1)))/2 + (a^2*ArcCsc[a*x])/2","A",3,3,12,0.2500,1,"{6169, 780, 216}"
40,1,76,0,0.0656624,"\int \frac{e^{-\coth ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^ArcCoth[a*x]*x^4),x]","\frac{1}{3} a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-a^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 x}-\frac{1}{2} a^3 \csc ^{-1}(a x)","\frac{1}{3} a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-a^3 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 x}-\frac{1}{2} a^3 \csc ^{-1}(a x)",1,"-(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (a^3*(1 - 1/(a^2*x^2))^(3/2))/3 + (a^2*Sqrt[1 - 1/(a^2*x^2)])/(2*x) - (a^3*ArcCsc[a*x])/2","A",7,5,12,0.4167,1,"{6169, 797, 641, 195, 216}"
41,1,88,0,0.0895651,"\int \frac{e^{-\coth ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^ArcCoth[a*x]*x^5),x]","\frac{1}{24} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(16 a-\frac{9}{x}\right)+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{3 x^2}-\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{4 x^3}+\frac{3}{8} a^4 \csc ^{-1}(a x)","\frac{1}{24} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(16 a-\frac{9}{x}\right)+\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{3 x^2}-\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{4 x^3}+\frac{3}{8} a^4 \csc ^{-1}(a x)",1,"(a^3*Sqrt[1 - 1/(a^2*x^2)]*(16*a - 9/x))/24 - (a*Sqrt[1 - 1/(a^2*x^2)])/(4*x^3) + (a^2*Sqrt[1 - 1/(a^2*x^2)])/(3*x^2) + (3*a^4*ArcCsc[a*x])/8","A",5,4,12,0.3333,1,"{6169, 833, 780, 216}"
42,1,42,0,0.0570863,"\int e^{-2 \coth ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
43,1,33,0,0.050608,"\int e^{-2 \coth ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
44,1,25,0,0.0323883,"\int e^{-2 \coth ^{-1}(a x)} x \, dx","Int[x/E^(2*ArcCoth[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",4,3,10,0.3000,1,"{6167, 6126, 77}"
45,1,13,0,0.013253,"\int e^{-2 \coth ^{-1}(a x)} \, dx","Int[E^(-2*ArcCoth[a*x]),x]","x-\frac{2 \log (a x+1)}{a}","x-\frac{2 \log (a x+1)}{a}",1,"x - (2*Log[1 + a*x])/a","A",4,3,8,0.3750,1,"{6167, 6125, 43}"
46,1,13,0,0.0401803,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{x} \, dx","Int[1/(E^(2*ArcCoth[a*x])*x),x]","2 \log (a x+1)-\log (x)","2 \log (a x+1)-\log (x)",1,"-Log[x] + 2*Log[1 + a*x]","A",4,3,12,0.2500,1,"{6167, 6126, 72}"
47,1,18,0,0.0432672,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
48,1,32,0,0.0457361,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
49,1,40,0,0.0496812,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(2*ArcCoth[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",4,3,12,0.2500,1,"{6167, 6126, 77}"
50,1,136,0,1.0192751,"\int e^{-3 \coth ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(3*ArcCoth[a*x]),x]","\frac{1}{4} x^4 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{19 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2}-\frac{6 x \sqrt{1-\frac{1}{a^2 x^2}}}{a^3}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a^3 \left(a+\frac{1}{x}\right)}+\frac{51 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a^4}","\frac{1}{4} x^4 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{19 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2}-\frac{6 x \sqrt{1-\frac{1}{a^2 x^2}}}{a^3}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a^3 \left(a+\frac{1}{x}\right)}+\frac{51 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a^4}",1,"(-4*Sqrt[1 - 1/(a^2*x^2)])/(a^3*(a + x^(-1))) - (6*Sqrt[1 - 1/(a^2*x^2)]*x)/a^3 + (19*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(8*a^2) - (Sqrt[1 - 1/(a^2*x^2)]*x^3)/a + (Sqrt[1 - 1/(a^2*x^2)]*x^4)/4 + (51*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a^4)","A",19,9,12,0.7500,1,"{6169, 6742, 266, 51, 63, 208, 271, 264, 651}"
51,1,116,0,0.8691775,"\int e^{-3 \coth ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(3*ArcCoth[a*x]),x]","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{14 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}+\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a^2 \left(a+\frac{1}{x}\right)}-\frac{11 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}","\frac{1}{3} x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a}+\frac{14 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^2}+\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a^2 \left(a+\frac{1}{x}\right)}-\frac{11 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^3}",1,"(4*Sqrt[1 - 1/(a^2*x^2)])/(a^2*(a + x^(-1))) + (14*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*a^2) - (3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(2*a) + (Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 - (11*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a^3)","A",14,9,12,0.7500,1,"{6169, 6742, 271, 264, 266, 51, 63, 208, 651}"
52,1,90,0,0.842227,"\int e^{-3 \coth ^{-1}(a x)} x \, dx","Int[x/E^(3*ArcCoth[a*x]),x]","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 x \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a \left(a+\frac{1}{x}\right)}+\frac{9 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}","\frac{1}{2} x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 x \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a \left(a+\frac{1}{x}\right)}+\frac{9 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a^2}",1,"(-4*Sqrt[1 - 1/(a^2*x^2)])/(a*(a + x^(-1))) - (3*Sqrt[1 - 1/(a^2*x^2)]*x)/a + (Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (9*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a^2)","A",12,8,10,0.8000,1,"{6169, 6742, 266, 51, 63, 208, 264, 651}"
53,1,60,0,0.7786594,"\int e^{-3 \coth ^{-1}(a x)} \, dx","Int[E^(-3*ArcCoth[a*x]),x]","x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a+\frac{1}{x}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}","x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{4 \sqrt{1-\frac{1}{a^2 x^2}}}{a+\frac{1}{x}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}",1,"(4*Sqrt[1 - 1/(a^2*x^2)])/(a + x^(-1)) + Sqrt[1 - 1/(a^2*x^2)]*x - (3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,7,8,0.8750,1,"{6168, 6742, 264, 266, 63, 208, 651}"
54,1,46,0,0.7607306,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{x} \, dx","Int[1/(E^(3*ArcCoth[a*x])*x),x]","-\frac{4 a \sqrt{1-\frac{1}{a^2 x^2}}}{a+\frac{1}{x}}+\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)-\csc ^{-1}(a x)","-\frac{4 a \sqrt{1-\frac{1}{a^2 x^2}}}{a+\frac{1}{x}}+\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)-\csc ^{-1}(a x)",1,"(-4*a*Sqrt[1 - 1/(a^2*x^2)])/(a + x^(-1)) - ArcCsc[a*x] + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]","A",8,7,12,0.5833,1,"{6169, 6742, 216, 266, 63, 208, 651}"
55,1,53,0,0.0775462,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(3*ArcCoth[a*x])*x^2),x]","\frac{2 \left(a-\frac{1}{x}\right)^2}{a \sqrt{1-\frac{1}{a^2 x^2}}}+3 a \sqrt{1-\frac{1}{a^2 x^2}}+3 a \csc ^{-1}(a x)","\frac{2 \left(a-\frac{1}{x}\right)^2}{a \sqrt{1-\frac{1}{a^2 x^2}}}+3 a \sqrt{1-\frac{1}{a^2 x^2}}+3 a \csc ^{-1}(a x)",1,"3*a*Sqrt[1 - 1/(a^2*x^2)] + (2*(a - x^(-1))^2)/(a*Sqrt[1 - 1/(a^2*x^2)]) + 3*a*ArcCsc[a*x]","A",5,5,12,0.4167,1,"{6169, 853, 669, 641, 216}"
56,1,87,0,0.4449773,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(3*ArcCoth[a*x])*x^3),x]","-\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(a+\frac{1}{x}\right)^3}-\frac{3 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(a+\frac{1}{x}\right)}-\frac{9}{2} a^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{9}{2} a^2 \csc ^{-1}(a x)","-\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(a+\frac{1}{x}\right)^3}-\frac{3 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(a+\frac{1}{x}\right)}-\frac{9}{2} a^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{9}{2} a^2 \csc ^{-1}(a x)",1,"(-9*a^2*Sqrt[1 - 1/(a^2*x^2)])/2 - (a^5*(1 - 1/(a^2*x^2))^(5/2))/(a + x^(-1))^3 - (3*a^3*(1 - 1/(a^2*x^2))^(3/2))/(2*(a + x^(-1))) - (9*a^2*ArcCsc[a*x])/2","A",9,7,12,0.5833,1,"{6169, 1633, 1593, 12, 793, 665, 216}"
57,1,96,0,0.7663508,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(3*ArcCoth[a*x])*x^4),x]","\frac{1}{6} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(28 a-\frac{3}{x}\right)+\frac{1}{3} a \sqrt{1-\frac{1}{a^2 x^2}} \left(3 a-\frac{1}{x}\right)^2+\frac{\left(a-\frac{1}{x}\right)^3}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{11}{2} a^3 \csc ^{-1}(a x)","\frac{1}{6} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(28 a-\frac{3}{x}\right)+\frac{1}{3} a \sqrt{1-\frac{1}{a^2 x^2}} \left(3 a-\frac{1}{x}\right)^2+\frac{\left(a-\frac{1}{x}\right)^3}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{11}{2} a^3 \csc ^{-1}(a x)",1,"(a^2*Sqrt[1 - 1/(a^2*x^2)]*(28*a - 3/x))/6 + (a - x^(-1))^3/Sqrt[1 - 1/(a^2*x^2)] + (a*Sqrt[1 - 1/(a^2*x^2)]*(3*a - x^(-1))^2)/3 + (11*a^3*ArcCsc[a*x])/2","A",10,9,12,0.7500,1,"{6169, 1633, 1593, 12, 852, 1635, 1654, 780, 216}"
58,1,133,0,0.8388,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{x^5} \, dx","Int[1/(E^(3*ArcCoth[a*x])*x^5),x]","-\frac{27}{4} a^4 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{9}{8} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a-\frac{3}{x}\right)-\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{x^2}-\frac{a \left(a-\frac{1}{x}\right)^3}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{4 x^3}-\frac{51}{8} a^4 \csc ^{-1}(a x)","-\frac{27}{4} a^4 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{9}{8} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a-\frac{3}{x}\right)-\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{x^2}-\frac{a \left(a-\frac{1}{x}\right)^3}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{4 x^3}-\frac{51}{8} a^4 \csc ^{-1}(a x)",1,"(-27*a^4*Sqrt[1 - 1/(a^2*x^2)])/4 - (9*a^3*Sqrt[1 - 1/(a^2*x^2)]*(2*a - 3/x))/8 - (a*(a - x^(-1))^3)/Sqrt[1 - 1/(a^2*x^2)] + (a*Sqrt[1 - 1/(a^2*x^2)])/(4*x^3) - (a^2*Sqrt[1 - 1/(a^2*x^2)])/x^2 - (51*a^4*ArcCsc[a*x])/8","A",14,11,12,0.9167,1,"{6169, 1633, 1593, 12, 852, 1635, 1815, 27, 743, 641, 216}"
59,1,253,0,0.1538663,"\int e^{\frac{1}{2} \coth ^{-1}(a x)} x^4 \, dx","Int[E^(ArcCoth[a*x]/2)*x^4,x]","\frac{11 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{48 a^2}+\frac{269 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{960 a^3}+\frac{611 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{1920 a^4}+\frac{31 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{31 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{9 x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{40 a}","\frac{11 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{48 a^2}+\frac{269 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{960 a^3}+\frac{611 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{1920 a^4}+\frac{31 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{31 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{9 x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{40 a}",1,"(611*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(1920*a^4) + (269*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^2)/(960*a^3) + (11*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^3)/(48*a^2) + (9*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^4)/(40*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^5)/5 + (31*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5) + (31*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5)","A",11,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 212, 206, 203}"
60,1,216,0,0.1190578,"\int e^{\frac{1}{2} \coth ^{-1}(a x)} x^3 \, dx","Int[E^(ArcCoth[a*x]/2)*x^3,x]","\frac{29 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{96 a^2}+\frac{83 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{192 a^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{11 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{7 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{24 a}","\frac{29 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{96 a^2}+\frac{83 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{192 a^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{11 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{7 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{24 a}",1,"(83*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(192*a^3) + (29*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^2)/(96*a^2) + (7*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^3)/(24*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^4)/4 + (11*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4) + (11*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4)","A",10,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 212, 206, 203}"
61,1,179,0,0.0946851,"\int e^{\frac{1}{2} \coth ^{-1}(a x)} x^2 \, dx","Int[E^(ArcCoth[a*x]/2)*x^2,x]","\frac{11 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{24 a^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{5 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{12 a}","\frac{11 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{24 a^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{5 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{12 a}",1,"(11*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(24*a^2) + (5*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^2)/(12*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^3)/3 + (3*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3) + (3*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3)","A",9,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 212, 206, 203}"
62,1,142,0,0.0604824,"\int e^{\frac{1}{2} \coth ^{-1}(a x)} x \, dx","Int[E^(ArcCoth[a*x]/2)*x,x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}+\frac{x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{4 a}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}+\frac{x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{4 a}",1,"((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(4*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(5/4)*x^2)/2 + ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(4*a^2) + ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(4*a^2)","A",7,7,12,0.5833,1,"{6171, 96, 94, 93, 212, 206, 203}"
63,1,96,0,0.0368659,"\int e^{\frac{1}{2} \coth ^{-1}(a x)} \, dx","Int[E^(ArcCoth[a*x]/2),x]","x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}","x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}",1,"(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x + ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/a + ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/a","A",6,6,10,0.6000,1,"{6170, 94, 93, 212, 206, 203}"
64,1,291,0,0.2461698,"\int \frac{e^{\frac{1}{2} \coth ^{-1}(a x)}}{x} \, dx","Int[E^(ArcCoth[a*x]/2)/x,x]","\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)","\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)",1,"-(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]) + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] + 2*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + 2*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6171, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
65,1,267,0,0.2250573,"\int \frac{e^{\frac{1}{2} \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^(ArcCoth[a*x]/2)/x^2,x]","a \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}","a \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}",1,"a*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4) - (a*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (a*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2]) - (a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2])","A",13,10,14,0.7143,1,"{6171, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
66,1,319,0,0.2490523,"\int \frac{e^{\frac{1}{2} \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^(ArcCoth[a*x]/2)/x^3,x]","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}+\frac{1}{4} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}+\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}+\frac{1}{4} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}+\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}",1,"(a^2*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4))/4 + (a^2*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(5/4))/2 - (a^2*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) + (a^2*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) + (a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2])","A",14,11,14,0.7857,1,"{6171, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
67,1,356,0,0.2917522,"\int \frac{e^{\frac{1}{2} \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^(ArcCoth[a*x]/2)/x^4,x]","\frac{1}{12} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}+\frac{3}{8} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}}{3 x}+\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{3 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{3 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}","\frac{1}{12} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}+\frac{3}{8} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}}{3 x}+\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{3 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{3 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}",1,"(3*a^3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4))/8 + (a^3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(5/4))/12 + (a^2*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(5/4))/(3*x) - (3*a^3*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (3*a^3*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (3*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2]) - (3*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2])","A",15,12,14,0.8571,1,"{6171, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
68,1,253,0,0.1397056,"\int e^{\frac{3}{2} \coth ^{-1}(a x)} x^4 \, dx","Int[E^((3*ArcCoth[a*x])/2)*x^4,x]","\frac{5 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{16 a^2}+\frac{157 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{320 a^3}+\frac{557 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{640 a^4}-\frac{237 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{237 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{11 x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{40 a}","\frac{5 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{16 a^2}+\frac{157 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{320 a^3}+\frac{557 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{640 a^4}-\frac{237 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{237 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{11 x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{40 a}",1,"(557*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(640*a^4) + (157*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^2)/(320*a^3) + (5*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^3)/(16*a^2) + (11*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^4)/(40*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^5)/5 - (237*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5) + (237*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5)","A",11,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 298, 203, 206}"
69,1,216,0,0.1175353,"\int e^{\frac{3}{2} \coth ^{-1}(a x)} x^3 \, dx","Int[E^((3*ArcCoth[a*x])/2)*x^3,x]","\frac{15 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{32 a^2}+\frac{63 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{64 a^3}-\frac{123 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{123 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{3 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{8 a}","\frac{15 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{32 a^2}+\frac{63 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{64 a^3}-\frac{123 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{123 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{3 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{8 a}",1,"(63*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(64*a^3) + (15*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^2)/(32*a^2) + (3*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^3)/(8*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^4)/4 - (123*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4) + (123*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4)","A",10,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 298, 203, 206}"
70,1,179,0,0.0936718,"\int e^{\frac{3}{2} \coth ^{-1}(a x)} x^2 \, dx","Int[E^((3*ArcCoth[a*x])/2)*x^2,x]","\frac{23 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{24 a^2}-\frac{17 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{17 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{7 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{12 a}","\frac{23 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{24 a^2}-\frac{17 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{17 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{7 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{12 a}",1,"(23*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(24*a^2) + (7*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^2)/(12*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^3)/3 - (17*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3) + (17*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3)","A",9,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 298, 203, 206}"
71,1,142,0,0.0590618,"\int e^{\frac{3}{2} \coth ^{-1}(a x)} x \, dx","Int[E^((3*ArcCoth[a*x])/2)*x,x]","-\frac{9 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{9 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}+\frac{3 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{4 a}","-\frac{9 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{9 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}+\frac{3 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{4 a}",1,"(3*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(4*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(7/4)*x^2)/2 - (9*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2) + (9*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2)","A",7,7,12,0.5833,1,"{6171, 96, 94, 93, 298, 203, 206}"
72,1,98,0,0.0371912,"\int e^{\frac{3}{2} \coth ^{-1}(a x)} \, dx","Int[E^((3*ArcCoth[a*x])/2),x]","x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}","x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}",1,"(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x - (3*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a + (3*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a","A",6,6,10,0.6000,1,"{6170, 94, 93, 298, 203, 206}"
73,1,291,0,0.2281258,"\int \frac{e^{\frac{3}{2} \coth ^{-1}(a x)}}{x} \, dx","Int[E^((3*ArcCoth[a*x])/2)/x,x]","-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)","-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)",1,"-(Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]) + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] - 2*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + 2*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] - Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6171, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
74,1,268,0,0.215381,"\int \frac{e^{\frac{3}{2} \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^((3*ArcCoth[a*x])/2)/x^2,x]","a \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}","a \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}",1,"a*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4) - (3*a*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (3*a*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] - (3*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2]) + (3*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2])","A",13,10,14,0.7143,1,"{6171, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
75,1,319,0,0.2461467,"\int \frac{e^{\frac{3}{2} \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^((3*ArcCoth[a*x])/2)/x^3,x]","\frac{1}{2} a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}+\frac{3}{4} a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{9 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}+\frac{9 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}","\frac{1}{2} a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}+\frac{3}{4} a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{9 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}+\frac{9 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}",1,"(3*a^2*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4))/4 + (a^2*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(7/4))/2 - (9*a^2*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) + (9*a^2*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (9*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (9*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2])","A",14,11,14,0.7857,1,"{6171, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
76,1,356,0,0.281635,"\int \frac{e^{\frac{3}{2} \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^((3*ArcCoth[a*x])/2)/x^4,x]","\frac{1}{4} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}+\frac{17}{24} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}}{3 x}-\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{17 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{17 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}","\frac{1}{4} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}+\frac{17}{24} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/4}}{3 x}-\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{17 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{17 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}",1,"(17*a^3*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4))/24 + (a^3*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(7/4))/4 + (a^2*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(7/4))/(3*x) - (17*a^3*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (17*a^3*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (17*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2]) + (17*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2])","A",15,12,14,0.8571,1,"{6171, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
77,1,287,0,0.1653202,"\int e^{\frac{5}{2} \coth ^{-1}(a x)} x^4 \, dx","Int[E^((5*ArcCoth[a*x])/2)*x^4,x]","\frac{181 x^3 \sqrt[4]{\frac{1}{a x}+1}}{240 a^2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{1189 x^2 \sqrt[4]{\frac{1}{a x}+1}}{960 a^3 \sqrt[4]{1-\frac{1}{a x}}}+\frac{5533 x \sqrt[4]{\frac{1}{a x}+1}}{1920 a^4 \sqrt[4]{1-\frac{1}{a x}}}-\frac{26111 \sqrt[4]{\frac{1}{a x}+1}}{1920 a^5 \sqrt[4]{1-\frac{1}{a x}}}+\frac{1003 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1003 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{x^5 \sqrt[4]{\frac{1}{a x}+1}}{5 \sqrt[4]{1-\frac{1}{a x}}}+\frac{21 x^4 \sqrt[4]{\frac{1}{a x}+1}}{40 a \sqrt[4]{1-\frac{1}{a x}}}","\frac{181 x^3 \sqrt[4]{\frac{1}{a x}+1}}{240 a^2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{1189 x^2 \sqrt[4]{\frac{1}{a x}+1}}{960 a^3 \sqrt[4]{1-\frac{1}{a x}}}+\frac{5533 x \sqrt[4]{\frac{1}{a x}+1}}{1920 a^4 \sqrt[4]{1-\frac{1}{a x}}}-\frac{26111 \sqrt[4]{\frac{1}{a x}+1}}{1920 a^5 \sqrt[4]{1-\frac{1}{a x}}}+\frac{1003 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1003 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{x^5 \sqrt[4]{\frac{1}{a x}+1}}{5 \sqrt[4]{1-\frac{1}{a x}}}+\frac{21 x^4 \sqrt[4]{\frac{1}{a x}+1}}{40 a \sqrt[4]{1-\frac{1}{a x}}}",1,"(-26111*(1 + 1/(a*x))^(1/4))/(1920*a^5*(1 - 1/(a*x))^(1/4)) + (5533*(1 + 1/(a*x))^(1/4)*x)/(1920*a^4*(1 - 1/(a*x))^(1/4)) + (1189*(1 + 1/(a*x))^(1/4)*x^2)/(960*a^3*(1 - 1/(a*x))^(1/4)) + (181*(1 + 1/(a*x))^(1/4)*x^3)/(240*a^2*(1 - 1/(a*x))^(1/4)) + (21*(1 + 1/(a*x))^(1/4)*x^4)/(40*a*(1 - 1/(a*x))^(1/4)) + ((1 + 1/(a*x))^(1/4)*x^5)/(5*(1 - 1/(a*x))^(1/4)) + (1003*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5) + (1003*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5)","A",12,9,14,0.6429,1,"{6171, 98, 151, 155, 12, 93, 212, 206, 203}"
78,1,250,0,0.1359907,"\int e^{\frac{5}{2} \coth ^{-1}(a x)} x^3 \, dx","Int[E^((5*ArcCoth[a*x])/2)*x^3,x]","\frac{113 x^2 \sqrt[4]{\frac{1}{a x}+1}}{96 a^2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{521 x \sqrt[4]{\frac{1}{a x}+1}}{192 a^3 \sqrt[4]{1-\frac{1}{a x}}}-\frac{2467 \sqrt[4]{\frac{1}{a x}+1}}{192 a^4 \sqrt[4]{1-\frac{1}{a x}}}+\frac{475 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{475 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{x^4 \sqrt[4]{\frac{1}{a x}+1}}{4 \sqrt[4]{1-\frac{1}{a x}}}+\frac{17 x^3 \sqrt[4]{\frac{1}{a x}+1}}{24 a \sqrt[4]{1-\frac{1}{a x}}}","\frac{113 x^2 \sqrt[4]{\frac{1}{a x}+1}}{96 a^2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{521 x \sqrt[4]{\frac{1}{a x}+1}}{192 a^3 \sqrt[4]{1-\frac{1}{a x}}}-\frac{2467 \sqrt[4]{\frac{1}{a x}+1}}{192 a^4 \sqrt[4]{1-\frac{1}{a x}}}+\frac{475 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{475 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{x^4 \sqrt[4]{\frac{1}{a x}+1}}{4 \sqrt[4]{1-\frac{1}{a x}}}+\frac{17 x^3 \sqrt[4]{\frac{1}{a x}+1}}{24 a \sqrt[4]{1-\frac{1}{a x}}}",1,"(-2467*(1 + 1/(a*x))^(1/4))/(192*a^4*(1 - 1/(a*x))^(1/4)) + (521*(1 + 1/(a*x))^(1/4)*x)/(192*a^3*(1 - 1/(a*x))^(1/4)) + (113*(1 + 1/(a*x))^(1/4)*x^2)/(96*a^2*(1 - 1/(a*x))^(1/4)) + (17*(1 + 1/(a*x))^(1/4)*x^3)/(24*a*(1 - 1/(a*x))^(1/4)) + ((1 + 1/(a*x))^(1/4)*x^4)/(4*(1 - 1/(a*x))^(1/4)) + (475*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4) + (475*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4)","A",11,9,14,0.6429,1,"{6171, 98, 151, 155, 12, 93, 212, 206, 203}"
79,1,213,0,0.1122022,"\int e^{\frac{5}{2} \coth ^{-1}(a x)} x^2 \, dx","Int[E^((5*ArcCoth[a*x])/2)*x^2,x]","\frac{61 x \sqrt[4]{\frac{1}{a x}+1}}{24 a^2 \sqrt[4]{1-\frac{1}{a x}}}-\frac{287 \sqrt[4]{\frac{1}{a x}+1}}{24 a^3 \sqrt[4]{1-\frac{1}{a x}}}+\frac{55 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{55 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{x^3 \sqrt[4]{\frac{1}{a x}+1}}{3 \sqrt[4]{1-\frac{1}{a x}}}+\frac{13 x^2 \sqrt[4]{\frac{1}{a x}+1}}{12 a \sqrt[4]{1-\frac{1}{a x}}}","\frac{61 x \sqrt[4]{\frac{1}{a x}+1}}{24 a^2 \sqrt[4]{1-\frac{1}{a x}}}-\frac{287 \sqrt[4]{\frac{1}{a x}+1}}{24 a^3 \sqrt[4]{1-\frac{1}{a x}}}+\frac{55 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{55 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{x^3 \sqrt[4]{\frac{1}{a x}+1}}{3 \sqrt[4]{1-\frac{1}{a x}}}+\frac{13 x^2 \sqrt[4]{\frac{1}{a x}+1}}{12 a \sqrt[4]{1-\frac{1}{a x}}}",1,"(-287*(1 + 1/(a*x))^(1/4))/(24*a^3*(1 - 1/(a*x))^(1/4)) + (61*(1 + 1/(a*x))^(1/4)*x)/(24*a^2*(1 - 1/(a*x))^(1/4)) + (13*(1 + 1/(a*x))^(1/4)*x^2)/(12*a*(1 - 1/(a*x))^(1/4)) + ((1 + 1/(a*x))^(1/4)*x^3)/(3*(1 - 1/(a*x))^(1/4)) + (55*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3) + (55*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3)","A",10,9,14,0.6429,1,"{6171, 98, 151, 155, 12, 93, 212, 206, 203}"
80,1,176,0,0.0676022,"\int e^{\frac{5}{2} \coth ^{-1}(a x)} x \, dx","Int[E^((5*ArcCoth[a*x])/2)*x,x]","-\frac{25 \sqrt[4]{\frac{1}{a x}+1}}{2 a^2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{25 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{25 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{x^2 \left(\frac{1}{a x}+1\right)^{9/4}}{2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{5 x \left(\frac{1}{a x}+1\right)^{5/4}}{4 a \sqrt[4]{1-\frac{1}{a x}}}","-\frac{25 \sqrt[4]{\frac{1}{a x}+1}}{2 a^2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{25 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{25 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{x^2 \left(\frac{1}{a x}+1\right)^{9/4}}{2 \sqrt[4]{1-\frac{1}{a x}}}+\frac{5 x \left(\frac{1}{a x}+1\right)^{5/4}}{4 a \sqrt[4]{1-\frac{1}{a x}}}",1,"(-25*(1 + 1/(a*x))^(1/4))/(2*a^2*(1 - 1/(a*x))^(1/4)) + (5*(1 + 1/(a*x))^(5/4)*x)/(4*a*(1 - 1/(a*x))^(1/4)) + ((1 + 1/(a*x))^(9/4)*x^2)/(2*(1 - 1/(a*x))^(1/4)) + (25*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2) + (25*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2)","A",8,7,12,0.5833,1,"{6171, 96, 94, 93, 212, 206, 203}"
81,1,130,0,0.0440145,"\int e^{\frac{5}{2} \coth ^{-1}(a x)} \, dx","Int[E^((5*ArcCoth[a*x])/2),x]","\frac{x \left(\frac{1}{a x}+1\right)^{5/4}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{10 \sqrt[4]{\frac{1}{a x}+1}}{a \sqrt[4]{1-\frac{1}{a x}}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}","\frac{x \left(\frac{1}{a x}+1\right)^{5/4}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{10 \sqrt[4]{\frac{1}{a x}+1}}{a \sqrt[4]{1-\frac{1}{a x}}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}",1,"(-10*(1 + 1/(a*x))^(1/4))/(a*(1 - 1/(a*x))^(1/4)) + ((1 + 1/(a*x))^(5/4)*x)/(1 - 1/(a*x))^(1/4) + (5*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a + (5*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a","A",7,6,10,0.6000,1,"{6170, 94, 93, 212, 206, 203}"
82,1,320,0,0.2972827,"\int \frac{e^{\frac{5}{2} \coth ^{-1}(a x)}}{x} \, dx","Int[E^((5*ArcCoth[a*x])/2)/x,x]","-\frac{8 \sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)","-\frac{8 \sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)",1,"(-8*(1 + 1/(a*x))^(1/4))/(1 - 1/(a*x))^(1/4) + Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] + 2*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + 2*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] - Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2]","A",19,16,14,1.143,1,"{6171, 98, 21, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
83,1,299,0,0.2567118,"\int \frac{e^{\frac{5}{2} \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^((5*ArcCoth[a*x])/2)/x^2,x]","-\frac{4 a \left(\frac{1}{a x}+1\right)^{5/4}}{\sqrt[4]{1-\frac{1}{a x}}}-5 a \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{5 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}-\frac{5 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}","-\frac{4 a \left(\frac{1}{a x}+1\right)^{5/4}}{\sqrt[4]{1-\frac{1}{a x}}}-5 a \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{5 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}-\frac{5 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}",1,"-5*a*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4) - (4*a*(1 + 1/(a*x))^(5/4))/(1 - 1/(a*x))^(1/4) + (5*a*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] - (5*a*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] - (5*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2]) + (5*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2])","A",14,11,14,0.7857,1,"{6171, 47, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
84,1,351,0,0.2849148,"\int \frac{e^{\frac{5}{2} \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^((5*ArcCoth[a*x])/2)/x^3,x]","-\frac{2 a^2 \left(\frac{1}{a x}+1\right)^{9/4}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{5}{2} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}-\frac{25}{4} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{25 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}-\frac{25 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}","-\frac{2 a^2 \left(\frac{1}{a x}+1\right)^{9/4}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{5}{2} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}-\frac{25}{4} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{25 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}-\frac{25 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}",1,"(-25*a^2*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4))/4 - (5*a^2*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(5/4))/2 - (2*a^2*(1 + 1/(a*x))^(9/4))/(1 - 1/(a*x))^(1/4) + (25*a^2*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (25*a^2*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (25*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (25*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2])","A",15,11,14,0.7857,1,"{6171, 78, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
85,1,385,0,0.3125297,"\int \frac{e^{\frac{5}{2} \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^((5*ArcCoth[a*x])/2)/x^4,x]","-\frac{1}{3} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{9/4}-\frac{2 a^3 \left(\frac{1}{a x}+1\right)^{9/4}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{11}{4} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}-\frac{55}{8} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{55 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}-\frac{55 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}","-\frac{1}{3} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{9/4}-\frac{2 a^3 \left(\frac{1}{a x}+1\right)^{9/4}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{11}{4} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \left(\frac{1}{a x}+1\right)^{5/4}-\frac{55}{8} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{55 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}-\frac{55 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}",1,"(-55*a^3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4))/8 - (11*a^3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(5/4))/4 - (2*a^3*(1 + 1/(a*x))^(9/4))/(1 - 1/(a*x))^(1/4) - (a^3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(9/4))/3 + (55*a^3*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (55*a^3*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (55*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2]) + (55*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2])","A",16,12,14,0.8571,1,"{6171, 89, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
86,1,253,0,0.1397152,"\int e^{-\frac{1}{2} \coth ^{-1}(a x)} x^4 \, dx","Int[x^4/E^(ArcCoth[a*x]/2),x]","\frac{11 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{48 a^2}-\frac{269 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{960 a^3}+\frac{611 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{1920 a^4}+\frac{31 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}-\frac{31 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{9 x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{40 a}","\frac{11 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{48 a^2}-\frac{269 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{960 a^3}+\frac{611 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{1920 a^4}+\frac{31 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}-\frac{31 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{9 x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{40 a}",1,"(611*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(1920*a^4) - (269*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^2)/(960*a^3) + (11*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^3)/(48*a^2) - (9*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^4)/(40*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^5)/5 + (31*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5) - (31*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5)","A",11,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 298, 203, 206}"
87,1,216,0,0.1148046,"\int e^{-\frac{1}{2} \coth ^{-1}(a x)} x^3 \, dx","Int[x^3/E^(ArcCoth[a*x]/2),x]","\frac{29 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{96 a^2}-\frac{83 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{192 a^3}-\frac{11 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{11 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{7 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{24 a}","\frac{29 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{96 a^2}-\frac{83 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{192 a^3}-\frac{11 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{11 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{7 x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{24 a}",1,"(-83*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(192*a^3) + (29*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^2)/(96*a^2) - (7*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^3)/(24*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^4)/4 - (11*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4) + (11*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4)","A",10,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 298, 203, 206}"
88,1,179,0,0.0915285,"\int e^{-\frac{1}{2} \coth ^{-1}(a x)} x^2 \, dx","Int[x^2/E^(ArcCoth[a*x]/2),x]","\frac{11 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{24 a^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{5 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{12 a}","\frac{11 x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{24 a^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{5 x^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{12 a}",1,"(11*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(24*a^2) - (5*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^2)/(12*a) + ((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x^3)/3 + (3*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3) - (3*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3)","A",9,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 298, 203, 206}"
89,1,142,0,0.0602726,"\int e^{-\frac{1}{2} \coth ^{-1}(a x)} x \, dx","Int[x/E^(ArcCoth[a*x]/2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{4 a}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}}{4 a}",1,"-((1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x)/(4*a) + ((1 - 1/(a*x))^(5/4)*(1 + 1/(a*x))^(3/4)*x^2)/2 - ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(4*a^2) + ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(4*a^2)","A",7,7,12,0.5833,1,"{6171, 96, 94, 93, 298, 203, 206}"
90,1,97,0,0.0355157,"\int e^{-\frac{1}{2} \coth ^{-1}(a x)} \, dx","Int[E^(-ArcCoth[a*x]/2),x]","x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}","x \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{\tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}",1,"(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)*x + ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/a - ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/a","A",6,6,10,0.6000,1,"{6170, 94, 93, 298, 203, 206}"
91,1,291,0,0.228066,"\int \frac{e^{-\frac{1}{2} \coth ^{-1}(a x)}}{x} \, dx","Int[1/(E^(ArcCoth[a*x]/2)*x),x]","\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)","\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)",1,"Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] - 2*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + 2*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2] - Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6171, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
92,1,268,0,0.2180812,"\int \frac{e^{-\frac{1}{2} \coth ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^(ArcCoth[a*x]/2)*x^2),x]","-a \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}","-a \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}",1,"-(a*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4)) - (a*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (a*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] - (a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2]) + (a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2])","A",13,10,14,0.7143,1,"{6171, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
93,1,319,0,0.2504361,"\int \frac{e^{-\frac{1}{2} \coth ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^(ArcCoth[a*x]/2)*x^3),x]","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{1}{4} a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{1}{4} a^2 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}",1,"(a^2*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4))/4 + (a^2*(1 - 1/(a*x))^(5/4)*(1 + 1/(a*x))^(3/4))/2 + (a^2*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (a^2*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) + (a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2])","A",14,11,14,0.7857,1,"{6171, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
94,1,356,0,0.2774495,"\int \frac{e^{-\frac{1}{2} \coth ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^(ArcCoth[a*x]/2)*x^4),x]","-\frac{1}{12} a^3 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{3}{8} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{a^2 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}}{3 x}-\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{3 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{3 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}","-\frac{1}{12} a^3 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}-\frac{3}{8} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{a^2 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}}{3 x}-\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{3 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{3 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{3 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}",1,"(-3*a^3*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4))/8 - (a^3*(1 - 1/(a*x))^(5/4)*(1 + 1/(a*x))^(3/4))/12 + (a^2*(1 - 1/(a*x))^(5/4)*(1 + 1/(a*x))^(3/4))/(3*x) - (3*a^3*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (3*a^3*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (3*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2]) + (3*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2])","A",15,12,14,0.8571,1,"{6171, 90, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
95,1,253,0,0.1402595,"\int e^{-\frac{3}{2} \coth ^{-1}(a x)} x^4 \, dx","Int[x^4/E^((3*ArcCoth[a*x])/2),x]","\frac{5 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{16 a^2}-\frac{157 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{320 a^3}+\frac{557 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{640 a^4}-\frac{237 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}-\frac{237 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{11 x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{40 a}","\frac{5 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{16 a^2}-\frac{157 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{320 a^3}+\frac{557 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{640 a^4}-\frac{237 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}-\frac{237 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{1}{5} x^5 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{11 x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{40 a}",1,"(557*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(640*a^4) - (157*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^2)/(320*a^3) + (5*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^3)/(16*a^2) - (11*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^4)/(40*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^5)/5 - (237*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5) - (237*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5)","A",11,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 212, 206, 203}"
96,1,216,0,0.1162045,"\int e^{-\frac{3}{2} \coth ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((3*ArcCoth[a*x])/2),x]","\frac{15 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{32 a^2}-\frac{63 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{64 a^3}+\frac{123 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{123 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{3 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{8 a}","\frac{15 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{32 a^2}-\frac{63 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{64 a^3}+\frac{123 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{123 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{1}{4} x^4 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{3 x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{8 a}",1,"(-63*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(64*a^3) + (15*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^2)/(32*a^2) - (3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^3)/(8*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^4)/4 + (123*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4) + (123*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4)","A",10,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 212, 206, 203}"
97,1,179,0,0.0919374,"\int e^{-\frac{3}{2} \coth ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((3*ArcCoth[a*x])/2),x]","\frac{23 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{24 a^2}-\frac{17 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}-\frac{17 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{7 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{12 a}","\frac{23 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{24 a^2}-\frac{17 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}-\frac{17 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{1}{3} x^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{7 x^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{12 a}",1,"(23*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(24*a^2) - (7*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^2)/(12*a) + ((1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x^3)/3 - (17*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3) - (17*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3)","A",9,8,14,0.5714,1,"{6171, 99, 151, 12, 93, 212, 206, 203}"
98,1,142,0,0.0586925,"\int e^{-\frac{3}{2} \coth ^{-1}(a x)} x \, dx","Int[x/E^((3*ArcCoth[a*x])/2),x]","\frac{9 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{9 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{3 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{4 a}","\frac{9 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{9 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{3 x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}}{4 a}",1,"(-3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x)/(4*a) + ((1 - 1/(a*x))^(7/4)*(1 + 1/(a*x))^(1/4)*x^2)/2 + (9*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2) + (9*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2)","A",7,7,12,0.5833,1,"{6171, 96, 94, 93, 212, 206, 203}"
99,1,98,0,0.0349385,"\int e^{-\frac{3}{2} \coth ^{-1}(a x)} \, dx","Int[E^((-3*ArcCoth[a*x])/2),x]","x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}","x \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{3 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}",1,"(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)*x - (3*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a - (3*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a","A",6,6,10,0.6000,1,"{6170, 94, 93, 212, 206, 203}"
100,1,291,0,0.2258587,"\int \frac{e^{-\frac{3}{2} \coth ^{-1}(a x)}}{x} \, dx","Int[1/(E^((3*ArcCoth[a*x])/2)*x),x]","-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)","-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)",1,"Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] - Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] + 2*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + 2*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] - Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2]","A",17,14,14,1.000,1,"{6171, 105, 63, 331, 297, 1162, 617, 204, 1165, 628, 93, 212, 206, 203}"
101,1,269,0,0.2140726,"\int \frac{e^{-\frac{3}{2} \coth ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((3*ArcCoth[a*x])/2)*x^2),x]","-a \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}","-a \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{3 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{3 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}+\frac{3 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}",1,"-(a*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4)) - (3*a*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (3*a*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (3*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2]) - (3*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2])","A",13,10,14,0.7143,1,"{6171, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
102,1,319,0,0.2465361,"\int \frac{e^{-\frac{3}{2} \coth ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((3*ArcCoth[a*x])/2)*x^3),x]","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{3}{4} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{9 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}-\frac{9 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{3}{4} a^2 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{9 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{9 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}-\frac{9 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}",1,"(3*a^2*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4))/4 + (a^2*(1 - 1/(a*x))^(7/4)*(1 + 1/(a*x))^(1/4))/2 + (9*a^2*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (9*a^2*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (9*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (9*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2])","A",14,11,14,0.7857,1,"{6171, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
103,1,356,0,0.28086,"\int \frac{e^{-\frac{3}{2} \coth ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((3*ArcCoth[a*x])/2)*x^4),x]","-\frac{1}{4} a^3 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{17}{24} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a^2 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}}{3 x}+\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{17 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{17 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}","-\frac{1}{4} a^3 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}-\frac{17}{24} a^3 \left(1-\frac{1}{a x}\right)^{3/4} \sqrt[4]{\frac{1}{a x}+1}+\frac{a^2 \left(1-\frac{1}{a x}\right)^{7/4} \sqrt[4]{\frac{1}{a x}+1}}{3 x}+\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{17 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{17 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}+\frac{17 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}",1,"(-17*a^3*(1 - 1/(a*x))^(3/4)*(1 + 1/(a*x))^(1/4))/24 - (a^3*(1 - 1/(a*x))^(7/4)*(1 + 1/(a*x))^(1/4))/4 + (a^2*(1 - 1/(a*x))^(7/4)*(1 + 1/(a*x))^(1/4))/(3*x) - (17*a^3*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (17*a^3*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (17*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2]) - (17*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2])","A",15,12,14,0.8571,1,"{6171, 90, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628}"
104,1,287,0,0.1620279,"\int e^{-\frac{5}{2} \coth ^{-1}(a x)} x^4 \, dx","Int[x^4/E^((5*ArcCoth[a*x])/2),x]","\frac{181 x^3 \sqrt[4]{1-\frac{1}{a x}}}{240 a^2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{1189 x^2 \sqrt[4]{1-\frac{1}{a x}}}{960 a^3 \sqrt[4]{\frac{1}{a x}+1}}+\frac{5533 x \sqrt[4]{1-\frac{1}{a x}}}{1920 a^4 \sqrt[4]{\frac{1}{a x}+1}}+\frac{26111 \sqrt[4]{1-\frac{1}{a x}}}{1920 a^5 \sqrt[4]{\frac{1}{a x}+1}}+\frac{1003 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}-\frac{1003 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{x^5 \sqrt[4]{1-\frac{1}{a x}}}{5 \sqrt[4]{\frac{1}{a x}+1}}-\frac{21 x^4 \sqrt[4]{1-\frac{1}{a x}}}{40 a \sqrt[4]{\frac{1}{a x}+1}}","\frac{181 x^3 \sqrt[4]{1-\frac{1}{a x}}}{240 a^2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{1189 x^2 \sqrt[4]{1-\frac{1}{a x}}}{960 a^3 \sqrt[4]{\frac{1}{a x}+1}}+\frac{5533 x \sqrt[4]{1-\frac{1}{a x}}}{1920 a^4 \sqrt[4]{\frac{1}{a x}+1}}+\frac{26111 \sqrt[4]{1-\frac{1}{a x}}}{1920 a^5 \sqrt[4]{\frac{1}{a x}+1}}+\frac{1003 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}-\frac{1003 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{128 a^5}+\frac{x^5 \sqrt[4]{1-\frac{1}{a x}}}{5 \sqrt[4]{\frac{1}{a x}+1}}-\frac{21 x^4 \sqrt[4]{1-\frac{1}{a x}}}{40 a \sqrt[4]{\frac{1}{a x}+1}}",1,"(26111*(1 - 1/(a*x))^(1/4))/(1920*a^5*(1 + 1/(a*x))^(1/4)) + (5533*(1 - 1/(a*x))^(1/4)*x)/(1920*a^4*(1 + 1/(a*x))^(1/4)) - (1189*(1 - 1/(a*x))^(1/4)*x^2)/(960*a^3*(1 + 1/(a*x))^(1/4)) + (181*(1 - 1/(a*x))^(1/4)*x^3)/(240*a^2*(1 + 1/(a*x))^(1/4)) - (21*(1 - 1/(a*x))^(1/4)*x^4)/(40*a*(1 + 1/(a*x))^(1/4)) + ((1 - 1/(a*x))^(1/4)*x^5)/(5*(1 + 1/(a*x))^(1/4)) + (1003*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5) - (1003*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*a^5)","A",12,9,14,0.6429,1,"{6171, 98, 151, 155, 12, 93, 298, 203, 206}"
105,1,250,0,0.1399891,"\int e^{-\frac{5}{2} \coth ^{-1}(a x)} x^3 \, dx","Int[x^3/E^((5*ArcCoth[a*x])/2),x]","\frac{113 x^2 \sqrt[4]{1-\frac{1}{a x}}}{96 a^2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{521 x \sqrt[4]{1-\frac{1}{a x}}}{192 a^3 \sqrt[4]{\frac{1}{a x}+1}}-\frac{2467 \sqrt[4]{1-\frac{1}{a x}}}{192 a^4 \sqrt[4]{\frac{1}{a x}+1}}-\frac{475 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{475 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{x^4 \sqrt[4]{1-\frac{1}{a x}}}{4 \sqrt[4]{\frac{1}{a x}+1}}-\frac{17 x^3 \sqrt[4]{1-\frac{1}{a x}}}{24 a \sqrt[4]{\frac{1}{a x}+1}}","\frac{113 x^2 \sqrt[4]{1-\frac{1}{a x}}}{96 a^2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{521 x \sqrt[4]{1-\frac{1}{a x}}}{192 a^3 \sqrt[4]{\frac{1}{a x}+1}}-\frac{2467 \sqrt[4]{1-\frac{1}{a x}}}{192 a^4 \sqrt[4]{\frac{1}{a x}+1}}-\frac{475 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{475 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{64 a^4}+\frac{x^4 \sqrt[4]{1-\frac{1}{a x}}}{4 \sqrt[4]{\frac{1}{a x}+1}}-\frac{17 x^3 \sqrt[4]{1-\frac{1}{a x}}}{24 a \sqrt[4]{\frac{1}{a x}+1}}",1,"(-2467*(1 - 1/(a*x))^(1/4))/(192*a^4*(1 + 1/(a*x))^(1/4)) - (521*(1 - 1/(a*x))^(1/4)*x)/(192*a^3*(1 + 1/(a*x))^(1/4)) + (113*(1 - 1/(a*x))^(1/4)*x^2)/(96*a^2*(1 + 1/(a*x))^(1/4)) - (17*(1 - 1/(a*x))^(1/4)*x^3)/(24*a*(1 + 1/(a*x))^(1/4)) + ((1 - 1/(a*x))^(1/4)*x^4)/(4*(1 + 1/(a*x))^(1/4)) - (475*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4) + (475*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(64*a^4)","A",11,9,14,0.6429,1,"{6171, 98, 151, 155, 12, 93, 298, 203, 206}"
106,1,213,0,0.1103273,"\int e^{-\frac{5}{2} \coth ^{-1}(a x)} x^2 \, dx","Int[x^2/E^((5*ArcCoth[a*x])/2),x]","\frac{61 x \sqrt[4]{1-\frac{1}{a x}}}{24 a^2 \sqrt[4]{\frac{1}{a x}+1}}+\frac{287 \sqrt[4]{1-\frac{1}{a x}}}{24 a^3 \sqrt[4]{\frac{1}{a x}+1}}+\frac{55 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}-\frac{55 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{x^3 \sqrt[4]{1-\frac{1}{a x}}}{3 \sqrt[4]{\frac{1}{a x}+1}}-\frac{13 x^2 \sqrt[4]{1-\frac{1}{a x}}}{12 a \sqrt[4]{\frac{1}{a x}+1}}","\frac{61 x \sqrt[4]{1-\frac{1}{a x}}}{24 a^2 \sqrt[4]{\frac{1}{a x}+1}}+\frac{287 \sqrt[4]{1-\frac{1}{a x}}}{24 a^3 \sqrt[4]{\frac{1}{a x}+1}}+\frac{55 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}-\frac{55 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{8 a^3}+\frac{x^3 \sqrt[4]{1-\frac{1}{a x}}}{3 \sqrt[4]{\frac{1}{a x}+1}}-\frac{13 x^2 \sqrt[4]{1-\frac{1}{a x}}}{12 a \sqrt[4]{\frac{1}{a x}+1}}",1,"(287*(1 - 1/(a*x))^(1/4))/(24*a^3*(1 + 1/(a*x))^(1/4)) + (61*(1 - 1/(a*x))^(1/4)*x)/(24*a^2*(1 + 1/(a*x))^(1/4)) - (13*(1 - 1/(a*x))^(1/4)*x^2)/(12*a*(1 + 1/(a*x))^(1/4)) + ((1 - 1/(a*x))^(1/4)*x^3)/(3*(1 + 1/(a*x))^(1/4)) + (55*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3) - (55*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(8*a^3)","A",10,9,14,0.6429,1,"{6171, 98, 151, 155, 12, 93, 298, 203, 206}"
107,1,176,0,0.0714863,"\int e^{-\frac{5}{2} \coth ^{-1}(a x)} x \, dx","Int[x/E^((5*ArcCoth[a*x])/2),x]","-\frac{25 \sqrt[4]{1-\frac{1}{a x}}}{2 a^2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{25 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{25 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{x^2 \left(1-\frac{1}{a x}\right)^{9/4}}{2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{5 x \left(1-\frac{1}{a x}\right)^{5/4}}{4 a \sqrt[4]{\frac{1}{a x}+1}}","-\frac{25 \sqrt[4]{1-\frac{1}{a x}}}{2 a^2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{25 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{25 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{4 a^2}+\frac{x^2 \left(1-\frac{1}{a x}\right)^{9/4}}{2 \sqrt[4]{\frac{1}{a x}+1}}-\frac{5 x \left(1-\frac{1}{a x}\right)^{5/4}}{4 a \sqrt[4]{\frac{1}{a x}+1}}",1,"(-25*(1 - 1/(a*x))^(1/4))/(2*a^2*(1 + 1/(a*x))^(1/4)) - (5*(1 - 1/(a*x))^(5/4)*x)/(4*a*(1 + 1/(a*x))^(1/4)) + ((1 - 1/(a*x))^(9/4)*x^2)/(2*(1 + 1/(a*x))^(1/4)) - (25*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2) + (25*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(4*a^2)","A",8,7,12,0.5833,1,"{6171, 96, 94, 93, 298, 203, 206}"
108,1,130,0,0.0464704,"\int e^{-\frac{5}{2} \coth ^{-1}(a x)} \, dx","Int[E^((-5*ArcCoth[a*x])/2),x]","\frac{x \left(1-\frac{1}{a x}\right)^{5/4}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{10 \sqrt[4]{1-\frac{1}{a x}}}{a \sqrt[4]{\frac{1}{a x}+1}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}","\frac{x \left(1-\frac{1}{a x}\right)^{5/4}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{10 \sqrt[4]{1-\frac{1}{a x}}}{a \sqrt[4]{\frac{1}{a x}+1}}+\frac{5 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)}{a}",1,"(10*(1 - 1/(a*x))^(1/4))/(a*(1 + 1/(a*x))^(1/4)) + ((1 - 1/(a*x))^(5/4)*x)/(1 + 1/(a*x))^(1/4) + (5*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a - (5*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/a","A",7,6,10,0.6000,1,"{6170, 94, 93, 298, 203, 206}"
109,1,320,0,0.2845884,"\int \frac{e^{-\frac{5}{2} \coth ^{-1}(a x)}}{x} \, dx","Int[1/(E^((5*ArcCoth[a*x])/2)*x),x]","-\frac{8 \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)","-\frac{8 \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)-2 \tan ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}\right)",1,"(-8*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4) - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)] - 2*ArcTan[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] + 2*ArcTanh[(1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)] - Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2] + Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)]/Sqrt[2]","A",19,16,14,1.143,1,"{6171, 98, 21, 105, 63, 240, 211, 1165, 628, 1162, 617, 204, 93, 298, 203, 206}"
110,1,299,0,0.2445753,"\int \frac{e^{-\frac{5}{2} \coth ^{-1}(a x)}}{x^2} \, dx","Int[1/(E^((5*ArcCoth[a*x])/2)*x^2),x]","\frac{4 a \left(1-\frac{1}{a x}\right)^{5/4}}{\sqrt[4]{\frac{1}{a x}+1}}+5 a \left(\frac{1}{a x}+1\right)^{3/4} \sqrt[4]{1-\frac{1}{a x}}+\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{5 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}-\frac{5 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}","\frac{4 a \left(1-\frac{1}{a x}\right)^{5/4}}{\sqrt[4]{\frac{1}{a x}+1}}+5 a \left(\frac{1}{a x}+1\right)^{3/4} \sqrt[4]{1-\frac{1}{a x}}+\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}-\frac{5 a \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{2 \sqrt{2}}+\frac{5 a \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{\sqrt{2}}-\frac{5 a \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{\sqrt{2}}",1,"(4*a*(1 - 1/(a*x))^(5/4))/(1 + 1/(a*x))^(1/4) + 5*a*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4) + (5*a*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] - (5*a*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/Sqrt[2] + (5*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2]) - (5*a*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(2*Sqrt[2])","A",14,11,14,0.7857,1,"{6171, 47, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
111,1,351,0,0.2807985,"\int \frac{e^{-\frac{5}{2} \coth ^{-1}(a x)}}{x^3} \, dx","Int[1/(E^((5*ArcCoth[a*x])/2)*x^3),x]","-\frac{2 a^2 \left(1-\frac{1}{a x}\right)^{9/4}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{5}{2} a^2 \left(\frac{1}{a x}+1\right)^{3/4} \left(1-\frac{1}{a x}\right)^{5/4}-\frac{25}{4} a^2 \left(\frac{1}{a x}+1\right)^{3/4} \sqrt[4]{1-\frac{1}{a x}}-\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{25 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}+\frac{25 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}","-\frac{2 a^2 \left(1-\frac{1}{a x}\right)^{9/4}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{5}{2} a^2 \left(\frac{1}{a x}+1\right)^{3/4} \left(1-\frac{1}{a x}\right)^{5/4}-\frac{25}{4} a^2 \left(\frac{1}{a x}+1\right)^{3/4} \sqrt[4]{1-\frac{1}{a x}}-\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}+\frac{25 a^2 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}-\frac{25 a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{4 \sqrt{2}}+\frac{25 a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{4 \sqrt{2}}",1,"(-2*a^2*(1 - 1/(a*x))^(9/4))/(1 + 1/(a*x))^(1/4) - (25*a^2*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4))/4 - (5*a^2*(1 - 1/(a*x))^(5/4)*(1 + 1/(a*x))^(3/4))/2 - (25*a^2*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) + (25*a^2*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(4*Sqrt[2]) - (25*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (25*a^2*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2])","A",15,11,14,0.7857,1,"{6171, 78, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
112,1,385,0,0.3090191,"\int \frac{e^{-\frac{5}{2} \coth ^{-1}(a x)}}{x^4} \, dx","Int[1/(E^((5*ArcCoth[a*x])/2)*x^4),x]","\frac{1}{3} a^3 \left(1-\frac{1}{a x}\right)^{9/4} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{11}{4} a^3 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{55}{8} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{2 a^3 \left(1-\frac{1}{a x}\right)^{9/4}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{55 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}-\frac{55 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}","\frac{1}{3} a^3 \left(1-\frac{1}{a x}\right)^{9/4} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{11}{4} a^3 \left(1-\frac{1}{a x}\right)^{5/4} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{55}{8} a^3 \sqrt[4]{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/4}+\frac{2 a^3 \left(1-\frac{1}{a x}\right)^{9/4}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}-\frac{55 a^3 \log \left(\frac{\sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1}}+\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{16 \sqrt{2}}+\frac{55 a^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}\right)}{8 \sqrt{2}}-\frac{55 a^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+1\right)}{8 \sqrt{2}}",1,"(2*a^3*(1 - 1/(a*x))^(9/4))/(1 + 1/(a*x))^(1/4) + (55*a^3*(1 - 1/(a*x))^(1/4)*(1 + 1/(a*x))^(3/4))/8 + (11*a^3*(1 - 1/(a*x))^(5/4)*(1 + 1/(a*x))^(3/4))/4 + (a^3*(1 - 1/(a*x))^(9/4)*(1 + 1/(a*x))^(3/4))/3 + (55*a^3*ArcTan[1 - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) - (55*a^3*ArcTan[1 + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(8*Sqrt[2]) + (55*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] - (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2]) - (55*a^3*Log[1 + Sqrt[1 - 1/(a*x)]/Sqrt[1 + 1/(a*x)] + (Sqrt[2]*(1 - 1/(a*x))^(1/4))/(1 + 1/(a*x))^(1/4)])/(16*Sqrt[2])","A",16,12,14,0.8571,1,"{6171, 89, 80, 50, 63, 240, 211, 1165, 628, 1162, 617, 204}"
113,1,285,0,0.2491458,"\int e^{\frac{1}{3} \coth ^{-1}(x)} x^2 \, dx","Int[E^(ArcCoth[x]/3)*x^2,x]","\frac{1}{3} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x^3+\frac{7}{18} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x^2+\frac{11}{27} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x-\frac{19}{324} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{19}{324} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)-\frac{19 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19 \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19}{81} \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)","\frac{1}{3} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x^3+\frac{7}{18} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x^2+\frac{11}{27} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x-\frac{19}{324} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{19}{324} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)-\frac{19 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19 \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)}{54 \sqrt{3}}+\frac{19}{81} \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)",1,"(11*(1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6)*x)/27 + (7*(1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6)*x^2)/18 + ((1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6)*x^3)/3 - (19*ArcTan[(1 - (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]])/(54*Sqrt[3]) + (19*ArcTan[(1 + (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]])/(54*Sqrt[3]) + (19*ArcTanh[(1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)])/81 - (19*Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) - (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)])/324 + (19*Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) + (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)])/324","A",16,11,12,0.9167,1,"{6171, 99, 151, 12, 93, 210, 634, 618, 204, 628, 206}"
114,1,258,0,0.2032628,"\int e^{\frac{1}{3} \coth ^{-1}(x)} x \, dx","Int[E^(ArcCoth[x]/3)*x,x]","\frac{1}{2} \left(\frac{1}{x}+1\right)^{7/6} \left(\frac{x-1}{x}\right)^{5/6} x^2+\frac{1}{6} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x-\frac{1}{36} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{36} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{1}{9} \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)","\frac{1}{2} \left(\frac{1}{x}+1\right)^{7/6} \left(\frac{x-1}{x}\right)^{5/6} x^2+\frac{1}{6} \sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x-\frac{1}{36} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{36} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}+\frac{1}{9} \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)",1,"((1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6)*x)/6 + ((1 + x^(-1))^(7/6)*((-1 + x)/x)^(5/6)*x^2)/2 - ArcTan[(1 - (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]]/(6*Sqrt[3]) + ArcTan[(1 + (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]]/(6*Sqrt[3]) + ArcTanh[(1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/9 - Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) - (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/36 + Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) + (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/36","A",14,10,10,1.000,1,"{6171, 96, 94, 93, 210, 634, 618, 204, 628, 206}"
115,1,223,0,0.1795956,"\int e^{\frac{1}{3} \coth ^{-1}(x)} \, dx","Int[E^(ArcCoth[x]/3),x]","\sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x-\frac{1}{6} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{6} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2}{3} \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)","\sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6} x-\frac{1}{6} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{6} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2}{3} \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)",1,"(1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6)*x - ArcTan[(1 - (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]]/Sqrt[3] + ArcTan[(1 + (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]]/Sqrt[3] + (2*ArcTanh[(1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)])/3 - Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) - (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/6 + Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) + (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/6","A",13,9,8,1.125,1,"{6170, 94, 93, 210, 634, 618, 204, 628, 206}"
116,1,402,0,0.525113,"\int \frac{e^{\frac{1}{3} \coth ^{-1}(x)}}{x} \, dx","Int[E^(ArcCoth[x]/3)/x,x]","-\frac{1}{2} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{2} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)-\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)-\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+2 \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)","-\frac{1}{2} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}-\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{2} \log \left(\frac{\sqrt[3]{\frac{1}{x}+1}}{\sqrt[3]{\frac{x-1}{x}}}+\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1\right)+\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)-\frac{1}{2} \sqrt{3} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)-\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}}{\sqrt{3}}\right)+\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}+1}{\sqrt{3}}\right)-\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+2 \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[6]{\frac{1}{x}+1}}{\sqrt[6]{\frac{x-1}{x}}}\right)",1,"-(Sqrt[3]*ArcTan[(1 - (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]]) + Sqrt[3]*ArcTan[(1 + (2*(1 + x^(-1))^(1/6))/((-1 + x)/x)^(1/6))/Sqrt[3]] - ArcTan[Sqrt[3] - (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)] + ArcTan[Sqrt[3] + (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)] + 2*ArcTan[((-1 + x)/x)^(1/6)/(1 + x^(-1))^(1/6)] + 2*ArcTanh[(1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)] - Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) - (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/2 + Log[1 + (1 + x^(-1))^(1/3)/((-1 + x)/x)^(1/3) + (1 + x^(-1))^(1/6)/((-1 + x)/x)^(1/6)]/2 + (Sqrt[3]*Log[1 - (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)])/2 - (Sqrt[3]*Log[1 + (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)])/2","A",25,13,12,1.083,1,"{6171, 105, 63, 331, 295, 634, 618, 204, 628, 203, 93, 210, 206}"
117,1,233,0,0.3674757,"\int \frac{e^{\frac{1}{3} \coth ^{-1}(x)}}{x^2} \, dx","Int[E^(ArcCoth[x]/3)/x^2,x]","\sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6}+\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{2 \sqrt{3}}-\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{2 \sqrt{3}}-\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\frac{1}{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+\frac{2}{3} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)","\sqrt[6]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{5/6}+\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{2 \sqrt{3}}-\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{2 \sqrt{3}}-\frac{1}{3} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\frac{1}{3} \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+\frac{2}{3} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)",1,"(1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6) - ArcTan[Sqrt[3] - (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)]/3 + ArcTan[Sqrt[3] + (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)]/3 + (2*ArcTan[((-1 + x)/x)^(1/6)/(1 + x^(-1))^(1/6)])/3 + Log[1 - (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)]/(2*Sqrt[3]) - Log[1 + (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)]/(2*Sqrt[3])","A",14,10,12,0.8333,1,"{6171, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
118,1,260,0,0.3791018,"\int \frac{e^{\frac{1}{3} \coth ^{-1}(x)}}{x^3} \, dx","Int[E^(ArcCoth[x]/3)/x^3,x]","\frac{1}{2} \left(\frac{x-1}{x}\right)^{5/6} \left(\frac{1}{x}+1\right)^{7/6}+\frac{1}{6} \left(\frac{x-1}{x}\right)^{5/6} \sqrt[6]{\frac{1}{x}+1}+\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{12 \sqrt{3}}-\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{12 \sqrt{3}}-\frac{1}{18} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\frac{1}{18} \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+\frac{1}{9} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)","\frac{1}{2} \left(\frac{x-1}{x}\right)^{5/6} \left(\frac{1}{x}+1\right)^{7/6}+\frac{1}{6} \left(\frac{x-1}{x}\right)^{5/6} \sqrt[6]{\frac{1}{x}+1}+\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{12 \sqrt{3}}-\frac{\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{12 \sqrt{3}}-\frac{1}{18} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\frac{1}{18} \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+\frac{1}{9} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)",1,"((1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6))/6 + ((1 + x^(-1))^(7/6)*((-1 + x)/x)^(5/6))/2 - ArcTan[Sqrt[3] - (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)]/18 + ArcTan[Sqrt[3] + (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)]/18 + ArcTan[((-1 + x)/x)^(1/6)/(1 + x^(-1))^(1/6)]/9 + Log[1 - (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)]/(12*Sqrt[3]) - Log[1 + (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)]/(12*Sqrt[3])","A",15,11,12,0.9167,1,"{6171, 80, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
