1,1,72,0,0.0441345,"\int x^4 \sinh ^{-1}(a x) \, dx","Int[x^4*ArcSinh[a*x],x]","-\frac{\left(a^2 x^2+1\right)^{5/2}}{25 a^5}+\frac{2 \left(a^2 x^2+1\right)^{3/2}}{15 a^5}-\frac{\sqrt{a^2 x^2+1}}{5 a^5}+\frac{1}{5} x^5 \sinh ^{-1}(a x)","-\frac{\left(a^2 x^2+1\right)^{5/2}}{25 a^5}+\frac{2 \left(a^2 x^2+1\right)^{3/2}}{15 a^5}-\frac{\sqrt{a^2 x^2+1}}{5 a^5}+\frac{1}{5} x^5 \sinh ^{-1}(a x)",1,"-Sqrt[1 + a^2*x^2]/(5*a^5) + (2*(1 + a^2*x^2)^(3/2))/(15*a^5) - (1 + a^2*x^2)^(5/2)/(25*a^5) + (x^5*ArcSinh[a*x])/5","A",4,3,8,0.3750,1,"{5661, 266, 43}"
2,1,67,0,0.0264488,"\int x^3 \sinh ^{-1}(a x) \, dx","Int[x^3*ArcSinh[a*x],x]","-\frac{x^3 \sqrt{a^2 x^2+1}}{16 a}+\frac{3 x \sqrt{a^2 x^2+1}}{32 a^3}-\frac{3 \sinh ^{-1}(a x)}{32 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)","-\frac{x^3 \sqrt{a^2 x^2+1}}{16 a}+\frac{3 x \sqrt{a^2 x^2+1}}{32 a^3}-\frac{3 \sinh ^{-1}(a x)}{32 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)",1,"(3*x*Sqrt[1 + a^2*x^2])/(32*a^3) - (x^3*Sqrt[1 + a^2*x^2])/(16*a) - (3*ArcSinh[a*x])/(32*a^4) + (x^4*ArcSinh[a*x])/4","A",4,3,8,0.3750,1,"{5661, 321, 215}"
3,1,52,0,0.0345017,"\int x^2 \sinh ^{-1}(a x) \, dx","Int[x^2*ArcSinh[a*x],x]","-\frac{\left(a^2 x^2+1\right)^{3/2}}{9 a^3}+\frac{\sqrt{a^2 x^2+1}}{3 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)","-\frac{\left(a^2 x^2+1\right)^{3/2}}{9 a^3}+\frac{\sqrt{a^2 x^2+1}}{3 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)",1,"Sqrt[1 + a^2*x^2]/(3*a^3) - (1 + a^2*x^2)^(3/2)/(9*a^3) + (x^3*ArcSinh[a*x])/3","A",4,3,8,0.3750,1,"{5661, 266, 43}"
4,1,44,0,0.0156758,"\int x \sinh ^{-1}(a x) \, dx","Int[x*ArcSinh[a*x],x]","-\frac{x \sqrt{a^2 x^2+1}}{4 a}+\frac{\sinh ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)","-\frac{x \sqrt{a^2 x^2+1}}{4 a}+\frac{\sinh ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)",1,"-(x*Sqrt[1 + a^2*x^2])/(4*a) + ArcSinh[a*x]/(4*a^2) + (x^2*ArcSinh[a*x])/2","A",3,3,6,0.5000,1,"{5661, 321, 215}"
5,1,25,0,0.0075172,"\int \sinh ^{-1}(a x) \, dx","Int[ArcSinh[a*x],x]","x \sinh ^{-1}(a x)-\frac{\sqrt{a^2 x^2+1}}{a}","x \sinh ^{-1}(a x)-\frac{\sqrt{a^2 x^2+1}}{a}",1,"-(Sqrt[1 + a^2*x^2]/a) + x*ArcSinh[a*x]","A",2,2,4,0.5000,1,"{5653, 261}"
6,1,43,0,0.0601096,"\int \frac{\sinh ^{-1}(a x)}{x} \, dx","Int[ArcSinh[a*x]/x,x]","\frac{1}{2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{2} \sinh ^{-1}(a x)^2+\sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)","\frac{1}{2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{2} \sinh ^{-1}(a x)^2+\sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)",1,"-ArcSinh[a*x]^2/2 + ArcSinh[a*x]*Log[1 - E^(2*ArcSinh[a*x])] + PolyLog[2, E^(2*ArcSinh[a*x])]/2","A",5,5,8,0.6250,1,"{5659, 3716, 2190, 2279, 2391}"
7,1,27,0,0.0214737,"\int \frac{\sinh ^{-1}(a x)}{x^2} \, dx","Int[ArcSinh[a*x]/x^2,x]","-a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)}{x}","-a \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)}{x}",1,"-(ArcSinh[a*x]/x) - a*ArcTanh[Sqrt[1 + a^2*x^2]]","A",4,4,8,0.5000,1,"{5661, 266, 63, 208}"
8,1,33,0,0.0136569,"\int \frac{\sinh ^{-1}(a x)}{x^3} \, dx","Int[ArcSinh[a*x]/x^3,x]","-\frac{a \sqrt{a^2 x^2+1}}{2 x}-\frac{\sinh ^{-1}(a x)}{2 x^2}","-\frac{a \sqrt{a^2 x^2+1}}{2 x}-\frac{\sinh ^{-1}(a x)}{2 x^2}",1,"-(a*Sqrt[1 + a^2*x^2])/(2*x) - ArcSinh[a*x]/(2*x^2)","A",2,2,8,0.2500,1,"{5661, 264}"
9,1,54,0,0.032432,"\int \frac{\sinh ^{-1}(a x)}{x^4} \, dx","Int[ArcSinh[a*x]/x^4,x]","-\frac{a \sqrt{a^2 x^2+1}}{6 x^2}+\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)}{3 x^3}","-\frac{a \sqrt{a^2 x^2+1}}{6 x^2}+\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)}{3 x^3}",1,"-(a*Sqrt[1 + a^2*x^2])/(6*x^2) - ArcSinh[a*x]/(3*x^3) + (a^3*ArcTanh[Sqrt[1 + a^2*x^2]])/6","A",5,5,8,0.6250,1,"{5661, 266, 51, 63, 208}"
10,1,56,0,0.0204082,"\int \frac{\sinh ^{-1}(a x)}{x^5} \, dx","Int[ArcSinh[a*x]/x^5,x]","\frac{a^3 \sqrt{a^2 x^2+1}}{6 x}-\frac{a \sqrt{a^2 x^2+1}}{12 x^3}-\frac{\sinh ^{-1}(a x)}{4 x^4}","\frac{a^3 \sqrt{a^2 x^2+1}}{6 x}-\frac{a \sqrt{a^2 x^2+1}}{12 x^3}-\frac{\sinh ^{-1}(a x)}{4 x^4}",1,"-(a*Sqrt[1 + a^2*x^2])/(12*x^3) + (a^3*Sqrt[1 + a^2*x^2])/(6*x) - ArcSinh[a*x]/(4*x^4)","A",3,3,8,0.3750,1,"{5661, 271, 264}"
11,1,77,0,0.0449983,"\int \frac{\sinh ^{-1}(a x)}{x^6} \, dx","Int[ArcSinh[a*x]/x^6,x]","\frac{3 a^3 \sqrt{a^2 x^2+1}}{40 x^2}-\frac{a \sqrt{a^2 x^2+1}}{20 x^4}-\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)}{5 x^5}","\frac{3 a^3 \sqrt{a^2 x^2+1}}{40 x^2}-\frac{a \sqrt{a^2 x^2+1}}{20 x^4}-\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)}{5 x^5}",1,"-(a*Sqrt[1 + a^2*x^2])/(20*x^4) + (3*a^3*Sqrt[1 + a^2*x^2])/(40*x^2) - ArcSinh[a*x]/(5*x^5) - (3*a^5*ArcTanh[Sqrt[1 + a^2*x^2]])/40","A",6,5,8,0.6250,1,"{5661, 266, 51, 63, 208}"
12,1,117,0,0.1882009,"\int x^4 \sinh ^{-1}(a x)^2 \, dx","Int[x^4*ArcSinh[a*x]^2,x]","-\frac{8 x^3}{225 a^2}-\frac{2 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{25 a}+\frac{8 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{75 a^3}-\frac{16 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{75 a^5}+\frac{16 x}{75 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^2+\frac{2 x^5}{125}","-\frac{8 x^3}{225 a^2}-\frac{2 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{25 a}+\frac{8 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{75 a^3}-\frac{16 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{75 a^5}+\frac{16 x}{75 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^2+\frac{2 x^5}{125}",1,"(16*x)/(75*a^4) - (8*x^3)/(225*a^2) + (2*x^5)/125 - (16*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(75*a^5) + (8*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(75*a^3) - (2*x^4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(25*a) + (x^5*ArcSinh[a*x]^2)/5","A",7,5,10,0.5000,1,"{5661, 5758, 5717, 8, 30}"
13,1,96,0,0.1653106,"\int x^3 \sinh ^{-1}(a x)^2 \, dx","Int[x^3*ArcSinh[a*x]^2,x]","-\frac{3 x^2}{32 a^2}-\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{8 a}+\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{16 a^3}-\frac{3 \sinh ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^2+\frac{x^4}{32}","-\frac{3 x^2}{32 a^2}-\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{8 a}+\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{16 a^3}-\frac{3 \sinh ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^2+\frac{x^4}{32}",1,"(-3*x^2)/(32*a^2) + x^4/32 + (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(16*a^3) - (x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(8*a) - (3*ArcSinh[a*x]^2)/(32*a^4) + (x^4*ArcSinh[a*x]^2)/4","A",6,4,10,0.4000,1,"{5661, 5758, 5675, 30}"
14,1,80,0,0.1229783,"\int x^2 \sinh ^{-1}(a x)^2 \, dx","Int[x^2*ArcSinh[a*x]^2,x]","-\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a}+\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^3}-\frac{4 x}{9 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^2+\frac{2 x^3}{27}","-\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a}+\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^3}-\frac{4 x}{9 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^2+\frac{2 x^3}{27}",1,"(-4*x)/(9*a^2) + (2*x^3)/27 + (4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(9*a^3) - (2*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(9*a) + (x^3*ArcSinh[a*x]^2)/3","A",5,5,10,0.5000,1,"{5661, 5758, 5717, 8, 30}"
15,1,59,0,0.0918002,"\int x \sinh ^{-1}(a x)^2 \, dx","Int[x*ArcSinh[a*x]^2,x]","-\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a}+\frac{\sinh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^2+\frac{x^2}{4}","-\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a}+\frac{\sinh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^2+\frac{x^2}{4}",1,"x^2/4 - (x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(2*a) + ArcSinh[a*x]^2/(4*a^2) + (x^2*ArcSinh[a*x]^2)/2","A",4,4,8,0.5000,1,"{5661, 5758, 5675, 30}"
16,1,34,0,0.0451432,"\int \sinh ^{-1}(a x)^2 \, dx","Int[ArcSinh[a*x]^2,x]","-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+x \sinh ^{-1}(a x)^2+2 x","-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+x \sinh ^{-1}(a x)^2+2 x",1,"2*x - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a + x*ArcSinh[a*x]^2","A",3,3,6,0.5000,1,"{5653, 5717, 8}"
17,1,60,0,0.0967535,"\int \frac{\sinh ^{-1}(a x)^2}{x} \, dx","Int[ArcSinh[a*x]^2/x,x]","\sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{3} \sinh ^{-1}(a x)^3+\sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)","\sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{3} \sinh ^{-1}(a x)^3+\sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)",1,"-ArcSinh[a*x]^3/3 + ArcSinh[a*x]^2*Log[1 - E^(2*ArcSinh[a*x])] + ArcSinh[a*x]*PolyLog[2, E^(2*ArcSinh[a*x])] - PolyLog[3, E^(2*ArcSinh[a*x])]/2","A",6,6,10,0.6000,1,"{5659, 3716, 2190, 2531, 2282, 6589}"
18,1,50,0,0.0997795,"\int \frac{\sinh ^{-1}(a x)^2}{x^2} \, dx","Int[ArcSinh[a*x]^2/x^2,x]","-2 a \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+2 a \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^2}{x}-4 a \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-2 a \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+2 a \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^2}{x}-4 a \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-(ArcSinh[a*x]^2/x) - 4*a*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] - 2*a*PolyLog[2, -E^ArcSinh[a*x]] + 2*a*PolyLog[2, E^ArcSinh[a*x]]","A",7,5,10,0.5000,1,"{5661, 5760, 4182, 2279, 2391}"
19,1,43,0,0.0804655,"\int \frac{\sinh ^{-1}(a x)^2}{x^3} \, dx","Int[ArcSinh[a*x]^2/x^3,x]","-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{x}+a^2 \log (x)-\frac{\sinh ^{-1}(a x)^2}{2 x^2}","-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{x}+a^2 \log (x)-\frac{\sinh ^{-1}(a x)^2}{2 x^2}",1,"-((a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/x) - ArcSinh[a*x]^2/(2*x^2) + a^2*Log[x]","A",3,3,10,0.3000,1,"{5661, 5723, 29}"
20,1,99,0,0.1625891,"\int \frac{\sinh ^{-1}(a x)^2}{x^4} \, dx","Int[ArcSinh[a*x]^2/x^4,x]","\frac{1}{3} a^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{3} a^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 x^2}-\frac{a^2}{3 x}+\frac{2}{3} a^3 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^2}{3 x^3}","\frac{1}{3} a^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{3} a^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 x^2}-\frac{a^2}{3 x}+\frac{2}{3} a^3 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^2}{3 x^3}",1,"-a^2/(3*x) - (a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(3*x^2) - ArcSinh[a*x]^2/(3*x^3) + (2*a^3*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]])/3 + (a^3*PolyLog[2, -E^ArcSinh[a*x]])/3 - (a^3*PolyLog[2, E^ArcSinh[a*x]])/3","A",9,7,10,0.7000,1,"{5661, 5747, 5760, 4182, 2279, 2391, 30}"
21,1,85,0,0.1379216,"\int \frac{\sinh ^{-1}(a x)^2}{x^5} \, dx","Int[ArcSinh[a*x]^2/x^5,x]","-\frac{a^2}{12 x^2}+\frac{a^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 x}-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{6 x^3}-\frac{1}{3} a^4 \log (x)-\frac{\sinh ^{-1}(a x)^2}{4 x^4}","-\frac{a^2}{12 x^2}+\frac{a^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 x}-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{6 x^3}-\frac{1}{3} a^4 \log (x)-\frac{\sinh ^{-1}(a x)^2}{4 x^4}",1,"-a^2/(12*x^2) - (a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(6*x^3) + (a^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(3*x) - ArcSinh[a*x]^2/(4*x^4) - (a^4*Log[x])/3","A",5,5,10,0.5000,1,"{5661, 5747, 5723, 29, 30}"
22,1,195,0,0.3659599,"\int x^4 \sinh ^{-1}(a x)^3 \, dx","Int[x^4*ArcSinh[a*x]^3,x]","-\frac{6 \left(a^2 x^2+1\right)^{5/2}}{625 a^5}+\frac{76 \left(a^2 x^2+1\right)^{3/2}}{1125 a^5}-\frac{298 \sqrt{a^2 x^2+1}}{375 a^5}-\frac{3 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a}-\frac{8 x^3 \sinh ^{-1}(a x)}{75 a^2}+\frac{4 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a^3}-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a^5}+\frac{16 x \sinh ^{-1}(a x)}{25 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^3+\frac{6}{125} x^5 \sinh ^{-1}(a x)","-\frac{6 \left(a^2 x^2+1\right)^{5/2}}{625 a^5}+\frac{76 \left(a^2 x^2+1\right)^{3/2}}{1125 a^5}-\frac{298 \sqrt{a^2 x^2+1}}{375 a^5}-\frac{3 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a}-\frac{8 x^3 \sinh ^{-1}(a x)}{75 a^2}+\frac{4 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a^3}-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a^5}+\frac{16 x \sinh ^{-1}(a x)}{25 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^3+\frac{6}{125} x^5 \sinh ^{-1}(a x)",1,"(-298*Sqrt[1 + a^2*x^2])/(375*a^5) + (76*(1 + a^2*x^2)^(3/2))/(1125*a^5) - (6*(1 + a^2*x^2)^(5/2))/(625*a^5) + (16*x*ArcSinh[a*x])/(25*a^4) - (8*x^3*ArcSinh[a*x])/(75*a^2) + (6*x^5*ArcSinh[a*x])/125 - (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(25*a^5) + (4*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(25*a^3) - (3*x^4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(25*a) + (x^5*ArcSinh[a*x]^3)/5","A",14,7,10,0.7000,1,"{5661, 5758, 5717, 5653, 261, 266, 43}"
23,1,163,0,0.2983679,"\int x^3 \sinh ^{-1}(a x)^3 \, dx","Int[x^3*ArcSinh[a*x]^3,x]","-\frac{3 x^3 \sqrt{a^2 x^2+1}}{128 a}+\frac{45 x \sqrt{a^2 x^2+1}}{256 a^3}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{16 a}-\frac{9 x^2 \sinh ^{-1}(a x)}{32 a^2}+\frac{9 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{32 a^3}-\frac{3 \sinh ^{-1}(a x)^3}{32 a^4}-\frac{45 \sinh ^{-1}(a x)}{256 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^3+\frac{3}{32} x^4 \sinh ^{-1}(a x)","-\frac{3 x^3 \sqrt{a^2 x^2+1}}{128 a}+\frac{45 x \sqrt{a^2 x^2+1}}{256 a^3}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{16 a}-\frac{9 x^2 \sinh ^{-1}(a x)}{32 a^2}+\frac{9 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{32 a^3}-\frac{3 \sinh ^{-1}(a x)^3}{32 a^4}-\frac{45 \sinh ^{-1}(a x)}{256 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^3+\frac{3}{32} x^4 \sinh ^{-1}(a x)",1,"(45*x*Sqrt[1 + a^2*x^2])/(256*a^3) - (3*x^3*Sqrt[1 + a^2*x^2])/(128*a) - (45*ArcSinh[a*x])/(256*a^4) - (9*x^2*ArcSinh[a*x])/(32*a^2) + (3*x^4*ArcSinh[a*x])/32 + (9*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(32*a^3) - (3*x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(16*a) - (3*ArcSinh[a*x]^3)/(32*a^4) + (x^4*ArcSinh[a*x]^3)/4","A",11,5,10,0.5000,1,"{5661, 5758, 5675, 321, 215}"
24,1,132,0,0.2214701,"\int x^2 \sinh ^{-1}(a x)^3 \, dx","Int[x^2*ArcSinh[a*x]^3,x]","-\frac{2 \left(a^2 x^2+1\right)^{3/2}}{27 a^3}+\frac{14 \sqrt{a^2 x^2+1}}{9 a^3}-\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a}+\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^3}-\frac{4 x \sinh ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^3+\frac{2}{9} x^3 \sinh ^{-1}(a x)","-\frac{2 \left(a^2 x^2+1\right)^{3/2}}{27 a^3}+\frac{14 \sqrt{a^2 x^2+1}}{9 a^3}-\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a}+\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^3}-\frac{4 x \sinh ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^3+\frac{2}{9} x^3 \sinh ^{-1}(a x)",1,"(14*Sqrt[1 + a^2*x^2])/(9*a^3) - (2*(1 + a^2*x^2)^(3/2))/(27*a^3) - (4*x*ArcSinh[a*x])/(3*a^2) + (2*x^3*ArcSinh[a*x])/9 + (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(3*a^3) - (x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(3*a) + (x^3*ArcSinh[a*x]^3)/3","A",9,7,10,0.7000,1,"{5661, 5758, 5717, 5653, 261, 266, 43}"
