1,1,50,72,0.0361503,"\int x^4 \sinh ^{-1}(a x) \, dx","Integrate[x^4*ArcSinh[a*x],x]","\frac{1}{5} x^5 \sinh ^{-1}(a x)-\frac{\sqrt{a^2 x^2+1} \left(3 a^4 x^4-4 a^2 x^2+8\right)}{75 a^5}","-\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,"-1/75*(Sqrt[1 + a^2*x^2]*(8 - 4*a^2*x^2 + 3*a^4*x^4))/a^5 + (x^5*ArcSinh[a*x])/5","A",1
2,1,49,67,0.0174731,"\int x^3 \sinh ^{-1}(a x) \, dx","Integrate[x^3*ArcSinh[a*x],x]","\frac{\left(8 a^4 x^4-3\right) \sinh ^{-1}(a x)+a x \sqrt{a^2 x^2+1} \left(3-2 a^2 x^2\right)}{32 a^4}","-\frac{3 \sinh ^{-1}(a x)}{32 a^4}-\frac{x^3 \sqrt{a^2 x^2+1}}{16 a}+\frac{3 x \sqrt{a^2 x^2+1}}{32 a^3}+\frac{1}{4} x^4 \sinh ^{-1}(a x)",1,"(a*x*(3 - 2*a^2*x^2)*Sqrt[1 + a^2*x^2] + (-3 + 8*a^4*x^4)*ArcSinh[a*x])/(32*a^4)","A",1
3,1,41,52,0.0240871,"\int x^2 \sinh ^{-1}(a x) \, dx","Integrate[x^2*ArcSinh[a*x],x]","\frac{1}{9} \left(\frac{\left(2-a^2 x^2\right) \sqrt{a^2 x^2+1}}{a^3}+3 x^3 \sinh ^{-1}(a x)\right)","-\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,"(((2 - a^2*x^2)*Sqrt[1 + a^2*x^2])/a^3 + 3*x^3*ArcSinh[a*x])/9","A",1
4,1,40,44,0.010734,"\int x \sinh ^{-1}(a x) \, dx","Integrate[x*ArcSinh[a*x],x]","\frac{\left(2 a^2 x^2+1\right) \sinh ^{-1}(a x)-a x \sqrt{a^2 x^2+1}}{4 a^2}","-\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,"(-(a*x*Sqrt[1 + a^2*x^2]) + (1 + 2*a^2*x^2)*ArcSinh[a*x])/(4*a^2)","A",1
5,1,25,25,0.0079672,"\int \sinh ^{-1}(a x) \, dx","Integrate[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",1
6,1,43,43,0.0033818,"\int \frac{\sinh ^{-1}(a x)}{x} \, dx","Integrate[ArcSinh[a*x]/x,x]","\frac{1}{2} \text{Li}_2\left(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{Li}_2\left(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,"-1/2*ArcSinh[a*x]^2 + ArcSinh[a*x]*Log[1 - E^(2*ArcSinh[a*x])] + PolyLog[2, E^(2*ArcSinh[a*x])]/2","A",1
7,1,27,27,0.0024492,"\int \frac{\sinh ^{-1}(a x)}{x^2} \, dx","Integrate[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",1
8,1,28,33,0.0082697,"\int \frac{\sinh ^{-1}(a x)}{x^3} \, dx","Integrate[ArcSinh[a*x]/x^3,x]","-\frac{a x \sqrt{a^2 x^2+1}+\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,"-1/2*(a*x*Sqrt[1 + a^2*x^2] + ArcSinh[a*x])/x^2","A",1
9,1,54,54,0.0104941,"\int \frac{\sinh ^{-1}(a x)}{x^4} \, dx","Integrate[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,"-1/6*(a*Sqrt[1 + a^2*x^2])/x^2 - ArcSinh[a*x]/(3*x^3) + (a^3*ArcTanh[Sqrt[1 + a^2*x^2]])/6","A",1
10,1,40,56,0.012932,"\int \frac{\sinh ^{-1}(a x)}{x^5} \, dx","Integrate[ArcSinh[a*x]/x^5,x]","\frac{a x \sqrt{a^2 x^2+1} \left(2 a^2 x^2-1\right)-3 \sinh ^{-1}(a x)}{12 x^4}","-\frac{a \sqrt{a^2 x^2+1}}{12 x^3}+\frac{a^3 \sqrt{a^2 x^2+1}}{6 x}-\frac{\sinh ^{-1}(a x)}{4 x^4}",1,"(a*x*Sqrt[1 + a^2*x^2]*(-1 + 2*a^2*x^2) - 3*ArcSinh[a*x])/(12*x^4)","A",1