119,1,287,0,0.3983509,"\int \frac{e^{\frac{1}{3} \coth ^{-1}(x)}}{x^4} \, dx","Int[E^(ArcCoth[x]/3)/x^4,x]","\frac{1}{18} \left(\frac{x-1}{x}\right)^{5/6} \left(\frac{1}{x}+1\right)^{7/6}+\frac{\left(\frac{x-1}{x}\right)^{5/6} \left(\frac{1}{x}+1\right)^{7/6}}{3 x}+\frac{19}{54} \left(\frac{x-1}{x}\right)^{5/6} \sqrt[6]{\frac{1}{x}+1}+\frac{19 \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{108 \sqrt{3}}-\frac{19 \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{108 \sqrt{3}}-\frac{19}{162} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\frac{19}{162} \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+\frac{19}{81} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)","\frac{1}{18} \left(\frac{x-1}{x}\right)^{5/6} \left(\frac{1}{x}+1\right)^{7/6}+\frac{\left(\frac{x-1}{x}\right)^{5/6} \left(\frac{1}{x}+1\right)^{7/6}}{3 x}+\frac{19}{54} \left(\frac{x-1}{x}\right)^{5/6} \sqrt[6]{\frac{1}{x}+1}+\frac{19 \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}-\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{108 \sqrt{3}}-\frac{19 \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+\frac{\sqrt{3} \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+1\right)}{108 \sqrt{3}}-\frac{19}{162} \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)+\frac{19}{162} \tan ^{-1}\left(\frac{2 \sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}+\sqrt{3}\right)+\frac{19}{81} \tan ^{-1}\left(\frac{\sqrt[6]{\frac{x-1}{x}}}{\sqrt[6]{\frac{1}{x}+1}}\right)",1,"(19*(1 + x^(-1))^(1/6)*((-1 + x)/x)^(5/6))/54 + ((1 + x^(-1))^(7/6)*((-1 + x)/x)^(5/6))/18 + ((1 + x^(-1))^(7/6)*((-1 + x)/x)^(5/6))/(3*x) - (19*ArcTan[Sqrt[3] - (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)])/162 + (19*ArcTan[Sqrt[3] + (2*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6)])/162 + (19*ArcTan[((-1 + x)/x)^(1/6)/(1 + x^(-1))^(1/6)])/81 + (19*Log[1 - (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)])/(108*Sqrt[3]) - (19*Log[1 + (Sqrt[3]*((-1 + x)/x)^(1/6))/(1 + x^(-1))^(1/6) + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)])/(108*Sqrt[3])","A",16,12,12,1.000,1,"{6171, 90, 80, 50, 63, 331, 295, 634, 618, 204, 628, 203}"
120,1,157,0,0.0701047,"\int e^{\frac{2}{3} \coth ^{-1}(x)} x^2 \, dx","Int[E^((2*ArcCoth[x])/3)*x^2,x]","\frac{1}{3} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x^3+\frac{4}{9} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x^2+\frac{14}{27} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x-\frac{11}{27} \log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{11 \log (x)}{81}-\frac{22 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3}}","\frac{1}{3} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x^3+\frac{4}{9} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x^2+\frac{14}{27} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x-\frac{11}{27} \log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{11 \log (x)}{81}-\frac{22 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)}{27 \sqrt{3}}",1,"(14*(1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3)*x)/27 + (4*(1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3)*x^2)/9 + ((1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3)*x^3)/3 - (22*ArcTan[1/Sqrt[3] + (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))])/(27*Sqrt[3]) - (11*Log[(1 + x^(-1))^(1/3) - ((-1 + x)/x)^(1/3)])/27 - (11*Log[x])/81","A",6,5,12,0.4167,1,"{6171, 99, 151, 12, 91}"
121,1,130,0,0.0466163,"\int e^{\frac{2}{3} \coth ^{-1}(x)} x \, dx","Int[E^((2*ArcCoth[x])/3)*x,x]","\frac{1}{2} \left(\frac{1}{x}+1\right)^{4/3} \left(\frac{x-1}{x}\right)^{2/3} x^2+\frac{1}{3} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x-\frac{1}{3} \log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{\log (x)}{9}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{1}{2} \left(\frac{1}{x}+1\right)^{4/3} \left(\frac{x-1}{x}\right)^{2/3} x^2+\frac{1}{3} \sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x-\frac{1}{3} \log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{\log (x)}{9}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"((1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3)*x)/3 + ((1 + x^(-1))^(4/3)*((-1 + x)/x)^(2/3)*x^2)/2 - (2*ArcTan[1/Sqrt[3] + (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))])/(3*Sqrt[3]) - Log[(1 + x^(-1))^(1/3) - ((-1 + x)/x)^(1/3)]/3 - Log[x]/9","A",4,4,10,0.4000,1,"{6171, 96, 94, 91}"
122,1,96,0,0.0286798,"\int e^{\frac{2}{3} \coth ^{-1}(x)} \, dx","Int[E^((2*ArcCoth[x])/3),x]","\sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x-\log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{\log (x)}{3}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}","\sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3} x-\log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{\log (x)}{3}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3)*x - (2*ArcTan[1/Sqrt[3] + (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))])/Sqrt[3] - Log[(1 + x^(-1))^(1/3) - ((-1 + x)/x)^(1/3)] - Log[x]/3","A",3,3,8,0.3750,1,"{6170, 94, 91}"
123,1,155,0,0.0512448,"\int \frac{e^{\frac{2}{3} \coth ^{-1}(x)}}{x} \, dx","Int[E^((2*ArcCoth[x])/3)/x,x]","-\frac{3}{2} \log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{3}{2} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+1\right)-\frac{1}{2} \log \left(\frac{1}{x}+1\right)-\frac{\log (x)}{2}-\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)","-\frac{3}{2} \log \left(\sqrt[3]{\frac{1}{x}+1}-\sqrt[3]{\frac{x-1}{x}}\right)-\frac{3}{2} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+1\right)-\frac{1}{2} \log \left(\frac{1}{x}+1\right)-\frac{\log (x)}{2}-\sqrt{3} \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}\right)-\sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}+\frac{1}{\sqrt{3}}\right)",1,"-(Sqrt[3]*ArcTan[1/Sqrt[3] - (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))]) - Sqrt[3]*ArcTan[1/Sqrt[3] + (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))] - (3*Log[(1 + x^(-1))^(1/3) - ((-1 + x)/x)^(1/3)])/2 - (3*Log[1 + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)])/2 - Log[1 + x^(-1)]/2 - Log[x]/2","A",4,4,12,0.3333,1,"{6171, 105, 60, 91}"
124,1,99,0,0.0429347,"\int \frac{e^{\frac{2}{3} \coth ^{-1}(x)}}{x^2} \, dx","Int[E^((2*ArcCoth[x])/3)/x^2,x]","\sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3}-\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+1\right)-\frac{1}{3} \log \left(\frac{1}{x}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}\right)}{\sqrt{3}}","\sqrt[3]{\frac{1}{x}+1} \left(\frac{x-1}{x}\right)^{2/3}-\log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+1\right)-\frac{1}{3} \log \left(\frac{1}{x}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}\right)}{\sqrt{3}}",1,"(1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3) - (2*ArcTan[1/Sqrt[3] - (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))])/Sqrt[3] - Log[1 + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)] - Log[1 + x^(-1)]/3","A",3,3,12,0.2500,1,"{6171, 50, 60}"
125,1,130,0,0.0533082,"\int \frac{e^{\frac{2}{3} \coth ^{-1}(x)}}{x^3} \, dx","Int[E^((2*ArcCoth[x])/3)/x^3,x]","\frac{1}{2} \left(\frac{x-1}{x}\right)^{2/3} \left(\frac{1}{x}+1\right)^{4/3}+\frac{1}{3} \left(\frac{x-1}{x}\right)^{2/3} \sqrt[3]{\frac{1}{x}+1}-\frac{1}{3} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+1\right)-\frac{1}{9} \log \left(\frac{1}{x}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}\right)}{3 \sqrt{3}}","\frac{1}{2} \left(\frac{x-1}{x}\right)^{2/3} \left(\frac{1}{x}+1\right)^{4/3}+\frac{1}{3} \left(\frac{x-1}{x}\right)^{2/3} \sqrt[3]{\frac{1}{x}+1}-\frac{1}{3} \log \left(\frac{\sqrt[3]{\frac{x-1}{x}}}{\sqrt[3]{\frac{1}{x}+1}}+1\right)-\frac{1}{9} \log \left(\frac{1}{x}+1\right)-\frac{2 \tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 \sqrt[3]{\frac{x-1}{x}}}{\sqrt{3} \sqrt[3]{\frac{1}{x}+1}}\right)}{3 \sqrt{3}}",1,"((1 + x^(-1))^(1/3)*((-1 + x)/x)^(2/3))/3 + ((1 + x^(-1))^(4/3)*((-1 + x)/x)^(2/3))/2 - (2*ArcTan[1/Sqrt[3] - (2*((-1 + x)/x)^(1/3))/(Sqrt[3]*(1 + x^(-1))^(1/3))])/(3*Sqrt[3]) - Log[1 + ((-1 + x)/x)^(1/3)/(1 + x^(-1))^(1/3)]/3 - Log[1 + x^(-1)]/9","A",4,4,12,0.3333,1,"{6171, 80, 50, 60}"
126,1,429,0,0.3432782,"\int e^{\frac{1}{4} \coth ^{-1}(a x)} x^2 \, dx","Int[E^(ArcCoth[a*x]/4)*x^2,x]","\frac{37 x \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}}{96 a^2}-\frac{11 \log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{128 \sqrt{2} a^3}+\frac{11 \log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{128 \sqrt{2} a^3}-\frac{11 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{64 \sqrt{2} a^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{64 \sqrt{2} a^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{64 a^3}+\frac{11 \tanh ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{64 a^3}+\frac{1}{3} x^3 \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}+\frac{3 x^2 \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}}{8 a}","\frac{37 x \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}}{96 a^2}-\frac{11 \log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{128 \sqrt{2} a^3}+\frac{11 \log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{128 \sqrt{2} a^3}-\frac{11 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{64 \sqrt{2} a^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{64 \sqrt{2} a^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{64 a^3}+\frac{11 \tanh ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{64 a^3}+\frac{1}{3} x^3 \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}+\frac{3 x^2 \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}}{8 a}",1,"(37*(1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8)*x)/(96*a^2) + (3*(1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8)*x^2)/(8*a) + ((1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8)*x^3)/3 - (11*ArcTan[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)])/(64*Sqrt[2]*a^3) + (11*ArcTan[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)])/(64*Sqrt[2]*a^3) + (11*ArcTan[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)])/(64*a^3) + (11*ArcTanh[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)])/(64*a^3) - (11*Log[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*Sqrt[2]*a^3) + (11*Log[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)])/(128*Sqrt[2]*a^3)","A",19,15,14,1.071,1,"{6171, 99, 151, 12, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
127,1,392,0,0.2471839,"\int e^{\frac{1}{4} \coth ^{-1}(a x)} x \, dx","Int[E^(ArcCoth[a*x]/4)*x,x]","-\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{32 \sqrt{2} a^2}+\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{32 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{16 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{16 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{16 a^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{16 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{7/8} \left(\frac{1}{a x}+1\right)^{9/8}+\frac{x \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}}{8 a}","-\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{32 \sqrt{2} a^2}+\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{32 \sqrt{2} a^2}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{16 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{16 \sqrt{2} a^2}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{16 a^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{16 a^2}+\frac{1}{2} x^2 \left(1-\frac{1}{a x}\right)^{7/8} \left(\frac{1}{a x}+1\right)^{9/8}+\frac{x \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}}{8 a}",1,"((1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8)*x)/(8*a) + ((1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(9/8)*x^2)/2 - ArcTan[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)]/(16*Sqrt[2]*a^2) + ArcTan[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)]/(16*Sqrt[2]*a^2) + ArcTan[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)]/(16*a^2) + ArcTanh[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)]/(16*a^2) - Log[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(32*Sqrt[2]*a^2) + Log[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(32*Sqrt[2]*a^2)","A",17,14,12,1.167,1,"{6171, 96, 94, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
128,1,352,0,0.200465,"\int e^{\frac{1}{4} \coth ^{-1}(a x)} \, dx","Int[E^(ArcCoth[a*x]/4),x]","x \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}-\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{4 \sqrt{2} a}+\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{4 \sqrt{2} a}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{2 a}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{2 a}","x \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}-\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{4 \sqrt{2} a}+\frac{\log \left(\frac{\sqrt[4]{\frac{1}{a x}+1}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{4 \sqrt{2} a}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{2 \sqrt{2} a}+\frac{\tan ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{2 a}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{\frac{1}{a x}+1}}{\sqrt[8]{1-\frac{1}{a x}}}\right)}{2 a}",1,"(1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8)*x - ArcTan[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)]/(2*Sqrt[2]*a) + ArcTan[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)]/(2*Sqrt[2]*a) + ArcTan[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)]/(2*a) + ArcTanh[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)]/(2*a) - Log[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(4*Sqrt[2]*a) + Log[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/(4*Sqrt[2]*a)","A",16,13,10,1.300,1,"{6170, 94, 93, 214, 212, 206, 203, 211, 1165, 628, 1162, 617, 204}"
129,1,919,0,0.8992969,"\int \frac{e^{\frac{1}{4} \coth ^{-1}(a x)}}{x} \, dx","Int[E^(ArcCoth[a*x]/4)/x,x]","-\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}}{\sqrt{2+\sqrt{2}}}\right)-\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}}{\sqrt{2-\sqrt{2}}}\right)+\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)-\frac{\log \left(\frac{\sqrt[4]{1+\frac{1}{a x}}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt[4]{1+\frac{1}{a x}}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{\sqrt{2}}","-\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}}{\sqrt{2+\sqrt{2}}}\right)-\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}}{\sqrt{2-\sqrt{2}}}\right)+\sqrt{2+\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\sqrt{2-\sqrt{2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)-\sqrt{2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}\right)+\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)+2 \tan ^{-1}\left(\frac{\sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}\right)+2 \tanh ^{-1}\left(\frac{\sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}\right)+\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)-\frac{1}{2} \sqrt{2-\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)+\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)-\frac{1}{2} \sqrt{2+\sqrt{2}} \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{1+\frac{1}{a x}}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{1+\frac{1}{a x}}}+1\right)-\frac{\log \left(\frac{\sqrt[4]{1+\frac{1}{a x}}}{\sqrt[4]{1-\frac{1}{a x}}}-\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{\sqrt{2}}+\frac{\log \left(\frac{\sqrt[4]{1+\frac{1}{a x}}}{\sqrt[4]{1-\frac{1}{a x}}}+\frac{\sqrt{2} \sqrt[8]{1+\frac{1}{a x}}}{\sqrt[8]{1-\frac{1}{a x}}}+1\right)}{\sqrt{2}}",1,"-(Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 + Sqrt[2]]]) - Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 - Sqrt[2]]] + Sqrt[2 + Sqrt[2]]*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 + Sqrt[2]]] + Sqrt[2 - Sqrt[2]]*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 - Sqrt[2]]] - Sqrt[2]*ArcTan[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)] + Sqrt[2]*ArcTan[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8)] + 2*ArcTan[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)] + 2*ArcTanh[(1 + 1/(a*x))^(1/8)/(1 - 1/(a*x))^(1/8)] + (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/2 - (Sqrt[2 - Sqrt[2]]*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/2 + (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/2 - (Sqrt[2 + Sqrt[2]]*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/2 - Log[1 - (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/Sqrt[2] + Log[1 + (Sqrt[2]*(1 + 1/(a*x))^(1/8))/(1 - 1/(a*x))^(1/8) + (1 + 1/(a*x))^(1/4)/(1 - 1/(a*x))^(1/4)]/Sqrt[2]","A",39,20,14,1.429,1,"{6171, 105, 63, 331, 299, 1122, 1169, 634, 618, 204, 628, 93, 214, 212, 206, 203, 211, 1165, 1162, 617}"
130,1,676,0,0.6052436,"\int \frac{e^{\frac{1}{4} \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^(ArcCoth[a*x]/4)/x^2,x]","a \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}+\frac{1}{8} \sqrt{2-\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{4} \sqrt{2+\sqrt{2}} a \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{4} \sqrt{2-\sqrt{2}} a \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2-\sqrt{2}}}\right)+\frac{1}{4} \sqrt{2+\sqrt{2}} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{4} \sqrt{2-\sqrt{2}} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)","a \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}+\frac{1}{8} \sqrt{2-\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{8} \sqrt{2-\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)+\frac{1}{8} \sqrt{2+\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{8} \sqrt{2+\sqrt{2}} a \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{4} \sqrt{2+\sqrt{2}} a \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{4} \sqrt{2-\sqrt{2}} a \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2-\sqrt{2}}}\right)+\frac{1}{4} \sqrt{2+\sqrt{2}} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{4} \sqrt{2-\sqrt{2}} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)",1,"a*(1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8) - (Sqrt[2 + Sqrt[2]]*a*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 + Sqrt[2]]])/4 - (Sqrt[2 - Sqrt[2]]*a*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 - Sqrt[2]]])/4 + (Sqrt[2 + Sqrt[2]]*a*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 + Sqrt[2]]])/4 + (Sqrt[2 - Sqrt[2]]*a*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 - Sqrt[2]]])/4 + (Sqrt[2 - Sqrt[2]]*a*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/8 - (Sqrt[2 - Sqrt[2]]*a*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/8 + (Sqrt[2 + Sqrt[2]]*a*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/8 - (Sqrt[2 + Sqrt[2]]*a*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/8","A",25,11,14,0.7857,1,"{6171, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
131,1,731,0,0.6586481,"\int \frac{e^{\frac{1}{4} \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^(ArcCoth[a*x]/4)/x^3,x]","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{7/8} \left(\frac{1}{a x}+1\right)^{9/8}+\frac{1}{8} a^2 \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}+\frac{1}{64} \sqrt{2-\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{64} \sqrt{2-\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)+\frac{1}{64} \sqrt{2+\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{64} \sqrt{2+\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{32} \sqrt{2+\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{32} \sqrt{2-\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2-\sqrt{2}}}\right)+\frac{1}{32} \sqrt{2+\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{32} \sqrt{2-\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)","\frac{1}{2} a^2 \left(1-\frac{1}{a x}\right)^{7/8} \left(\frac{1}{a x}+1\right)^{9/8}+\frac{1}{8} a^2 \left(1-\frac{1}{a x}\right)^{7/8} \sqrt[8]{\frac{1}{a x}+1}+\frac{1}{64} \sqrt{2-\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{64} \sqrt{2-\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2-\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)+\frac{1}{64} \sqrt{2+\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}-\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{64} \sqrt{2+\sqrt{2}} a^2 \log \left(\frac{\sqrt[4]{1-\frac{1}{a x}}}{\sqrt[4]{\frac{1}{a x}+1}}+\frac{\sqrt{2+\sqrt{2}} \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+1\right)-\frac{1}{32} \sqrt{2+\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2+\sqrt{2}}}\right)-\frac{1}{32} \sqrt{2-\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}}{\sqrt{2-\sqrt{2}}}\right)+\frac{1}{32} \sqrt{2+\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)+\frac{1}{32} \sqrt{2-\sqrt{2}} a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[8]{1-\frac{1}{a x}}}{\sqrt[8]{\frac{1}{a x}+1}}+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)",1,"(a^2*(1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(1/8))/8 + (a^2*(1 - 1/(a*x))^(7/8)*(1 + 1/(a*x))^(9/8))/2 - (Sqrt[2 + Sqrt[2]]*a^2*ArcTan[(Sqrt[2 - Sqrt[2]] - (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 + Sqrt[2]]])/32 - (Sqrt[2 - Sqrt[2]]*a^2*ArcTan[(Sqrt[2 + Sqrt[2]] - (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 - Sqrt[2]]])/32 + (Sqrt[2 + Sqrt[2]]*a^2*ArcTan[(Sqrt[2 - Sqrt[2]] + (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 + Sqrt[2]]])/32 + (Sqrt[2 - Sqrt[2]]*a^2*ArcTan[(Sqrt[2 + Sqrt[2]] + (2*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8))/Sqrt[2 - Sqrt[2]]])/32 + (Sqrt[2 - Sqrt[2]]*a^2*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) - (Sqrt[2 - Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/64 - (Sqrt[2 - Sqrt[2]]*a^2*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) + (Sqrt[2 - Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/64 + (Sqrt[2 + Sqrt[2]]*a^2*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) - (Sqrt[2 + Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/64 - (Sqrt[2 + Sqrt[2]]*a^2*Log[1 + (1 - 1/(a*x))^(1/4)/(1 + 1/(a*x))^(1/4) + (Sqrt[2 + Sqrt[2]]*(1 - 1/(a*x))^(1/8))/(1 + 1/(a*x))^(1/8)])/64","A",26,12,14,0.8571,1,"{6171, 80, 50, 63, 331, 299, 1122, 1169, 634, 618, 204, 628}"
132,1,45,0,0.0570997,"\int e^{4 \coth ^{-1}(a x)} x^m \, dx","Int[E^(4*ArcCoth[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",5,5,12,0.4167,1,"{6167, 6126, 89, 80, 64}"
133,1,151,0,1.2308588,"\int e^{3 \coth ^{-1}(a x)} x^m \, dx","Int[E^(3*ArcCoth[a*x])*x^m,x]","-\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}+\frac{4 x^m \, _2F_1\left(\frac{3}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}-\frac{3 x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}+\frac{4 x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}","-\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}+\frac{4 x^m \, _2F_1\left(\frac{3}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}-\frac{3 x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}+\frac{4 x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}",1,"(-3*x^(1 + m)*Hypergeometric2F1[1/2, (-1 - m)/2, (1 - m)/2, 1/(a^2*x^2)])/(1 + m) - (x^m*Hypergeometric2F1[1/2, -m/2, 1 - m/2, 1/(a^2*x^2)])/(a*m) + (4*x^(1 + m)*Hypergeometric2F1[3/2, (-1 - m)/2, (1 - m)/2, 1/(a^2*x^2)])/(1 + m) + (4*x^m*Hypergeometric2F1[3/2, -m/2, 1 - m/2, 1/(a^2*x^2)])/(a*m)","A",9,5,12,0.4167,1,"{6172, 6742, 364, 850, 808}"
134,1,35,0,0.0412795,"\int e^{2 \coth ^{-1}(a x)} x^m \, dx","Int[E^(2*ArcCoth[a*x])*x^m,x]","\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}-\frac{2 x^{m+1} \, _2F_1(1,m+1;m+2;a x)}{m+1}",1,"x^(1 + m)/(1 + m) - (2*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/(1 + m)","A",4,4,12,0.3333,1,"{6167, 6126, 80, 64}"
135,1,74,0,0.0615149,"\int e^{\coth ^{-1}(a x)} x^m \, dx","Int[E^ArcCoth[a*x]*x^m,x]","\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}+\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}","\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}+\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, (-1 - m)/2, (1 - m)/2, 1/(a^2*x^2)])/(1 + m) + (x^m*Hypergeometric2F1[1/2, -m/2, 1 - m/2, 1/(a^2*x^2)])/(a*m)","A",4,3,10,0.3000,1,"{6172, 808, 364}"
136,1,75,0,0.0601647,"\int e^{-\coth ^{-1}(a x)} x^m \, dx","Int[x^m/E^ArcCoth[a*x],x]","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}-\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}","\frac{x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}-\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}",1,"(x^(1 + m)*Hypergeometric2F1[1/2, (-1 - m)/2, (1 - m)/2, 1/(a^2*x^2)])/(1 + m) - (x^m*Hypergeometric2F1[1/2, -m/2, 1 - m/2, 1/(a^2*x^2)])/(a*m)","A",4,3,12,0.2500,1,"{6172, 808, 364}"
137,1,36,0,0.0412358,"\int e^{-2 \coth ^{-1}(a x)} x^m \, dx","Int[x^m/E^(2*ArcCoth[a*x]),x]","\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}-\frac{2 x^{m+1} \, _2F_1(1,m+1;m+2;-a x)}{m+1}",1,"x^(1 + m)/(1 + m) - (2*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)])/(1 + m)","A",4,4,12,0.3333,1,"{6167, 6126, 80, 64}"
138,1,150,0,1.0507207,"\int e^{-3 \coth ^{-1}(a x)} x^m \, dx","Int[x^m/E^(3*ArcCoth[a*x]),x]","\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}-\frac{4 x^m \, _2F_1\left(\frac{3}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}-\frac{3 x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}+\frac{4 x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}","\frac{x^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}-\frac{4 x^m \, _2F_1\left(\frac{3}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{a^2 x^2}\right)}{a m}-\frac{3 x^{m+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}+\frac{4 x^{m+1} \, _2F_1\left(\frac{3}{2},\frac{1}{2} (-m-1);\frac{1-m}{2};\frac{1}{a^2 x^2}\right)}{m+1}",1,"(-3*x^(1 + m)*Hypergeometric2F1[1/2, (-1 - m)/2, (1 - m)/2, 1/(a^2*x^2)])/(1 + m) + (x^m*Hypergeometric2F1[1/2, -m/2, 1 - m/2, 1/(a^2*x^2)])/(a*m) + (4*x^(1 + m)*Hypergeometric2F1[3/2, (-1 - m)/2, (1 - m)/2, 1/(a^2*x^2)])/(1 + m) - (4*x^m*Hypergeometric2F1[3/2, -m/2, 1 - m/2, 1/(a^2*x^2)])/(a*m)","A",9,5,12,0.4167,1,"{6172, 6742, 364, 850, 808}"
139,1,41,0,0.0379282,"\int e^{\frac{5}{2} \coth ^{-1}(a x)} x^m \, dx","Int[E^((5*ArcCoth[a*x])/2)*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{5}{4},-\frac{5}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{5}{4},-\frac{5}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, 5/4, -5/4, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
140,1,41,0,0.0381142,"\int e^{\frac{3}{2} \coth ^{-1}(a x)} x^m \, dx","Int[E^((3*ArcCoth[a*x])/2)*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{3}{4},-\frac{3}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{3}{4},-\frac{3}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, 3/4, -3/4, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
141,1,41,0,0.0374394,"\int e^{\frac{1}{2} \coth ^{-1}(a x)} x^m \, dx","Int[E^(ArcCoth[a*x]/2)*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{4},-\frac{1}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{4},-\frac{1}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, 1/4, -1/4, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
142,1,41,0,0.036163,"\int e^{-\frac{1}{2} \coth ^{-1}(a x)} x^m \, dx","Int[x^m/E^(ArcCoth[a*x]/2),x]","\frac{x^{m+1} F_1\left(-m-1;-\frac{1}{4},\frac{1}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;-\frac{1}{4},\frac{1}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, -1/4, 1/4, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
143,1,41,0,0.0372282,"\int e^{-\frac{3}{2} \coth ^{-1}(a x)} x^m \, dx","Int[x^m/E^((3*ArcCoth[a*x])/2),x]","\frac{x^{m+1} F_1\left(-m-1;-\frac{3}{4},\frac{3}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;-\frac{3}{4},\frac{3}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, -3/4, 3/4, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
144,1,41,0,0.0378658,"\int e^{-\frac{5}{2} \coth ^{-1}(a x)} x^m \, dx","Int[x^m/E^((5*ArcCoth[a*x])/2),x]","\frac{x^{m+1} F_1\left(-m-1;-\frac{5}{4},\frac{5}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;-\frac{5}{4},\frac{5}{4};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, -5/4, 5/4, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
145,1,34,0,0.0329036,"\int e^{\frac{2}{3} \coth ^{-1}(x)} x^m \, dx","Int[E^((2*ArcCoth[x])/3)*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{3},-\frac{1}{3};-m;\frac{1}{x},-\frac{1}{x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{3},-\frac{1}{3};-m;\frac{1}{x},-\frac{1}{x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, 1/3, -1/3, -m, x^(-1), -x^(-1)])/(1 + m)","A",2,2,12,0.1667,1,"{6173, 133}"
146,1,34,0,0.0332118,"\int e^{\frac{1}{3} \coth ^{-1}(x)} x^m \, dx","Int[E^(ArcCoth[x]/3)*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{6},-\frac{1}{6};-m;\frac{1}{x},-\frac{1}{x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{6},-\frac{1}{6};-m;\frac{1}{x},-\frac{1}{x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, 1/6, -1/6, -m, x^(-1), -x^(-1)])/(1 + m)","A",2,2,12,0.1667,1,"{6173, 133}"
147,1,41,0,0.0352318,"\int e^{\frac{1}{4} \coth ^{-1}(a x)} x^m \, dx","Int[E^(ArcCoth[a*x]/4)*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{8},-\frac{1}{8};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{1}{8},-\frac{1}{8};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, 1/8, -1/8, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,14,0.1429,1,"{6173, 133}"
148,1,45,0,0.0390925,"\int e^{n \coth ^{-1}(a x)} x^m \, dx","Int[E^(n*ArcCoth[a*x])*x^m,x]","\frac{x^{m+1} F_1\left(-m-1;\frac{n}{2},-\frac{n}{2};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}","\frac{x^{m+1} F_1\left(-m-1;\frac{n}{2},-\frac{n}{2};-m;\frac{1}{a x},-\frac{1}{a x}\right)}{m+1}",1,"(x^(1 + m)*AppellF1[-1 - m, n/2, -n/2, -m, 1/(a*x), -(1/(a*x))])/(1 + m)","A",2,2,12,0.1667,1,"{6173, 133}"
149,1,174,0,0.0923241,"\int e^{n \coth ^{-1}(a x)} x^2 \, dx","Int[E^(n*ArcCoth[a*x])*x^2,x]","\frac{2 \left(n^2+2\right) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{3 a^3 (2-n)}+\frac{1}{3} x^3 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}+\frac{n x^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{6 a}","\frac{2 \left(n^2+2\right) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{3 a^3 (2-n)}+\frac{1}{3} x^3 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}+\frac{n x^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{6 a}",1,"(n*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x^2)/(6*a) + ((1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x^3)/3 + (2*(2 + n^2)*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (a - x^(-1))/(a + x^(-1))])/(3*a^3*(2 - n))","A",5,5,12,0.4167,1,"{6171, 129, 151, 12, 131}"
150,1,122,0,0.0565528,"\int e^{n \coth ^{-1}(a x)} x \, dx","Int[E^(n*ArcCoth[a*x])*x,x]","\frac{2 n \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^2 (2-n)}+\frac{1}{2} x^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}","\frac{2 n \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^2 (2-n)}+\frac{1}{2} x^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}",1,"((1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x^2)/2 + (2*n*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (a - x^(-1))/(a + x^(-1))])/(a^2*(2 - n))","A",3,3,10,0.3000,1,"{6171, 96, 131}"
151,1,78,0,0.0230922,"\int e^{n \coth ^{-1}(a x)} \, dx","Int[E^(n*ArcCoth[a*x]),x]","\frac{4 \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (2-n)}","\frac{4 \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (2-n)}",1,"(4*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(2 - n))","A",2,2,8,0.2500,1,"{6170, 131}"
152,1,127,0,0.0614067,"\int \frac{e^{n \coth ^{-1}(a x)}}{x} \, dx","Int[E^(n*ArcCoth[a*x])/x,x]","\frac{2^{\frac{n}{2}+1} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{n}-\frac{2 \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{n}","\frac{2^{\frac{n}{2}+1} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(-\frac{n}{2},-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{n}-\frac{2 \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{n}",1,"(-2*(1 + 1/(a*x))^(n/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, (a - x^(-1))/(a + x^(-1))])/(n*(1 - 1/(a*x))^(n/2)) + (2^(1 + n/2)*Hypergeometric2F1[-n/2, -n/2, 1 - n/2, (a - x^(-1))/(2*a)])/(n*(1 - 1/(a*x))^(n/2))","A",4,4,12,0.3333,1,"{6171, 105, 69, 131}"
153,1,70,0,0.0336342,"\int \frac{e^{n \coth ^{-1}(a x)}}{x^2} \, dx","Int[E^(n*ArcCoth[a*x])/x^2,x]","\frac{a 2^{\frac{n}{2}+1} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{2-n}","\frac{a 2^{\frac{n}{2}+1} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{2-n}",1,"(2^(1 + n/2)*a*(1 - 1/(a*x))^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (a - x^(-1))/(2*a)])/(2 - n)","A",2,2,12,0.1667,1,"{6171, 69}"
154,1,114,0,0.0560491,"\int \frac{e^{n \coth ^{-1}(a x)}}{x^3} \, dx","Int[E^(n*ArcCoth[a*x])/x^3,x]","\frac{a^2 2^{n/2} n \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{2-n}+\frac{1}{2} a^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}","\frac{a^2 2^{n/2} n \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{2-n}+\frac{1}{2} a^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}",1,"(a^2*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/2 + (2^(n/2)*a^2*n*(1 - 1/(a*x))^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (a - x^(-1))/(2*a)])/(2 - n)","A",3,3,12,0.2500,1,"{6171, 80, 69}"
155,1,167,0,0.1100673,"\int \frac{e^{n \coth ^{-1}(a x)}}{x^4} \, dx","Int[E^(n*ArcCoth[a*x])/x^4,x]","\frac{a^3 2^{n/2} \left(n^2+2\right) \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{3 (2-n)}+\frac{1}{6} a^3 n \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}+\frac{a^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{3 x}","\frac{a^3 2^{n/2} \left(n^2+2\right) \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{3 (2-n)}+\frac{1}{6} a^3 n \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}+\frac{a^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{3 x}",1,"(a^3*n*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/6 + (a^2*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(3*x) + (2^(n/2)*a^3*(2 + n^2)*(1 - 1/(a*x))^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (a - x^(-1))/(2*a)])/(3*(2 - n))","A",4,4,12,0.3333,1,"{6171, 90, 80, 69}"
156,1,183,0,0.1233818,"\int \frac{e^{n \coth ^{-1}(a x)}}{x^5} \, dx","Int[E^(n*ArcCoth[a*x])/x^5,x]","\frac{a^4 2^{\frac{n}{2}-2} n \left(n^2+8\right) \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{3 (2-n)}+\frac{1}{24} a^3 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(a \left(n^2+6\right)+\frac{2 n}{x}\right) \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}+\frac{a^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{4 x^2}","\frac{a^4 2^{\frac{n}{2}-2} n \left(n^2+8\right) \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{3 (2-n)}+\frac{1}{24} a^3 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(a \left(n^2+6\right)+\frac{2 n}{x}\right) \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}+\frac{a^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{4 x^2}",1,"(a^3*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*(a*(6 + n^2) + (2*n)/x))/24 + (a^2*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(4*x^2) + (2^(-2 + n/2)*a^4*n*(8 + n^2)*(1 - 1/(a*x))^(1 - n/2)*Hypergeometric2F1[1 - n/2, -n/2, 2 - n/2, (a - x^(-1))/(2*a)])/(3*(2 - n))","A",4,4,12,0.3333,1,"{6171, 100, 147, 69}"
157,1,143,0,0.1571839,"\int e^{\coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^p,x]","\frac{\sqrt{\frac{1}{a x}+1} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2}-p} (c-a c x)^p \, _2F_1\left(\frac{1}{2}-p,-p;1-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{a p (p+1) \sqrt{1-\frac{1}{a x}}}+\frac{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1} (c-a c x)^p}{p+1}","\frac{\sqrt{\frac{1}{a x}+1} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2}-p} (c-a c x)^p \, _2F_1\left(\frac{1}{2}-p,-p;1-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{a p (p+1) \sqrt{1-\frac{1}{a x}}}+\frac{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1} (c-a c x)^p}{p+1}",1,"(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x*(c - a*c*x)^p)/(1 + p) + (((a - x^(-1))/(a + x^(-1)))^(1/2 - p)*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^p*Hypergeometric2F1[1/2 - p, -p, 1 - p, 2/((a + x^(-1))*x)])/(a*p*(1 + p)*Sqrt[1 - 1/(a*x)])","A",4,4,16,0.2500,1,"{6176, 6181, 94, 132}"
158,1,132,0,0.3028496,"\int e^{\coth ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^4,x]","\frac{1}{5} a^4 c^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{3}{4} a^3 c^4 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{17}{15} a^2 c^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{7}{8} a c^4 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{7 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}","\frac{1}{5} a^4 c^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{3}{4} a^3 c^4 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{17}{15} a^2 c^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{7}{8} a c^4 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{7 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}",1,"(-7*a*c^4*Sqrt[1 - 1/(a^2*x^2)]*x^2)/8 + (17*a^2*c^4*(1 - 1/(a^2*x^2))^(3/2)*x^3)/15 - (3*a^3*c^4*(1 - 1/(a^2*x^2))^(3/2)*x^4)/4 + (a^4*c^4*(1 - 1/(a^2*x^2))^(3/2)*x^5)/5 + (7*c^4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a)","A",9,8,16,0.5000,1,"{6175, 6178, 1807, 807, 266, 47, 63, 208}"
159,1,105,0,0.2255171,"\int e^{\coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^3,x]","-\frac{1}{4} a^3 c^3 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{2}{3} a^2 c^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{5}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{5 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}","-\frac{1}{4} a^3 c^3 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{2}{3} a^2 c^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{5}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{5 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}",1,"(-5*a*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/8 + (2*a^2*c^3*(1 - 1/(a^2*x^2))^(3/2)*x^3)/3 - (a^3*c^3*(1 - 1/(a^2*x^2))^(3/2)*x^4)/4 + (5*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a)","A",8,8,16,0.5000,1,"{6175, 6178, 1807, 807, 266, 47, 63, 208}"
160,1,78,0,0.1362119,"\int e^{\coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^2,x]","\frac{1}{3} a^2 c^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{1}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","\frac{1}{3} a^2 c^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{1}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"-(a*c^2*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (a^2*c^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/3 + (c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",7,7,16,0.4375,1,"{6175, 6178, 807, 266, 47, 63, 208}"
161,1,47,0,0.0706478,"\int e^{\coth ^{-1}(a x)} (c-a c x) \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x),x]","\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}","\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}",1,"-(a*c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",6,6,14,0.4286,1,"{6175, 6178, 266, 47, 63, 208}"
162,1,51,0,0.2062061,"\int \frac{e^{\coth ^{-1}(a x)}}{c-a c x} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x),x]","\frac{2 \left(a+\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","\frac{2 \left(a+\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"(2*(a + x^(-1)))/(a^2*c*Sqrt[1 - 1/(a^2*x^2)]) - ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c)","A",7,7,16,0.4375,1,"{6175, 6178, 852, 1805, 266, 63, 208}"
163,1,33,0,0.0990949,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^2,x]","-\frac{a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 c^2 \left(a-\frac{1}{x}\right)^3}","-\frac{a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 c^2 \left(a-\frac{1}{x}\right)^3}",1,"-(a^2*(1 - 1/(a^2*x^2))^(3/2))/(3*c^2*(a - x^(-1))^3)","A",3,3,16,0.1875,1,"{6175, 6178, 651}"
164,1,67,0,0.1245276,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^3,x]","\frac{a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{5 c^3 \left(a-\frac{1}{x}\right)^4}-\frac{4 a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{15 c^3 \left(a-\frac{1}{x}\right)^3}","\frac{a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{5 c^3 \left(a-\frac{1}{x}\right)^4}-\frac{4 a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{15 c^3 \left(a-\frac{1}{x}\right)^3}",1,"(a^3*(1 - 1/(a^2*x^2))^(3/2))/(5*c^3*(a - x^(-1))^4) - (4*a^2*(1 - 1/(a^2*x^2))^(3/2))/(15*c^3*(a - x^(-1))^3)","A",4,4,16,0.2500,1,"{6175, 6178, 793, 651}"
165,1,100,0,0.2295823,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^4,x]","-\frac{a^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{7 c^4 \left(a-\frac{1}{x}\right)^5}+\frac{12 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{35 c^4 \left(a-\frac{1}{x}\right)^4}-\frac{23 a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 c^4 \left(a-\frac{1}{x}\right)^3}","-\frac{a^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{7 c^4 \left(a-\frac{1}{x}\right)^5}+\frac{12 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{35 c^4 \left(a-\frac{1}{x}\right)^4}-\frac{23 a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 c^4 \left(a-\frac{1}{x}\right)^3}",1,"-(a^4*(1 - 1/(a^2*x^2))^(3/2))/(7*c^4*(a - x^(-1))^5) + (12*a^3*(1 - 1/(a^2*x^2))^(3/2))/(35*c^4*(a - x^(-1))^4) - (23*a^2*(1 - 1/(a^2*x^2))^(3/2))/(105*c^4*(a - x^(-1))^3)","A",6,6,16,0.3750,1,"{6175, 6178, 1639, 793, 659, 651}"
166,1,133,0,0.3423904,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^5,x]","\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{9 c^5 \left(a-\frac{1}{x}\right)^6}-\frac{8 a^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{21 c^5 \left(a-\frac{1}{x}\right)^5}+\frac{47 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 c^5 \left(a-\frac{1}{x}\right)^4}-\frac{58 a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{315 c^5 \left(a-\frac{1}{x}\right)^3}","\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{9 c^5 \left(a-\frac{1}{x}\right)^6}-\frac{8 a^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{21 c^5 \left(a-\frac{1}{x}\right)^5}+\frac{47 a^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 c^5 \left(a-\frac{1}{x}\right)^4}-\frac{58 a^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{315 c^5 \left(a-\frac{1}{x}\right)^3}",1,"(a^5*(1 - 1/(a^2*x^2))^(3/2))/(9*c^5*(a - x^(-1))^6) - (8*a^4*(1 - 1/(a^2*x^2))^(3/2))/(21*c^5*(a - x^(-1))^5) + (47*a^3*(1 - 1/(a^2*x^2))^(3/2))/(105*c^5*(a - x^(-1))^4) - (58*a^2*(1 - 1/(a^2*x^2))^(3/2))/(315*c^5*(a - x^(-1))^3)","A",8,6,16,0.3750,1,"{6175, 6178, 1639, 793, 659, 651}"
167,1,42,0,0.0666535,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^p,x]","\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}-\frac{(c-a c x)^{p+1}}{a c (p+1)}",1,"(2*(c - a*c*x)^p)/(a*p) - (c - a*c*x)^(1 + p)/(a*c*(1 + p))","A",5,4,18,0.2222,1,"{6167, 6130, 21, 43}"
168,1,37,0,0.0597232,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^5 \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^5,x]","\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}-\frac{c^5 (1-a x)^6}{6 a}",1,"(2*c^5*(1 - a*x)^5)/(5*a) - (c^5*(1 - a*x)^6)/(6*a)","A",4,3,18,0.1667,1,"{6167, 6129, 43}"
169,1,37,0,0.0555531,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^4,x]","\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}-\frac{c^4 (1-a x)^5}{5 a}",1,"(c^4*(1 - a*x)^4)/(2*a) - (c^4*(1 - a*x)^5)/(5*a)","A",4,3,18,0.1667,1,"{6167, 6129, 43}"
170,1,37,0,0.0591795,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^3,x]","\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}-\frac{c^3 (1-a x)^4}{4 a}",1,"(2*c^3*(1 - a*x)^3)/(3*a) - (c^3*(1 - a*x)^4)/(4*a)","A",4,3,18,0.1667,1,"{6167, 6129, 43}"
171,1,20,0,0.0482971,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^2,x]","\frac{1}{3} a^2 c^2 x^3-c^2 x","\frac{1}{3} a^2 c^2 x^3-c^2 x",1,"-(c^2*x) + (a^2*c^2*x^3)/3","A",4,3,18,0.1667,1,"{6167, 6129, 41}"
172,1,26,0,0.0120579,"\int e^{2 \coth ^{-1}(a x)} (c-a c x) \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x),x]","\frac{c \left(1-a^2 x^2\right) e^{2 \coth ^{-1}(a x)}}{2 a}","-\frac{1}{2} a c x^2-c x",1,"(c*E^(2*ArcCoth[a*x])*(1 - a^2*x^2))/(2*a)","C",1,1,16,0.06250,1,"{2288}"
173,1,32,0,0.0637809,"\int \frac{e^{2 \coth ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(2*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
174,1,14,0,0.0510269,"\int \frac{e^{2 \coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^(2*ArcCoth[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",3,3,18,0.1667,1,"{6167, 6129, 34}"
175,1,37,0,0.0623262,"\int \frac{e^{2 \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(2*ArcCoth[a*x])/(c - a*c*x)^3,x]","\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}-\frac{2}{3 a c^3 (1-a x)^3}",1,"-2/(3*a*c^3*(1 - a*x)^3) + 1/(2*a*c^3*(1 - a*x)^2)","A",4,3,18,0.1667,1,"{6167, 6129, 43}"
176,1,37,0,0.0607729,"\int \frac{e^{2 \coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(2*ArcCoth[a*x])/(c - a*c*x)^4,x]","\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}-\frac{1}{2 a c^4 (1-a x)^4}",1,"-1/(2*a*c^4*(1 - a*x)^4) + 1/(3*a*c^4*(1 - a*x)^3)","A",4,3,18,0.1667,1,"{6167, 6129, 43}"
177,1,202,0,0.2060493,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^p,x]","-\frac{3 \sqrt{\frac{1}{a x}+1} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{3}{2}-p} (c-a c x)^p \, _2F_1\left(1-p,\frac{3}{2}-p;2-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{a^2 p \left(1-p^2\right) x \left(1-\frac{1}{a x}\right)^{3/2}}+\frac{x \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^p}{(p+1) \sqrt{1-\frac{1}{a x}}}+\frac{3 \sqrt{\frac{1}{a x}+1} (c-a c x)^p}{a p (p+1) \sqrt{1-\frac{1}{a x}}}","-\frac{3 \sqrt{\frac{1}{a x}+1} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{3}{2}-p} (c-a c x)^p \, _2F_1\left(1-p,\frac{3}{2}-p;2-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{a^2 p \left(1-p^2\right) x \left(1-\frac{1}{a x}\right)^{3/2}}+\frac{x \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^p}{(p+1) \sqrt{1-\frac{1}{a x}}}+\frac{3 \sqrt{\frac{1}{a x}+1} (c-a c x)^p}{a p (p+1) \sqrt{1-\frac{1}{a x}}}",1,"(3*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^p)/(a*p*(1 + p)*Sqrt[1 - 1/(a*x)]) + ((1 + 1/(a*x))^(3/2)*x*(c - a*c*x)^p)/((1 + p)*Sqrt[1 - 1/(a*x)]) - (3*((a - x^(-1))/(a + x^(-1)))^(3/2 - p)*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^p*Hypergeometric2F1[1 - p, 3/2 - p, 2 - p, 2/((a + x^(-1))*x)])/(a^2*p*(1 - p^2)*(1 - 1/(a*x))^(3/2)*x)","A",5,4,18,0.2222,1,"{6176, 6181, 94, 132}"
178,1,105,0,0.1656611,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^4,x]","\frac{1}{5} a^4 c^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}-\frac{1}{4} a^3 c^4 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{3}{8} a c^4 x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}","\frac{1}{5} a^4 c^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}-\frac{1}{4} a^3 c^4 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{3}{8} a c^4 x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}",1,"(3*a*c^4*Sqrt[1 - 1/(a^2*x^2)]*x^2)/8 - (a^3*c^4*(1 - 1/(a^2*x^2))^(3/2)*x^4)/4 + (a^4*c^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/5 - (3*c^4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a)","A",8,7,18,0.3889,1,"{6175, 6178, 807, 266, 47, 63, 208}"
179,1,78,0,0.1413547,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^3,x]","-\frac{1}{4} a^3 c^3 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{3}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}","-\frac{1}{4} a^3 c^3 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{3}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}",1,"(3*a*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/8 - (a^3*c^3*(1 - 1/(a^2*x^2))^(3/2)*x^4)/4 - (3*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a)","A",7,6,18,0.3333,1,"{6175, 6178, 266, 47, 63, 208}"
180,1,78,0,0.1700044,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^2,x]","\frac{1}{3} a^2 c^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{1}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","\frac{1}{3} a^2 c^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{1}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"(a*c^2*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (a^2*c^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/3 - (c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",8,8,18,0.4444,1,"{6175, 6178, 850, 807, 266, 47, 63, 208}"
181,1,65,0,0.1854701,"\int e^{3 \coth ^{-1}(a x)} (c-a c x) \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x),x]","-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}-2 c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}-2 c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"-2*c*Sqrt[1 - 1/(a^2*x^2)]*x - (a*c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 - (3*c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",8,8,16,0.5000,1,"{6175, 6178, 852, 1807, 807, 266, 63, 208}"
182,1,80,0,0.2840559,"\int \frac{e^{3 \coth ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x),x]","\frac{8 \left(a+\frac{1}{x}\right)}{3 a^2 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}+\frac{4}{3 a^2 c x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","\frac{8 \left(a+\frac{1}{x}\right)}{3 a^2 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}+\frac{4}{3 a^2 c x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"(8*(a + x^(-1)))/(3*a^2*c*(1 - 1/(a^2*x^2))^(3/2)) + 4/(3*a^2*c*Sqrt[1 - 1/(a^2*x^2)]*x) - ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c)","A",9,8,18,0.4444,1,"{6175, 6178, 852, 1805, 12, 266, 63, 208}"
183,1,33,0,0.1051901,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^2,x]","-\frac{a^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{5 c^2 \left(a-\frac{1}{x}\right)^5}","-\frac{a^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{5 c^2 \left(a-\frac{1}{x}\right)^5}",1,"-(a^4*(1 - 1/(a^2*x^2))^(5/2))/(5*c^2*(a - x^(-1))^5)","A",3,3,18,0.1667,1,"{6175, 6178, 651}"
184,1,67,0,0.1340015,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^3,x]","\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{7 c^3 \left(a-\frac{1}{x}\right)^6}-\frac{6 a^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{35 c^3 \left(a-\frac{1}{x}\right)^5}","\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{7 c^3 \left(a-\frac{1}{x}\right)^6}-\frac{6 a^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{35 c^3 \left(a-\frac{1}{x}\right)^5}",1,"(a^5*(1 - 1/(a^2*x^2))^(5/2))/(7*c^3*(a - x^(-1))^6) - (6*a^4*(1 - 1/(a^2*x^2))^(5/2))/(35*c^3*(a - x^(-1))^5)","A",4,4,18,0.2222,1,"{6175, 6178, 793, 651}"
185,1,94,0,0.2752228,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^4,x]","-\frac{\left(a+\frac{1}{x}\right)^7}{9 a^8 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{16 \left(a+\frac{1}{x}\right)^6}{63 a^7 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{47 \left(a+\frac{1}{x}\right)^5}{315 a^6 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}","-\frac{\left(a+\frac{1}{x}\right)^7}{9 a^8 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{16 \left(a+\frac{1}{x}\right)^6}{63 a^7 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{47 \left(a+\frac{1}{x}\right)^5}{315 a^6 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}",1,"(-47*(a + x^(-1))^5)/(315*a^6*c^4*(1 - 1/(a^2*x^2))^(5/2)) + (16*(a + x^(-1))^6)/(63*a^7*c^4*(1 - 1/(a^2*x^2))^(7/2)) - (a + x^(-1))^7/(9*a^8*c^4*(1 - 1/(a^2*x^2))^(9/2))","A",6,6,18,0.3333,1,"{6175, 6178, 852, 1635, 789, 651}"
186,1,125,0,0.3890615,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^5,x]","\frac{\left(a+\frac{1}{x}\right)^8}{11 a^9 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{11/2}}-\frac{10 \left(a+\frac{1}{x}\right)^7}{33 a^8 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{79 \left(a+\frac{1}{x}\right)^6}{231 a^7 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{152 \left(a+\frac{1}{x}\right)^5}{1155 a^6 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}","\frac{\left(a+\frac{1}{x}\right)^8}{11 a^9 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{11/2}}-\frac{10 \left(a+\frac{1}{x}\right)^7}{33 a^8 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{79 \left(a+\frac{1}{x}\right)^6}{231 a^7 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{152 \left(a+\frac{1}{x}\right)^5}{1155 a^6 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}",1,"(-152*(a + x^(-1))^5)/(1155*a^6*c^5*(1 - 1/(a^2*x^2))^(5/2)) + (79*(a + x^(-1))^6)/(231*a^7*c^5*(1 - 1/(a^2*x^2))^(7/2)) - (10*(a + x^(-1))^7)/(33*a^8*c^5*(1 - 1/(a^2*x^2))^(9/2)) + (a + x^(-1))^8/(11*a^9*c^5*(1 - 1/(a^2*x^2))^(11/2))","A",7,6,18,0.3333,1,"{6175, 6178, 852, 1635, 789, 651}"
187,1,66,0,0.0810893,"\int e^{4 \coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(4*ArcCoth[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",5,4,18,0.2222,1,"{6167, 6130, 21, 43}"
188,1,53,0,0.0680539,"\int e^{4 \coth ^{-1}(a x)} (c-a c x)^5 \, dx","Int[E^(4*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
189,1,32,0,0.0550847,"\int e^{4 \coth ^{-1}(a x)} (c-a c x)^4 \, dx","Int[E^(4*ArcCoth[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",5,4,18,0.2222,1,"{6167, 6129, 41, 194}"
190,1,35,0,0.0585238,"\int e^{4 \coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(4*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
191,1,17,0,0.0464065,"\int e^{4 \coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(4*ArcCoth[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",3,3,18,0.1667,1,"{6167, 6129, 32}"
192,1,27,0,0.0366372,"\int e^{4 \coth ^{-1}(a x)} (c-a c x) \, dx","Int[E^(4*ArcCoth[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",4,3,16,0.1875,1,"{6167, 6129, 43}"
193,1,48,0,0.0677062,"\int \frac{e^{4 \coth ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(4*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
194,1,25,0,0.0504695,"\int \frac{e^{4 \coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^(4*ArcCoth[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",3,3,18,0.1667,1,"{6167, 6129, 37}"
195,1,52,0,0.0680686,"\int \frac{e^{4 \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(4*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
196,1,53,0,0.0669647,"\int \frac{e^{4 \coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(4*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
197,1,94,0,0.1217307,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^ArcCoth[a*x],x]","\frac{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{1}{2}} (c-a c x)^p \, _2F_1\left(-p-1,-p-\frac{1}{2};-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{p+1}","\frac{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{1}{2}} (c-a c x)^p \, _2F_1\left(-p-1,-p-\frac{1}{2};-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^(-1/2 - p)*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x*(c - a*c*x)^p*Hypergeometric2F1[-1 - p, -1/2 - p, -p, 2/((a + x^(-1))*x)])/(1 + p)","A",3,3,18,0.1667,1,"{6176, 6181, 132}"
198,1,127,0,0.3517609,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[(c - a*c*x)^3/E^ArcCoth[a*x],x]","-\frac{1}{4} a^3 c^3 x^4 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{4}{3} a^2 c^3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{27}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{20}{3} c^3 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{35 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}","-\frac{1}{4} a^3 c^3 x^4 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{4}{3} a^2 c^3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{27}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{20}{3} c^3 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{35 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}",1,"(20*c^3*Sqrt[1 - 1/(a^2*x^2)]*x)/3 - (27*a*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/8 + (4*a^2*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 - (a^3*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^4)/4 - (35*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a)","A",9,7,18,0.3889,1,"{6175, 6178, 1807, 807, 266, 63, 208}"
199,1,100,0,0.2861644,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[(c - a*c*x)^2/E^ArcCoth[a*x],x]","\frac{1}{3} a^2 c^2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{11}{3} c^2 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{5 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","\frac{1}{3} a^2 c^2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{11}{3} c^2 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{5 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"(11*c^2*Sqrt[1 - 1/(a^2*x^2)]*x)/3 - (3*a*c^2*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (a^2*c^2*Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 - (5*c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",8,7,18,0.3889,1,"{6175, 6178, 1807, 807, 266, 63, 208}"
200,1,65,0,0.1670514,"\int e^{-\coth ^{-1}(a x)} (c-a c x) \, dx","Int[(c - a*c*x)/E^ArcCoth[a*x],x]","-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}+2 c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}+2 c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"2*c*Sqrt[1 - 1/(a^2*x^2)]*x - (a*c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 - (3*c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",7,7,16,0.4375,1,"{6175, 6178, 1807, 807, 266, 63, 208}"
201,1,23,0,0.1006352,"\int \frac{e^{-\coth ^{-1}(a x)}}{c-a c x} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)),x]","-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"-(ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c))","A",5,5,18,0.2778,1,"{6175, 6178, 266, 63, 208}"
202,1,28,0,0.1011266,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^2),x]","-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \left(a-\frac{1}{x}\right)}","-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \left(a-\frac{1}{x}\right)}",1,"-(Sqrt[1 - 1/(a^2*x^2)]/(c^2*(a - x^(-1))))","A",3,3,18,0.1667,1,"{6175, 6178, 651}"
203,1,62,0,0.1252375,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^3),x]","\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{3 c^3 \left(a-\frac{1}{x}\right)^2}-\frac{2 \sqrt{1-\frac{1}{a^2 x^2}}}{3 c^3 \left(a-\frac{1}{x}\right)}","\frac{a \sqrt{1-\frac{1}{a^2 x^2}}}{3 c^3 \left(a-\frac{1}{x}\right)^2}-\frac{2 \sqrt{1-\frac{1}{a^2 x^2}}}{3 c^3 \left(a-\frac{1}{x}\right)}",1,"(a*Sqrt[1 - 1/(a^2*x^2)])/(3*c^3*(a - x^(-1))^2) - (2*Sqrt[1 - 1/(a^2*x^2)])/(3*c^3*(a - x^(-1)))","A",4,4,18,0.2222,1,"{6175, 6178, 793, 651}"
204,1,95,0,0.2292058,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^4),x]","-\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{5 c^4 \left(a-\frac{1}{x}\right)^3}+\frac{8 a \sqrt{1-\frac{1}{a^2 x^2}}}{15 c^4 \left(a-\frac{1}{x}\right)^2}-\frac{7 \sqrt{1-\frac{1}{a^2 x^2}}}{15 c^4 \left(a-\frac{1}{x}\right)}","-\frac{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{5 c^4 \left(a-\frac{1}{x}\right)^3}+\frac{8 a \sqrt{1-\frac{1}{a^2 x^2}}}{15 c^4 \left(a-\frac{1}{x}\right)^2}-\frac{7 \sqrt{1-\frac{1}{a^2 x^2}}}{15 c^4 \left(a-\frac{1}{x}\right)}",1,"-(a^2*Sqrt[1 - 1/(a^2*x^2)])/(5*c^4*(a - x^(-1))^3) + (8*a*Sqrt[1 - 1/(a^2*x^2)])/(15*c^4*(a - x^(-1))^2) - (7*Sqrt[1 - 1/(a^2*x^2)])/(15*c^4*(a - x^(-1)))","A",6,6,18,0.3333,1,"{6175, 6178, 1639, 793, 659, 651}"
205,1,128,0,0.2545139,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^5),x]","\frac{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}{7 c^5 \left(a-\frac{1}{x}\right)^4}-\frac{18 a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{35 c^5 \left(a-\frac{1}{x}\right)^3}+\frac{23 a \sqrt{1-\frac{1}{a^2 x^2}}}{35 c^5 \left(a-\frac{1}{x}\right)^2}-\frac{12 \sqrt{1-\frac{1}{a^2 x^2}}}{35 c^5 \left(a-\frac{1}{x}\right)}","\frac{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}{7 c^5 \left(a-\frac{1}{x}\right)^4}-\frac{18 a^2 \sqrt{1-\frac{1}{a^2 x^2}}}{35 c^5 \left(a-\frac{1}{x}\right)^3}+\frac{23 a \sqrt{1-\frac{1}{a^2 x^2}}}{35 c^5 \left(a-\frac{1}{x}\right)^2}-\frac{12 \sqrt{1-\frac{1}{a^2 x^2}}}{35 c^5 \left(a-\frac{1}{x}\right)}",1,"(a^3*Sqrt[1 - 1/(a^2*x^2)])/(7*c^5*(a - x^(-1))^4) - (18*a^2*Sqrt[1 - 1/(a^2*x^2)])/(35*c^5*(a - x^(-1))^3) + (23*a*Sqrt[1 - 1/(a^2*x^2)])/(35*c^5*(a - x^(-1))^2) - (12*Sqrt[1 - 1/(a^2*x^2)])/(35*c^5*(a - x^(-1)))","A",7,6,18,0.3333,1,"{6175, 6178, 1639, 793, 659, 651}"
206,1,44,0,0.0617144,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^(2*ArcCoth[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",4,4,18,0.2222,1,"{6167, 6130, 21, 68}"
207,1,91,0,0.0706506,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^4 \, dx","Int[(c - a*c*x)^4/E^(2*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
208,1,73,0,0.0645011,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[(c - a*c*x)^3/E^(2*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
209,1,55,0,0.0582331,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[(c - a*c*x)^2/E^(2*ArcCoth[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",4,3,18,0.1667,1,"{6167, 6129, 43}"
210,1,26,0,0.0350002,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x) \, dx","Int[(c - a*c*x)/E^(2*ArcCoth[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",4,3,16,0.1875,1,"{6167, 6129, 43}"
211,1,14,0,0.0546414,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{c-a c x} \, dx","Int[1/(E^(2*ArcCoth[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",3,3,18,0.1667,1,"{6167, 6129, 31}"
212,1,12,0,0.0487918,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[1/(E^(2*ArcCoth[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",4,4,18,0.2222,1,"{6167, 6129, 35, 206}"
213,1,33,0,0.0626256,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,18,0.2222,1,"{6167, 6129, 44, 207}"
214,1,51,0,0.0675194,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,18,0.2222,1,"{6167, 6129, 44, 207}"
215,1,69,0,0.0796972,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,18,0.2222,1,"{6167, 6129, 44, 207}"
216,1,94,0,0.1255349,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[(c - a*c*x)^p/E^(3*ArcCoth[a*x]),x]","\frac{x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{3}{2}} (c-a c x)^p \, _2F_1\left(-p-\frac{3}{2},-p-1;-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{(p+1) \sqrt{\frac{1}{a x}+1}}","\frac{x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{3}{2}} (c-a c x)^p \, _2F_1\left(-p-\frac{3}{2},-p-1;-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{(p+1) \sqrt{\frac{1}{a x}+1}}",1,"(((a - x^(-1))/(a + x^(-1)))^(-3/2 - p)*(1 - 1/(a*x))^(3/2)*x*(c - a*c*x)^p*Hypergeometric2F1[-3/2 - p, -1 - p, -p, 2/((a + x^(-1))*x)])/((1 + p)*Sqrt[1 + 1/(a*x)])","A",3,3,18,0.1667,1,"{6176, 6181, 132}"
217,1,152,0,0.43646,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[(c - a*c*x)^3/E^(3*ArcCoth[a*x]),x]","-\frac{1}{4} a^3 c^3 x^4 \sqrt{1-\frac{1}{a^2 x^2}}+2 a^2 c^3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{67}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+30 c^3 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{32 c^3 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{315 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}","-\frac{1}{4} a^3 c^3 x^4 \sqrt{1-\frac{1}{a^2 x^2}}+2 a^2 c^3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{67}{8} a c^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+30 c^3 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{32 c^3 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{315 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{8 a}",1,"(32*c^3*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + 30*c^3*Sqrt[1 - 1/(a^2*x^2)]*x - (67*a*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^2)/8 + 2*a^2*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^3 - (a^3*c^3*Sqrt[1 - 1/(a^2*x^2)]*x^4)/4 - (315*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(8*a)","A",10,8,18,0.4444,1,"{6175, 6178, 1805, 1807, 807, 266, 63, 208}"
218,1,129,0,0.3496696,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[(c - a*c*x)^2/E^(3*ArcCoth[a*x]),x]","\frac{1}{3} a^2 c^2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{5}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{35}{3} c^2 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{16 c^2 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{35 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","\frac{1}{3} a^2 c^2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}-\frac{5}{2} a c^2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}+\frac{35}{3} c^2 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{16 c^2 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{35 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"(16*c^2*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + (35*c^2*Sqrt[1 - 1/(a^2*x^2)]*x)/3 - (5*a*c^2*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 + (a^2*c^2*Sqrt[1 - 1/(a^2*x^2)]*x^3)/3 - (35*c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",9,8,18,0.4444,1,"{6175, 6178, 1805, 1807, 807, 266, 63, 208}"
219,1,92,0,0.2437975,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x) \, dx","Int[(c - a*c*x)/E^(3*ArcCoth[a*x]),x]","-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}+4 c x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{8 c \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{15 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}","-\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a^2 x^2}}+4 c x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{8 c \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{15 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{2 a}",1,"(8*c*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + 4*c*Sqrt[1 - 1/(a^2*x^2)]*x - (a*c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/2 - (15*c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(2*a)","A",8,8,16,0.5000,1,"{6175, 6178, 1805, 1807, 807, 266, 63, 208}"
220,1,53,0,0.1982964,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{c-a c x} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)),x]","\frac{2 \left(a-\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","\frac{2 \left(a-\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"(2*(a - x^(-1)))/(a^2*c*Sqrt[1 - 1/(a^2*x^2)]) - ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c)","A",6,6,18,0.3333,1,"{6175, 6178, 1805, 266, 63, 208}"
221,1,28,0,0.1037641,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^2),x]","\frac{a-\frac{1}{x}}{a^2 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{a-\frac{1}{x}}{a^2 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(a - x^(-1))/(a^2*c^2*Sqrt[1 - 1/(a^2*x^2)])","A",3,3,18,0.1667,1,"{6175, 6178, 637}"
222,1,21,0,0.1006883,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^3),x]","\frac{1}{a c^3 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{1}{a c^3 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"1/(a*c^3*Sqrt[1 - 1/(a^2*x^2)])","A",3,3,18,0.1667,1,"{6175, 6178, 261}"
223,1,61,0,0.1366967,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^4),x]","\frac{2}{3 a c^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{1}{3 a^2 c^4 x^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(a-\frac{1}{x}\right)}","\frac{2}{3 a c^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{1}{3 a^2 c^4 x^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(a-\frac{1}{x}\right)}",1,"2/(3*a*c^4*Sqrt[1 - 1/(a^2*x^2)]) - 1/(3*a^2*c^4*Sqrt[1 - 1/(a^2*x^2)]*(a - x^(-1))*x^2)","A",5,5,18,0.2778,1,"{6175, 6178, 855, 12, 261}"
224,1,94,0,0.3127662,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^5} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^5),x]","\frac{\left(a+\frac{1}{x}\right)^2}{5 a^3 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 \left(a+\frac{1}{x}\right)}{5 a^2 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}+\frac{5 a+\frac{2}{x}}{5 a^2 c^5 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\left(a+\frac{1}{x}\right)^2}{5 a^3 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 \left(a+\frac{1}{x}\right)}{5 a^2 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}+\frac{5 a+\frac{2}{x}}{5 a^2 c^5 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-4*(a + x^(-1)))/(5*a^2*c^5*(1 - 1/(a^2*x^2))^(3/2)) + (a + x^(-1))^2/(5*a^3*c^5*(1 - 1/(a^2*x^2))^(5/2)) + (5*a + 2/x)/(5*a^2*c^5*Sqrt[1 - 1/(a^2*x^2)])","A",6,5,18,0.2778,1,"{6175, 6178, 852, 1635, 637}"
225,1,125,0,0.4105545,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^6} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^6),x]","-\frac{\left(a+\frac{1}{x}\right)^3}{7 a^4 c^6 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{24 \left(a+\frac{1}{x}\right)^2}{35 a^3 c^6 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{46 \left(a+\frac{1}{x}\right)}{35 a^2 c^6 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}+\frac{35 a+\frac{13}{x}}{35 a^2 c^6 \sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{\left(a+\frac{1}{x}\right)^3}{7 a^4 c^6 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{24 \left(a+\frac{1}{x}\right)^2}{35 a^3 c^6 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{46 \left(a+\frac{1}{x}\right)}{35 a^2 c^6 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}+\frac{35 a+\frac{13}{x}}{35 a^2 c^6 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-46*(a + x^(-1)))/(35*a^2*c^6*(1 - 1/(a^2*x^2))^(3/2)) + (24*(a + x^(-1))^2)/(35*a^3*c^6*(1 - 1/(a^2*x^2))^(5/2)) - (a + x^(-1))^3/(7*a^4*c^6*(1 - 1/(a^2*x^2))^(7/2)) + (35*a + 13/x)/(35*a^2*c^6*Sqrt[1 - 1/(a^2*x^2)])","A",7,5,18,0.2778,1,"{6175, 6178, 852, 1635, 637}"
226,1,254,0,0.2208077,"\int e^{\coth ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^(9/2),x]","-\frac{768 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{385 a^3 x^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{9088 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{3465 a^4 x^3 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{32 \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{99 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{2 x \left(a-\frac{1}{x}\right)^4 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{11 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{128 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{231 a^2 x \left(1-\frac{1}{a x}\right)^{9/2}}","-\frac{768 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{385 a^3 x^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{9088 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{3465 a^4 x^3 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{32 \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{99 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{2 x \left(a-\frac{1}{x}\right)^4 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{11 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{128 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{9/2}}{231 a^2 x \left(1-\frac{1}{a x}\right)^{9/2}}",1,"(-32*(a - x^(-1))^3*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(9/2))/(99*a^4*(1 - 1/(a*x))^(9/2)) + (9088*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(9/2))/(3465*a^4*(1 - 1/(a*x))^(9/2)*x^3) - (768*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(9/2))/(385*a^3*(1 - 1/(a*x))^(9/2)*x^2) + (128*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(9/2))/(231*a^2*(1 - 1/(a*x))^(9/2)*x) + (2*(a - x^(-1))^4*(1 + 1/(a*x))^(3/2)*x*(c - a*c*x)^(9/2))/(11*a^4*(1 - 1/(a*x))^(9/2))","A",7,6,18,0.3333,1,"{6176, 6181, 94, 89, 78, 37}"
227,1,197,0,0.1897353,"\int e^{\coth ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^(7/2),x]","-\frac{568 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{315 a^3 x^2 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{2 x \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{9 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{48 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{35 a^2 x \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{8 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{21 a \left(1-\frac{1}{a x}\right)^{7/2}}","-\frac{568 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{315 a^3 x^2 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{2 x \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{9 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{48 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{35 a^2 x \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{8 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{7/2}}{21 a \left(1-\frac{1}{a x}\right)^{7/2}}",1,"(-8*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(7/2))/(21*a*(1 - 1/(a*x))^(7/2)) - (568*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(7/2))/(315*a^3*(1 - 1/(a*x))^(7/2)*x^2) + (48*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(7/2))/(35*a^2*(1 - 1/(a*x))^(7/2)*x) + (2*(a - x^(-1))^3*(1 + 1/(a*x))^(3/2)*x*(c - a*c*x)^(7/2))/(9*a^3*(1 - 1/(a*x))^(7/2))","A",6,6,18,0.3333,1,"{6176, 6181, 94, 89, 78, 37}"
228,1,137,0,0.1711918,"\int e^{\coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^(5/2),x]","\frac{142 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{5/2}}{105 a^2 x \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{36 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{5/2}}{35 a \left(1-\frac{1}{a x}\right)^{5/2}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{5/2}}{7 \left(1-\frac{1}{a x}\right)^{5/2}}","\frac{64 a^2 c^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 (c-a c x)^{3/2}}+\frac{16 a^2 c^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{35 \sqrt{c-a c x}}+\frac{2}{7} a^2 c^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \sqrt{c-a c x}",1,"(-36*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(5/2))/(35*a*(1 - 1/(a*x))^(5/2)) + (142*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(5/2))/(105*a^2*(1 - 1/(a*x))^(5/2)*x) + (2*(1 + 1/(a*x))^(3/2)*x*(c - a*c*x)^(5/2))/(7*(1 - 1/(a*x))^(5/2))","A",5,5,18,0.2778,0,"{6176, 6181, 89, 78, 37}"
229,1,89,0,0.1580098,"\int e^{\coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^ArcCoth[a*x]*(c - a*c*x)^(3/2),x]","\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{3/2}}{5 \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{14 \left(\frac{1}{a x}+1\right)^{3/2} (c-a c x)^{3/2}}{15 a \left(1-\frac{1}{a x}\right)^{3/2}}","\frac{2 a^2 c^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{5 \sqrt{c-a c x}}+\frac{8 a^2 c^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{15 (c-a c x)^{3/2}}",1,"(-14*(1 + 1/(a*x))^(3/2)*(c - a*c*x)^(3/2))/(15*a*(1 - 1/(a*x))^(3/2)) + (2*(1 + 1/(a*x))^(3/2)*x*(c - a*c*x)^(3/2))/(5*(1 - 1/(a*x))^(3/2))","A",4,4,18,0.2222,0,"{6176, 6181, 78, 37}"
230,1,29,0,0.0341808,"\int e^{\coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - a*c*x],x]","\frac{2 (a x+1) \sqrt{c-a c x} e^{\coth ^{-1}(a x)}}{3 a}","\frac{2 (a x+1) \sqrt{c-a c x} e^{\coth ^{-1}(a x)}}{3 a}",1,"(2*E^ArcCoth[a*x]*(1 + a*x)*Sqrt[c - a*c*x])/(3*a)","A",1,1,18,0.05556,1,"{6174}"
231,1,118,0,0.1664919,"\int \frac{e^{\coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^ArcCoth[a*x]/Sqrt[c - a*c*x],x]","\frac{2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\sqrt{c-a c x}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x}}","\frac{2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\sqrt{c-a c x}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x}}",1,"(2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/Sqrt[c - a*c*x] - (2*Sqrt[2]*Sqrt[1 - 1/(a*x)]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x])","A",5,5,18,0.2778,1,"{6176, 6181, 94, 93, 206}"