25,1,97,0,0.1526151,"\int x \sinh ^{-1}(a x)^3 \, dx","Int[x*ArcSinh[a*x]^3,x]","-\frac{3 x \sqrt{a^2 x^2+1}}{8 a}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{4 a}+\frac{\sinh ^{-1}(a x)^3}{4 a^2}+\frac{3 \sinh ^{-1}(a x)}{8 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^3+\frac{3}{4} x^2 \sinh ^{-1}(a x)","-\frac{3 x \sqrt{a^2 x^2+1}}{8 a}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{4 a}+\frac{\sinh ^{-1}(a x)^3}{4 a^2}+\frac{3 \sinh ^{-1}(a x)}{8 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^3+\frac{3}{4} x^2 \sinh ^{-1}(a x)",1,"(-3*x*Sqrt[1 + a^2*x^2])/(8*a) + (3*ArcSinh[a*x])/(8*a^2) + (3*x^2*ArcSinh[a*x])/4 - (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(4*a) + ArcSinh[a*x]^3/(4*a^2) + (x^2*ArcSinh[a*x]^3)/2","A",6,5,8,0.6250,1,"{5661, 5758, 5675, 321, 215}"
26,1,58,0,0.0808533,"\int \sinh ^{-1}(a x)^3 \, dx","Int[ArcSinh[a*x]^3,x]","-\frac{6 \sqrt{a^2 x^2+1}}{a}-\frac{3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{a}+x \sinh ^{-1}(a x)^3+6 x \sinh ^{-1}(a x)","-\frac{6 \sqrt{a^2 x^2+1}}{a}-\frac{3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{a}+x \sinh ^{-1}(a x)^3+6 x \sinh ^{-1}(a x)",1,"(-6*Sqrt[1 + a^2*x^2])/a + 6*x*ArcSinh[a*x] - (3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/a + x*ArcSinh[a*x]^3","A",4,3,6,0.5000,1,"{5653, 5717, 261}"
27,1,83,0,0.1123345,"\int \frac{\sinh ^{-1}(a x)^3}{x} \, dx","Int[ArcSinh[a*x]^3/x,x]","\frac{3}{2} \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)+\frac{3}{4} \text{PolyLog}\left(4,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{4} \sinh ^{-1}(a x)^4+\sinh ^{-1}(a x)^3 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)","\frac{3}{2} \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)+\frac{3}{4} \text{PolyLog}\left(4,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{4} \sinh ^{-1}(a x)^4+\sinh ^{-1}(a x)^3 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)",1,"-ArcSinh[a*x]^4/4 + ArcSinh[a*x]^3*Log[1 - E^(2*ArcSinh[a*x])] + (3*ArcSinh[a*x]^2*PolyLog[2, E^(2*ArcSinh[a*x])])/2 - (3*ArcSinh[a*x]*PolyLog[3, E^(2*ArcSinh[a*x])])/2 + (3*PolyLog[4, E^(2*ArcSinh[a*x])])/4","A",7,7,10,0.7000,1,"{5659, 3716, 2190, 2531, 6609, 2282, 6589}"
28,1,84,0,0.1591376,"\int \frac{\sinh ^{-1}(a x)^3}{x^2} \, dx","Int[ArcSinh[a*x]^3/x^2,x]","-6 a \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+6 a \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{x}-6 a \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-6 a \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+6 a \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{x}-6 a \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-(ArcSinh[a*x]^3/x) - 6*a*ArcSinh[a*x]^2*ArcTanh[E^ArcSinh[a*x]] - 6*a*ArcSinh[a*x]*PolyLog[2, -E^ArcSinh[a*x]] + 6*a*ArcSinh[a*x]*PolyLog[2, E^ArcSinh[a*x]] + 6*a*PolyLog[3, -E^ArcSinh[a*x]] - 6*a*PolyLog[3, E^ArcSinh[a*x]]","A",9,6,10,0.6000,1,"{5661, 5760, 4182, 2531, 2282, 6589}"
29,1,93,0,0.1681331,"\int \frac{\sinh ^{-1}(a x)^3}{x^3} \, dx","Int[ArcSinh[a*x]^3/x^3,x]","\frac{3}{2} a^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3 a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x}-\frac{3}{2} a^2 \sinh ^{-1}(a x)^2+3 a^2 \sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{2 x^2}","\frac{3}{2} a^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3 a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x}-\frac{3}{2} a^2 \sinh ^{-1}(a x)^2+3 a^2 \sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{2 x^2}",1,"(-3*a^2*ArcSinh[a*x]^2)/2 - (3*a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(2*x) - ArcSinh[a*x]^3/(2*x^2) + 3*a^2*ArcSinh[a*x]*Log[1 - E^(2*ArcSinh[a*x])] + (3*a^2*PolyLog[2, E^(2*ArcSinh[a*x])])/2","A",7,7,10,0.7000,1,"{5661, 5723, 5659, 3716, 2190, 2279, 2391}"
30,1,151,0,0.2771812,"\int \frac{\sinh ^{-1}(a x)^3}{x^4} \, dx","Int[ArcSinh[a*x]^3/x^4,x]","a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-a^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+a^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x^2}-a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{a^2 \sinh ^{-1}(a x)}{x}+a^3 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{3 x^3}","a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-a^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+a^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x^2}-a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{a^2 \sinh ^{-1}(a x)}{x}+a^3 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{3 x^3}",1,"-((a^2*ArcSinh[a*x])/x) - (a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(2*x^2) - ArcSinh[a*x]^3/(3*x^3) + a^3*ArcSinh[a*x]^2*ArcTanh[E^ArcSinh[a*x]] - a^3*ArcTanh[Sqrt[1 + a^2*x^2]] + a^3*ArcSinh[a*x]*PolyLog[2, -E^ArcSinh[a*x]] - a^3*ArcSinh[a*x]*PolyLog[2, E^ArcSinh[a*x]] - a^3*PolyLog[3, -E^ArcSinh[a*x]] + a^3*PolyLog[3, E^ArcSinh[a*x]]","A",14,10,10,1.000,1,"{5661, 5747, 5760, 4182, 2531, 2282, 6589, 266, 63, 208}"
31,1,159,0,0.2858836,"\int \frac{\sinh ^{-1}(a x)^3}{x^5} \, dx","Int[ArcSinh[a*x]^3/x^5,x]","-\frac{1}{2} a^4 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{a^3 \sqrt{a^2 x^2+1}}{4 x}+\frac{a^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x}-\frac{a^2 \sinh ^{-1}(a x)}{4 x^2}-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{4 x^3}+\frac{1}{2} a^4 \sinh ^{-1}(a x)^2-a^4 \sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{4 x^4}","-\frac{1}{2} a^4 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{a^3 \sqrt{a^2 x^2+1}}{4 x}+\frac{a^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x}-\frac{a^2 \sinh ^{-1}(a x)}{4 x^2}-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{4 x^3}+\frac{1}{2} a^4 \sinh ^{-1}(a x)^2-a^4 \sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{4 x^4}",1,"-(a^3*Sqrt[1 + a^2*x^2])/(4*x) - (a^2*ArcSinh[a*x])/(4*x^2) + (a^4*ArcSinh[a*x]^2)/2 - (a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(4*x^3) + (a^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(2*x) - ArcSinh[a*x]^3/(4*x^4) - a^4*ArcSinh[a*x]*Log[1 - E^(2*ArcSinh[a*x])] - (a^4*PolyLog[2, E^(2*ArcSinh[a*x])])/2","A",10,9,10,0.9000,1,"{5661, 5747, 5723, 5659, 3716, 2190, 2279, 2391, 264}"
32,1,276,0,0.8557825,"\int x^5 \sinh ^{-1}(a x)^4 \, dx","Int[x^5*ArcSinh[a*x]^4,x]","-\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}-\frac{x^5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a}-\frac{x^5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{54 a}-\frac{5 x^4 \sinh ^{-1}(a x)^2}{48 a^2}+\frac{5 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{36 a^3}+\frac{65 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{864 a^3}+\frac{5 x^2 \sinh ^{-1}(a x)^2}{16 a^4}-\frac{5 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{24 a^5}-\frac{245 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{576 a^5}+\frac{5 \sinh ^{-1}(a x)^4}{96 a^6}+\frac{245 \sinh ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \sinh ^{-1}(a x)^4+\frac{1}{18} x^6 \sinh ^{-1}(a x)^2+\frac{x^6}{324}","-\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}-\frac{x^5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a}-\frac{x^5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{54 a}-\frac{5 x^4 \sinh ^{-1}(a x)^2}{48 a^2}+\frac{5 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{36 a^3}+\frac{65 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{864 a^3}+\frac{5 x^2 \sinh ^{-1}(a x)^2}{16 a^4}-\frac{5 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{24 a^5}-\frac{245 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{576 a^5}+\frac{5 \sinh ^{-1}(a x)^4}{96 a^6}+\frac{245 \sinh ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \sinh ^{-1}(a x)^4+\frac{1}{18} x^6 \sinh ^{-1}(a x)^2+\frac{x^6}{324}",1,"(245*x^2)/(1152*a^4) - (65*x^4)/(3456*a^2) + x^6/324 - (245*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(576*a^5) + (65*x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(864*a^3) - (x^5*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(54*a) + (245*ArcSinh[a*x]^2)/(1152*a^6) + (5*x^2*ArcSinh[a*x]^2)/(16*a^4) - (5*x^4*ArcSinh[a*x]^2)/(48*a^2) + (x^6*ArcSinh[a*x]^2)/18 - (5*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(24*a^5) + (5*x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(36*a^3) - (x^5*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(9*a) + (5*ArcSinh[a*x]^4)/(96*a^6) + (x^6*ArcSinh[a*x]^4)/6","A",23,4,10,0.4000,1,"{5661, 5758, 5675, 30}"
33,1,244,0,0.6571659,"\int x^4 \sinh ^{-1}(a x)^4 \, dx","Int[x^4*ArcSinh[a*x]^4,x]","-\frac{1088 x^3}{16875 a^2}-\frac{4 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{25 a}-\frac{24 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{625 a}-\frac{16 x^3 \sinh ^{-1}(a x)^2}{75 a^2}+\frac{16 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{75 a^3}+\frac{1088 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{5625 a^3}-\frac{32 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{75 a^5}-\frac{16576 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{5625 a^5}+\frac{16576 x}{5625 a^4}+\frac{32 x \sinh ^{-1}(a x)^2}{25 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^4+\frac{12}{125} x^5 \sinh ^{-1}(a x)^2+\frac{24 x^5}{3125}","-\frac{1088 x^3}{16875 a^2}-\frac{4 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{25 a}-\frac{24 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{625 a}-\frac{16 x^3 \sinh ^{-1}(a x)^2}{75 a^2}+\frac{16 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{75 a^3}+\frac{1088 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{5625 a^3}-\frac{32 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{75 a^5}-\frac{16576 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{5625 a^5}+\frac{16576 x}{5625 a^4}+\frac{32 x \sinh ^{-1}(a x)^2}{25 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^4+\frac{12}{125} x^5 \sinh ^{-1}(a x)^2+\frac{24 x^5}{3125}",1,"(16576*x)/(5625*a^4) - (1088*x^3)/(16875*a^2) + (24*x^5)/3125 - (16576*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(5625*a^5) + (1088*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(5625*a^3) - (24*x^4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(625*a) + (32*x*ArcSinh[a*x]^2)/(25*a^4) - (16*x^3*ArcSinh[a*x]^2)/(75*a^2) + (12*x^5*ArcSinh[a*x]^2)/125 - (32*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(75*a^5) + (16*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(75*a^3) - (4*x^4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(25*a) + (x^5*ArcSinh[a*x]^4)/5","A",19,6,10,0.6000,1,"{5661, 5758, 5717, 5653, 8, 30}"
34,1,194,0,0.504404,"\int x^3 \sinh ^{-1}(a x)^4 \, dx","Int[x^3*ArcSinh[a*x]^4,x]","-\frac{45 x^2}{128 a^2}-\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{4 a}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{32 a}-\frac{9 x^2 \sinh ^{-1}(a x)^2}{16 a^2}+\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{8 a^3}+\frac{45 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{64 a^3}-\frac{3 \sinh ^{-1}(a x)^4}{32 a^4}-\frac{45 \sinh ^{-1}(a x)^2}{128 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^4+\frac{3}{16} x^4 \sinh ^{-1}(a x)^2+\frac{3 x^4}{128}","-\frac{45 x^2}{128 a^2}-\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{4 a}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{32 a}-\frac{9 x^2 \sinh ^{-1}(a x)^2}{16 a^2}+\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{8 a^3}+\frac{45 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{64 a^3}-\frac{3 \sinh ^{-1}(a x)^4}{32 a^4}-\frac{45 \sinh ^{-1}(a x)^2}{128 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^4+\frac{3}{16} x^4 \sinh ^{-1}(a x)^2+\frac{3 x^4}{128}",1,"(-45*x^2)/(128*a^2) + (3*x^4)/128 + (45*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(64*a^3) - (3*x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(32*a) - (45*ArcSinh[a*x]^2)/(128*a^4) - (9*x^2*ArcSinh[a*x]^2)/(16*a^2) + (3*x^4*ArcSinh[a*x]^2)/16 + (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(8*a^3) - (x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(4*a) - (3*ArcSinh[a*x]^4)/(32*a^4) + (x^4*ArcSinh[a*x]^4)/4","A",14,4,10,0.4000,1,"{5661, 5758, 5675, 30}"
35,1,162,0,0.3630753,"\int x^2 \sinh ^{-1}(a x)^4 \, dx","Int[x^2*ArcSinh[a*x]^4,x]","-\frac{4 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a^3}-\frac{8 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a}+\frac{160 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a^3}-\frac{160 x}{27 a^2}-\frac{8 x \sinh ^{-1}(a x)^2}{3 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^4+\frac{4}{9} x^3 \sinh ^{-1}(a x)^2+\frac{8 x^3}{81}","-\frac{4 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a^3}-\frac{8 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a}+\frac{160 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a^3}-\frac{160 x}{27 a^2}-\frac{8 x \sinh ^{-1}(a x)^2}{3 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^4+\frac{4}{9} x^3 \sinh ^{-1}(a x)^2+\frac{8 x^3}{81}",1,"(-160*x)/(27*a^2) + (8*x^3)/81 + (160*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(27*a^3) - (8*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(27*a) - (8*x*ArcSinh[a*x]^2)/(3*a^2) + (4*x^3*ArcSinh[a*x]^2)/9 + (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(9*a^3) - (4*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(9*a) + (x^3*ArcSinh[a*x]^4)/3","A",11,6,10,0.6000,1,"{5661, 5758, 5717, 5653, 8, 30}"
36,1,110,0,0.2394126,"\int x \sinh ^{-1}(a x)^4 \, dx","Int[x*ArcSinh[a*x]^4,x]","-\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a}+\frac{\sinh ^{-1}(a x)^4}{4 a^2}+\frac{3 \sinh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^4+\frac{3}{2} x^2 \sinh ^{-1}(a x)^2+\frac{3 x^2}{4}","-\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a}+\frac{\sinh ^{-1}(a x)^4}{4 a^2}+\frac{3 \sinh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^4+\frac{3}{2} x^2 \sinh ^{-1}(a x)^2+\frac{3 x^2}{4}",1,"(3*x^2)/4 - (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(2*a) + (3*ArcSinh[a*x]^2)/(4*a^2) + (3*x^2*ArcSinh[a*x]^2)/2 - (x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/a + ArcSinh[a*x]^4/(4*a^2) + (x^2*ArcSinh[a*x]^4)/2","A",7,4,8,0.5000,1,"{5661, 5758, 5675, 30}"
37,1,67,0,0.1251147,"\int \sinh ^{-1}(a x)^4 \, dx","Int[ArcSinh[a*x]^4,x]","-\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a}-\frac{24 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+x \sinh ^{-1}(a x)^4+12 x \sinh ^{-1}(a x)^2+24 x","-\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a}-\frac{24 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+x \sinh ^{-1}(a x)^4+12 x \sinh ^{-1}(a x)^2+24 x",1,"24*x - (24*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a + 12*x*ArcSinh[a*x]^2 - (4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/a + x*ArcSinh[a*x]^4","A",5,3,6,0.5000,1,"{5653, 5717, 8}"