11,1,49,77,0.012852,"\int \frac{\sinh ^{-1}(a x)}{x^6} \, dx","Integrate[ArcSinh[a*x]/x^6,x]","-\frac{1}{5} a^5 \sqrt{a^2 x^2+1} \, _2F_1\left(\frac{1}{2},3;\frac{3}{2};a^2 x^2+1\right)-\frac{\sinh ^{-1}(a x)}{5 x^5}","-\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{3 a^3 \sqrt{a^2 x^2+1}}{40 x^2}-\frac{\sinh ^{-1}(a x)}{5 x^5}",1,"-1/5*ArcSinh[a*x]/x^5 - (a^5*Sqrt[1 + a^2*x^2]*Hypergeometric2F1[1/2, 3, 3/2, 1 + a^2*x^2])/5","C",1
12,1,75,117,0.0683013,"\int x^4 \sinh ^{-1}(a x)^2 \, dx","Integrate[x^4*ArcSinh[a*x]^2,x]","\frac{\frac{240 x}{a^4}-\frac{40 x^3}{a^2}-\frac{30 \sqrt{a^2 x^2+1} \left(3 a^4 x^4-4 a^2 x^2+8\right) \sinh ^{-1}(a x)}{a^5}+225 x^5 \sinh ^{-1}(a x)^2+18 x^5}{1125}","\frac{16 x}{75 a^4}-\frac{8 x^3}{225 a^2}-\frac{2 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{25 a}-\frac{16 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{75 a^5}+\frac{8 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{75 a^3}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^2+\frac{2 x^5}{125}",1,"((240*x)/a^4 - (40*x^3)/a^2 + 18*x^5 - (30*Sqrt[1 + a^2*x^2]*(8 - 4*a^2*x^2 + 3*a^4*x^4)*ArcSinh[a*x])/a^5 + 225*x^5*ArcSinh[a*x]^2)/1125","A",1
13,1,72,96,0.0468515,"\int x^3 \sinh ^{-1}(a x)^2 \, dx","Integrate[x^3*ArcSinh[a*x]^2,x]","\frac{\left(8 a^4 x^4-3\right) \sinh ^{-1}(a x)^2+a^2 x^2 \left(a^2 x^2-3\right)-2 a x \sqrt{a^2 x^2+1} \left(2 a^2 x^2-3\right) \sinh ^{-1}(a x)}{32 a^4}","-\frac{3 \sinh ^{-1}(a x)^2}{32 a^4}-\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{1}{4} x^4 \sinh ^{-1}(a x)^2+\frac{x^4}{32}",1,"(a^2*x^2*(-3 + a^2*x^2) - 2*a*x*Sqrt[1 + a^2*x^2]*(-3 + 2*a^2*x^2)*ArcSinh[a*x] + (-3 + 8*a^4*x^4)*ArcSinh[a*x]^2)/(32*a^4)","A",1
14,1,59,80,0.0627142,"\int x^2 \sinh ^{-1}(a x)^2 \, dx","Integrate[x^2*ArcSinh[a*x]^2,x]","\frac{1}{27} \left(2 x \left(x^2-\frac{6}{a^2}\right)-\frac{6 \left(a^2 x^2-2\right) \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^3}+9 x^3 \sinh ^{-1}(a x)^2\right)","-\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a}-\frac{4 x}{9 a^2}+\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^2+\frac{2 x^3}{27}",1,"(2*x*(-6/a^2 + x^2) - (6*(-2 + a^2*x^2)*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a^3 + 9*x^3*ArcSinh[a*x]^2)/27","A",1
15,1,53,59,0.0315757,"\int x \sinh ^{-1}(a x)^2 \, dx","Integrate[x*ArcSinh[a*x]^2,x]","\frac{a^2 x^2-2 a x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)+\left(2 a^2 x^2+1\right) \sinh ^{-1}(a x)^2}{4 a^2}","-\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,"(a^2*x^2 - 2*a*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + (1 + 2*a^2*x^2)*ArcSinh[a*x]^2)/(4*a^2)","A",1
16,1,34,34,0.0154501,"\int \sinh ^{-1}(a x)^2 \, dx","Integrate[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",1