232,1,128,0,0.1849567,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^(3/2),x]","-\frac{a x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(a-\frac{1}{x}\right) (c-a c x)^{3/2}}-\frac{\sqrt{a} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{2} \left(\frac{1}{x}\right)^{3/2} (c-a c x)^{3/2}}","-\frac{a x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(a-\frac{1}{x}\right) (c-a c x)^{3/2}}-\frac{\sqrt{a} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{2} \left(\frac{1}{x}\right)^{3/2} (c-a c x)^{3/2}}",1,"-((a*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))*(c - a*c*x)^(3/2))) - (Sqrt[a]*(1 - 1/(a*x))^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(Sqrt[2]*(x^(-1))^(3/2)*(c - a*c*x)^(3/2))","A",5,5,18,0.2778,1,"{6176, 6181, 94, 93, 206}"
233,1,193,0,0.2019126,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^(5/2),x]","-\frac{a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}{4 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{5/2}}+\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{8 \left(a-\frac{1}{x}\right) (c-a c x)^{5/2}}+\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{8 \sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}","-\frac{a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}{4 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{5/2}}+\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{8 \left(a-\frac{1}{x}\right) (c-a c x)^{5/2}}+\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{8 \sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}",1,"(a^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x^2)/(8*(a - x^(-1))*(c - a*c*x)^(5/2)) - (a^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)*x^2)/(4*(a - x^(-1))^2*(c - a*c*x)^(5/2)) + (a^(3/2)*(1 - 1/(a*x))^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(8*Sqrt[2]*(x^(-1))^(5/2)*(c - a*c*x)^(5/2))","A",6,5,18,0.2778,1,"{6176, 6181, 94, 93, 206}"
234,1,250,0,0.2208502,"\int \frac{e^{\coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a*c*x)^(7/2),x]","\frac{a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}{16 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{7/2}}-\frac{a^4 x^2 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}{6 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}-\frac{a^3 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}{32 \left(a-\frac{1}{x}\right) (c-a c x)^{7/2}}-\frac{a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{32 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}","\frac{a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}{16 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{7/2}}-\frac{a^4 x^2 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}{6 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}-\frac{a^3 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}{32 \left(a-\frac{1}{x}\right) (c-a c x)^{7/2}}-\frac{a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{32 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}",1,"-(a^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(3/2)*x^2)/(6*(a - x^(-1))^3*(c - a*c*x)^(7/2)) - (a^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^3)/(32*(a - x^(-1))*(c - a*c*x)^(7/2)) + (a^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(3/2)*x^3)/(16*(a - x^(-1))^2*(c - a*c*x)^(7/2)) - (a^(5/2)*(1 - 1/(a*x))^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(32*Sqrt[2]*(x^(-1))^(7/2)*(c - a*c*x)^(7/2))","A",7,5,18,0.2778,1,"{6176, 6181, 94, 93, 206}"
235,1,40,0,0.0876759,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^(7/2),x]","\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}-\frac{2 (c-a c x)^{9/2}}{9 a c}",1,"(4*(c - a*c*x)^(7/2))/(7*a) - (2*(c - a*c*x)^(9/2))/(9*a*c)","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
236,1,40,0,0.0876669,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^(5/2),x]","\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}-\frac{2 (c-a c x)^{7/2}}{7 a c}",1,"(4*(c - a*c*x)^(5/2))/(5*a) - (2*(c - a*c*x)^(7/2))/(7*a*c)","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
237,1,40,0,0.0891647,"\int e^{2 \coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^(2*ArcCoth[a*x])*(c - a*c*x)^(3/2),x]","\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}-\frac{2 (c-a c x)^{5/2}}{5 a c}",1,"(4*(c - a*c*x)^(3/2))/(3*a) - (2*(c - a*c*x)^(5/2))/(5*a*c)","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
238,1,38,0,0.0781572,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(2*ArcCoth[a*x])*Sqrt[c - a*c*x],x]","\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}-\frac{2 (c-a c x)^{3/2}}{3 a c}",1,"(4*Sqrt[c - a*c*x])/a - (2*(c - a*c*x)^(3/2))/(3*a*c)","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
239,1,36,0,0.0839535,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^(2*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
240,1,38,0,0.0859509,"\int \frac{e^{2 \coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^(2*ArcCoth[a*x])/(c - a*c*x)^(3/2),x]","\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}}-\frac{4}{3 a (c-a c x)^{3/2}}",1,"-4/(3*a*(c - a*c*x)^(3/2)) + 2/(a*c*Sqrt[c - a*c*x])","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
241,1,40,0,0.0886908,"\int \frac{e^{2 \coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^(2*ArcCoth[a*x])/(c - a*c*x)^(5/2),x]","\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}}-\frac{4}{5 a (c-a c x)^{5/2}}",1,"-4/(5*a*(c - a*c*x)^(5/2)) + 2/(3*a*c*(c - a*c*x)^(3/2))","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
242,1,40,0,0.0863602,"\int \frac{e^{2 \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^(2*ArcCoth[a*x])/(c - a*c*x)^(7/2),x]","\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}}-\frac{4}{7 a (c-a c x)^{7/2}}",1,"-4/(7*a*(c - a*c*x)^(7/2)) + 2/(5*a*c*(c - a*c*x)^(5/2))","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
243,1,197,0,0.1926785,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^(9/2),x]","-\frac{856 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{1155 a^3 x^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{2 x \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{11 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{16 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{21 a^2 x \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{8 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{33 a \left(1-\frac{1}{a x}\right)^{9/2}}","-\frac{856 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{1155 a^3 x^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{2 x \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{11 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{16 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{21 a^2 x \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{8 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{9/2}}{33 a \left(1-\frac{1}{a x}\right)^{9/2}}",1,"(-8*(1 + 1/(a*x))^(5/2)*(c - a*c*x)^(9/2))/(33*a*(1 - 1/(a*x))^(9/2)) - (856*(1 + 1/(a*x))^(5/2)*(c - a*c*x)^(9/2))/(1155*a^3*(1 - 1/(a*x))^(9/2)*x^2) + (16*(1 + 1/(a*x))^(5/2)*(c - a*c*x)^(9/2))/(21*a^2*(1 - 1/(a*x))^(9/2)*x) + (2*(a - x^(-1))^3*(1 + 1/(a*x))^(5/2)*x*(c - a*c*x)^(9/2))/(11*a^3*(1 - 1/(a*x))^(9/2))","A",6,6,20,0.3000,1,"{6176, 6181, 94, 89, 78, 37}"
244,1,137,0,0.1727306,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^(7/2),x]","\frac{214 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{7/2}}{315 a^2 x \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{44 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{7/2}}{63 a \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{7/2}}{9 \left(1-\frac{1}{a x}\right)^{7/2}}","\frac{214 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{7/2}}{315 a^2 x \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{44 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{7/2}}{63 a \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{7/2}}{9 \left(1-\frac{1}{a x}\right)^{7/2}}",1,"(-44*(1 + 1/(a*x))^(5/2)*(c - a*c*x)^(7/2))/(63*a*(1 - 1/(a*x))^(7/2)) + (214*(1 + 1/(a*x))^(5/2)*(c - a*c*x)^(7/2))/(315*a^2*(1 - 1/(a*x))^(7/2)*x) + (2*(1 + 1/(a*x))^(5/2)*x*(c - a*c*x)^(7/2))/(9*(1 - 1/(a*x))^(7/2))","A",5,5,20,0.2500,1,"{6176, 6181, 89, 78, 37}"
245,1,89,0,0.158009,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^(5/2),x]","\frac{2 x \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{5/2}}{7 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{18 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{5/2}}{35 a \left(1-\frac{1}{a x}\right)^{5/2}}","\frac{2 x \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{5/2}}{7 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{18 \left(\frac{1}{a x}+1\right)^{5/2} (c-a c x)^{5/2}}{35 a \left(1-\frac{1}{a x}\right)^{5/2}}",1,"(-18*(1 + 1/(a*x))^(5/2)*(c - a*c*x)^(5/2))/(35*a*(1 - 1/(a*x))^(5/2)) + (2*(1 + 1/(a*x))^(5/2)*x*(c - a*c*x)^(5/2))/(7*(1 - 1/(a*x))^(5/2))","A",4,4,20,0.2000,1,"{6176, 6181, 78, 37}"
246,1,31,0,0.0365437,"\int e^{3 \coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a*c*x)^(3/2),x]","\frac{2 (a x+1) (c-a c x)^{3/2} e^{3 \coth ^{-1}(a x)}}{5 a}","\frac{2 (a x+1) (c-a c x)^{3/2} e^{3 \coth ^{-1}(a x)}}{5 a}",1,"(2*E^(3*ArcCoth[a*x])*(1 + a*x)*(c - a*c*x)^(3/2))/(5*a)","A",1,1,20,0.05000,1,"{6174}"
247,1,163,0,0.1769824,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x],x]","-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{3/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{a \sqrt{1-\frac{1}{a x}}}","-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{3/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{a \sqrt{1-\frac{1}{a x}}}",1,"(4*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(a*Sqrt[1 - 1/(a*x)]) + (2*(1 + 1/(a*x))^(3/2)*x*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(a^(3/2)*Sqrt[1 - 1/(a*x)])","A",6,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
248,1,177,0,0.1802344,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^(3*ArcCoth[a*x])/Sqrt[c - a*c*x],x]","\frac{2 a x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{\left(a-\frac{1}{x}\right) \sqrt{c-a c x}}-\frac{6 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right) \sqrt{c-a c x}}-\frac{3 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x}}","\frac{2 a x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{\left(a-\frac{1}{x}\right) \sqrt{c-a c x}}-\frac{6 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right) \sqrt{c-a c x}}-\frac{3 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x}}",1,"(-6*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/((a - x^(-1))*Sqrt[c - a*c*x]) + (2*a*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x)/((a - x^(-1))*Sqrt[c - a*c*x]) - (3*Sqrt[2]*Sqrt[1 - 1/(a*x)]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x])","A",6,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
249,1,187,0,0.1938257,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^(3/2),x]","-\frac{a^2 x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}}{2 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{3/2}}-\frac{3 a x \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{4 \left(a-\frac{1}{x}\right) (c-a c x)^{3/2}}-\frac{3 \sqrt{a} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{4 \sqrt{2} \left(\frac{1}{x}\right)^{3/2} (c-a c x)^{3/2}}","-\frac{a^2 x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}}{2 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{3/2}}-\frac{3 a x \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{4 \left(a-\frac{1}{x}\right) (c-a c x)^{3/2}}-\frac{3 \sqrt{a} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{4 \sqrt{2} \left(\frac{1}{x}\right)^{3/2} (c-a c x)^{3/2}}",1,"(-3*a*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x)/(4*(a - x^(-1))*(c - a*c*x)^(3/2)) - (a^2*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2)*x)/(2*(a - x^(-1))^2*(c - a*c*x)^(3/2)) - (3*Sqrt[a]*(1 - 1/(a*x))^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(4*Sqrt[2]*(x^(-1))^(3/2)*(c - a*c*x)^(3/2))","A",6,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
250,1,250,0,0.2180193,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^(5/2),x]","-\frac{a^4 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}}{6 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{5/2}}+\frac{a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}{24 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{5/2}}+\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{16 \left(a-\frac{1}{x}\right) (c-a c x)^{5/2}}+\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{16 \sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}","-\frac{a^4 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}}{6 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{5/2}}+\frac{a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}{24 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{5/2}}+\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{16 \left(a-\frac{1}{x}\right) (c-a c x)^{5/2}}+\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{16 \sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}",1,"(a^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x^2)/(16*(a - x^(-1))*(c - a*c*x)^(5/2)) + (a^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)*x^2)/(24*(a - x^(-1))^2*(c - a*c*x)^(5/2)) - (a^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(5/2)*x^2)/(6*(a - x^(-1))^3*(c - a*c*x)^(5/2)) + (a^(3/2)*(1 - 1/(a*x))^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(16*Sqrt[2]*(x^(-1))^(5/2)*(c - a*c*x)^(5/2))","A",7,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
251,1,307,0,0.2388291,"\int \frac{e^{3 \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a*c*x)^(7/2),x]","\frac{a^5 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}{32 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}-\frac{a^5 x^2 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}{8 \left(a-\frac{1}{x}\right)^4 (c-a c x)^{7/2}}-\frac{a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}{128 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{7/2}}-\frac{3 a^3 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}{256 \left(a-\frac{1}{x}\right) (c-a c x)^{7/2}}-\frac{3 a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{256 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}","\frac{a^5 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}{32 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}-\frac{a^5 x^2 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}{8 \left(a-\frac{1}{x}\right)^4 (c-a c x)^{7/2}}-\frac{a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}{128 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{7/2}}-\frac{3 a^3 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}{256 \left(a-\frac{1}{x}\right) (c-a c x)^{7/2}}-\frac{3 a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{256 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}",1,"-(a^5*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2)*x^2)/(8*(a - x^(-1))^4*(c - a*c*x)^(7/2)) - (3*a^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^3)/(256*(a - x^(-1))*(c - a*c*x)^(7/2)) - (a^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(3/2)*x^3)/(128*(a - x^(-1))^2*(c - a*c*x)^(7/2)) + (a^5*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2)*x^3)/(32*(a - x^(-1))^3*(c - a*c*x)^(7/2)) - (3*a^(5/2)*(1 - 1/(a*x))^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(256*Sqrt[2]*(x^(-1))^(7/2)*(c - a*c*x)^(7/2))","A",8,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
252,1,311,0,0.2256617,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[(c - a*c*x)^(9/2)/E^ArcCoth[a*x],x]","-\frac{512 \sqrt{\frac{1}{a x}+1} (c-a c x)^{9/2}}{231 a^3 x^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{1024 \sqrt{\frac{1}{a x}+1} (c-a c x)^{9/2}}{99 a^4 x^3 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{22016 \sqrt{\frac{1}{a x}+1} (c-a c x)^{9/2}}{693 a^5 x^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{2 x \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^5 (c-a c x)^{9/2}}{11 a^5 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{40 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^4 (c-a c x)^{9/2}}{99 a^5 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{640 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^3 (c-a c x)^{9/2}}{693 a^5 x \left(1-\frac{1}{a x}\right)^{9/2}}","\frac{16384 c^5 x \sqrt{1-\frac{1}{a^2 x^2}}}{693 \sqrt{c-a c x}}+\frac{4096}{693} c^4 x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}+\frac{512}{231} c^3 x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}+\frac{640}{693} c^2 x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{5/2}+\frac{40}{99} c x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{7/2}+\frac{2}{11} x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{9/2}",1,"(-40*(a - x^(-1))^4*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(9/2))/(99*a^5*(1 - 1/(a*x))^(9/2)) - (22016*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(9/2))/(693*a^5*(1 - 1/(a*x))^(9/2)*x^4) + (1024*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(9/2))/(99*a^4*(1 - 1/(a*x))^(9/2)*x^3) - (512*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(9/2))/(231*a^3*(1 - 1/(a*x))^(9/2)*x^2) + (640*(a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(9/2))/(693*a^5*(1 - 1/(a*x))^(9/2)*x) + (2*(a - x^(-1))^5*Sqrt[1 + 1/(a*x)]*x*(c - a*c*x)^(9/2))/(11*a^5*(1 - 1/(a*x))^(9/2))","A",8,6,20,0.3000,0,"{6176, 6181, 94, 89, 78, 37}"
253,1,254,0,0.222049,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[(c - a*c*x)^(7/2)/E^ArcCoth[a*x],x]","-\frac{256 \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}{45 a^3 x^2 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{5504 \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}{315 a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{2 x \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^4 (c-a c x)^{7/2}}{9 a^4 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{32 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}{63 a^4 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{128 \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}{105 a^2 x \left(1-\frac{1}{a x}\right)^{7/2}}","\frac{4096 c^4 x \sqrt{1-\frac{1}{a^2 x^2}}}{315 \sqrt{c-a c x}}+\frac{1024}{315} c^3 x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}+\frac{128}{105} c^2 x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}+\frac{32}{63} c x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{5/2}+\frac{2}{9} x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{7/2}",1,"(-32*(a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(7/2))/(63*a^4*(1 - 1/(a*x))^(7/2)) + (5504*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(7/2))/(315*a^4*(1 - 1/(a*x))^(7/2)*x^3) - (256*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(7/2))/(45*a^3*(1 - 1/(a*x))^(7/2)*x^2) + (128*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(7/2))/(105*a^2*(1 - 1/(a*x))^(7/2)*x) + (2*(a - x^(-1))^4*Sqrt[1 + 1/(a*x)]*x*(c - a*c*x)^(7/2))/(9*a^4*(1 - 1/(a*x))^(7/2))","A",7,6,20,0.3000,0,"{6176, 6181, 94, 89, 78, 37}"
254,1,197,0,0.2029144,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[(c - a*c*x)^(5/2)/E^ArcCoth[a*x],x]","-\frac{344 \sqrt{\frac{1}{a x}+1} (c-a c x)^{5/2}}{35 a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2}}+\frac{2 x \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^3 (c-a c x)^{5/2}}{7 a^3 \left(1-\frac{1}{a x}\right)^{5/2}}+\frac{16 \sqrt{\frac{1}{a x}+1} (c-a c x)^{5/2}}{5 a^2 x \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{24 \sqrt{\frac{1}{a x}+1} (c-a c x)^{5/2}}{35 a \left(1-\frac{1}{a x}\right)^{5/2}}","\frac{256 c^3 x \sqrt{1-\frac{1}{a^2 x^2}}}{35 \sqrt{c-a c x}}+\frac{64}{35} c^2 x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}+\frac{24}{35} c x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}+\frac{2}{7} x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{5/2}",1,"(-24*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(5/2))/(35*a*(1 - 1/(a*x))^(5/2)) - (344*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(5/2))/(35*a^3*(1 - 1/(a*x))^(5/2)*x^2) + (16*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(5/2))/(5*a^2*(1 - 1/(a*x))^(5/2)*x) + (2*(a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*x*(c - a*c*x)^(5/2))/(7*a^3*(1 - 1/(a*x))^(5/2))","A",6,6,20,0.3000,0,"{6176, 6181, 94, 89, 78, 37}"
255,1,137,0,0.1859463,"\int e^{-\coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[(c - a*c*x)^(3/2)/E^ArcCoth[a*x],x]","\frac{86 \sqrt{\frac{1}{a x}+1} (c-a c x)^{3/2}}{15 a^2 x \left(1-\frac{1}{a x}\right)^{3/2}}+\frac{2 x \sqrt{\frac{1}{a x}+1} (c-a c x)^{3/2}}{5 \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{28 \sqrt{\frac{1}{a x}+1} (c-a c x)^{3/2}}{15 a \left(1-\frac{1}{a x}\right)^{3/2}}","\frac{64 c^2 x \sqrt{1-\frac{1}{a^2 x^2}}}{15 \sqrt{c-a c x}}+\frac{16}{15} c x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}+\frac{2}{5} x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}",1,"(-28*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(3/2))/(15*a*(1 - 1/(a*x))^(3/2)) + (86*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(3/2))/(15*a^2*(1 - 1/(a*x))^(3/2)*x) + (2*Sqrt[1 + 1/(a*x)]*x*(c - a*c*x)^(3/2))/(5*(1 - 1/(a*x))^(3/2))","A",5,5,20,0.2500,0,"{6176, 6181, 89, 78, 37}"
256,1,89,0,0.1534063,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^ArcCoth[a*x],x]","\frac{2 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}}}-\frac{10 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}}}","\frac{2}{3} x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}+\frac{8 c x \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-a c x}}",1,"(-10*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - 1/(a*x)]) + (2*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)])","A",4,4,20,0.2000,0,"{6176, 6181, 78, 37}"
257,1,29,0,0.0378088,"\int \frac{e^{-\coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[1/(E^ArcCoth[a*x]*Sqrt[c - a*c*x]),x]","\frac{2 (a x+1) e^{-\coth ^{-1}(a x)}}{a \sqrt{c-a c x}}","\frac{2 (a x+1) e^{-\coth ^{-1}(a x)}}{a \sqrt{c-a c x}}",1,"(2*(1 + a*x))/(a*E^ArcCoth[a*x]*Sqrt[c - a*c*x])","A",1,1,20,0.05000,1,"{6174}"
258,1,76,0,0.1800511,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^(3/2)),x]","-\frac{\sqrt{2} \sqrt{a} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\left(\frac{1}{x}\right)^{3/2} (c-a c x)^{3/2}}","-\frac{\sqrt{2} \sqrt{a} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\left(\frac{1}{x}\right)^{3/2} (c-a c x)^{3/2}}",1,"-((Sqrt[2]*Sqrt[a]*(1 - 1/(a*x))^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/((x^(-1))^(3/2)*(c - a*c*x)^(3/2)))","A",4,4,20,0.2000,1,"{6176, 6181, 93, 206}"
259,1,136,0,0.1926433,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^(5/2)),x]","\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{2 \sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}-\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{2 \left(a-\frac{1}{x}\right) (c-a c x)^{5/2}}","\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{2 \sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}-\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{2 \left(a-\frac{1}{x}\right) (c-a c x)^{5/2}}",1,"-(a^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x^2)/(2*(a - x^(-1))*(c - a*c*x)^(5/2)) + (a^(3/2)*(1 - 1/(a*x))^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(2*Sqrt[2]*(x^(-1))^(5/2)*(c - a*c*x)^(5/2))","A",5,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
260,1,193,0,0.2032838,"\int \frac{e^{-\coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a*c*x)^(7/2)),x]","\frac{3 a^3 x^3 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{16 \left(a-\frac{1}{x}\right) (c-a c x)^{7/2}}-\frac{a^3 x^2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{4 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{7/2}}-\frac{3 a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{16 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}","\frac{3 a^3 x^3 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{16 \left(a-\frac{1}{x}\right) (c-a c x)^{7/2}}-\frac{a^3 x^2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{4 \left(a-\frac{1}{x}\right)^2 (c-a c x)^{7/2}}-\frac{3 a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{16 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}",1,"-(a^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^2)/(4*(a - x^(-1))^2*(c - a*c*x)^(7/2)) + (3*a^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^3)/(16*(a - x^(-1))*(c - a*c*x)^(7/2)) - (3*a^(5/2)*(1 - 1/(a*x))^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(16*Sqrt[2]*(x^(-1))^(7/2)*(c - a*c*x)^(7/2))","A",6,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
261,1,137,0,0.1557181,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[(c - a*c*x)^(7/2)/E^(2*ArcCoth[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",10,6,20,0.3000,1,"{6167, 6130, 21, 50, 63, 206}"
262,1,116,0,0.1316324,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[(c - a*c*x)^(5/2)/E^(2*ArcCoth[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",9,6,20,0.3000,1,"{6167, 6130, 21, 50, 63, 206}"
263,1,95,0,0.1197009,"\int e^{-2 \coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[(c - a*c*x)^(3/2)/E^(2*ArcCoth[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",8,6,20,0.3000,1,"{6167, 6130, 21, 50, 63, 206}"
264,1,76,0,0.1020951,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(2*ArcCoth[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",7,6,20,0.3000,1,"{6167, 6130, 21, 50, 63, 206}"
265,1,58,0,0.0985863,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[1/(E^(2*ArcCoth[a*x])*Sqrt[c - a*c*x]),x]","\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}}-\frac{2 \sqrt{c-a c x}}{a 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",6,6,20,0.3000,1,"{6167, 6130, 21, 50, 63, 206}"
266,1,37,0,0.0927469,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[1/(E^(2*ArcCoth[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",5,5,20,0.2500,1,"{6167, 6130, 21, 63, 206}"
267,1,57,0,0.1034793,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[1/(E^(2*ArcCoth[a*x])*(c - a*c*x)^(5/2)),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}}-\frac{1}{a c^2 \sqrt{c-a c x}}",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",6,6,20,0.3000,1,"{6167, 6130, 21, 51, 63, 206}"
268,1,83,0,0.1159629,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[1/(E^(2*ArcCoth[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",7,6,20,0.3000,1,"{6167, 6130, 21, 51, 63, 206}"
269,1,104,0,0.1262111,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{(c-a c x)^{9/2}} \, dx","Int[1/(E^(2*ArcCoth[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",8,6,20,0.3000,1,"{6167, 6130, 21, 51, 63, 206}"
270,1,368,0,0.2668331,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^{9/2} \, dx","Int[(c - a*c*x)^(9/2)/E^(3*ArcCoth[a*x]),x]","-\frac{1024 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{9/2}}{231 a^6 x^2 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{4096 (c-a c x)^{9/2}}{231 a^4 x^3 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}-\frac{40960 (c-a c x)^{9/2}}{231 a^5 x^4 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}-\frac{94208 (c-a c x)^{9/2}}{231 a^6 x^5 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^6 (c-a c x)^{9/2}}{11 a^6 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}-\frac{16 \left(a-\frac{1}{x}\right)^5 (c-a c x)^{9/2}}{33 a^6 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{320 \left(a-\frac{1}{x}\right)^4 (c-a c x)^{9/2}}{231 a^6 x \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}","-\frac{1024 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{9/2}}{231 a^6 x^2 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{4096 (c-a c x)^{9/2}}{231 a^4 x^3 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}-\frac{40960 (c-a c x)^{9/2}}{231 a^5 x^4 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}-\frac{94208 (c-a c x)^{9/2}}{231 a^6 x^5 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^6 (c-a c x)^{9/2}}{11 a^6 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}-\frac{16 \left(a-\frac{1}{x}\right)^5 (c-a c x)^{9/2}}{33 a^6 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{320 \left(a-\frac{1}{x}\right)^4 (c-a c x)^{9/2}}{231 a^6 x \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}",1,"(-16*(a - x^(-1))^5*(c - a*c*x)^(9/2))/(33*a^6*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]) - (94208*(c - a*c*x)^(9/2))/(231*a^6*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]*x^5) - (40960*(c - a*c*x)^(9/2))/(231*a^5*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]*x^4) + (4096*(c - a*c*x)^(9/2))/(231*a^4*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]*x^3) - (1024*(a - x^(-1))^3*(c - a*c*x)^(9/2))/(231*a^6*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]*x^2) + (320*(a - x^(-1))^4*(c - a*c*x)^(9/2))/(231*a^6*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]*x) + (2*(a - x^(-1))^6*x*(c - a*c*x)^(9/2))/(11*a^6*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)])","A",9,6,20,0.3000,1,"{6176, 6181, 94, 89, 78, 37}"
271,1,311,0,0.2361384,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^{7/2} \, dx","Int[(c - a*c*x)^(7/2)/E^(3*ArcCoth[a*x]),x]","-\frac{512 (c-a c x)^{7/2}}{63 a^3 x^2 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{5120 (c-a c x)^{7/2}}{63 a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{11776 (c-a c x)^{7/2}}{63 a^5 x^4 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^5 (c-a c x)^{7/2}}{9 a^5 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}-\frac{40 \left(a-\frac{1}{x}\right)^4 (c-a c x)^{7/2}}{63 a^5 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{128 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}{63 a^5 x \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}","-\frac{512 (c-a c x)^{7/2}}{63 a^3 x^2 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{5120 (c-a c x)^{7/2}}{63 a^4 x^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{11776 (c-a c x)^{7/2}}{63 a^5 x^4 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^5 (c-a c x)^{7/2}}{9 a^5 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}-\frac{40 \left(a-\frac{1}{x}\right)^4 (c-a c x)^{7/2}}{63 a^5 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{128 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{7/2}}{63 a^5 x \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}",1,"(-40*(a - x^(-1))^4*(c - a*c*x)^(7/2))/(63*a^5*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]) + (11776*(c - a*c*x)^(7/2))/(63*a^5*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^4) + (5120*(c - a*c*x)^(7/2))/(63*a^4*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^3) - (512*(c - a*c*x)^(7/2))/(63*a^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x^2) + (128*(a - x^(-1))^3*(c - a*c*x)^(7/2))/(63*a^5*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x) + (2*(a - x^(-1))^5*x*(c - a*c*x)^(7/2))/(9*a^5*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)])","A",8,6,20,0.3000,1,"{6176, 6181, 94, 89, 78, 37}"
272,1,254,0,0.2132662,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[(c - a*c*x)^(5/2)/E^(3*ArcCoth[a*x]),x]","-\frac{256 (c-a c x)^{5/2}}{7 a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}-\frac{2944 (c-a c x)^{5/2}}{35 a^4 x^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^4 (c-a c x)^{5/2}}{7 a^4 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}-\frac{32 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{5/2}}{35 a^4 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{128 (c-a c x)^{5/2}}{35 a^2 x \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}","-\frac{256 (c-a c x)^{5/2}}{7 a^3 x^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}-\frac{2944 (c-a c x)^{5/2}}{35 a^4 x^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^4 (c-a c x)^{5/2}}{7 a^4 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}-\frac{32 \left(a-\frac{1}{x}\right)^3 (c-a c x)^{5/2}}{35 a^4 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{128 (c-a c x)^{5/2}}{35 a^2 x \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}",1,"(-32*(a - x^(-1))^3*(c - a*c*x)^(5/2))/(35*a^4*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]) - (2944*(c - a*c*x)^(5/2))/(35*a^4*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x^3) - (256*(c - a*c*x)^(5/2))/(7*a^3*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x^2) + (128*(c - a*c*x)^(5/2))/(35*a^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x) + (2*(a - x^(-1))^4*x*(c - a*c*x)^(5/2))/(7*a^4*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])","A",7,6,20,0.3000,1,"{6176, 6181, 94, 89, 78, 37}"
273,1,195,0,0.191599,"\int e^{-3 \coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[(c - a*c*x)^(3/2)/E^(3*ArcCoth[a*x]),x]","\frac{184 (c-a c x)^{3/2}}{5 a^3 x^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^3 (c-a c x)^{3/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{16 (c-a c x)^{3/2}}{a^2 x \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}-\frac{8 (c-a c x)^{3/2}}{5 a \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}","\frac{184 (c-a c x)^{3/2}}{5 a^3 x^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \left(a-\frac{1}{x}\right)^3 (c-a c x)^{3/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{16 (c-a c x)^{3/2}}{a^2 x \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}-\frac{8 (c-a c x)^{3/2}}{5 a \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}",1,"(-8*(c - a*c*x)^(3/2))/(5*a*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]) + (184*(c - a*c*x)^(3/2))/(5*a^3*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x^2) + (16*(c - a*c*x)^(3/2))/(a^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x) + (2*(a - x^(-1))^3*x*(c - a*c*x)^(3/2))/(5*a^3*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)])","A",6,6,20,0.3000,1,"{6176, 6181, 94, 89, 78, 37}"
274,1,137,0,0.1554767,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(3*ArcCoth[a*x]),x]","-\frac{46 \sqrt{c-a c x}}{3 a^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{20 \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","-\frac{46 \sqrt{c-a c x}}{3 a^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{20 \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-20*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (46*Sqrt[c - a*c*x])/(3*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x) + (2*x*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])","A",5,5,20,0.2500,1,"{6176, 6181, 89, 78, 37}"
275,1,85,0,0.1434415,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x]),x]","\frac{2 x \sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}+\frac{6 \sqrt{1-\frac{1}{a x}}}{a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}","\frac{2 x \sqrt{1-\frac{1}{a x}}}{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}+\frac{6 \sqrt{1-\frac{1}{a x}}}{a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}",1,"(6*Sqrt[1 - 1/(a*x)])/(a*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x]) + (2*Sqrt[1 - 1/(a*x)]*x)/(Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])","A",4,4,20,0.2000,1,"{6176, 6181, 78, 37}"
276,1,29,0,0.0380544,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^(3/2)),x]","-\frac{2 (a x+1) e^{-3 \coth ^{-1}(a x)}}{a (c-a c x)^{3/2}}","-\frac{2 (a x+1) e^{-3 \coth ^{-1}(a x)}}{a (c-a c x)^{3/2}}",1,"(-2*(1 + a*x))/(a*E^(3*ArcCoth[a*x])*(c - a*c*x)^(3/2))","A",1,1,20,0.05000,1,"{6174}"
277,1,120,0,0.1796308,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^(5/2)),x]","\frac{a x^2 \left(1-\frac{1}{a x}\right)^{5/2}}{\sqrt{\frac{1}{a x}+1} (c-a c x)^{5/2}}-\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}","\frac{a x^2 \left(1-\frac{1}{a x}\right)^{5/2}}{\sqrt{\frac{1}{a x}+1} (c-a c x)^{5/2}}-\frac{a^{3/2} \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{2} \left(\frac{1}{x}\right)^{5/2} (c-a c x)^{5/2}}",1,"(a*(1 - 1/(a*x))^(5/2)*x^2)/(Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(5/2)) - (a^(3/2)*(1 - 1/(a*x))^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(Sqrt[2]*(x^(-1))^(5/2)*(c - a*c*x)^(5/2))","A",5,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
278,1,184,0,0.1979428,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a*c*x)^(7/2)),x]","-\frac{3 a^2 x^3 \left(1-\frac{1}{a x}\right)^{7/2}}{4 \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}-\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{7/2}}{2 \left(a-\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}+\frac{3 a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{4 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}","-\frac{3 a^2 x^3 \left(1-\frac{1}{a x}\right)^{7/2}}{4 \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}-\frac{a^2 x^2 \left(1-\frac{1}{a x}\right)^{7/2}}{2 \left(a-\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} (c-a c x)^{7/2}}+\frac{3 a^{5/2} \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{4 \sqrt{2} \left(\frac{1}{x}\right)^{7/2} (c-a c x)^{7/2}}",1,"-(a^2*(1 - 1/(a*x))^(7/2)*x^2)/(2*(a - x^(-1))*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(7/2)) - (3*a^2*(1 - 1/(a*x))^(7/2)*x^3)/(4*Sqrt[1 + 1/(a*x)]*(c - a*c*x)^(7/2)) + (3*a^(5/2)*(1 - 1/(a*x))^(7/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(4*Sqrt[2]*(x^(-1))^(7/2)*(c - a*c*x)^(7/2))","A",6,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
279,1,99,0,0.0697388,"\int e^{\coth ^{-1}(x)} x (1+x) \, dx","Int[E^ArcCoth[x]*x*(1 + x),x]","\frac{1}{3} \left(\frac{1}{x}+1\right)^{5/2} \sqrt{\frac{x-1}{x}} x^3+\frac{1}{3} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)","\frac{1}{3} \left(\frac{1}{x}+1\right)^{5/2} \sqrt{\frac{x-1}{x}} x^3+\frac{1}{3} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)",1,"Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]*x + ((1 + x^(-1))^(3/2)*Sqrt[(-1 + x)/x]*x^2)/3 + ((1 + x^(-1))^(5/2)*Sqrt[(-1 + x)/x]*x^3)/3 + ArcTanh[Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]]","A",7,6,9,0.6667,1,"{6175, 6180, 96, 94, 92, 206}"
280,1,79,0,0.046782,"\int e^{\coth ^{-1}(x)} (1+x) \, dx","Int[E^ArcCoth[x]*(1 + x),x]","\frac{1}{2} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\frac{3}{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\frac{3}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)","\frac{1}{2} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\frac{3}{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\frac{3}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)",1,"(3*Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]*x)/2 + ((1 + x^(-1))^(3/2)*Sqrt[(-1 + x)/x]*x^2)/2 + (3*ArcTanh[Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]])/2","A",6,5,8,0.6250,1,"{6175, 6180, 94, 92, 206}"
281,1,18,0,0.0525726,"\int e^{\coth ^{-1}(x)} (1-x) x \, dx","Int[E^ArcCoth[x]*(1 - x)*x,x]","-\frac{1}{3} \left(1-\frac{1}{x^2}\right)^{3/2} x^3","-\frac{1}{3} \left(1-\frac{1}{x^2}\right)^{3/2} x^3",1,"-((1 - x^(-2))^(3/2)*x^3)/3","A",3,3,11,0.2727,1,"{6175, 6178, 264}"
282,1,35,0,0.0466511,"\int e^{\coth ^{-1}(x)} (1-x) \, dx","Int[E^ArcCoth[x]*(1 - x),x]","\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)-\frac{1}{2} \sqrt{1-\frac{1}{x^2}} x^2","\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)-\frac{1}{2} \sqrt{1-\frac{1}{x^2}} x^2",1,"-(Sqrt[1 - x^(-2)]*x^2)/2 + ArcTanh[Sqrt[1 - x^(-2)]]/2","A",6,6,10,0.6000,1,"{6175, 6178, 266, 47, 63, 206}"
283,1,133,0,0.111144,"\int e^{\coth ^{-1}(x)} x (1+x)^2 \, dx","Int[E^ArcCoth[x]*x*(1 + x)^2,x]","\frac{1}{4} \left(\frac{1}{x}+1\right)^{7/2} \sqrt{\frac{x-1}{x}} x^4+\frac{1}{4} \left(\frac{1}{x}+1\right)^{5/2} \sqrt{\frac{x-1}{x}} x^3+\frac{5}{8} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\frac{15}{8} \sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\frac{15}{8} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)","\frac{1}{4} \left(\frac{1}{x}+1\right)^{7/2} \sqrt{\frac{x-1}{x}} x^4+\frac{1}{4} \left(\frac{1}{x}+1\right)^{5/2} \sqrt{\frac{x-1}{x}} x^3+\frac{5}{8} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\frac{15}{8} \sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\frac{15}{8} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)",1,"(15*Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]*x)/8 + (5*(1 + x^(-1))^(3/2)*Sqrt[(-1 + x)/x]*x^2)/8 + ((1 + x^(-1))^(5/2)*Sqrt[(-1 + x)/x]*x^3)/4 + ((1 + x^(-1))^(7/2)*Sqrt[(-1 + x)/x]*x^4)/4 + (15*ArcTanh[Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]])/8","A",8,6,11,0.5455,1,"{6175, 6180, 96, 94, 92, 206}"
284,1,106,0,0.0901089,"\int e^{\coth ^{-1}(x)} (1+x)^2 \, dx","Int[E^ArcCoth[x]*(1 + x)^2,x]","\frac{1}{3} \left(\frac{1}{x}+1\right)^{5/2} \sqrt{\frac{x-1}{x}} x^3+\frac{5}{6} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\frac{5}{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\frac{5}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)","\frac{1}{3} \left(\frac{1}{x}+1\right)^{5/2} \sqrt{\frac{x-1}{x}} x^3+\frac{5}{6} \left(\frac{1}{x}+1\right)^{3/2} \sqrt{\frac{x-1}{x}} x^2+\frac{5}{2} \sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x+\frac{5}{2} \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)",1,"(5*Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]*x)/2 + (5*(1 + x^(-1))^(3/2)*Sqrt[(-1 + x)/x]*x^2)/6 + ((1 + x^(-1))^(5/2)*Sqrt[(-1 + x)/x]*x^3)/3 + (5*ArcTanh[Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]])/2","A",7,5,10,0.5000,1,"{6175, 6180, 94, 92, 206}"
285,1,71,0,0.1163437,"\int e^{\coth ^{-1}(x)} (1-x)^2 x \, dx","Int[E^ArcCoth[x]*(1 - x)^2*x,x]","\frac{1}{4} \left(1-\frac{1}{x^2}\right)^{3/2} x^4-\frac{1}{3} \left(1-\frac{1}{x^2}\right)^{3/2} x^3+\frac{1}{8} \sqrt{1-\frac{1}{x^2}} x^2-\frac{1}{8} \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)","\frac{1}{4} \left(1-\frac{1}{x^2}\right)^{3/2} x^4-\frac{1}{3} \left(1-\frac{1}{x^2}\right)^{3/2} x^3+\frac{1}{8} \sqrt{1-\frac{1}{x^2}} x^2-\frac{1}{8} \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"(Sqrt[1 - x^(-2)]*x^2)/8 - ((1 - x^(-2))^(3/2)*x^3)/3 + ((1 - x^(-2))^(3/2)*x^4)/4 - ArcTanh[Sqrt[1 - x^(-2)]]/8","A",8,8,13,0.6154,1,"{6175, 6178, 835, 807, 266, 47, 63, 206}"
286,1,53,0,0.0904612,"\int e^{\coth ^{-1}(x)} (1-x)^2 \, dx","Int[E^ArcCoth[x]*(1 - x)^2,x]","\frac{1}{3} \left(1-\frac{1}{x^2}\right)^{3/2} x^3-\frac{1}{2} \sqrt{1-\frac{1}{x^2}} x^2+\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)","\frac{1}{3} \left(1-\frac{1}{x^2}\right)^{3/2} x^3-\frac{1}{2} \sqrt{1-\frac{1}{x^2}} x^2+\frac{1}{2} \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"-(Sqrt[1 - x^(-2)]*x^2)/2 + ((1 - x^(-2))^(3/2)*x^3)/3 + ArcTanh[Sqrt[1 - x^(-2)]]/2","A",7,7,12,0.5833,1,"{6175, 6178, 807, 266, 47, 63, 206}"
287,1,22,0,0.0536301,"\int \frac{e^{\coth ^{-1}(x)} x}{1+x} \, dx","Int[(E^ArcCoth[x]*x)/(1 + x),x]","\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x","\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}} x",1,"Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]*x","A",3,3,11,0.2727,1,"{6175, 6179, 95}"
288,1,22,0,0.0660964,"\int \frac{e^{\coth ^{-1}(x)}}{1+x} \, dx","Int[E^ArcCoth[x]/(1 + x),x]","\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)","\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)",1,"ArcTanh[Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]]","A",4,4,10,0.4000,1,"{6175, 6180, 92, 206}"
289,1,47,0,0.1353159,"\int \frac{e^{\coth ^{-1}(x)} x}{1-x} \, dx","Int[(E^ArcCoth[x]*x)/(1 - x),x]","\frac{2 \left(\frac{1}{x}+1\right)}{\sqrt{1-\frac{1}{x^2}}}-\sqrt{1-\frac{1}{x^2}} x-2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)","\frac{2 \left(\frac{1}{x}+1\right)}{\sqrt{1-\frac{1}{x^2}}}-\sqrt{1-\frac{1}{x^2}} x-2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"(2*(1 + x^(-1)))/Sqrt[1 - x^(-2)] - Sqrt[1 - x^(-2)]*x - 2*ArcTanh[Sqrt[1 - x^(-2)]]","A",8,8,13,0.6154,1,"{6175, 6177, 852, 1805, 807, 266, 63, 206}"
290,1,33,0,0.1316167,"\int \frac{e^{\coth ^{-1}(x)}}{1-x} \, dx","Int[E^ArcCoth[x]/(1 - x),x]","\frac{2 \left(\frac{1}{x}+1\right)}{\sqrt{1-\frac{1}{x^2}}}-\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)","\frac{2 \left(\frac{1}{x}+1\right)}{\sqrt{1-\frac{1}{x^2}}}-\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"(2*(1 + x^(-1)))/Sqrt[1 - x^(-2)] - ArcTanh[Sqrt[1 - x^(-2)]]","A",7,7,12,0.5833,1,"{6175, 6178, 852, 1805, 266, 63, 206}"
291,1,45,0,0.0826707,"\int \frac{e^{\coth ^{-1}(x)} x}{(1+x)^2} \, dx","Int[(E^ArcCoth[x]*x)/(1 + x)^2,x]","\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)-\frac{\sqrt{\frac{x-1}{x}}}{\sqrt{\frac{1}{x}+1}}","\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1} \sqrt{\frac{x-1}{x}}\right)-\frac{\sqrt{\frac{x-1}{x}}}{\sqrt{\frac{1}{x}+1}}",1,"-(Sqrt[(-1 + x)/x]/Sqrt[1 + x^(-1)]) + ArcTanh[Sqrt[1 + x^(-1)]*Sqrt[(-1 + x)/x]]","A",5,5,11,0.4545,1,"{6175, 6180, 96, 92, 206}"
292,1,21,0,0.0651539,"\int \frac{e^{\coth ^{-1}(x)}}{(1+x)^2} \, dx","Int[E^ArcCoth[x]/(1 + x)^2,x]","\frac{\sqrt{\frac{x-1}{x}}}{\sqrt{\frac{1}{x}+1}}","\frac{\sqrt{\frac{x-1}{x}}}{\sqrt{\frac{1}{x}+1}}",1,"Sqrt[(-1 + x)/x]/Sqrt[1 + x^(-1)]","A",3,3,10,0.3000,1,"{6175, 6180, 37}"
293,1,55,0,0.1549103,"\int \frac{e^{\coth ^{-1}(x)} x}{(1-x)^2} \, dx","Int[(E^ArcCoth[x]*x)/(1 - x)^2,x]","-\frac{4 \left(\frac{1}{x}+1\right)}{3 \left(1-\frac{1}{x^2}\right)^{3/2}}-\frac{\frac{5}{x}+3}{3 \sqrt{1-\frac{1}{x^2}}}+\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)","-\frac{4 \left(\frac{1}{x}+1\right)}{3 \left(1-\frac{1}{x^2}\right)^{3/2}}-\frac{\frac{5}{x}+3}{3 \sqrt{1-\frac{1}{x^2}}}+\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"(-4*(1 + x^(-1)))/(3*(1 - x^(-2))^(3/2)) - (3 + 5/x)/(3*Sqrt[1 - x^(-2)]) + ArcTanh[Sqrt[1 - x^(-2)]]","A",9,9,13,0.6923,1,"{6175, 6178, 852, 1805, 823, 12, 266, 63, 206}"
294,1,24,0,0.0714459,"\int \frac{e^{\coth ^{-1}(x)}}{(1-x)^2} \, dx","Int[E^ArcCoth[x]/(1 - x)^2,x]","-\frac{\left(1-\frac{1}{x^2}\right)^{3/2}}{3 \left(1-\frac{1}{x}\right)^3}","-\frac{\left(1-\frac{1}{x^2}\right)^{3/2}}{3 \left(1-\frac{1}{x}\right)^3}",1,"-(1 - x^(-2))^(3/2)/(3*(1 - x^(-1))^3)","A",3,3,12,0.2500,1,"{6175, 6178, 651}"
295,1,65,0,0.1919085,"\int e^{\coth ^{-1}(a x)} x^m \sqrt{c-a c x} \, dx","Int[E^ArcCoth[a*x]*x^m*Sqrt[c - a*c*x],x]","\frac{2 x^{m+1} \sqrt{c-a c x} \, _2F_1\left(-\frac{1}{2},-m-\frac{3}{2};-m-\frac{1}{2};-\frac{1}{a x}\right)}{(2 m+3) \sqrt{1-\frac{1}{a x}}}","\frac{2 x^{m+1} \sqrt{c-a c x} \, _2F_1\left(-\frac{1}{2},-m-\frac{3}{2};-m-\frac{1}{2};-\frac{1}{a x}\right)}{(2 m+3) \sqrt{1-\frac{1}{a x}}}",1,"(2*x^(1 + m)*Sqrt[c - a*c*x]*Hypergeometric2F1[-1/2, -3/2 - m, -1/2 - m, -(1/(a*x))])/((3 + 2*m)*Sqrt[1 - 1/(a*x)])","A",3,3,21,0.1429,1,"{6176, 6181, 64}"
296,1,140,0,0.2153093,"\int e^{\coth ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[E^ArcCoth[a*x]*x^2*Sqrt[c - a*c*x],x]","\frac{16 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}}}-\frac{8 x^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{35 a \sqrt{1-\frac{1}{a x}}}","\frac{16 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}}}-\frac{8 x^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{35 a \sqrt{1-\frac{1}{a x}}}",1,"(16*(1 + 1/(a*x))^(3/2)*x*Sqrt[c - a*c*x])/(105*a^2*Sqrt[1 - 1/(a*x)]) - (8*(1 + 1/(a*x))^(3/2)*x^2*Sqrt[c - a*c*x])/(35*a*Sqrt[1 - 1/(a*x)]) + (2*(1 + 1/(a*x))^(3/2)*x^3*Sqrt[c - a*c*x])/(7*Sqrt[1 - 1/(a*x)])","A",5,4,21,0.1905,1,"{6176, 6181, 45, 37}"
297,1,92,0,0.1726315,"\int e^{\coth ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[E^ArcCoth[a*x]*x*Sqrt[c - a*c*x],x]","\frac{2 x^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}}}-\frac{4 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{15 a \sqrt{1-\frac{1}{a x}}}","\frac{2 x^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}}}-\frac{4 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{15 a \sqrt{1-\frac{1}{a x}}}",1,"(-4*(1 + 1/(a*x))^(3/2)*x*Sqrt[c - a*c*x])/(15*a*Sqrt[1 - 1/(a*x)]) + (2*(1 + 1/(a*x))^(3/2)*x^2*Sqrt[c - a*c*x])/(5*Sqrt[1 - 1/(a*x)])","A",4,4,19,0.2105,1,"{6176, 6181, 45, 37}"
298,1,29,0,0.0330856,"\int e^{\coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - a*c*x],x]","\frac{2 (a x+1) \sqrt{c-a c x} e^{\coth ^{-1}(a x)}}{3 a}","\frac{2 (a x+1) \sqrt{c-a c x} e^{\coth ^{-1}(a x)}}{3 a}",1,"(2*E^ArcCoth[a*x]*(1 + a*x)*Sqrt[c - a*c*x])/(3*a)","A",1,1,18,0.05556,1,"{6174}"
299,1,94,0,0.1946953,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - a*c*x])/x,x]","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}}}-\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}}}-\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}",1,"(2*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/Sqrt[1 - 1/(a*x)] - (2*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(Sqrt[a]*Sqrt[1 - 1/(a*x)])","A",5,5,21,0.2381,1,"{6176, 6181, 47, 54, 215}"
300,1,97,0,0.1948011,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - a*c*x])/x^2,x]","-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}","-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"-((Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*x)) - (Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/Sqrt[1 - 1/(a*x)]","A",5,5,21,0.2381,1,"{6176, 6181, 50, 54, 215}"
301,1,101,0,0.2251808,"\int e^{2 \coth ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[E^(2*ArcCoth[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",5,4,23,0.1739,1,"{6167, 6130, 21, 77}"
302,1,80,0,0.2241537,"\int e^{2 \coth ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[E^(2*ArcCoth[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",5,4,23,0.1739,1,"{6167, 6130, 21, 77}"
303,1,57,0,0.152234,"\int e^{2 \coth ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[E^(2*ArcCoth[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",5,4,21,0.1905,1,"{6167, 6130, 21, 77}"
304,1,38,0,0.0813062,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(2*ArcCoth[a*x])*Sqrt[c - a*c*x],x]","\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}-\frac{2 (c-a c x)^{3/2}}{3 a c}",1,"(4*Sqrt[c - a*c*x])/a - (2*(c - a*c*x)^(3/2))/(3*a*c)","A",5,4,20,0.2000,1,"{6167, 6130, 21, 43}"
305,1,39,0,0.198014,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[(E^(2*ArcCoth[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",6,6,23,0.2609,1,"{6167, 6130, 21, 80, 63, 208}"
306,1,42,0,0.2033167,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[(E^(2*ArcCoth[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",6,6,23,0.2609,1,"{6167, 6130, 21, 78, 63, 208}"
307,1,68,0,0.2104136,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[(E^(2*ArcCoth[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",7,7,23,0.3043,1,"{6167, 6130, 21, 78, 51, 63, 208}"
308,1,89,0,0.2192417,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[(E^(2*ArcCoth[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",8,7,23,0.3043,1,"{6167, 6130, 21, 78, 51, 63, 208}"
309,1,110,0,0.2341806,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[(E^(2*ArcCoth[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",9,7,23,0.3043,1,"{6167, 6130, 21, 78, 51, 63, 208}"
310,1,309,0,0.3241916,"\int e^{3 \coth ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[E^(3*ArcCoth[a*x])*x^3*Sqrt[c - a*c*x],x]","\frac{92 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{472 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{315 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{1576 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{315 a^4 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{9/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{9 \sqrt{1-\frac{1}{a x}}}+\frac{38 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{63 a \sqrt{1-\frac{1}{a x}}}","\frac{92 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{472 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{315 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{1576 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{315 a^4 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{9/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{9 \sqrt{1-\frac{1}{a x}}}+\frac{38 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{63 a \sqrt{1-\frac{1}{a x}}}",1,"(1576*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(315*a^4*Sqrt[1 - 1/(a*x)]) + (472*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(315*a^3*Sqrt[1 - 1/(a*x)]) + (92*Sqrt[1 + 1/(a*x)]*x^2*Sqrt[c - a*c*x])/(105*a^2*Sqrt[1 - 1/(a*x)]) + (38*Sqrt[1 + 1/(a*x)]*x^3*Sqrt[c - a*c*x])/(63*a*Sqrt[1 - 1/(a*x)]) + (2*Sqrt[1 + 1/(a*x)]*x^4*Sqrt[c - a*c*x])/(9*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(a^(9/2)*Sqrt[1 - 1/(a*x)])","A",10,7,23,0.3043,1,"{6176, 6181, 98, 152, 12, 93, 206}"
311,1,261,0,0.299959,"\int e^{3 \coth ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[E^(3*ArcCoth[a*x])*x^2*Sqrt[c - a*c*x],x]","\frac{32 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{21 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{104 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{21 a^3 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{7/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}}}+\frac{6 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{7 a \sqrt{1-\frac{1}{a x}}}","\frac{32 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{21 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{104 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{21 a^3 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{7/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}}}+\frac{6 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{7 a \sqrt{1-\frac{1}{a x}}}",1,"(104*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(21*a^3*Sqrt[1 - 1/(a*x)]) + (32*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(21*a^2*Sqrt[1 - 1/(a*x)]) + (6*Sqrt[1 + 1/(a*x)]*x^2*Sqrt[c - a*c*x])/(7*a*Sqrt[1 - 1/(a*x)]) + (2*Sqrt[1 + 1/(a*x)]*x^3*Sqrt[c - a*c*x])/(7*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(a^(7/2)*Sqrt[1 - 1/(a*x)])","A",9,7,23,0.3043,1,"{6176, 6181, 98, 152, 12, 93, 206}"
312,1,211,0,0.2363035,"\int e^{3 \coth ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[E^(3*ArcCoth[a*x])*x*Sqrt[c - a*c*x],x]","\frac{4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{a^2 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{5/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x^2 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}}}","\frac{4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{a^2 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{5/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x^2 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}}}",1,"(4*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(a^2*Sqrt[1 - 1/(a*x)]) + (2*(1 + 1/(a*x))^(3/2)*x*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - 1/(a*x)]) + (2*(1 + 1/(a*x))^(5/2)*x^2*Sqrt[c - a*c*x])/(5*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(a^(5/2)*Sqrt[1 - 1/(a*x)])","A",7,6,21,0.2857,1,"{6176, 6181, 96, 94, 93, 206}"
313,1,163,0,0.1873241,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x],x]","-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{3/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{a \sqrt{1-\frac{1}{a x}}}","-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{a^{3/2} \sqrt{1-\frac{1}{a x}}}+\frac{2 x \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{4 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{a \sqrt{1-\frac{1}{a x}}}",1,"(4*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(a*Sqrt[1 - 1/(a*x)]) + (2*(1 + 1/(a*x))^(3/2)*x*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(a^(3/2)*Sqrt[1 - 1/(a*x)])","A",6,5,20,0.2500,1,"{6176, 6181, 94, 93, 206}"
314,1,170,0,0.2400865,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x])/x,x]","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}}}+\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}}}+\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}",1,"(2*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/Sqrt[1 - 1/(a*x)] + (2*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(Sqrt[a]*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/(Sqrt[a]*Sqrt[1 - 1/(a*x)])","A",8,8,23,0.3478,1,"{6176, 6181, 98, 157, 54, 215, 93, 206}"
315,1,172,0,0.2514926,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x])/x^2,x]","\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}+\frac{5 \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}","\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}+\frac{5 \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"(Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*x) + (5*Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/Sqrt[1 - 1/(a*x)] - (4*Sqrt[2]*Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/Sqrt[1 - 1/(a*x)]","A",8,8,23,0.3478,1,"{6176, 6181, 102, 157, 54, 215, 93, 206}"
316,1,224,0,0.2645017,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x])/x^3,x]","\frac{23 a^{3/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{4 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^{3/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}+\frac{a \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{2 x \sqrt{1-\frac{1}{a x}}}+\frac{7 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{4 x \sqrt{1-\frac{1}{a x}}}","\frac{23 a^{3/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{4 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^{3/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}+\frac{a \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{2 x \sqrt{1-\frac{1}{a x}}}+\frac{7 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{4 x \sqrt{1-\frac{1}{a x}}}",1,"(7*a*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(4*Sqrt[1 - 1/(a*x)]*x) + (a*(1 + 1/(a*x))^(3/2)*Sqrt[c - a*c*x])/(2*Sqrt[1 - 1/(a*x)]*x) + (23*a^(3/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(4*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*a^(3/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/Sqrt[1 - 1/(a*x)]","A",9,9,23,0.3913,1,"{6176, 6181, 101, 154, 157, 54, 215, 93, 206}"
317,1,274,0,0.2816188,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x])/x^4,x]","\frac{3 a^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{4 x \sqrt{1-\frac{1}{a x}}}+\frac{13 a^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{8 x \sqrt{1-\frac{1}{a x}}}+\frac{45 a^{5/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{8 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^{5/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}+\frac{a \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 x^2 \sqrt{1-\frac{1}{a x}}}","\frac{3 a^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{4 x \sqrt{1-\frac{1}{a x}}}+\frac{13 a^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{8 x \sqrt{1-\frac{1}{a x}}}+\frac{45 a^{5/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{8 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^{5/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}+\frac{a \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{3 x^2 \sqrt{1-\frac{1}{a x}}}",1,"(a*(1 + 1/(a*x))^(3/2)*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)]*x^2) + (13*a^2*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(8*Sqrt[1 - 1/(a*x)]*x) + (3*a^2*(1 + 1/(a*x))^(3/2)*Sqrt[c - a*c*x])/(4*Sqrt[1 - 1/(a*x)]*x) + (45*a^(5/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(8*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*a^(5/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/Sqrt[1 - 1/(a*x)]","A",10,9,23,0.3913,1,"{6176, 6181, 101, 154, 157, 54, 215, 93, 206}"
318,1,322,0,0.30185,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a*c*x])/x^5,x]","\frac{11 a^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{24 x^2 \sqrt{1-\frac{1}{a x}}}+\frac{21 a^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{32 x \sqrt{1-\frac{1}{a x}}}+\frac{107 a^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{64 x \sqrt{1-\frac{1}{a x}}}+\frac{363 a^{7/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{64 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^{7/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}+\frac{a \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{4 x^3 \sqrt{1-\frac{1}{a x}}}","\frac{11 a^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{24 x^2 \sqrt{1-\frac{1}{a x}}}+\frac{21 a^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{32 x \sqrt{1-\frac{1}{a x}}}+\frac{107 a^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{64 x \sqrt{1-\frac{1}{a x}}}+\frac{363 a^{7/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{64 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^{7/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{a} \sqrt{\frac{1}{a x}+1}}\right)}{\sqrt{1-\frac{1}{a x}}}+\frac{a \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-a c x}}{4 x^3 \sqrt{1-\frac{1}{a x}}}",1,"(a*(1 + 1/(a*x))^(3/2)*Sqrt[c - a*c*x])/(4*Sqrt[1 - 1/(a*x)]*x^3) + (11*a^2*(1 + 1/(a*x))^(3/2)*Sqrt[c - a*c*x])/(24*Sqrt[1 - 1/(a*x)]*x^2) + (107*a^3*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(64*Sqrt[1 - 1/(a*x)]*x) + (21*a^3*(1 + 1/(a*x))^(3/2)*Sqrt[c - a*c*x])/(32*Sqrt[1 - 1/(a*x)]*x) + (363*a^(7/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(64*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*a^(7/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/(Sqrt[a]*Sqrt[1 + 1/(a*x)])])/Sqrt[1 - 1/(a*x)]","A",11,9,23,0.3913,1,"{6176, 6181, 101, 154, 157, 54, 215, 93, 206}"
319,1,144,0,0.1276488,"\int e^{\coth ^{-1}(x)} x (1+x)^{3/2} \, dx","Int[E^ArcCoth[x]*x*(1 + x)^(3/2),x]","\frac{2 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2} x^2}{7 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{8 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2} x}{7 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{46 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{21 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{92 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{21 \left(\frac{1}{x}+1\right)^{3/2} x}","\frac{2 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2} x^2}{7 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{8 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2} x}{7 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{46 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{21 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{92 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{21 \left(\frac{1}{x}+1\right)^{3/2} x}",1,"(46*Sqrt[-((1 - x)/x)]*(1 + x)^(3/2))/(21*(1 + x^(-1))^(3/2)) + (92*Sqrt[-((1 - x)/x)]*(1 + x)^(3/2))/(21*(1 + x^(-1))^(3/2)*x) + (8*Sqrt[-((1 - x)/x)]*x*(1 + x)^(3/2))/(7*(1 + x^(-1))^(3/2)) + (2*Sqrt[-((1 - x)/x)]*x^2*(1 + x)^(3/2))/(7*(1 + x^(-1))^(3/2))","A",6,6,13,0.4615,1,"{6176, 6181, 89, 78, 45, 37}"
320,1,107,0,0.1073555,"\int e^{\coth ^{-1}(x)} (1+x)^{3/2} \, dx","Int[E^ArcCoth[x]*(1 + x)^(3/2),x]","\frac{2 \sqrt{-\frac{1-x}{x}} x (x+1)^{3/2}}{5 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{28 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{15 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{86 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{15 \left(\frac{1}{x}+1\right)^{3/2} x}","\frac{2 \sqrt{-\frac{1-x}{x}} x (x+1)^{3/2}}{5 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{28 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{15 \left(\frac{1}{x}+1\right)^{3/2}}+\frac{86 \sqrt{-\frac{1-x}{x}} (x+1)^{3/2}}{15 \left(\frac{1}{x}+1\right)^{3/2} x}",1,"(28*Sqrt[-((1 - x)/x)]*(1 + x)^(3/2))/(15*(1 + x^(-1))^(3/2)) + (86*Sqrt[-((1 - x)/x)]*(1 + x)^(3/2))/(15*(1 + x^(-1))^(3/2)*x) + (2*Sqrt[-((1 - x)/x)]*x*(1 + x)^(3/2))/(5*(1 + x^(-1))^(3/2))","A",5,5,12,0.4167,1,"{6176, 6181, 89, 78, 37}"
321,1,104,0,0.1261038,"\int e^{\coth ^{-1}(x)} (1-x)^{3/2} x \, dx","Int[E^ArcCoth[x]*(1 - x)^(3/2)*x,x]","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2} x^2}{7 \left(1-\frac{1}{x}\right)^{3/2}}-\frac{22 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2} x}{35 \left(1-\frac{1}{x}\right)^{3/2}}+\frac{44 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2}}{105 \left(1-\frac{1}{x}\right)^{3/2}}","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2} x^2}{7 \left(1-\frac{1}{x}\right)^{3/2}}-\frac{22 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2} x}{35 \left(1-\frac{1}{x}\right)^{3/2}}+\frac{44 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2}}{105 \left(1-\frac{1}{x}\right)^{3/2}}",1,"(44*(1 + x^(-1))^(3/2)*(1 - x)^(3/2))/(105*(1 - x^(-1))^(3/2)) - (22*(1 + x^(-1))^(3/2)*(1 - x)^(3/2)*x)/(35*(1 - x^(-1))^(3/2)) + (2*(1 + x^(-1))^(3/2)*(1 - x)^(3/2)*x^2)/(7*(1 - x^(-1))^(3/2))","A",5,5,15,0.3333,1,"{6176, 6181, 78, 45, 37}"
322,1,68,0,0.0991177,"\int e^{\coth ^{-1}(x)} (1-x)^{3/2} \, dx","Int[E^ArcCoth[x]*(1 - x)^(3/2),x]","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2} x}{5 \left(1-\frac{1}{x}\right)^{3/2}}-\frac{14 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2}}{15 \left(1-\frac{1}{x}\right)^{3/2}}","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2} x}{5 \left(1-\frac{1}{x}\right)^{3/2}}-\frac{14 \left(\frac{1}{x}+1\right)^{3/2} (1-x)^{3/2}}{15 \left(1-\frac{1}{x}\right)^{3/2}}",1,"(-14*(1 + x^(-1))^(3/2)*(1 - x)^(3/2))/(15*(1 - x^(-1))^(3/2)) + (2*(1 + x^(-1))^(3/2)*(1 - x)^(3/2)*x)/(5*(1 - x^(-1))^(3/2))","A",4,4,14,0.2857,1,"{6176, 6181, 78, 37}"
323,1,107,0,0.1064775,"\int e^{\coth ^{-1}(x)} x \sqrt{1+x} \, dx","Int[E^ArcCoth[x]*x*Sqrt[1 + x],x]","\frac{2 \sqrt{-\frac{1-x}{x}} \sqrt{x+1} x^2}{5 \sqrt{\frac{1}{x}+1}}+\frac{6 \sqrt{-\frac{1-x}{x}} \sqrt{x+1} x}{5 \sqrt{\frac{1}{x}+1}}+\frac{12 \sqrt{-\frac{1-x}{x}} \sqrt{x+1}}{5 \sqrt{\frac{1}{x}+1}}","\frac{2 \sqrt{-\frac{1-x}{x}} \sqrt{x+1} x^2}{5 \sqrt{\frac{1}{x}+1}}+\frac{6 \sqrt{-\frac{1-x}{x}} \sqrt{x+1} x}{5 \sqrt{\frac{1}{x}+1}}+\frac{12 \sqrt{-\frac{1-x}{x}} \sqrt{x+1}}{5 \sqrt{\frac{1}{x}+1}}",1,"(12*Sqrt[-((1 - x)/x)]*Sqrt[1 + x])/(5*Sqrt[1 + x^(-1)]) + (6*Sqrt[-((1 - x)/x)]*x*Sqrt[1 + x])/(5*Sqrt[1 + x^(-1)]) + (2*Sqrt[-((1 - x)/x)]*x^2*Sqrt[1 + x])/(5*Sqrt[1 + x^(-1)])","A",5,5,13,0.3846,1,"{6176, 6181, 78, 45, 37}"
324,1,70,0,0.0811716,"\int e^{\coth ^{-1}(x)} \sqrt{1+x} \, dx","Int[E^ArcCoth[x]*Sqrt[1 + x],x]","\frac{2 \sqrt{-\frac{1-x}{x}} \sqrt{x+1} x}{3 \sqrt{\frac{1}{x}+1}}+\frac{10 \sqrt{-\frac{1-x}{x}} \sqrt{x+1}}{3 \sqrt{\frac{1}{x}+1}}","\frac{2 \sqrt{-\frac{1-x}{x}} \sqrt{x+1} x}{3 \sqrt{\frac{1}{x}+1}}+\frac{10 \sqrt{-\frac{1-x}{x}} \sqrt{x+1}}{3 \sqrt{\frac{1}{x}+1}}",1,"(10*Sqrt[-((1 - x)/x)]*Sqrt[1 + x])/(3*Sqrt[1 + x^(-1)]) + (2*Sqrt[-((1 - x)/x)]*x*Sqrt[1 + x])/(3*Sqrt[1 + x^(-1)])","A",4,4,12,0.3333,1,"{6176, 6181, 78, 37}"
325,1,71,0,0.103072,"\int e^{\coth ^{-1}(x)} \sqrt{1-x} x \, dx","Int[E^ArcCoth[x]*Sqrt[1 - x]*x,x]","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} \sqrt{1-x} x^2}{5 \sqrt{1-\frac{1}{x}}}-\frac{4 \left(\frac{1}{x}+1\right)^{3/2} \sqrt{1-x} x}{15 \sqrt{1-\frac{1}{x}}}","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} \sqrt{1-x} x^2}{5 \sqrt{1-\frac{1}{x}}}-\frac{4 \left(\frac{1}{x}+1\right)^{3/2} \sqrt{1-x} x}{15 \sqrt{1-\frac{1}{x}}}",1,"(-4*(1 + x^(-1))^(3/2)*Sqrt[1 - x]*x)/(15*Sqrt[1 - x^(-1)]) + (2*(1 + x^(-1))^(3/2)*Sqrt[1 - x]*x^2)/(5*Sqrt[1 - x^(-1)])","A",4,4,15,0.2667,1,"{6176, 6181, 45, 37}"
326,1,20,0,0.0196056,"\int e^{\coth ^{-1}(x)} \sqrt{1-x} \, dx","Int[E^ArcCoth[x]*Sqrt[1 - x],x]","\frac{2}{3} \sqrt{1-x} (x+1) e^{\coth ^{-1}(x)}","\frac{2}{3} \sqrt{1-x} (x+1) e^{\coth ^{-1}(x)}",1,"(2*E^ArcCoth[x]*Sqrt[1 - x]*(1 + x))/3","A",1,1,14,0.07143,1,"{6174}"
327,1,73,0,0.096523,"\int \frac{e^{\coth ^{-1}(x)} x}{\sqrt{1+x}} \, dx","Int[(E^ArcCoth[x]*x)/Sqrt[1 + x],x]","\frac{2 \sqrt{\frac{1}{x}+1} \sqrt{-\frac{1-x}{x}} x^2}{3 \sqrt{x+1}}+\frac{4 \sqrt{\frac{1}{x}+1} \sqrt{-\frac{1-x}{x}} x}{3 \sqrt{x+1}}","\frac{2 \sqrt{\frac{1}{x}+1} \sqrt{-\frac{1-x}{x}} x^2}{3 \sqrt{x+1}}+\frac{4 \sqrt{\frac{1}{x}+1} \sqrt{-\frac{1-x}{x}} x}{3 \sqrt{x+1}}",1,"(4*Sqrt[1 + x^(-1)]*Sqrt[-((1 - x)/x)]*x)/(3*Sqrt[1 + x]) + (2*Sqrt[1 + x^(-1)]*Sqrt[-((1 - x)/x)]*x^2)/(3*Sqrt[1 + x])","A",4,4,13,0.3077,1,"{6176, 6181, 45, 37}"
328,1,33,0,0.0750883,"\int \frac{e^{\coth ^{-1}(x)}}{\sqrt{1+x}} \, dx","Int[E^ArcCoth[x]/Sqrt[1 + x],x]","\frac{2 \sqrt{\frac{1}{x}+1} \sqrt{-\frac{1-x}{x}} x}{\sqrt{x+1}}","\frac{2 \sqrt{\frac{1}{x}+1} \sqrt{-\frac{1-x}{x}} x}{\sqrt{x+1}}",1,"(2*Sqrt[1 + x^(-1)]*Sqrt[-((1 - x)/x)]*x)/Sqrt[1 + x]","A",3,3,12,0.2500,1,"{6176, 6181, 37}"
329,1,126,0,0.1145027,"\int \frac{e^{\coth ^{-1}(x)} x}{\sqrt{1-x}} \, dx","Int[(E^ArcCoth[x]*x)/Sqrt[1 - x],x]","\frac{2 \sqrt{1-\frac{1}{x}} \left(\frac{1}{x}+1\right)^{3/2} x^2}{3 \sqrt{1-x}}+\frac{2 \sqrt{1-\frac{1}{x}} \sqrt{\frac{1}{x}+1} x}{\sqrt{1-x}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{1-x} \sqrt{\frac{1}{x}}}","\frac{2 \sqrt{1-\frac{1}{x}} \left(\frac{1}{x}+1\right)^{3/2} x^2}{3 \sqrt{1-x}}+\frac{2 \sqrt{1-\frac{1}{x}} \sqrt{\frac{1}{x}+1} x}{\sqrt{1-x}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{1-x} \sqrt{\frac{1}{x}}}",1,"(2*Sqrt[1 - x^(-1)]*Sqrt[1 + x^(-1)]*x)/Sqrt[1 - x] + (2*Sqrt[1 - x^(-1)]*(1 + x^(-1))^(3/2)*x^2)/(3*Sqrt[1 - x]) - (2*Sqrt[2]*Sqrt[1 - x^(-1)]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/Sqrt[1 + x^(-1)]])/(Sqrt[1 - x]*Sqrt[x^(-1)])","A",6,6,15,0.4000,1,"{6176, 6181, 96, 94, 93, 206}"
330,1,90,0,0.0925382,"\int \frac{e^{\coth ^{-1}(x)}}{\sqrt{1-x}} \, dx","Int[E^ArcCoth[x]/Sqrt[1 - x],x]","\frac{2 \sqrt{1-\frac{1}{x}} \sqrt{\frac{1}{x}+1} x}{\sqrt{1-x}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{1-x} \sqrt{\frac{1}{x}}}","\frac{2 \sqrt{1-\frac{1}{x}} \sqrt{\frac{1}{x}+1} x}{\sqrt{1-x}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{x}} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{1-x} \sqrt{\frac{1}{x}}}",1,"(2*Sqrt[1 - x^(-1)]*Sqrt[1 + x^(-1)]*x)/Sqrt[1 - x] - (2*Sqrt[2]*Sqrt[1 - x^(-1)]*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/Sqrt[1 + x^(-1)]])/(Sqrt[1 - x]*Sqrt[x^(-1)])","A",5,5,14,0.3571,1,"{6176, 6181, 94, 93, 206}"
331,1,93,0,0.1168479,"\int \frac{e^{\coth ^{-1}(x)} x}{(1+x)^{3/2}} \, dx","Int[(E^ArcCoth[x]*x)/(1 + x)^(3/2),x]","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} \sqrt{-\frac{1-x}{x}} x^2}{(x+1)^{3/2}}+\frac{\sqrt{2} \left(\frac{1}{x}+1\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{-\frac{1-x}{x}}}\right)}{\left(\frac{1}{x}\right)^{3/2} (x+1)^{3/2}}","\frac{2 \left(\frac{1}{x}+1\right)^{3/2} \sqrt{-\frac{1-x}{x}} x^2}{(x+1)^{3/2}}+\frac{\sqrt{2} \left(\frac{1}{x}+1\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{-\frac{1-x}{x}}}\right)}{\left(\frac{1}{x}\right)^{3/2} (x+1)^{3/2}}",1,"(2*(1 + x^(-1))^(3/2)*Sqrt[-((1 - x)/x)]*x^2)/(1 + x)^(3/2) + (Sqrt[2]*(1 + x^(-1))^(3/2)*ArcTan[(Sqrt[2]*Sqrt[x^(-1)])/Sqrt[-((1 - x)/x)]])/((x^(-1))^(3/2)*(1 + x)^(3/2))","A",5,5,13,0.3846,1,"{6176, 6181, 96, 93, 203}"
332,1,58,0,0.0965376,"\int \frac{e^{\coth ^{-1}(x)}}{(1+x)^{3/2}} \, dx","Int[E^ArcCoth[x]/(1 + x)^(3/2),x]","-\frac{\sqrt{2} \left(\frac{1}{x}+1\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{-\frac{1-x}{x}}}\right)}{\left(\frac{1}{x}\right)^{3/2} (x+1)^{3/2}}","-\frac{\sqrt{2} \left(\frac{1}{x}+1\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{-\frac{1-x}{x}}}\right)}{\left(\frac{1}{x}\right)^{3/2} (x+1)^{3/2}}",1,"-((Sqrt[2]*(1 + x^(-1))^(3/2)*ArcTan[(Sqrt[2]*Sqrt[x^(-1)])/Sqrt[-((1 - x)/x)]])/((x^(-1))^(3/2)*(1 + x)^(3/2)))","A",4,4,12,0.3333,1,"{6176, 6181, 93, 203}"
333,1,130,0,0.1316296,"\int \frac{e^{\coth ^{-1}(x)} x}{(1-x)^{3/2}} \, dx","Int[(E^ArcCoth[x]*x)/(1 - x)^(3/2),x]","-\frac{\sqrt{1-\frac{1}{x}} \left(\frac{1}{x}+1\right)^{3/2} x^2}{2 (1-x)^{3/2}}+\frac{5 \left(1-\frac{1}{x}\right)^{3/2} \sqrt{\frac{1}{x}+1} x^2}{2 (1-x)^{3/2}}-\frac{5 \left(1-\frac{1}{x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{2} (1-x)^{3/2} \left(\frac{1}{x}\right)^{3/2}}","-\frac{\sqrt{1-\frac{1}{x}} \left(\frac{1}{x}+1\right)^{3/2} x^2}{2 (1-x)^{3/2}}+\frac{5 \left(1-\frac{1}{x}\right)^{3/2} \sqrt{\frac{1}{x}+1} x^2}{2 (1-x)^{3/2}}-\frac{5 \left(1-\frac{1}{x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{2} (1-x)^{3/2} \left(\frac{1}{x}\right)^{3/2}}",1,"(5*(1 - x^(-1))^(3/2)*Sqrt[1 + x^(-1)]*x^2)/(2*(1 - x)^(3/2)) - (Sqrt[1 - x^(-1)]*(1 + x^(-1))^(3/2)*x^2)/(2*(1 - x)^(3/2)) - (5*(1 - x^(-1))^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/Sqrt[1 + x^(-1)]])/(Sqrt[2]*(1 - x)^(3/2)*(x^(-1))^(3/2))","A",6,6,15,0.4000,1,"{6176, 6181, 96, 94, 93, 206}"
334,1,90,0,0.1095521,"\int \frac{e^{\coth ^{-1}(x)}}{(1-x)^{3/2}} \, dx","Int[E^ArcCoth[x]/(1 - x)^(3/2),x]","-\frac{\sqrt{\frac{1}{x}+1} x \sqrt{1-\frac{1}{x}}}{(1-x)^{3/2}}-\frac{\left(1-\frac{1}{x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{2} (1-x)^{3/2} \left(\frac{1}{x}\right)^{3/2}}","-\frac{\sqrt{\frac{1}{x}+1} x \sqrt{1-\frac{1}{x}}}{(1-x)^{3/2}}-\frac{\left(1-\frac{1}{x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+1}}\right)}{\sqrt{2} (1-x)^{3/2} \left(\frac{1}{x}\right)^{3/2}}",1,"-((Sqrt[1 - x^(-1)]*Sqrt[1 + x^(-1)]*x)/(1 - x)^(3/2)) - ((1 - x^(-1))^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[x^(-1)])/Sqrt[1 + x^(-1)]])/(Sqrt[2]*(1 - x)^(3/2)*(x^(-1))^(3/2))","A",5,5,14,0.3571,1,"{6176, 6181, 94, 93, 206}"
335,1,131,0,0.2317377,"\int e^{-\coth ^{-1}(a x)} x^m \sqrt{c-a c x} \, dx","Int[(x^m*Sqrt[c - a*c*x])/E^ArcCoth[a*x],x]","\frac{2 \sqrt{\frac{1}{a x}+1} x^{m+1} \sqrt{c-a c x}}{(2 m+3) \sqrt{1-\frac{1}{a x}}}-\frac{2 (4 m+5) x^m \sqrt{c-a c x} \, _2F_1\left(\frac{1}{2},-m-\frac{1}{2};\frac{1}{2}-m;-\frac{1}{a x}\right)}{a (2 m+1) (2 m+3) \sqrt{1-\frac{1}{a x}}}","\frac{2 \sqrt{\frac{1}{a x}+1} x^{m+1} \sqrt{c-a c x}}{(2 m+3) \sqrt{1-\frac{1}{a x}}}-\frac{2 (4 m+5) x^m \sqrt{c-a c x} \, _2F_1\left(\frac{1}{2},-m-\frac{1}{2};\frac{1}{2}-m;-\frac{1}{a x}\right)}{a (2 m+1) (2 m+3) \sqrt{1-\frac{1}{a x}}}",1,"(2*Sqrt[1 + 1/(a*x)]*x^(1 + m)*Sqrt[c - a*c*x])/((3 + 2*m)*Sqrt[1 - 1/(a*x)]) - (2*(5 + 4*m)*x^m*Sqrt[c - a*c*x]*Hypergeometric2F1[1/2, -1/2 - m, 1/2 - m, -(1/(a*x))])/(a*(1 + 2*m)*(3 + 2*m)*Sqrt[1 - 1/(a*x)])","A",4,4,23,0.1739,1,"{6176, 6181, 79, 64}"
336,1,185,0,0.2367833,"\int e^{-\coth ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[(x^2*Sqrt[c - a*c*x])/E^ArcCoth[a*x],x]","\frac{104 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{208 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}}}-\frac{26 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{35 a \sqrt{1-\frac{1}{a x}}}","-\frac{2 x^2 \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}}{7 a c}+\frac{6 x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}}{35 a^2 c}+\frac{38 x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}}{105 a^2}+\frac{152 c x \sqrt{1-\frac{1}{a^2 x^2}}}{105 a^2 \sqrt{c-a c x}}",1,"(-208*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(105*a^3*Sqrt[1 - 1/(a*x)]) + (104*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(105*a^2*Sqrt[1 - 1/(a*x)]) - (26*Sqrt[1 + 1/(a*x)]*x^2*Sqrt[c - a*c*x])/(35*a*Sqrt[1 - 1/(a*x)]) + (2*Sqrt[1 + 1/(a*x)]*x^3*Sqrt[c - a*c*x])/(7*Sqrt[1 - 1/(a*x)])","A",6,5,23,0.2174,0,"{6176, 6181, 78, 45, 37}"
337,1,137,0,0.1935054,"\int e^{-\coth ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[(x*Sqrt[c - a*c*x])/E^ArcCoth[a*x],x]","\frac{12 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{5 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}}}-\frac{6 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{5 a \sqrt{1-\frac{1}{a x}}}","-\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}} (c-a c x)^{3/2}}{5 a c}-\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}}{5 a}-\frac{8 c x \sqrt{1-\frac{1}{a^2 x^2}}}{5 a \sqrt{c-a c x}}",1,"(12*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(5*a^2*Sqrt[1 - 1/(a*x)]) - (6*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(5*a*Sqrt[1 - 1/(a*x)]) + (2*Sqrt[1 + 1/(a*x)]*x^2*Sqrt[c - a*c*x])/(5*Sqrt[1 - 1/(a*x)])","A",5,5,21,0.2381,0,"{6176, 6181, 78, 45, 37}"
338,1,89,0,0.1534164,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^ArcCoth[a*x],x]","\frac{2 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}}}-\frac{10 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}}}","\frac{2}{3} x \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-a c x}+\frac{8 c x \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-a c x}}",1,"(-10*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - 1/(a*x)]) + (2*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)])","A",4,4,20,0.2000,0,"{6176, 6181, 78, 37}"