38,1,97,0,0.122107,"\int \frac{\sinh ^{-1}(a x)^4}{x} \, dx","Int[ArcSinh[a*x]^4/x,x]","2 \sinh ^{-1}(a x)^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)+3 \sinh ^{-1}(a x) \text{PolyLog}\left(4,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{5} \sinh ^{-1}(a x)^5+\sinh ^{-1}(a x)^4 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)","2 \sinh ^{-1}(a x)^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)+3 \sinh ^{-1}(a x) \text{PolyLog}\left(4,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{5} \sinh ^{-1}(a x)^5+\sinh ^{-1}(a x)^4 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)",1,"-ArcSinh[a*x]^5/5 + ArcSinh[a*x]^4*Log[1 - E^(2*ArcSinh[a*x])] + 2*ArcSinh[a*x]^3*PolyLog[2, E^(2*ArcSinh[a*x])] - 3*ArcSinh[a*x]^2*PolyLog[3, E^(2*ArcSinh[a*x])] + 3*ArcSinh[a*x]*PolyLog[4, E^(2*ArcSinh[a*x])] - (3*PolyLog[5, E^(2*ArcSinh[a*x])])/2","A",8,7,10,0.7000,1,"{5659, 3716, 2190, 2531, 6609, 2282, 6589}"
39,1,120,0,0.1883493,"\int \frac{\sinh ^{-1}(a x)^4}{x^2} \, dx","Int[ArcSinh[a*x]^4/x^2,x]","-12 a \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+12 a \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+24 a \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-24 a \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-24 a \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)+24 a \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^4}{x}-8 a \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-12 a \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+12 a \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+24 a \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-24 a \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-24 a \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)+24 a \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^4}{x}-8 a \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-(ArcSinh[a*x]^4/x) - 8*a*ArcSinh[a*x]^3*ArcTanh[E^ArcSinh[a*x]] - 12*a*ArcSinh[a*x]^2*PolyLog[2, -E^ArcSinh[a*x]] + 12*a*ArcSinh[a*x]^2*PolyLog[2, E^ArcSinh[a*x]] + 24*a*ArcSinh[a*x]*PolyLog[3, -E^ArcSinh[a*x]] - 24*a*ArcSinh[a*x]*PolyLog[3, E^ArcSinh[a*x]] - 24*a*PolyLog[4, -E^ArcSinh[a*x]] + 24*a*PolyLog[4, E^ArcSinh[a*x]]","A",11,7,10,0.7000,1,"{5661, 5760, 4182, 2531, 6609, 2282, 6589}"
40,1,108,0,0.2071399,"\int \frac{\sinh ^{-1}(a x)^4}{x^3} \, dx","Int[ArcSinh[a*x]^4/x^3,x]","6 a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)-\frac{2 a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{x}-2 a^2 \sinh ^{-1}(a x)^3+6 a^2 \sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^4}{2 x^2}","6 a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)-\frac{2 a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{x}-2 a^2 \sinh ^{-1}(a x)^3+6 a^2 \sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^4}{2 x^2}",1,"-2*a^2*ArcSinh[a*x]^3 - (2*a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/x - ArcSinh[a*x]^4/(2*x^2) + 6*a^2*ArcSinh[a*x]^2*Log[1 - E^(2*ArcSinh[a*x])] + 6*a^2*ArcSinh[a*x]*PolyLog[2, E^(2*ArcSinh[a*x])] - 3*a^2*PolyLog[3, E^(2*ArcSinh[a*x])]","A",8,8,10,0.8000,1,"{5661, 5723, 5659, 3716, 2190, 2531, 2282, 6589}"
41,1,223,0,0.3931552,"\int \frac{\sinh ^{-1}(a x)^4}{x^4} \, dx","Int[ArcSinh[a*x]^4/x^4,x]","2 a^3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-2 a^3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-4 a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+4 a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-4 a^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+4 a^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+4 a^3 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)-4 a^3 \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-\frac{2 a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 x^2}-\frac{2 a^2 \sinh ^{-1}(a x)^2}{x}+\frac{4}{3} a^3 \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-8 a^3 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^4}{3 x^3}","2 a^3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-2 a^3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-4 a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+4 a^3 \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-4 a^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+4 a^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+4 a^3 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)-4 a^3 \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-\frac{2 a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 x^2}-\frac{2 a^2 \sinh ^{-1}(a x)^2}{x}+\frac{4}{3} a^3 \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-8 a^3 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^4}{3 x^3}",1,"(-2*a^2*ArcSinh[a*x]^2)/x - (2*a*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(3*x^2) - ArcSinh[a*x]^4/(3*x^3) - 8*a^3*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] + (4*a^3*ArcSinh[a*x]^3*ArcTanh[E^ArcSinh[a*x]])/3 - 4*a^3*PolyLog[2, -E^ArcSinh[a*x]] + 2*a^3*ArcSinh[a*x]^2*PolyLog[2, -E^ArcSinh[a*x]] + 4*a^3*PolyLog[2, E^ArcSinh[a*x]] - 2*a^3*ArcSinh[a*x]^2*PolyLog[2, E^ArcSinh[a*x]] - 4*a^3*ArcSinh[a*x]*PolyLog[3, -E^ArcSinh[a*x]] + 4*a^3*ArcSinh[a*x]*PolyLog[3, E^ArcSinh[a*x]] + 4*a^3*PolyLog[4, -E^ArcSinh[a*x]] - 4*a^3*PolyLog[4, E^ArcSinh[a*x]]","A",19,10,10,1.000,1,"{5661, 5747, 5760, 4182, 2531, 6609, 2282, 6589, 2279, 2391}"
42,1,55,0,0.1002605,"\int \frac{x^6}{\sinh ^{-1}(a x)} \, dx","Int[x^6/ArcSinh[a*x],x]","-\frac{5 \text{Chi}\left(\sinh ^{-1}(a x)\right)}{64 a^7}+\frac{9 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{64 a^7}-\frac{5 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{64 a^7}+\frac{\text{Chi}\left(7 \sinh ^{-1}(a x)\right)}{64 a^7}","-\frac{5 \text{Chi}\left(\sinh ^{-1}(a x)\right)}{64 a^7}+\frac{9 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{64 a^7}-\frac{5 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{64 a^7}+\frac{\text{Chi}\left(7 \sinh ^{-1}(a x)\right)}{64 a^7}",1,"(-5*CoshIntegral[ArcSinh[a*x]])/(64*a^7) + (9*CoshIntegral[3*ArcSinh[a*x]])/(64*a^7) - (5*CoshIntegral[5*ArcSinh[a*x]])/(64*a^7) + CoshIntegral[7*ArcSinh[a*x]]/(64*a^7)","A",7,3,10,0.3000,1,"{5669, 5448, 3301}"
43,1,43,0,0.0826723,"\int \frac{x^5}{\sinh ^{-1}(a x)} \, dx","Int[x^5/ArcSinh[a*x],x]","\frac{5 \text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Shi}\left(6 \sinh ^{-1}(a x)\right)}{32 a^6}","\frac{5 \text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Shi}\left(6 \sinh ^{-1}(a x)\right)}{32 a^6}",1,"(5*SinhIntegral[2*ArcSinh[a*x]])/(32*a^6) - SinhIntegral[4*ArcSinh[a*x]]/(8*a^6) + SinhIntegral[6*ArcSinh[a*x]]/(32*a^6)","A",6,3,10,0.3000,1,"{5669, 5448, 3298}"
44,1,41,0,0.0837777,"\int \frac{x^4}{\sinh ^{-1}(a x)} \, dx","Int[x^4/ArcSinh[a*x],x]","\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{16 a^5}","\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{16 a^5}",1,"CoshIntegral[ArcSinh[a*x]]/(8*a^5) - (3*CoshIntegral[3*ArcSinh[a*x]])/(16*a^5) + CoshIntegral[5*ArcSinh[a*x]]/(16*a^5)","A",6,3,10,0.3000,1,"{5669, 5448, 3301}"
45,1,29,0,0.0679608,"\int \frac{x^3}{\sinh ^{-1}(a x)} \, dx","Int[x^3/ArcSinh[a*x],x]","\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{8 a^4}-\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{4 a^4}","\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{8 a^4}-\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{4 a^4}",1,"-SinhIntegral[2*ArcSinh[a*x]]/(4*a^4) + SinhIntegral[4*ArcSinh[a*x]]/(8*a^4)","A",5,3,10,0.3000,1,"{5669, 5448, 3298}"
46,1,27,0,0.0667451,"\int \frac{x^2}{\sinh ^{-1}(a x)} \, dx","Int[x^2/ArcSinh[a*x],x]","\frac{\text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^3}-\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{4 a^3}","\frac{\text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^3}-\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{4 a^3}",1,"-CoshIntegral[ArcSinh[a*x]]/(4*a^3) + CoshIntegral[3*ArcSinh[a*x]]/(4*a^3)","A",5,3,10,0.3000,1,"{5669, 5448, 3301}"
47,1,14,0,0.0379933,"\int \frac{x}{\sinh ^{-1}(a x)} \, dx","Int[x/ArcSinh[a*x],x]","\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^2}","\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^2}",1,"SinhIntegral[2*ArcSinh[a*x]]/(2*a^2)","A",4,4,8,0.5000,1,"{5669, 5448, 12, 3298}"
48,1,9,0,0.017505,"\int \frac{1}{\sinh ^{-1}(a x)} \, dx","Int[ArcSinh[a*x]^(-1),x]","\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{a}","\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{a}",1,"CoshIntegral[ArcSinh[a*x]]/a","A",2,2,6,0.3333,1,"{5657, 3301}"
49,0,0,0,0.0140428,"\int \frac{1}{x \sinh ^{-1}(a x)} \, dx","Int[1/(x*ArcSinh[a*x]),x]","\int \frac{1}{x \sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.0149415,"\int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx","Int[1/(x^2*ArcSinh[a*x]),x]","\int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \sinh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x^2*ArcSinh[a*x]), x]","A",0,0,0,0,-1,"{}"
51,1,82,0,0.0811772,"\int \frac{x^6}{\sinh ^{-1}(a x)^2} \, dx","Int[x^6/ArcSinh[a*x]^2,x]","-\frac{5 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{64 a^7}+\frac{27 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{64 a^7}-\frac{25 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{64 a^7}+\frac{7 \text{Shi}\left(7 \sinh ^{-1}(a x)\right)}{64 a^7}-\frac{x^6 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","-\frac{5 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{64 a^7}+\frac{27 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{64 a^7}-\frac{25 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{64 a^7}+\frac{7 \text{Shi}\left(7 \sinh ^{-1}(a x)\right)}{64 a^7}-\frac{x^6 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-((x^6*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x])) - (5*SinhIntegral[ArcSinh[a*x]])/(64*a^7) + (27*SinhIntegral[3*ArcSinh[a*x]])/(64*a^7) - (25*SinhIntegral[5*ArcSinh[a*x]])/(64*a^7) + (7*SinhIntegral[7*ArcSinh[a*x]])/(64*a^7)","A",6,2,10,0.2000,1,"{5665, 3298}"
52,1,70,0,0.0664206,"\int \frac{x^5}{\sinh ^{-1}(a x)^2} \, dx","Int[x^5/ArcSinh[a*x]^2,x]","\frac{5 \text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{16 a^6}-\frac{\text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{2 a^6}+\frac{3 \text{Chi}\left(6 \sinh ^{-1}(a x)\right)}{16 a^6}-\frac{x^5 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","\frac{5 \text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{16 a^6}-\frac{\text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{2 a^6}+\frac{3 \text{Chi}\left(6 \sinh ^{-1}(a x)\right)}{16 a^6}-\frac{x^5 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-((x^5*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x])) + (5*CoshIntegral[2*ArcSinh[a*x]])/(16*a^6) - CoshIntegral[4*ArcSinh[a*x]]/(2*a^6) + (3*CoshIntegral[6*ArcSinh[a*x]])/(16*a^6)","A",5,2,10,0.2000,1,"{5665, 3301}"
53,1,68,0,0.0658968,"\int \frac{x^4}{\sinh ^{-1}(a x)^2} \, dx","Int[x^4/ArcSinh[a*x]^2,x]","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{8 a^5}-\frac{9 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{16 a^5}+\frac{5 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{16 a^5}-\frac{x^4 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{8 a^5}-\frac{9 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{16 a^5}+\frac{5 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{16 a^5}-\frac{x^4 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-((x^4*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x])) + SinhIntegral[ArcSinh[a*x]]/(8*a^5) - (9*SinhIntegral[3*ArcSinh[a*x]])/(16*a^5) + (5*SinhIntegral[5*ArcSinh[a*x]])/(16*a^5)","A",5,2,10,0.2000,1,"{5665, 3298}"
54,1,56,0,0.0494046,"\int \frac{x^3}{\sinh ^{-1}(a x)^2} \, dx","Int[x^3/ArcSinh[a*x]^2,x]","-\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{2 a^4}-\frac{x^3 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","-\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{2 a^4}-\frac{x^3 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-((x^3*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x])) - CoshIntegral[2*ArcSinh[a*x]]/(2*a^4) + CoshIntegral[4*ArcSinh[a*x]]/(2*a^4)","A",4,2,10,0.2000,1,"{5665, 3301}"
55,1,54,0,0.0474095,"\int \frac{x^2}{\sinh ^{-1}(a x)^2} \, dx","Int[x^2/ArcSinh[a*x]^2,x]","-\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{4 a^3}+\frac{3 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^3}-\frac{x^2 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","-\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{4 a^3}+\frac{3 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^3}-\frac{x^2 \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-((x^2*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x])) - SinhIntegral[ArcSinh[a*x]]/(4*a^3) + (3*SinhIntegral[3*ArcSinh[a*x]])/(4*a^3)","A",4,2,10,0.2000,1,"{5665, 3298}"
56,1,37,0,0.0246061,"\int \frac{x}{\sinh ^{-1}(a x)^2} \, dx","Int[x/ArcSinh[a*x]^2,x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-((x*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x])) + CoshIntegral[2*ArcSinh[a*x]]/a^2","A",2,2,8,0.2500,1,"{5665, 3301}"
57,1,34,0,0.0833157,"\int \frac{1}{\sinh ^{-1}(a x)^2} \, dx","Int[ArcSinh[a*x]^(-2),x]","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{a}-\frac{\sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{a}-\frac{\sqrt{a^2 x^2+1}}{a \sinh ^{-1}(a x)}",1,"-(Sqrt[1 + a^2*x^2]/(a*ArcSinh[a*x])) + SinhIntegral[ArcSinh[a*x]]/a","A",3,3,6,0.5000,1,"{5655, 5779, 3298}"
58,0,0,0,0.0131018,"\int \frac{1}{x \sinh ^{-1}(a x)^2} \, dx","Int[1/(x*ArcSinh[a*x]^2),x]","\int \frac{1}{x \sinh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
59,0,0,0,0.0136163,"\int \frac{1}{x^2 \sinh ^{-1}(a x)^2} \, dx","Int[1/(x^2*ArcSinh[a*x]^2),x]","\int \frac{1}{x^2 \sinh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \sinh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x^2*ArcSinh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
60,1,97,0,0.3543386,"\int \frac{x^4}{\sinh ^{-1}(a x)^3} \, dx","Int[x^4/ArcSinh[a*x]^3,x]","\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{16 a^5}-\frac{27 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{32 a^5}+\frac{25 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{x^4 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{2 x^3}{a^2 \sinh ^{-1}(a x)}-\frac{5 x^5}{2 \sinh ^{-1}(a x)}","\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{16 a^5}-\frac{27 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{32 a^5}+\frac{25 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{x^4 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{2 x^3}{a^2 \sinh ^{-1}(a x)}-\frac{5 x^5}{2 \sinh ^{-1}(a x)}",1,"-(x^4*Sqrt[1 + a^2*x^2])/(2*a*ArcSinh[a*x]^2) - (2*x^3)/(a^2*ArcSinh[a*x]) - (5*x^5)/(2*ArcSinh[a*x]) + CoshIntegral[ArcSinh[a*x]]/(16*a^5) - (27*CoshIntegral[3*ArcSinh[a*x]])/(32*a^5) + (25*CoshIntegral[5*ArcSinh[a*x]])/(32*a^5)","A",14,5,10,0.5000,1,"{5667, 5774, 5669, 5448, 3301}"
61,1,82,0,0.3040089,"\int \frac{x^3}{\sinh ^{-1}(a x)^3} \, dx","Int[x^3/ArcSinh[a*x]^3,x]","-\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{a^4}-\frac{x^3 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \sinh ^{-1}(a x)}-\frac{2 x^4}{\sinh ^{-1}(a x)}","-\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{a^4}-\frac{x^3 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \sinh ^{-1}(a x)}-\frac{2 x^4}{\sinh ^{-1}(a x)}",1,"-(x^3*Sqrt[1 + a^2*x^2])/(2*a*ArcSinh[a*x]^2) - (3*x^2)/(2*a^2*ArcSinh[a*x]) - (2*x^4)/ArcSinh[a*x] - SinhIntegral[2*ArcSinh[a*x]]/(2*a^4) + SinhIntegral[4*ArcSinh[a*x]]/a^4","A",12,6,10,0.6000,1,"{5667, 5774, 5669, 5448, 3298, 12}"