17,1,60,60,0.0062331,"\int \frac{\sinh ^{-1}(a x)^2}{x} \, dx","Integrate[ArcSinh[a*x]^2/x,x]","\sinh ^{-1}(a x) \text{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{2} \text{Li}_3\left(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{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-\frac{1}{2} \text{Li}_3\left(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,"-1/3*ArcSinh[a*x]^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",1
18,1,75,50,0.212962,"\int \frac{\sinh ^{-1}(a x)^2}{x^2} \, dx","Integrate[ArcSinh[a*x]^2/x^2,x]","a \left(2 \text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)-2 \text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)-\sinh ^{-1}(a x) \left(\frac{\sinh ^{-1}(a x)}{a x}-2 \log \left(1-e^{-\sinh ^{-1}(a x)}\right)+2 \log \left(e^{-\sinh ^{-1}(a x)}+1\right)\right)\right)","-2 a \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)+2 a \text{Li}_2\left(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,"a*(-(ArcSinh[a*x]*(ArcSinh[a*x]/(a*x) - 2*Log[1 - E^(-ArcSinh[a*x])] + 2*Log[1 + E^(-ArcSinh[a*x])])) + 2*PolyLog[2, -E^(-ArcSinh[a*x])] - 2*PolyLog[2, E^(-ArcSinh[a*x])])","A",0
19,1,43,43,0.0341428,"\int \frac{\sinh ^{-1}(a x)^2}{x^3} \, dx","Integrate[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",1
20,1,125,99,0.5308376,"\int \frac{\sinh ^{-1}(a x)^2}{x^4} \, dx","Integrate[ArcSinh[a*x]^2/x^4,x]","-\frac{a^3 x^3 \text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)-a^3 x^3 \text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)+a^3 x^3 \sinh ^{-1}(a x) \log \left(1-e^{-\sinh ^{-1}(a x)}\right)-a^3 x^3 \sinh ^{-1}(a x) \log \left(e^{-\sinh ^{-1}(a x)}+1\right)+a^2 x^2+a x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)+\sinh ^{-1}(a x)^2}{3 x^3}","\frac{1}{3} a^3 \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{3} a^3 \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)+\frac{2}{3} a^3 \sinh ^{-1}(a x) \tanh ^{-1}\left(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{\sinh ^{-1}(a x)^2}{3 x^3}",1,"-1/3*(a^2*x^2 + a*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + ArcSinh[a*x]^2 + a^3*x^3*ArcSinh[a*x]*Log[1 - E^(-ArcSinh[a*x])] - a^3*x^3*ArcSinh[a*x]*Log[1 + E^(-ArcSinh[a*x])] + a^3*x^3*PolyLog[2, -E^(-ArcSinh[a*x])] - a^3*x^3*PolyLog[2, E^(-ArcSinh[a*x])])/x^3","A",0
21,1,64,85,0.0652505,"\int \frac{\sinh ^{-1}(a x)^2}{x^5} \, dx","Integrate[ArcSinh[a*x]^2/x^5,x]","-\frac{4 a^4 x^4 \log (x)+a^2 x^2-2 a x \sqrt{a^2 x^2+1} \left(2 a^2 x^2-1\right) \sinh ^{-1}(a x)+3 \sinh ^{-1}(a x)^2}{12 x^4}","-\frac{1}{3} a^4 \log (x)-\frac{a^2}{12 x^2}-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{6 x^3}+\frac{a^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 x}-\frac{\sinh ^{-1}(a x)^2}{4 x^4}",1,"-1/12*(a^2*x^2 - 2*a*x*Sqrt[1 + a^2*x^2]*(-1 + 2*a^2*x^2)*ArcSinh[a*x] + 3*ArcSinh[a*x]^2 + 4*a^4*x^4*Log[x])/x^4","A",1