339,1,94,0,0.2089929,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[Sqrt[c - a*c*x]/(E^ArcCoth[a*x]*x),x]","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}}}+\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}}}+\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}",1,"(2*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/Sqrt[1 - 1/(a*x)] + (2*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(Sqrt[a]*Sqrt[1 - 1/(a*x)])","A",5,5,23,0.2174,1,"{6176, 6181, 78, 54, 215}"
340,1,96,0,0.2036054,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[Sqrt[c - a*c*x]/(E^ArcCoth[a*x]*x^2),x]","\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}-\frac{3 \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}","\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}-\frac{3 \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"(Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*x) - (3*Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/Sqrt[1 - 1/(a*x)]","A",5,5,23,0.2174,1,"{6176, 6181, 80, 54, 215}"
341,1,139,0,0.2641815,"\int e^{-2 \coth ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[(x^3*Sqrt[c - a*c*x])/E^(2*ArcCoth[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",9,7,23,0.3043,1,"{6167, 6130, 21, 88, 50, 63, 206}"
342,1,97,0,0.2484653,"\int e^{-2 \coth ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[(x^2*Sqrt[c - a*c*x])/E^(2*ArcCoth[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",9,7,23,0.3043,1,"{6167, 6130, 21, 88, 50, 63, 206}"
343,1,97,0,0.1703438,"\int e^{-2 \coth ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[(x*Sqrt[c - a*c*x])/E^(2*ArcCoth[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",8,7,21,0.3333,1,"{6167, 6130, 21, 80, 50, 63, 206}"
344,1,76,0,0.0992223,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(2*ArcCoth[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",7,6,20,0.3000,1,"{6167, 6130, 21, 50, 63, 206}"
345,1,74,0,0.2324922,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcCoth[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",9,8,23,0.3478,1,"{6167, 6130, 21, 84, 156, 63, 208, 206}"
346,1,78,0,0.2261141,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcCoth[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",9,8,23,0.3478,1,"{6167, 6130, 21, 98, 156, 63, 208, 206}"
347,1,106,0,0.259572,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcCoth[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",10,9,23,0.3913,1,"{6167, 6130, 21, 98, 151, 156, 63, 208, 206}"
348,1,127,0,0.277919,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcCoth[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",11,9,23,0.3913,1,"{6167, 6130, 21, 98, 151, 156, 63, 208, 206}"
349,1,148,0,0.3052075,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[Sqrt[c - a*c*x]/(E^(2*ArcCoth[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",12,9,23,0.3913,1,"{6167, 6130, 21, 98, 151, 156, 63, 208, 206}"
350,1,281,0,0.286094,"\int e^{-3 \coth ^{-1}(a x)} x^3 \sqrt{c-a c x} \, dx","Int[(x^3*Sqrt[c - a*c*x])/E^(3*ArcCoth[a*x]),x]","\frac{164 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{15 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{82 x^2 \sqrt{c-a c x}}{9 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{656 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{45 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{1312 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{45 a^4 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^4 \sqrt{c-a c x}}{9 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{8 x^3 \sqrt{c-a c x}}{9 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","\frac{164 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{15 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{82 x^2 \sqrt{c-a c x}}{9 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{656 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{45 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{1312 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{45 a^4 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^4 \sqrt{c-a c x}}{9 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{8 x^3 \sqrt{c-a c x}}{9 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(1312*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(45*a^4*Sqrt[1 - 1/(a*x)]) - (656*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(45*a^3*Sqrt[1 - 1/(a*x)]) - (82*x^2*Sqrt[c - a*c*x])/(9*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (164*Sqrt[1 + 1/(a*x)]*x^2*Sqrt[c - a*c*x])/(15*a^2*Sqrt[1 - 1/(a*x)]) - (8*x^3*Sqrt[c - a*c*x])/(9*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (2*x^4*Sqrt[c - a*c*x])/(9*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])","A",8,6,23,0.2609,1,"{6176, 6181, 89, 78, 45, 37}"
351,1,231,0,0.2613845,"\int e^{-3 \coth ^{-1}(a x)} x^2 \sqrt{c-a c x} \, dx","Int[(x^2*Sqrt[c - a*c*x])/E^(3*ArcCoth[a*x]),x]","\frac{1336 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{334 x \sqrt{c-a c x}}{35 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{2672 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{44 x^2 \sqrt{c-a c x}}{35 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","\frac{1336 x \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{334 x \sqrt{c-a c x}}{35 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{2672 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{105 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{2 x^3 \sqrt{c-a c x}}{7 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{44 x^2 \sqrt{c-a c x}}{35 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-2672*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(105*a^3*Sqrt[1 - 1/(a*x)]) - (334*x*Sqrt[c - a*c*x])/(35*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (1336*Sqrt[1 + 1/(a*x)]*x*Sqrt[c - a*c*x])/(105*a^2*Sqrt[1 - 1/(a*x)]) - (44*x^2*Sqrt[c - a*c*x])/(35*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (2*x^3*Sqrt[c - a*c*x])/(7*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])","A",7,6,23,0.2609,1,"{6176, 6181, 89, 78, 45, 37}"
352,1,182,0,0.2161731,"\int e^{-3 \coth ^{-1}(a x)} x \sqrt{c-a c x} \, dx","Int[(x*Sqrt[c - a*c*x])/E^(3*ArcCoth[a*x]),x]","\frac{316 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{15 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{158 \sqrt{c-a c x}}{15 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 x^2 \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{32 x \sqrt{c-a c x}}{15 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","\frac{316 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{15 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{158 \sqrt{c-a c x}}{15 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 x^2 \sqrt{c-a c x}}{5 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{32 x \sqrt{c-a c x}}{15 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-158*Sqrt[c - a*c*x])/(15*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (316*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(15*a^2*Sqrt[1 - 1/(a*x)]) - (32*x*Sqrt[c - a*c*x])/(15*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (2*x^2*Sqrt[c - a*c*x])/(5*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])","A",6,6,21,0.2857,1,"{6176, 6181, 89, 78, 45, 37}"
353,1,137,0,0.1626814,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[Sqrt[c - a*c*x]/E^(3*ArcCoth[a*x]),x]","-\frac{46 \sqrt{c-a c x}}{3 a^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{20 \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","-\frac{46 \sqrt{c-a c x}}{3 a^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 x \sqrt{c-a c x}}{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{20 \sqrt{c-a c x}}{3 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-20*Sqrt[c - a*c*x])/(3*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (46*Sqrt[c - a*c*x])/(3*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x) + (2*x*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])","A",5,5,20,0.2500,1,"{6176, 6181, 89, 78, 37}"
354,1,140,0,0.2214204,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcCoth[a*x])*x),x]","\frac{2 \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{10 \sqrt{c-a c x}}{a x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}","\frac{2 \sqrt{c-a c x}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{10 \sqrt{c-a c x}}{a x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{2 \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{1-\frac{1}{a x}}}",1,"(2*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (10*Sqrt[c - a*c*x])/(a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x) - (2*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(Sqrt[a]*Sqrt[1 - 1/(a*x)])","A",6,6,23,0.2609,1,"{6176, 6181, 89, 78, 54, 215}"
355,1,140,0,0.2229956,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^2} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcCoth[a*x])*x^2),x]","-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{7 \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}","-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{7 \sqrt{a} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"(-8*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x) - (Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*x) + (7*Sqrt[a]*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/Sqrt[1 - 1/(a*x)]","A",6,6,23,0.2609,1,"{6176, 6181, 89, 80, 54, 215}"
356,1,190,0,0.2317783,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^3} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcCoth[a*x])*x^3),x]","-\frac{47 a^{3/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{4 \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{2 x^2 \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{47 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{4 x \sqrt{1-\frac{1}{a x}}}","-\frac{47 a^{3/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{4 \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{2 x^2 \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{47 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{4 x \sqrt{1-\frac{1}{a x}}}",1,"(-8*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x^2) - (Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(2*Sqrt[1 - 1/(a*x)]*x^2) + (47*a*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(4*Sqrt[1 - 1/(a*x)]*x) - (47*a^(3/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(4*Sqrt[1 - 1/(a*x)])","A",7,7,23,0.3043,1,"{6176, 6181, 89, 80, 50, 54, 215}"
357,1,238,0,0.2463449,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^4} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcCoth[a*x])*x^4),x]","-\frac{119 a^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{8 x \sqrt{1-\frac{1}{a x}}}+\frac{119 a^{5/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{8 \sqrt{1-\frac{1}{a x}}}+\frac{119 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{12 x^2 \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{3 x^3 \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","-\frac{119 a^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{8 x \sqrt{1-\frac{1}{a x}}}+\frac{119 a^{5/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{8 \sqrt{1-\frac{1}{a x}}}+\frac{119 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{12 x^2 \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{3 x^3 \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-8*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x^3) - (Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(3*Sqrt[1 - 1/(a*x)]*x^3) + (119*a*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(12*Sqrt[1 - 1/(a*x)]*x^2) - (119*a^2*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(8*Sqrt[1 - 1/(a*x)]*x) + (119*a^(5/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(8*Sqrt[1 - 1/(a*x)])","A",8,7,23,0.3043,1,"{6176, 6181, 89, 80, 50, 54, 215}"
358,1,286,0,0.2635507,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a c x}}{x^5} \, dx","Int[Sqrt[c - a*c*x]/(E^(3*ArcCoth[a*x])*x^5),x]","-\frac{1115 a^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{96 x^2 \sqrt{1-\frac{1}{a x}}}+\frac{1115 a^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{64 x \sqrt{1-\frac{1}{a x}}}-\frac{1115 a^{7/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{64 \sqrt{1-\frac{1}{a x}}}+\frac{223 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{24 x^3 \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{4 x^4 \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","-\frac{1115 a^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{96 x^2 \sqrt{1-\frac{1}{a x}}}+\frac{1115 a^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{64 x \sqrt{1-\frac{1}{a x}}}-\frac{1115 a^{7/2} \sqrt{\frac{1}{x}} \sqrt{c-a c x} \sinh ^{-1}\left(\frac{\sqrt{\frac{1}{x}}}{\sqrt{a}}\right)}{64 \sqrt{1-\frac{1}{a x}}}+\frac{223 a \sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{24 x^3 \sqrt{1-\frac{1}{a x}}}-\frac{\sqrt{\frac{1}{a x}+1} \sqrt{c-a c x}}{4 x^4 \sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-a c x}}{x^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-8*Sqrt[c - a*c*x])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x^4) - (Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(4*Sqrt[1 - 1/(a*x)]*x^4) + (223*a*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(24*Sqrt[1 - 1/(a*x)]*x^3) - (1115*a^2*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(96*Sqrt[1 - 1/(a*x)]*x^2) + (1115*a^3*Sqrt[1 + 1/(a*x)]*Sqrt[c - a*c*x])/(64*Sqrt[1 - 1/(a*x)]*x) - (1115*a^(7/2)*Sqrt[x^(-1)]*Sqrt[c - a*c*x]*ArcSinh[Sqrt[x^(-1)]/Sqrt[a]])/(64*Sqrt[1 - 1/(a*x)])","A",9,7,23,0.3043,1,"{6176, 6181, 89, 80, 50, 54, 215}"
359,1,278,0,0.2675825,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{2+\frac{n}{2}} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(2 + n/2),x]","\frac{2 \left(n^2+14 n+56\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{a^2 (n+6) \left(n^2+6 n+8\right) x}-\frac{\left(n^2+14 n+56\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{a (n+4) (n+6)}+\frac{(n+8) x \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{n+6}-\frac{x \left(a-\frac{1}{x}\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{a}","\frac{2 \left(n^2+14 n+56\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{a^2 (n+6) \left(n^2+6 n+8\right) x}-\frac{\left(n^2+14 n+56\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{a (n+4) (n+6)}+\frac{(n+8) x \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{n+6}-\frac{x \left(a-\frac{1}{x}\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} (c-a c x)^{\frac{n+4}{2}}}{a}",1,"-(((56 + 14*n + n^2)*(1 - 1/(a*x))^(-2 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*(c - a*c*x)^((4 + n)/2))/(a*(4 + n)*(6 + n))) + (2*(56 + 14*n + n^2)*(1 - 1/(a*x))^(-2 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*(c - a*c*x)^((4 + n)/2))/(a^2*(6 + n)*(8 + 6*n + n^2)*x) + ((8 + n)*(1 - 1/(a*x))^(-2 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x*(c - a*c*x)^((4 + n)/2))/(6 + n) - ((a - x^(-1))*(1 - 1/(a*x))^(-2 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x*(c - a*c*x)^((4 + n)/2))/a","A",6,6,24,0.2500,1,"{6176, 6181, 90, 79, 45, 37}"
360,1,127,0,0.157131,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{1+\frac{n}{2}} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(1 + n/2),x]","\frac{2 x \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} (c-a c x)^{\frac{n+2}{2}}}{n+4}-\frac{2 (n+6) \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} (c-a c x)^{\frac{n+2}{2}}}{a (n+2) (n+4)}","\frac{2 x \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} (c-a c x)^{\frac{n+2}{2}}}{n+4}-\frac{2 (n+6) \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} (c-a c x)^{\frac{n+2}{2}}}{a (n+2) (n+4)}",1,"(-2*(6 + n)*(1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*(c - a*c*x)^((2 + n)/2))/(a*(2 + n)*(4 + n)) + (2*(1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x*(c - a*c*x)^((2 + n)/2))/(4 + n)","A",4,4,24,0.1667,1,"{6176, 6181, 79, 37}"
361,1,36,0,0.0298995,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{n/2} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(n/2),x]","\frac{2 (a x+1) (c-a c x)^{n/2} e^{n \coth ^{-1}(a x)}}{a (n+2)}","\frac{2 (a x+1) (c-a c x)^{n/2} e^{n \coth ^{-1}(a x)}}{a (n+2)}",1,"(2*E^(n*ArcCoth[a*x])*(1 + a*x)*(c - a*c*x)^(n/2))/(a*(2 + n))","A",1,1,22,0.04545,1,"{6174}"
362,1,80,0,0.1463416,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{-1+\frac{n}{2}} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(-1 + n/2),x]","\frac{2 x \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{n/2} (c-a c x)^{\frac{n-2}{2}} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{n}","\frac{2 x \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{n/2} (c-a c x)^{\frac{n-2}{2}} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{n}",1,"(2*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^(n/2)*x*(c - a*c*x)^((-2 + n)/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, 2/((a + x^(-1))*x)])/n","A",3,3,24,0.1250,1,"{6176, 6181, 131}"
363,1,88,0,0.1473178,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{-2+\frac{n}{2}} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(-2 + n/2),x]","-\frac{2 x \left(1-\frac{1}{a x}\right)^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} (c-a c x)^{\frac{n-4}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2-n}","-\frac{2 x \left(1-\frac{1}{a x}\right)^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} (c-a c x)^{\frac{n-4}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2-n}",1,"(-2*(1 - 1/(a*x))^(2 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*x*(c - a*c*x)^((-4 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, 2/((a + x^(-1))*x)])/(2 - n)","A",3,3,24,0.1250,1,"{6176, 6181, 131}"
364,1,104,0,0.1275911,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^p \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^p,x]","\frac{x \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} (c-a c x)^p \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2} (n-2 p)} \, _2F_1\left(\frac{1}{2} (n-2 p),-p-1;-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{p+1}","\frac{x \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} (c-a c x)^p \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2} (n-2 p)} \, _2F_1\left(\frac{1}{2} (n-2 p),-p-1;-p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^((n - 2*p)/2)*(1 + 1/(a*x))^((2 + n)/2)*x*(c - a*c*x)^p*Hypergeometric2F1[(n - 2*p)/2, -1 - p, -p, 2/((a + x^(-1))*x)])/((1 + p)*(1 - 1/(a*x))^(n/2))","A",3,3,18,0.1667,1,"{6176, 6181, 132}"
365,1,81,0,0.1273038,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^3 \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^3,x]","-\frac{32 c^3 \left(1-\frac{1}{a x}\right)^{4-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-8}{2}} \, _2F_1\left(5,4-\frac{n}{2};5-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (8-n)}","-\frac{32 c^3 \left(1-\frac{1}{a x}\right)^{4-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-8}{2}} \, _2F_1\left(5,4-\frac{n}{2};5-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (8-n)}",1,"(-32*c^3*(1 - 1/(a*x))^(4 - n/2)*(1 + 1/(a*x))^((-8 + n)/2)*Hypergeometric2F1[5, 4 - n/2, 5 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(8 - n))","A",3,3,18,0.1667,1,"{6175, 6180, 131}"
366,1,81,0,0.1280742,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^2 \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^2,x]","\frac{16 c^2 \left(1-\frac{1}{a x}\right)^{3-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-6}{2}} \, _2F_1\left(4,3-\frac{n}{2};4-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (6-n)}","\frac{16 c^2 \left(1-\frac{1}{a x}\right)^{3-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-6}{2}} \, _2F_1\left(4,3-\frac{n}{2};4-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (6-n)}",1,"(16*c^2*(1 - 1/(a*x))^(3 - n/2)*(1 + 1/(a*x))^((-6 + n)/2)*Hypergeometric2F1[4, 3 - n/2, 4 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(6 - n))","A",3,3,18,0.1667,1,"{6175, 6180, 131}"
367,1,79,0,0.075156,"\int e^{n \coth ^{-1}(a x)} (c-a c x) \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x),x]","-\frac{8 c \left(1-\frac{1}{a x}\right)^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-4}{2}} \, _2F_1\left(3,2-\frac{n}{2};3-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (4-n)}","-\frac{8 c \left(1-\frac{1}{a x}\right)^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-4}{2}} \, _2F_1\left(3,2-\frac{n}{2};3-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (4-n)}",1,"(-8*c*(1 - 1/(a*x))^(2 - n/2)*(1 + 1/(a*x))^((-4 + n)/2)*Hypergeometric2F1[3, 2 - n/2, 3 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(4 - n))","A",3,3,16,0.1875,1,"{6175, 6180, 131}"
368,1,71,0,0.1212976,"\int \frac{e^{n \coth ^{-1}(a x)}}{c-a c x} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x),x]","\frac{2 \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c n}","\frac{2 \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c n}",1,"(2*(1 + 1/(a*x))^(n/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*c*n*(1 - 1/(a*x))^(n/2))","A",3,3,18,0.1667,1,"{6175, 6180, 131}"
369,1,48,0,0.1092063,"\int \frac{e^{n \coth ^{-1}(a x)}}{(c-a c x)^2} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x)^2,x]","-\frac{\left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{a c^2 (n+2)}","-\frac{\left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{a c^2 (n+2)}",1,"-(((1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^2*(2 + n)))","A",3,3,18,0.1667,1,"{6175, 6180, 37}"
370,1,104,0,0.1493306,"\int \frac{e^{n \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x)^3,x]","\frac{\left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{a c^3 (n+4)}-\frac{(n+3) \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{a c^3 (n+2) (n+4)}","\frac{\left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{a c^3 (n+4)}-\frac{(n+3) \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{a c^3 (n+2) (n+4)}",1,"((1 - 1/(a*x))^(-2 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^3*(4 + n)) - ((3 + n)*(1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^3*(2 + n)*(4 + n))","A",4,4,18,0.2222,1,"{6175, 6180, 79, 37}"
371,1,224,0,0.2616593,"\int \frac{e^{n \coth ^{-1}(a x)}}{(c-a c x)^4} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x)^4,x]","-\frac{\left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-3}}{a^2 c^4 x}-\frac{\left(n^2+8 n+14\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2}}{a c^4 (n+4) (n+6)}-\frac{\left(n^2+8 n+14\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{a c^4 (n+6) \left(n^2+6 n+8\right)}+\frac{(n+5) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-3}}{a c^4 (n+6)}","-\frac{\left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-3}}{a^2 c^4 x}-\frac{\left(n^2+8 n+14\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-2}}{a c^4 (n+4) (n+6)}-\frac{\left(n^2+8 n+14\right) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{a c^4 (n+6) \left(n^2+6 n+8\right)}+\frac{(n+5) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-3}}{a c^4 (n+6)}",1,"((5 + n)*(1 - 1/(a*x))^(-3 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^4*(6 + n)) - ((14 + 8*n + n^2)*(1 - 1/(a*x))^(-2 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^4*(4 + n)*(6 + n)) - ((14 + 8*n + n^2)*(1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^4*(6 + n)*(8 + 6*n + n^2)) - ((1 - 1/(a*x))^(-3 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a^2*c^4*x)","A",6,6,18,0.3333,1,"{6175, 6180, 90, 79, 45, 37}"
372,1,98,0,0.1990314,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{5/2} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(5/2),x]","\frac{2}{7} x (c-a c x)^{5/2} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n-5}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{7}{2},\frac{n-5}{2};-\frac{5}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)","\frac{2}{7} x (c-a c x)^{5/2} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n-5}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{7}{2},\frac{n-5}{2};-\frac{5}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)",1,"(2*((a - x^(-1))/(a + x^(-1)))^((-5 + n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x*(c - a*c*x)^(5/2)*Hypergeometric2F1[-7/2, (-5 + n)/2, -5/2, 2/((a + x^(-1))*x)])/(7*(1 - 1/(a*x))^(n/2))","A",3,3,20,0.1500,1,"{6176, 6181, 132}"
373,1,98,0,0.1992182,"\int e^{n \coth ^{-1}(a x)} (c-a c x)^{3/2} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a*c*x)^(3/2),x]","\frac{2}{5} x (c-a c x)^{3/2} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{5}{2},\frac{n-3}{2};-\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)","\frac{2}{5} x (c-a c x)^{3/2} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{5}{2},\frac{n-3}{2};-\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)",1,"(2*((a - x^(-1))/(a + x^(-1)))^((-3 + n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x*(c - a*c*x)^(3/2)*Hypergeometric2F1[-5/2, (-3 + n)/2, -3/2, 2/((a + x^(-1))*x)])/(5*(1 - 1/(a*x))^(n/2))","A",3,3,20,0.1500,1,"{6176, 6181, 132}"
374,1,98,0,0.1773475,"\int e^{n \coth ^{-1}(a x)} \sqrt{c-a c x} \, dx","Int[E^(n*ArcCoth[a*x])*Sqrt[c - a*c*x],x]","\frac{2}{3} x \sqrt{c-a c x} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{3}{2},\frac{n-1}{2};-\frac{1}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)","\frac{2}{3} x \sqrt{c-a c x} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{3}{2},\frac{n-1}{2};-\frac{1}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)",1,"(2*((a - x^(-1))/(a + x^(-1)))^((-1 + n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x*Sqrt[c - a*c*x]*Hypergeometric2F1[-3/2, (-1 + n)/2, -1/2, 2/((a + x^(-1))*x)])/(3*(1 - 1/(a*x))^(n/2))","A",3,3,20,0.1500,1,"{6176, 6181, 132}"
375,1,96,0,0.179679,"\int \frac{e^{n \coth ^{-1}(a x)}}{\sqrt{c-a c x}} \, dx","Int[E^(n*ArcCoth[a*x])/Sqrt[c - a*c*x],x]","\frac{2 x \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+1}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{1}{2},\frac{n+1}{2};\frac{1}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{\sqrt{c-a c x}}","\frac{2 x \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+1}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(-\frac{1}{2},\frac{n+1}{2};\frac{1}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{\sqrt{c-a c x}}",1,"(2*((a - x^(-1))/(a + x^(-1)))^((1 + n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x*Hypergeometric2F1[-1/2, (1 + n)/2, 1/2, 2/((a + x^(-1))*x)])/((1 - 1/(a*x))^(n/2)*Sqrt[c - a*c*x])","A",3,3,20,0.1500,1,"{6176, 6181, 132}"
376,1,96,0,0.2002636,"\int \frac{e^{n \coth ^{-1}(a x)}}{(c-a c x)^{3/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x)^(3/2),x]","-\frac{2 x \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+3}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{(c-a c x)^{3/2}}","-\frac{2 x \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+3}{2}} \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{(c-a c x)^{3/2}}",1,"(-2*((a - x^(-1))/(a + x^(-1)))^((3 + n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x*Hypergeometric2F1[1/2, (3 + n)/2, 3/2, 2/((a + x^(-1))*x)])/((1 - 1/(a*x))^(n/2)*(c - a*c*x)^(3/2))","A",3,3,20,0.1500,1,"{6176, 6181, 132}"
377,1,167,0,0.2282358,"\int \frac{e^{n \coth ^{-1}(a x)}}{(c-a c x)^{5/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x)^(5/2),x]","\frac{a x^2 \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{2-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{(n+3) (c-a c x)^{5/2}}-\frac{a x^2 \left(1-\frac{1}{a x}\right)^{\frac{2-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{(n+3) (c-a c x)^{5/2}}","\frac{a x^2 \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{2-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{(n+3) (c-a c x)^{5/2}}-\frac{a x^2 \left(1-\frac{1}{a x}\right)^{\frac{2-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{(n+3) (c-a c x)^{5/2}}",1,"-((a*(1 - 1/(a*x))^((2 - n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x^2)/((3 + n)*(c - a*c*x)^(5/2))) + (a*((a - x^(-1))/(a + x^(-1)))^((3 + n)/2)*(1 - 1/(a*x))^((2 - n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x^2*Hypergeometric2F1[1/2, (3 + n)/2, 3/2, 2/((a + x^(-1))*x)])/((3 + n)*(c - a*c*x)^(5/2))","A",4,4,20,0.2000,1,"{6176, 6181, 94, 132}"
378,1,245,0,0.2705514,"\int \frac{e^{n \coth ^{-1}(a x)}}{(c-a c x)^{7/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a*c*x)^(7/2),x]","-\frac{3 a^2 x^3 \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+3}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{\frac{4-n}{2}} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 \left(n^2+8 n+15\right) (c-a c x)^{7/2}}+\frac{3 a^2 x^3 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{\frac{4-n}{2}}}{2 \left(n^2+8 n+15\right) (c-a c x)^{7/2}}-\frac{a x^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{\frac{2-n}{2}}}{(n+5) (c-a c x)^{7/2}}","-\frac{3 a^2 x^3 \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{n+3}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{\frac{4-n}{2}} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{3}{2};\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 \left(n^2+8 n+15\right) (c-a c x)^{7/2}}+\frac{3 a^2 x^3 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{\frac{4-n}{2}}}{2 \left(n^2+8 n+15\right) (c-a c x)^{7/2}}-\frac{a x^2 \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{\frac{2-n}{2}}}{(n+5) (c-a c x)^{7/2}}",1,"-((a*(1 - 1/(a*x))^((2 - n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x^2)/((5 + n)*(c - a*c*x)^(7/2))) + (3*a^2*(1 - 1/(a*x))^((4 - n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x^3)/(2*(15 + 8*n + n^2)*(c - a*c*x)^(7/2)) - (3*a^2*((a - x^(-1))/(a + x^(-1)))^((3 + n)/2)*(1 - 1/(a*x))^((4 - n)/2)*(1 + 1/(a*x))^((2 + n)/2)*x^3*Hypergeometric2F1[1/2, (3 + n)/2, 3/2, 2/((a + x^(-1))*x)])/(2*(15 + 8*n + n^2)*(c - a*c*x)^(7/2))","A",5,4,20,0.2000,1,"{6176, 6181, 94, 132}"
379,1,114,0,0.2662015,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^4,x]","-\frac{c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 a}+\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}} \left(6 a-\frac{1}{x}\right)}{2 a^2}+c^4 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{c^4 \csc ^{-1}(a x)}{2 a}","-\frac{c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 a}+\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}} \left(6 a-\frac{1}{x}\right)}{2 a^2}+c^4 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{c^4 \csc ^{-1}(a x)}{2 a}",1,"-(c^4*(1 - 1/(a^2*x^2))^(3/2))/(3*a) + (c^4*Sqrt[1 - 1/(a^2*x^2)]*(6*a - x^(-1)))/(2*a^2) + c^4*(1 - 1/(a^2*x^2))^(3/2)*x - (c^4*ArcCsc[a*x])/(2*a) - (3*c^4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",9,9,20,0.4500,1,"{6177, 1807, 1809, 815, 844, 216, 266, 63, 208}"
380,1,88,0,0.1906264,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^3,x]","\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(4 a+\frac{1}{x}\right)}{2 a^2}+c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{2 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c^3 \csc ^{-1}(a x)}{2 a}","\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(4 a+\frac{1}{x}\right)}{2 a^2}+c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}-\frac{2 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c^3 \csc ^{-1}(a x)}{2 a}",1,"(c^3*Sqrt[1 - 1/(a^2*x^2)]*(4*a + x^(-1)))/(2*a^2) + c^3*(1 - 1/(a^2*x^2))^(3/2)*x + (c^3*ArcCsc[a*x])/(2*a) - (2*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,8,20,0.4000,1,"{6177, 1807, 815, 844, 216, 266, 63, 208}"
381,1,62,0,0.0960085,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^2,x]","\frac{c^2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(a+\frac{1}{x}\right)}{a}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c^2 \csc ^{-1}(a x)}{a}","\frac{c^2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(a+\frac{1}{x}\right)}{a}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c^2 \csc ^{-1}(a x)}{a}",1,"(c^2*Sqrt[1 - 1/(a^2*x^2)]*(a + x^(-1))*x)/a + (c^2*ArcCsc[a*x])/a - (c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",7,7,20,0.3500,1,"{6177, 813, 844, 216, 266, 63, 208}"
382,1,27,0,0.0290766,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x)),x]","c x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{c \csc ^{-1}(a x)}{a}","c x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{c \csc ^{-1}(a x)}{a}",1,"c*Sqrt[1 - 1/(a^2*x^2)]*x + (c*ArcCsc[a*x])/a","A",3,3,18,0.1667,1,"{6177, 277, 216}"
383,1,70,0,0.1955775,"\int \frac{e^{\coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a*x)),x]","-\frac{2 \left(a+\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","-\frac{2 \left(a+\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"(-2*(a + x^(-1)))/(a^2*c*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c + (2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c)","A",7,7,20,0.3500,1,"{6177, 852, 1805, 807, 266, 63, 208}"
384,1,105,0,0.2926316,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a*x))^2,x]","-\frac{4 \left(a+\frac{1}{x}\right)}{3 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{9 a+\frac{11}{x}}{3 a^2 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}","-\frac{4 \left(a+\frac{1}{x}\right)}{3 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{9 a+\frac{11}{x}}{3 a^2 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}",1,"(-4*(a + x^(-1)))/(3*a^2*c^2*(1 - 1/(a^2*x^2))^(3/2)) - (9*a + 11/x)/(3*a^2*c^2*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^2 + (3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^2)","A",8,7,20,0.3500,1,"{6177, 852, 1805, 807, 266, 63, 208}"
385,1,138,0,0.3930374,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a*x))^3,x]","-\frac{8 \left(a+\frac{1}{x}\right)}{5 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 \left(5 a+\frac{8}{x}\right)}{15 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{60 a+\frac{79}{x}}{15 a^2 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3}+\frac{4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^3}","-\frac{8 \left(a+\frac{1}{x}\right)}{5 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 \left(5 a+\frac{8}{x}\right)}{15 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{60 a+\frac{79}{x}}{15 a^2 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3}+\frac{4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^3}",1,"(-8*(a + x^(-1)))/(5*a^2*c^3*(1 - 1/(a^2*x^2))^(5/2)) - (4*(5*a + 8/x))/(15*a^2*c^3*(1 - 1/(a^2*x^2))^(3/2)) - (60*a + 79/x)/(15*a^2*c^3*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^3 + (4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^3)","A",9,7,20,0.3500,1,"{6177, 852, 1805, 807, 266, 63, 208}"
386,1,171,0,0.5007261,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a*x))^4,x]","-\frac{16 \left(a+\frac{1}{x}\right)}{7 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{4 \left(7 a+\frac{17}{x}\right)}{35 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{175 a+\frac{307}{x}}{105 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{525 a+\frac{719}{x}}{105 a^2 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^4}+\frac{5 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}","-\frac{16 \left(a+\frac{1}{x}\right)}{7 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{4 \left(7 a+\frac{17}{x}\right)}{35 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{175 a+\frac{307}{x}}{105 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{525 a+\frac{719}{x}}{105 a^2 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^4}+\frac{5 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}",1,"(-16*(a + x^(-1)))/(7*a^2*c^4*(1 - 1/(a^2*x^2))^(7/2)) - (4*(7*a + 17/x))/(35*a^2*c^4*(1 - 1/(a^2*x^2))^(5/2)) - (175*a + 307/x)/(105*a^2*c^4*(1 - 1/(a^2*x^2))^(3/2)) - (525*a + 719/x)/(105*a^2*c^4*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^4 + (5*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^4)","A",10,7,20,0.3500,1,"{6177, 852, 1805, 807, 266, 63, 208}"
387,1,61,0,0.1367102,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^5 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 75}"
388,1,40,0,0.130371,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 75}"
389,1,39,0,0.1282526,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 75}"
390,1,16,0,0.1213489,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^(2*ArcCoth[a*x])*(c - c/(a*x))^2,x]","\frac{c^2}{a^2 x}+c^2 x","\frac{c^2}{a^2 x}+c^2 x",1,"c^2/(a^2*x) + c^2*x","A",6,5,22,0.2273,1,"{6167, 6131, 6129, 73, 14}"
391,1,11,0,0.0746432,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^(2*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6131, 6129, 43}"
392,1,37,0,0.1240736,"\int \frac{e^{2 \coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 77}"
393,1,53,0,0.1546702,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 77}"
394,1,73,0,0.164493,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 77}"
395,1,87,0,0.1729458,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 77}"
396,1,103,0,0.1332603,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^4,x]","\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a+\frac{3}{x}\right)}{2 a^2}+\frac{c^4 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(3 a+\frac{1}{x}\right)}{3 a}-\frac{c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{3 c^4 \csc ^{-1}(a x)}{2 a}","\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}} \left(2 a+\frac{3}{x}\right)}{2 a^2}+\frac{c^4 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(3 a+\frac{1}{x}\right)}{3 a}-\frac{c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{3 c^4 \csc ^{-1}(a x)}{2 a}",1,"(c^4*Sqrt[1 - 1/(a^2*x^2)]*(2*a + 3/x))/(2*a^2) + (c^4*(1 - 1/(a^2*x^2))^(3/2)*(3*a + x^(-1))*x)/(3*a) + (3*c^4*ArcCsc[a*x])/(2*a) - (c^4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,8,22,0.3636,1,"{6177, 813, 815, 844, 216, 266, 63, 208}"
397,1,61,0,0.0557759,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^3,x]","c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{3 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}+\frac{3 c^3 \csc ^{-1}(a x)}{2 a}","c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}+\frac{3 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}+\frac{3 c^3 \csc ^{-1}(a x)}{2 a}",1,"(3*c^3*Sqrt[1 - 1/(a^2*x^2)])/(2*a^2*x) + c^3*(1 - 1/(a^2*x^2))^(3/2)*x + (3*c^3*ArcCsc[a*x])/(2*a)","A",4,4,22,0.1818,1,"{6177, 277, 195, 216}"
398,1,63,0,0.1313107,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^2,x]","\frac{c^2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(a-\frac{1}{x}\right)}{a}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c^2 \csc ^{-1}(a x)}{a}","\frac{c^2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(a-\frac{1}{x}\right)}{a}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c^2 \csc ^{-1}(a x)}{a}",1,"(c^2*Sqrt[1 - 1/(a^2*x^2)]*(a - x^(-1))*x)/a + (c^2*ArcCsc[a*x])/a + (c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,8,22,0.3636,1,"{6177, 850, 813, 844, 216, 266, 63, 208}"
399,1,49,0,0.1738079,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x)),x]","c x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{2 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{c \csc ^{-1}(a x)}{a}","c x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{2 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{c \csc ^{-1}(a x)}{a}",1,"c*Sqrt[1 - 1/(a^2*x^2)]*x - (c*ArcCsc[a*x])/a + (2*c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,8,20,0.4000,1,"{6177, 852, 1807, 844, 216, 266, 63, 208}"
400,1,105,0,0.3018136,"\int \frac{e^{3 \coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a*x)),x]","-\frac{8 \left(a+\frac{1}{x}\right)}{3 a^2 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{4 \left(3 a+\frac{4}{x}\right)}{3 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}+\frac{4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","-\frac{8 \left(a+\frac{1}{x}\right)}{3 a^2 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{4 \left(3 a+\frac{4}{x}\right)}{3 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}+\frac{4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"(-8*(a + x^(-1)))/(3*a^2*c*(1 - 1/(a^2*x^2))^(3/2)) - (4*(3*a + 4/x))/(3*a^2*c*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c + (4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c)","A",8,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
401,1,138,0,0.401889,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a*x))^2,x]","-\frac{16 \left(a+\frac{1}{x}\right)}{5 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 \left(5 a+\frac{11}{x}\right)}{15 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{75 a+\frac{103}{x}}{15 a^2 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}+\frac{5 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}","-\frac{16 \left(a+\frac{1}{x}\right)}{5 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 \left(5 a+\frac{11}{x}\right)}{15 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{75 a+\frac{103}{x}}{15 a^2 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}+\frac{5 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}",1,"(-16*(a + x^(-1)))/(5*a^2*c^2*(1 - 1/(a^2*x^2))^(5/2)) - (4*(5*a + 11/x))/(15*a^2*c^2*(1 - 1/(a^2*x^2))^(3/2)) - (75*a + 103/x)/(15*a^2*c^2*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^2 + (5*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^2)","A",9,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
402,1,165,0,0.5211176,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a*x))^3,x]","-\frac{32 \left(a+\frac{1}{x}\right)}{7 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{2 \left(7 a+\frac{13}{x}\right)}{7 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{42 a+\frac{59}{x}}{7 a^2 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3}-\frac{16}{7 a^2 c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}+\frac{6 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^3}","-\frac{32 \left(a+\frac{1}{x}\right)}{7 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{2 \left(7 a+\frac{13}{x}\right)}{7 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{42 a+\frac{59}{x}}{7 a^2 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3}-\frac{16}{7 a^2 c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}+\frac{6 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^3}",1,"(-32*(a + x^(-1)))/(7*a^2*c^3*(1 - 1/(a^2*x^2))^(7/2)) - (2*(7*a + 13/x))/(7*a^2*c^3*(1 - 1/(a^2*x^2))^(3/2)) - (42*a + 59/x)/(7*a^2*c^3*Sqrt[1 - 1/(a^2*x^2)]) - 16/(7*a^2*c^3*(1 - 1/(a^2*x^2))^(5/2)*x) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^3 + (6*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^3)","A",10,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
403,1,204,0,0.6399137,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a*x))^4,x]","\frac{16 \left(9 a-\frac{5}{x}\right)}{63 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{64 \left(a+\frac{1}{x}\right)}{9 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 \left(21 a+\frac{41}{x}\right)}{105 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{735 a+\frac{1417}{x}}{315 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{2205 a+\frac{3149}{x}}{315 a^2 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^4}+\frac{7 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}","\frac{16 \left(9 a-\frac{5}{x}\right)}{63 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{64 \left(a+\frac{1}{x}\right)}{9 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 \left(21 a+\frac{41}{x}\right)}{105 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{735 a+\frac{1417}{x}}{315 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{2205 a+\frac{3149}{x}}{315 a^2 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^4}+\frac{7 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}",1,"(16*(9*a - 5/x))/(63*a^2*c^4*(1 - 1/(a^2*x^2))^(7/2)) - (64*(a + x^(-1)))/(9*a^2*c^4*(1 - 1/(a^2*x^2))^(9/2)) - (8*(21*a + 41/x))/(105*a^2*c^4*(1 - 1/(a^2*x^2))^(5/2)) - (735*a + 1417/x)/(315*a^2*c^4*(1 - 1/(a^2*x^2))^(3/2)) - (2205*a + 3149/x)/(315*a^2*c^4*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^4 + (7*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^4)","A",11,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
404,1,64,0,0.1374426,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^5 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
405,1,30,0,0.1264722,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[E^(4*ArcCoth[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",6,5,22,0.2273,1,"{6167, 6131, 6129, 73, 270}"
406,1,38,0,0.1271074,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 75}"
407,1,27,0,0.1211865,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 43}"
408,1,25,0,0.0816088,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^(4*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6131, 6129, 72}"
409,1,53,0,0.1334206,"\int \frac{e^{4 \coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 77}"
410,1,71,0,0.1583271,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
411,1,89,0,0.1720509,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
412,1,105,0,0.1828401,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
413,1,135,0,0.437769,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[(c - c/(a*x))^4/E^ArcCoth[a*x],x]","c^4 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{32 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}+\frac{5 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}-\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3 x^2}-\frac{5 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{25 c^4 \csc ^{-1}(a x)}{2 a}","c^4 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{32 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}+\frac{5 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}-\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3 x^2}-\frac{5 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{25 c^4 \csc ^{-1}(a x)}{2 a}",1,"(-32*c^4*Sqrt[1 - 1/(a^2*x^2)])/(3*a) - (c^4*Sqrt[1 - 1/(a^2*x^2)])/(3*a^3*x^2) + (5*c^4*Sqrt[1 - 1/(a^2*x^2)])/(2*a^2*x) + c^4*Sqrt[1 - 1/(a^2*x^2)]*x - (25*c^4*ArcCsc[a*x])/(2*a) - (5*c^4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",10,8,22,0.3636,1,"{6177, 1807, 1809, 844, 216, 266, 63, 208}"
414,1,106,0,0.3311997,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[(c - c/(a*x))^3/E^ArcCoth[a*x],x]","c^3 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{4 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}-\frac{4 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{13 c^3 \csc ^{-1}(a x)}{2 a}","c^3 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{4 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a}+\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}-\frac{4 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{13 c^3 \csc ^{-1}(a x)}{2 a}",1,"(-4*c^3*Sqrt[1 - 1/(a^2*x^2)])/a + (c^3*Sqrt[1 - 1/(a^2*x^2)])/(2*a^2*x) + c^3*Sqrt[1 - 1/(a^2*x^2)]*x - (13*c^3*ArcCsc[a*x])/(2*a) - (4*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",9,8,22,0.3636,1,"{6177, 1807, 1809, 844, 216, 266, 63, 208}"
415,1,77,0,0.2380342,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[(c - c/(a*x))^2/E^ArcCoth[a*x],x]","c^2 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{3 c^2 \csc ^{-1}(a x)}{a}","c^2 x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{3 c^2 \csc ^{-1}(a x)}{a}",1,"-((c^2*Sqrt[1 - 1/(a^2*x^2)])/a) + c^2*Sqrt[1 - 1/(a^2*x^2)]*x - (3*c^2*ArcCsc[a*x])/a - (3*c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,8,22,0.3636,1,"{6177, 1807, 1809, 844, 216, 266, 63, 208}"
416,1,49,0,0.1454069,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[(c - c/(a*x))/E^ArcCoth[a*x],x]","c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{2 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{c \csc ^{-1}(a x)}{a}","c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{2 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}-\frac{c \csc ^{-1}(a x)}{a}",1,"c*Sqrt[1 - 1/(a^2*x^2)]*x - (c*ArcCsc[a*x])/a - (2*c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",7,7,20,0.3500,1,"{6177, 1807, 844, 216, 266, 63, 208}"
417,1,19,0,0.0397154,"\int \frac{e^{-\coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/c","A",2,2,22,0.09091,1,"{6177, 264}"
418,1,73,0,0.1111301,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))^2),x]","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}-\frac{a x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \left(a-\frac{1}{x}\right)}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}-\frac{a x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \left(a-\frac{1}{x}\right)}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/c^2 - (a*Sqrt[1 - 1/(a^2*x^2)]*x)/(c^2*(a - x^(-1))) + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c^2)","A",6,6,22,0.2727,1,"{6177, 857, 807, 266, 63, 208}"
419,1,105,0,0.2933303,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))^3),x]","-\frac{2 \left(a+\frac{1}{x}\right)}{3 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{6 a+\frac{7}{x}}{3 a^2 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^3}","-\frac{2 \left(a+\frac{1}{x}\right)}{3 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{6 a+\frac{7}{x}}{3 a^2 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^3}",1,"(-2*(a + x^(-1)))/(3*a^2*c^3*(1 - 1/(a^2*x^2))^(3/2)) - (6*a + 7/x)/(3*a^2*c^3*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^3 + (2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^3)","A",8,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
420,1,138,0,0.3900159,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))^4),x]","-\frac{4 \left(a+\frac{1}{x}\right)}{5 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{5 a+\frac{7}{x}}{5 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{15 a+\frac{19}{x}}{5 a^2 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^4}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}","-\frac{4 \left(a+\frac{1}{x}\right)}{5 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{5 a+\frac{7}{x}}{5 a^2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{15 a+\frac{19}{x}}{5 a^2 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^4}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}",1,"(-4*(a + x^(-1)))/(5*a^2*c^4*(1 - 1/(a^2*x^2))^(5/2)) - (5*a + 7/x)/(5*a^2*c^4*(1 - 1/(a^2*x^2))^(3/2)) - (15*a + 19/x)/(5*a^2*c^4*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^4 + (3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^4)","A",9,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
421,1,65,0,0.1453994,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[(c - c/(a*x))^4/E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
422,1,54,0,0.1410775,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[(c - c/(a*x))^3/E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
423,1,40,0,0.1345085,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[(c - c/(a*x))^2/E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
424,1,23,0,0.0822374,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[(c - c/(a*x))/E^(2*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6131, 6129, 72}"
425,1,20,0,0.1150897,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[1/(E^(2*ArcCoth[a*x])*(c - c/(a*x))),x]","\frac{x}{c}-\frac{\log (a x+1)}{a c}","\frac{x}{c}-\frac{\log (a x+1)}{a c}",1,"x/c - Log[1 + a*x]/(a*c)","A",5,4,22,0.1818,1,"{6167, 6131, 6129, 43}"
426,1,18,0,0.1369954,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[1/(E^(2*ArcCoth[a*x])*(c - c/(a*x))^2),x]","\frac{x}{c^2}-\frac{\tanh ^{-1}(a x)}{a c^2}","\frac{x}{c^2}-\frac{\tanh ^{-1}(a x)}{a c^2}",1,"x/c^2 - ArcTanh[a*x]/(a*c^2)","A",6,5,22,0.2273,1,"{6167, 6131, 6129, 72, 207}"
427,1,57,0,0.1502837,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
428,1,75,0,0.1620126,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6131, 6129, 88}"
429,1,164,0,0.5524186,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^4 \, dx","Int[(c - c/(a*x))^4/E^(3*ArcCoth[a*x]),x]","\frac{64 c^4 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c^4 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{68 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}-\frac{7 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}+\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3 x^2}-\frac{7 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{91 c^4 \csc ^{-1}(a x)}{2 a}","\frac{64 c^4 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c^4 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{68 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a}-\frac{7 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}+\frac{c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{3 a^3 x^2}-\frac{7 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{91 c^4 \csc ^{-1}(a x)}{2 a}",1,"(68*c^4*Sqrt[1 - 1/(a^2*x^2)])/(3*a) + (64*c^4*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + (c^4*Sqrt[1 - 1/(a^2*x^2)])/(3*a^3*x^2) - (7*c^4*Sqrt[1 - 1/(a^2*x^2)])/(2*a^2*x) + c^4*Sqrt[1 - 1/(a^2*x^2)]*x + (91*c^4*ArcCsc[a*x])/(2*a) - (7*c^4*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",11,9,22,0.4091,1,"{6177, 1805, 1807, 1809, 844, 216, 266, 63, 208}"
430,1,135,0,0.4296224,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^3 \, dx","Int[(c - c/(a*x))^3/E^(3*ArcCoth[a*x]),x]","\frac{32 c^3 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c^3 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{6 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}-\frac{6 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{33 c^3 \csc ^{-1}(a x)}{2 a}","\frac{32 c^3 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c^3 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{6 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a^2 x}-\frac{6 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{33 c^3 \csc ^{-1}(a x)}{2 a}",1,"(6*c^3*Sqrt[1 - 1/(a^2*x^2)])/a + (32*c^3*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) - (c^3*Sqrt[1 - 1/(a^2*x^2)])/(2*a^2*x) + c^3*Sqrt[1 - 1/(a^2*x^2)]*x + (33*c^3*ArcCsc[a*x])/(2*a) - (6*c^3*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",10,9,22,0.4091,1,"{6177, 1805, 1807, 1809, 844, 216, 266, 63, 208}"
431,1,105,0,0.3256725,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^2 \, dx","Int[(c - c/(a*x))^2/E^(3*ArcCoth[a*x]),x]","\frac{16 c^2 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c^2 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{5 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{5 c^2 \csc ^{-1}(a x)}{a}","\frac{16 c^2 \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c^2 x \sqrt{1-\frac{1}{a^2 x^2}}+\frac{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a}-\frac{5 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{5 c^2 \csc ^{-1}(a x)}{a}",1,"(c^2*Sqrt[1 - 1/(a^2*x^2)])/a + (16*c^2*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + c^2*Sqrt[1 - 1/(a^2*x^2)]*x + (5*c^2*ArcCsc[a*x])/a - (5*c^2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",9,9,22,0.4091,1,"{6177, 1805, 1807, 1809, 844, 216, 266, 63, 208}"
432,1,75,0,0.224189,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[(c - c/(a*x))/E^(3*ArcCoth[a*x]),x]","\frac{8 c \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{4 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c \csc ^{-1}(a x)}{a}","\frac{8 c \left(a-\frac{1}{x}\right)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+c x \sqrt{1-\frac{1}{a^2 x^2}}-\frac{4 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a}+\frac{c \csc ^{-1}(a x)}{a}",1,"(8*c*(a - x^(-1)))/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + c*Sqrt[1 - 1/(a^2*x^2)]*x + (c*ArcCsc[a*x])/a - (4*c*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/a","A",8,8,20,0.4000,1,"{6177, 1805, 1807, 844, 216, 266, 63, 208}"
433,1,72,0,0.1733467,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))),x]","\frac{2 \left(a-\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}-\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}","\frac{2 \left(a-\frac{1}{x}\right)}{a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c}-\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c}",1,"(2*(a - x^(-1)))/(a^2*c*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c - (2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c)","A",6,6,22,0.2727,1,"{6177, 1805, 807, 266, 63, 208}"
434,1,74,0,0.1014281,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^2),x]","-\frac{x \left(a-\frac{1}{x}\right)}{a c^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}","-\frac{x \left(a-\frac{1}{x}\right)}{a c^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^2}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/c^2 - ((a - x^(-1))*x)/(a*c^2*Sqrt[1 - 1/(a^2*x^2)]) - ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c^2)","A",6,6,22,0.2727,1,"{6177, 823, 807, 266, 63, 208}"
435,1,45,0,0.0494055,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^3} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^3),x]","\frac{x}{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2}{a^2 c^3 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x}{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2}{a^2 c^3 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-2/(a^2*c^3*Sqrt[1 - 1/(a^2*x^2)]*x) + x/(c^3*Sqrt[1 - 1/(a^2*x^2)])","A",3,3,22,0.1364,1,"{6177, 271, 191}"
436,1,111,0,0.150347,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^4} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^4),x]","-\frac{x \left(4 a+\frac{3}{x}\right)}{3 a c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{8 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 c^4}-\frac{a x}{3 c^4 \sqrt{1-\frac{1}{a^2 x^2}} \left(a-\frac{1}{x}\right)}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}","-\frac{x \left(4 a+\frac{3}{x}\right)}{3 a c^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{8 x \sqrt{1-\frac{1}{a^2 x^2}}}{3 c^4}-\frac{a x}{3 c^4 \sqrt{1-\frac{1}{a^2 x^2}} \left(a-\frac{1}{x}\right)}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^4}",1,"(8*Sqrt[1 - 1/(a^2*x^2)]*x)/(3*c^4) - (a*x)/(3*c^4*Sqrt[1 - 1/(a^2*x^2)]*(a - x^(-1))) - ((4*a + 3/x)*x)/(3*a*c^4*Sqrt[1 - 1/(a^2*x^2)]) + ArcTanh[Sqrt[1 - 1/(a^2*x^2)]]/(a*c^4)","A",7,7,22,0.3182,1,"{6177, 857, 823, 807, 266, 63, 208}"
437,1,138,0,0.3895766,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^5} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^5),x]","-\frac{2 \left(a+\frac{1}{x}\right)}{5 a^2 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{10 a+\frac{13}{x}}{15 a^2 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{30 a+\frac{41}{x}}{15 a^2 c^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^5}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^5}","-\frac{2 \left(a+\frac{1}{x}\right)}{5 a^2 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{10 a+\frac{13}{x}}{15 a^2 c^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{30 a+\frac{41}{x}}{15 a^2 c^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^5}+\frac{2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a^2 x^2}}\right)}{a c^5}",1,"(-2*(a + x^(-1)))/(5*a^2*c^5*(1 - 1/(a^2*x^2))^(5/2)) - (10*a + 13/x)/(15*a^2*c^5*(1 - 1/(a^2*x^2))^(3/2)) - (30*a + 41/x)/(15*a^2*c^5*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[1 - 1/(a^2*x^2)]*x)/c^5 + (2*ArcTanh[Sqrt[1 - 1/(a^2*x^2)]])/(a*c^5)","A",9,7,22,0.3182,1,"{6177, 852, 1805, 807, 266, 63, 208}"
438,1,279,0,0.1637884,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^(9/2),x]","\frac{x \left(a-\frac{1}{x}\right)^4 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{9 \left(a-\frac{1}{x}\right)^3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{59 \left(a-\frac{1}{x}\right)^2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{35 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{\left(400 a-\frac{227}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{105 a^2 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{7 \left(c-\frac{c}{a x}\right)^{9/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{9/2}}","\frac{173 c^5 \sqrt{1-\frac{1}{a^2 x^2}}}{105 a \sqrt{c-\frac{c}{a x}}}+\frac{227 c^4 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}}{105 a}+\frac{59 c^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{35 a}+\frac{9 c^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{5/2}}{7 a}-\frac{7 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}+c x \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{7/2}",1,"((400*a - 227/x)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(105*a^2*(1 - 1/(a*x))^(9/2)) + (59*(a - x^(-1))^2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(35*a^3*(1 - 1/(a*x))^(9/2)) + (9*(a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(7*a^4*(1 - 1/(a*x))^(9/2)) + ((a - x^(-1))^4*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2)*x)/(a^4*(1 - 1/(a*x))^(9/2)) - (7*(c - c/(a*x))^(9/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(9/2))","A",8,7,22,0.3182,0,"{6182, 6179, 97, 153, 147, 63, 208}"
439,1,221,0,0.1481262,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^(7/2),x]","\frac{x \left(a-\frac{1}{x}\right)^3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{7 \left(a-\frac{1}{x}\right)^2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\left(80 a-\frac{31}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{15 a^2 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{5 \left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}","\frac{49 c^4 \sqrt{1-\frac{1}{a^2 x^2}}}{15 a \sqrt{c-\frac{c}{a x}}}+\frac{31 c^3 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}}{15 a}+\frac{7 c^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{5 a}-\frac{5 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}+c x \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{5/2}",1,"((80*a - 31/x)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(15*a^2*(1 - 1/(a*x))^(7/2)) + (7*(a - x^(-1))^2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(5*a^3*(1 - 1/(a*x))^(7/2)) + ((a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2)*x)/(a^3*(1 - 1/(a*x))^(7/2)) - (5*(c - c/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(7/2))","A",7,7,22,0.3182,0,"{6182, 6179, 97, 153, 147, 63, 208}"
440,1,189,0,0.132817,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^(5/2),x]","-\frac{2 \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{5/2}}{3 a \left(1-\frac{1}{a x}\right)^{5/2}}+\frac{x \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{5/2}}{\left(1-\frac{1}{a x}\right)^{5/2}}+\frac{3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{a \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{3 \left(c-\frac{c}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{5/2}}","\frac{c^4 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 a \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{3 c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}-\frac{3 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(3*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(5/2))/(a*(1 - 1/(a*x))^(5/2)) - (2*(1 + 1/(a*x))^(3/2)*(c - c/(a*x))^(5/2))/(3*a*(1 - 1/(a*x))^(5/2)) + ((1 + 1/(a*x))^(3/2)*(c - c/(a*x))^(5/2)*x)/(1 - 1/(a*x))^(5/2) - (3*(c - c/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(5/2))","A",7,7,22,0.3182,0,"{6182, 6179, 89, 80, 50, 63, 208}"
441,1,117,0,0.2232041,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^(3/2),x]","\frac{c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}+\frac{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}+\frac{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(c^2*Sqrt[1 - 1/(a^2*x^2)])/(a*Sqrt[c - c/(a*x)]) + (c^3*(1 - 1/(a^2*x^2))^(3/2)*x)/(c - c/(a*x))^(3/2) - (c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",5,5,22,0.2273,1,"{6177, 879, 865, 875, 208}"
442,1,78,0,0.1552131,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a*x)],x]","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(c*Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a*x)] + (Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",4,4,22,0.1818,1,"{6177, 863, 875, 208}"
443,1,152,0,0.1348147,"\int \frac{e^{\coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^ArcCoth[a*x]/Sqrt[c - c/(a*x)],x]","\frac{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\sqrt{c-\frac{c}{a x}}}+\frac{3 \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{c-\frac{c}{a x}}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{c-\frac{c}{a x}}}","\frac{x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\sqrt{c-\frac{c}{a x}}}+\frac{3 \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{c-\frac{c}{a x}}}-\frac{2 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{c-\frac{c}{a x}}}",1,"(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/Sqrt[c - c/(a*x)] + (3*Sqrt[1 - 1/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*Sqrt[c - c/(a*x)]) - (2*Sqrt[2]*Sqrt[1 - 1/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a*Sqrt[c - c/(a*x)])","A",8,7,22,0.3182,1,"{6182, 6179, 99, 156, 63, 208, 206}"
444,1,215,0,0.1548,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a*x))^(3/2),x]","\frac{a x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{5 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{7 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{2} a \left(c-\frac{c}{a x}\right)^{3/2}}","\frac{a x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{5 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{7 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{2} a \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(-2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)])/((a - x^(-1))*(c - c/(a*x))^(3/2)) + (a*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))*(c - c/(a*x))^(3/2)) + (5*(1 - 1/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(3/2)) - (7*(1 - 1/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(Sqrt[2]*a*(c - c/(a*x))^(3/2))","A",9,8,22,0.3636,1,"{6182, 6179, 99, 151, 156, 63, 208, 206}"
445,1,277,0,0.1711972,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a*x))^(5/2),x]","\frac{a^2 x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{23 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{8 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{3 a \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{2 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{7 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{79 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{8 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}","\frac{a^2 x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{23 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{8 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{3 a \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{2 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{7 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{79 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{8 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(-3*a*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(2*(a - x^(-1))^2*(c - c/(a*x))^(5/2)) - (23*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(8*(a - x^(-1))*(c - c/(a*x))^(5/2)) + (a^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))^2*(c - c/(a*x))^(5/2)) + (7*(1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(5/2)) - (79*(1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(8*Sqrt[2]*a*(c - c/(a*x))^(5/2))","A",10,8,22,0.3636,1,"{6182, 6179, 99, 151, 156, 63, 208, 206}"
446,1,143,0,0.2384599,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[E^(2*ArcCoth[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",12,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 50, 63, 208}"
447,1,118,0,0.225019,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[E^(2*ArcCoth[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",11,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 50, 63, 208}"
448,1,95,0,0.2014499,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[E^(2*ArcCoth[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",10,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 50, 63, 208}"
449,1,70,0,0.1775873,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^(2*ArcCoth[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",9,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 50, 63, 208}"
450,1,50,0,0.1586757,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(2*ArcCoth[a*x])*Sqrt[c - c/(a*x)],x]","x \sqrt{c-\frac{c}{a x}}+\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}","x \sqrt{c-\frac{c}{a x}}+\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",8,8,24,0.3333,1,"{6167, 6133, 25, 514, 375, 78, 63, 208}"
451,1,70,0,0.1792451,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^(2*ArcCoth[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",9,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 51, 63, 208}"
452,1,95,0,0.2002354,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^(2*ArcCoth[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",10,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 51, 63, 208}"
453,1,118,0,0.2156164,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[E^(2*ArcCoth[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",11,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 51, 63, 208}"
454,1,145,0,0.2296527,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[E^(2*ArcCoth[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",12,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 78, 51, 63, 208}"
455,1,268,0,0.1632738,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^(9/2),x]","\frac{9 \left(a-\frac{1}{x}\right)^2 \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{3 \left(28 a-\frac{17}{x}\right) \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{35 a^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{x \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{a \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{3 \left(c-\frac{c}{a x}\right)^{9/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{9/2}}","\frac{9 \left(a-\frac{1}{x}\right)^2 \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{3 \left(28 a-\frac{17}{x}\right) \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{35 a^2 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{x \left(a-\frac{1}{x}\right)^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{9/2}}{a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{a \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{3 \left(c-\frac{c}{a x}\right)^{9/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{9/2}}",1,"(3*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(a*(1 - 1/(a*x))^(9/2)) + (3*(28*a - 17/x)*(1 + 1/(a*x))^(3/2)*(c - c/(a*x))^(9/2))/(35*a^2*(1 - 1/(a*x))^(9/2)) + (9*(a - x^(-1))^2*(1 + 1/(a*x))^(3/2)*(c - c/(a*x))^(9/2))/(7*a^3*(1 - 1/(a*x))^(9/2)) + ((a - x^(-1))^3*(1 + 1/(a*x))^(3/2)*(c - c/(a*x))^(9/2)*x)/(a^3*(1 - 1/(a*x))^(9/2)) - (3*(c - c/(a*x))^(9/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(9/2))","A",8,8,24,0.3333,1,"{6182, 6179, 97, 153, 147, 50, 63, 208}"
456,1,237,0,0.1455124,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^(7/2),x]","-\frac{2 \left(\frac{1}{a x}+1\right)^{5/2} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{7/2}}{3 a \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{x \left(\frac{1}{a x}+1\right)^{5/2} \left(c-\frac{c}{a x}\right)^{7/2}}{\left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{a \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{\left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}","-\frac{2 \left(\frac{1}{a x}+1\right)^{5/2} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\left(\frac{1}{a x}+1\right)^{3/2} \left(c-\frac{c}{a x}\right)^{7/2}}{3 a \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{x \left(\frac{1}{a x}+1\right)^{5/2} \left(c-\frac{c}{a x}\right)^{7/2}}{\left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{a \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{\left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}",1,"(Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(a*(1 - 1/(a*x))^(7/2)) + ((1 + 1/(a*x))^(3/2)*(c - c/(a*x))^(7/2))/(3*a*(1 - 1/(a*x))^(7/2)) - (2*(1 + 1/(a*x))^(5/2)*(c - c/(a*x))^(7/2))/(5*a*(1 - 1/(a*x))^(7/2)) + ((1 + 1/(a*x))^(5/2)*(c - c/(a*x))^(7/2)*x)/(1 - 1/(a*x))^(7/2) - ((c - c/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(7/2))","A",8,7,24,0.2917,1,"{6182, 6179, 89, 80, 50, 63, 208}"
457,1,156,0,0.2680857,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^(5/2),x]","\frac{c^5 x \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(c-\frac{c}{a x}\right)^{5/2}}-\frac{c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}+\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c^5 x \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(c-\frac{c}{a x}\right)^{5/2}}-\frac{c^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}+\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"-(c^4*(1 - 1/(a^2*x^2))^(3/2))/(3*a*(c - c/(a*x))^(3/2)) - (c^3*Sqrt[1 - 1/(a^2*x^2)])/(a*Sqrt[c - c/(a*x)]) + (c^5*(1 - 1/(a^2*x^2))^(5/2)*x)/(c - c/(a*x))^(5/2) + (c^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",6,5,24,0.2083,1,"{6177, 879, 865, 875, 208}"
458,1,118,0,0.2146014,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a*x))^(3/2),x]","\frac{c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}-\frac{3 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}+\frac{3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}-\frac{3 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}{a \sqrt{c-\frac{c}{a x}}}+\frac{3 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(-3*c^2*Sqrt[1 - 1/(a^2*x^2)])/(a*Sqrt[c - c/(a*x)]) + (c^3*(1 - 1/(a^2*x^2))^(3/2)*x)/(c - c/(a*x))^(3/2) + (3*c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",5,5,24,0.2083,1,"{6177, 863, 865, 875, 208}"
459,1,152,0,0.1336913,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)],x]","\frac{x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}+\frac{5 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{1-\frac{1}{a x}}}","\frac{x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}+\frac{5 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{1-\frac{1}{a x}}}",1,"(Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/Sqrt[1 - 1/(a*x)] + (5*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a*Sqrt[1 - 1/(a*x)])","A",8,7,24,0.2917,1,"{6182, 6179, 98, 156, 63, 208, 206}"
460,1,215,0,0.1501934,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^(3*ArcCoth[a*x])/Sqrt[c - c/(a*x)],x]","\frac{a x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right) \sqrt{c-\frac{c}{a x}}}-\frac{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right) \sqrt{c-\frac{c}{a x}}}+\frac{7 \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{c-\frac{c}{a x}}}-\frac{5 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{c-\frac{c}{a x}}}","\frac{a x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right) \sqrt{c-\frac{c}{a x}}}-\frac{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right) \sqrt{c-\frac{c}{a x}}}+\frac{7 \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{c-\frac{c}{a x}}}-\frac{5 \sqrt{2} \sqrt{1-\frac{1}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{c-\frac{c}{a x}}}",1,"(-3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/((a - x^(-1))*Sqrt[c - c/(a*x)]) + (a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))*Sqrt[c - c/(a*x)]) + (7*Sqrt[1 - 1/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*Sqrt[c - c/(a*x)]) - (5*Sqrt[2]*Sqrt[1 - 1/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a*Sqrt[c - c/(a*x)])","A",9,8,24,0.3333,1,"{6182, 6179, 98, 151, 156, 63, 208, 206}"