62,1,81,0,0.2525725,"\int \frac{x^2}{\sinh ^{-1}(a x)^3} \, dx","Int[x^2/ArcSinh[a*x]^3,x]","-\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{8 a^3}-\frac{x^2 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{x}{a^2 \sinh ^{-1}(a x)}-\frac{3 x^3}{2 \sinh ^{-1}(a x)}","-\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{8 a^3}-\frac{x^2 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{x}{a^2 \sinh ^{-1}(a x)}-\frac{3 x^3}{2 \sinh ^{-1}(a x)}",1,"-(x^2*Sqrt[1 + a^2*x^2])/(2*a*ArcSinh[a*x]^2) - x/(a^2*ArcSinh[a*x]) - (3*x^3)/(2*ArcSinh[a*x]) - CoshIntegral[ArcSinh[a*x]]/(8*a^3) + (9*CoshIntegral[3*ArcSinh[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{5667, 5774, 5669, 5448, 3301, 5657}"
63,1,63,0,0.1707109,"\int \frac{x}{\sinh ^{-1}(a x)^3} \, dx","Int[x/ArcSinh[a*x]^3,x]","\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{1}{2 a^2 \sinh ^{-1}(a x)}-\frac{x^2}{\sinh ^{-1}(a x)}","\frac{\text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{1}{2 a^2 \sinh ^{-1}(a x)}-\frac{x^2}{\sinh ^{-1}(a x)}",1,"-(x*Sqrt[1 + a^2*x^2])/(2*a*ArcSinh[a*x]^2) - 1/(2*a^2*ArcSinh[a*x]) - x^2/ArcSinh[a*x] + SinhIntegral[2*ArcSinh[a*x]]/a^2","A",7,7,8,0.8750,1,"{5667, 5774, 5669, 5448, 12, 3298, 5675}"
64,1,50,0,0.0826796,"\int \frac{1}{\sinh ^{-1}(a x)^3} \, dx","Int[ArcSinh[a*x]^(-3),x]","-\frac{\sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}+\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{2 a}-\frac{x}{2 \sinh ^{-1}(a x)}","-\frac{\sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}+\frac{\text{Chi}\left(\sinh ^{-1}(a x)\right)}{2 a}-\frac{x}{2 \sinh ^{-1}(a x)}",1,"-Sqrt[1 + a^2*x^2]/(2*a*ArcSinh[a*x]^2) - x/(2*ArcSinh[a*x]) + CoshIntegral[ArcSinh[a*x]]/(2*a)","A",4,4,6,0.6667,1,"{5655, 5774, 5657, 3301}"
65,0,0,0,0.0131602,"\int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx","Int[1/(x*ArcSinh[a*x]^3),x]","\int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]^3), x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0137973,"\int \frac{1}{x^2 \sinh ^{-1}(a x)^3} \, dx","Int[1/(x^2*ArcSinh[a*x]^3),x]","\int \frac{1}{x^2 \sinh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x^2 \sinh ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(x^2*ArcSinh[a*x]^3), x]","A",0,0,0,0,-1,"{}"
67,1,155,0,0.3198252,"\int \frac{x^4}{\sinh ^{-1}(a x)^4} \, dx","Int[x^4/ArcSinh[a*x]^4,x]","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{48 a^5}-\frac{27 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{96 a^5}-\frac{25 x^4 \sqrt{a^2 x^2+1}}{6 a \sinh ^{-1}(a x)}-\frac{x^4 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{2 x^3}{3 a^2 \sinh ^{-1}(a x)^2}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{a^3 \sinh ^{-1}(a x)}-\frac{5 x^5}{6 \sinh ^{-1}(a x)^2}","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{48 a^5}-\frac{27 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{96 a^5}-\frac{25 x^4 \sqrt{a^2 x^2+1}}{6 a \sinh ^{-1}(a x)}-\frac{x^4 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{2 x^3}{3 a^2 \sinh ^{-1}(a x)^2}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{a^3 \sinh ^{-1}(a x)}-\frac{5 x^5}{6 \sinh ^{-1}(a x)^2}",1,"-(x^4*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^3) - (2*x^3)/(3*a^2*ArcSinh[a*x]^2) - (5*x^5)/(6*ArcSinh[a*x]^2) - (2*x^2*Sqrt[1 + a^2*x^2])/(a^3*ArcSinh[a*x]) - (25*x^4*Sqrt[1 + a^2*x^2])/(6*a*ArcSinh[a*x]) + SinhIntegral[ArcSinh[a*x]]/(48*a^5) - (27*SinhIntegral[3*ArcSinh[a*x]])/(32*a^5) + (125*SinhIntegral[5*ArcSinh[a*x]])/(96*a^5)","A",12,4,10,0.4000,1,"{5667, 5774, 5665, 3298}"
68,1,141,0,0.2832968,"\int \frac{x^3}{\sinh ^{-1}(a x)^4} \, dx","Int[x^3/ArcSinh[a*x]^4,x]","-\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{3 a^4}-\frac{8 x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)}-\frac{x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{x^2}{2 a^2 \sinh ^{-1}(a x)^2}-\frac{x \sqrt{a^2 x^2+1}}{a^3 \sinh ^{-1}(a x)}-\frac{2 x^4}{3 \sinh ^{-1}(a x)^2}","-\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{3 a^4}-\frac{8 x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)}-\frac{x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{x^2}{2 a^2 \sinh ^{-1}(a x)^2}-\frac{x \sqrt{a^2 x^2+1}}{a^3 \sinh ^{-1}(a x)}-\frac{2 x^4}{3 \sinh ^{-1}(a x)^2}",1,"-(x^3*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^3) - x^2/(2*a^2*ArcSinh[a*x]^2) - (2*x^4)/(3*ArcSinh[a*x]^2) - (x*Sqrt[1 + a^2*x^2])/(a^3*ArcSinh[a*x]) - (8*x^3*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]) - CoshIntegral[2*ArcSinh[a*x]]/(3*a^4) + (4*CoshIntegral[4*ArcSinh[a*x]])/(3*a^4)","A",9,4,10,0.4000,1,"{5667, 5774, 5665, 3301}"
69,1,138,0,0.3058339,"\int \frac{x^2}{\sinh ^{-1}(a x)^4} \, dx","Int[x^2/ArcSinh[a*x]^4,x]","-\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{24 a^3}+\frac{9 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{8 a^3}-\frac{3 x^2 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)}-\frac{x^2 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{\sqrt{a^2 x^2+1}}{3 a^3 \sinh ^{-1}(a x)}-\frac{x}{3 a^2 \sinh ^{-1}(a x)^2}-\frac{x^3}{2 \sinh ^{-1}(a x)^2}","-\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{24 a^3}+\frac{9 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{8 a^3}-\frac{3 x^2 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)}-\frac{x^2 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{\sqrt{a^2 x^2+1}}{3 a^3 \sinh ^{-1}(a x)}-\frac{x}{3 a^2 \sinh ^{-1}(a x)^2}-\frac{x^3}{2 \sinh ^{-1}(a x)^2}",1,"-(x^2*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^3) - x/(3*a^2*ArcSinh[a*x]^2) - x^3/(2*ArcSinh[a*x]^2) - Sqrt[1 + a^2*x^2]/(3*a^3*ArcSinh[a*x]) - (3*x^2*Sqrt[1 + a^2*x^2])/(2*a*ArcSinh[a*x]) - SinhIntegral[ArcSinh[a*x]]/(24*a^3) + (9*SinhIntegral[3*ArcSinh[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{5667, 5774, 5665, 3298, 5655, 5779}"
70,1,95,0,0.1633693,"\int \frac{x}{\sinh ^{-1}(a x)^4} \, dx","Int[x/ArcSinh[a*x]^4,x]","\frac{2 \text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{3 a^2}-\frac{2 x \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)}-\frac{x \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{1}{6 a^2 \sinh ^{-1}(a x)^2}-\frac{x^2}{3 \sinh ^{-1}(a x)^2}","\frac{2 \text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{3 a^2}-\frac{2 x \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)}-\frac{x \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}-\frac{1}{6 a^2 \sinh ^{-1}(a x)^2}-\frac{x^2}{3 \sinh ^{-1}(a x)^2}",1,"-(x*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^3) - 1/(6*a^2*ArcSinh[a*x]^2) - x^2/(3*ArcSinh[a*x]^2) - (2*x*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]) + (2*CoshIntegral[2*ArcSinh[a*x]])/(3*a^2)","A",5,5,8,0.6250,1,"{5667, 5774, 5665, 3301, 5675}"
71,1,76,0,0.1497464,"\int \frac{1}{\sinh ^{-1}(a x)^4} \, dx","Int[ArcSinh[a*x]^(-4),x]","-\frac{\sqrt{a^2 x^2+1}}{6 a \sinh ^{-1}(a x)}-\frac{\sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}+\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{6 a}-\frac{x}{6 \sinh ^{-1}(a x)^2}","-\frac{\sqrt{a^2 x^2+1}}{6 a \sinh ^{-1}(a x)}-\frac{\sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^3}+\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{6 a}-\frac{x}{6 \sinh ^{-1}(a x)^2}",1,"-Sqrt[1 + a^2*x^2]/(3*a*ArcSinh[a*x]^3) - x/(6*ArcSinh[a*x]^2) - Sqrt[1 + a^2*x^2]/(6*a*ArcSinh[a*x]) + SinhIntegral[ArcSinh[a*x]]/(6*a)","A",5,4,6,0.6667,1,"{5655, 5774, 5779, 3298}"
72,0,0,0,0.0127958,"\int \frac{1}{x \sinh ^{-1}(a x)^4} \, dx","Int[1/(x*ArcSinh[a*x]^4),x]","\int \frac{1}{x \sinh ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)^4},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]^4), x]","A",0,0,0,0,-1,"{}"
73,0,0,0,0.0141296,"\int \frac{1}{x^2 \sinh ^{-1}(a x)^4} \, dx","Int[1/(x^2*ArcSinh[a*x]^4),x]","\int \frac{1}{x^2 \sinh ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x^2 \sinh ^{-1}(a x)^4},x\right)",0,"Defer[Int][1/(x^2*ArcSinh[a*x]^4), x]","A",0,0,0,0,-1,"{}"
74,1,182,0,0.3244555,"\int x^4 \sqrt{\sinh ^{-1}(a x)} \, dx","Int[x^4*Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{320 a^5}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{320 a^5}+\frac{1}{5} x^5 \sqrt{\sinh ^{-1}(a x)}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{320 a^5}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{320 a^5}+\frac{1}{5} x^5 \sqrt{\sinh ^{-1}(a x)}",1,"(x^5*Sqrt[ArcSinh[a*x]])/5 + (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(32*a^5) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(64*a^5) + (Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(320*a^5) - (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(32*a^5) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(64*a^5) - (Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(320*a^5)","A",19,7,12,0.5833,1,"{5663, 5779, 3312, 3308, 2180, 2204, 2205}"
75,1,139,0,0.2615949,"\int x^3 \sqrt{\sinh ^{-1}(a x)} \, dx","Int[x^3*Sqrt[ArcSinh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}-\frac{3 \sqrt{\sinh ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\sinh ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}-\frac{3 \sqrt{\sinh ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\sinh ^{-1}(a x)}",1,"(-3*Sqrt[ArcSinh[a*x]])/(32*a^4) + (x^4*Sqrt[ArcSinh[a*x]])/4 - (Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(256*a^4) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(32*a^4) - (Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(256*a^4) + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(32*a^4)","A",14,7,12,0.5833,1,"{5663, 5779, 3312, 3307, 2180, 2204, 2205}"
76,1,120,0,0.2443176,"\int x^2 \sqrt{\sinh ^{-1}(a x)} \, dx","Int[x^2*Sqrt[ArcSinh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{48 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{48 a^3}+\frac{1}{3} x^3 \sqrt{\sinh ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{48 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{48 a^3}+\frac{1}{3} x^3 \sqrt{\sinh ^{-1}(a x)}",1,"(x^3*Sqrt[ArcSinh[a*x]])/3 - (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(16*a^3) + (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(48*a^3) + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(16*a^3) - (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(48*a^3)","A",14,7,12,0.5833,1,"{5663, 5779, 3312, 3308, 2180, 2204, 2205}"
77,1,93,0,0.1910498,"\int x \sqrt{\sinh ^{-1}(a x)} \, dx","Int[x*Sqrt[ArcSinh[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^2}+\frac{\sqrt{\sinh ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\sinh ^{-1}(a x)}","-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^2}+\frac{\sqrt{\sinh ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\sinh ^{-1}(a x)}",1,"Sqrt[ArcSinh[a*x]]/(4*a^2) + (x^2*Sqrt[ArcSinh[a*x]])/2 - (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a^2) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a^2)","A",9,7,10,0.7000,1,"{5663, 5779, 3312, 3307, 2180, 2204, 2205}"
78,1,53,0,0.1071909,"\int \sqrt{\sinh ^{-1}(a x)} \, dx","Int[Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a}+x \sqrt{\sinh ^{-1}(a x)}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a}+x \sqrt{\sinh ^{-1}(a x)}",1,"x*Sqrt[ArcSinh[a*x]] + (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(4*a) - (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(4*a)","A",7,6,8,0.7500,1,"{5653, 5779, 3308, 2180, 2204, 2205}"
79,0,0,0,0.0136434,"\int \frac{\sqrt{\sinh ^{-1}(a x)}}{x} \, dx","Int[Sqrt[ArcSinh[a*x]]/x,x]","\int \frac{\sqrt{\sinh ^{-1}(a x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{\sinh ^{-1}(a x)}}{x},x\right)",0,"Defer[Int][Sqrt[ArcSinh[a*x]]/x, x]","A",0,0,0,0,-1,"{}"
80,1,330,0,0.7127642,"\int x^4 \sinh ^{-1}(a x)^{3/2} \, dx","Int[x^4*ArcSinh[a*x]^(3/2),x]","\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{200 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}-\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{200 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}-\frac{3 x^4 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{50 a}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{25 a^3}-\frac{4 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^{3/2}","\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{200 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^5}-\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{200 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{3200 a^5}-\frac{3 x^4 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{50 a}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{25 a^3}-\frac{4 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^{3/2}",1,"(-4*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(25*a^5) + (2*x^2*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(25*a^3) - (3*x^4*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(50*a) + (x^5*ArcSinh[a*x]^(3/2))/5 + (3*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(64*a^5) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(200*a^5) - (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(3200*a^5) + (3*Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(3200*a^5) + (3*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(64*a^5) - (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(200*a^5) - (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(3200*a^5) + (3*Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(3200*a^5)","A",41,10,12,0.8333,1,"{5663, 5758, 5717, 5657, 3307, 2180, 2204, 2205, 5669, 5448}"
81,1,199,0,0.4873717,"\int x^3 \sinh ^{-1}(a x)^{3/2} \, dx","Int[x^3*ArcSinh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a^4}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{128 a^4}+\frac{3 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a^4}-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{128 a^4}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{32 a}+\frac{9 x \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{64 a^3}-\frac{3 \sinh ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^{3/2}","-\frac{3 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a^4}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{128 a^4}+\frac{3 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a^4}-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{128 a^4}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{32 a}+\frac{9 x \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{64 a^3}-\frac{3 \sinh ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^{3/2}",1,"(9*x*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(64*a^3) - (3*x^3*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(32*a) - (3*ArcSinh[a*x]^(3/2))/(32*a^4) + (x^4*ArcSinh[a*x]^(3/2))/4 - (3*Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(2048*a^4) + (3*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(128*a^4) + (3*Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(2048*a^4) - (3*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(128*a^4)","A",25,10,12,0.8333,1,"{5663, 5758, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