22,1,120,195,0.0761015,"\int x^4 \sinh ^{-1}(a x)^3 \, dx","Integrate[x^4*ArcSinh[a*x]^3,x]","\frac{1125 a^5 x^5 \sinh ^{-1}(a x)^3-2 \sqrt{a^2 x^2+1} \left(27 a^4 x^4-136 a^2 x^2+2072\right)+30 a x \left(9 a^4 x^4-20 a^2 x^2+120\right) \sinh ^{-1}(a x)-225 \sqrt{a^2 x^2+1} \left(3 a^4 x^4-4 a^2 x^2+8\right) \sinh ^{-1}(a x)^2}{5625 a^5}","\frac{16 x \sinh ^{-1}(a x)}{25 a^4}-\frac{8 x^3 \sinh ^{-1}(a x)}{75 a^2}-\frac{3 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a}-\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{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a^5}+\frac{4 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{25 a^3}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^3+\frac{6}{125} x^5 \sinh ^{-1}(a x)",1,"(-2*Sqrt[1 + a^2*x^2]*(2072 - 136*a^2*x^2 + 27*a^4*x^4) + 30*a*x*(120 - 20*a^2*x^2 + 9*a^4*x^4)*ArcSinh[a*x] - 225*Sqrt[1 + a^2*x^2]*(8 - 4*a^2*x^2 + 3*a^4*x^4)*ArcSinh[a*x]^2 + 1125*a^5*x^5*ArcSinh[a*x]^3)/(5625*a^5)","A",1
23,1,110,163,0.0704492,"\int x^3 \sinh ^{-1}(a x)^3 \, dx","Integrate[x^3*ArcSinh[a*x]^3,x]","\frac{8 \left(8 a^4 x^4-3\right) \sinh ^{-1}(a x)^3+3 a x \left(15-2 a^2 x^2\right) \sqrt{a^2 x^2+1}-24 a x \sqrt{a^2 x^2+1} \left(2 a^2 x^2-3\right) \sinh ^{-1}(a x)^2+3 \left(8 a^4 x^4-24 a^2 x^2-15\right) \sinh ^{-1}(a x)}{256 a^4}","-\frac{3 \sinh ^{-1}(a x)^3}{32 a^4}-\frac{45 \sinh ^{-1}(a x)}{256 a^4}-\frac{9 x^2 \sinh ^{-1}(a x)}{32 a^2}-\frac{3 x^3 \sqrt{a^2 x^2+1}}{128 a}-\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{16 a}+\frac{45 x \sqrt{a^2 x^2+1}}{256 a^3}+\frac{9 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{32 a^3}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^3+\frac{3}{32} x^4 \sinh ^{-1}(a x)",1,"(3*a*x*(15 - 2*a^2*x^2)*Sqrt[1 + a^2*x^2] + 3*(-15 - 24*a^2*x^2 + 8*a^4*x^4)*ArcSinh[a*x] - 24*a*x*Sqrt[1 + a^2*x^2]*(-3 + 2*a^2*x^2)*ArcSinh[a*x]^2 + 8*(-3 + 8*a^4*x^4)*ArcSinh[a*x]^3)/(256*a^4)","A",1
24,1,93,132,0.060332,"\int x^2 \sinh ^{-1}(a x)^3 \, dx","Integrate[x^2*ArcSinh[a*x]^3,x]","\frac{9 a^3 x^3 \sinh ^{-1}(a x)^3-2 \left(a^2 x^2-20\right) \sqrt{a^2 x^2+1}-9 \left(a^2 x^2-2\right) \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2+6 a x \left(a^2 x^2-6\right) \sinh ^{-1}(a x)}{27 a^3}","-\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a}-\frac{4 x \sinh ^{-1}(a x)}{3 a^2}-\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{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^3+\frac{2}{9} x^3 \sinh ^{-1}(a x)",1,"(-2*(-20 + a^2*x^2)*Sqrt[1 + a^2*x^2] + 6*a*x*(-6 + a^2*x^2)*ArcSinh[a*x] - 9*(-2 + a^2*x^2)*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2 + 9*a^3*x^3*ArcSinh[a*x]^3)/(27*a^3)","A",1
25,1,80,97,0.0475237,"\int x \sinh ^{-1}(a x)^3 \, dx","Integrate[x*ArcSinh[a*x]^3,x]","\frac{-3 a x \sqrt{a^2 x^2+1}+\left(4 a^2 x^2+2\right) \sinh ^{-1}(a x)^3-6 a x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2+\left(6 a^2 x^2+3\right) \sinh ^{-1}(a x)}{8 a^2}","-\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*a*x*Sqrt[1 + a^2*x^2] + (3 + 6*a^2*x^2)*ArcSinh[a*x] - 6*a*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2 + (2 + 4*a^2*x^2)*ArcSinh[a*x]^3)/(8*a^2)","A",1