461,1,275,0,0.1713352,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a*x))^(3/2),x]","\frac{a^2 x \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 a \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{15 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{4 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{9 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{51 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{4 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{3/2}}","\frac{a^2 x \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 a \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{15 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}{4 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{9 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{51 \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{4 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(-2*a*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)])/((a - x^(-1))^2*(c - c/(a*x))^(3/2)) - (15*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)])/(4*(a - x^(-1))*(c - c/(a*x))^(3/2)) + (a^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))^2*(c - c/(a*x))^(3/2)) + (9*(1 - 1/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(3/2)) - (51*(1 - 1/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(4*Sqrt[2]*a*(c - c/(a*x))^(3/2))","A",10,8,24,0.3333,1,"{6182, 6179, 98, 151, 156, 63, 208, 206}"
462,1,335,0,0.191238,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a*x))^(5/2),x]","\frac{a^3 x \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{5 a^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{3 \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{29 a \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{12 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{73 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{16 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{11 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{249 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{16 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}","\frac{a^3 x \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{\left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{5 a^2 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{3 \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{29 a \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{12 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{73 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}{16 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{11 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{249 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{16 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(-5*a^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(3*(a - x^(-1))^3*(c - c/(a*x))^(5/2)) - (29*a*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(12*(a - x^(-1))^2*(c - c/(a*x))^(5/2)) - (73*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(16*(a - x^(-1))*(c - c/(a*x))^(5/2)) + (a^3*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))^3*(c - c/(a*x))^(5/2)) + (11*(1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(5/2)) - (249*(1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(16*Sqrt[2]*a*(c - c/(a*x))^(5/2))","A",11,8,24,0.3333,1,"{6182, 6179, 98, 151, 156, 63, 208, 206}"
463,1,221,0,0.1444358,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[(c - c/(a*x))^(7/2)/E^ArcCoth[a*x],x]","\frac{x \left(a-\frac{1}{x}\right)^3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{3 \left(a-\frac{1}{x}\right)^2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{\left(80 a-\frac{7}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^2 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{9 \left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}","\frac{x \left(a-\frac{1}{x}\right)^3 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{3 \left(a-\frac{1}{x}\right)^2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{\left(80 a-\frac{7}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^2 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{9 \left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}",1,"-((80*a - 7/x)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(5*a^2*(1 - 1/(a*x))^(7/2)) + (3*(a - x^(-1))^2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(5*a^3*(1 - 1/(a*x))^(7/2)) + ((a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2)*x)/(a^3*(1 - 1/(a*x))^(7/2)) - (9*(c - c/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(7/2))","A",7,7,24,0.2917,1,"{6182, 6179, 98, 153, 147, 63, 208}"
464,1,161,0,0.1245718,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[(c - c/(a*x))^(5/2)/E^ArcCoth[a*x],x]","\frac{x \left(a-\frac{1}{x}\right)^2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{a^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{\left(16 a+\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{3 a^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{7 \left(c-\frac{c}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{5/2}}","\frac{x \left(a-\frac{1}{x}\right)^2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{a^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{\left(16 a+\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{3 a^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{7 \left(c-\frac{c}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{5/2}}",1,"-((16*a + x^(-1))*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(5/2))/(3*a^2*(1 - 1/(a*x))^(5/2)) + ((a - x^(-1))^2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(5/2)*x)/(a^2*(1 - 1/(a*x))^(5/2)) - (7*(c - c/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(5/2))","A",6,6,24,0.2500,1,"{6182, 6179, 98, 147, 63, 208}"
465,1,140,0,0.1255434,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[(c - c/(a*x))^(3/2)/E^ArcCoth[a*x],x]","\frac{x \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{3/2}}{\left(1-\frac{1}{a x}\right)^{3/2}}-\frac{2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{3/2}}{a \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{5 \left(c-\frac{c}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{3/2}}","\frac{x \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{3/2}}{\left(1-\frac{1}{a x}\right)^{3/2}}-\frac{2 \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{3/2}}{a \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{5 \left(c-\frac{c}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{3/2}}",1,"(-2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(3/2))/(a*(1 - 1/(a*x))^(3/2)) + (Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(3/2)*x)/(1 - 1/(a*x))^(3/2) - (5*(c - c/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(3/2))","A",6,6,24,0.2500,1,"{6182, 6179, 89, 80, 63, 208}"
466,1,79,0,0.1564393,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^ArcCoth[a*x],x]","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(c*Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a*x)] - (3*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",4,4,24,0.1667,1,"{6177, 879, 875, 208}"
467,1,78,0,0.156713,"\int \frac{e^{-\coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[1/(E^ArcCoth[a*x]*Sqrt[c - c/(a*x)]),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a \sqrt{c}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a \sqrt{c}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a*x)] - ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]]/(a*Sqrt[c])","A",4,4,24,0.1667,1,"{6177, 873, 875, 208}"
468,1,151,0,0.139191,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))^(3/2)),x]","\frac{x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}+\frac{\left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{\sqrt{2} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}","\frac{x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{\left(c-\frac{c}{a x}\right)^{3/2}}+\frac{\left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{\sqrt{2} \left(1-\frac{1}{a x}\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \left(c-\frac{c}{a x}\right)^{3/2}}",1,"((1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x)/(c - c/(a*x))^(3/2) + ((1 - 1/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(3/2)) - (Sqrt[2]*(1 - 1/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a*(c - c/(a*x))^(3/2))","A",9,8,24,0.3333,1,"{6182, 6179, 103, 21, 83, 63, 208, 206}"
469,1,219,0,0.1489604,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))^(5/2)),x]","\frac{a x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{\left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{3 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{2 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{3 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{9 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{2 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}","\frac{a x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{\left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{3 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{2 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{3 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{9 \left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{2 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(-3*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(2*(a - x^(-1))*(c - c/(a*x))^(5/2)) + (a*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))*(c - c/(a*x))^(5/2)) + (3*(1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(5/2)) - (9*(1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(2*Sqrt[2]*a*(c - c/(a*x))^(5/2))","A",10,9,24,0.3750,1,"{6182, 6179, 103, 21, 99, 156, 63, 208, 206}"
470,1,277,0,0.1694334,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a*x))^(7/2)),x]","\frac{a^2 x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{35 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{16 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{5 a \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{4 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{5 \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{115 \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{16 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{7/2}}","\frac{a^2 x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{\left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{35 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{16 \left(a-\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{5 a \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}}{4 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{5 \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{115 \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{16 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{7/2}}",1,"(-5*a*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)])/(4*(a - x^(-1))^2*(c - c/(a*x))^(7/2)) - (35*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)])/(16*(a - x^(-1))*(c - c/(a*x))^(7/2)) + (a^2*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x)/((a - x^(-1))^2*(c - c/(a*x))^(7/2)) + (5*(1 - 1/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(7/2)) - (115*(1 - 1/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(16*Sqrt[2]*a*(c - c/(a*x))^(7/2))","A",11,10,24,0.4167,1,"{6182, 6179, 103, 21, 99, 151, 156, 63, 208, 206}"
471,1,163,0,0.2802992,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[(c - c/(a*x))^(7/2)/E^(2*ArcCoth[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",14,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 98, 154, 156, 63, 208}"
472,1,138,0,0.2541727,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[(c - c/(a*x))^(5/2)/E^(2*ArcCoth[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",13,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 98, 154, 156, 63, 208}"
473,1,113,0,0.2384252,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[(c - c/(a*x))^(3/2)/E^(2*ArcCoth[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",12,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 98, 154, 156, 63, 208}"
474,1,92,0,0.2091881,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^(2*ArcCoth[a*x]),x]","x \sqrt{c-\frac{c}{a x}}-\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 \sqrt{c-\frac{c}{a x}}-\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",11,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 98, 156, 63, 208}"
475,1,95,0,0.2064424,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[1/(E^(2*ArcCoth[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",11,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 99, 156, 63, 208}"
476,1,94,0,0.2154604,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[1/(E^(2*ArcCoth[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",12,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 103, 21, 83, 63, 208}"
477,1,116,0,0.2354399,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[1/(E^(2*ArcCoth[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",12,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 103, 152, 156, 63, 208}"
478,1,147,0,0.264219,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[1/(E^(2*ArcCoth[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",13,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 103, 152, 156, 63, 208}"
479,1,172,0,0.2932866,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{9/2}} \, dx","Int[1/(E^(2*ArcCoth[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",14,10,24,0.4167,1,"{6167, 6133, 25, 514, 375, 103, 152, 156, 63, 208}"
480,1,335,0,0.2003087,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{9/2} \, dx","Int[(c - c/(a*x))^(9/2)/E^(3*ArcCoth[a*x]),x]","\frac{x \left(a-\frac{1}{x}\right)^5 \left(c-\frac{c}{a x}\right)^{9/2}}{a^5 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{10 \left(a-\frac{1}{x}\right)^4 \left(c-\frac{c}{a x}\right)^{9/2}}{a^5 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{65 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{135 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{5 \left(304 a-\frac{65}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^2 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{15 \left(c-\frac{c}{a x}\right)^{9/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{9/2}}","\frac{x \left(a-\frac{1}{x}\right)^5 \left(c-\frac{c}{a x}\right)^{9/2}}{a^5 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{10 \left(a-\frac{1}{x}\right)^4 \left(c-\frac{c}{a x}\right)^{9/2}}{a^5 \left(1-\frac{1}{a x}\right)^{9/2} \sqrt{\frac{1}{a x}+1}}+\frac{65 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^4 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{135 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^3 \left(1-\frac{1}{a x}\right)^{9/2}}+\frac{5 \left(304 a-\frac{65}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{9/2}}{7 a^2 \left(1-\frac{1}{a x}\right)^{9/2}}-\frac{15 \left(c-\frac{c}{a x}\right)^{9/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{9/2}}",1,"(10*(a - x^(-1))^4*(c - c/(a*x))^(9/2))/(a^5*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]) + (5*(304*a - 65/x)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(7*a^2*(1 - 1/(a*x))^(9/2)) + (135*(a - x^(-1))^2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(7*a^3*(1 - 1/(a*x))^(9/2)) + (65*(a - x^(-1))^3*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(9/2))/(7*a^4*(1 - 1/(a*x))^(9/2)) + ((a - x^(-1))^5*(c - c/(a*x))^(9/2)*x)/(a^5*(1 - 1/(a*x))^(9/2)*Sqrt[1 + 1/(a*x)]) - (15*(c - c/(a*x))^(9/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(9/2))","A",9,8,24,0.3333,1,"{6182, 6179, 98, 150, 153, 147, 63, 208}"
481,1,277,0,0.1705891,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{7/2} \, dx","Int[(c - c/(a*x))^(7/2)/E^(3*ArcCoth[a*x]),x]","\frac{x \left(a-\frac{1}{x}\right)^4 \left(c-\frac{c}{a x}\right)^{7/2}}{a^4 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{10 \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{7/2}}{a^4 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{47 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\left(1360 a-\frac{311}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{15 a^2 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{13 \left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}","\frac{x \left(a-\frac{1}{x}\right)^4 \left(c-\frac{c}{a x}\right)^{7/2}}{a^4 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{10 \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{7/2}}{a^4 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{47 \sqrt{\frac{1}{a x}+1} \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{7/2}}{5 a^3 \left(1-\frac{1}{a x}\right)^{7/2}}+\frac{\left(1360 a-\frac{311}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}{15 a^2 \left(1-\frac{1}{a x}\right)^{7/2}}-\frac{13 \left(c-\frac{c}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{7/2}}",1,"(10*(a - x^(-1))^3*(c - c/(a*x))^(7/2))/(a^4*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]) + ((1360*a - 311/x)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(15*a^2*(1 - 1/(a*x))^(7/2)) + (47*(a - x^(-1))^2*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2))/(5*a^3*(1 - 1/(a*x))^(7/2)) + ((a - x^(-1))^4*(c - c/(a*x))^(7/2)*x)/(a^4*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]) - (13*(c - c/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(7/2))","A",8,8,24,0.3333,1,"{6182, 6179, 98, 150, 153, 147, 63, 208}"
482,1,219,0,0.1500096,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{5/2} \, dx","Int[(c - c/(a*x))^(5/2)/E^(3*ArcCoth[a*x]),x]","\frac{x \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{5/2}}{a^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{10 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}{a^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{\left(112 a-\frac{29}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{3 a^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{11 \left(c-\frac{c}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{5/2}}","\frac{x \left(a-\frac{1}{x}\right)^3 \left(c-\frac{c}{a x}\right)^{5/2}}{a^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{10 \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{5/2}}{a^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}+\frac{\left(112 a-\frac{29}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}{3 a^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{11 \left(c-\frac{c}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{5/2}}",1,"(10*(a - x^(-1))^2*(c - c/(a*x))^(5/2))/(a^3*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]) + ((112*a - 29/x)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(5/2))/(3*a^2*(1 - 1/(a*x))^(5/2)) + ((a - x^(-1))^3*(c - c/(a*x))^(5/2)*x)/(a^3*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]) - (11*(c - c/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(5/2))","A",7,7,24,0.2917,1,"{6182, 6179, 98, 150, 147, 63, 208}"
483,1,158,0,0.1332935,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[(c - c/(a*x))^(3/2)/E^(3*ArcCoth[a*x]),x]","\frac{x \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{3/2}}{a^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{\left(21 a+\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}{a^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}-\frac{9 \left(c-\frac{c}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{3/2}}","\frac{x \left(a-\frac{1}{x}\right)^2 \left(c-\frac{c}{a x}\right)^{3/2}}{a^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{\left(21 a+\frac{1}{x}\right) \left(c-\frac{c}{a x}\right)^{3/2}}{a^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}-\frac{9 \left(c-\frac{c}{a x}\right)^{3/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(1-\frac{1}{a x}\right)^{3/2}}",1,"((21*a + x^(-1))*(c - c/(a*x))^(3/2))/(a^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]) + ((a - x^(-1))^2*(c - c/(a*x))^(3/2)*x)/(a^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]) - (9*(c - c/(a*x))^(3/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(1 - 1/(a*x))^(3/2))","A",6,6,24,0.2500,1,"{6182, 6179, 98, 146, 63, 208}"
484,1,140,0,0.1178833,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^(3*ArcCoth[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{9 \sqrt{c-\frac{c}{a x}}}{a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{7 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}","\frac{x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{9 \sqrt{c-\frac{c}{a x}}}{a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{7 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}",1,"(9*Sqrt[c - c/(a*x)])/(a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (Sqrt[c - c/(a*x)]*x)/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (7*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*Sqrt[1 - 1/(a*x)])","A",6,6,24,0.2500,1,"{6182, 6179, 89, 78, 63, 208}"
485,1,118,0,0.2210267,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)]),x]","\frac{x \sqrt{c-\frac{c}{a x}}}{c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 \sqrt{c-\frac{c}{a x}}}{a c \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a \sqrt{c}}","\frac{x \sqrt{c-\frac{c}{a x}}}{c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 \sqrt{c-\frac{c}{a x}}}{a c \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a \sqrt{c}}",1,"(5*Sqrt[c - c/(a*x)])/(a*c*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a*x)]*x)/(c*Sqrt[1 - 1/(a^2*x^2)]) - (5*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/(a*Sqrt[c])","A",5,5,24,0.2083,1,"{6177, 879, 869, 875, 208}"
486,1,117,0,0.222819,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^(3/2)),x]","-\frac{2 x \sqrt{c-\frac{c}{a x}}}{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a c^{3/2}}+\frac{3 x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a x}}}","-\frac{2 x \sqrt{c-\frac{c}{a x}}}{c^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a c^{3/2}}+\frac{3 x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a x}}}",1,"(3*Sqrt[1 - 1/(a^2*x^2)]*x)/(c*Sqrt[c - c/(a*x)]) - (2*Sqrt[c - c/(a*x)]*x)/(c^2*Sqrt[1 - 1/(a^2*x^2)]) - (3*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/(a*c^(3/2))","A",5,5,24,0.2083,1,"{6177, 869, 873, 875, 208}"
487,1,199,0,0.1677209,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{5/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^(5/2)),x]","\frac{x \left(1-\frac{1}{a x}\right)^{5/2}}{\sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{2 \left(1-\frac{1}{a x}\right)^{5/2}}{a \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{\left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{\left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}","\frac{x \left(1-\frac{1}{a x}\right)^{5/2}}{\sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{2 \left(1-\frac{1}{a x}\right)^{5/2}}{a \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{\left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{5/2}}-\frac{\left(1-\frac{1}{a x}\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{2} a \left(c-\frac{c}{a x}\right)^{5/2}}",1,"(2*(1 - 1/(a*x))^(5/2))/(a*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(5/2)) + ((1 - 1/(a*x))^(5/2)*x)/(Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(5/2)) - ((1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(5/2)) - ((1 - 1/(a*x))^(5/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(Sqrt[2]*a*(c - c/(a*x))^(5/2))","A",9,8,24,0.3333,1,"{6182, 6179, 103, 152, 156, 63, 208, 206}"
488,1,267,0,0.1717207,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{7/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a*x))^(7/2)),x]","\frac{a x \left(1-\frac{1}{a x}\right)^{7/2}}{\left(a-\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{7 \left(1-\frac{1}{a x}\right)^{7/2}}{4 a \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{3 \left(1-\frac{1}{a x}\right)^{7/2}}{2 \left(a-\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{\left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{11 \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{4 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{7/2}}","\frac{a x \left(1-\frac{1}{a x}\right)^{7/2}}{\left(a-\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{7 \left(1-\frac{1}{a x}\right)^{7/2}}{4 a \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{3 \left(1-\frac{1}{a x}\right)^{7/2}}{2 \left(a-\frac{1}{x}\right) \sqrt{\frac{1}{a x}+1} \left(c-\frac{c}{a x}\right)^{7/2}}+\frac{\left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \left(c-\frac{c}{a x}\right)^{7/2}}-\frac{11 \left(1-\frac{1}{a x}\right)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{4 \sqrt{2} a \left(c-\frac{c}{a x}\right)^{7/2}}",1,"(7*(1 - 1/(a*x))^(7/2))/(4*a*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2)) - (3*(1 - 1/(a*x))^(7/2))/(2*(a - x^(-1))*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2)) + (a*(1 - 1/(a*x))^(7/2)*x)/((a - x^(-1))*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^(7/2)) + ((1 - 1/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*(c - c/(a*x))^(7/2)) - (11*(1 - 1/(a*x))^(7/2)*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(4*Sqrt[2]*a*(c - c/(a*x))^(7/2))","A",10,9,24,0.3750,1,"{6182, 6179, 103, 151, 152, 156, 63, 208, 206}"
489,1,60,0,0.2216819,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^m \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a*x)]*x^m,x]","\frac{x^{m+1} \sqrt{c-\frac{c}{a x}} \, _2F_1\left(-\frac{1}{2},-m-1;-m;-\frac{1}{a x}\right)}{(m+1) \sqrt{1-\frac{1}{a x}}}","\frac{x^{m+1} \sqrt{c-\frac{c}{a x}} \, _2F_1\left(-\frac{1}{2},-m-1;-m;-\frac{1}{a x}\right)}{(m+1) \sqrt{1-\frac{1}{a x}}}",1,"(Sqrt[c - c/(a*x)]*x^(1 + m)*Hypergeometric2F1[-1/2, -1 - m, -m, -(1/(a*x))])/((1 + m)*Sqrt[1 - 1/(a*x)])","A",3,3,25,0.1200,1,"{6182, 6181, 64}"
490,1,164,0,0.3422059,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a*x)]*x^2,x]","\frac{c x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-\frac{c}{a x}}}+\frac{c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{12 a \sqrt{c-\frac{c}{a x}}}-\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2 \sqrt{c-\frac{c}{a x}}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{8 a^3}","\frac{c x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-\frac{c}{a x}}}+\frac{c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{12 a \sqrt{c-\frac{c}{a x}}}-\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2 \sqrt{c-\frac{c}{a x}}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{8 a^3}",1,"-(c*Sqrt[1 - 1/(a^2*x^2)]*x)/(8*a^2*Sqrt[c - c/(a*x)]) + (c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(12*a*Sqrt[c - c/(a*x)]) + (c*Sqrt[1 - 1/(a^2*x^2)]*x^3)/(3*Sqrt[c - c/(a*x)]) + (Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/(8*a^3)","A",6,5,25,0.2000,1,"{6178, 863, 873, 875, 208}"
491,1,124,0,0.2397764,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a*x)]*x,x]","\frac{c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 \sqrt{c-\frac{c}{a x}}}+\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{4 a \sqrt{c-\frac{c}{a x}}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{4 a^2}","\frac{c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 \sqrt{c-\frac{c}{a x}}}+\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{4 a \sqrt{c-\frac{c}{a x}}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{4 a^2}",1,"(c*Sqrt[1 - 1/(a^2*x^2)]*x)/(4*a*Sqrt[c - c/(a*x)]) + (c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(2*Sqrt[c - c/(a*x)]) - (Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/(4*a^2)","A",5,5,23,0.2174,1,"{6178, 863, 873, 875, 208}"
492,1,78,0,0.1535583,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a*x)],x]","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}+\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(c*Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a*x)] + (Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",4,4,22,0.1818,1,"{6177, 863, 875, 208}"
493,1,76,0,0.2273358,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - c/(a*x)])/x,x]","2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)-\frac{2 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}","2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)-\frac{2 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}",1,"(-2*c*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)] + 2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]]","A",4,4,25,0.1600,1,"{6178, 865, 875, 208}"
494,1,37,0,0.1477608,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - c/(a*x)])/x^2,x]","-\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}","-\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(-2*a*c^2*(1 - 1/(a^2*x^2))^(3/2))/(3*(c - c/(a*x))^(3/2))","A",2,2,25,0.08000,1,"{6178, 649}"
495,1,77,0,0.188534,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - c/(a*x)])/x^3,x]","\frac{2 a^2 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{5 \sqrt{c-\frac{c}{a x}}}-\frac{2 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{15 \left(c-\frac{c}{a x}\right)^{3/2}}","\frac{2 a^2 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{5 \sqrt{c-\frac{c}{a x}}}-\frac{2 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{15 \left(c-\frac{c}{a x}\right)^{3/2}}",1,"(-2*a^2*c^2*(1 - 1/(a^2*x^2))^(3/2))/(15*(c - c/(a*x))^(3/2)) + (2*a^2*c*(1 - 1/(a^2*x^2))^(3/2))/(5*Sqrt[c - c/(a*x)])","A",3,3,25,0.1200,1,"{6178, 795, 649}"
496,1,117,0,0.2460819,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - c/(a*x)])/x^4,x]","\frac{8 a^3 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{7 x^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{8 a^3 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{35 \sqrt{c-\frac{c}{a x}}}","\frac{8 a^3 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{7 x^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{8 a^3 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{35 \sqrt{c-\frac{c}{a x}}}",1,"(8*a^3*c^2*(1 - 1/(a^2*x^2))^(3/2))/(105*(c - c/(a*x))^(3/2)) - (8*a^3*c*(1 - 1/(a^2*x^2))^(3/2))/(35*Sqrt[c - c/(a*x)]) - (2*a*c^2*(1 - 1/(a^2*x^2))^(3/2))/(7*(c - c/(a*x))^(3/2)*x^2)","A",4,4,25,0.1600,1,"{6178, 871, 795, 649}"
497,1,159,0,0.3060076,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - c/(a*x)])/x^5,x]","-\frac{16 a^4 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{315 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{21 x^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{9 x^3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{16 a^4 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 \sqrt{c-\frac{c}{a x}}}","-\frac{16 a^4 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{315 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{21 x^2 \left(c-\frac{c}{a x}\right)^{3/2}}-\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{9 x^3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{16 a^4 c \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{105 \sqrt{c-\frac{c}{a x}}}",1,"(-16*a^4*c^2*(1 - 1/(a^2*x^2))^(3/2))/(315*(c - c/(a*x))^(3/2)) + (16*a^4*c*(1 - 1/(a^2*x^2))^(3/2))/(105*Sqrt[c - c/(a*x)]) - (2*a*c^2*(1 - 1/(a^2*x^2))^(3/2))/(9*(c - c/(a*x))^(3/2)*x^3) + (4*a^2*c^2*(1 - 1/(a^2*x^2))^(3/2))/(21*(c - c/(a*x))^(3/2)*x^2)","A",5,4,25,0.1600,1,"{6178, 871, 795, 649}"
498,1,130,0,0.3773546,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[E^(2*ArcCoth[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",11,9,27,0.3333,1,"{6167, 6133, 25, 514, 446, 78, 51, 63, 208}"
499,1,105,0,0.3522725,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[E^(2*ArcCoth[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",10,9,27,0.3333,1,"{6167, 6133, 25, 514, 446, 78, 51, 63, 208}"
500,1,80,0,0.2408538,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[E^(2*ArcCoth[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",9,9,25,0.3600,1,"{6167, 6133, 25, 434, 446, 78, 51, 63, 208}"
501,1,50,0,0.1462724,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(2*ArcCoth[a*x])*Sqrt[c - c/(a*x)],x]","x \sqrt{c-\frac{c}{a x}}+\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-\frac{c}{a x}}}{\sqrt{c}}\right)}{a}","x \sqrt{c-\frac{c}{a x}}+\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",8,8,24,0.3333,1,"{6167, 6133, 25, 514, 375, 78, 63, 208}"
502,1,47,0,0.3297592,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[(E^(2*ArcCoth[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",8,8,27,0.2963,1,"{6167, 6133, 25, 514, 446, 80, 63, 208}"
503,1,42,0,0.3239601,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[(E^(2*ArcCoth[a*x])*Sqrt[c - c/(a*x)])/x^2,x]","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}}-\frac{2 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c}",1,"4*a*Sqrt[c - c/(a*x)] - (2*a*(c - c/(a*x))^(3/2))/(3*c)","A",7,6,27,0.2222,1,"{6167, 6133, 25, 514, 444, 43}"
504,1,69,0,0.3328056,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[(E^(2*ArcCoth[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",7,6,27,0.2222,1,"{6167, 6133, 25, 514, 446, 77}"
505,1,96,0,0.3515007,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[(E^(2*ArcCoth[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",7,6,27,0.2222,1,"{6167, 6133, 25, 514, 446, 77}"
506,1,121,0,0.3776407,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[(E^(2*ArcCoth[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",7,6,27,0.2222,1,"{6167, 6133, 25, 514, 446, 77}"
507,1,313,0,0.3491431,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)]*x^3,x]","\frac{107 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{96 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{149 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{64 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{363 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{64 a^4 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a^4 \sqrt{1-\frac{1}{a x}}}+\frac{x^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{4 \sqrt{1-\frac{1}{a x}}}+\frac{17 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{24 a \sqrt{1-\frac{1}{a x}}}","\frac{107 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{96 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{149 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{64 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{363 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{64 a^4 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a^4 \sqrt{1-\frac{1}{a x}}}+\frac{x^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{4 \sqrt{1-\frac{1}{a x}}}+\frac{17 x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{24 a \sqrt{1-\frac{1}{a x}}}",1,"(149*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/(64*a^3*Sqrt[1 - 1/(a*x)]) + (107*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^2)/(96*a^2*Sqrt[1 - 1/(a*x)]) + (17*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^3)/(24*a*Sqrt[1 - 1/(a*x)]) + (Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^4)/(4*Sqrt[1 - 1/(a*x)]) + (363*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(64*a^4*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a^4*Sqrt[1 - 1/(a*x)])","A",11,8,27,0.2963,1,"{6182, 6180, 98, 151, 156, 63, 208, 206}"
508,1,261,0,0.3168856,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)]*x^2,x]","\frac{19 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{45 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{8 a^3 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a^3 \sqrt{1-\frac{1}{a x}}}+\frac{x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{13 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-\frac{1}{a x}}}","\frac{19 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{45 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{8 a^3 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a^3 \sqrt{1-\frac{1}{a x}}}+\frac{x^3 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{13 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-\frac{1}{a x}}}",1,"(19*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/(8*a^2*Sqrt[1 - 1/(a*x)]) + (13*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^2)/(12*a*Sqrt[1 - 1/(a*x)]) + (Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^3)/(3*Sqrt[1 - 1/(a*x)]) + (45*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(8*a^3*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a^3*Sqrt[1 - 1/(a*x)])","A",10,8,27,0.2963,1,"{6182, 6180, 98, 151, 156, 63, 208, 206}"
509,1,209,0,0.2189201,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)]*x,x]","\frac{23 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{4 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a^2 \sqrt{1-\frac{1}{a x}}}+\frac{x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{2 \sqrt{1-\frac{1}{a x}}}+\frac{9 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-\frac{1}{a x}}}","\frac{23 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{4 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a^2 \sqrt{1-\frac{1}{a x}}}+\frac{x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{2 \sqrt{1-\frac{1}{a x}}}+\frac{9 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-\frac{1}{a x}}}",1,"(9*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/(4*a*Sqrt[1 - 1/(a*x)]) + (Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^2)/(2*Sqrt[1 - 1/(a*x)]) + (23*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(4*a^2*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a^2*Sqrt[1 - 1/(a*x)])","A",9,8,25,0.3200,1,"{6182, 6180, 98, 151, 156, 63, 208, 206}"
510,1,152,0,0.1260634,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)],x]","\frac{x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}+\frac{5 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{1-\frac{1}{a x}}}","\frac{x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}+\frac{5 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{a \sqrt{1-\frac{1}{a x}}}",1,"(Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/Sqrt[1 - 1/(a*x)] + (5*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/(a*Sqrt[1 - 1/(a*x)])","A",8,7,24,0.2917,1,"{6182, 6179, 98, 156, 63, 208, 206}"
511,1,146,0,0.2726234,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)])/x,x]","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}+\frac{2 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{\sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{1-\frac{1}{a x}}}","\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}+\frac{2 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{\sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"(2*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)])/Sqrt[1 - 1/(a*x)] + (2*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/Sqrt[1 - 1/(a*x)] - (4*Sqrt[2]*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/Sqrt[1 - 1/(a*x)]","A",8,7,27,0.2593,1,"{6182, 6180, 84, 156, 63, 208, 206}"
512,1,125,0,0.2392222,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)])/x^2,x]","\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-4 \sqrt{2} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{2} \sqrt{c-\frac{c}{a x}}}\right)","\frac{2 a c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-4 \sqrt{2} a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{2} \sqrt{c-\frac{c}{a x}}}\right)",1,"(2*a*c^2*(1 - 1/(a^2*x^2))^(3/2))/(3*(c - c/(a*x))^(3/2)) + (4*a*c*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)] - 4*Sqrt[2]*a*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/(Sqrt[2]*Sqrt[c - c/(a*x)])]","A",5,4,27,0.1481,1,"{6178, 665, 661, 208}"
513,1,170,0,0.2997056,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)])/x^3,x]","\frac{2 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{5 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{2 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-4 \sqrt{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{2} \sqrt{c-\frac{c}{a x}}}\right)","\frac{2 a^2 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{5 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{2 a^2 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-4 \sqrt{2} a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{2} \sqrt{c-\frac{c}{a x}}}\right)",1,"(2*a^2*c^3*(1 - 1/(a^2*x^2))^(5/2))/(5*(c - c/(a*x))^(5/2)) + (2*a^2*c^2*(1 - 1/(a^2*x^2))^(3/2))/(3*(c - c/(a*x))^(3/2)) + (4*a^2*c*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)] - 4*Sqrt[2]*a^2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/(Sqrt[2]*Sqrt[c - c/(a*x)])]","A",6,5,27,0.1852,1,"{6178, 795, 665, 661, 208}"
514,1,209,0,0.4760014,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)])/x^4,x]","-\frac{2 a^3 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{7 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{2 a^3 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a^3 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{7 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{4 a^3 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-4 \sqrt{2} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{2} \sqrt{c-\frac{c}{a x}}}\right)","-\frac{2 a^3 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{7 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{2 a^3 c^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{3 \left(c-\frac{c}{a x}\right)^{3/2}}+\frac{4 a^3 c^3 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{7 \left(c-\frac{c}{a x}\right)^{5/2}}+\frac{4 a^3 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-4 \sqrt{2} a^3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{2} \sqrt{c-\frac{c}{a x}}}\right)",1,"(4*a^3*c^3*(1 - 1/(a^2*x^2))^(5/2))/(7*(c - c/(a*x))^(5/2)) + (2*a^3*c^2*(1 - 1/(a^2*x^2))^(3/2))/(3*(c - c/(a*x))^(3/2)) - (2*a^3*c^2*(1 - 1/(a^2*x^2))^(5/2))/(7*(c - c/(a*x))^(3/2)) + (4*a^3*c*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)] - 4*Sqrt[2]*a^3*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/(Sqrt[2]*Sqrt[c - c/(a*x)])]","A",7,6,27,0.2222,1,"{6178, 1639, 795, 665, 661, 208}"
515,1,303,0,0.3203361,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a*x)])/x^5,x]","\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{9/2} \sqrt{c-\frac{c}{a x}}}{9 \sqrt{1-\frac{1}{a x}}}-\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{7/2} \sqrt{c-\frac{c}{a x}}}{7 \sqrt{1-\frac{1}{a x}}}+\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{c-\frac{c}{a x}}}{5 \sqrt{1-\frac{1}{a x}}}+\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{4 a^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^4 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{1-\frac{1}{a x}}}","\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{9/2} \sqrt{c-\frac{c}{a x}}}{9 \sqrt{1-\frac{1}{a x}}}-\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{7/2} \sqrt{c-\frac{c}{a x}}}{7 \sqrt{1-\frac{1}{a x}}}+\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{c-\frac{c}{a x}}}{5 \sqrt{1-\frac{1}{a x}}}+\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}}}+\frac{4 a^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{4 \sqrt{2} a^4 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{a x}+1}}{\sqrt{2}}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"(4*a^4*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)])/Sqrt[1 - 1/(a*x)] + (2*a^4*(1 + 1/(a*x))^(3/2)*Sqrt[c - c/(a*x)])/(3*Sqrt[1 - 1/(a*x)]) + (2*a^4*(1 + 1/(a*x))^(5/2)*Sqrt[c - c/(a*x)])/(5*Sqrt[1 - 1/(a*x)]) - (2*a^4*(1 + 1/(a*x))^(7/2)*Sqrt[c - c/(a*x)])/(7*Sqrt[1 - 1/(a*x)]) + (2*a^4*(1 + 1/(a*x))^(9/2)*Sqrt[c - c/(a*x)])/(9*Sqrt[1 - 1/(a*x)]) - (4*Sqrt[2]*a^4*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]/Sqrt[2]])/Sqrt[1 - 1/(a*x)]","A",8,6,27,0.2222,1,"{6182, 6180, 88, 50, 63, 206}"
516,1,126,0,0.2668437,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^m \, dx","Int[(Sqrt[c - c/(a*x)]*x^m)/E^ArcCoth[a*x],x]","\frac{\sqrt{\frac{1}{a x}+1} x^{m+1} \sqrt{c-\frac{c}{a x}}}{(m+1) \sqrt{1-\frac{1}{a x}}}-\frac{(4 m+3) x^m \sqrt{c-\frac{c}{a x}} \, _2F_1\left(\frac{1}{2},-m;1-m;-\frac{1}{a x}\right)}{2 a m (m+1) \sqrt{1-\frac{1}{a x}}}","\frac{\sqrt{\frac{1}{a x}+1} x^{m+1} \sqrt{c-\frac{c}{a x}}}{(m+1) \sqrt{1-\frac{1}{a x}}}-\frac{(4 m+3) x^m \sqrt{c-\frac{c}{a x}} \, _2F_1\left(\frac{1}{2},-m;1-m;-\frac{1}{a x}\right)}{2 a m (m+1) \sqrt{1-\frac{1}{a x}}}",1,"(Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^(1 + m))/((1 + m)*Sqrt[1 - 1/(a*x)]) - ((3 + 4*m)*Sqrt[c - c/(a*x)]*x^m*Hypergeometric2F1[1/2, -m, 1 - m, -(1/(a*x))])/(2*a*m*(1 + m)*Sqrt[1 - 1/(a*x)])","A",4,4,27,0.1481,1,"{6182, 6181, 79, 64}"
517,1,164,0,0.3603751,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[(Sqrt[c - c/(a*x)]*x^2)/E^ArcCoth[a*x],x]","\frac{c x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-\frac{c}{a x}}}-\frac{11 c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{12 a \sqrt{c-\frac{c}{a x}}}+\frac{11 c x \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2 \sqrt{c-\frac{c}{a x}}}-\frac{11 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{8 a^3}","\frac{c x^3 \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-\frac{c}{a x}}}-\frac{11 c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{12 a \sqrt{c-\frac{c}{a x}}}+\frac{11 c x \sqrt{1-\frac{1}{a^2 x^2}}}{8 a^2 \sqrt{c-\frac{c}{a x}}}-\frac{11 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{8 a^3}",1,"(11*c*Sqrt[1 - 1/(a^2*x^2)]*x)/(8*a^2*Sqrt[c - c/(a*x)]) - (11*c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(12*a*Sqrt[c - c/(a*x)]) + (c*Sqrt[1 - 1/(a^2*x^2)]*x^3)/(3*Sqrt[c - c/(a*x)]) - (11*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/(8*a^3)","A",6,5,27,0.1852,1,"{6178, 879, 873, 875, 208}"
518,1,124,0,0.2549088,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[(Sqrt[c - c/(a*x)]*x)/E^ArcCoth[a*x],x]","\frac{c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 \sqrt{c-\frac{c}{a x}}}-\frac{7 c x \sqrt{1-\frac{1}{a^2 x^2}}}{4 a \sqrt{c-\frac{c}{a x}}}+\frac{7 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{4 a^2}","\frac{c x^2 \sqrt{1-\frac{1}{a^2 x^2}}}{2 \sqrt{c-\frac{c}{a x}}}-\frac{7 c x \sqrt{1-\frac{1}{a^2 x^2}}}{4 a \sqrt{c-\frac{c}{a x}}}+\frac{7 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{4 a^2}",1,"(-7*c*Sqrt[1 - 1/(a^2*x^2)]*x)/(4*a*Sqrt[c - c/(a*x)]) + (c*Sqrt[1 - 1/(a^2*x^2)]*x^2)/(2*Sqrt[c - c/(a*x)]) + (7*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/(4*a^2)","A",5,5,25,0.2000,1,"{6178, 879, 873, 875, 208}"
519,1,79,0,0.1580533,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^ArcCoth[a*x],x]","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}","\frac{c x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)}{a}",1,"(c*Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a*x)] - (3*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]])/a","A",4,4,24,0.1667,1,"{6177, 879, 875, 208}"
520,1,76,0,0.2440239,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcCoth[a*x]*x),x]","\frac{2 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}+2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)","\frac{2 c \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}+2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a x}}}\right)",1,"(2*c*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)] + 2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[1 - 1/(a^2*x^2)])/Sqrt[c - c/(a*x)]]","A",4,4,27,0.1481,1,"{6178, 881, 875, 208}"
521,1,70,0,0.1849619,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcCoth[a*x]*x^2),x]","-\frac{2}{3} a \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}-\frac{8 a c \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-\frac{c}{a x}}}","-\frac{2}{3} a \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}-\frac{8 a c \sqrt{1-\frac{1}{a^2 x^2}}}{3 \sqrt{c-\frac{c}{a x}}}",1,"(-8*a*c*Sqrt[1 - 1/(a^2*x^2)])/(3*Sqrt[c - c/(a*x)]) - (2*a*Sqrt[1 - 1/(a^2*x^2)]*Sqrt[c - c/(a*x)])/3","A",3,3,27,0.1111,1,"{6178, 657, 649}"
522,1,113,0,0.2238327,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcCoth[a*x]*x^3),x]","\frac{2 a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{5 c}+\frac{2}{5} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}+\frac{8 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}{5 \sqrt{c-\frac{c}{a x}}}","\frac{2 a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{5 c}+\frac{2}{5} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}+\frac{8 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}{5 \sqrt{c-\frac{c}{a x}}}",1,"(8*a^2*c*Sqrt[1 - 1/(a^2*x^2)])/(5*Sqrt[c - c/(a*x)]) + (2*a^2*Sqrt[1 - 1/(a^2*x^2)]*Sqrt[c - c/(a*x)])/5 + (2*a^2*Sqrt[1 - 1/(a^2*x^2)]*(c - c/(a*x))^(3/2))/(5*c)","A",4,4,27,0.1481,1,"{6178, 795, 657, 649}"
523,1,149,0,0.3028014,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[Sqrt[c - c/(a*x)]/(E^ArcCoth[a*x]*x^4),x]","-\frac{104}{105} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}-\frac{104 a^3 c \sqrt{1-\frac{1}{a^2 x^2}}}{105 \sqrt{c-\frac{c}{a x}}}-\frac{26 a c \sqrt{1-\frac{1}{a^2 x^2}}}{35 x^2 \sqrt{c-\frac{c}{a x}}}+\frac{2 c \sqrt{1-\frac{1}{a^2 x^2}}}{7 x^3 \sqrt{c-\frac{c}{a x}}}","-\frac{104}{105} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}-\frac{104 a^3 c \sqrt{1-\frac{1}{a^2 x^2}}}{105 \sqrt{c-\frac{c}{a x}}}-\frac{26 a c \sqrt{1-\frac{1}{a^2 x^2}}}{35 x^2 \sqrt{c-\frac{c}{a x}}}+\frac{2 c \sqrt{1-\frac{1}{a^2 x^2}}}{7 x^3 \sqrt{c-\frac{c}{a x}}}",1,"(-104*a^3*c*Sqrt[1 - 1/(a^2*x^2)])/(105*Sqrt[c - c/(a*x)]) - (104*a^3*Sqrt[1 - 1/(a^2*x^2)]*Sqrt[c - c/(a*x)])/105 + (2*c*Sqrt[1 - 1/(a^2*x^2)])/(7*Sqrt[c - c/(a*x)]*x^3) - (26*a*c*Sqrt[1 - 1/(a^2*x^2)])/(35*Sqrt[c - c/(a*x)]*x^2)","A",5,5,27,0.1852,1,"{6178, 881, 871, 795, 649}"
524,1,172,0,0.4695434,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[(Sqrt[c - c/(a*x)]*x^3)/E^(2*ArcCoth[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",14,10,27,0.3704,1,"{6167, 6133, 25, 514, 446, 98, 151, 156, 63, 208}"
525,1,147,0,0.4514106,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[(Sqrt[c - c/(a*x)]*x^2)/E^(2*ArcCoth[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",13,10,27,0.3704,1,"{6167, 6133, 25, 514, 446, 98, 151, 156, 63, 208}"
526,1,122,0,0.3239087,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[(Sqrt[c - c/(a*x)]*x)/E^(2*ArcCoth[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",12,10,25,0.4000,1,"{6167, 6133, 25, 514, 446, 98, 151, 156, 63, 208}"
527,1,92,0,0.1981317,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^(2*ArcCoth[a*x]),x]","x \sqrt{c-\frac{c}{a x}}-\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 \sqrt{c-\frac{c}{a x}}-\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",11,9,24,0.3750,1,"{6167, 6133, 25, 514, 375, 98, 156, 63, 208}"
528,1,86,0,0.3732194,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcCoth[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",11,9,27,0.3333,1,"{6167, 6133, 25, 434, 446, 84, 156, 63, 208}"
529,1,82,0,0.3759404,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcCoth[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",9,8,27,0.2963,1,"{6167, 6133, 25, 514, 444, 50, 63, 208}"
530,1,113,0,0.3937064,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcCoth[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",10,9,27,0.3333,1,"{6167, 6133, 25, 514, 446, 80, 50, 63, 208}"
531,1,113,0,0.4160165,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcCoth[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",11,9,27,0.3333,1,"{6167, 6133, 25, 514, 446, 88, 50, 63, 208}"
532,1,163,0,0.4581305,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(2*ArcCoth[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",11,9,27,0.3333,1,"{6167, 6133, 25, 514, 446, 88, 50, 63, 208}"
533,1,306,0,0.3183344,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^3 \, dx","Int[(Sqrt[c - c/(a*x)]*x^3)/E^(3*ArcCoth[a*x]),x]","\frac{1115 x^2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{96 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{223 x^2 \sqrt{c-\frac{c}{a x}}}{24 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{1115 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{64 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{1115 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{64 a^4 \sqrt{1-\frac{1}{a x}}}+\frac{x^4 \sqrt{c-\frac{c}{a x}}}{4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{25 x^3 \sqrt{c-\frac{c}{a x}}}{24 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","\frac{223 x^2 \sqrt{c-\frac{c}{a x}}}{96 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{1115 x \sqrt{c-\frac{c}{a x}}}{192 a^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{1115 \sqrt{c-\frac{c}{a x}}}{64 a^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{1115 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{64 a^4 \sqrt{1-\frac{1}{a x}}}+\frac{x^4 \sqrt{c-\frac{c}{a x}}}{4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{25 x^3 \sqrt{c-\frac{c}{a x}}}{24 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-1115*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/(64*a^3*Sqrt[1 - 1/(a*x)]) - (223*Sqrt[c - c/(a*x)]*x^2)/(24*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (1115*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x^2)/(96*a^2*Sqrt[1 - 1/(a*x)]) - (25*Sqrt[c - c/(a*x)]*x^3)/(24*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (Sqrt[c - c/(a*x)]*x^4)/(4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (1115*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(64*a^4*Sqrt[1 - 1/(a*x)])","A",9,7,27,0.2593,1,"{6182, 6180, 89, 78, 51, 63, 208}"
534,1,252,0,0.2928241,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x^2 \, dx","Int[(Sqrt[c - c/(a*x)]*x^2)/E^(3*ArcCoth[a*x]),x]","\frac{119 x \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{8 a^2 \sqrt{1-\frac{1}{a x}}}-\frac{119 x \sqrt{c-\frac{c}{a x}}}{12 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{119 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{8 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{x^3 \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{19 x^2 \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","\frac{119 x \sqrt{c-\frac{c}{a x}}}{24 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{119 \sqrt{c-\frac{c}{a x}}}{8 a^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{119 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{8 a^3 \sqrt{1-\frac{1}{a x}}}+\frac{x^3 \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{19 x^2 \sqrt{c-\frac{c}{a x}}}{12 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-119*Sqrt[c - c/(a*x)]*x)/(12*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (119*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)]*x)/(8*a^2*Sqrt[1 - 1/(a*x)]) - (19*Sqrt[c - c/(a*x)]*x^2)/(12*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (Sqrt[c - c/(a*x)]*x^3)/(3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (119*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(8*a^3*Sqrt[1 - 1/(a*x)])","A",8,7,27,0.2593,1,"{6182, 6180, 89, 78, 51, 63, 208}"
535,1,199,0,0.1995646,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} x \, dx","Int[(Sqrt[c - c/(a*x)]*x)/E^(3*ArcCoth[a*x]),x]","-\frac{47 \sqrt{c-\frac{c}{a x}}}{4 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{47 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{4 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{x^2 \sqrt{c-\frac{c}{a x}}}{2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{13 x \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","-\frac{47 \sqrt{c-\frac{c}{a x}}}{4 a^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{47 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{4 a^2 \sqrt{1-\frac{1}{a x}}}+\frac{x^2 \sqrt{c-\frac{c}{a x}}}{2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{13 x \sqrt{c-\frac{c}{a x}}}{4 a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-47*Sqrt[c - c/(a*x)])/(4*a^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (13*Sqrt[c - c/(a*x)]*x)/(4*a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (Sqrt[c - c/(a*x)]*x^2)/(2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (47*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(4*a^2*Sqrt[1 - 1/(a*x)])","A",7,7,25,0.2800,1,"{6182, 6180, 89, 78, 51, 63, 208}"
536,1,140,0,0.1136657,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[Sqrt[c - c/(a*x)]/E^(3*ArcCoth[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{9 \sqrt{c-\frac{c}{a x}}}{a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{7 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}","\frac{x \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{9 \sqrt{c-\frac{c}{a x}}}{a \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{7 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{a \sqrt{1-\frac{1}{a x}}}",1,"(9*Sqrt[c - c/(a*x)])/(a*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (Sqrt[c - c/(a*x)]*x)/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (7*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/(a*Sqrt[1 - 1/(a*x)])","A",6,6,24,0.2500,1,"{6182, 6179, 89, 78, 63, 208}"
537,1,134,0,0.2615106,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcCoth[a*x])*x),x]","-\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{\sqrt{1-\frac{1}{a x}}}","-\frac{2 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{8 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}+\frac{2 \sqrt{c-\frac{c}{a x}} \tanh ^{-1}\left(\sqrt{\frac{1}{a x}+1}\right)}{\sqrt{1-\frac{1}{a x}}}",1,"(-8*Sqrt[c - c/(a*x)])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (2*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)])/Sqrt[1 - 1/(a*x)] + (2*Sqrt[c - c/(a*x)]*ArcTanh[Sqrt[1 + 1/(a*x)]])/Sqrt[1 - 1/(a*x)]","A",6,5,27,0.1852,1,"{6182, 6180, 87, 63, 208}"
538,1,109,0,0.2162144,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^2} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcCoth[a*x])*x^2),x]","-\frac{2 a \left(c-\frac{c}{a x}\right)^{5/2}}{3 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{16 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{64 a \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{2 a \left(c-\frac{c}{a x}\right)^{5/2}}{3 c^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{16 a \left(c-\frac{c}{a x}\right)^{3/2}}{3 c \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{64 a \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(64*a*Sqrt[c - c/(a*x)])/(3*Sqrt[1 - 1/(a^2*x^2)]) - (16*a*(c - c/(a*x))^(3/2))/(3*c*Sqrt[1 - 1/(a^2*x^2)]) - (2*a*(c - c/(a*x))^(5/2))/(3*c^2*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6178, 657, 649}"
539,1,150,0,0.2660108,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^3} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcCoth[a*x])*x^3),x]","-\frac{a^2 \left(c-\frac{c}{a x}\right)^{7/2}}{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{7 a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{5 c}-\frac{56}{15} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}-\frac{224 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}{15 \sqrt{c-\frac{c}{a x}}}","-\frac{a^2 \left(c-\frac{c}{a x}\right)^{7/2}}{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{7 a^2 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{5 c}-\frac{56}{15} a^2 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}-\frac{224 a^2 c \sqrt{1-\frac{1}{a^2 x^2}}}{15 \sqrt{c-\frac{c}{a x}}}",1,"(-224*a^2*c*Sqrt[1 - 1/(a^2*x^2)])/(15*Sqrt[c - c/(a*x)]) - (56*a^2*Sqrt[1 - 1/(a^2*x^2)]*Sqrt[c - c/(a*x)])/15 - (7*a^2*Sqrt[1 - 1/(a^2*x^2)]*(c - c/(a*x))^(3/2))/(5*c) - (a^2*(c - c/(a*x))^(7/2))/(c^3*Sqrt[1 - 1/(a^2*x^2)])","A",5,4,27,0.1481,1,"{6178, 789, 657, 649}"
540,1,188,0,0.4138273,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^4} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcCoth[a*x])*x^4),x]","\frac{a^3 \left(c-\frac{c}{a x}\right)^{7/2}}{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{5/2}}{7 c^2}+\frac{59 a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{35 c}+\frac{472}{105} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}+\frac{1888 a^3 c \sqrt{1-\frac{1}{a^2 x^2}}}{105 \sqrt{c-\frac{c}{a x}}}","\frac{a^3 \left(c-\frac{c}{a x}\right)^{7/2}}{c^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{5/2}}{7 c^2}+\frac{59 a^3 \sqrt{1-\frac{1}{a^2 x^2}} \left(c-\frac{c}{a x}\right)^{3/2}}{35 c}+\frac{472}{105} a^3 \sqrt{1-\frac{1}{a^2 x^2}} \sqrt{c-\frac{c}{a x}}+\frac{1888 a^3 c \sqrt{1-\frac{1}{a^2 x^2}}}{105 \sqrt{c-\frac{c}{a x}}}",1,"(1888*a^3*c*Sqrt[1 - 1/(a^2*x^2)])/(105*Sqrt[c - c/(a*x)]) + (472*a^3*Sqrt[1 - 1/(a^2*x^2)]*Sqrt[c - c/(a*x)])/105 + (59*a^3*Sqrt[1 - 1/(a^2*x^2)]*(c - c/(a*x))^(3/2))/(35*c) + (2*a^3*Sqrt[1 - 1/(a^2*x^2)]*(c - c/(a*x))^(5/2))/(7*c^2) + (a^3*(c - c/(a*x))^(7/2))/(c^3*Sqrt[1 - 1/(a^2*x^2)])","A",6,5,27,0.1852,1,"{6178, 1635, 795, 657, 649}"
541,1,289,0,0.2933522,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}}}{x^5} \, dx","Int[Sqrt[c - c/(a*x)]/(E^(3*ArcCoth[a*x])*x^5),x]","-\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{9/2} \sqrt{c-\frac{c}{a x}}}{9 \sqrt{1-\frac{1}{a x}}}+\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{7/2} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{38 a^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{c-\frac{c}{a x}}}{5 \sqrt{1-\frac{1}{a x}}}+\frac{50 a^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}}}-\frac{32 a^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{8 a^4 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}","-\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{9/2} \sqrt{c-\frac{c}{a x}}}{9 \sqrt{1-\frac{1}{a x}}}+\frac{2 a^4 \left(\frac{1}{a x}+1\right)^{7/2} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{38 a^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{c-\frac{c}{a x}}}{5 \sqrt{1-\frac{1}{a x}}}+\frac{50 a^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{c-\frac{c}{a x}}}{3 \sqrt{1-\frac{1}{a x}}}-\frac{32 a^4 \sqrt{\frac{1}{a x}+1} \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}}}-\frac{8 a^4 \sqrt{c-\frac{c}{a x}}}{\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}",1,"(-8*a^4*Sqrt[c - c/(a*x)])/(Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) - (32*a^4*Sqrt[1 + 1/(a*x)]*Sqrt[c - c/(a*x)])/Sqrt[1 - 1/(a*x)] + (50*a^4*(1 + 1/(a*x))^(3/2)*Sqrt[c - c/(a*x)])/(3*Sqrt[1 - 1/(a*x)]) - (38*a^4*(1 + 1/(a*x))^(5/2)*Sqrt[c - c/(a*x)])/(5*Sqrt[1 - 1/(a*x)]) + (2*a^4*(1 + 1/(a*x))^(7/2)*Sqrt[c - c/(a*x)])/Sqrt[1 - 1/(a*x)] - (2*a^4*(1 + 1/(a*x))^(9/2)*Sqrt[c - c/(a*x)])/(9*Sqrt[1 - 1/(a*x)])","A",4,3,27,0.1111,1,"{6182, 6180, 88}"
542,1,81,0,0.0645511,"\int e^{n \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right) \, dx","Int[E^(n*ArcCoth[a*x])*(c - c/(a*x)),x]","-\frac{c 2^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n-2}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2)}","-\frac{c 2^{n/2} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{a (2-n)}-\frac{2 c (1-n) \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a+\frac{1}{x}}{a-\frac{1}{x}}\right)}{a n}+c x \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}",1,"-((2^(2 - n/2)*c*(1 + 1/(a*x))^((2 + n)/2)*AppellF1[(2 + n)/2, (-2 + n)/2, 2, (4 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n)))","C",2,2,20,0.1000,0,"{6179, 136}"
543,1,113,0,0.0849104,"\int \frac{e^{n \coth ^{-1}(a x)}}{c-\frac{c}{a x}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - c/(a*x)),x]","\frac{x \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{c}-\frac{2 (n+1) \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c n}","\frac{x \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}}}{c}-\frac{2 (n+1) \left(1-\frac{1}{a x}\right)^{-n/2} \left(\frac{1}{a x}+1\right)^{n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c n}",1,"((1 + 1/(a*x))^((2 + n)/2)*x)/(c*(1 - 1/(a*x))^(n/2)) - (2*(1 + n)*(1 + 1/(a*x))^(n/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*c*n*(1 - 1/(a*x))^(n/2))","A",3,3,22,0.1364,1,"{6179, 96, 131}"
544,1,166,0,0.1154707,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^2} \, dx","Int[E^(n*ArcCoth[a*x])/(c - c/(a*x))^2,x]","-\frac{2 (n+2) \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c^2 n}-\frac{(n+3) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{a c^2 (n+2)}+\frac{x \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{c^2}","-\frac{2 (n+2) \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(1,-\frac{n}{2};1-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c^2 n}-\frac{(n+3) \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{a c^2 (n+2)}+\frac{x \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{c^2}",1,"-(((3 + n)*(1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2))/(a*c^2*(2 + n))) + ((1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*x)/c^2 - (2*(2 + n)*(1 + 1/(a*x))^(n/2)*Hypergeometric2F1[1, -n/2, 1 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*c^2*n*(1 - 1/(a*x))^(n/2))","A",5,5,22,0.2273,1,"{6179, 129, 155, 12, 131}"
545,1,111,0,0.1523186,"\int e^{n \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^{3/2} \, dx","Int[E^(n*ArcCoth[a*x])*(c - c/(a*x))^(3/2),x]","-\frac{2^{\frac{5}{2}-\frac{n}{2}} \left(c-\frac{c}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n-3}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \left(1-\frac{1}{a x}\right)^{3/2}}","-\frac{2^{\frac{5}{2}-\frac{n}{2}} \left(c-\frac{c}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n-3}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \left(1-\frac{1}{a x}\right)^{3/2}}",1,"-((2^(5/2 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*(c - c/(a*x))^(3/2)*AppellF1[(2 + n)/2, (-3 + n)/2, 2, (4 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n)*(1 - 1/(a*x))^(3/2)))","A",3,3,24,0.1250,1,"{6182, 6179, 136}"
546,1,111,0,0.1435435,"\int e^{n \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a x}} \, dx","Int[E^(n*ArcCoth[a*x])*Sqrt[c - c/(a*x)],x]","-\frac{2^{\frac{3}{2}-\frac{n}{2}} \sqrt{c-\frac{c}{a x}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n-1}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \sqrt{1-\frac{1}{a x}}}","-\frac{2^{\frac{3}{2}-\frac{n}{2}} \sqrt{c-\frac{c}{a x}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n-1}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \sqrt{1-\frac{1}{a x}}}",1,"-((2^(3/2 - n/2)*(1 + 1/(a*x))^((2 + n)/2)*Sqrt[c - c/(a*x)]*AppellF1[(2 + n)/2, (-1 + n)/2, 2, (4 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n)*Sqrt[1 - 1/(a*x)]))","A",3,3,24,0.1250,1,"{6182, 6179, 136}"
547,1,111,0,0.1498656,"\int \frac{e^{n \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a x}}} \, dx","Int[E^(n*ArcCoth[a*x])/Sqrt[c - c/(a*x)],x]","-\frac{2^{\frac{1}{2}-\frac{n}{2}} \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n+1}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \sqrt{c-\frac{c}{a x}}}","-\frac{2^{\frac{1}{2}-\frac{n}{2}} \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n+1}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \sqrt{c-\frac{c}{a x}}}",1,"-((2^(1/2 - n/2)*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^((2 + n)/2)*AppellF1[(2 + n)/2, (1 + n)/2, 2, (4 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n)*Sqrt[c - c/(a*x)]))","A",3,3,24,0.1250,1,"{6182, 6179, 136}"
548,1,111,0,0.1553923,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-\frac{c}{a x}\right)^{3/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - c/(a*x))^(3/2),x]","-\frac{2^{-\frac{n}{2}-\frac{1}{2}} \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n+3}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \left(c-\frac{c}{a x}\right)^{3/2}}","-\frac{2^{-\frac{n}{2}-\frac{1}{2}} \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} F_1\left(\frac{n+2}{2};\frac{n+3}{2},2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2) \left(c-\frac{c}{a x}\right)^{3/2}}",1,"-((2^(-1/2 - n/2)*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^((2 + n)/2)*AppellF1[(2 + n)/2, (3 + n)/2, 2, (4 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n)*(c - c/(a*x))^(3/2)))","A",3,3,24,0.1250,1,"{6182, 6179, 136}"
549,1,110,0,0.1061452,"\int e^{n \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^(n*ArcCoth[a*x])*(c - c/(a*x))^p,x]","-\frac{2^{-\frac{n}{2}+p+1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-p} \left(c-\frac{c}{a x}\right)^p F_1\left(\frac{n+2}{2};\frac{1}{2} (n-2 p),2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2)}","-\frac{2^{-\frac{n}{2}+p+1} \left(\frac{1}{a x}+1\right)^{\frac{n+2}{2}} \left(1-\frac{1}{a x}\right)^{-p} \left(c-\frac{c}{a x}\right)^p F_1\left(\frac{n+2}{2};\frac{1}{2} (n-2 p),2;\frac{n+4}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2)}",1,"-((2^(1 - n/2 + p)*(1 + 1/(a*x))^((2 + n)/2)*(c - c/(a*x))^p*AppellF1[(2 + n)/2, (n - 2*p)/2, 2, (4 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n)*(1 - 1/(a*x))^p))","A",3,3,22,0.1364,1,"{6182, 6179, 136}"
550,1,67,0,0.0769245,"\int e^{2 p \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^(2*p*ArcCoth[a*x])*(c - c/(a*x))^p,x]","-\frac{\left(1-\frac{1}{a x}\right)^{-p} \left(\frac{1}{a x}+1\right)^{p+1} \left(c-\frac{c}{a x}\right)^p \, _2F_1\left(2,p+1;p+2;1+\frac{1}{a x}\right)}{a (p+1)}","-\frac{\left(1-\frac{1}{a x}\right)^{-p} \left(\frac{1}{a x}+1\right)^{p+1} \left(c-\frac{c}{a x}\right)^p \, _2F_1\left(2,p+1;p+2;1+\frac{1}{a x}\right)}{a (p+1)}",1,"-(((1 + 1/(a*x))^(1 + p)*(c - c/(a*x))^p*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + 1/(a*x)])/(a*(1 + p)*(1 - 1/(a*x))^p))","A",3,3,23,0.1304,1,"{6182, 6179, 65}"
551,1,93,0,0.0995908,"\int e^{-2 p \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[(c - c/(a*x))^p/E^(2*p*ArcCoth[a*x]),x]","-\frac{4^p \left(1-\frac{1}{a x}\right)^{-p} \left(\frac{1}{a x}+1\right)^{1-p} F_1\left(1-p;-2 p,2;2-p;\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right) \left(c-\frac{c}{a x}\right)^p}{a (1-p)}","-\frac{4^p \left(1-\frac{1}{a x}\right)^{-p} \left(\frac{1}{a x}+1\right)^{1-p} F_1\left(1-p;-2 p,2;2-p;\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right) \left(c-\frac{c}{a x}\right)^p}{a (1-p)}",1,"-((4^p*(1 + 1/(a*x))^(1 - p)*(c - c/(a*x))^p*AppellF1[1 - p, -2*p, 2, 2 - p, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(1 - p)*(1 - 1/(a*x))^p))","A",3,3,23,0.1304,1,"{6182, 6179, 136}"
552,1,57,0,0.1065466,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^(2*ArcCoth[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",7,7,22,0.3182,1,"{6167, 6133, 25, 514, 375, 78, 65}"
553,1,90,0,0.0795841,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[E^ArcCoth[a*x]*(c - c/(a*x))^p,x]","-\frac{2^{p+\frac{1}{2}} \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{-p} F_1\left(\frac{3}{2};\frac{1}{2}-p,2;\frac{5}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right) \left(c-\frac{c}{a x}\right)^p}{3 a}","-\frac{2^{p+\frac{1}{2}} \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{-p} F_1\left(\frac{3}{2};\frac{1}{2}-p,2;\frac{5}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right) \left(c-\frac{c}{a x}\right)^p}{3 a}",1,"-(2^(1/2 + p)*(1 + 1/(a*x))^(3/2)*(c - c/(a*x))^p*AppellF1[3/2, 1/2 - p, 2, 5/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(3*a*(1 - 1/(a*x))^p)","A",3,3,20,0.1500,1,"{6182, 6179, 136}"
554,1,88,0,0.0853336,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[(c - c/(a*x))^p/E^ArcCoth[a*x],x]","-\frac{2^{p+\frac{3}{2}} \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{-p} F_1\left(\frac{1}{2};-p-\frac{1}{2},2;\frac{3}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right) \left(c-\frac{c}{a x}\right)^p}{a}","-\frac{2^{p+\frac{3}{2}} \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{-p} F_1\left(\frac{1}{2};-p-\frac{1}{2},2;\frac{3}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right) \left(c-\frac{c}{a x}\right)^p}{a}",1,"-((2^(3/2 + p)*Sqrt[1 + 1/(a*x)]*(c - c/(a*x))^p*AppellF1[1/2, -1/2 - p, 2, 3/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(1 - 1/(a*x))^p))","A",3,3,22,0.1364,1,"{6182, 6179, 136}"
555,1,114,0,0.1524683,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a x}\right)^p \, dx","Int[(c - c/(a*x))^p/E^(2*ArcCoth[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",9,9,22,0.4091,1,"{6167, 6133, 25, 514, 375, 103, 156, 65, 68}"
556,1,393,0,0.3366701,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^4,x]","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{11/2}-\frac{7}{72} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{5}{72} a^6 c^4 x^7 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{11/2}-\frac{5}{144} a^5 c^4 x^6 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{1}{144} a^4 c^4 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{64} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{7}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{35}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{35}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{35 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{11/2}-\frac{7}{72} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{5}{72} a^6 c^4 x^7 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{11/2}-\frac{5}{144} a^5 c^4 x^6 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{1}{144} a^4 c^4 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{64} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{7}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{35}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{35}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{35 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}",1,"(35*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/128 + (35*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/384 + (7*a^2*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/192 + (a^3*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/64 + (a^4*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)*x^5)/144 - (5*a^5*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(11/2)*x^6)/144 + (5*a^6*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(11/2)*x^7)/72 - (7*a^7*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(11/2)*x^8)/72 + (a^8*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(11/2)*x^9)/9 + (35*c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(128*a)","A",13,5,20,0.2500,1,"{6191, 6195, 94, 92, 208}"
557,1,313,0,0.2506564,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^3,x]","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{5}{42} a^5 c^3 x^6 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{14} a^4 c^3 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{56} a^3 c^3 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{24} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{5}{48} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{5}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{5 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{5}{42} a^5 c^3 x^6 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{14} a^4 c^3 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{56} a^3 c^3 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{24} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{5}{48} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{5}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{5 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}",1,"(5*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/16 + (5*a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/48 + (a^2*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/24 + (a^3*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/56 - (a^4*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)*x^5)/14 + (5*a^5*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(9/2)*x^6)/42 - (a^6*c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(9/2)*x^7)/7 + (5*c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(16*a)","A",11,5,20,0.2500,1,"{6191, 6195, 94, 92, 208}"
558,1,233,0,0.1935149,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^2,x]","\frac{1}{5} a^4 c^2 x^5 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{3}{20} a^3 c^2 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{20} a^2 c^2 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{1}{8} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{3}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}","\frac{1}{5} a^4 c^2 x^5 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{3}{20} a^3 c^2 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{20} a^2 c^2 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{1}{8} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{3}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}",1,"(3*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/8 + (a*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/8 + (a^2*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/20 - (3*a^3*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/20 + (a^4*c^2*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(7/2)*x^5)/5 + (3*c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(8*a)","A",9,5,20,0.2500,1,"{6191, 6195, 94, 92, 208}"