82,1,179,0,0.3713505,"\int x^2 \sinh ^{-1}(a x)^{3/2} \, dx","Int[x^2*ArcSinh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{96 a^3}-\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{96 a^3}-\frac{x^2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{6 a}+\frac{\sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^{3/2}","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{96 a^3}-\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{32 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{96 a^3}-\frac{x^2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{6 a}+\frac{\sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^{3/2}",1,"(Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(3*a^3) - (x^2*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(6*a) + (x^3*ArcSinh[a*x]^(3/2))/3 - (3*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(32*a^3) + (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(96*a^3) - (3*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(32*a^3) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(96*a^3)","A",22,10,12,0.8333,1,"{5663, 5758, 5717, 5657, 3307, 2180, 2204, 2205, 5669, 5448}"
83,1,122,0,0.219252,"\int x \sinh ^{-1}(a x)^{3/2} \, dx","Int[x*ArcSinh[a*x]^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^2}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^2}-\frac{3 x \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{8 a}+\frac{\sinh ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^2}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a^2}-\frac{3 x \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{8 a}+\frac{\sinh ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^{3/2}",1,"(-3*x*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(8*a) + ArcSinh[a*x]^(3/2)/(4*a^2) + (x^2*ArcSinh[a*x]^(3/2))/2 - (3*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a^2) + (3*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a^2)","A",11,10,10,1.000,1,"{5663, 5758, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
84,1,81,0,0.1186188,"\int \sinh ^{-1}(a x)^{3/2} \, dx","Int[ArcSinh[a*x]^(3/2),x]","-\frac{3 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{2 a}+\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a}+x \sinh ^{-1}(a x)^{3/2}","-\frac{3 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{2 a}+\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a}+x \sinh ^{-1}(a x)^{3/2}",1,"(-3*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(2*a) + x*ArcSinh[a*x]^(3/2) + (3*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(8*a) + (3*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(8*a)","A",8,7,8,0.8750,1,"{5653, 5717, 5657, 3307, 2180, 2204, 2205}"
85,0,0,0,0.0149503,"\int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx","Int[ArcSinh[a*x]^(3/2)/x,x]","\int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\sinh ^{-1}(a x)^{3/2}}{x},x\right)",0,"Defer[Int][ArcSinh[a*x]^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
86,1,379,0,0.9963917,"\int x^4 \sinh ^{-1}(a x)^{5/2} \, dx","Int[x^4*ArcSinh[a*x]^(5/2),x]","\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{128 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{1280 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{240 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{6400 a^5}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{128 a^5}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{1280 a^5}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{240 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{6400 a^5}-\frac{x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{10 a}-\frac{x^3 \sqrt{\sinh ^{-1}(a x)}}{15 a^2}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{15 a^3}-\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{15 a^5}+\frac{2 x \sqrt{\sinh ^{-1}(a x)}}{5 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^{5/2}+\frac{3}{100} x^5 \sqrt{\sinh ^{-1}(a x)}","\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{128 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{1280 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{240 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{6400 a^5}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{128 a^5}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{1280 a^5}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{240 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{6400 a^5}-\frac{x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{10 a}-\frac{x^3 \sqrt{\sinh ^{-1}(a x)}}{15 a^2}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{15 a^3}-\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{15 a^5}+\frac{2 x \sqrt{\sinh ^{-1}(a x)}}{5 a^4}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^{5/2}+\frac{3}{100} x^5 \sqrt{\sinh ^{-1}(a x)}",1,"(2*x*Sqrt[ArcSinh[a*x]])/(5*a^4) - (x^3*Sqrt[ArcSinh[a*x]])/(15*a^2) + (3*x^5*Sqrt[ArcSinh[a*x]])/100 - (4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(15*a^5) + (2*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(15*a^3) - (x^4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(10*a) + (x^5*ArcSinh[a*x]^(5/2))/5 + (15*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(128*a^5) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(240*a^5) - (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(1280*a^5) + (3*Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(6400*a^5) - (15*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(128*a^5) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(240*a^5) + (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(1280*a^5) - (3*Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(6400*a^5)","A",44,10,12,0.8333,1,"{5663, 5758, 5717, 5653, 5779, 3308, 2180, 2204, 2205, 3312}"
87,1,247,0,0.7107699,"\int x^3 \sinh ^{-1}(a x)^{5/2} \, dx","Int[x^3*ArcSinh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a^4}+\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{512 a^4}-\frac{15 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a^4}+\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{512 a^4}-\frac{5 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{32 a}-\frac{45 x^2 \sqrt{\sinh ^{-1}(a x)}}{256 a^2}+\frac{15 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \sinh ^{-1}(a x)^{5/2}}{32 a^4}-\frac{225 \sqrt{\sinh ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^{5/2}+\frac{15}{256} x^4 \sqrt{\sinh ^{-1}(a x)}","-\frac{15 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a^4}+\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{512 a^4}-\frac{15 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a^4}+\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{512 a^4}-\frac{5 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{32 a}-\frac{45 x^2 \sqrt{\sinh ^{-1}(a x)}}{256 a^2}+\frac{15 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \sinh ^{-1}(a x)^{5/2}}{32 a^4}-\frac{225 \sqrt{\sinh ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^{5/2}+\frac{15}{256} x^4 \sqrt{\sinh ^{-1}(a x)}",1,"(-225*Sqrt[ArcSinh[a*x]])/(2048*a^4) - (45*x^2*Sqrt[ArcSinh[a*x]])/(256*a^2) + (15*x^4*Sqrt[ArcSinh[a*x]])/256 + (15*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(64*a^3) - (5*x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(32*a) - (3*ArcSinh[a*x]^(5/2))/(32*a^4) + (x^4*ArcSinh[a*x]^(5/2))/4 - (15*Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(16384*a^4) + (15*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(512*a^4) - (15*Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(16384*a^4) + (15*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(512*a^4)","A",27,9,12,0.7500,1,"{5663, 5758, 5675, 5779, 3312, 3307, 2180, 2204, 2205}"
88,1,210,0,0.5507601,"\int x^2 \sinh ^{-1}(a x)^{5/2} \, dx","Int[x^2*ArcSinh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^3}+\frac{5 \sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{576 a^3}+\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^3}-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{576 a^3}-\frac{5 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{18 a}+\frac{5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{9 a^3}-\frac{5 x \sqrt{\sinh ^{-1}(a x)}}{6 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^{5/2}+\frac{5}{36} x^3 \sqrt{\sinh ^{-1}(a x)}","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^3}+\frac{5 \sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{576 a^3}+\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{64 a^3}-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{576 a^3}-\frac{5 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{18 a}+\frac{5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{9 a^3}-\frac{5 x \sqrt{\sinh ^{-1}(a x)}}{6 a^2}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^{5/2}+\frac{5}{36} x^3 \sqrt{\sinh ^{-1}(a x)}",1,"(-5*x*Sqrt[ArcSinh[a*x]])/(6*a^2) + (5*x^3*Sqrt[ArcSinh[a*x]])/36 + (5*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(9*a^3) - (5*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(18*a) + (x^3*ArcSinh[a*x]^(5/2))/3 - (15*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(64*a^3) + (5*Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(576*a^3) + (15*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(64*a^3) - (5*Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(576*a^3)","A",24,10,12,0.8333,1,"{5663, 5758, 5717, 5653, 5779, 3308, 2180, 2204, 2205, 3312}"
89,1,152,0,0.3368084,"\int x \sinh ^{-1}(a x)^{5/2} \, dx","Int[x*ArcSinh[a*x]^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^2}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^2}-\frac{5 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{8 a}+\frac{\sinh ^{-1}(a x)^{5/2}}{4 a^2}+\frac{15 \sqrt{\sinh ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^{5/2}+\frac{15}{32} x^2 \sqrt{\sinh ^{-1}(a x)}","-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^2}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a^2}-\frac{5 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{8 a}+\frac{\sinh ^{-1}(a x)^{5/2}}{4 a^2}+\frac{15 \sqrt{\sinh ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \sinh ^{-1}(a x)^{5/2}+\frac{15}{32} x^2 \sqrt{\sinh ^{-1}(a x)}",1,"(15*Sqrt[ArcSinh[a*x]])/(64*a^2) + (15*x^2*Sqrt[ArcSinh[a*x]])/32 - (5*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(8*a) + ArcSinh[a*x]^(5/2)/(4*a^2) + (x^2*ArcSinh[a*x]^(5/2))/2 - (15*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(256*a^2) - (15*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(256*a^2)","A",12,9,10,0.9000,1,"{5663, 5758, 5675, 5779, 3312, 3307, 2180, 2204, 2205}"
90,1,94,0,0.1843986,"\int \sinh ^{-1}(a x)^{5/2} \, dx","Int[ArcSinh[a*x]^(5/2),x]","-\frac{5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{2 a}+\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a}+x \sinh ^{-1}(a x)^{5/2}+\frac{15}{4} x \sqrt{\sinh ^{-1}(a x)}","-\frac{5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{2 a}+\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a}+x \sinh ^{-1}(a x)^{5/2}+\frac{15}{4} x \sqrt{\sinh ^{-1}(a x)}",1,"(15*x*Sqrt[ArcSinh[a*x]])/4 - (5*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(2*a) + x*ArcSinh[a*x]^(5/2) + (15*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(16*a) - (15*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(16*a)","A",9,7,8,0.8750,1,"{5653, 5717, 5779, 3308, 2180, 2204, 2205}"
91,0,0,0,0.0128579,"\int \frac{\sinh ^{-1}(a x)^{5/2}}{x} \, dx","Int[ArcSinh[a*x]^(5/2)/x,x]","\int \frac{\sinh ^{-1}(a x)^{5/2}}{x} \, dx","\text{Int}\left(\frac{\sinh ^{-1}(a x)^{5/2}}{x},x\right)",0,"Defer[Int][ArcSinh[a*x]^(5/2)/x, x]","A",0,0,0,0,-1,"{}"
92,1,163,0,0.2041893,"\int \frac{x^4}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[x^4/Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^5}",1,"(Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(16*a^5) - (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(32*a^5) + (Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(32*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(16*a^5) - (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(32*a^5) + (Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(32*a^5)","A",18,6,12,0.5000,1,"{5669, 5448, 3307, 2180, 2204, 2205}"
93,1,109,0,0.1478355,"\int \frac{x^3}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[x^3/Sqrt[ArcSinh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^4}","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^4}",1,"-(Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(32*a^4) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(8*a^4) + (Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(32*a^4) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(8*a^4)","A",13,6,12,0.5000,1,"{5669, 5448, 3308, 2180, 2204, 2205}"
94,1,105,0,0.1429044,"\int \frac{x^2}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[x^2/Sqrt[ArcSinh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^3}",1,"-(Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(8*a^3) + (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(8*a^3) - (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(8*a^3) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(8*a^3)","A",13,6,12,0.5000,1,"{5669, 5448, 3307, 2180, 2204, 2205}"
95,1,63,0,0.0765867,"\int \frac{x}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[x/Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^2}","\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^2}",1,"-(Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(4*a^2) + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(4*a^2)","A",8,7,10,0.7000,1,"{5669, 5448, 12, 3308, 2180, 2204, 2205}"
96,1,43,0,0.0471502,"\int \frac{1}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[1/Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{2 a}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{2 a}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{2 a}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{2 a}",1,"(Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(2*a) + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(2*a)","A",6,5,8,0.6250,1,"{5657, 3307, 2180, 2204, 2205}"
97,0,0,0,0.0134009,"\int \frac{1}{x \sqrt{\sinh ^{-1}(a x)}} \, dx","Int[1/(x*Sqrt[ArcSinh[a*x]]),x]","\int \frac{1}{x \sqrt{\sinh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{\sinh ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[ArcSinh[a*x]]), x]","A",0,0,0,0,-1,"{}"
98,0,0,0,0.0154198,"\int \frac{1}{x^2 \sqrt{\sinh ^{-1}(a x)}} \, dx","Int[1/(x^2*Sqrt[ArcSinh[a*x]]),x]","\int \frac{1}{x^2 \sqrt{\sinh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{\sinh ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x^2*Sqrt[ArcSinh[a*x]]), x]","A",0,0,0,0,-1,"{}"
99,1,188,0,0.1851154,"\int \frac{x^4}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[x^4/ArcSinh[a*x]^(3/2),x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}+\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}-\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}+\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}-\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a^5}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x^4*Sqrt[1 + a^2*x^2])/(a*Sqrt[ArcSinh[a*x]]) - (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(8*a^5) + (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(16*a^5) - (Sqrt[5*Pi]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(16*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(8*a^5) - (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(16*a^5) + (Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(16*a^5)","A",17,5,12,0.4167,1,"{5665, 3308, 2180, 2204, 2205}"