559,1,145,0,0.1163318,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2),x]","-\frac{1}{3} a^2 c x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{1}{6} a c x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{1}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}","-\frac{1}{3} a^2 c x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{1}{6} a c x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{1}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}",1,"(c*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/2 + (a*c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/6 - (a^2*c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/3 + (c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(2*a)","A",7,5,18,0.2778,1,"{6191, 6195, 94, 92, 208}"
560,1,13,0,0.0288307,"\int \frac{e^{\coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2),x]","\frac{e^{\coth ^{-1}(a x)}}{a c}","\frac{e^{\coth ^{-1}(a x)}}{a c}",1,"E^ArcCoth[a*x]/(a*c)","A",1,1,20,0.05000,1,"{6183}"
561,1,51,0,0.0604559,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^2,x]","\frac{2 e^{\coth ^{-1}(a x)}}{3 a c^2}-\frac{(1-2 a x) e^{\coth ^{-1}(a x)}}{3 a c^2 \left(1-a^2 x^2\right)}","\frac{2 e^{\coth ^{-1}(a x)}}{3 a c^2}-\frac{(1-2 a x) e^{\coth ^{-1}(a x)}}{3 a c^2 \left(1-a^2 x^2\right)}",1,"(2*E^ArcCoth[a*x])/(3*a*c^2) - (E^ArcCoth[a*x]*(1 - 2*a*x))/(3*a*c^2*(1 - a^2*x^2))","A",2,2,20,0.1000,1,"{6185, 6183}"
562,1,85,0,0.0929698,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^3,x]","-\frac{(1-4 a x) e^{\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)^2}-\frac{4 (1-2 a x) e^{\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)}+\frac{8 e^{\coth ^{-1}(a x)}}{15 a c^3}","-\frac{(1-4 a x) e^{\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)^2}-\frac{4 (1-2 a x) e^{\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)}+\frac{8 e^{\coth ^{-1}(a x)}}{15 a c^3}",1,"(8*E^ArcCoth[a*x])/(15*a*c^3) - (E^ArcCoth[a*x]*(1 - 4*a*x))/(15*a*c^3*(1 - a^2*x^2)^2) - (4*E^ArcCoth[a*x]*(1 - 2*a*x))/(15*a*c^3*(1 - a^2*x^2))","A",3,2,20,0.1000,1,"{6185, 6183}"
563,1,119,0,0.1279878,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^4,x]","-\frac{(1-6 a x) e^{\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^3}-\frac{8 (1-2 a x) e^{\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)}-\frac{2 (1-4 a x) e^{\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^2}+\frac{16 e^{\coth ^{-1}(a x)}}{35 a c^4}","-\frac{(1-6 a x) e^{\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^3}-\frac{8 (1-2 a x) e^{\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)}-\frac{2 (1-4 a x) e^{\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^2}+\frac{16 e^{\coth ^{-1}(a x)}}{35 a c^4}",1,"(16*E^ArcCoth[a*x])/(35*a*c^4) - (E^ArcCoth[a*x]*(1 - 6*a*x))/(35*a*c^4*(1 - a^2*x^2)^3) - (2*E^ArcCoth[a*x]*(1 - 4*a*x))/(35*a*c^4*(1 - a^2*x^2)^2) - (8*E^ArcCoth[a*x]*(1 - 2*a*x))/(35*a*c^4*(1 - a^2*x^2))","A",4,2,20,0.1000,1,"{6185, 6183}"
564,1,84,0,0.0988688,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^5 \, dx","Int[E^(2*ArcCoth[a*x])*(c - a^2*c*x^2)^5,x]","-\frac{c^5 (a x+1)^{11}}{11 a}+\frac{4 c^5 (a x+1)^{10}}{5 a}-\frac{8 c^5 (a x+1)^9}{3 a}+\frac{4 c^5 (a x+1)^8}{a}-\frac{16 c^5 (a x+1)^7}{7 a}","-\frac{c^5 (a x+1)^{11}}{11 a}+\frac{4 c^5 (a x+1)^{10}}{5 a}-\frac{8 c^5 (a x+1)^9}{3 a}+\frac{4 c^5 (a x+1)^8}{a}-\frac{16 c^5 (a x+1)^7}{7 a}",1,"(-16*c^5*(1 + a*x)^7)/(7*a) + (4*c^5*(1 + a*x)^8)/a - (8*c^5*(1 + a*x)^9)/(3*a) + (4*c^5*(1 + a*x)^10)/(5*a) - (c^5*(1 + a*x)^11)/(11*a)","A",4,3,22,0.1364,1,"{6167, 6140, 43}"
565,1,69,0,0.0850346,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^(2*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
566,1,52,0,0.076907,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(2*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
567,1,35,0,0.0668577,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(2*ArcCoth[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)^4}{2 a}","\frac{c^2 (a x+1)^5}{5 a}-\frac{c^2 (a x+1)^4}{2 a}",1,"-(c^2*(1 + a*x)^4)/(2*a) + (c^2*(1 + a*x)^5)/(5*a)","A",4,3,22,0.1364,1,"{6167, 6140, 43}"
568,1,15,0,0.033691,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(2*ArcCoth[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",3,3,20,0.1500,1,"{6167, 6140, 32}"
569,1,16,0,0.0653081,"\int \frac{e^{2 \coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",3,3,22,0.1364,1,"{6167, 6140, 32}"
570,1,51,0,0.0787354,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
571,1,86,0,0.100349,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
572,1,121,0,0.1230692,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
573,1,393,0,0.3325926,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^4,x]","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{13/2}-\frac{5}{72} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{13/2}+\frac{5}{168} a^6 c^4 x^7 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{13/2}-\frac{5 a^5 c^4 x^6 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}}{1008}-\frac{11 a^4 c^4 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{1008}-\frac{11}{448} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{55}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{55}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{55 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{13/2}-\frac{5}{72} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{13/2}+\frac{5}{168} a^6 c^4 x^7 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{13/2}-\frac{5 a^5 c^4 x^6 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}}{1008}-\frac{11 a^4 c^4 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{1008}-\frac{11}{448} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{55}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{55}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{55 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}",1,"(-55*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/128 - (55*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/384 - (11*a^2*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/192 - (11*a^3*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/448 - (11*a^4*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)*x^5)/1008 - (5*a^5*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(11/2)*x^6)/1008 + (5*a^6*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(13/2)*x^7)/168 - (5*a^7*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(13/2)*x^8)/72 + (a^8*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(13/2)*x^9)/9 - (55*c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(128*a)","A",13,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
574,1,313,0,0.2535842,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^3,x]","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{1}{14} a^5 c^3 x^6 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}-\frac{1}{70} a^4 c^3 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{9}{280} a^3 c^3 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{3}{40} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{3}{16} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{9}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{9 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{1}{14} a^5 c^3 x^6 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}-\frac{1}{70} a^4 c^3 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{9}{280} a^3 c^3 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{3}{40} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{3}{16} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{9}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{9 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}",1,"(-9*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/16 - (3*a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/16 - (3*a^2*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/40 - (9*a^3*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/280 - (a^4*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)*x^5)/70 + (a^5*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(11/2)*x^6)/14 - (a^6*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(11/2)*x^7)/7 - (9*c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(16*a)","A",11,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
575,1,233,0,0.2126443,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^2,x]","\frac{1}{5} a^4 c^2 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{20} a^3 c^2 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{7}{60} a^2 c^2 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{7}{24} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{7}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{7 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}","\frac{1}{5} a^4 c^2 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{20} a^3 c^2 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{7}{60} a^2 c^2 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{7}{24} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{7}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{7 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}",1,"(-7*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/8 - (7*a*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/24 - (7*a^2*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/60 - (a^3*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/20 + (a^4*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)*x^5)/5 - (7*c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(8*a)","A",9,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
576,1,145,0,0.1190832,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2),x]","-\frac{1}{3} a^2 c x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{5}{6} a c x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{5}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{5 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}","-\frac{1}{3} a^2 c x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{5}{6} a c x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{5}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{5 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}",1,"(-5*c*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/2 - (5*a*c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/6 - (a^2*c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/3 - (5*c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(2*a)","A",7,5,20,0.2500,1,"{6191, 6195, 94, 92, 208}"
577,1,18,0,0.0313877,"\int \frac{e^{3 \coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2),x]","\frac{e^{3 \coth ^{-1}(a x)}}{3 a c}","\frac{e^{3 \coth ^{-1}(a x)}}{3 a c}",1,"E^(3*ArcCoth[a*x])/(3*a*c)","A",1,1,22,0.04545,1,"{6183}"
578,1,55,0,0.0650561,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2)^2,x]","\frac{(3-2 a x) e^{3 \coth ^{-1}(a x)}}{5 a c^2 \left(1-a^2 x^2\right)}-\frac{2 e^{3 \coth ^{-1}(a x)}}{15 a c^2}","\frac{(3-2 a x) e^{3 \coth ^{-1}(a x)}}{5 a c^2 \left(1-a^2 x^2\right)}-\frac{2 e^{3 \coth ^{-1}(a x)}}{15 a c^2}",1,"(-2*E^(3*ArcCoth[a*x]))/(15*a*c^2) + (E^(3*ArcCoth[a*x])*(3 - 2*a*x))/(5*a*c^2*(1 - a^2*x^2))","A",2,2,22,0.09091,1,"{6185, 6183}"
579,1,91,0,0.1004687,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2)^3,x]","-\frac{(3-4 a x) e^{3 \coth ^{-1}(a x)}}{7 a c^3 \left(1-a^2 x^2\right)^2}+\frac{12 (3-2 a x) e^{3 \coth ^{-1}(a x)}}{35 a c^3 \left(1-a^2 x^2\right)}-\frac{8 e^{3 \coth ^{-1}(a x)}}{35 a c^3}","-\frac{(3-4 a x) e^{3 \coth ^{-1}(a x)}}{7 a c^3 \left(1-a^2 x^2\right)^2}+\frac{12 (3-2 a x) e^{3 \coth ^{-1}(a x)}}{35 a c^3 \left(1-a^2 x^2\right)}-\frac{8 e^{3 \coth ^{-1}(a x)}}{35 a c^3}",1,"(-8*E^(3*ArcCoth[a*x]))/(35*a*c^3) - (E^(3*ArcCoth[a*x])*(3 - 4*a*x))/(7*a*c^3*(1 - a^2*x^2)^2) + (12*E^(3*ArcCoth[a*x])*(3 - 2*a*x))/(35*a*c^3*(1 - a^2*x^2))","A",3,2,22,0.09091,1,"{6185, 6183}"
580,1,127,0,0.1387257,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2)^4,x]","-\frac{10 (3-4 a x) e^{3 \coth ^{-1}(a x)}}{63 a c^4 \left(1-a^2 x^2\right)^2}+\frac{8 (3-2 a x) e^{3 \coth ^{-1}(a x)}}{21 a c^4 \left(1-a^2 x^2\right)}-\frac{(1-2 a x) e^{3 \coth ^{-1}(a x)}}{9 a c^4 \left(1-a^2 x^2\right)^3}-\frac{16 e^{3 \coth ^{-1}(a x)}}{63 a c^4}","-\frac{10 (3-4 a x) e^{3 \coth ^{-1}(a x)}}{63 a c^4 \left(1-a^2 x^2\right)^2}+\frac{8 (3-2 a x) e^{3 \coth ^{-1}(a x)}}{21 a c^4 \left(1-a^2 x^2\right)}-\frac{(1-2 a x) e^{3 \coth ^{-1}(a x)}}{9 a c^4 \left(1-a^2 x^2\right)^3}-\frac{16 e^{3 \coth ^{-1}(a x)}}{63 a c^4}",1,"(-16*E^(3*ArcCoth[a*x]))/(63*a*c^4) - (E^(3*ArcCoth[a*x])*(1 - 2*a*x))/(9*a*c^4*(1 - a^2*x^2)^3) - (10*E^(3*ArcCoth[a*x])*(3 - 4*a*x))/(63*a*c^4*(1 - a^2*x^2)^2) + (8*E^(3*ArcCoth[a*x])*(3 - 2*a*x))/(21*a*c^4*(1 - a^2*x^2))","A",4,2,22,0.09091,1,"{6185, 6183}"
581,1,66,0,0.0849376,"\int e^{4 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^5 \, dx","Int[E^(4*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
582,1,52,0,0.0788417,"\int e^{4 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[E^(4*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
583,1,35,0,0.0628281,"\int e^{4 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(4*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
584,1,17,0,0.0571792,"\int e^{4 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(4*ArcCoth[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",3,3,22,0.1364,1,"{6167, 6140, 32}"
585,1,46,0,0.0477622,"\int e^{4 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(4*ArcCoth[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{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",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",4,3,20,0.1500,1,"{6167, 6140, 43}"
586,1,13,0,0.0625637,"\int \frac{e^{4 \coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(4*ArcCoth[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",3,3,22,0.1364,1,"{6167, 6140, 34}"
587,1,18,0,0.0597022,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(4*ArcCoth[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",3,3,22,0.1364,1,"{6167, 6140, 32}"
588,1,87,0,0.0933569,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
589,1,122,0,0.117967,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
590,1,393,0,0.3218842,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[(c - a^2*c*x^2)^4/E^ArcCoth[a*x],x]","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{8} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{8} a^6 c^4 x^7 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{5}{48} a^5 c^4 x^6 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{16} a^4 c^4 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{64} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{7}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{35}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{35}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{35 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{8} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{8} a^6 c^4 x^7 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{5}{48} a^5 c^4 x^6 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{1}{16} a^4 c^4 x^5 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}-\frac{1}{64} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{7}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{35}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{35}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{35 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}",1,"(-35*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/128 - (35*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/384 - (7*a^2*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/192 - (a^3*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/64 + (a^4*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)*x^5)/16 - (5*a^5*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(9/2)*x^6)/48 + (a^6*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(9/2)*x^7)/8 - (a^7*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(9/2)*x^8)/8 + (a^8*c^4*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(9/2)*x^9)/9 - (35*c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(128*a)","A",13,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
591,1,313,0,0.2548621,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[(c - a^2*c*x^2)^3/E^ArcCoth[a*x],x]","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{6} a^5 c^3 x^6 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{1}{6} a^4 c^3 x^5 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{8} a^3 c^3 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{1}{24} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{5}{48} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{5}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{5 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{6} a^5 c^3 x^6 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{1}{6} a^4 c^3 x^5 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{1}{8} a^3 c^3 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{1}{24} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{5}{48} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{5}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{5 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}",1,"(-5*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/16 - (5*a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/48 - (a^2*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/24 + (a^3*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/8 - (a^4*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(7/2)*x^5)/6 + (a^5*c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(7/2)*x^6)/6 - (a^6*c^3*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(7/2)*x^7)/7 - (5*c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(16*a)","A",11,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
592,1,233,0,0.1993305,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[(c - a^2*c*x^2)^2/E^ArcCoth[a*x],x]","\frac{1}{5} a^4 c^2 x^5 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{1}{4} a^3 c^2 x^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{1}{4} a^2 c^2 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{1}{8} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{3}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}","\frac{1}{5} a^4 c^2 x^5 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{1}{4} a^3 c^2 x^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{1}{4} a^2 c^2 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{1}{8} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{3}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}",1,"(-3*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/8 - (a*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/8 + (a^2*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/4 - (a^3*c^2*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2)*x^4)/4 + (a^4*c^2*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(5/2)*x^5)/5 - (3*c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(8*a)","A",9,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
593,1,145,0,0.1145816,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[(c - a^2*c*x^2)/E^ArcCoth[a*x],x]","-\frac{1}{3} a^2 c x^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{1}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}","-\frac{1}{3} a^2 c x^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{1}{2} a c x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{1}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}-\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}",1,"-(c*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/2 + (a*c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/2 - (a^2*c*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2)*x^3)/3 - (c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(2*a)","A",7,5,20,0.2500,1,"{6191, 6195, 94, 92, 208}"
594,1,16,0,0.0301235,"\int \frac{e^{-\coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)),x]","-\frac{e^{-\coth ^{-1}(a x)}}{a c}","-\frac{e^{-\coth ^{-1}(a x)}}{a c}",1,"-(1/(a*c*E^ArcCoth[a*x]))","A",1,1,22,0.04545,1,"{6183}"
595,1,55,0,0.0622484,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)^2),x]","\frac{(2 a x+1) e^{-\coth ^{-1}(a x)}}{3 a c^2 \left(1-a^2 x^2\right)}-\frac{2 e^{-\coth ^{-1}(a x)}}{3 a c^2}","\frac{(2 a x+1) e^{-\coth ^{-1}(a x)}}{3 a c^2 \left(1-a^2 x^2\right)}-\frac{2 e^{-\coth ^{-1}(a x)}}{3 a c^2}",1,"-2/(3*a*c^2*E^ArcCoth[a*x]) + (1 + 2*a*x)/(3*a*c^2*E^ArcCoth[a*x]*(1 - a^2*x^2))","A",2,2,22,0.09091,1,"{6185, 6183}"
596,1,91,0,0.0969696,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)^3),x]","\frac{4 (2 a x+1) e^{-\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)}+\frac{(4 a x+1) e^{-\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)^2}-\frac{8 e^{-\coth ^{-1}(a x)}}{15 a c^3}","\frac{4 (2 a x+1) e^{-\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)}+\frac{(4 a x+1) e^{-\coth ^{-1}(a x)}}{15 a c^3 \left(1-a^2 x^2\right)^2}-\frac{8 e^{-\coth ^{-1}(a x)}}{15 a c^3}",1,"-8/(15*a*c^3*E^ArcCoth[a*x]) + (1 + 4*a*x)/(15*a*c^3*E^ArcCoth[a*x]*(1 - a^2*x^2)^2) + (4*(1 + 2*a*x))/(15*a*c^3*E^ArcCoth[a*x]*(1 - a^2*x^2))","A",3,2,22,0.09091,1,"{6185, 6183}"
597,1,127,0,0.1357551,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)^4),x]","\frac{8 (2 a x+1) e^{-\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)}+\frac{2 (4 a x+1) e^{-\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^2}+\frac{(6 a x+1) e^{-\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^3}-\frac{16 e^{-\coth ^{-1}(a x)}}{35 a c^4}","\frac{8 (2 a x+1) e^{-\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)}+\frac{2 (4 a x+1) e^{-\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^2}+\frac{(6 a x+1) e^{-\coth ^{-1}(a x)}}{35 a c^4 \left(1-a^2 x^2\right)^3}-\frac{16 e^{-\coth ^{-1}(a x)}}{35 a c^4}",1,"-16/(35*a*c^4*E^ArcCoth[a*x]) + (1 + 6*a*x)/(35*a*c^4*E^ArcCoth[a*x]*(1 - a^2*x^2)^3) + (2*(1 + 4*a*x))/(35*a*c^4*E^ArcCoth[a*x]*(1 - a^2*x^2)^2) + (8*(1 + 2*a*x))/(35*a*c^4*E^ArcCoth[a*x]*(1 - a^2*x^2))","A",4,2,22,0.09091,1,"{6185, 6183}"
598,1,73,0,0.0805593,"\int e^{-2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[(c - a^2*c*x^2)^4/E^(2*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
599,1,55,0,0.0754054,"\int e^{-2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[(c - a^2*c*x^2)^3/E^(2*ArcCoth[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",4,3,22,0.1364,1,"{6167, 6140, 43}"
600,1,37,0,0.063194,"\int e^{-2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[(c - a^2*c*x^2)^2/E^(2*ArcCoth[a*x]),x]","\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}-\frac{c^2 (1-a x)^5}{5 a}",1,"(c^2*(1 - a*x)^4)/(2*a) - (c^2*(1 - a*x)^5)/(5*a)","A",4,3,22,0.1364,1,"{6167, 6140, 43}"
601,1,16,0,0.0340112,"\int e^{-2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[(c - a^2*c*x^2)/E^(2*ArcCoth[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",3,3,20,0.1500,1,"{6167, 6140, 32}"
602,1,14,0,0.0611401,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[1/(E^(2*ArcCoth[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",3,3,22,0.1364,1,"{6167, 6140, 32}"
603,1,49,0,0.0764191,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
604,1,84,0,0.1004298,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
605,1,119,0,0.1197554,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6140, 44, 207}"
606,1,393,0,0.337411,"\int e^{-3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^4 \, dx","Int[(c - a^2*c*x^2)^4/E^(3*ArcCoth[a*x]),x]","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{11/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{72} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{11}{56} a^6 c^4 x^7 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{48} a^5 c^4 x^6 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{11}{48} a^4 c^4 x^5 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{64} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{11}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{55}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{55}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{55 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}","\frac{1}{9} a^8 c^4 x^9 \left(1-\frac{1}{a x}\right)^{11/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{72} a^7 c^4 x^8 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{11}{56} a^6 c^4 x^7 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{48} a^5 c^4 x^6 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{11}{48} a^4 c^4 x^5 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{11}{64} a^3 c^4 x^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{11}{192} a^2 c^4 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{55}{384} a c^4 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{55}{128} c^4 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{55 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{128 a}",1,"(55*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/128 + (55*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/384 + (11*a^2*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/192 - (11*a^3*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x^4)/64 + (11*a^4*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(7/2)*x^5)/48 - (11*a^5*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(7/2)*x^6)/48 + (11*a^6*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(7/2)*x^7)/56 - (11*a^7*c^4*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(7/2)*x^8)/72 + (a^8*c^4*(1 - 1/(a*x))^(11/2)*(1 + 1/(a*x))^(7/2)*x^9)/9 + (55*c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(128*a)","A",13,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
607,1,313,0,0.2637751,"\int e^{-3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[(c - a^2*c*x^2)^3/E^(3*ArcCoth[a*x]),x]","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{3}{14} a^5 c^3 x^6 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{3}{10} a^4 c^3 x^5 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{3}{8} a^3 c^3 x^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{3}{8} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{3}{16} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{9}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{9 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}","-\frac{1}{7} a^6 c^3 x^7 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{3}{14} a^5 c^3 x^6 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{3}{10} a^4 c^3 x^5 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{3}{8} a^3 c^3 x^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}-\frac{3}{8} a^2 c^3 x^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{3}{16} a c^3 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{9}{16} c^3 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{9 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{16 a}",1,"(9*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/16 + (3*a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/16 - (3*a^2*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)*x^3)/8 + (3*a^3*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2)*x^4)/8 - (3*a^4*c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(5/2)*x^5)/10 + (3*a^5*c^3*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2)*x^6)/14 - (a^6*c^3*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(5/2)*x^7)/7 + (9*c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(16*a)","A",11,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
608,1,233,0,0.2036626,"\int e^{-3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[(c - a^2*c*x^2)^2/E^(3*ArcCoth[a*x]),x]","\frac{1}{5} a^4 c^2 x^5 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{7}{20} a^3 c^2 x^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{7}{12} a^2 c^2 x^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{7}{8} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{7}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{7 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}","\frac{1}{5} a^4 c^2 x^5 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{7}{20} a^3 c^2 x^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{7}{12} a^2 c^2 x^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{7}{8} a c^2 x^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}+\frac{7}{8} c^2 x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{7 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{8 a}",1,"(7*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/8 - (7*a*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x^2)/8 + (7*a^2*c^2*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2)*x^3)/12 - (7*a^3*c^2*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)*x^4)/20 + (a^4*c^2*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(3/2)*x^5)/5 + (7*c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(8*a)","A",9,5,22,0.2273,1,"{6191, 6195, 94, 92, 208}"
609,1,145,0,0.1201299,"\int e^{-3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[(c - a^2*c*x^2)/E^(3*ArcCoth[a*x]),x]","-\frac{1}{3} a^2 c x^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}+\frac{5}{6} a c x^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}-\frac{5}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{5 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}","-\frac{1}{3} a^2 c x^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}+\frac{5}{6} a c x^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}-\frac{5}{2} c x \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}+\frac{5 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{2 a}",1,"(-5*c*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]*x)/2 + (5*a*c*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x^2)/6 - (a^2*c*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]*x^3)/3 + (5*c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(2*a)","A",7,5,20,0.2500,1,"{6191, 6195, 94, 92, 208}"
610,1,18,0,0.03191,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)),x]","-\frac{e^{-3 \coth ^{-1}(a x)}}{3 a c}","-\frac{e^{-3 \coth ^{-1}(a x)}}{3 a c}",1,"-1/(3*a*c*E^(3*ArcCoth[a*x]))","A",1,1,22,0.04545,1,"{6183}"
611,1,55,0,0.0662282,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^2),x]","\frac{2 e^{-3 \coth ^{-1}(a x)}}{15 a c^2}-\frac{(2 a x+3) e^{-3 \coth ^{-1}(a x)}}{5 a c^2 \left(1-a^2 x^2\right)}","\frac{2 e^{-3 \coth ^{-1}(a x)}}{15 a c^2}-\frac{(2 a x+3) e^{-3 \coth ^{-1}(a x)}}{5 a c^2 \left(1-a^2 x^2\right)}",1,"2/(15*a*c^2*E^(3*ArcCoth[a*x])) - (3 + 2*a*x)/(5*a*c^2*E^(3*ArcCoth[a*x])*(1 - a^2*x^2))","A",2,2,22,0.09091,1,"{6185, 6183}"
612,1,91,0,0.1009994,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^3),x]","-\frac{12 (2 a x+3) e^{-3 \coth ^{-1}(a x)}}{35 a c^3 \left(1-a^2 x^2\right)}+\frac{(4 a x+3) e^{-3 \coth ^{-1}(a x)}}{7 a c^3 \left(1-a^2 x^2\right)^2}+\frac{8 e^{-3 \coth ^{-1}(a x)}}{35 a c^3}","-\frac{12 (2 a x+3) e^{-3 \coth ^{-1}(a x)}}{35 a c^3 \left(1-a^2 x^2\right)}+\frac{(4 a x+3) e^{-3 \coth ^{-1}(a x)}}{7 a c^3 \left(1-a^2 x^2\right)^2}+\frac{8 e^{-3 \coth ^{-1}(a x)}}{35 a c^3}",1,"8/(35*a*c^3*E^(3*ArcCoth[a*x])) + (3 + 4*a*x)/(7*a*c^3*E^(3*ArcCoth[a*x])*(1 - a^2*x^2)^2) - (12*(3 + 2*a*x))/(35*a*c^3*E^(3*ArcCoth[a*x])*(1 - a^2*x^2))","A",3,2,22,0.09091,1,"{6185, 6183}"
613,1,127,0,0.1378224,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^4),x]","\frac{(2 a x+1) e^{-3 \coth ^{-1}(a x)}}{9 a c^4 \left(1-a^2 x^2\right)^3}-\frac{8 (2 a x+3) e^{-3 \coth ^{-1}(a x)}}{21 a c^4 \left(1-a^2 x^2\right)}+\frac{10 (4 a x+3) e^{-3 \coth ^{-1}(a x)}}{63 a c^4 \left(1-a^2 x^2\right)^2}+\frac{16 e^{-3 \coth ^{-1}(a x)}}{63 a c^4}","\frac{(2 a x+1) e^{-3 \coth ^{-1}(a x)}}{9 a c^4 \left(1-a^2 x^2\right)^3}-\frac{8 (2 a x+3) e^{-3 \coth ^{-1}(a x)}}{21 a c^4 \left(1-a^2 x^2\right)}+\frac{10 (4 a x+3) e^{-3 \coth ^{-1}(a x)}}{63 a c^4 \left(1-a^2 x^2\right)^2}+\frac{16 e^{-3 \coth ^{-1}(a x)}}{63 a c^4}",1,"16/(63*a*c^4*E^(3*ArcCoth[a*x])) + (1 + 2*a*x)/(9*a*c^4*E^(3*ArcCoth[a*x])*(1 - a^2*x^2)^3) + (10*(3 + 4*a*x))/(63*a*c^4*E^(3*ArcCoth[a*x])*(1 - a^2*x^2)^2) - (8*(3 + 2*a*x))/(21*a*c^4*E^(3*ArcCoth[a*x])*(1 - a^2*x^2))","A",4,2,22,0.09091,1,"{6185, 6183}"
614,1,229,0,0.2002542,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^(9/2),x]","\frac{(a x+1)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (a x+1)^9 \left(c-a^2 c x^2\right)^{9/2}}{9 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (a x+1)^8 \left(c-a^2 c x^2\right)^{9/2}}{a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{32 (a x+1)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{8 (a x+1)^6 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}","\frac{(a x+1)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (a x+1)^9 \left(c-a^2 c x^2\right)^{9/2}}{9 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (a x+1)^8 \left(c-a^2 c x^2\right)^{9/2}}{a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{32 (a x+1)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{8 (a x+1)^6 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}",1,"(8*(1 + a*x)^6*(c - a^2*c*x^2)^(9/2))/(3*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) - (32*(1 + a*x)^7*(c - a^2*c*x^2)^(9/2))/(7*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + (3*(1 + a*x)^8*(c - a^2*c*x^2)^(9/2))/(a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) - (8*(1 + a*x)^9*(c - a^2*c*x^2)^(9/2))/(9*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + ((1 + a*x)^10*(c - a^2*c*x^2)^(9/2))/(10*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9)","A",4,3,22,0.1364,1,"{6192, 6193, 43}"
615,1,183,0,0.1828184,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^(7/2),x]","\frac{(a x+1)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{6 (a x+1)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (a x+1)^6 \left(c-a^2 c x^2\right)^{7/2}}{a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{8 (a x+1)^5 \left(c-a^2 c x^2\right)^{7/2}}{5 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}","\frac{(a x+1)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{6 (a x+1)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (a x+1)^6 \left(c-a^2 c x^2\right)^{7/2}}{a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{8 (a x+1)^5 \left(c-a^2 c x^2\right)^{7/2}}{5 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}",1,"(-8*(1 + a*x)^5*(c - a^2*c*x^2)^(7/2))/(5*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) + (2*(1 + a*x)^6*(c - a^2*c*x^2)^(7/2))/(a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) - (6*(1 + a*x)^7*(c - a^2*c*x^2)^(7/2))/(7*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) + ((1 + a*x)^8*(c - a^2*c*x^2)^(7/2))/(8*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7)","A",4,3,22,0.1364,1,"{6192, 6193, 43}"
616,1,136,0,0.1755293,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^(5/2),x]","\frac{(a x+1)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 (a x+1)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}+\frac{(a x+1)^4 \left(c-a^2 c x^2\right)^{5/2}}{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}","\frac{(a x+1)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 (a x+1)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}+\frac{(a x+1)^4 \left(c-a^2 c x^2\right)^{5/2}}{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}",1,"((1 + a*x)^4*(c - a^2*c*x^2)^(5/2))/(a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5) - (4*(1 + a*x)^5*(c - a^2*c*x^2)^(5/2))/(5*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5) + ((1 + a*x)^6*(c - a^2*c*x^2)^(5/2))/(6*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)","A",4,3,22,0.1364,1,"{6192, 6193, 43}"
617,1,93,0,0.166046,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^(3/2),x]","\frac{(a x+1)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{2 (a x+1)^3 \left(c-a^2 c x^2\right)^{3/2}}{3 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}","\frac{(a x+1)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{2 (a x+1)^3 \left(c-a^2 c x^2\right)^{3/2}}{3 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}",1,"(-2*(1 + a*x)^3*(c - a^2*c*x^2)^(3/2))/(3*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3) + ((1 + a*x)^4*(c - a^2*c*x^2)^(3/2))/(4*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3)","A",4,3,22,0.1364,1,"{6192, 6193, 43}"
618,1,68,0,0.1087359,"\int e^{\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - a^2*c*x^2],x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)])","A",3,2,22,0.09091,1,"{6192, 6193}"
619,1,38,0,0.146069,"\int \frac{e^{\coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^ArcCoth[a*x]/Sqrt[c - a^2*c*x^2],x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{\sqrt{c-a^2 c x^2}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{\sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[c - a^2*c*x^2]","A",3,3,22,0.1364,1,"{6192, 6193, 31}"
620,1,91,0,0.1658578,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^(3/2),x]","\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}",1,"(a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3*ArcTanh[a*x])/(2*(c - a^2*c*x^2)^(3/2))","A",5,4,22,0.1818,1,"{6192, 6193, 44, 207}"
621,1,184,0,0.1854663,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^(5/2),x]","-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"-(a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) - (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(4*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) - (3*a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,22,0.1818,1,"{6192, 6193, 44, 207}"
622,1,277,0,0.2098379,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^(7/2),x]","\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}+\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x)^2 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1)^2 \left(c-a^2 c x^2\right)^{7/2}}+\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{24 (1-a x)^3 \left(c-a^2 c x^2\right)^{7/2}}+\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{16 \left(c-a^2 c x^2\right)^{7/2}}","\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}+\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x)^2 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1)^2 \left(c-a^2 c x^2\right)^{7/2}}+\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{24 (1-a x)^3 \left(c-a^2 c x^2\right)^{7/2}}+\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{16 \left(c-a^2 c x^2\right)^{7/2}}",1,"(a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(24*(1 - a*x)^3*(c - a^2*c*x^2)^(7/2)) + (3*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 - a*x)^2*(c - a^2*c*x^2)^(7/2)) + (3*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(16*(1 - a*x)*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 + a*x)^2*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(8*(1 + a*x)*(c - a^2*c*x^2)^(7/2)) + (5*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7*ArcTanh[a*x])/(16*(c - a^2*c*x^2)^(7/2))","A",5,4,22,0.1818,1,"{6192, 6193, 44, 207}"
623,1,176,0,0.1652626,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[E^(2*ArcCoth[a*x])*(c - a^2*c*x^2)^(9/2),x]","-\frac{77}{256} c^4 x \sqrt{c-a^2 c x^2}-\frac{77}{384} c^3 x \left(c-a^2 c x^2\right)^{3/2}-\frac{77}{480} c^2 x \left(c-a^2 c x^2\right)^{5/2}-\frac{77 c^{9/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{256 a}-\frac{11}{80} c x \left(c-a^2 c x^2\right)^{7/2}+\frac{(a x+1) \left(c-a^2 c x^2\right)^{9/2}}{10 a}+\frac{11 \left(c-a^2 c x^2\right)^{9/2}}{90 a}","-\frac{77}{256} c^4 x \sqrt{c-a^2 c x^2}-\frac{77}{384} c^3 x \left(c-a^2 c x^2\right)^{3/2}-\frac{77}{480} c^2 x \left(c-a^2 c x^2\right)^{5/2}-\frac{77 c^{9/2} \tan ^{-1}\left(\frac{a \sqrt{c} x}{\sqrt{c-a^2 c x^2}}\right)}{256 a}-\frac{11}{80} c x \left(c-a^2 c x^2\right)^{7/2}+\frac{(a x+1) \left(c-a^2 c x^2\right)^{9/2}}{10 a}+\frac{11 \left(c-a^2 c x^2\right)^{9/2}}{90 a}",1,"(-77*c^4*x*Sqrt[c - a^2*c*x^2])/256 - (77*c^3*x*(c - a^2*c*x^2)^(3/2))/384 - (77*c^2*x*(c - a^2*c*x^2)^(5/2))/480 - (11*c*x*(c - a^2*c*x^2)^(7/2))/80 + (11*(c - a^2*c*x^2)^(9/2))/(90*a) + ((1 + a*x)*(c - a^2*c*x^2)^(9/2))/(10*a) - (77*c^(9/2)*ArcTan[(a*Sqrt[c]*x)/Sqrt[c - a^2*c*x^2]])/(256*a)","A",10,7,24,0.2917,1,"{6167, 6141, 671, 641, 195, 217, 203}"
624,1,153,0,0.1528733,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[E^(2*ArcCoth[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",9,7,24,0.2917,1,"{6167, 6141, 671, 641, 195, 217, 203}"
625,1,130,0,0.1377163,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(2*ArcCoth[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",8,7,24,0.2917,1,"{6167, 6141, 671, 641, 195, 217, 203}"
626,1,107,0,0.1266532,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(2*ArcCoth[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",7,7,24,0.2917,1,"{6167, 6141, 671, 641, 195, 217, 203}"
627,1,86,0,0.1097817,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",6,6,24,0.2500,1,"{6167, 6141, 671, 641, 217, 203}"
628,1,59,0,0.1046672,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^(2*ArcCoth[a*x])/Sqrt[c - a^2*c*x^2],x]","\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}}-\frac{2 (a x+1)}{a \sqrt{c-a^2 c x^2}}",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",5,5,24,0.2083,1,"{6167, 6141, 653, 217, 203}"
629,1,51,0,0.1049676,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(2*ArcCoth[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",4,4,24,0.1667,1,"{6167, 6141, 653, 191}"
630,1,74,0,0.1103836,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(2*ArcCoth[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",5,5,24,0.2083,1,"{6167, 6141, 653, 192, 191}"
631,1,97,0,0.1195157,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(2*ArcCoth[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",6,5,24,0.2083,1,"{6167, 6141, 653, 192, 191}"
632,1,120,0,0.1313837,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/2}} \, dx","Int[E^(2*ArcCoth[a*x])/(c - a^2*c*x^2)^(9/2),x]","-\frac{16 x}{45 c^4 \sqrt{c-a^2 c x^2}}-\frac{8 x}{45 c^3 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 x}{15 c^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{x}{9 c \left(c-a^2 c x^2\right)^{7/2}}-\frac{2 (a x+1)}{9 a \left(c-a^2 c x^2\right)^{9/2}}","-\frac{16 x}{45 c^4 \sqrt{c-a^2 c x^2}}-\frac{8 x}{45 c^3 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 x}{15 c^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{x}{9 c \left(c-a^2 c x^2\right)^{7/2}}-\frac{2 (a x+1)}{9 a \left(c-a^2 c x^2\right)^{9/2}}",1,"(-2*(1 + a*x))/(9*a*(c - a^2*c*x^2)^(9/2)) - x/(9*c*(c - a^2*c*x^2)^(7/2)) - (2*x)/(15*c^2*(c - a^2*c*x^2)^(5/2)) - (8*x)/(45*c^3*(c - a^2*c*x^2)^(3/2)) - (16*x)/(45*c^4*Sqrt[c - a^2*c*x^2])","A",7,5,24,0.2083,1,"{6167, 6141, 653, 192, 191}"
633,1,185,0,0.1998099,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(9/2),x]","\frac{(a x+1)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{2 (a x+1)^9 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (a x+1)^8 \left(c-a^2 c x^2\right)^{9/2}}{2 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (a x+1)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}","\frac{(a x+1)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{2 (a x+1)^9 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (a x+1)^8 \left(c-a^2 c x^2\right)^{9/2}}{2 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (a x+1)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}",1,"(-8*(1 + a*x)^7*(c - a^2*c*x^2)^(9/2))/(7*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + (3*(1 + a*x)^8*(c - a^2*c*x^2)^(9/2))/(2*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) - (2*(1 + a*x)^9*(c - a^2*c*x^2)^(9/2))/(3*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + ((1 + a*x)^10*(c - a^2*c*x^2)^(9/2))/(10*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
634,1,139,0,0.1932898,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(7/2),x]","\frac{(a x+1)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{4 (a x+1)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (a x+1)^6 \left(c-a^2 c x^2\right)^{7/2}}{3 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}","\frac{(a x+1)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{4 (a x+1)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (a x+1)^6 \left(c-a^2 c x^2\right)^{7/2}}{3 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}",1,"(2*(1 + a*x)^6*(c - a^2*c*x^2)^(7/2))/(3*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) - (4*(1 + a*x)^7*(c - a^2*c*x^2)^(7/2))/(7*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) + ((1 + a*x)^8*(c - a^2*c*x^2)^(7/2))/(8*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
635,1,93,0,0.1845985,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(5/2),x]","\frac{(a x+1)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{2 (a x+1)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}","\frac{(a x+1)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{2 (a x+1)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}",1,"(-2*(1 + a*x)^5*(c - a^2*c*x^2)^(5/2))/(5*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5) + ((1 + a*x)^6*(c - a^2*c*x^2)^(5/2))/(6*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
636,1,46,0,0.176097,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(3/2),x]","\frac{(a x+1)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}","\frac{(a x+1)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}",1,"((1 + a*x)^4*(c - a^2*c*x^2)^(3/2))/(4*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3)","A",3,3,24,0.1250,1,"{6192, 6193, 32}"
637,1,113,0,0.1330944,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2],x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(3*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
638,1,79,0,0.1671644,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^(3*ArcCoth[a*x])/Sqrt[c - a^2*c*x^2],x]","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{(1-a x) \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{\sqrt{c-a^2 c x^2}}","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{(1-a x) \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{\sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/((1 - a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - 1/(a^2*x^2)]*x*Log[1 - a*x])/Sqrt[c - a^2*c*x^2]","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
639,1,47,0,0.1717145,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2)^(3/2),x]","-\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x)^2 \left(c-a^2 c x^2\right)^{3/2}}","-\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x)^2 \left(c-a^2 c x^2\right)^{3/2}}",1,"-(a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)^2*(c - a^2*c*x^2)^(3/2))","A",3,3,24,0.1250,1,"{6192, 6193, 32}"
640,1,185,0,0.2037369,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2)^(5/2),x]","\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{6 (1-a x)^3 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{6 (1-a x)^3 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"(a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(6*(1 - a*x)^3*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
641,1,278,0,0.2251888,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - a^2*c*x^2)^(7/2),x]","-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}+\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}-\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x)^2 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{12 (1-a x)^3 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (1-a x)^4 \left(c-a^2 c x^2\right)^{7/2}}-\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{32 \left(c-a^2 c x^2\right)^{7/2}}","-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}+\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}-\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x)^2 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{12 (1-a x)^3 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (1-a x)^4 \left(c-a^2 c x^2\right)^{7/2}}-\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{32 \left(c-a^2 c x^2\right)^{7/2}}",1,"-(a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(16*(1 - a*x)^4*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(12*(1 - a*x)^3*(c - a^2*c*x^2)^(7/2)) - (3*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 - a*x)^2*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(8*(1 - a*x)*(c - a^2*c*x^2)^(7/2)) + (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 + a*x)*(c - a^2*c*x^2)^(7/2)) - (5*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7*ArcTanh[a*x])/(32*(c - a^2*c*x^2)^(7/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
642,1,234,0,0.2113006,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{9/2} \, dx","Int[(c - a^2*c*x^2)^(9/2)/E^ArcCoth[a*x],x]","\frac{(1-a x)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (1-a x)^9 \left(c-a^2 c x^2\right)^{9/2}}{9 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (1-a x)^8 \left(c-a^2 c x^2\right)^{9/2}}{a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{32 (1-a x)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{8 (1-a x)^6 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}","\frac{(1-a x)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (1-a x)^9 \left(c-a^2 c x^2\right)^{9/2}}{9 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (1-a x)^8 \left(c-a^2 c x^2\right)^{9/2}}{a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{32 (1-a x)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{8 (1-a x)^6 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}",1,"(8*(1 - a*x)^6*(c - a^2*c*x^2)^(9/2))/(3*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) - (32*(1 - a*x)^7*(c - a^2*c*x^2)^(9/2))/(7*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + (3*(1 - a*x)^8*(c - a^2*c*x^2)^(9/2))/(a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) - (8*(1 - a*x)^9*(c - a^2*c*x^2)^(9/2))/(9*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + ((1 - a*x)^10*(c - a^2*c*x^2)^(9/2))/(10*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
643,1,187,0,0.20121,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{7/2} \, dx","Int[(c - a^2*c*x^2)^(7/2)/E^ArcCoth[a*x],x]","\frac{(1-a x)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{6 (1-a x)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (1-a x)^6 \left(c-a^2 c x^2\right)^{7/2}}{a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{8 (1-a x)^5 \left(c-a^2 c x^2\right)^{7/2}}{5 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}","\frac{(1-a x)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{6 (1-a x)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (1-a x)^6 \left(c-a^2 c x^2\right)^{7/2}}{a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{8 (1-a x)^5 \left(c-a^2 c x^2\right)^{7/2}}{5 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}",1,"(-8*(1 - a*x)^5*(c - a^2*c*x^2)^(7/2))/(5*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) + (2*(1 - a*x)^6*(c - a^2*c*x^2)^(7/2))/(a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) - (6*(1 - a*x)^7*(c - a^2*c*x^2)^(7/2))/(7*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) + ((1 - a*x)^8*(c - a^2*c*x^2)^(7/2))/(8*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
644,1,139,0,0.1928717,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{5/2} \, dx","Int[(c - a^2*c*x^2)^(5/2)/E^ArcCoth[a*x],x]","\frac{(1-a x)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 (1-a x)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}+\frac{(1-a x)^4 \left(c-a^2 c x^2\right)^{5/2}}{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}","\frac{(1-a x)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{4 (1-a x)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}+\frac{(1-a x)^4 \left(c-a^2 c x^2\right)^{5/2}}{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}",1,"((1 - a*x)^4*(c - a^2*c*x^2)^(5/2))/(a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5) - (4*(1 - a*x)^5*(c - a^2*c*x^2)^(5/2))/(5*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5) + ((1 - a*x)^6*(c - a^2*c*x^2)^(5/2))/(6*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
645,1,95,0,0.1802666,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)/E^ArcCoth[a*x],x]","\frac{(1-a x)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{2 (1-a x)^3 \left(c-a^2 c x^2\right)^{3/2}}{3 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}","\frac{(1-a x)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}-\frac{2 (1-a x)^3 \left(c-a^2 c x^2\right)^{3/2}}{3 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}",1,"(-2*(1 - a*x)^3*(c - a^2*c*x^2)^(3/2))/(3*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3) + ((1 - a*x)^4*(c - a^2*c*x^2)^(3/2))/(4*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
646,1,69,0,0.1174386,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^ArcCoth[a*x],x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)])) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)])","A",3,2,24,0.08333,1,"{6192, 6193}"
647,1,37,0,0.1525391,"\int \frac{e^{-\coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[1/(E^ArcCoth[a*x]*Sqrt[c - a^2*c*x^2]),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{\sqrt{c-a^2 c x^2}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{\sqrt{c-a^2 c x^2}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[c - a^2*c*x^2]","A",3,3,24,0.1250,1,"{6192, 6193, 31}"
648,1,90,0,0.1835341,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)^(3/2)),x]","\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (a x+1) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (a x+1) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}",1,"(a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 + a*x)*(c - a^2*c*x^2)^(3/2)) - (a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3*ArcTanh[a*x])/(2*(c - a^2*c*x^2)^(3/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
649,1,183,0,0.197224,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)^(5/2)),x]","\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{3 a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{3 a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"(a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) - (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)^2*(c - a^2*c*x^2)^(5/2)) - (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(4*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) + (3*a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
650,1,276,0,0.2207847,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - a^2*c*x^2)^(7/2)),x]","-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}+\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x)^2 \left(c-a^2 c x^2\right)^{7/2}}+\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1)^2 \left(c-a^2 c x^2\right)^{7/2}}+\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{24 (a x+1)^3 \left(c-a^2 c x^2\right)^{7/2}}-\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{16 \left(c-a^2 c x^2\right)^{7/2}}","-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}+\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x)^2 \left(c-a^2 c x^2\right)^{7/2}}+\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1)^2 \left(c-a^2 c x^2\right)^{7/2}}+\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{24 (a x+1)^3 \left(c-a^2 c x^2\right)^{7/2}}-\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{16 \left(c-a^2 c x^2\right)^{7/2}}",1,"-(a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 - a*x)^2*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(8*(1 - a*x)*(c - a^2*c*x^2)^(7/2)) + (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(24*(1 + a*x)^3*(c - a^2*c*x^2)^(7/2)) + (3*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 + a*x)^2*(c - a^2*c*x^2)^(7/2)) + (3*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(16*(1 + a*x)*(c - a^2*c*x^2)^(7/2)) - (5*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7*ArcTanh[a*x])/(16*(c - a^2*c*x^2)^(7/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
651,1,131,0,0.1411858,"\int e^{-2 \coth ^{-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*ArcCoth[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",8,7,24,0.2917,1,"{6167, 6142, 671, 641, 195, 217, 203}"
652,1,108,0,0.1270538,"\int e^{-2 \coth ^{-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*ArcCoth[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",7,7,24,0.2917,1,"{6167, 6142, 671, 641, 195, 217, 203}"
653,1,87,0,0.1106897,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^(2*ArcCoth[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",6,6,24,0.2500,1,"{6167, 6142, 671, 641, 217, 203}"
654,1,60,0,0.1039319,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[1/(E^(2*ArcCoth[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",5,5,24,0.2083,1,"{6167, 6142, 653, 217, 203}"
655,1,52,0,0.1041152,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^(2*ArcCoth[a*x])*(c - a^2*c*x^2)^(3/2)),x]","\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}}-\frac{x}{3 c \sqrt{c-a^2 c x^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",4,4,24,0.1667,1,"{6167, 6142, 653, 191}"
656,1,75,0,0.1149499,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^(2*ArcCoth[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",5,5,24,0.2083,1,"{6167, 6142, 653, 192, 191}"
657,1,98,0,0.1242153,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^(2*ArcCoth[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",6,5,24,0.2083,1,"{6167, 6142, 653, 192, 191}"
658,1,121,0,0.1409976,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/2}} \, dx","Int[1/(E^(2*ArcCoth[a*x])*(c - a^2*c*x^2)^(9/2)),x]","-\frac{16 x}{45 c^4 \sqrt{c-a^2 c x^2}}-\frac{8 x}{45 c^3 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 x}{15 c^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{x}{9 c \left(c-a^2 c x^2\right)^{7/2}}+\frac{2 (1-a x)}{9 a \left(c-a^2 c x^2\right)^{9/2}}","-\frac{16 x}{45 c^4 \sqrt{c-a^2 c x^2}}-\frac{8 x}{45 c^3 \left(c-a^2 c x^2\right)^{3/2}}-\frac{2 x}{15 c^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{x}{9 c \left(c-a^2 c x^2\right)^{7/2}}+\frac{2 (1-a x)}{9 a \left(c-a^2 c x^2\right)^{9/2}}",1,"(2*(1 - a*x))/(9*a*(c - a^2*c*x^2)^(9/2)) - x/(9*c*(c - a^2*c*x^2)^(7/2)) - (2*x)/(15*c^2*(c - a^2*c*x^2)^(5/2)) - (8*x)/(45*c^3*(c - a^2*c*x^2)^(3/2)) - (16*x)/(45*c^4*Sqrt[c - a^2*c*x^2])","A",7,5,24,0.2083,1,"{6167, 6142, 653, 192, 191}"
659,1,189,0,0.2023433,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{(1-a x)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{2 (1-a x)^9 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (1-a x)^8 \left(c-a^2 c x^2\right)^{9/2}}{2 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (1-a x)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}","\frac{(1-a x)^{10} \left(c-a^2 c x^2\right)^{9/2}}{10 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{2 (1-a x)^9 \left(c-a^2 c x^2\right)^{9/2}}{3 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}+\frac{3 (1-a x)^8 \left(c-a^2 c x^2\right)^{9/2}}{2 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}-\frac{8 (1-a x)^7 \left(c-a^2 c x^2\right)^{9/2}}{7 a^{10} x^9 \left(1-\frac{1}{a^2 x^2}\right)^{9/2}}",1,"(-8*(1 - a*x)^7*(c - a^2*c*x^2)^(9/2))/(7*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + (3*(1 - a*x)^8*(c - a^2*c*x^2)^(9/2))/(2*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) - (2*(1 - a*x)^9*(c - a^2*c*x^2)^(9/2))/(3*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9) + ((1 - a*x)^10*(c - a^2*c*x^2)^(9/2))/(10*a^10*(1 - 1/(a^2*x^2))^(9/2)*x^9)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
660,1,142,0,0.1912452,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{(1-a x)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{4 (1-a x)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (1-a x)^6 \left(c-a^2 c x^2\right)^{7/2}}{3 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}","\frac{(1-a x)^8 \left(c-a^2 c x^2\right)^{7/2}}{8 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}-\frac{4 (1-a x)^7 \left(c-a^2 c x^2\right)^{7/2}}{7 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}+\frac{2 (1-a x)^6 \left(c-a^2 c x^2\right)^{7/2}}{3 a^8 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}",1,"(2*(1 - a*x)^6*(c - a^2*c*x^2)^(7/2))/(3*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) - (4*(1 - a*x)^7*(c - a^2*c*x^2)^(7/2))/(7*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7) + ((1 - a*x)^8*(c - a^2*c*x^2)^(7/2))/(8*a^8*(1 - 1/(a^2*x^2))^(7/2)*x^7)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
661,1,95,0,0.179096,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{(1-a x)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{2 (1-a x)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}","\frac{(1-a x)^6 \left(c-a^2 c x^2\right)^{5/2}}{6 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}-\frac{2 (1-a x)^5 \left(c-a^2 c x^2\right)^{5/2}}{5 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}",1,"(-2*(1 - a*x)^5*(c - a^2*c*x^2)^(5/2))/(5*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5) + ((1 - a*x)^6*(c - a^2*c*x^2)^(5/2))/(6*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
662,1,47,0,0.1683544,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{(1-a x)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}","\frac{(1-a x)^4 \left(c-a^2 c x^2\right)^{3/2}}{4 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}",1,"((1 - a*x)^4*(c - a^2*c*x^2)^(3/2))/(4*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3)","A",3,3,24,0.1250,1,"{6192, 6193, 32}"
663,1,112,0,0.1272538,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^(3*ArcCoth[a*x]),x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-3*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
664,1,77,0,0.1631861,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2]),x]","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{(a x+1) \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{\sqrt{c-a^2 c x^2}}","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}}}{(a x+1) \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{\sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*x)/((1 + a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[1 - 1/(a^2*x^2)]*x*Log[1 + a*x])/Sqrt[c - a^2*c*x^2]","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
665,1,46,0,0.1690285,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(3/2)),x]","-\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (a x+1)^2 \left(c-a^2 c x^2\right)^{3/2}}","-\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (a x+1)^2 \left(c-a^2 c x^2\right)^{3/2}}",1,"-(a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 + a*x)^2*(c - a^2*c*x^2)^(3/2))","A",3,3,24,0.1250,1,"{6192, 6193, 32}"
666,1,182,0,0.1981965,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(5/2)),x]","\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{6 (a x+1)^3 \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{6 (a x+1)^3 \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"(a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(6*(1 + a*x)^3*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)^2*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) - (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
667,1,275,0,0.2218697,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^(7/2)),x]","\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}-\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1)^2 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{12 (a x+1)^3 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (a x+1)^4 \left(c-a^2 c x^2\right)^{7/2}}+\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{32 \left(c-a^2 c x^2\right)^{7/2}}","\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (1-a x) \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{7/2}}-\frac{3 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{32 (a x+1)^2 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{12 (a x+1)^3 \left(c-a^2 c x^2\right)^{7/2}}-\frac{a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2}}{16 (a x+1)^4 \left(c-a^2 c x^2\right)^{7/2}}+\frac{5 a^6 x^7 \left(1-\frac{1}{a^2 x^2}\right)^{7/2} \tanh ^{-1}(a x)}{32 \left(c-a^2 c x^2\right)^{7/2}}",1,"(a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 - a*x)*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(16*(1 + a*x)^4*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(12*(1 + a*x)^3*(c - a^2*c*x^2)^(7/2)) - (3*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(32*(1 + a*x)^2*(c - a^2*c*x^2)^(7/2)) - (a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7)/(8*(1 + a*x)*(c - a^2*c*x^2)^(7/2)) + (5*a^6*(1 - 1/(a^2*x^2))^(7/2)*x^7*ArcTanh[a*x])/(32*(c - a^2*c*x^2)^(7/2))","A",5,4,24,0.1667,1,"{6192, 6193, 44, 207}"
668,1,76,0,0.2028351,"\int e^{\coth ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcCoth[a*x]*x^2*Sqrt[c - a^2*c*x^2],x]","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^2 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^2 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(x^2*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^3*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6192, 6193, 43}"
669,1,74,0,0.1737182,"\int e^{\coth ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcCoth[a*x]*x*Sqrt[c - a^2*c*x^2],x]","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(x*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^2*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,23,0.1304,1,"{6192, 6193, 43}"
670,1,68,0,0.1079727,"\int e^{\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - a^2*c*x^2],x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)])","A",3,2,22,0.09091,1,"{6192, 6193}"
671,1,69,0,0.1386357,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - a^2*c*x^2])/x,x]","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/Sqrt[1 - 1/(a^2*x^2)] + (Sqrt[c - a^2*c*x^2]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,25,0.1200,1,"{6192, 6193, 43}"
672,1,73,0,0.1945284,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - a^2*c*x^2])/x^2,x]","\frac{\log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)]*x^2)) + (Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,25,0.1200,1,"{6192, 6193, 43}"
673,1,137,0,0.4126573,"\int e^{2 \coth ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",8,7,27,0.2593,1,"{6167, 6151, 1809, 833, 780, 217, 203}"
674,1,112,0,0.3870162,"\int e^{2 \coth ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",7,7,27,0.2593,1,"{6167, 6151, 1809, 833, 780, 217, 203}"
675,1,85,0,0.2507333,"\int e^{2 \coth ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",6,6,25,0.2400,1,"{6167, 6151, 1809, 780, 217, 203}"
676,1,86,0,0.1139275,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",6,6,24,0.2500,1,"{6167, 6141, 671, 641, 217, 203}"
677,1,75,0,0.3446032,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^(2*ArcCoth[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",9,9,27,0.3333,1,"{6167, 6151, 1809, 844, 217, 203, 266, 63, 208}"
678,1,82,0,0.3479033,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^(2*ArcCoth[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",9,9,27,0.3333,1,"{6167, 6151, 1807, 844, 217, 203, 266, 63, 208}"
679,1,78,0,0.3394997,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[(E^(2*ArcCoth[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",7,7,27,0.2593,1,"{6167, 6151, 1807, 807, 266, 63, 208}"
680,1,99,0,0.3780295,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[(E^(2*ArcCoth[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 \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",8,8,27,0.2963,1,"{6167, 6151, 1807, 835, 807, 266, 63, 208}"
681,1,130,0,0.4028531,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[(E^(2*ArcCoth[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",9,8,27,0.2963,1,"{6167, 6151, 1807, 835, 807, 266, 63, 208}"
682,1,228,0,0.2703497,"\int e^{3 \coth ^{-1}(a x)} x^3 \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])*x^3*Sqrt[c - a^2*c*x^2],x]","\frac{x^4 \sqrt{c-a^2 c x^2}}{5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x^3 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x^2 \sqrt{c-a^2 c x^2}}{3 a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^5 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^4 \sqrt{c-a^2 c x^2}}{5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x^3 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x^2 \sqrt{c-a^2 c x^2}}{3 a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^5 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - a^2*c*x^2])/(a^4*Sqrt[1 - 1/(a^2*x^2)]) + (2*x*Sqrt[c - a^2*c*x^2])/(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (4*x^2*Sqrt[c - a^2*c*x^2])/(3*a^2*Sqrt[1 - 1/(a^2*x^2)]) + (3*x^3*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^4*Sqrt[c - a^2*c*x^2])/(5*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^5*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
683,1,186,0,0.252277,"\int e^{3 \coth ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])*x^2*Sqrt[c - a^2*c*x^2],x]","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^2 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^4 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^2 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^4 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - a^2*c*x^2])/(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (2*x*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + (x^2*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x^3*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
684,1,152,0,0.2241137,"\int e^{3 \coth ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])*x*Sqrt[c - a^2*c*x^2],x]","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^3 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^3 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + (3*x*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^2*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,25,0.1200,1,"{6192, 6193, 77}"
685,1,113,0,0.1331747,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2],x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(3*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
686,1,114,0,0.1612232,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2])/x,x]","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{a x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/Sqrt[1 - 1/(a^2*x^2)] - (Sqrt[c - a^2*c*x^2]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]*x) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(a*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 72}"
687,1,114,0,0.2378442,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2])/x^2,x]","\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (3*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
688,1,153,0,0.240446,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2])/x^3,x]","\frac{3 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{2 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{3 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{2 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(2*a*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (3*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) - (4*a*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*a*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
689,1,194,0,0.2478032,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2])/x^4,x]","\frac{4 a \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{3 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{3 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(3*a*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (3*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (4*a*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) - (4*a^2*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*a^2*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
690,1,228,0,0.2529877,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2])/x^5,x]","\frac{4 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{4 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{4 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \sqrt{c-a^2 c x^2} \log (1-a x)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(4*a*Sqrt[1 - 1/(a^2*x^2)]*x^5) + Sqrt[c - a^2*c*x^2]/(Sqrt[1 - 1/(a^2*x^2)]*x^4) + (2*a*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^3) + (4*a^2*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) - (4*a^3*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*a^3*Sqrt[c - a^2*c*x^2]*Log[1 - a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
691,1,211,0,0.2304258,"\int \frac{e^{\coth ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcCoth[a*x]*x^4)/(c - a^2*c*x^2)^(3/2),x]","\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{a \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 a^2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{7 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 a^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 a^2 \left(c-a^2 c x^2\right)^{3/2}}","\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{a \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 a^2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{7 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 a^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 a^2 \left(c-a^2 c x^2\right)^{3/2}}",1,"((1 - 1/(a^2*x^2))^(3/2)*x^4)/(a*(c - a^2*c*x^2)^(3/2)) + ((1 - 1/(a^2*x^2))^(3/2)*x^5)/(2*(c - a^2*c*x^2)^(3/2)) + ((1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*a^2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (7*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 - a*x])/(4*a^2*(c - a^2*c*x^2)^(3/2)) + ((1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 + a*x])/(4*a^2*(c - a^2*c*x^2)^(3/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
692,1,172,0,0.1995984,"\int \frac{e^{\coth ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcCoth[a*x]*x^3)/(c - a^2*c*x^2)^(3/2),x]","\frac{x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 a (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 a \left(c-a^2 c x^2\right)^{3/2}}-\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 a \left(c-a^2 c x^2\right)^{3/2}}","\frac{x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 a (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 a \left(c-a^2 c x^2\right)^{3/2}}-\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 a \left(c-a^2 c x^2\right)^{3/2}}",1,"((1 - 1/(a^2*x^2))^(3/2)*x^4)/(c - a^2*c*x^2)^(3/2) + ((1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*a*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (5*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 - a*x])/(4*a*(c - a^2*c*x^2)^(3/2)) - ((1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 + a*x])/(4*a*(c - a^2*c*x^2)^(3/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
693,1,130,0,0.2540497,"\int \frac{e^{\coth ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcCoth[a*x]*x^2)/(c - a^2*c*x^2)^(3/2),x]","\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}","\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}",1,"((1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (3*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 - a*x])/(4*(c - a^2*c*x^2)^(3/2)) + ((1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 + a*x])/(4*(c - a^2*c*x^2)^(3/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
694,1,87,0,0.2109954,"\int \frac{e^{\coth ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^ArcCoth[a*x]*x)/(c - a^2*c*x^2)^(3/2),x]","\frac{a x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}",1,"(a*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) - (a*(1 - 1/(a^2*x^2))^(3/2)*x^3*ArcTanh[a*x])/(2*(c - a^2*c*x^2)^(3/2))","A",5,4,23,0.1739,1,"{6192, 6193, 77, 207}"
695,1,91,0,0.1709307,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^(3/2),x]","\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^2 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \tanh ^{-1}(a x)}{2 \left(c-a^2 c x^2\right)^{3/2}}",1,"(a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (a^2*(1 - 1/(a^2*x^2))^(3/2)*x^3*ArcTanh[a*x])/(2*(c - a^2*c*x^2)^(3/2))","A",5,4,22,0.1818,1,"{6192, 6193, 44, 207}"
696,1,177,0,0.2524736,"\int \frac{e^{\coth ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(x*(c - a^2*c*x^2)^(3/2)),x]","\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (x)}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{3 a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (x)}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{3 a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}",1,"(a^3*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (a^3*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[x])/(c - a^2*c*x^2)^(3/2) - (3*a^3*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 - a*x])/(4*(c - a^2*c*x^2)^(3/2)) - (a^3*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 + a*x])/(4*(c - a^2*c*x^2)^(3/2))","A",4,3,25,0.1200,1,"{6192, 6193, 72}"
697,1,214,0,0.2654692,"\int \frac{e^{\coth ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(x^2*(c - a^2*c*x^2)^(3/2)),x]","\frac{a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}}+\frac{a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (x)}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{5 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}}+\frac{a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (x)}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{5 a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^4 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}",1,"-((a^3*(1 - 1/(a^2*x^2))^(3/2)*x^2)/(c - a^2*c*x^2)^(3/2)) + (a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[x])/(c - a^2*c*x^2)^(3/2) - (5*a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 - a*x])/(4*(c - a^2*c*x^2)^(3/2)) + (a^4*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 + a*x])/(4*(c - a^2*c*x^2)^(3/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
698,1,252,0,0.2717506,"\int \frac{e^{\coth ^{-1}(a x)}}{x^3 \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(x^3*(c - a^2*c*x^2)^(3/2)),x]","\frac{a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^4 x^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{2 a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (x)}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{7 a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}","\frac{a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^4 x^2 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}{2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{2 a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (x)}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{7 a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (1-a x)}{4 \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^5 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \log (a x+1)}{4 \left(c-a^2 c x^2\right)^{3/2}}",1,"-(a^3*(1 - 1/(a^2*x^2))^(3/2)*x)/(2*(c - a^2*c*x^2)^(3/2)) - (a^4*(1 - 1/(a^2*x^2))^(3/2)*x^2)/(c - a^2*c*x^2)^(3/2) + (a^5*(1 - 1/(a^2*x^2))^(3/2)*x^3)/(2*(1 - a*x)*(c - a^2*c*x^2)^(3/2)) + (2*a^5*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[x])/(c - a^2*c*x^2)^(3/2) - (7*a^5*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 - a*x])/(4*(c - a^2*c*x^2)^(3/2)) - (a^5*(1 - 1/(a^2*x^2))^(3/2)*x^3*Log[1 + a*x])/(4*(c - a^2*c*x^2)^(3/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
699,1,262,0,0.2422562,"\int \frac{e^{\coth ^{-1}(a x)} x^5}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcCoth[a*x]*x^5)/(c - a^2*c*x^2)^(5/2),x]","\frac{x^6 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(c-a^2 c x^2\right)^{5/2}}+\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{a (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 a (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 a (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{23 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 a \left(c-a^2 c x^2\right)^{5/2}}-\frac{7 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 a \left(c-a^2 c x^2\right)^{5/2}}","\frac{x^6 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(c-a^2 c x^2\right)^{5/2}}+\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{a (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 a (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 a (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{23 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 a \left(c-a^2 c x^2\right)^{5/2}}-\frac{7 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 a \left(c-a^2 c x^2\right)^{5/2}}",1,"((1 - 1/(a^2*x^2))^(5/2)*x^6)/(c - a^2*c*x^2)^(5/2) - ((1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*a*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) + ((1 - 1/(a^2*x^2))^(5/2)*x^5)/(a*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) - ((1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*a*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) + (23*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 - a*x])/(16*a*(c - a^2*c*x^2)^(5/2)) - (7*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 + a*x])/(16*a*(c - a^2*c*x^2)^(5/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
700,1,217,0,0.277597,"\int \frac{e^{\coth ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcCoth[a*x]*x^4)/(c - a^2*c*x^2)^(5/2),x]","\frac{3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{11 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 \left(c-a^2 c x^2\right)^{5/2}}+\frac{5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 \left(c-a^2 c x^2\right)^{5/2}}","\frac{3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{11 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 \left(c-a^2 c x^2\right)^{5/2}}+\frac{5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 \left(c-a^2 c x^2\right)^{5/2}}",1,"-((1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) + (3*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(4*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) + ((1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) + (11*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 - a*x])/(16*(c - a^2*c*x^2)^(5/2)) + (5*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 + a*x])/(16*(c - a^2*c*x^2)^(5/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
701,1,176,0,0.2679244,"\int \frac{e^{\coth ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcCoth[a*x]*x^3)/(c - a^2*c*x^2)^(5/2),x]","\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"-(a*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) + (a*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(2*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) - (a*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) - (3*a*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,25,0.1600,1,"{6192, 6193, 88, 207}"
702,1,184,0,0.2723298,"\int \frac{e^{\coth ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcCoth[a*x]*x^2)/(c - a^2*c*x^2)^(5/2),x]","\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"-(a^2*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) + (a^2*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(4*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) + (a^2*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) + (a^2*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,25,0.1600,1,"{6192, 6193, 88, 207}"
703,1,137,0,0.2211755,"\int \frac{e^{\coth ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^ArcCoth[a*x]*x)/(c - a^2*c*x^2)^(5/2),x]","-\frac{a^3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","-\frac{a^3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^3 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"-(a^3*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) - (a^3*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) + (a^3*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,23,0.1739,1,"{6192, 6193, 77, 207}"
704,1,184,0,0.1965463,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(c - a^2*c*x^2)^(5/2),x]","-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}","-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a^4 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \tanh ^{-1}(a x)}{8 \left(c-a^2 c x^2\right)^{5/2}}",1,"-(a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) - (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(4*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) + (a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) - (3*a^4*(1 - 1/(a^2*x^2))^(5/2)*x^5*ArcTanh[a*x])/(8*(c - a^2*c*x^2)^(5/2))","A",5,4,22,0.1818,1,"{6192, 6193, 44, 207}"
705,1,271,0,0.2835995,"\int \frac{e^{\coth ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(x*(c - a^2*c*x^2)^(5/2)),x]","-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (x)}{\left(c-a^2 c x^2\right)^{5/2}}+\frac{11 a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 \left(c-a^2 c x^2\right)^{5/2}}+\frac{5 a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 \left(c-a^2 c x^2\right)^{5/2}}","-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{2 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (x)}{\left(c-a^2 c x^2\right)^{5/2}}+\frac{11 a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 \left(c-a^2 c x^2\right)^{5/2}}+\frac{5 a^5 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 \left(c-a^2 c x^2\right)^{5/2}}",1,"-(a^5*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) - (a^5*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(2*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) - (a^5*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) - (a^5*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[x])/(c - a^2*c*x^2)^(5/2) + (11*a^5*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 - a*x])/(16*(c - a^2*c*x^2)^(5/2)) + (5*a^5*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 + a*x])/(16*(c - a^2*c*x^2)^(5/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
706,1,307,0,0.2928589,"\int \frac{e^{\coth ^{-1}(a x)}}{x^2 \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(x^2*(c - a^2*c*x^2)^(5/2)),x]","-\frac{3 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^5 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(c-a^2 c x^2\right)^{5/2}}-\frac{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (x)}{\left(c-a^2 c x^2\right)^{5/2}}+\frac{23 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 \left(c-a^2 c x^2\right)^{5/2}}-\frac{7 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 \left(c-a^2 c x^2\right)^{5/2}}","-\frac{3 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{4 (1-a x) \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (a x+1) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{8 (1-a x)^2 \left(c-a^2 c x^2\right)^{5/2}}+\frac{a^5 x^4 \left(1-\frac{1}{a^2 x^2}\right)^{5/2}}{\left(c-a^2 c x^2\right)^{5/2}}-\frac{a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (x)}{\left(c-a^2 c x^2\right)^{5/2}}+\frac{23 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (1-a x)}{16 \left(c-a^2 c x^2\right)^{5/2}}-\frac{7 a^6 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \log (a x+1)}{16 \left(c-a^2 c x^2\right)^{5/2}}",1,"(a^5*(1 - 1/(a^2*x^2))^(5/2)*x^4)/(c - a^2*c*x^2)^(5/2) - (a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 - a*x)^2*(c - a^2*c*x^2)^(5/2)) - (3*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(4*(1 - a*x)*(c - a^2*c*x^2)^(5/2)) + (a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5)/(8*(1 + a*x)*(c - a^2*c*x^2)^(5/2)) - (a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[x])/(c - a^2*c*x^2)^(5/2) + (23*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 - a*x])/(16*(c - a^2*c*x^2)^(5/2)) - (7*a^6*(1 - 1/(a^2*x^2))^(5/2)*x^5*Log[1 + a*x])/(16*(c - a^2*c*x^2)^(5/2))","A",4,3,25,0.1200,1,"{6192, 6193, 88}"
707,1,76,0,0.2245633,"\int e^{-\coth ^{-1}(a x)} x^2 \sqrt{c-a^2 c x^2} \, dx","Int[(x^2*Sqrt[c - a^2*c*x^2])/E^ArcCoth[a*x],x]","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^2 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^2 \sqrt{c-a^2 c x^2}}{3 a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(x^2*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^3*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6192, 6193, 43}"
708,1,74,0,0.1926597,"\int e^{-\coth ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[(x*Sqrt[c - a^2*c*x^2])/E^ArcCoth[a*x],x]","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(x*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^2*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6192, 6193, 43}"
709,1,69,0,0.120105,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^ArcCoth[a*x],x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)])) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)])","A",3,2,24,0.08333,1,"{6192, 6193}"
710,1,70,0,0.1461066,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^ArcCoth[a*x]*x),x]","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/Sqrt[1 - 1/(a^2*x^2)] - (Sqrt[c - a^2*c*x^2]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 43}"
711,1,72,0,0.2156735,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^ArcCoth[a*x]*x^2),x]","\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 43}"
712,1,137,0,0.429526,"\int e^{-2 \coth ^{-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*ArcCoth[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",8,7,27,0.2593,1,"{6167, 6152, 1809, 833, 780, 217, 203}"
713,1,112,0,0.3962586,"\int e^{-2 \coth ^{-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*ArcCoth[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",7,7,27,0.2593,1,"{6167, 6152, 1809, 833, 780, 217, 203}"
714,1,84,0,0.2536702,"\int e^{-2 \coth ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[(x*Sqrt[c - a^2*c*x^2])/E^(2*ArcCoth[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",6,6,25,0.2400,1,"{6167, 6152, 1809, 780, 217, 203}"
715,1,87,0,0.1132089,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^(2*ArcCoth[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",6,6,24,0.2500,1,"{6167, 6142, 671, 641, 217, 203}"
716,1,75,0,0.3490852,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcCoth[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",9,9,27,0.3333,1,"{6167, 6152, 1809, 844, 217, 203, 266, 63, 208}"
717,1,82,0,0.3465693,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcCoth[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",9,9,27,0.3333,1,"{6167, 6152, 1807, 844, 217, 203, 266, 63, 208}"
718,1,78,0,0.3472626,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcCoth[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",7,7,27,0.2593,1,"{6167, 6152, 1807, 807, 266, 63, 208}"
719,1,101,0,0.3683848,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcCoth[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 \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",8,8,27,0.2963,1,"{6167, 6152, 1807, 835, 807, 266, 63, 208}"
720,1,130,0,0.4024212,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(2*ArcCoth[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",9,8,27,0.2963,1,"{6167, 6152, 1807, 835, 807, 266, 63, 208}"
721,1,227,0,0.2614072,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{x^4 \sqrt{c-a^2 c x^2}}{5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x^3 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x^2 \sqrt{c-a^2 c x^2}}{3 a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 x \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^5 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^4 \sqrt{c-a^2 c x^2}}{5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x^3 \sqrt{c-a^2 c x^2}}{4 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x^2 \sqrt{c-a^2 c x^2}}{3 a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 x \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^5 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - a^2*c*x^2])/(a^4*Sqrt[1 - 1/(a^2*x^2)]) - (2*x*Sqrt[c - a^2*c*x^2])/(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (4*x^2*Sqrt[c - a^2*c*x^2])/(3*a^2*Sqrt[1 - 1/(a^2*x^2)]) - (3*x^3*Sqrt[c - a^2*c*x^2])/(4*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^4*Sqrt[c - a^2*c*x^2])/(5*Sqrt[1 - 1/(a^2*x^2)]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^5*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
722,1,186,0,0.2579819,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^2 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^4 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-a^2 c x^2}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^2 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^4 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-4*Sqrt[c - a^2*c*x^2])/(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (2*x*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - 1/(a^2*x^2)]) - (x^2*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x^3*Sqrt[c - a^2*c*x^2])/(4*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
723,1,151,0,0.2118502,"\int e^{-3 \coth ^{-1}(a x)} x \sqrt{c-a^2 c x^2} \, dx","Int[(x*Sqrt[c - a^2*c*x^2])/E^(3*ArcCoth[a*x]),x]","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^3 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-a^2 c x^2}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x \sqrt{c-a^2 c x^2}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^3 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - a^2*c*x^2])/(a^2*Sqrt[1 - 1/(a^2*x^2)]) - (3*x*Sqrt[c - a^2*c*x^2])/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (x^2*Sqrt[c - a^2*c*x^2])/(3*Sqrt[1 - 1/(a^2*x^2)]) - (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,25,0.1200,1,"{6192, 6193, 77}"
724,1,112,0,0.1292403,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/E^(3*ArcCoth[a*x]),x]","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-a^2 c x^2}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \sqrt{c-a^2 c x^2}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-3*Sqrt[c - a^2*c*x^2])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (x*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,24,0.1250,1,"{6192, 6193, 43}"
725,1,112,0,0.1602212,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcCoth[a*x])*x),x]","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-a^2 c x^2}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-a^2 c x^2}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{a x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - a^2*c*x^2]/Sqrt[1 - 1/(a^2*x^2)] + (Sqrt[c - a^2*c*x^2]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]*x) - (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(a*Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 72}"
726,1,114,0,0.2330587,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^2} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcCoth[a*x])*x^2),x]","-\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{\sqrt{c-a^2 c x^2}}{a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - a^2*c*x^2]/(a*Sqrt[1 - 1/(a^2*x^2)]*x^2)) - (3*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
727,1,152,0,0.2387695,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^3} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcCoth[a*x])*x^3),x]","\frac{3 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{2 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{3 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{2 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - a^2*c*x^2]/(2*a*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (3*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) + (4*a*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
728,1,193,0,0.2451032,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^4} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcCoth[a*x])*x^4),x]","-\frac{4 a \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{3 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{4 a \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-a^2 c x^2}}{2 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{3 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - a^2*c*x^2]/(3*a*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (3*Sqrt[c - a^2*c*x^2])/(2*Sqrt[1 - 1/(a^2*x^2)]*x^3) - (4*a*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) - (4*a^2*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*a^2*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
729,1,227,0,0.2505254,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2}}{x^5} \, dx","Int[Sqrt[c - a^2*c*x^2]/(E^(3*ArcCoth[a*x])*x^5),x]","\frac{4 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{4 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a^2 \sqrt{c-a^2 c x^2}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 a \sqrt{c-a^2 c x^2}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-a^2 c x^2}}{x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-a^2 c x^2}}{4 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \log (x) \sqrt{c-a^2 c x^2}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \sqrt{c-a^2 c x^2} \log (a x+1)}{x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - a^2*c*x^2]/(4*a*Sqrt[1 - 1/(a^2*x^2)]*x^5) + Sqrt[c - a^2*c*x^2]/(Sqrt[1 - 1/(a^2*x^2)]*x^4) - (2*a*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^3) + (4*a^2*Sqrt[c - a^2*c*x^2])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) + (4*a^3*Sqrt[c - a^2*c*x^2]*Log[x])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a^3*Sqrt[c - a^2*c*x^2]*Log[1 + a*x])/(Sqrt[1 - 1/(a^2*x^2)]*x)","A",4,3,27,0.1111,1,"{6192, 6193, 88}"
730,1,136,0,0.2428371,"\int e^{3 \coth ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[E^(3*ArcCoth[a*x])*x^m*Sqrt[c - a^2*c*x^2],x]","-\frac{4 x^m \sqrt{c-a^2 c x^2} \, _2F_1(1,m+1;m+2;a x)}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{4 x^m \sqrt{c-a^2 c x^2} \, _2F_1(1,m+1;m+2;a x)}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(3*x^m*Sqrt[c - a^2*c*x^2])/(a*(1 + m)*Sqrt[1 - 1/(a^2*x^2)]) + (x^(1 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - 1/(a^2*x^2)]) - (4*x^m*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[1, 1 + m, 2 + m, a*x])/(a*(1 + m)*Sqrt[1 - 1/(a^2*x^2)])","A",5,4,27,0.1481,1,"{6192, 6193, 88, 64}"
731,1,172,0,0.3865239,"\int e^{2 \coth ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[E^(2*ArcCoth[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",8,6,27,0.2222,1,"{6167, 6151, 1809, 808, 365, 364}"
732,1,82,0,0.2129451,"\int e^{\coth ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[E^ArcCoth[a*x]*x^m*Sqrt[c - a^2*c*x^2],x]","\frac{x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(x^m*Sqrt[c - a^2*c*x^2])/(a*(1 + m)*Sqrt[1 - 1/(a^2*x^2)]) + (x^(1 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6192, 6193, 43}"
733,1,83,0,0.2266492,"\int e^{-\coth ^{-1}(a x)} x^m \sqrt{c-a^2 c x^2} \, dx","Int[(x^m*Sqrt[c - a^2*c*x^2])/E^ArcCoth[a*x],x]","\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-((x^m*Sqrt[c - a^2*c*x^2])/(a*(1 + m)*Sqrt[1 - 1/(a^2*x^2)])) + (x^(1 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6192, 6193, 43}"
734,1,172,0,0.3778941,"\int e^{-2 \coth ^{-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*ArcCoth[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",8,6,27,0.2222,1,"{6167, 6152, 1809, 808, 365, 364}"
735,1,137,0,0.2434946,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{4 x^m \sqrt{c-a^2 c x^2} \, _2F_1(1,m+1;m+2;-a x)}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 x^m \sqrt{c-a^2 c x^2} \, _2F_1(1,m+1;m+2;-a x)}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x^m \sqrt{c-a^2 c x^2}}{a (m+1) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-a^2 c x^2}}{(m+2) \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-3*x^m*Sqrt[c - a^2*c*x^2])/(a*(1 + m)*Sqrt[1 - 1/(a^2*x^2)]) + (x^(1 + m)*Sqrt[c - a^2*c*x^2])/((2 + m)*Sqrt[1 - 1/(a^2*x^2)]) + (4*x^m*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[1, 1 + m, 2 + m, -(a*x)])/(a*(1 + m)*Sqrt[1 - 1/(a^2*x^2)])","A",5,4,27,0.1481,1,"{6192, 6193, 88, 64}"
736,1,81,0,0.1351661,"\int e^{n \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^3 \, dx","Int[E^(n*ArcCoth[a*x])*(c - a^2*c*x^2)^3,x]","-\frac{256 c^3 \left(1-\frac{1}{a x}\right)^{4-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-8}{2}} \, _2F_1\left(8,4-\frac{n}{2};5-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (8-n)}","-\frac{256 c^3 \left(1-\frac{1}{a x}\right)^{4-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-8}{2}} \, _2F_1\left(8,4-\frac{n}{2};5-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (8-n)}",1,"(-256*c^3*(1 - 1/(a*x))^(4 - n/2)*(1 + 1/(a*x))^((-8 + n)/2)*Hypergeometric2F1[8, 4 - n/2, 5 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(8 - n))","A",3,3,22,0.1364,1,"{6191, 6195, 131}"
737,1,81,0,0.1443604,"\int e^{n \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^2 \, dx","Int[E^(n*ArcCoth[a*x])*(c - a^2*c*x^2)^2,x]","\frac{64 c^2 \left(1-\frac{1}{a x}\right)^{3-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-6}{2}} \, _2F_1\left(6,3-\frac{n}{2};4-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (6-n)}","\frac{64 c^2 \left(1-\frac{1}{a x}\right)^{3-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-6}{2}} \, _2F_1\left(6,3-\frac{n}{2};4-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (6-n)}",1,"(64*c^2*(1 - 1/(a*x))^(3 - n/2)*(1 + 1/(a*x))^((-6 + n)/2)*Hypergeometric2F1[6, 3 - n/2, 4 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(6 - n))","A",3,3,22,0.1364,1,"{6191, 6195, 131}"
738,1,79,0,0.0925007,"\int e^{n \coth ^{-1}(a x)} \left(c-a^2 c x^2\right) \, dx","Int[E^(n*ArcCoth[a*x])*(c - a^2*c*x^2),x]","-\frac{16 c \left(1-\frac{1}{a x}\right)^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-4}{2}} \, _2F_1\left(4,2-\frac{n}{2};3-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (4-n)}","-\frac{16 c \left(1-\frac{1}{a x}\right)^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-4}{2}} \, _2F_1\left(4,2-\frac{n}{2};3-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (4-n)}",1,"(-16*c*(1 - 1/(a*x))^(2 - n/2)*(1 + 1/(a*x))^((-4 + n)/2)*Hypergeometric2F1[4, 2 - n/2, 3 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(4 - n))","A",3,3,20,0.1500,1,"{6191, 6195, 131}"
739,1,78,0,0.0229457,"\int e^{n \coth ^{-1}(a x)} \, dx","Int[E^(n*ArcCoth[a*x]),x]","\frac{4 \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (2-n)}","\frac{4 \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (2-n)}",1,"(4*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*Hypergeometric2F1[2, 1 - n/2, 2 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*(2 - n))","A",2,2,8,0.2500,1,"{6170, 131}"
740,1,18,0,0.0345959,"\int \frac{e^{n \coth ^{-1}(a x)}}{c-a^2 c x^2} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2),x]","\frac{e^{n \coth ^{-1}(a x)}}{a c n}","\frac{e^{n \coth ^{-1}(a x)}}{a c n}",1,"E^(n*ArcCoth[a*x])/(a*c*n)","A",1,1,22,0.04545,1,"{6183}"
741,1,72,0,0.0778262,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^2} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^2,x]","\frac{2 e^{n \coth ^{-1}(a x)}}{a c^2 n \left(4-n^2\right)}-\frac{(n-2 a x) e^{n \coth ^{-1}(a x)}}{a c^2 \left(4-n^2\right) \left(1-a^2 x^2\right)}","\frac{2 e^{n \coth ^{-1}(a x)}}{a c^2 n \left(4-n^2\right)}-\frac{(n-2 a x) e^{n \coth ^{-1}(a x)}}{a c^2 \left(4-n^2\right) \left(1-a^2 x^2\right)}",1,"(2*E^(n*ArcCoth[a*x]))/(a*c^2*n*(4 - n^2)) - (E^(n*ArcCoth[a*x])*(n - 2*a*x))/(a*c^2*(4 - n^2)*(1 - a^2*x^2))","A",2,2,22,0.09091,1,"{6185, 6183}"
742,1,127,0,0.1295112,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^3} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^3,x]","-\frac{(n-4 a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a c^3 n \left(n^4-20 n^2+64\right)}","-\frac{(n-4 a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a c^3 n \left(n^4-20 n^2+64\right)}",1,"(24*E^(n*ArcCoth[a*x]))/(a*c^3*n*(64 - 20*n^2 + n^4)) - (E^(n*ArcCoth[a*x])*(n - 4*a*x))/(a*c^3*(16 - n^2)*(1 - a^2*x^2)^2) - (12*E^(n*ArcCoth[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,"{6185, 6183}"
743,1,197,0,0.1809545,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^4} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^4,x]","-\frac{(n-6 a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a c^4 n \left(36-n^2\right) \left(n^4-20 n^2+64\right)}",1,"(720*E^(n*ArcCoth[a*x]))/(a*c^4*n*(36 - n^2)*(64 - 20*n^2 + n^4)) - (E^(n*ArcCoth[a*x])*(n - 6*a*x))/(a*c^4*(36 - n^2)*(1 - a^2*x^2)^3) - (30*E^(n*ArcCoth[a*x])*(n - 4*a*x))/(a*c^4*(16 - n^2)*(36 - n^2)*(1 - a^2*x^2)^2) - (360*E^(n*ArcCoth[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,"{6185, 6183}"
744,1,116,0,0.2136567,"\int e^{n \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^{3/2} \, dx","Int[E^(n*ArcCoth[a*x])*(c - a^2*c*x^2)^(3/2),x]","\frac{32 \left(c-a^2 c x^2\right)^{3/2} \left(1-\frac{1}{a x}\right)^{\frac{5-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-5}{2}} \, _2F_1\left(5,\frac{5-n}{2};\frac{7-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^4 (5-n) x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}","\frac{32 \left(c-a^2 c x^2\right)^{3/2} \left(1-\frac{1}{a x}\right)^{\frac{5-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-5}{2}} \, _2F_1\left(5,\frac{5-n}{2};\frac{7-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^4 (5-n) x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2}}",1,"(32*(1 - 1/(a*x))^((5 - n)/2)*(1 + 1/(a*x))^((-5 + n)/2)*(c - a^2*c*x^2)^(3/2)*Hypergeometric2F1[5, (5 - n)/2, (7 - n)/2, (a - x^(-1))/(a + x^(-1))])/(a^4*(5 - n)*(1 - 1/(a^2*x^2))^(3/2)*x^3)","A",3,3,24,0.1250,1,"{6192, 6195, 131}"
745,1,116,0,0.1630975,"\int e^{n \coth ^{-1}(a x)} \sqrt{c-a^2 c x^2} \, dx","Int[E^(n*ArcCoth[a*x])*Sqrt[c - a^2*c*x^2],x]","\frac{8 \sqrt{c-a^2 c x^2} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \, _2F_1\left(3,\frac{3-n}{2};\frac{5-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^2 (3-n) x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{8 \sqrt{c-a^2 c x^2} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \, _2F_1\left(3,\frac{3-n}{2};\frac{5-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^2 (3-n) x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(8*(1 - 1/(a*x))^((3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*Sqrt[c - a^2*c*x^2]*Hypergeometric2F1[3, (3 - n)/2, (5 - n)/2, (a - x^(-1))/(a + x^(-1))])/(a^2*(3 - n)*Sqrt[1 - 1/(a^2*x^2)]*x)","A",3,3,24,0.1250,1,"{6192, 6195, 131}"
746,1,111,0,0.1968795,"\int \frac{e^{n \coth ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[E^(n*ArcCoth[a*x])/Sqrt[c - a^2*c*x^2],x]","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{(1-n) \sqrt{c-a^2 c x^2}}","\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{(1-n) \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[1 - 1/(a^2*x^2)]*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, (a - x^(-1))/(a + x^(-1))])/((1 - n)*Sqrt[c - a^2*c*x^2])","A",3,3,24,0.1250,1,"{6192, 6195, 131}"
747,1,46,0,0.0539141,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^(3/2),x]","-\frac{(n-a x) e^{n \coth ^{-1}(a x)}}{a c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}","-\frac{(n-a x) e^{n \coth ^{-1}(a x)}}{a c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"-((E^(n*ArcCoth[a*x])*(n - a*x))/(a*c*(1 - n^2)*Sqrt[c - a^2*c*x^2]))","A",1,1,24,0.04167,1,"{6184}"
748,1,102,0,0.1122368,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^(5/2),x]","-\frac{6 (n-a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}",1,"-((E^(n*ArcCoth[a*x])*(n - 3*a*x))/(a*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2))) - (6*E^(n*ArcCoth[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,"{6185, 6184}"
749,1,166,0,0.1766483,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^(7/2),x]","-\frac{120 (n-a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a c \left(25-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}",1,"-((E^(n*ArcCoth[a*x])*(n - 5*a*x))/(a*c*(25 - n^2)*(c - a^2*c*x^2)^(5/2))) - (20*E^(n*ArcCoth[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*ArcCoth[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,"{6185, 6184}"
750,1,239,0,0.2543897,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{9/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^(9/2),x]","-\frac{5040 (n-a x) e^{n \coth ^{-1}(a x)}}{a c^4 \left(1-n^2\right) \left(9-n^2\right) \left(25-n^2\right) \left(49-n^2\right) \sqrt{c-a^2 c x^2}}-\frac{840 (n-3 a x) e^{n \coth ^{-1}(a x)}}{a c^3 \left(9-n^2\right) \left(25-n^2\right) \left(49-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}-\frac{42 (n-5 a x) e^{n \coth ^{-1}(a x)}}{a c^2 \left(25-n^2\right) \left(49-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{(n-7 a x) e^{n \coth ^{-1}(a x)}}{a c \left(49-n^2\right) \left(c-a^2 c x^2\right)^{7/2}}","-\frac{5040 (n-a x) e^{n \coth ^{-1}(a x)}}{a c^4 \left(1-n^2\right) \left(9-n^2\right) \left(25-n^2\right) \left(49-n^2\right) \sqrt{c-a^2 c x^2}}-\frac{840 (n-3 a x) e^{n \coth ^{-1}(a x)}}{a c^3 \left(9-n^2\right) \left(25-n^2\right) \left(49-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}-\frac{42 (n-5 a x) e^{n \coth ^{-1}(a x)}}{a c^2 \left(25-n^2\right) \left(49-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{(n-7 a x) e^{n \coth ^{-1}(a x)}}{a c \left(49-n^2\right) \left(c-a^2 c x^2\right)^{7/2}}",1,"-((E^(n*ArcCoth[a*x])*(n - 7*a*x))/(a*c*(49 - n^2)*(c - a^2*c*x^2)^(7/2))) - (42*E^(n*ArcCoth[a*x])*(n - 5*a*x))/(a*c^2*(25 - n^2)*(49 - n^2)*(c - a^2*c*x^2)^(5/2)) - (840*E^(n*ArcCoth[a*x])*(n - 3*a*x))/(a*c^3*(9 - n^2)*(25 - n^2)*(49 - n^2)*(c - a^2*c*x^2)^(3/2)) - (5040*E^(n*ArcCoth[a*x])*(n - a*x))/(a*c^4*(1 - n^2)*(9 - n^2)*(25 - n^2)*(49 - n^2)*Sqrt[c - a^2*c*x^2])","A",4,2,24,0.08333,1,"{6185, 6184}"
751,1,363,0,0.3325937,"\int \frac{e^{n \coth ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x^3)/(c - a^2*c*x^2)^(3/2),x]","\frac{2 n x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (3-n) \left(c-a^2 c x^2\right)^{3/2}}+\frac{\left(n^2+2 n+2\right) x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{a (1-n) (n+1) \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{(n+2) x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{a (n+1) \left(c-a^2 c x^2\right)^{3/2}}","-\frac{2 n x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a+\frac{1}{x}}{a-\frac{1}{x}}\right)}{a (1-n) \left(c-a^2 c x^2\right)^{3/2}}+\frac{\left(n^2+2 n+2\right) x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{a (1-n) (n+1) \left(c-a^2 c x^2\right)^{3/2}}+\frac{x^4 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(c-a^2 c x^2\right)^{3/2}}-\frac{(n+2) x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{a (n+1) \left(c-a^2 c x^2\right)^{3/2}}",1,"-(((2 + n)*(1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^3)/(a*(1 + n)*(c - a^2*c*x^2)^(3/2))) + ((2 + 2*n + n^2)*(1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^3)/(a*(1 - n)*(1 + n)*(c - a^2*c*x^2)^(3/2)) + ((1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^4)/(c - a^2*c*x^2)^(3/2) + (2*n*(1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^3*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (a - x^(-1))/(a + x^(-1))])/(a*(3 - n)*(c - a^2*c*x^2)^(3/2))","A",7,6,27,0.2222,0,"{6192, 6194, 129, 155, 12, 131}"
752,1,164,0,0.3351449,"\int \frac{e^{n \coth ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x^2)/(c - a^2*c*x^2)^(3/2),x]","-\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^2 c (1-n) \sqrt{c-a^2 c x^2}}-\frac{(n-a x) e^{n \coth ^{-1}(a x)}}{a^3 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}","-\frac{2 x \sqrt{1-\frac{1}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a^2 c (1-n) \sqrt{c-a^2 c x^2}}-\frac{(n-a x) e^{n \coth ^{-1}(a x)}}{a^3 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"-((E^(n*ArcCoth[a*x])*(n - a*x))/(a^3*c*(1 - n^2)*Sqrt[c - a^2*c*x^2])) - (2*Sqrt[1 - 1/(a^2*x^2)]*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, (a - x^(-1))/(a + x^(-1))])/(a^2*c*(1 - n)*Sqrt[c - a^2*c*x^2])","A",4,4,27,0.1481,1,"{6189, 6192, 6195, 131}"
753,1,46,0,0.0923765,"\int \frac{e^{n \coth ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x)/(c - a^2*c*x^2)^(3/2),x]","\frac{(1-a n x) e^{n \coth ^{-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 \coth ^{-1}(a x)}}{a^2 c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"(E^(n*ArcCoth[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,"{6186}"
754,1,46,0,0.0524908,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^(3/2),x]","-\frac{(n-a x) e^{n \coth ^{-1}(a x)}}{a c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}","-\frac{(n-a x) e^{n \coth ^{-1}(a x)}}{a c \left(1-n^2\right) \sqrt{c-a^2 c x^2}}",1,"-((E^(n*ArcCoth[a*x])*(n - a*x))/(a*c*(1 - n^2)*Sqrt[c - a^2*c*x^2]))","A",1,1,24,0.04167,1,"{6184}"
755,1,277,0,0.3735345,"\int \frac{e^{n \coth ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(x*(c - a^2*c*x^2)^(3/2)),x]","-\frac{a^3 2^{\frac{n+1}{2}} x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{(1-n) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{\left(1-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{(n+1) \left(c-a^2 c x^2\right)^{3/2}}","-\frac{a^3 2^{\frac{n+1}{2}} x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{(1-n) \left(c-a^2 c x^2\right)^{3/2}}+\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{\left(1-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}-\frac{a^3 x^3 \left(1-\frac{1}{a^2 x^2}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{(n+1) \left(c-a^2 c x^2\right)^{3/2}}",1,"-((a^3*(1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^3)/((1 + n)*(c - a^2*c*x^2)^(3/2))) + (a^3*(1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^3)/((1 - n^2)*(c - a^2*c*x^2)^(3/2)) - (2^((1 + n)/2)*a^3*(1 - 1/(a^2*x^2))^(3/2)*(1 - 1/(a*x))^((1 - n)/2)*x^3*Hypergeometric2F1[(1 - n)/2, (1 - n)/2, (3 - n)/2, (a - x^(-1))/(2*a)])/((1 - n)*(c - a^2*c*x^2)^(3/2))","A",5,5,27,0.1852,1,"{6192, 6195, 89, 79, 69}"
756,1,467,0,0.5348577,"\int \frac{e^{n \coth ^{-1}(a x)} x^4}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x^4)/(c - a^2*c*x^2)^(5/2),x]","\frac{2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}} \, _2F_1\left(1,\frac{3-n}{2};\frac{5-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{(3-n) \left(c-a^2 c x^2\right)^{5/2}}+\frac{\left(n^2+6 n+15\right) x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(1-n) (n+1) (n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{\left(-n^3-2 n^2+7 n+18\right) x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}}}{\left(n^4-10 n^2+9\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{(n+6) x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{(n+1) (n+3) \left(c-a^2 c x^2\right)^{5/2}}","-\frac{2 x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};\frac{a+\frac{1}{x}}{a-\frac{1}{x}}\right)}{(1-n) \left(c-a^2 c x^2\right)^{5/2}}+\frac{\left(n^2+6 n+15\right) x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(1-n) (n+1) (n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{\left(-n^3-2 n^2+7 n+18\right) x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}}}{\left(n^4-10 n^2+9\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{(n+6) x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{(n+1) (n+3) \left(c-a^2 c x^2\right)^{5/2}}",1,"-(((1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + n)*(c - a^2*c*x^2)^(5/2))) - ((6 + n)*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((1 + n)*(3 + n)*(c - a^2*c*x^2)^(5/2)) + ((15 + 6*n + n^2)*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((1 - n)*(1 + n)*(3 + n)*(c - a^2*c*x^2)^(5/2)) - ((18 + 7*n - 2*n^2 - n^3)*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((9 - 10*n^2 + n^4)*(c - a^2*c*x^2)^(5/2)) + (2*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5*Hypergeometric2F1[1, (3 - n)/2, (5 - n)/2, (a - x^(-1))/(a + x^(-1))])/((3 - n)*(c - a^2*c*x^2)^(5/2))","A",8,6,27,0.2222,0,"{6192, 6195, 129, 155, 12, 131}"
757,1,330,0,0.3666948,"\int \frac{e^{n \coth ^{-1}(a x)} x^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x^3)/(c - a^2*c*x^2)^(5/2),x]","-\frac{3 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}+\frac{6 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(n+3) \left(1-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}}}{\left(n^4-10 n^2+9\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}","-\frac{3 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}+\frac{6 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(n+3) \left(1-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}}}{\left(n^4-10 n^2+9\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a x^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{\frac{n-3}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}",1,"-((a*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + n)*(c - a^2*c*x^2)^(5/2))) - (3*a*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + 4*n + n^2)*(c - a^2*c*x^2)^(5/2)) + (6*a*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + n)*(1 - n^2)*(c - a^2*c*x^2)^(5/2)) - (6*a*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((9 - 10*n^2 + n^4)*(c - a^2*c*x^2)^(5/2))","A",6,4,27,0.1481,1,"{6192, 6195, 45, 37}"
758,1,102,0,0.1892524,"\int \frac{e^{n \coth ^{-1}(a x)} x^2}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x^2)/(c - a^2*c*x^2)^(5/2),x]","\frac{\left(3-n^2\right) (n-a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a^3 c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}",1,"-((E^(n*ArcCoth[a*x])*(n - 3*a*x))/(a^3*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2))) + (E^(n*ArcCoth[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,"{6189, 6184}"
759,1,97,0,0.1473211,"\int \frac{e^{n \coth ^{-1}(a x)} x}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[(E^(n*ArcCoth[a*x])*x)/(c - a^2*c*x^2)^(5/2),x]","\frac{2 n (n-a x) e^{n \coth ^{-1}(a x)}}{a^2 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}+\frac{(3-a n x) e^{n \coth ^{-1}(a x)}}{a^2 c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}","\frac{2 n (n-a x) e^{n \coth ^{-1}(a x)}}{a^2 c^2 \left(n^4-10 n^2+9\right) \sqrt{c-a^2 c x^2}}+\frac{(3-a n x) e^{n \coth ^{-1}(a x)}}{a^2 c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}",1,"(E^(n*ArcCoth[a*x])*(3 - a*n*x))/(a^2*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2)) + (2*E^(n*ArcCoth[a*x])*n*(n - a*x))/(a^2*c^2*(9 - 10*n^2 + n^4)*Sqrt[c - a^2*c*x^2])","A",2,2,25,0.08000,1,"{6187, 6184}"
760,1,102,0,0.1064209,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - a^2*c*x^2)^(5/2),x]","-\frac{6 (n-a x) e^{n \coth ^{-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 \coth ^{-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 \coth ^{-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 \coth ^{-1}(a x)}}{a c \left(9-n^2\right) \left(c-a^2 c x^2\right)^{3/2}}",1,"-((E^(n*ArcCoth[a*x])*(n - 3*a*x))/(a*c*(9 - n^2)*(c - a^2*c*x^2)^(3/2))) - (6*E^(n*ArcCoth[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,"{6185, 6184}"
761,1,944,0,0.6321431,"\int \frac{e^{n \coth ^{-1}(a x)}}{x \left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[E^(n*ArcCoth[a*x])/(x*(c - a^2*c*x^2)^(5/2)),x]","-\frac{2^{\frac{n+5}{2}} a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} x^5 \, _2F_1\left(\frac{1}{2} (-n-3),\frac{1}{2} (-n-3);\frac{1}{2} (-n-1);\frac{a-\frac{1}{x}}{2 a}\right) \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}+\frac{4 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n+1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}+\frac{4 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n+3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}+\frac{8 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n+1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}+\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(n+3) \left(1-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{8 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(n+3) \left(1-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}}}{\left(n^4-10 n^2+9\right) \left(c-a^2 c x^2\right)^{5/2}}","-\frac{2^{\frac{n+5}{2}} a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} x^5 \, _2F_1\left(\frac{1}{2} (-n-3),\frac{1}{2} (-n-3);\frac{1}{2} (-n-1);\frac{a-\frac{1}{x}}{2 a}\right) \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}+\frac{4 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n+1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}+\frac{4 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n+3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-3)}}{(n+3) \left(c-a^2 c x^2\right)^{5/2}}-\frac{3 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}+\frac{8 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n+1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1}{2} (-n-1)}}{\left(n^2+4 n+3\right) \left(c-a^2 c x^2\right)^{5/2}}+\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(n+3) \left(1-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{8 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-1}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{(n+3) \left(1-n^2\right) \left(c-a^2 c x^2\right)^{5/2}}-\frac{6 a^5 \left(1-\frac{1}{a^2 x^2}\right)^{5/2} \left(1+\frac{1}{a x}\right)^{\frac{n-3}{2}} x^5 \left(1-\frac{1}{a x}\right)^{\frac{3-n}{2}}}{\left(n^4-10 n^2+9\right) \left(c-a^2 c x^2\right)^{5/2}}",1,"-((a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + n)*(c - a^2*c*x^2)^(5/2))) - (3*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + 4*n + n^2)*(c - a^2*c*x^2)^(5/2)) + (6*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((3 + n)*(1 - n^2)*(c - a^2*c*x^2)^(5/2)) - (6*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((3 - n)/2)*(1 + 1/(a*x))^((-3 + n)/2)*x^5)/((9 - 10*n^2 + n^4)*(c - a^2*c*x^2)^(5/2)) + (4*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^5)/((3 + n)*(c - a^2*c*x^2)^(5/2)) + (8*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^5)/((3 + 4*n + n^2)*(c - a^2*c*x^2)^(5/2)) - (8*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*x^5)/((3 + n)*(1 - n^2)*(c - a^2*c*x^2)^(5/2)) - (6*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*(1 + 1/(a*x))^((1 + n)/2)*x^5)/((3 + n)*(c - a^2*c*x^2)^(5/2)) - (6*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-1 - n)/2)*(1 + 1/(a*x))^((1 + n)/2)*x^5)/((3 + 4*n + n^2)*(c - a^2*c*x^2)^(5/2)) + (4*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*(1 + 1/(a*x))^((3 + n)/2)*x^5)/((3 + n)*(c - a^2*c*x^2)^(5/2)) - (2^((5 + n)/2)*a^5*(1 - 1/(a^2*x^2))^(5/2)*(1 - 1/(a*x))^((-3 - n)/2)*x^5*Hypergeometric2F1[(-3 - n)/2, (-3 - n)/2, (-1 - n)/2, (a - x^(-1))/(2*a)])/((3 + n)*(c - a^2*c*x^2)^(5/2))","A",15,6,27,0.2222,1,"{6192, 6195, 128, 45, 37, 69}"
762,1,127,0,0.1495856,"\int e^{n \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(n*ArcCoth[a*x])*(c - a^2*c*x^2)^p,x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2} (n-2 p)} \left(1-\frac{1}{a x}\right)^{p-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n}{2}+p+1} \, _2F_1\left(-2 p-1,\frac{1}{2} (n-2 p);-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(c-a^2 c x^2\right)^p \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2} (n-2 p)} \left(1-\frac{1}{a x}\right)^{p-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n}{2}+p+1} \, _2F_1\left(-2 p-1,\frac{1}{2} (n-2 p);-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^((n - 2*p)/2)*(1 - 1/(a*x))^(-n/2 + p)*(1 + 1/(a*x))^(1 + n/2 + p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - 2*p, (n - 2*p)/2, -2*p, 2/((a + x^(-1))*x)])/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,22,0.1364,1,"{6192, 6196, 132}"
763,1,51,0,0.1232236,"\int e^{2 p \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(2*p*ArcCoth[a*x])*(c - a^2*c*x^2)^p,x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{1}{a x}+1\right)^{2 p+1} \left(c-a^2 c x^2\right)^p}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{1}{a x}+1\right)^{2 p+1} \left(c-a^2 c x^2\right)^p}{2 p+1}",1,"((1 + 1/(a*x))^(1 + 2*p)*x*(c - a^2*c*x^2)^p)/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,23,0.1304,1,"{6192, 6196, 37}"
764,1,52,0,0.1219514,"\int e^{-2 p \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^(2*p*ArcCoth[a*x]),x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(1-\frac{1}{a x}\right)^{2 p+1} \left(c-a^2 c x^2\right)^p}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(1-\frac{1}{a x}\right)^{2 p+1} \left(c-a^2 c x^2\right)^p}{2 p+1}",1,"((1 - 1/(a*x))^(1 + 2*p)*x*(c - a^2*c*x^2)^p)/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,23,0.1304,1,"{6192, 6196, 37}"
765,1,63,0,0.1041803,"\int e^{4 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(4*ArcCoth[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",4,4,22,0.1818,1,"{6167, 6141, 678, 69}"
766,1,118,0,0.1450591,"\int e^{3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(3*ArcCoth[a*x])*(c - a^2*c*x^2)^p,x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{3}{2}-p} \left(1-\frac{1}{a x}\right)^{p-\frac{3}{2}} \left(\frac{1}{a x}+1\right)^{p+\frac{5}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,\frac{3}{2}-p;-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{3}{2}-p} \left(1-\frac{1}{a x}\right)^{p-\frac{3}{2}} \left(\frac{1}{a x}+1\right)^{p+\frac{5}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,\frac{3}{2}-p;-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^(3/2 - p)*(1 - 1/(a*x))^(-3/2 + p)*(1 + 1/(a*x))^(5/2 + p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - 2*p, 3/2 - p, -2*p, 2/((a + x^(-1))*x)])/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,22,0.1364,1,"{6192, 6196, 132}"
767,1,54,0,0.0884693,"\int e^{2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^(2*ArcCoth[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",4,4,22,0.1818,1,"{6167, 6141, 678, 69}"
768,1,118,0,0.132645,"\int e^{\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[E^ArcCoth[a*x]*(c - a^2*c*x^2)^p,x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2}-p} \left(1-\frac{1}{a x}\right)^{p-\frac{1}{2}} \left(\frac{1}{a x}+1\right)^{p+\frac{3}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,\frac{1}{2}-p;-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{\frac{1}{2}-p} \left(1-\frac{1}{a x}\right)^{p-\frac{1}{2}} \left(\frac{1}{a x}+1\right)^{p+\frac{3}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,\frac{1}{2}-p;-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^(1/2 - p)*(1 - 1/(a*x))^(-1/2 + p)*(1 + 1/(a*x))^(3/2 + p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - 2*p, 1/2 - p, -2*p, 2/((a + x^(-1))*x)])/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,20,0.1500,1,"{6192, 6196, 132}"
769,1,118,0,0.1387247,"\int e^{-\coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^ArcCoth[a*x],x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{1}{2}} \left(1-\frac{1}{a x}\right)^{p+\frac{1}{2}} \left(\frac{1}{a x}+1\right)^{p+\frac{1}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,-p-\frac{1}{2};-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{1}{2}} \left(1-\frac{1}{a x}\right)^{p+\frac{1}{2}} \left(\frac{1}{a x}+1\right)^{p+\frac{1}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,-p-\frac{1}{2};-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^(-1/2 - p)*(1 - 1/(a*x))^(1/2 + p)*(1 + 1/(a*x))^(1/2 + p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -1/2 - p, -2*p, 2/((a + x^(-1))*x)])/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,22,0.1364,1,"{6192, 6196, 132}"
770,1,55,0,0.0864525,"\int e^{-2 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^(2*ArcCoth[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",4,4,22,0.1818,1,"{6167, 6142, 678, 69}"
771,1,118,0,0.1442689,"\int e^{-3 \coth ^{-1}(a x)} \left(c-a^2 c x^2\right)^p \, dx","Int[(c - a^2*c*x^2)^p/E^(3*ArcCoth[a*x]),x]","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{3}{2}} \left(1-\frac{1}{a x}\right)^{p+\frac{3}{2}} \left(\frac{1}{a x}+1\right)^{p-\frac{1}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,-p-\frac{3}{2};-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}","\frac{x \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)^{-p-\frac{3}{2}} \left(1-\frac{1}{a x}\right)^{p+\frac{3}{2}} \left(\frac{1}{a x}+1\right)^{p-\frac{1}{2}} \left(c-a^2 c x^2\right)^p \, _2F_1\left(-2 p-1,-p-\frac{3}{2};-2 p;\frac{2}{\left(a+\frac{1}{x}\right) x}\right)}{2 p+1}",1,"(((a - x^(-1))/(a + x^(-1)))^(-3/2 - p)*(1 - 1/(a*x))^(3/2 + p)*(1 + 1/(a*x))^(-1/2 + p)*x*(c - a^2*c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -3/2 - p, -2*p, 2/((a + x^(-1))*x)])/((1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,22,0.1364,1,"{6192, 6196, 132}"
772,1,342,0,0.2455097,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2))^4,x]","\frac{8 c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{9/2}}{7 a}+\frac{47 c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}}{42 a}+c^4 x \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{61 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{70 a}-\frac{131 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{280 a}-\frac{91 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{120 a}-\frac{67 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{48 a}-\frac{51 c^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{16 a}+\frac{35 c^4 \csc ^{-1}(a x)}{16 a}+\frac{c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","\frac{8 c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{9/2}}{7 a}+\frac{47 c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}}{42 a}+c^4 x \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{61 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{70 a}-\frac{131 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{280 a}-\frac{91 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{120 a}-\frac{67 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{48 a}-\frac{51 c^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{16 a}+\frac{35 c^4 \csc ^{-1}(a x)}{16 a}+\frac{c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-51*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(16*a) - (67*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(48*a) - (91*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(120*a) - (131*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2))/(280*a) + (61*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2))/(70*a) + (47*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(9/2))/(42*a) + (8*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(9/2))/(7*a) + c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(9/2)*x + (35*c^4*ArcCsc[a*x])/(16*a) + (c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",14,8,20,0.4000,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
773,1,268,0,0.1876671,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2))^3,x]","\frac{6 c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}}{5 a}+c^3 x \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{23 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{20 a}-\frac{43 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{60 a}-\frac{31 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{24 a}-\frac{23 c^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{8 a}+\frac{15 c^3 \csc ^{-1}(a x)}{8 a}+\frac{c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","\frac{6 c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}}{5 a}+c^3 x \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}+\frac{23 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{20 a}-\frac{43 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{60 a}-\frac{31 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{24 a}-\frac{23 c^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{8 a}+\frac{15 c^3 \csc ^{-1}(a x)}{8 a}+\frac{c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-23*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(8*a) - (31*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(24*a) - (43*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(60*a) + (23*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2))/(20*a) + (6*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(7/2))/(5*a) + c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(7/2)*x + (15*c^3*ArcCsc[a*x])/(8*a) + (c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",12,8,20,0.4000,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
774,1,194,0,0.1341115,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2))^2,x]","c^2 x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{4 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{3 a}-\frac{7 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{6 a}-\frac{5 c^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{2 a}+\frac{3 c^2 \csc ^{-1}(a x)}{2 a}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^2 x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}+\frac{4 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{3 a}-\frac{7 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{6 a}-\frac{5 c^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{2 a}+\frac{3 c^2 \csc ^{-1}(a x)}{2 a}+\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-5*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(2*a) - (7*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(6*a) + (4*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(3*a) + c^2*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2)*x + (3*c^2*ArcCsc[a*x])/(2*a) + (c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",10,8,20,0.4000,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
775,1,107,0,0.0711992,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2)),x]","c x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{2 c \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{a}+\frac{c \csc ^{-1}(a x)}{a}+\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{2 c \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{a}+\frac{c \csc ^{-1}(a x)}{a}+\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-2*c*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/a + c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x + (c*ArcCsc[a*x])/a + (c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",9,9,18,0.5000,1,"{6194, 97, 154, 21, 105, 41, 216, 92, 208}"
776,1,104,0,0.0750737,"\int \frac{e^{\coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2)),x]","\frac{x \sqrt{\frac{1}{a x}+1}}{c \sqrt{1-\frac{1}{a x}}}-\frac{2 \sqrt{\frac{1}{a x}+1}}{a c \sqrt{1-\frac{1}{a x}}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}","\frac{x \sqrt{\frac{1}{a x}+1}}{c \sqrt{1-\frac{1}{a x}}}-\frac{2 \sqrt{\frac{1}{a x}+1}}{a c \sqrt{1-\frac{1}{a x}}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}",1,"(-2*Sqrt[1 + 1/(a*x)])/(a*c*Sqrt[1 - 1/(a*x)]) + (Sqrt[1 + 1/(a*x)]*x)/(c*Sqrt[1 - 1/(a*x)]) + ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c)","A",6,6,20,0.3000,1,"{6194, 103, 21, 94, 92, 208}"
777,1,180,0,0.1159333,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2))^2,x]","\frac{x}{c^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{8 \sqrt{1-\frac{1}{a x}}}{3 a c^2 \sqrt{\frac{1}{a x}+1}}-\frac{11}{3 a c^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{4}{3 a c^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}","\frac{x}{c^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{8 \sqrt{1-\frac{1}{a x}}}{3 a c^2 \sqrt{\frac{1}{a x}+1}}-\frac{11}{3 a c^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{4}{3 a c^2 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}",1,"-4/(3*a*c^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]) - 11/(3*a*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (8*Sqrt[1 - 1/(a*x)])/(3*a*c^2*Sqrt[1 + 1/(a*x)]) + x/(c^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]) + ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c^2)","A",8,6,20,0.3000,1,"{6194, 103, 152, 12, 92, 208}"
778,1,254,0,0.1656648,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2))^3,x]","\frac{x}{c^3 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{16 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \sqrt{\frac{1}{a x}+1}}+\frac{21 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{34}{5 a c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{29}{15 a c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{6}{5 a c^3 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}","\frac{x}{c^3 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{16 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \sqrt{\frac{1}{a x}+1}}+\frac{21 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{34}{5 a c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{29}{15 a c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{6}{5 a c^3 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}",1,"-6/(5*a*c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)) - 29/(15*a*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2)) - 34/(5*a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)) + (21*Sqrt[1 - 1/(a*x)])/(5*a*c^3*(1 + 1/(a*x))^(3/2)) + (16*Sqrt[1 - 1/(a*x)])/(5*a*c^3*Sqrt[1 + 1/(a*x)]) + x/(c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)) + ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c^3)","A",10,6,20,0.3000,1,"{6194, 103, 152, 12, 92, 208}"
779,1,328,0,0.2284357,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2))^4,x]","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{128 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{163 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{262 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{269}{21 a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{62}{21 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{11}{7 a c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{8}{7 a c^4 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{128 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{163 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{262 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{269}{21 a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{62}{21 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{11}{7 a c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{8}{7 a c^4 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}",1,"-8/(7*a*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2)) - 11/(7*a*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(5/2)) - 62/(21*a*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2)) - 269/(21*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)) + (262*Sqrt[1 - 1/(a*x)])/(35*a*c^4*(1 + 1/(a*x))^(5/2)) + (163*Sqrt[1 - 1/(a*x)])/(35*a*c^4*(1 + 1/(a*x))^(3/2)) + (128*Sqrt[1 - 1/(a*x)])/(35*a*c^4*Sqrt[1 + 1/(a*x)]) + x/(c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2)) + ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c^4)","A",12,6,20,0.3000,1,"{6194, 103, 152, 12, 92, 208}"
780,1,127,0,0.1751851,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^5 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
781,1,90,0,0.1600542,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
782,1,76,0,0.1592866,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
783,1,39,0,0.1468535,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 75}"
784,1,21,0,0.0854281,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^(2*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6157, 6150, 43}"
785,1,36,0,0.1595082,"\int \frac{e^{2 \coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 43}"
786,1,75,0,0.1762539,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
787,1,110,0,0.1994581,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
788,1,145,0,0.2284406,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
789,1,343,0,0.2565872,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^4,x]","\frac{8 c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{11/2}}{7 a}+c^4 x \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{15 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}}{14 a}-\frac{57 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{70 a}-\frac{303 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{280 a}-\frac{61 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{40 a}-\frac{37 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{16 a}-\frac{63 c^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{16 a}+\frac{15 c^4 \csc ^{-1}(a x)}{16 a}+\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","\frac{8 c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{11/2}}{7 a}+c^4 x \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{11/2}+\frac{15 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{11/2}}{14 a}-\frac{57 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{70 a}-\frac{303 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{280 a}-\frac{61 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{40 a}-\frac{37 c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{16 a}-\frac{63 c^4 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{16 a}+\frac{15 c^4 \csc ^{-1}(a x)}{16 a}+\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-63*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(16*a) - (37*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(16*a) - (61*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(40*a) - (303*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2))/(280*a) - (57*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2))/(70*a) + (15*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(11/2))/(14*a) + (8*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(11/2))/(7*a) + c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(11/2)*x + (15*c^4*ArcCsc[a*x])/(16*a) + (3*c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",14,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
790,1,269,0,0.1919174,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^3,x]","c^3 x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{6 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{5 a}-\frac{21 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{20 a}-\frac{29 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{20 a}-\frac{17 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{8 a}-\frac{27 c^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{8 a}+\frac{3 c^3 \csc ^{-1}(a x)}{8 a}+\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^3 x \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}+\frac{6 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}{5 a}-\frac{21 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}{20 a}-\frac{29 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{20 a}-\frac{17 c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{8 a}-\frac{27 c^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{8 a}+\frac{3 c^3 \csc ^{-1}(a x)}{8 a}+\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-27*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(8*a) - (17*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(8*a) - (29*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(20*a) - (21*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2))/(20*a) + (6*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2))/(5*a) + c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(9/2)*x + (3*c^3*ArcCsc[a*x])/(8*a) + (3*c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",12,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
791,1,195,0,0.1346312,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^2,x]","c^2 x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{4 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{3 a}-\frac{11 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{6 a}-\frac{5 c^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{2 a}-\frac{c^2 \csc ^{-1}(a x)}{2 a}+\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^2 x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}-\frac{4 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}{3 a}-\frac{11 c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}{6 a}-\frac{5 c^2 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}{2 a}-\frac{c^2 \csc ^{-1}(a x)}{2 a}+\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-5*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(2*a) - (11*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(6*a) - (4*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(3*a) + c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)*x - (c^2*ArcCsc[a*x])/(2*a) + (3*c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",10,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
792,1,76,0,0.0581777,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2)),x]","c x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{3 c \csc ^{-1}(a x)}{a}+\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c x \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}-\frac{3 c \csc ^{-1}(a x)}{a}+\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"c*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)*x - (3*c*ArcCsc[a*x])/a + (3*c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",8,8,20,0.4000,1,"{6194, 98, 12, 105, 41, 216, 92, 208}"
793,1,144,0,0.1014111,"\int \frac{e^{3 \coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2)),x]","\frac{x \sqrt{\frac{1}{a x}+1}}{c \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{14 \sqrt{\frac{1}{a x}+1}}{3 a c \sqrt{1-\frac{1}{a x}}}-\frac{5 \sqrt{\frac{1}{a x}+1}}{3 a c \left(1-\frac{1}{a x}\right)^{3/2}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}","\frac{x \sqrt{\frac{1}{a x}+1}}{c \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{14 \sqrt{\frac{1}{a x}+1}}{3 a c \sqrt{1-\frac{1}{a x}}}-\frac{5 \sqrt{\frac{1}{a x}+1}}{3 a c \left(1-\frac{1}{a x}\right)^{3/2}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}",1,"(-5*Sqrt[1 + 1/(a*x)])/(3*a*c*(1 - 1/(a*x))^(3/2)) - (14*Sqrt[1 + 1/(a*x)])/(3*a*c*Sqrt[1 - 1/(a*x)]) + (Sqrt[1 + 1/(a*x)]*x)/(c*(1 - 1/(a*x))^(3/2)) + (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c)","A",7,6,22,0.2727,1,"{6194, 99, 152, 12, 92, 208}"
794,1,181,0,0.1282645,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2))^2,x]","\frac{x \sqrt{\frac{1}{a x}+1}}{c^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{24 \sqrt{\frac{1}{a x}+1}}{5 a c^2 \sqrt{1-\frac{1}{a x}}}-\frac{9 \sqrt{\frac{1}{a x}+1}}{5 a c^2 \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{6 \sqrt{\frac{1}{a x}+1}}{5 a c^2 \left(1-\frac{1}{a x}\right)^{5/2}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}","\frac{x \sqrt{\frac{1}{a x}+1}}{c^2 \left(1-\frac{1}{a x}\right)^{5/2}}-\frac{24 \sqrt{\frac{1}{a x}+1}}{5 a c^2 \sqrt{1-\frac{1}{a x}}}-\frac{9 \sqrt{\frac{1}{a x}+1}}{5 a c^2 \left(1-\frac{1}{a x}\right)^{3/2}}-\frac{6 \sqrt{\frac{1}{a x}+1}}{5 a c^2 \left(1-\frac{1}{a x}\right)^{5/2}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}",1,"(-6*Sqrt[1 + 1/(a*x)])/(5*a*c^2*(1 - 1/(a*x))^(5/2)) - (9*Sqrt[1 + 1/(a*x)])/(5*a*c^2*(1 - 1/(a*x))^(3/2)) - (24*Sqrt[1 + 1/(a*x)])/(5*a*c^2*Sqrt[1 - 1/(a*x)]) + (Sqrt[1 + 1/(a*x)]*x)/(c^2*(1 - 1/(a*x))^(5/2)) + (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c^2)","A",9,8,22,0.3636,1,"{6194, 103, 21, 99, 152, 12, 92, 208}"
795,1,255,0,0.1722832,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2))^3,x]","\frac{x}{c^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{176 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \sqrt{\frac{1}{a x}+1}}-\frac{281}{35 a c^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{88}{35 a c^3 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}-\frac{53}{35 a c^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}-\frac{8}{7 a c^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}","\frac{x}{c^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{176 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \sqrt{\frac{1}{a x}+1}}-\frac{281}{35 a c^3 \sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}}-\frac{88}{35 a c^3 \left(1-\frac{1}{a x}\right)^{3/2} \sqrt{\frac{1}{a x}+1}}-\frac{53}{35 a c^3 \left(1-\frac{1}{a x}\right)^{5/2} \sqrt{\frac{1}{a x}+1}}-\frac{8}{7 a c^3 \left(1-\frac{1}{a x}\right)^{7/2} \sqrt{\frac{1}{a x}+1}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}",1,"-8/(7*a*c^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]) - 53/(35*a*c^3*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)]) - 88/(35*a*c^3*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]) - 281/(35*a*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]) + (176*Sqrt[1 - 1/(a*x)])/(35*a*c^3*Sqrt[1 + 1/(a*x)]) + x/(c^3*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]) + (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c^3)","A",10,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
796,1,329,0,0.2363872,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2))^4,x]","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{1664 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{2609 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{1462}{105 a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{1147}{315 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{208}{105 a c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{29}{21 a c^4 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{10}{9 a c^4 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{1664 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{2609 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{1462}{105 a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{1147}{315 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{208}{105 a c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{29}{21 a c^4 \left(1-\frac{1}{a x}\right)^{7/2} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{10}{9 a c^4 \left(1-\frac{1}{a x}\right)^{9/2} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}",1,"-10/(9*a*c^4*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(3/2)) - 29/(21*a*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(3/2)) - 208/(105*a*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)) - 1147/(315*a*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2)) - 1462/(105*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)) + (2609*Sqrt[1 - 1/(a*x)])/(315*a*c^4*(1 + 1/(a*x))^(3/2)) + (1664*Sqrt[1 - 1/(a*x)])/(315*a*c^4*Sqrt[1 + 1/(a*x)]) + x/(c^4*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(3/2)) + (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c^4)","A",12,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
797,1,116,0,0.1706964,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^5 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
798,1,100,0,0.1662979,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
799,1,63,0,0.1516947,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 75}"
800,1,51,0,0.1477419,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 43}"
801,1,33,0,0.0933374,"\int e^{4 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^(4*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6157, 6150, 88}"
802,1,53,0,0.1684437,"\int \frac{e^{4 \coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 77}"
803,1,71,0,0.1723367,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 43}"
804,1,111,0,0.1959595,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
805,1,146,0,0.221346,"\int \frac{e^{4 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[E^(4*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