100,1,138,0,0.1328076,"\int \frac{x^3}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[x^3/ArcSinh[a*x]^(3/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^4}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^4}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x^3*Sqrt[1 + a^2*x^2])/(a*Sqrt[ArcSinh[a*x]]) + (Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(4*a^4) - (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(2*a^4) + (Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(4*a^4) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(2*a^4)","A",12,5,12,0.4167,1,"{5665, 3307, 2180, 2204, 2205}"
101,1,130,0,0.1220157,"\int \frac{x^2}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[x^2/ArcSinh[a*x]^(3/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a^3}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x^2*Sqrt[1 + a^2*x^2])/(a*Sqrt[ArcSinh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(4*a^3) - (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(4*a^3) - (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(4*a^3) + (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(4*a^3)","A",12,5,12,0.4167,1,"{5665, 3308, 2180, 2204, 2205}"
102,1,84,0,0.0663937,"\int \frac{x}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[x/ArcSinh[a*x]^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a^2}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a^2}-\frac{2 x \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}","\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a^2}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a^2}-\frac{2 x \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x*Sqrt[1 + a^2*x^2])/(a*Sqrt[ArcSinh[a*x]]) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/a^2 + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/a^2","A",6,5,10,0.5000,1,"{5665, 3307, 2180, 2204, 2205}"
103,1,64,0,0.1102998,"\int \frac{1}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[ArcSinh[a*x]^(-3/2),x]","-\frac{2 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{a}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{a}","-\frac{2 \sqrt{a^2 x^2+1}}{a \sqrt{\sinh ^{-1}(a x)}}-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{a}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{a}",1,"(-2*Sqrt[1 + a^2*x^2])/(a*Sqrt[ArcSinh[a*x]]) - (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/a + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/a","A",7,6,8,0.7500,1,"{5655, 5779, 3308, 2180, 2204, 2205}"
104,0,0,0,0.0131123,"\int \frac{1}{x \sinh ^{-1}(a x)^{3/2}} \, dx","Int[1/(x*ArcSinh[a*x]^(3/2)),x]","\int \frac{1}{x \sinh ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]^(3/2)), x]","A",0,0,0,0,-1,"{}"
105,1,223,0,0.5837915,"\int \frac{x^4}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[x^4/ArcSinh[a*x]^(5/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}+\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{24 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}-\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{24 a^5}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{16 x^3}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{20 x^5}{3 \sqrt{\sinh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}+\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{24 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}-\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{8 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{24 a^5}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{16 x^3}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{20 x^5}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x^4*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^(3/2)) - (16*x^3)/(3*a^2*Sqrt[ArcSinh[a*x]]) - (20*x^5)/(3*Sqrt[ArcSinh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(12*a^5) - (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(8*a^5) + (5*Sqrt[5*Pi]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(24*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(12*a^5) - (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(8*a^5) + (5*Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(24*a^5)","A",34,8,12,0.6667,1,"{5667, 5774, 5669, 5448, 3307, 2180, 2204, 2205}"
106,1,167,0,0.4413748,"\int \frac{x^3}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[x^3/ArcSinh[a*x]^(5/2),x]","-\frac{2 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}+\frac{\sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}+\frac{2 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}-\frac{\sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{4 x^2}{a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{16 x^4}{3 \sqrt{\sinh ^{-1}(a x)}}","-\frac{2 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}+\frac{\sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}+\frac{2 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}-\frac{\sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^4}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{4 x^2}{a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{16 x^4}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x^3*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^(3/2)) - (4*x^2)/(a^2*Sqrt[ArcSinh[a*x]]) - (16*x^4)/(3*Sqrt[ArcSinh[a*x]]) - (2*Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(3*a^4) + (Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a^4) + (2*Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(3*a^4) - (Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a^4)","A",24,9,12,0.7500,1,"{5667, 5774, 5669, 5448, 3308, 2180, 2204, 2205, 12}"
107,1,161,0,0.372393,"\int \frac{x^2}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[x^2/ArcSinh[a*x]^(5/2),x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{6 a^3}+\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{6 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^3}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{8 x}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{4 x^3}{\sqrt{\sinh ^{-1}(a x)}}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{6 a^3}+\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{6 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{2 a^3}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{8 x}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{4 x^3}{\sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x^2*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^(3/2)) - (8*x)/(3*a^2*Sqrt[ArcSinh[a*x]]) - (4*x^3)/Sqrt[ArcSinh[a*x]] - (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(6*a^3) + (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(2*a^3) - (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(6*a^3) + (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(2*a^3)","A",22,9,12,0.7500,1,"{5667, 5774, 5669, 5448, 3307, 2180, 2204, 2205, 5657}"
108,1,118,0,0.2226223,"\int \frac{x}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[x/ArcSinh[a*x]^(5/2),x]","-\frac{2 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^2}+\frac{2 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^2}-\frac{2 x \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{4}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{8 x^2}{3 \sqrt{\sinh ^{-1}(a x)}}","-\frac{2 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^2}+\frac{2 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a^2}-\frac{2 x \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{4}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{8 x^2}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*x*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^(3/2)) - 4/(3*a^2*Sqrt[ArcSinh[a*x]]) - (8*x^2)/(3*Sqrt[ArcSinh[a*x]]) - (2*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a^2) + (2*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a^2)","A",11,10,10,1.000,1,"{5667, 5774, 5669, 5448, 12, 3308, 2180, 2204, 2205, 5675}"
109,1,84,0,0.1173994,"\int \frac{1}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[ArcSinh[a*x]^(-5/2),x]","-\frac{2 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}+\frac{2 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{3 a}+\frac{2 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{3 a}-\frac{4 x}{3 \sqrt{\sinh ^{-1}(a x)}}","-\frac{2 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}+\frac{2 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{3 a}+\frac{2 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{3 a}-\frac{4 x}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*Sqrt[1 + a^2*x^2])/(3*a*ArcSinh[a*x]^(3/2)) - (4*x)/(3*Sqrt[ArcSinh[a*x]]) + (2*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(3*a) + (2*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(3*a)","A",8,7,8,0.8750,1,"{5655, 5774, 5657, 3307, 2180, 2204, 2205}"
110,0,0,0,0.0135873,"\int \frac{1}{x \sinh ^{-1}(a x)^{5/2}} \, dx","Int[1/(x*ArcSinh[a*x]^(5/2)),x]","\int \frac{1}{x \sinh ^{-1}(a x)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)^{5/2}},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]^(5/2)), x]","A",0,0,0,0,-1,"{}"
111,1,285,0,0.5437112,"\int \frac{x^4}{\sinh ^{-1}(a x)^{7/2}} \, dx","Int[x^4/ArcSinh[a*x]^(7/2),x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{30 a^5}+\frac{9 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{20 a^5}-\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{30 a^5}-\frac{9 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{20 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}-\frac{40 x^4 \sqrt{a^2 x^2+1}}{3 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{16 x^3}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{32 x^2 \sqrt{a^2 x^2+1}}{5 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{4 x^5}{3 \sinh ^{-1}(a x)^{3/2}}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{30 a^5}+\frac{9 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{20 a^5}-\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{30 a^5}-\frac{9 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{20 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\sinh ^{-1}(a x)}\right)}{12 a^5}-\frac{40 x^4 \sqrt{a^2 x^2+1}}{3 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{16 x^3}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{32 x^2 \sqrt{a^2 x^2+1}}{5 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{4 x^5}{3 \sinh ^{-1}(a x)^{3/2}}",1,"(-2*x^4*Sqrt[1 + a^2*x^2])/(5*a*ArcSinh[a*x]^(5/2)) - (16*x^3)/(15*a^2*ArcSinh[a*x]^(3/2)) - (4*x^5)/(3*ArcSinh[a*x]^(3/2)) - (32*x^2*Sqrt[1 + a^2*x^2])/(5*a^3*Sqrt[ArcSinh[a*x]]) - (40*x^4*Sqrt[1 + a^2*x^2])/(3*a*Sqrt[ArcSinh[a*x]]) - (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(30*a^5) + (9*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(20*a^5) - (5*Sqrt[5*Pi]*Erf[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(12*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(30*a^5) - (9*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(20*a^5) + (5*Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ArcSinh[a*x]]])/(12*a^5)","A",32,7,12,0.5833,1,"{5667, 5774, 5665, 3308, 2180, 2204, 2205}"
112,1,229,0,0.4277139,"\int \frac{x^3}{\sinh ^{-1}(a x)^{7/2}} \, dx","Int[x^3/ArcSinh[a*x]^(7/2),x]","\frac{16 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}-\frac{4 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}+\frac{16 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}-\frac{4 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}-\frac{128 x^3 \sqrt{a^2 x^2+1}}{15 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{4 x^2}{5 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{16 x \sqrt{a^2 x^2+1}}{5 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{16 x^4}{15 \sinh ^{-1}(a x)^{3/2}}","\frac{16 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}-\frac{4 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}+\frac{16 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}-\frac{4 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^4}-\frac{128 x^3 \sqrt{a^2 x^2+1}}{15 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{4 x^2}{5 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{16 x \sqrt{a^2 x^2+1}}{5 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{16 x^4}{15 \sinh ^{-1}(a x)^{3/2}}",1,"(-2*x^3*Sqrt[1 + a^2*x^2])/(5*a*ArcSinh[a*x]^(5/2)) - (4*x^2)/(5*a^2*ArcSinh[a*x]^(3/2)) - (16*x^4)/(15*ArcSinh[a*x]^(3/2)) - (16*x*Sqrt[1 + a^2*x^2])/(5*a^3*Sqrt[ArcSinh[a*x]]) - (128*x^3*Sqrt[1 + a^2*x^2])/(15*a*Sqrt[ArcSinh[a*x]]) + (16*Sqrt[Pi]*Erf[2*Sqrt[ArcSinh[a*x]]])/(15*a^4) - (4*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(15*a^4) + (16*Sqrt[Pi]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(15*a^4) - (4*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(15*a^4)","A",21,7,12,0.5833,1,"{5667, 5774, 5665, 3307, 2180, 2204, 2205}"
113,1,222,0,0.4339306,"\int \frac{x^2}{\sinh ^{-1}(a x)^{7/2}} \, dx","Int[x^2/ArcSinh[a*x]^(7/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a^3}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{5 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a^3}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{5 a^3}-\frac{24 x^2 \sqrt{a^2 x^2+1}}{5 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{16 \sqrt{a^2 x^2+1}}{15 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{8 x}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{4 x^3}{5 \sinh ^{-1}(a x)^{3/2}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a^3}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{5 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a^3}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\sinh ^{-1}(a x)}\right)}{5 a^3}-\frac{24 x^2 \sqrt{a^2 x^2+1}}{5 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^2 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{16 \sqrt{a^2 x^2+1}}{15 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{8 x}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{4 x^3}{5 \sinh ^{-1}(a x)^{3/2}}",1,"(-2*x^2*Sqrt[1 + a^2*x^2])/(5*a*ArcSinh[a*x]^(5/2)) - (8*x)/(15*a^2*ArcSinh[a*x]^(3/2)) - (4*x^3)/(5*ArcSinh[a*x]^(3/2)) - (16*Sqrt[1 + a^2*x^2])/(15*a^3*Sqrt[ArcSinh[a*x]]) - (24*x^2*Sqrt[1 + a^2*x^2])/(5*a*Sqrt[ArcSinh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(15*a^3) - (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(5*a^3) - (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(15*a^3) + (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcSinh[a*x]]])/(5*a^3)","A",22,9,12,0.7500,1,"{5667, 5774, 5665, 3308, 2180, 2204, 2205, 5655, 5779}"
114,1,147,0,0.2117506,"\int \frac{x}{\sinh ^{-1}(a x)^{7/2}} \, dx","Int[x/ArcSinh[a*x]^(7/2),x]","\frac{8 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^2}+\frac{8 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^2}-\frac{32 x \sqrt{a^2 x^2+1}}{15 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{4}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{8 x^2}{15 \sinh ^{-1}(a x)^{3/2}}","\frac{8 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^2}+\frac{8 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{15 a^2}-\frac{32 x \sqrt{a^2 x^2+1}}{15 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{4}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{8 x^2}{15 \sinh ^{-1}(a x)^{3/2}}",1,"(-2*x*Sqrt[1 + a^2*x^2])/(5*a*ArcSinh[a*x]^(5/2)) - 4/(15*a^2*ArcSinh[a*x]^(3/2)) - (8*x^2)/(15*ArcSinh[a*x]^(3/2)) - (32*x*Sqrt[1 + a^2*x^2])/(15*a*Sqrt[ArcSinh[a*x]]) + (8*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(15*a^2) + (8*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(15*a^2)","A",9,8,10,0.8000,1,"{5667, 5774, 5665, 3307, 2180, 2204, 2205, 5675}"
115,1,112,0,0.1891011,"\int \frac{1}{\sinh ^{-1}(a x)^{7/2}} \, dx","Int[ArcSinh[a*x]^(-7/2),x]","-\frac{8 \sqrt{a^2 x^2+1}}{15 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{4 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a}+\frac{4 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a}-\frac{4 x}{15 \sinh ^{-1}(a x)^{3/2}}","-\frac{8 \sqrt{a^2 x^2+1}}{15 a \sqrt{\sinh ^{-1}(a x)}}-\frac{2 \sqrt{a^2 x^2+1}}{5 a \sinh ^{-1}(a x)^{5/2}}-\frac{4 \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a}+\frac{4 \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(a x)}\right)}{15 a}-\frac{4 x}{15 \sinh ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[1 + a^2*x^2])/(5*a*ArcSinh[a*x]^(5/2)) - (4*x)/(15*ArcSinh[a*x]^(3/2)) - (8*Sqrt[1 + a^2*x^2])/(15*a*Sqrt[ArcSinh[a*x]]) - (4*Sqrt[Pi]*Erf[Sqrt[ArcSinh[a*x]]])/(15*a) + (4*Sqrt[Pi]*Erfi[Sqrt[ArcSinh[a*x]]])/(15*a)","A",9,7,8,0.8750,1,"{5655, 5774, 5779, 3308, 2180, 2204, 2205}"
116,0,0,0,0.0143787,"\int \frac{1}{x \sinh ^{-1}(a x)^{7/2}} \, dx","Int[1/(x*ArcSinh[a*x]^(7/2)),x]","\int \frac{1}{x \sinh ^{-1}(a x)^{7/2}} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a x)^{7/2}},x\right)",0,"Defer[Int][1/(x*ArcSinh[a*x]^(7/2)), x]","A",0,0,0,0,-1,"{}"
117,0,0,0,0.1103588,"\int x^m \sinh ^{-1}(a x)^4 \, dx","Int[x^m*ArcSinh[a*x]^4,x]","\int x^m \sinh ^{-1}(a x)^4 \, dx","\frac{x^{m+1} \sinh ^{-1}(a x)^4}{m+1}-\frac{4 a \text{Int}\left(\frac{x^{m+1} \sinh ^{-1}(a x)^3}{\sqrt{a^2 x^2+1}},x\right)}{m+1}",0,"(x^(1 + m)*ArcSinh[a*x]^4)/(1 + m) - (4*a*Defer[Int][(x^(1 + m)*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2], x])/(1 + m)","A",0,0,0,0,-1,"{}"
118,0,0,0,0.1059947,"\int x^m \sinh ^{-1}(a x)^3 \, dx","Int[x^m*ArcSinh[a*x]^3,x]","\int x^m \sinh ^{-1}(a x)^3 \, dx","\frac{x^{m+1} \sinh ^{-1}(a x)^3}{m+1}-\frac{3 a \text{Int}\left(\frac{x^{m+1} \sinh ^{-1}(a x)^2}{\sqrt{a^2 x^2+1}},x\right)}{m+1}",0,"(x^(1 + m)*ArcSinh[a*x]^3)/(1 + m) - (3*a*Defer[Int][(x^(1 + m)*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2], x])/(1 + m)","A",0,0,0,0,-1,"{}"
119,1,137,0,0.0998867,"\int x^m \sinh ^{-1}(a x)^2 \, dx","Int[x^m*ArcSinh[a*x]^2,x]","\frac{2 a^2 x^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};-a^2 x^2\right)}{m^3+6 m^2+11 m+6}-\frac{2 a x^{m+2} \sinh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-a^2 x^2\right)}{m^2+3 m+2}+\frac{x^{m+1} \sinh ^{-1}(a x)^2}{m+1}","\frac{2 a^2 x^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};-a^2 x^2\right)}{m^3+6 m^2+11 m+6}-\frac{2 a x^{m+2} \sinh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-a^2 x^2\right)}{m^2+3 m+2}+\frac{x^{m+1} \sinh ^{-1}(a x)^2}{m+1}",1,"(x^(1 + m)*ArcSinh[a*x]^2)/(1 + m) - (2*a*x^(2 + m)*ArcSinh[a*x]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + 3*m + m^2) + (2*a^2*x^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, -(a^2*x^2)])/(6 + 11*m + 6*m^2 + m^3)","A",2,2,10,0.2000,1,"{5661, 5762}"
120,1,60,0,0.0195273,"\int x^m \sinh ^{-1}(a x) \, dx","Int[x^m*ArcSinh[a*x],x]","\frac{x^{m+1} \sinh ^{-1}(a x)}{m+1}-\frac{a x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-a^2 x^2\right)}{m^2+3 m+2}","\frac{x^{m+1} \sinh ^{-1}(a x)}{m+1}-\frac{a x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-a^2 x^2\right)}{m^2+3 m+2}",1,"(x^(1 + m)*ArcSinh[a*x])/(1 + m) - (a*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)])/(2 + 3*m + m^2)","A",2,2,8,0.2500,1,"{5661, 364}"
121,0,0,0,0.0148593,"\int \frac{x^m}{\sinh ^{-1}(a x)} \, dx","Int[x^m/ArcSinh[a*x],x]","\int \frac{x^m}{\sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^m}{\sinh ^{-1}(a x)},x\right)",0,"Defer[Int][x^m/ArcSinh[a*x], x]","A",0,0,0,0,-1,"{}"
122,0,0,0,0.0136401,"\int \frac{x^m}{\sinh ^{-1}(a x)^2} \, dx","Int[x^m/ArcSinh[a*x]^2,x]","\int \frac{x^m}{\sinh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x^m}{\sinh ^{-1}(a x)^2},x\right)",0,"Defer[Int][x^m/ArcSinh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
123,0,0,0,0.0150432,"\int x^m \sinh ^{-1}(a x)^{5/2} \, dx","Int[x^m*ArcSinh[a*x]^(5/2),x]","\int x^m \sinh ^{-1}(a x)^{5/2} \, dx","\text{Int}\left(x^m \sinh ^{-1}(a x)^{5/2},x\right)",0,"Defer[Int][x^m*ArcSinh[a*x]^(5/2), x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.0141627,"\int x^m \sinh ^{-1}(a x)^{3/2} \, dx","Int[x^m*ArcSinh[a*x]^(3/2),x]","\int x^m \sinh ^{-1}(a x)^{3/2} \, dx","\text{Int}\left(x^m \sinh ^{-1}(a x)^{3/2},x\right)",0,"Defer[Int][x^m*ArcSinh[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.0131903,"\int x^m \sqrt{\sinh ^{-1}(a x)} \, dx","Int[x^m*Sqrt[ArcSinh[a*x]],x]","\int x^m \sqrt{\sinh ^{-1}(a x)} \, dx","\text{Int}\left(x^m \sqrt{\sinh ^{-1}(a x)},x\right)",0,"Defer[Int][x^m*Sqrt[ArcSinh[a*x]], x]","A",0,0,0,0,-1,"{}"
126,0,0,0,0.013785,"\int \frac{x^m}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[x^m/Sqrt[ArcSinh[a*x]],x]","\int \frac{x^m}{\sqrt{\sinh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{x^m}{\sqrt{\sinh ^{-1}(a x)}},x\right)",0,"Defer[Int][x^m/Sqrt[ArcSinh[a*x]], x]","A",0,0,0,0,-1,"{}"
127,0,0,0,0.0148467,"\int \frac{x^m}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[x^m/ArcSinh[a*x]^(3/2),x]","\int \frac{x^m}{\sinh ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{x^m}{\sinh ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][x^m/ArcSinh[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
128,0,0,0,0.0176584,"\int (b x)^m \sinh ^{-1}(a x)^n \, dx","Int[(b*x)^m*ArcSinh[a*x]^n,x]","\int (b x)^m \sinh ^{-1}(a x)^n \, dx","\text{Int}\left((b x)^m \sinh ^{-1}(a x)^n,x\right)",0,"Defer[Int][(b*x)^m*ArcSinh[a*x]^n, x]","A",0,0,0,0,-1,"{}"
129,1,173,0,0.2163634,"\int x^4 \sinh ^{-1}(a x)^n \, dx","Int[x^4*ArcSinh[a*x]^n,x]","\frac{5^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-5 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{3^{-n} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \sinh ^{-1}(a x)\right)}{32 a^5}+\frac{\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{16 a^5}-\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{16 a^5}+\frac{3^{-n} \text{Gamma}\left(n+1,3 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{5^{-n-1} \text{Gamma}\left(n+1,5 \sinh ^{-1}(a x)\right)}{32 a^5}","\frac{5^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-5 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{3^{-n} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \sinh ^{-1}(a x)\right)}{32 a^5}+\frac{\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{16 a^5}-\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{16 a^5}+\frac{3^{-n} \text{Gamma}\left(n+1,3 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{5^{-n-1} \text{Gamma}\left(n+1,5 \sinh ^{-1}(a x)\right)}{32 a^5}",1,"(5^(-1 - n)*ArcSinh[a*x]^n*Gamma[1 + n, -5*ArcSinh[a*x]])/(32*a^5*(-ArcSinh[a*x])^n) - (ArcSinh[a*x]^n*Gamma[1 + n, -3*ArcSinh[a*x]])/(32*3^n*a^5*(-ArcSinh[a*x])^n) + (ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(16*a^5*(-ArcSinh[a*x])^n) - Gamma[1 + n, ArcSinh[a*x]]/(16*a^5) + Gamma[1 + n, 3*ArcSinh[a*x]]/(32*3^n*a^5) - (5^(-1 - n)*Gamma[1 + n, 5*ArcSinh[a*x]])/(32*a^5)","A",12,4,10,0.4000,1,"{5669, 5448, 3307, 2181}"
130,1,119,0,0.1741192,"\int x^3 \sinh ^{-1}(a x)^n \, dx","Int[x^3*ArcSinh[a*x]^n,x]","\frac{2^{-2 (n+3)} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-4 \sinh ^{-1}(a x)\right)}{a^4}-\frac{2^{-n-4} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^4}-\frac{2^{-n-4} \text{Gamma}\left(n+1,2 \sinh ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \text{Gamma}\left(n+1,4 \sinh ^{-1}(a x)\right)}{a^4}","\frac{2^{-2 (n+3)} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-4 \sinh ^{-1}(a x)\right)}{a^4}-\frac{2^{-n-4} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^4}-\frac{2^{-n-4} \text{Gamma}\left(n+1,2 \sinh ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \text{Gamma}\left(n+1,4 \sinh ^{-1}(a x)\right)}{a^4}",1,"(ArcSinh[a*x]^n*Gamma[1 + n, -4*ArcSinh[a*x]])/(2^(2*(3 + n))*a^4*(-ArcSinh[a*x])^n) - (2^(-4 - n)*ArcSinh[a*x]^n*Gamma[1 + n, -2*ArcSinh[a*x]])/(a^4*(-ArcSinh[a*x])^n) - (2^(-4 - n)*Gamma[1 + n, 2*ArcSinh[a*x]])/a^4 + Gamma[1 + n, 4*ArcSinh[a*x]]/(2^(2*(3 + n))*a^4)","A",9,4,10,0.4000,1,"{5669, 5448, 3308, 2181}"
131,1,113,0,0.1450621,"\int x^2 \sinh ^{-1}(a x)^n \, dx","Int[x^2*ArcSinh[a*x]^n,x]","\frac{3^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \sinh ^{-1}(a x)\right)}{8 a^3}-\frac{\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{8 a^3}+\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{8 a^3}-\frac{3^{-n-1} \text{Gamma}\left(n+1,3 \sinh ^{-1}(a x)\right)}{8 a^3}","\frac{3^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \sinh ^{-1}(a x)\right)}{8 a^3}-\frac{\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{8 a^3}+\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{8 a^3}-\frac{3^{-n-1} \text{Gamma}\left(n+1,3 \sinh ^{-1}(a x)\right)}{8 a^3}",1,"(3^(-1 - n)*ArcSinh[a*x]^n*Gamma[1 + n, -3*ArcSinh[a*x]])/(8*a^3*(-ArcSinh[a*x])^n) - (ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(8*a^3*(-ArcSinh[a*x])^n) + Gamma[1 + n, ArcSinh[a*x]]/(8*a^3) - (3^(-1 - n)*Gamma[1 + n, 3*ArcSinh[a*x]])/(8*a^3)","A",9,4,10,0.4000,1,"{5669, 5448, 3307, 2181}"
132,1,59,0,0.0841649,"\int x \sinh ^{-1}(a x)^n \, dx","Int[x*ArcSinh[a*x]^n,x]","\frac{2^{-n-3} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \text{Gamma}\left(n+1,2 \sinh ^{-1}(a x)\right)}{a^2}","\frac{2^{-n-3} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \text{Gamma}\left(n+1,2 \sinh ^{-1}(a x)\right)}{a^2}",1,"(2^(-3 - n)*ArcSinh[a*x]^n*Gamma[1 + n, -2*ArcSinh[a*x]])/(a^2*(-ArcSinh[a*x])^n) + (2^(-3 - n)*Gamma[1 + n, 2*ArcSinh[a*x]])/a^2","A",6,5,8,0.6250,1,"{5669, 5448, 12, 3308, 2181}"
133,1,49,0,0.0467243,"\int \sinh ^{-1}(a x)^n \, dx","Int[ArcSinh[a*x]^n,x]","\frac{\left(-\sinh ^{-1}(a x)\right)^{-n} \sinh ^{-1}(a x)^n \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{2 a}-\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{2 a}","\frac{\left(-\sinh ^{-1}(a x)\right)^{-n} \sinh ^{-1}(a x)^n \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{2 a}-\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{2 a}",1,"(ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(2*a*(-ArcSinh[a*x])^n) - Gamma[1 + n, ArcSinh[a*x]]/(2*a)","A",4,3,6,0.5000,1,"{5657, 3307, 2181}"
134,0,0,0,0.0152087,"\int \frac{\sinh ^{-1}(a x)^n}{x} \, dx","Int[ArcSinh[a*x]^n/x,x]","\int \frac{\sinh ^{-1}(a x)^n}{x} \, dx","\text{Int}\left(\frac{\sinh ^{-1}(a x)^n}{x},x\right)",0,"Defer[Int][ArcSinh[a*x]^n/x, x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.0164332,"\int \frac{\sinh ^{-1}(a x)^n}{x^2} \, dx","Int[ArcSinh[a*x]^n/x^2,x]","\int \frac{\sinh ^{-1}(a x)^n}{x^2} \, dx","\text{Int}\left(\frac{\sinh ^{-1}(a x)^n}{x^2},x\right)",0,"Defer[Int][ArcSinh[a*x]^n/x^2, x]","A",0,0,0,0,-1,"{}"
136,1,213,0,0.6046366,"\int x^2 \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Int[x^2*Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}+\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}+\frac{1}{3} x^3 \sqrt{a+b \sinh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}+\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}+\frac{1}{3} x^3 \sqrt{a+b \sinh ^{-1}(c x)}",1,"(x^3*Sqrt[a + b*ArcSinh[c*x]])/3 - (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*c^3) + (Sqrt[b]*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(48*c^3) + (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*c^3*E^(a/b)) - (Sqrt[b]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(48*c^3*E^((3*a)/b))","A",14,7,16,0.4375,1,"{5663, 5779, 3312, 3308, 2180, 2204, 2205}"
137,1,145,0,0.43199,"\int x \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Int[x*Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^2}+\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \sinh ^{-1}(c x)}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^2}+\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \sinh ^{-1}(c x)}",1,"Sqrt[a + b*ArcSinh[c*x]]/(4*c^2) + (x^2*Sqrt[a + b*ArcSinh[c*x]])/2 - (Sqrt[b]*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*c^2) - (Sqrt[b]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*c^2*E^((2*a)/b))","A",9,7,14,0.5000,1,"{5663, 5779, 3312, 3307, 2180, 2204, 2205}"
138,1,102,0,0.2504027,"\int \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcSinh[c*x]],x]","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \sinh ^{-1}(c x)}","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \sinh ^{-1}(c x)}",1,"x*Sqrt[a + b*ArcSinh[c*x]] + (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c*E^(a/b))","A",7,6,12,0.5000,1,"{5653, 5779, 3308, 2180, 2204, 2205}"
139,1,282,0,0.862231,"\int x^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Int[x^2*(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{b x^2 \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{6 c}+\frac{b \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{b x^2 \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{6 c}+\frac{b \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}",1,"(b*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(3*c^3) - (b*x^2*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(6*c) + (x^3*(a + b*ArcSinh[c*x])^(3/2))/3 - (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(32*c^3) + (b^(3/2)*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(96*c^3) - (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(32*c^3*E^(a/b)) + (b^(3/2)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(96*c^3*E^((3*a)/b))","A",22,10,16,0.6250,1,"{5663, 5758, 5717, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
140,1,179,0,0.4782032,"\int x \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Int[x*(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^2}-\frac{3 b x \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{8 c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^2}-\frac{3 b x \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{8 c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}",1,"(-3*b*x*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(8*c) + (a + b*ArcSinh[c*x])^(3/2)/(4*c^2) + (x^2*(a + b*ArcSinh[c*x])^(3/2))/2 - (3*b^(3/2)*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(64*c^2) + (3*b^(3/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(64*c^2*E^((2*a)/b))","A",11,10,14,0.7143,1,"{5663, 5758, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
141,1,135,0,0.2546326,"\int \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcSinh[c*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{2 c}+x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{2 c}+x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}",1,"(-3*b*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(2*c) + x*(a + b*ArcSinh[c*x])^(3/2) + (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c*E^(a/b))","A",8,7,12,0.5833,1,"{5653, 5717, 5657, 3307, 2180, 2205, 2204}"