806,1,343,0,0.2566632,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[(c - c/(a^2*x^2))^4/E^ArcCoth[a*x],x]","c^4 x \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{9/2}+\frac{8 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{7/2}}{7 a}+\frac{7 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{5/2}}{6 a}+\frac{29 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{3/2}}{30 a}+\frac{19 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \sqrt{1-\frac{1}{a x}}}{40 a}+\frac{7 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{1-\frac{1}{a x}}}{40 a}-\frac{c^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{16 a}-\frac{19 c^4 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{16 a}+\frac{35 c^4 \csc ^{-1}(a x)}{16 a}-\frac{c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^4 x \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{9/2}+\frac{8 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{7/2}}{7 a}+\frac{7 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{5/2}}{6 a}+\frac{29 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \left(1-\frac{1}{a x}\right)^{3/2}}{30 a}+\frac{19 c^4 \left(\frac{1}{a x}+1\right)^{7/2} \sqrt{1-\frac{1}{a x}}}{40 a}+\frac{7 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{1-\frac{1}{a x}}}{40 a}-\frac{c^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{16 a}-\frac{19 c^4 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{16 a}+\frac{35 c^4 \csc ^{-1}(a x)}{16 a}-\frac{c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-19*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(16*a) - (c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(16*a) + (7*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(40*a) + (19*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2))/(40*a) + (29*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(7/2))/(30*a) + (7*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(7/2))/(6*a) + (8*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(7/2))/(7*a) + c^4*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(7/2)*x + (35*c^4*ArcCsc[a*x])/(16*a) - (c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",14,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
807,1,269,0,0.1858208,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[(c - c/(a^2*x^2))^3/E^ArcCoth[a*x],x]","c^3 x \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{7/2}+\frac{6 c^3 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{5/2}}{5 a}+\frac{5 c^3 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{3/2}}{4 a}+\frac{11 c^3 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{1-\frac{1}{a x}}}{12 a}+\frac{c^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{24 a}-\frac{7 c^3 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{15 c^3 \csc ^{-1}(a x)}{8 a}-\frac{c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^3 x \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{7/2}+\frac{6 c^3 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{5/2}}{5 a}+\frac{5 c^3 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{3/2}}{4 a}+\frac{11 c^3 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{1-\frac{1}{a x}}}{12 a}+\frac{c^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{24 a}-\frac{7 c^3 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{15 c^3 \csc ^{-1}(a x)}{8 a}-\frac{c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(-7*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(8*a) + (c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(24*a) + (11*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(12*a) + (5*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2))/(4*a) + (6*c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(5/2))/(5*a) + c^3*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2)*x + (15*c^3*ArcCsc[a*x])/(8*a) - (c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",12,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
808,1,195,0,0.1316599,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[(c - c/(a^2*x^2))^2/E^ArcCoth[a*x],x]","c^2 x \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{5/2}+\frac{4 c^2 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{3/2}}{3 a}+\frac{3 c^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{2 a}-\frac{c^2 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{2 a}+\frac{3 c^2 \csc ^{-1}(a x)}{2 a}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^2 x \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{5/2}+\frac{4 c^2 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{3/2}}{3 a}+\frac{3 c^2 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{2 a}-\frac{c^2 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{2 a}+\frac{3 c^2 \csc ^{-1}(a x)}{2 a}-\frac{c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"-(c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(2*a) + (3*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(2*a) + (4*c^2*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2))/(3*a) + c^2*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2)*x + (3*c^2*ArcCsc[a*x])/(2*a) - (c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",10,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
809,1,108,0,0.0763682,"\int e^{-\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[(c - c/(a^2*x^2))/E^ArcCoth[a*x],x]","c x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}+\frac{2 c \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{a}+\frac{c \csc ^{-1}(a x)}{a}-\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}+\frac{2 c \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{a}+\frac{c \csc ^{-1}(a x)}{a}-\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(2*c*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/a + c*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x + (c*ArcCsc[a*x])/a - (c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",9,9,20,0.4500,1,"{6194, 97, 154, 21, 105, 41, 216, 92, 208}"
810,1,105,0,0.0773693,"\int \frac{e^{-\coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))),x]","\frac{x \sqrt{1-\frac{1}{a x}}}{c \sqrt{\frac{1}{a x}+1}}+\frac{2 \sqrt{1-\frac{1}{a x}}}{a c \sqrt{\frac{1}{a x}+1}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}","\frac{x \sqrt{1-\frac{1}{a x}}}{c \sqrt{\frac{1}{a x}+1}}+\frac{2 \sqrt{1-\frac{1}{a x}}}{a c \sqrt{\frac{1}{a x}+1}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}",1,"(2*Sqrt[1 - 1/(a*x)])/(a*c*Sqrt[1 + 1/(a*x)]) + (Sqrt[1 - 1/(a*x)]*x)/(c*Sqrt[1 + 1/(a*x)]) - ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c)","A",6,6,22,0.2727,1,"{6194, 103, 21, 94, 92, 208}"
811,1,179,0,0.1176099,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))^2),x]","\frac{x}{c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{8 \sqrt{1-\frac{1}{a x}}}{3 a c^2 \sqrt{\frac{1}{a x}+1}}+\frac{5 \sqrt{1-\frac{1}{a x}}}{3 a c^2 \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{2}{a c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}","\frac{x}{c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{8 \sqrt{1-\frac{1}{a x}}}{3 a c^2 \sqrt{\frac{1}{a x}+1}}+\frac{5 \sqrt{1-\frac{1}{a x}}}{3 a c^2 \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{2}{a c^2 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}",1,"-2/(a*c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)) + (5*Sqrt[1 - 1/(a*x)])/(3*a*c^2*(1 + 1/(a*x))^(3/2)) + (8*Sqrt[1 - 1/(a*x)])/(3*a*c^2*Sqrt[1 + 1/(a*x)]) + x/(c^2*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2)) - ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c^2)","A",8,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
812,1,255,0,0.1655576,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))^3),x]","\frac{x}{c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{16 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \sqrt{\frac{1}{a x}+1}}+\frac{11 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{14 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{13}{3 a c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{4}{3 a c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}","\frac{x}{c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{16 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \sqrt{\frac{1}{a x}+1}}+\frac{11 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{14 \sqrt{1-\frac{1}{a x}}}{5 a c^3 \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{13}{3 a c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{4}{3 a c^3 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}",1,"-4/(3*a*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2)) - 13/(3*a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2)) + (14*Sqrt[1 - 1/(a*x)])/(5*a*c^3*(1 + 1/(a*x))^(5/2)) + (11*Sqrt[1 - 1/(a*x)])/(5*a*c^3*(1 + 1/(a*x))^(3/2)) + (16*Sqrt[1 - 1/(a*x)])/(5*a*c^3*Sqrt[1 + 1/(a*x)]) + x/(c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2)) - ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c^3)","A",10,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
813,1,329,0,0.2250707,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))^4),x]","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}}+\frac{128 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{93 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{122 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{115 \sqrt{1-\frac{1}{a x}}}{21 a c^4 \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{28}{3 a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{31}{15 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{6}{5 a c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}}+\frac{128 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{93 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{122 \sqrt{1-\frac{1}{a x}}}{35 a c^4 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{115 \sqrt{1-\frac{1}{a x}}}{21 a c^4 \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{28}{3 a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{31}{15 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{6}{5 a c^4 \left(1-\frac{1}{a x}\right)^{5/2} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}",1,"-6/(5*a*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(7/2)) - 31/(15*a*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(7/2)) - 28/(3*a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)) + (115*Sqrt[1 - 1/(a*x)])/(21*a*c^4*(1 + 1/(a*x))^(7/2)) + (122*Sqrt[1 - 1/(a*x)])/(35*a*c^4*(1 + 1/(a*x))^(5/2)) + (93*Sqrt[1 - 1/(a*x)])/(35*a*c^4*(1 + 1/(a*x))^(3/2)) + (128*Sqrt[1 - 1/(a*x)])/(35*a*c^4*Sqrt[1 + 1/(a*x)]) + x/(c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(7/2)) - ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]]/(a*c^4)","A",12,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
814,1,90,0,0.153422,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[(c - c/(a^2*x^2))^4/E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
815,1,76,0,0.1559483,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[(c - c/(a^2*x^2))^3/E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
816,1,40,0,0.1410851,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[(c - c/(a^2*x^2))^2/E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 75}"
817,1,21,0,0.0848482,"\int e^{-2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[(c - c/(a^2*x^2))/E^(2*ArcCoth[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",5,4,20,0.2000,1,"{6167, 6157, 6150, 43}"
818,1,35,0,0.1552788,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 43}"
819,1,73,0,0.1743101,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
820,1,108,0,0.202373,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
821,1,143,0,0.2312393,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[1/(E^(2*ArcCoth[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",5,4,22,0.1818,1,"{6167, 6157, 6150, 88}"
822,1,343,0,0.2497052,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^4 \, dx","Int[(c - c/(a^2*x^2))^4/E^(3*ArcCoth[a*x]),x]","c^4 x \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{11/2}+\frac{8 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{9/2}}{7 a}+\frac{17 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{7/2}}{14 a}+\frac{11 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{5/2}}{10 a}+\frac{5 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{3/2}}{8 a}-\frac{3 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{27 c^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{16 a}+\frac{33 c^4 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{16 a}+\frac{15 c^4 \csc ^{-1}(a x)}{16 a}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^4 x \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{11/2}+\frac{8 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{9/2}}{7 a}+\frac{17 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{7/2}}{14 a}+\frac{11 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{5/2}}{10 a}+\frac{5 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \left(1-\frac{1}{a x}\right)^{3/2}}{8 a}-\frac{3 c^4 \left(\frac{1}{a x}+1\right)^{5/2} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{27 c^4 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{16 a}+\frac{33 c^4 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{16 a}+\frac{15 c^4 \csc ^{-1}(a x)}{16 a}-\frac{3 c^4 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(33*c^4*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(16*a) + (27*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(16*a) - (3*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(5/2))/(8*a) + (5*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(5/2))/(8*a) + (11*c^4*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(5/2))/(10*a) + (17*c^4*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(5/2))/(14*a) + (8*c^4*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(5/2))/(7*a) + c^4*(1 - 1/(a*x))^(11/2)*(1 + 1/(a*x))^(5/2)*x + (15*c^4*ArcCsc[a*x])/(16*a) - (3*c^4*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",14,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
823,1,269,0,0.1843087,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^3 \, dx","Int[(c - c/(a^2*x^2))^3/E^(3*ArcCoth[a*x]),x]","c^3 x \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{9/2}+\frac{6 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{7/2}}{5 a}+\frac{27 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{5/2}}{20 a}+\frac{5 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{3/2}}{4 a}+\frac{3 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{21 c^3 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{3 c^3 \csc ^{-1}(a x)}{8 a}-\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^3 x \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{9/2}+\frac{6 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{7/2}}{5 a}+\frac{27 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{5/2}}{20 a}+\frac{5 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \left(1-\frac{1}{a x}\right)^{3/2}}{4 a}+\frac{3 c^3 \left(\frac{1}{a x}+1\right)^{3/2} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{21 c^3 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{8 a}+\frac{3 c^3 \csc ^{-1}(a x)}{8 a}-\frac{3 c^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(21*c^3*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(8*a) + (3*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(3/2))/(8*a) + (5*c^3*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(3/2))/(4*a) + (27*c^3*(1 - 1/(a*x))^(5/2)*(1 + 1/(a*x))^(3/2))/(20*a) + (6*c^3*(1 - 1/(a*x))^(7/2)*(1 + 1/(a*x))^(3/2))/(5*a) + c^3*(1 - 1/(a*x))^(9/2)*(1 + 1/(a*x))^(3/2)*x + (3*c^3*ArcCsc[a*x])/(8*a) - (3*c^3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",12,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
824,1,195,0,0.1313507,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^2 \, dx","Int[(c - c/(a^2*x^2))^2/E^(3*ArcCoth[a*x]),x]","c^2 x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}+\frac{4 c^2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{3 a}+\frac{11 c^2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{6 a}+\frac{5 c^2 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{2 a}-\frac{c^2 \csc ^{-1}(a x)}{2 a}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c^2 x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{7/2}+\frac{4 c^2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{5/2}}{3 a}+\frac{11 c^2 \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}}{6 a}+\frac{5 c^2 \sqrt{\frac{1}{a x}+1} \sqrt{1-\frac{1}{a x}}}{2 a}-\frac{c^2 \csc ^{-1}(a x)}{2 a}-\frac{3 c^2 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"(5*c^2*Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)])/(2*a) + (11*c^2*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)])/(6*a) + (4*c^2*(1 - 1/(a*x))^(5/2)*Sqrt[1 + 1/(a*x)])/(3*a) + c^2*(1 - 1/(a*x))^(7/2)*Sqrt[1 + 1/(a*x)]*x - (c^2*ArcCsc[a*x])/(2*a) - (3*c^2*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",10,8,22,0.3636,1,"{6194, 97, 154, 157, 41, 216, 92, 208}"
825,1,76,0,0.0567363,"\int e^{-3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[(c - c/(a^2*x^2))/E^(3*ArcCoth[a*x]),x]","c x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}-\frac{3 c \csc ^{-1}(a x)}{a}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}","c x \sqrt{\frac{1}{a x}+1} \left(1-\frac{1}{a x}\right)^{3/2}-\frac{3 c \csc ^{-1}(a x)}{a}-\frac{3 c \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a}",1,"c*(1 - 1/(a*x))^(3/2)*Sqrt[1 + 1/(a*x)]*x - (3*c*ArcCsc[a*x])/a - (3*c*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/a","A",8,8,20,0.4000,1,"{6194, 98, 12, 105, 41, 216, 92, 208}"
826,1,144,0,0.0981175,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))),x]","\frac{x \sqrt{1-\frac{1}{a x}}}{c \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{14 \sqrt{1-\frac{1}{a x}}}{3 a c \sqrt{\frac{1}{a x}+1}}+\frac{5 \sqrt{1-\frac{1}{a x}}}{3 a c \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}","\frac{x \sqrt{1-\frac{1}{a x}}}{c \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{14 \sqrt{1-\frac{1}{a x}}}{3 a c \sqrt{\frac{1}{a x}+1}}+\frac{5 \sqrt{1-\frac{1}{a x}}}{3 a c \left(\frac{1}{a x}+1\right)^{3/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c}",1,"(5*Sqrt[1 - 1/(a*x)])/(3*a*c*(1 + 1/(a*x))^(3/2)) + (14*Sqrt[1 - 1/(a*x)])/(3*a*c*Sqrt[1 + 1/(a*x)]) + (Sqrt[1 - 1/(a*x)]*x)/(c*(1 + 1/(a*x))^(3/2)) - (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c)","A",7,6,22,0.2727,1,"{6194, 99, 152, 12, 92, 208}"
827,1,181,0,0.1235859,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^2),x]","\frac{x \sqrt{1-\frac{1}{a x}}}{c^2 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{24 \sqrt{1-\frac{1}{a x}}}{5 a c^2 \sqrt{\frac{1}{a x}+1}}+\frac{9 \sqrt{1-\frac{1}{a x}}}{5 a c^2 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{6 \sqrt{1-\frac{1}{a x}}}{5 a c^2 \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}","\frac{x \sqrt{1-\frac{1}{a x}}}{c^2 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{24 \sqrt{1-\frac{1}{a x}}}{5 a c^2 \sqrt{\frac{1}{a x}+1}}+\frac{9 \sqrt{1-\frac{1}{a x}}}{5 a c^2 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{6 \sqrt{1-\frac{1}{a x}}}{5 a c^2 \left(\frac{1}{a x}+1\right)^{5/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^2}",1,"(6*Sqrt[1 - 1/(a*x)])/(5*a*c^2*(1 + 1/(a*x))^(5/2)) + (9*Sqrt[1 - 1/(a*x)])/(5*a*c^2*(1 + 1/(a*x))^(3/2)) + (24*Sqrt[1 - 1/(a*x)])/(5*a*c^2*Sqrt[1 + 1/(a*x)]) + (Sqrt[1 - 1/(a*x)]*x)/(c^2*(1 + 1/(a*x))^(5/2)) - (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c^2)","A",9,8,22,0.3636,1,"{6194, 103, 21, 99, 152, 12, 92, 208}"
828,1,253,0,0.1667503,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^3} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^3),x]","\frac{x}{c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}+\frac{176 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \sqrt{\frac{1}{a x}+1}}+\frac{71 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{54 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{11 \sqrt{1-\frac{1}{a x}}}{7 a c^3 \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{2}{a c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}","\frac{x}{c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}+\frac{176 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \sqrt{\frac{1}{a x}+1}}+\frac{71 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{54 \sqrt{1-\frac{1}{a x}}}{35 a c^3 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{11 \sqrt{1-\frac{1}{a x}}}{7 a c^3 \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{2}{a c^3 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{7/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^3}",1,"-2/(a*c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)) + (11*Sqrt[1 - 1/(a*x)])/(7*a*c^3*(1 + 1/(a*x))^(7/2)) + (54*Sqrt[1 - 1/(a*x)])/(35*a*c^3*(1 + 1/(a*x))^(5/2)) + (71*Sqrt[1 - 1/(a*x)])/(35*a*c^3*(1 + 1/(a*x))^(3/2)) + (176*Sqrt[1 - 1/(a*x)])/(35*a*c^3*Sqrt[1 + 1/(a*x)]) + x/(c^3*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(7/2)) - (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c^3)","A",10,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
829,1,327,0,0.221861,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^4} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^4),x]","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}}+\frac{1664 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{719 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{202 \sqrt{1-\frac{1}{a x}}}{105 a c^4 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{139 \sqrt{1-\frac{1}{a x}}}{63 a c^4 \left(\frac{1}{a x}+1\right)^{7/2}}+\frac{28 \sqrt{1-\frac{1}{a x}}}{9 a c^4 \left(\frac{1}{a x}+1\right)^{9/2}}-\frac{5}{a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}-\frac{4}{3 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}","\frac{x}{c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}}+\frac{1664 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \sqrt{\frac{1}{a x}+1}}+\frac{719 \sqrt{1-\frac{1}{a x}}}{315 a c^4 \left(\frac{1}{a x}+1\right)^{3/2}}+\frac{202 \sqrt{1-\frac{1}{a x}}}{105 a c^4 \left(\frac{1}{a x}+1\right)^{5/2}}+\frac{139 \sqrt{1-\frac{1}{a x}}}{63 a c^4 \left(\frac{1}{a x}+1\right)^{7/2}}+\frac{28 \sqrt{1-\frac{1}{a x}}}{9 a c^4 \left(\frac{1}{a x}+1\right)^{9/2}}-\frac{5}{a c^4 \sqrt{1-\frac{1}{a x}} \left(\frac{1}{a x}+1\right)^{9/2}}-\frac{4}{3 a c^4 \left(1-\frac{1}{a x}\right)^{3/2} \left(\frac{1}{a x}+1\right)^{9/2}}-\frac{3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{a x}} \sqrt{\frac{1}{a x}+1}\right)}{a c^4}",1,"-4/(3*a*c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(9/2)) - 5/(a*c^4*Sqrt[1 - 1/(a*x)]*(1 + 1/(a*x))^(9/2)) + (28*Sqrt[1 - 1/(a*x)])/(9*a*c^4*(1 + 1/(a*x))^(9/2)) + (139*Sqrt[1 - 1/(a*x)])/(63*a*c^4*(1 + 1/(a*x))^(7/2)) + (202*Sqrt[1 - 1/(a*x)])/(105*a*c^4*(1 + 1/(a*x))^(5/2)) + (719*Sqrt[1 - 1/(a*x)])/(315*a*c^4*(1 + 1/(a*x))^(3/2)) + (1664*Sqrt[1 - 1/(a*x)])/(315*a*c^4*Sqrt[1 + 1/(a*x)]) + x/(c^4*(1 - 1/(a*x))^(3/2)*(1 + 1/(a*x))^(9/2)) - (3*ArcTanh[Sqrt[1 - 1/(a*x)]*Sqrt[1 + 1/(a*x)]])/(a*c^4)","A",12,6,22,0.2727,1,"{6194, 103, 152, 12, 92, 208}"
830,1,321,0,0.1499862,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2))^(7/2),x]","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c^3*Sqrt[c - c/(a^2*x^2)])/(6*a^7*Sqrt[1 - 1/(a^2*x^2)]*x^6) + (c^3*Sqrt[c - c/(a^2*x^2)])/(5*a^6*Sqrt[1 - 1/(a^2*x^2)]*x^5) - (3*c^3*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) - (c^3*Sqrt[c - c/(a^2*x^2)])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (3*c^3*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (3*c^3*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^3*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (c^3*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 88}"
831,1,236,0,0.1298674,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2))^(5/2),x]","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c^2*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) - (c^2*Sqrt[c - c/(a^2*x^2)])/(3*a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (c^2*Sqrt[c - c/(a^2*x^2)])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (2*c^2*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^2*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (c^2*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 88}"
832,1,146,0,0.1175657,"\int e^{\coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^ArcCoth[a*x]*(c - c/(a^2*x^2))^(3/2),x]","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (c*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (c*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 75}"
833,1,67,0,0.1001968,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 43}"
834,1,72,0,0.1063631,"\int \frac{e^{\coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^ArcCoth[a*x]/Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{a \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{a \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a^2*x^2)] + (Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(a*Sqrt[c - c/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 43}"
835,1,173,0,0.1334288,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2))^(3/2),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{5 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{5 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c*Sqrt[c - c/(a^2*x^2)]) + Sqrt[1 - 1/(a^2*x^2)]/(2*a*c*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + (5*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(4*a*c*Sqrt[c - c/(a^2*x^2)]) - (Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(4*a*c*Sqrt[c - c/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 88}"
836,1,263,0,0.1594711,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2))^(5/2),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{a c^2 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{23 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{7 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{a c^2 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{23 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{7 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^2*Sqrt[c - c/(a^2*x^2)]) - Sqrt[1 - 1/(a^2*x^2)]/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2) + Sqrt[1 - 1/(a^2*x^2)]/(a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) - Sqrt[1 - 1/(a^2*x^2)]/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (23*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)]) - (7*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 88}"
837,1,359,0,0.1948754,"\int \frac{e^{\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[E^ArcCoth[a*x]/(c - c/(a^2*x^2))^(7/2),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{5 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{11 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{24 a c^3 (1-a x)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{51 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{19 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{5 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{11 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{24 a c^3 (1-a x)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{51 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{19 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^3*Sqrt[c - c/(a^2*x^2)]) + Sqrt[1 - 1/(a^2*x^2)]/(24*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^3) - (11*Sqrt[1 - 1/(a^2*x^2)])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2) + (3*Sqrt[1 - 1/(a^2*x^2)])/(2*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + Sqrt[1 - 1/(a^2*x^2)]/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2) - (5*Sqrt[1 - 1/(a^2*x^2)])/(16*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (51*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]) - (19*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 88}"
838,1,372,0,0.5421877,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[E^(2*ArcCoth[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",15,11,24,0.4583,1,"{6167, 6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
839,1,294,0,0.4953013,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[E^(2*ArcCoth[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",13,11,24,0.4583,1,"{6167, 6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
840,1,213,0,0.4590267,"\int e^{2 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^(2*ArcCoth[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",11,11,24,0.4583,1,"{6167, 6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
841,1,116,0,0.3601916,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(2*ArcCoth[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",9,9,24,0.3750,1,"{6167, 6159, 6129, 102, 157, 41, 216, 92, 208}"
842,1,111,0,0.3073124,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^(2*ArcCoth[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",7,7,24,0.2917,1,"{6167, 6159, 6129, 78, 50, 41, 216}"
843,1,123,0,0.4359828,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^(2*ArcCoth[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",7,7,24,0.2917,1,"{6167, 6159, 6129, 98, 143, 41, 216}"
844,1,203,0,0.4633394,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^(2*ArcCoth[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",9,8,24,0.3333,1,"{6167, 6159, 6129, 98, 150, 143, 41, 216}"
845,1,283,0,0.5020571,"\int \frac{e^{2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[E^(2*ArcCoth[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",11,8,24,0.3333,1,"{6167, 6159, 6129, 98, 150, 143, 41, 216}"
846,1,322,0,0.1653369,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{9/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(9/2),x]","\frac{c^4 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{8 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{7 a^8 x^7 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{8 a^9 x^8 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^4 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{8 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{7 a^8 x^7 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{8 a^9 x^8 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c^4*Sqrt[c - c/(a^2*x^2)])/(8*a^9*Sqrt[1 - 1/(a^2*x^2)]*x^8) + (3*c^4*Sqrt[c - c/(a^2*x^2)])/(7*a^8*Sqrt[1 - 1/(a^2*x^2)]*x^7) - (8*c^4*Sqrt[c - c/(a^2*x^2)])/(5*a^6*Sqrt[1 - 1/(a^2*x^2)]*x^5) - (3*c^4*Sqrt[c - c/(a^2*x^2)])/(2*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (2*c^4*Sqrt[c - c/(a^2*x^2)])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (4*c^4*Sqrt[c - c/(a^2*x^2)])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (c^4*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (3*c^4*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
847,1,324,0,0.1588297,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{7/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(7/2),x]","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c^3*Sqrt[c - c/(a^2*x^2)])/(6*a^7*Sqrt[1 - 1/(a^2*x^2)]*x^6) - (3*c^3*Sqrt[c - c/(a^2*x^2)])/(5*a^6*Sqrt[1 - 1/(a^2*x^2)]*x^5) - (c^3*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (5*c^3*Sqrt[c - c/(a^2*x^2)])/(3*a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (5*c^3*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (c^3*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^3*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (3*c^3*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
848,1,234,0,0.1420423,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{5/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(5/2),x]","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c^2*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (c^2*Sqrt[c - c/(a^2*x^2)])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (c^2*Sqrt[c - c/(a^2*x^2)])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (2*c^2*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^2*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (3*c^2*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 75}"
849,1,148,0,0.1280517,"\int e^{3 \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^{3/2} \, dx","Int[E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(3/2),x]","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (3*c*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (3*c*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
850,1,109,0,0.1199702,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 72}"
851,1,115,0,0.1236769,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^(3*ArcCoth[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 \sqrt{1-\frac{1}{a^2 x^2}}}{a (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{a \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}+\frac{2 \sqrt{1-\frac{1}{a^2 x^2}}}{a (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{a \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a^2*x^2)] + (2*Sqrt[1 - 1/(a^2*x^2)])/(a*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + (3*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(a*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 77}"
852,1,171,0,0.1456682,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2))^(3/2),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{a c (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{a c \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{a c (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{a c \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c*Sqrt[c - c/(a^2*x^2)]) - Sqrt[1 - 1/(a^2*x^2)]/(2*a*c*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2) + (3*Sqrt[1 - 1/(a^2*x^2)])/(a*c*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + (3*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(a*c*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
853,1,267,0,0.1765672,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2))^(5/2),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{31 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{9 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{6 a c^2 (1-a x)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{49 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{31 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{9 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{6 a c^2 (1-a x)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{49 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^2*Sqrt[c - c/(a^2*x^2)]) + Sqrt[1 - 1/(a^2*x^2)]/(6*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^3) - (9*Sqrt[1 - 1/(a^2*x^2)])/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2) + (31*Sqrt[1 - 1/(a^2*x^2)])/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + (49*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)]) - (Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
854,1,360,0,0.2061082,"\int \frac{e^{3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[E^(3*ArcCoth[a*x])/(c - c/(a^2*x^2))^(7/2),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{75 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{59 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (1-a x)^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (1-a x)^4 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{201 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{9 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{75 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{59 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (1-a x)^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (1-a x)^4 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{201 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{9 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^3*Sqrt[c - c/(a^2*x^2)]) - Sqrt[1 - 1/(a^2*x^2)]/(16*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^4) + Sqrt[1 - 1/(a^2*x^2)]/(2*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^3) - (59*Sqrt[1 - 1/(a^2*x^2)])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2) + (75*Sqrt[1 - 1/(a^2*x^2)])/(16*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) - Sqrt[1 - 1/(a^2*x^2)]/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (201*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(64*a*c^3*Sqrt[c - c/(a^2*x^2)]) - (9*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(64*a*c^3*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
855,1,322,0,0.172026,"\int e^{-\coth ^{-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^ArcCoth[a*x],x]","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c^3*Sqrt[c - c/(a^2*x^2)])/(6*a^7*Sqrt[1 - 1/(a^2*x^2)]*x^6) + (c^3*Sqrt[c - c/(a^2*x^2)])/(5*a^6*Sqrt[1 - 1/(a^2*x^2)]*x^5) + (3*c^3*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) - (c^3*Sqrt[c - c/(a^2*x^2)])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) - (3*c^3*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (3*c^3*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^3*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (c^3*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
856,1,238,0,0.1457825,"\int e^{-\coth ^{-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^ArcCoth[a*x],x]","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c^2*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) - (c^2*Sqrt[c - c/(a^2*x^2)])/(3*a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) - (c^2*Sqrt[c - c/(a^2*x^2)])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (2*c^2*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^2*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (c^2*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
857,1,147,0,0.1244963,"\int e^{-\coth ^{-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^ArcCoth[a*x],x]","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (c*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (c*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 75}"
858,1,68,0,0.1066061,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^ArcCoth[a*x],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
859,1,72,0,0.1130048,"\int \frac{e^{-\coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[1/(E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)]),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{a \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{a \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a^2*x^2)] - (Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(a*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
860,1,172,0,0.1428997,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))^(3/2)),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{5 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{5 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{4 a c \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c*Sqrt[c - c/(a^2*x^2)]) - Sqrt[1 - 1/(a^2*x^2)]/(2*a*c*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(4*a*c*Sqrt[c - c/(a^2*x^2)]) - (5*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(4*a*c*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
861,1,263,0,0.1694109,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))^(5/2)),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{a c^2 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{7 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{23 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{a c^2 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{7 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{23 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^2*Sqrt[c - c/(a^2*x^2)]) + Sqrt[1 - 1/(a^2*x^2)]/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + Sqrt[1 - 1/(a^2*x^2)]/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2) - Sqrt[1 - 1/(a^2*x^2)]/(a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (7*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)]) - (23*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
862,1,358,0,0.1982834,"\int \frac{e^{-\coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[1/(E^ArcCoth[a*x]*(c - c/(a^2*x^2))^(7/2)),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{5 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{11 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{24 a c^3 (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{19 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{51 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{5 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{11 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{24 a c^3 (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{19 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{51 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{32 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^3*Sqrt[c - c/(a^2*x^2)]) - Sqrt[1 - 1/(a^2*x^2)]/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2) + (5*Sqrt[1 - 1/(a^2*x^2)])/(16*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) - Sqrt[1 - 1/(a^2*x^2)]/(24*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^3) + (11*Sqrt[1 - 1/(a^2*x^2)])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2) - (3*Sqrt[1 - 1/(a^2*x^2)])/(2*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (19*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]) - (51*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
863,1,375,0,0.5412867,"\int e^{-2 \coth ^{-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*ArcCoth[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",15,11,24,0.4583,1,"{6167, 6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
864,1,293,0,0.4834585,"\int e^{-2 \coth ^{-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*ArcCoth[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",13,11,24,0.4583,1,"{6167, 6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
865,1,213,0,0.4460747,"\int e^{-2 \coth ^{-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*ArcCoth[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",11,11,24,0.4583,1,"{6167, 6159, 6129, 97, 149, 154, 157, 41, 216, 92, 208}"
866,1,116,0,0.3574855,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(2*ArcCoth[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",9,9,24,0.3750,1,"{6167, 6159, 6129, 102, 157, 41, 216, 92, 208}"
867,1,112,0,0.2905431,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[1/(E^(2*ArcCoth[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",7,7,24,0.2917,1,"{6167, 6159, 6129, 78, 50, 41, 216}"
868,1,124,0,0.4220615,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[1/(E^(2*ArcCoth[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",7,7,24,0.2917,1,"{6167, 6159, 6129, 98, 143, 41, 216}"
869,1,195,0,0.4513424,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[1/(E^(2*ArcCoth[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",9,8,24,0.3333,1,"{6167, 6159, 6129, 98, 150, 143, 41, 216}"
870,1,270,0,0.4893315,"\int \frac{e^{-2 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[1/(E^(2*ArcCoth[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",11,8,24,0.3333,1,"{6167, 6159, 6129, 98, 150, 143, 41, 216}"
871,1,322,0,0.1559471,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{c^4 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{8 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{7 a^8 x^7 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{8 a^9 x^8 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^4 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{8 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{7 a^8 x^7 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^4 \sqrt{c-\frac{c}{a^2 x^2}}}{8 a^9 x^8 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c^4*Sqrt[c - c/(a^2*x^2)])/(8*a^9*Sqrt[1 - 1/(a^2*x^2)]*x^8) + (3*c^4*Sqrt[c - c/(a^2*x^2)])/(7*a^8*Sqrt[1 - 1/(a^2*x^2)]*x^7) - (8*c^4*Sqrt[c - c/(a^2*x^2)])/(5*a^6*Sqrt[1 - 1/(a^2*x^2)]*x^5) + (3*c^4*Sqrt[c - c/(a^2*x^2)])/(2*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (2*c^4*Sqrt[c - c/(a^2*x^2)])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) - (4*c^4*Sqrt[c - c/(a^2*x^2)])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (c^4*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (3*c^4*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
872,1,324,0,0.1560967,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^3 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{5 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{5 a^6 x^5 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}{6 a^7 x^6 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c^3*Sqrt[c - c/(a^2*x^2)])/(6*a^7*Sqrt[1 - 1/(a^2*x^2)]*x^6) - (3*c^3*Sqrt[c - c/(a^2*x^2)])/(5*a^6*Sqrt[1 - 1/(a^2*x^2)]*x^5) + (c^3*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (5*c^3*Sqrt[c - c/(a^2*x^2)])/(3*a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) - (5*c^3*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (c^3*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^3*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (3*c^3*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
873,1,235,0,0.1388055,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c^2 x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^4 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}{4 a^5 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(c^2*Sqrt[c - c/(a^2*x^2)])/(4*a^5*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (c^2*Sqrt[c - c/(a^2*x^2)])/(a^4*Sqrt[1 - 1/(a^2*x^2)]*x^3) - (c^2*Sqrt[c - c/(a^2*x^2)])/(a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (2*c^2*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c^2*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (3*c^2*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 75}"
874,1,148,0,0.123455,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{c x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{c \sqrt{c-\frac{c}{a^2 x^2}}}{2 a^3 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 c \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(c*Sqrt[c - c/(a^2*x^2)])/(2*a^3*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (3*c*Sqrt[c - c/(a^2*x^2)])/(a^2*Sqrt[1 - 1/(a^2*x^2)]*x) + (c*Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (3*c*Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
875,1,107,0,0.1124327,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(3*ArcCoth[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]) - (4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 72}"
876,1,113,0,0.1249856,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)]),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}-\frac{2 \sqrt{1-\frac{1}{a^2 x^2}}}{a (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{a \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}-\frac{2 \sqrt{1-\frac{1}{a^2 x^2}}}{a (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{a \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/Sqrt[c - c/(a^2*x^2)] - (2*Sqrt[1 - 1/(a^2*x^2)])/(a*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) - (3*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(a*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 77}"
877,1,168,0,0.1406516,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{3/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(3/2)),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{a c (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{a c \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}}}{a c (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{3 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{a c \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c*Sqrt[c - c/(a^2*x^2)]) + Sqrt[1 - 1/(a^2*x^2)]/(2*a*c*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2) - (3*Sqrt[1 - 1/(a^2*x^2)])/(a*c*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) - (3*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(a*c*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
878,1,264,0,0.1658073,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{5/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(5/2)),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{31 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{9 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{6 a c^2 (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{49 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{31 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{9 \sqrt{1-\frac{1}{a^2 x^2}}}{8 a c^2 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{6 a c^2 (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{49 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{16 a c^2 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^2*Sqrt[c - c/(a^2*x^2)]) - Sqrt[1 - 1/(a^2*x^2)]/(6*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^3) + (9*Sqrt[1 - 1/(a^2*x^2)])/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2) - (31*Sqrt[1 - 1/(a^2*x^2)])/(8*a*c^2*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)]) - (49*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(16*a*c^2*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
879,1,357,0,0.1985469,"\int \frac{e^{-3 \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^{7/2}} \, dx","Int[1/(E^(3*ArcCoth[a*x])*(c - c/(a^2*x^2))^(7/2)),x]","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{75 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{59 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (a x+1)^4 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{9 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{201 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}","\frac{x \sqrt{1-\frac{1}{a^2 x^2}}}{c^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (1-a x) \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{75 \sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (a x+1) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{59 \sqrt{1-\frac{1}{a^2 x^2}}}{32 a c^3 (a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{2 a c^3 (a x+1)^3 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{\sqrt{1-\frac{1}{a^2 x^2}}}{16 a c^3 (a x+1)^4 \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{9 \sqrt{1-\frac{1}{a^2 x^2}} \log (1-a x)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}-\frac{201 \sqrt{1-\frac{1}{a^2 x^2}} \log (a x+1)}{64 a c^3 \sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*x)/(c^3*Sqrt[c - c/(a^2*x^2)]) + Sqrt[1 - 1/(a^2*x^2)]/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 - a*x)) + Sqrt[1 - 1/(a^2*x^2)]/(16*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^4) - Sqrt[1 - 1/(a^2*x^2)]/(2*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^3) + (59*Sqrt[1 - 1/(a^2*x^2)])/(32*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2) - (75*Sqrt[1 - 1/(a^2*x^2)])/(16*a*c^3*Sqrt[c - c/(a^2*x^2)]*(1 + a*x)) + (9*Sqrt[1 - 1/(a^2*x^2)]*Log[1 - a*x])/(64*a*c^3*Sqrt[c - c/(a^2*x^2)]) - (201*Sqrt[1 - 1/(a^2*x^2)]*Log[1 + a*x])/(64*a*c^3*Sqrt[c - c/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 88}"
880,1,80,0,0.2448712,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^m \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)]*x^m,x]","\frac{x^m \sqrt{c-\frac{c}{a^2 x^2}}}{a m \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-\frac{c}{a^2 x^2}}}{(m+1) \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^m \sqrt{c-\frac{c}{a^2 x^2}}}{a m \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^{m+1} \sqrt{c-\frac{c}{a^2 x^2}}}{(m+1) \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x^m)/(a*m*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^(1 + m))/((1 + m)*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6197, 6193, 43}"
881,1,76,0,0.2606664,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)]*x^2,x]","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x^2)/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^3)/(3*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6197, 6193, 43}"
882,1,71,0,0.1722915,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)]*x,x]","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/(a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^2)/(2*Sqrt[1 - 1/(a^2*x^2)])","A",3,2,23,0.08696,1,"{6197, 6193}"
883,1,67,0,0.0978782,"\int e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,22,0.1364,1,"{6197, 6193, 43}"
884,1,70,0,0.2501644,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[(E^ArcCoth[a*x]*Sqrt[c - c/(a^2*x^2)])/x,x]","\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - c/(a^2*x^2)]/(a*Sqrt[1 - 1/(a^2*x^2)]*x)) + (Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,25,0.1200,1,"{6197, 6193, 43}"
885,1,46,0,0.2439694,"\int \frac{e^{\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[(E^ArcCoth[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 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{(a x+1)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - c/(a^2*x^2)]*(1 + a*x)^2)/(2*a*Sqrt[1 - 1/(a^2*x^2)]*x^2)","A",3,3,25,0.1200,1,"{6197, 6193, 37}"
886,1,160,0,0.5575362,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Int[E^(2*ArcCoth[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",9,8,27,0.2963,1,"{6167, 6159, 6129, 90, 80, 50, 41, 216}"
887,1,123,0,0.4720209,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[E^(2*ArcCoth[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",8,7,27,0.2593,1,"{6167, 6159, 6129, 80, 50, 41, 216}"
888,1,98,0,0.3103317,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[E^(2*ArcCoth[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",7,6,25,0.2400,1,"{6167, 6159, 6129, 50, 41, 216}"
889,1,116,0,0.3409492,"\int e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(2*ArcCoth[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",9,9,24,0.3750,1,"{6167, 6159, 6129, 102, 157, 41, 216, 92, 208}"
890,1,117,0,0.5505375,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[(E^(2*ArcCoth[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",9,9,27,0.3333,1,"{6167, 6159, 6129, 98, 157, 41, 216, 92, 208}"
891,1,111,0,0.51467,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[(E^(2*ArcCoth[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",7,6,27,0.2222,1,"{6167, 6159, 6129, 94, 92, 208}"
892,1,137,0,0.528254,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[(E^(2*ArcCoth[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",8,7,27,0.2593,1,"{6167, 6159, 6129, 96, 94, 92, 208}"
893,1,156,0,0.556423,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[(E^(2*ArcCoth[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",10,8,27,0.2963,1,"{6167, 6159, 6129, 98, 151, 12, 92, 208}"
894,1,181,0,0.5754201,"\int \frac{e^{2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[(E^(2*ArcCoth[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",11,8,27,0.2963,1,"{6167, 6159, 6129, 98, 151, 12, 92, 208}"
895,1,186,0,0.2934783,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^3 \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)]*x^3,x]","\frac{x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - c/(a^2*x^2)]*x)/(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (2*Sqrt[c - c/(a^2*x^2)]*x^2)/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^3)/(a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^4)/(4*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/(a^4*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
896,1,152,0,0.286066,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x^2 \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)]*x^2,x]","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - c/(a^2*x^2)]*x)/(a^2*Sqrt[1 - 1/(a^2*x^2)]) + (3*Sqrt[c - c/(a^2*x^2)]*x^2)/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^3)/(3*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/(a^3*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6197, 6193, 77}"
897,1,113,0,0.1865945,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)]*x,x]","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(3*Sqrt[c - c/(a^2*x^2)]*x)/(a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^2)/(2*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/(a^2*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6197, 6193, 43}"
898,1,109,0,0.1107568,"\int e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 72}"
899,1,108,0,0.2716691,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)])/x,x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - c/(a^2*x^2)]/(a*Sqrt[1 - 1/(a^2*x^2)]*x) - (3*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
900,1,147,0,0.2767824,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)])/x^2,x]","\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - c/(a^2*x^2)]/(2*a*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (3*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*a*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
901,1,188,0,0.288252,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)])/x^3,x]","\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{3 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{3 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - c/(a^2*x^2)]/(3*a*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (3*Sqrt[c - c/(a^2*x^2)])/(2*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (4*a*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a^2*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*a^2*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
902,1,222,0,0.2947343,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)])/x^4,x]","\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - c/(a^2*x^2)]/(4*a*Sqrt[1 - 1/(a^2*x^2)]*x^4) + Sqrt[c - c/(a^2*x^2)]/(Sqrt[1 - 1/(a^2*x^2)]*x^3) + (2*a*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) + (4*a^2*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a^3*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*a^3*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
903,1,264,0,0.3044025,"\int \frac{e^{3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[(E^(3*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)])/x^5,x]","\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^4 \sqrt{c-\frac{c}{a^2 x^2}} \log (1-a x)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - c/(a^2*x^2)]/(5*a*Sqrt[1 - 1/(a^2*x^2)]*x^5) + (3*Sqrt[c - c/(a^2*x^2)])/(4*Sqrt[1 - 1/(a^2*x^2)]*x^4) + (4*a*Sqrt[c - c/(a^2*x^2)])/(3*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (2*a^2*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) + (4*a^3*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a^4*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*a^4*Sqrt[c - c/(a^2*x^2)]*Log[1 - a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
904,1,81,0,0.2494162,"\int e^{-\coth ^{-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^ArcCoth[a*x],x]","\frac{x^{m+1} \sqrt{c-\frac{c}{a^2 x^2}}}{(m+1) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^m \sqrt{c-\frac{c}{a^2 x^2}}}{a m \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^{m+1} \sqrt{c-\frac{c}{a^2 x^2}}}{(m+1) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^m \sqrt{c-\frac{c}{a^2 x^2}}}{a m \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-((Sqrt[c - c/(a^2*x^2)]*x^m)/(a*m*Sqrt[1 - 1/(a^2*x^2)])) + (Sqrt[c - c/(a^2*x^2)]*x^(1 + m))/((1 + m)*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6197, 6193, 43}"
905,1,76,0,0.2625057,"\int e^{-\coth ^{-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^ArcCoth[a*x],x]","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - c/(a^2*x^2)]*x^2)/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^3)/(3*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6197, 6193, 43}"
906,1,72,0,0.1762378,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x)/E^ArcCoth[a*x],x]","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"-((Sqrt[c - c/(a^2*x^2)]*x)/(a*Sqrt[1 - 1/(a^2*x^2)])) + (Sqrt[c - c/(a^2*x^2)]*x^2)/(2*Sqrt[1 - 1/(a^2*x^2)])","A",3,2,25,0.08000,1,"{6197, 6193}"
907,1,68,0,0.0994955,"\int e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^ArcCoth[a*x],x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] - (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 43}"
908,1,69,0,0.2556696,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^ArcCoth[a*x]*x),x]","\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"Sqrt[c - c/(a^2*x^2)]/(a*Sqrt[1 - 1/(a^2*x^2)]*x) + (Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 43}"
909,1,47,0,0.2461089,"\int \frac{e^{-\coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^ArcCoth[a*x]*x^2),x]","\frac{(1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{(1-a x)^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*(1 - a*x)^2)/(2*a*Sqrt[1 - 1/(a^2*x^2)]*x^2)","A",3,3,27,0.1111,1,"{6197, 6193, 37}"
910,1,163,0,0.5472073,"\int e^{-2 \coth ^{-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*ArcCoth[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",9,8,27,0.2963,1,"{6167, 6159, 6129, 90, 80, 50, 41, 216}"
911,1,124,0,0.4700534,"\int e^{-2 \coth ^{-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*ArcCoth[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",8,7,27,0.2593,1,"{6167, 6159, 6129, 80, 50, 41, 216}"
912,1,99,0,0.3053467,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x)/E^(2*ArcCoth[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",7,6,25,0.2400,1,"{6167, 6159, 6129, 50, 41, 216}"
913,1,116,0,0.3399775,"\int e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(2*ArcCoth[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",9,9,24,0.3750,1,"{6167, 6159, 6129, 102, 157, 41, 216, 92, 208}"
914,1,117,0,0.5254264,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcCoth[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",9,9,27,0.3333,1,"{6167, 6159, 6129, 98, 157, 41, 216, 92, 208}"
915,1,112,0,0.5233907,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcCoth[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",7,6,27,0.2222,1,"{6167, 6159, 6129, 94, 92, 208}"
916,1,140,0,0.5336979,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcCoth[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",8,7,27,0.2593,1,"{6167, 6159, 6129, 96, 94, 92, 208}"
917,1,156,0,0.5535792,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcCoth[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",10,8,27,0.2963,1,"{6167, 6159, 6129, 98, 151, 12, 92, 208}"
918,1,181,0,0.5852543,"\int \frac{e^{-2 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(2*ArcCoth[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",11,8,27,0.2963,1,"{6167, 6159, 6129, 98, 151, 12, 92, 208}"
919,1,186,0,0.2897745,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^4 \sqrt{c-\frac{c}{a^2 x^2}}}{4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^4 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-4*Sqrt[c - c/(a^2*x^2)]*x)/(a^3*Sqrt[1 - 1/(a^2*x^2)]) + (2*Sqrt[c - c/(a^2*x^2)]*x^2)/(a^2*Sqrt[1 - 1/(a^2*x^2)]) - (Sqrt[c - c/(a^2*x^2)]*x^3)/(a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^4)/(4*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/(a^4*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
920,1,151,0,0.2869422,"\int e^{-3 \coth ^{-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*ArcCoth[a*x]),x]","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^3 \sqrt{c-\frac{c}{a^2 x^2}}}{3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 x \sqrt{c-\frac{c}{a^2 x^2}}}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^3 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(4*Sqrt[c - c/(a^2*x^2)]*x)/(a^2*Sqrt[1 - 1/(a^2*x^2)]) - (3*Sqrt[c - c/(a^2*x^2)]*x^2)/(2*a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^3)/(3*Sqrt[1 - 1/(a^2*x^2)]) - (4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/(a^3*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,27,0.1111,1,"{6197, 6193, 77}"
921,1,112,0,0.1888489,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} x \, dx","Int[(Sqrt[c - c/(a^2*x^2)]*x)/E^(3*ArcCoth[a*x]),x]","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x^2 \sqrt{c-\frac{c}{a^2 x^2}}}{2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 x \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a^2 \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(-3*Sqrt[c - c/(a^2*x^2)]*x)/(a*Sqrt[1 - 1/(a^2*x^2)]) + (Sqrt[c - c/(a^2*x^2)]*x^2)/(2*Sqrt[1 - 1/(a^2*x^2)]) + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/(a^2*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,25,0.1200,1,"{6197, 6193, 43}"
922,1,107,0,0.1110377,"\int e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/E^(3*ArcCoth[a*x]),x]","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{x \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{a \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{a \sqrt{1-\frac{1}{a^2 x^2}}}",1,"(Sqrt[c - c/(a^2*x^2)]*x)/Sqrt[1 - 1/(a^2*x^2)] + (Sqrt[c - c/(a^2*x^2)]*Log[x])/(a*Sqrt[1 - 1/(a^2*x^2)]) - (4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/(a*Sqrt[1 - 1/(a^2*x^2)])","A",4,3,24,0.1250,1,"{6197, 6193, 72}"
923,1,108,0,0.2721521,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcCoth[a*x])*x),x]","-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{a x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"-(Sqrt[c - c/(a^2*x^2)]/(a*Sqrt[1 - 1/(a^2*x^2)]*x)) - (3*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
924,1,146,0,0.2780664,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^2} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcCoth[a*x])*x^2),x]","\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{2 a x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - c/(a^2*x^2)]/(2*a*Sqrt[1 - 1/(a^2*x^2)]*x^2) + (3*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*a*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] - (4*a*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
925,1,187,0,0.2798131,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^3} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcCoth[a*x])*x^3),x]","-\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{3 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{2 x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{3 a x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^2 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - c/(a^2*x^2)]/(3*a*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (3*Sqrt[c - c/(a^2*x^2)])/(2*Sqrt[1 - 1/(a^2*x^2)]*x^2) - (4*a*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a^2*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*a^2*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
926,1,221,0,0.287234,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^4} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcCoth[a*x])*x^4),x]","\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 a \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}","\frac{4 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2 a \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{x^3 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{4 a x^4 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^3 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - c/(a^2*x^2)]/(4*a*Sqrt[1 - 1/(a^2*x^2)]*x^4) + Sqrt[c - c/(a^2*x^2)]/(Sqrt[1 - 1/(a^2*x^2)]*x^3) - (2*a*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) + (4*a^2*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) + (4*a^3*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] - (4*a^3*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
927,1,263,0,0.2952753,"\int \frac{e^{-3 \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}}}{x^5} \, dx","Int[Sqrt[c - c/(a^2*x^2)]/(E^(3*ArcCoth[a*x])*x^5),x]","-\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}","-\frac{4 a^3 \sqrt{c-\frac{c}{a^2 x^2}}}{x \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{2 a^2 \sqrt{c-\frac{c}{a^2 x^2}}}{x^2 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a \sqrt{c-\frac{c}{a^2 x^2}}}{3 x^3 \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{3 \sqrt{c-\frac{c}{a^2 x^2}}}{4 x^4 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{\sqrt{c-\frac{c}{a^2 x^2}}}{5 a x^5 \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{4 a^4 \log (x) \sqrt{c-\frac{c}{a^2 x^2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}+\frac{4 a^4 \sqrt{c-\frac{c}{a^2 x^2}} \log (a x+1)}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"-Sqrt[c - c/(a^2*x^2)]/(5*a*Sqrt[1 - 1/(a^2*x^2)]*x^5) + (3*Sqrt[c - c/(a^2*x^2)])/(4*Sqrt[1 - 1/(a^2*x^2)]*x^4) - (4*a*Sqrt[c - c/(a^2*x^2)])/(3*Sqrt[1 - 1/(a^2*x^2)]*x^3) + (2*a^2*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x^2) - (4*a^3*Sqrt[c - c/(a^2*x^2)])/(Sqrt[1 - 1/(a^2*x^2)]*x) - (4*a^4*Sqrt[c - c/(a^2*x^2)]*Log[x])/Sqrt[1 - 1/(a^2*x^2)] + (4*a^4*Sqrt[c - c/(a^2*x^2)]*Log[1 + a*x])/Sqrt[1 - 1/(a^2*x^2)]","A",4,3,27,0.1111,1,"{6197, 6193, 88}"
928,1,81,0,0.0652096,"\int e^{n \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right) \, dx","Int[E^(n*ArcCoth[a*x])*(c - c/(a^2*x^2)),x]","-\frac{c 2^{2-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n+4}{2}} F_1\left(\frac{n+4}{2};\frac{n-2}{2},2;\frac{n+6}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+4)}","\frac{4 c \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \, _2F_1\left(2,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (2-n)}-\frac{c 2^{\frac{n}{2}+1} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1-\frac{n}{2},-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{a (2-n)}",1,"-((2^(2 - n/2)*c*(1 + 1/(a*x))^((4 + n)/2)*AppellF1[(4 + n)/2, (-2 + n)/2, 2, (6 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(4 + n)))","C",2,2,20,0.1000,0,"{6194, 136}"
929,1,164,0,0.1236793,"\int \frac{e^{n \coth ^{-1}(a x)}}{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(n*ArcCoth[a*x])/(c - c/(a^2*x^2)),x]","\frac{2 n \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c (2-n)}-\frac{(n+1) \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2}}{a c n}+\frac{x \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2}}{c}","\frac{2 \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a+\frac{1}{x}}{a-\frac{1}{x}}\right)}{a c}-\frac{(n+1) \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2}}{a c n}+\frac{x \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2}}{c}",1,"-(((1 + n)*(1 + 1/(a*x))^(n/2))/(a*c*n*(1 - 1/(a*x))^(n/2))) + ((1 + 1/(a*x))^(n/2)*x)/(c*(1 - 1/(a*x))^(n/2)) + (2*n*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*c*(2 - n))","A",5,5,22,0.2273,0,"{6194, 129, 155, 12, 131}"
930,1,303,0,0.2508657,"\int \frac{e^{n \coth ^{-1}(a x)}}{\left(c-\frac{c}{a^2 x^2}\right)^2} \, dx","Int[E^(n*ArcCoth[a*x])/(c - c/(a^2*x^2))^2,x]","\frac{2 n \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}} \, _2F_1\left(1,1-\frac{n}{2};2-\frac{n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a c^2 (2-n)}+\frac{\left(-n^3-n^2+4 n+6\right) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{a c^2 (2-n) n (n+2)}-\frac{\left(n^2+4 n+6\right) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{-n/2}}{a c^2 n (n+2)}-\frac{(n+3) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{a c^2 (n+2)}+\frac{x \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{c^2}","\frac{2 \left(\frac{1}{a x}+1\right)^{n/2} \left(1-\frac{1}{a x}\right)^{-n/2} \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};\frac{a+\frac{1}{x}}{a-\frac{1}{x}}\right)}{a c^2}+\frac{\left(-n^3-n^2+4 n+6\right) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{1-\frac{n}{2}}}{a c^2 (2-n) n (n+2)}-\frac{\left(n^2+4 n+6\right) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{-n/2}}{a c^2 n (n+2)}-\frac{(n+3) \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{a c^2 (n+2)}+\frac{x \left(\frac{1}{a x}+1\right)^{\frac{n-2}{2}} \left(1-\frac{1}{a x}\right)^{-\frac{n}{2}-1}}{c^2}",1,"-(((3 + n)*(1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2))/(a*c^2*(2 + n))) + ((6 + 4*n - n^2 - n^3)*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2))/(a*c^2*(2 - n)*n*(2 + n)) - ((6 + 4*n + n^2)*(1 + 1/(a*x))^((-2 + n)/2))/(a*c^2*n*(2 + n)*(1 - 1/(a*x))^(n/2)) + ((1 - 1/(a*x))^(-1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*x)/c^2 + (2*n*(1 - 1/(a*x))^(1 - n/2)*(1 + 1/(a*x))^((-2 + n)/2)*Hypergeometric2F1[1, 1 - n/2, 2 - n/2, (a - x^(-1))/(a + x^(-1))])/(a*c^2*(2 - n))","A",7,5,22,0.2273,0,"{6194, 129, 155, 12, 131}"
931,1,111,0,0.1546204,"\int e^{n \coth ^{-1}(a x)} \sqrt{c-\frac{c}{a^2 x^2}} \, dx","Int[E^(n*ArcCoth[a*x])*Sqrt[c - c/(a^2*x^2)],x]","-\frac{2^{\frac{3}{2}-\frac{n}{2}} \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n+3}{2}} F_1\left(\frac{n+3}{2};\frac{n-1}{2},2;\frac{n+5}{2};\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+3) \sqrt{1-\frac{1}{a^2 x^2}}}","\frac{2 n \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (1-n) \sqrt{1-\frac{1}{a^2 x^2}}}-\frac{2^{\frac{n+1}{2}} \sqrt{c-\frac{c}{a^2 x^2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(\frac{1-n}{2},\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{2 a}\right)}{a (1-n) \sqrt{1-\frac{1}{a^2 x^2}}}+\frac{x \sqrt{c-\frac{c}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n+1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{\sqrt{1-\frac{1}{a^2 x^2}}}",1,"-((2^(3/2 - n/2)*Sqrt[c - c/(a^2*x^2)]*(1 + 1/(a*x))^((3 + n)/2)*AppellF1[(3 + n)/2, (-1 + n)/2, 2, (5 + n)/2, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(3 + n)*Sqrt[1 - 1/(a^2*x^2)]))","C",3,3,24,0.1250,0,"{6197, 6194, 136}"
932,1,183,0,0.1653453,"\int \frac{e^{n \coth ^{-1}(a x)}}{\sqrt{c-\frac{c}{a^2 x^2}}} \, dx","Int[E^(n*ArcCoth[a*x])/Sqrt[c - c/(a^2*x^2)],x]","\frac{2 n \sqrt{1-\frac{1}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (1-n) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n+1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}","\frac{2 n \sqrt{1-\frac{1}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n-1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\frac{a-\frac{1}{x}}{a+\frac{1}{x}}\right)}{a (1-n) \sqrt{c-\frac{c}{a^2 x^2}}}+\frac{x \sqrt{1-\frac{1}{a^2 x^2}} \left(\frac{1}{a x}+1\right)^{\frac{n+1}{2}} \left(1-\frac{1}{a x}\right)^{\frac{1-n}{2}}}{\sqrt{c-\frac{c}{a^2 x^2}}}",1,"(Sqrt[1 - 1/(a^2*x^2)]*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((1 + n)/2)*x)/Sqrt[c - c/(a^2*x^2)] + (2*n*Sqrt[1 - 1/(a^2*x^2)]*(1 - 1/(a*x))^((1 - n)/2)*(1 + 1/(a*x))^((-1 + n)/2)*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, (a - x^(-1))/(a + x^(-1))])/(a*(1 - n)*Sqrt[c - c/(a^2*x^2)])","A",4,4,24,0.1667,1,"{6197, 6194, 96, 131}"
933,1,116,0,0.1148463,"\int e^{n \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[E^(n*ArcCoth[a*x])*(c - c/(a^2*x^2))^p,x]","-\frac{2^{-\frac{n}{2}+p+1} \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(\frac{1}{a x}+1\right)^{\frac{n}{2}+p+1} F_1\left(\frac{n}{2}+p+1;\frac{1}{2} (n-2 p),2;\frac{n}{2}+p+2;\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2 p+2)}","-\frac{2^{-\frac{n}{2}+p+1} \left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(c-\frac{c}{a^2 x^2}\right)^p \left(\frac{1}{a x}+1\right)^{\frac{n}{2}+p+1} F_1\left(\frac{n}{2}+p+1;\frac{1}{2} (n-2 p),2;\frac{n}{2}+p+2;\frac{a+\frac{1}{x}}{2 a},1+\frac{1}{a x}\right)}{a (n+2 p+2)}",1,"-((2^(1 - n/2 + p)*(c - c/(a^2*x^2))^p*(1 + 1/(a*x))^(1 + n/2 + p)*AppellF1[1 + n/2 + p, (n - 2*p)/2, 2, 2 + n/2 + p, (a + x^(-1))/(2*a), 1 + 1/(a*x)])/(a*(2 + n + 2*p)*(1 - 1/(a^2*x^2))^p))","A",3,3,22,0.1364,1,"{6197, 6194, 136}"
934,1,76,0,0.0850554,"\int e^{-2 p \coth ^{-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*ArcCoth[a*x]),x]","\frac{\left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(1-\frac{1}{a x}\right)^{2 p+1} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);1-\frac{1}{a x}\right)}{a (2 p+1)}","\frac{\left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(1-\frac{1}{a x}\right)^{2 p+1} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);1-\frac{1}{a x}\right)}{a (2 p+1)}",1,"((c - c/(a^2*x^2))^p*(1 - 1/(a*x))^(1 + 2*p)*Hypergeometric2F1[2, 1 + 2*p, 2*(1 + p), 1 - 1/(a*x)])/(a*(1 + 2*p)*(1 - 1/(a^2*x^2))^p)","A",3,3,23,0.1304,1,"{6197, 6194, 65}"
935,1,75,0,0.0841536,"\int e^{2 p \coth ^{-1}(a x)} \left(c-\frac{c}{a^2 x^2}\right)^p \, dx","Int[E^(2*p*ArcCoth[a*x])*(c - c/(a^2*x^2))^p,x]","-\frac{\left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{1}{a x}+1\right)^{2 p+1} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);1+\frac{1}{a x}\right)}{a (2 p+1)}","-\frac{\left(1-\frac{1}{a^2 x^2}\right)^{-p} \left(\frac{1}{a x}+1\right)^{2 p+1} \left(c-\frac{c}{a^2 x^2}\right)^p \, _2F_1\left(2,2 p+1;2 (p+1);1+\frac{1}{a x}\right)}{a (2 p+1)}",1,"-(((c - c/(a^2*x^2))^p*(1 + 1/(a*x))^(1 + 2*p)*Hypergeometric2F1[2, 1 + 2*p, 2*(1 + p), 1 + 1/(a*x)])/(a*(1 + 2*p)*(1 - 1/(a^2*x^2))^p))","A",3,3,23,0.1304,1,"{6197, 6194, 65}"