142,1,327,0,1.250316,"\int x^2 \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \, dx","Int[x^2*(a + b*ArcSinh[c*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^3}+\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{576 c^3}+\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^3}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{576 c^3}-\frac{5 b^2 x \sqrt{a+b \sinh ^{-1}(c x)}}{6 c^2}+\frac{5}{36} b^2 x^3 \sqrt{a+b \sinh ^{-1}(c x)}-\frac{5 b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{18 c}+\frac{5 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \sinh ^{-1}(c x)\right)^{5/2}","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^3}+\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{576 c^3}+\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^3}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{576 c^3}-\frac{5 b^2 x \sqrt{a+b \sinh ^{-1}(c x)}}{6 c^2}+\frac{5}{36} b^2 x^3 \sqrt{a+b \sinh ^{-1}(c x)}-\frac{5 b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{18 c}+\frac{5 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \sinh ^{-1}(c x)\right)^{5/2}",1,"(-5*b^2*x*Sqrt[a + b*ArcSinh[c*x]])/(6*c^2) + (5*b^2*x^3*Sqrt[a + b*ArcSinh[c*x]])/36 + (5*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^(3/2))/(9*c^3) - (5*b*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^(3/2))/(18*c) + (x^3*(a + b*ArcSinh[c*x])^(5/2))/3 - (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(64*c^3) + (5*b^(5/2)*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(576*c^3) + (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(64*c^3*E^(a/b)) - (5*b^(5/2)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(576*c^3*E^((3*a)/b))","A",24,10,16,0.6250,1,"{5663, 5758, 5717, 5653, 5779, 3308, 2180, 2204, 2205, 3312}"
143,1,223,0,0.7508582,"\int x \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \, dx","Int[x*(a + b*ArcSinh[c*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{256 c^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{256 c^2}+\frac{15 b^2 \sqrt{a+b \sinh ^{-1}(c x)}}{64 c^2}+\frac{15}{32} b^2 x^2 \sqrt{a+b \sinh ^{-1}(c x)}-\frac{5 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{8 c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sinh ^{-1}(c x)\right)^{5/2}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{256 c^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{256 c^2}+\frac{15 b^2 \sqrt{a+b \sinh ^{-1}(c x)}}{64 c^2}+\frac{15}{32} b^2 x^2 \sqrt{a+b \sinh ^{-1}(c x)}-\frac{5 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{8 c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \sinh ^{-1}(c x)\right)^{5/2}",1,"(15*b^2*Sqrt[a + b*ArcSinh[c*x]])/(64*c^2) + (15*b^2*x^2*Sqrt[a + b*ArcSinh[c*x]])/32 - (5*b*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^(3/2))/(8*c) + (a + b*ArcSinh[c*x])^(5/2)/(4*c^2) + (x^2*(a + b*ArcSinh[c*x])^(5/2))/2 - (15*b^(5/2)*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(256*c^2) - (15*b^(5/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(256*c^2*E^((2*a)/b))","A",12,9,14,0.6429,1,"{5663, 5758, 5675, 5779, 3312, 3307, 2180, 2204, 2205}"
144,1,155,0,0.4063924,"\int \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \, dx","Int[(a + b*ArcSinh[c*x])^(5/2),x]","\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c}+\frac{15}{4} b^2 x \sqrt{a+b \sinh ^{-1}(c x)}-\frac{5 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \sinh ^{-1}(c x)\right)^{5/2}","\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c}+\frac{15}{4} b^2 x \sqrt{a+b \sinh ^{-1}(c x)}-\frac{5 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \sinh ^{-1}(c x)\right)^{5/2}",1,"(15*b^2*x*Sqrt[a + b*ArcSinh[c*x]])/4 - (5*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^(3/2))/(2*c) + x*(a + b*ArcSinh[c*x])^(5/2) + (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*c) - (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*c*E^(a/b))","A",9,7,12,0.5833,1,"{5653, 5717, 5779, 3308, 2180, 2204, 2205}"
145,1,194,0,0.3501433,"\int \frac{x^2}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[x^2/Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3) + (E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3) - (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3*E^(a/b)) + (Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3*E^((3*a)/b))","A",13,6,16,0.3750,1,"{5669, 5448, 3307, 2180, 2204, 2205}"
146,1,107,0,0.1790854,"\int \frac{x}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[x/Sqrt[a + b*ArcSinh[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^2}-\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^2}","\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^2}-\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^2}",1,"-(E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^2) + (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^2*E^((2*a)/b))","A",8,7,14,0.5000,1,"{5669, 5448, 12, 3308, 2180, 2204, 2205}"
147,1,88,0,0.1042047,"\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcSinh[c*x]],x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b))","A",6,5,12,0.4167,1,"{5657, 3307, 2180, 2205, 2204}"
148,1,226,0,0.3238647,"\int \frac{x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[x^2/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{\sqrt{3 \pi } e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{3 \pi } e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{2 x^2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{\sqrt{3 \pi } e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{3 \pi } e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{2 x^2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*x^2*Sqrt[1 + c^2*x^2])/(b*c*Sqrt[a + b*ArcSinh[c*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3) - (E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3) - (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3*E^(a/b)) + (Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3*E^((3*a)/b))","A",12,5,16,0.3125,1,"{5665, 3308, 2180, 2204, 2205}"
149,1,135,0,0.1617028,"\int \frac{x}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[x/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 x \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 x \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*x*Sqrt[1 + c^2*x^2])/(b*c*Sqrt[a + b*ArcSinh[c*x]]) + (E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(b^(3/2)*c^2) + (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(b^(3/2)*c^2*E^((2*a)/b))","A",6,5,14,0.3571,1,"{5665, 3307, 2180, 2204, 2205}"
150,1,116,0,0.2556439,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^(-3/2),x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*Sqrt[1 + c^2*x^2])/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(b^(3/2)*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(b^(3/2)*c*E^(a/b))","A",7,6,12,0.5000,1,"{5655, 5779, 3308, 2180, 2204, 2205}"
151,1,271,0,0.899481,"\int \frac{x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}} \, dx","Int[x^2/(a + b*ArcSinh[c*x])^(5/2),x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{6 b^{5/2} c^3}+\frac{\sqrt{3 \pi } e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{5/2} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{6 b^{5/2} c^3}+\frac{\sqrt{3 \pi } e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{5/2} c^3}-\frac{8 x}{3 b^2 c^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{4 x^3}{b^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 x^2 \sqrt{c^2 x^2+1}}{3 b c \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{6 b^{5/2} c^3}+\frac{\sqrt{3 \pi } e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{5/2} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{6 b^{5/2} c^3}+\frac{\sqrt{3 \pi } e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{5/2} c^3}-\frac{8 x}{3 b^2 c^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{4 x^3}{b^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 x^2 \sqrt{c^2 x^2+1}}{3 b c \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}",1,"(-2*x^2*Sqrt[1 + c^2*x^2])/(3*b*c*(a + b*ArcSinh[c*x])^(3/2)) - (8*x)/(3*b^2*c^2*Sqrt[a + b*ArcSinh[c*x]]) - (4*x^3)/(b^2*Sqrt[a + b*ArcSinh[c*x]]) - (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(6*b^(5/2)*c^3) + (E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(2*b^(5/2)*c^3) - (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(6*b^(5/2)*c^3*E^(a/b)) + (Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(2*b^(5/2)*c^3*E^((3*a)/b))","A",22,9,16,0.5625,1,"{5667, 5774, 5669, 5448, 3307, 2180, 2204, 2205, 5657}"
152,1,183,0,0.5172664,"\int \frac{x}{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}} \, dx","Int[x/(a + b*ArcSinh[c*x])^(5/2),x]","-\frac{2 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^2}+\frac{2 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^2}-\frac{4}{3 b^2 c^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{8 x^2}{3 b^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 x \sqrt{c^2 x^2+1}}{3 b c \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}","-\frac{2 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^2}+\frac{2 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^2}-\frac{4}{3 b^2 c^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{8 x^2}{3 b^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 x \sqrt{c^2 x^2+1}}{3 b c \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}",1,"(-2*x*Sqrt[1 + c^2*x^2])/(3*b*c*(a + b*ArcSinh[c*x])^(3/2)) - 4/(3*b^2*c^2*Sqrt[a + b*ArcSinh[c*x]]) - (8*x^2)/(3*b^2*Sqrt[a + b*ArcSinh[c*x]]) - (2*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(3*b^(5/2)*c^2) + (2*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(3*b^(5/2)*c^2*E^((2*a)/b))","A",11,10,14,0.7143,1,"{5667, 5774, 5669, 5448, 12, 3308, 2180, 2204, 2205, 5675}"
153,1,143,0,0.2728544,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^(-5/2),x]","\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}-\frac{4 x}{3 b^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 \sqrt{c^2 x^2+1}}{3 b c \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}","\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}-\frac{4 x}{3 b^2 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 \sqrt{c^2 x^2+1}}{3 b c \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}",1,"(-2*Sqrt[1 + c^2*x^2])/(3*b*c*(a + b*ArcSinh[c*x])^(3/2)) - (4*x)/(3*b^2*Sqrt[a + b*ArcSinh[c*x]]) + (2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(3*b^(5/2)*c) + (2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(3*b^(5/2)*c*E^(a/b))","A",8,7,12,0.5833,1,"{5655, 5774, 5657, 3307, 2180, 2205, 2204}"
154,1,346,0,1.0326458,"\int \frac{x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{7/2}} \, dx","Int[x^2/(a + b*ArcSinh[c*x])^(7/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^3}-\frac{3 \sqrt{3 \pi } e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{5 b^{7/2} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^3}+\frac{3 \sqrt{3 \pi } e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{5 b^{7/2} c^3}-\frac{24 x^2 \sqrt{c^2 x^2+1}}{5 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{16 \sqrt{c^2 x^2+1}}{15 b^3 c^3 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{8 x}{15 b^2 c^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{4 x^3}{5 b^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{2 x^2 \sqrt{c^2 x^2+1}}{5 b c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^3}-\frac{3 \sqrt{3 \pi } e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{5 b^{7/2} c^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^3}+\frac{3 \sqrt{3 \pi } e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{5 b^{7/2} c^3}-\frac{24 x^2 \sqrt{c^2 x^2+1}}{5 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{16 \sqrt{c^2 x^2+1}}{15 b^3 c^3 \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{8 x}{15 b^2 c^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{4 x^3}{5 b^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{2 x^2 \sqrt{c^2 x^2+1}}{5 b c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}",1,"(-2*x^2*Sqrt[1 + c^2*x^2])/(5*b*c*(a + b*ArcSinh[c*x])^(5/2)) - (8*x)/(15*b^2*c^2*(a + b*ArcSinh[c*x])^(3/2)) - (4*x^3)/(5*b^2*(a + b*ArcSinh[c*x])^(3/2)) - (16*Sqrt[1 + c^2*x^2])/(15*b^3*c^3*Sqrt[a + b*ArcSinh[c*x]]) - (24*x^2*Sqrt[1 + c^2*x^2])/(5*b^3*c*Sqrt[a + b*ArcSinh[c*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c^3) - (3*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(5*b^(7/2)*c^3) - (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c^3*E^(a/b)) + (3*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(5*b^(7/2)*c^3*E^((3*a)/b))","A",22,9,16,0.5625,1,"{5667, 5774, 5665, 3308, 2180, 2204, 2205, 5655, 5779}"
155,1,219,0,0.5055738,"\int \frac{x}{\left(a+b \sinh ^{-1}(c x)\right)^{7/2}} \, dx","Int[x/(a + b*ArcSinh[c*x])^(7/2),x]","\frac{8 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^2}+\frac{8 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^2}-\frac{32 x \sqrt{c^2 x^2+1}}{15 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{4}{15 b^2 c^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{8 x^2}{15 b^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{2 x \sqrt{c^2 x^2+1}}{5 b c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}","\frac{8 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^2}+\frac{8 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^2}-\frac{32 x \sqrt{c^2 x^2+1}}{15 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{4}{15 b^2 c^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{8 x^2}{15 b^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{2 x \sqrt{c^2 x^2+1}}{5 b c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}",1,"(-2*x*Sqrt[1 + c^2*x^2])/(5*b*c*(a + b*ArcSinh[c*x])^(5/2)) - 4/(15*b^2*c^2*(a + b*ArcSinh[c*x])^(3/2)) - (8*x^2)/(15*b^2*(a + b*ArcSinh[c*x])^(3/2)) - (32*x*Sqrt[1 + c^2*x^2])/(15*b^3*c*Sqrt[a + b*ArcSinh[c*x]]) + (8*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(15*b^(7/2)*c^2) + (8*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(15*b^(7/2)*c^2*E^((2*a)/b))","A",9,8,14,0.5714,1,"{5667, 5774, 5665, 3307, 2180, 2204, 2205, 5675}"
156,1,178,0,0.4473223,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{7/2}} \, dx","Int[(a + b*ArcSinh[c*x])^(-7/2),x]","-\frac{8 \sqrt{c^2 x^2+1}}{15 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c}-\frac{4 x}{15 b^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{2 \sqrt{c^2 x^2+1}}{5 b c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}","-\frac{8 \sqrt{c^2 x^2+1}}{15 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c}-\frac{4 x}{15 b^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}}-\frac{2 \sqrt{c^2 x^2+1}}{5 b c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}",1,"(-2*Sqrt[1 + c^2*x^2])/(5*b*c*(a + b*ArcSinh[c*x])^(5/2)) - (4*x)/(15*b^2*(a + b*ArcSinh[c*x])^(3/2)) - (8*Sqrt[1 + c^2*x^2])/(15*b^3*c*Sqrt[a + b*ArcSinh[c*x]]) - (4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c) + (4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c*E^(a/b))","A",9,7,12,0.5833,1,"{5655, 5774, 5779, 3308, 2180, 2204, 2205}"