26,1,58,58,0.016703,"\int \sinh ^{-1}(a x)^3 \, dx","Integrate[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",1
27,1,83,83,0.0068687,"\int \frac{\sinh ^{-1}(a x)^3}{x} \, dx","Integrate[ArcSinh[a*x]^3/x,x]","\frac{3}{2} \sinh ^{-1}(a x)^2 \text{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \sinh ^{-1}(a x) \text{Li}_3\left(e^{2 \sinh ^{-1}(a x)}\right)+\frac{3}{4} \text{Li}_4\left(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{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \sinh ^{-1}(a x) \text{Li}_3\left(e^{2 \sinh ^{-1}(a x)}\right)+\frac{3}{4} \text{Li}_4\left(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,"-1/4*ArcSinh[a*x]^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",1
28,1,117,84,0.1268441,"\int \frac{\sinh ^{-1}(a x)^3}{x^2} \, dx","Integrate[ArcSinh[a*x]^3/x^2,x]","a \left(6 \sinh ^{-1}(a x) \text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)-6 \sinh ^{-1}(a x) \text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)+6 \text{Li}_3\left(-e^{-\sinh ^{-1}(a x)}\right)-6 \text{Li}_3\left(e^{-\sinh ^{-1}(a x)}\right)-\frac{\sinh ^{-1}(a x)^3}{a x}+3 \sinh ^{-1}(a x)^2 \log \left(1-e^{-\sinh ^{-1}(a x)}\right)-3 \sinh ^{-1}(a x)^2 \log \left(e^{-\sinh ^{-1}(a x)}+1\right)\right)","-6 a \sinh ^{-1}(a x) \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)+6 a \sinh ^{-1}(a x) \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)+6 a \text{Li}_3\left(-e^{\sinh ^{-1}(a x)}\right)-6 a \text{Li}_3\left(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,"a*(-(ArcSinh[a*x]^3/(a*x)) + 3*ArcSinh[a*x]^2*Log[1 - E^(-ArcSinh[a*x])] - 3*ArcSinh[a*x]^2*Log[1 + E^(-ArcSinh[a*x])] + 6*ArcSinh[a*x]*PolyLog[2, -E^(-ArcSinh[a*x])] - 6*ArcSinh[a*x]*PolyLog[2, E^(-ArcSinh[a*x])] + 6*PolyLog[3, -E^(-ArcSinh[a*x])] - 6*PolyLog[3, E^(-ArcSinh[a*x])])","A",0
29,1,80,93,0.3454353,"\int \frac{\sinh ^{-1}(a x)^3}{x^3} \, dx","Integrate[ArcSinh[a*x]^3/x^3,x]","-\frac{\sinh ^{-1}(a x)^3-3 a x \left(\sinh ^{-1}(a x) \left(\left(a x-\sqrt{a^2 x^2+1}\right) \sinh ^{-1}(a x)+2 a x \log \left(1-e^{-2 \sinh ^{-1}(a x)}\right)\right)-a x \text{Li}_2\left(e^{-2 \sinh ^{-1}(a x)}\right)\right)}{2 x^2}","\frac{3}{2} a^2 \text{Li}_2\left(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,"-1/2*(ArcSinh[a*x]^3 - 3*a*x*(ArcSinh[a*x]*((a*x - Sqrt[1 + a^2*x^2])*ArcSinh[a*x] + 2*a*x*Log[1 - E^(-2*ArcSinh[a*x])]) - a*x*PolyLog[2, E^(-2*ArcSinh[a*x])]))/x^2","A",0
30,1,268,151,2.2503809,"\int \frac{\sinh ^{-1}(a x)^3}{x^4} \, dx","Integrate[ArcSinh[a*x]^3/x^4,x]","\frac{1}{48} a^3 \left(-\frac{16 \sinh ^{-1}(a x)^3 \sinh ^4\left(\frac{1}{2} \sinh ^{-1}(a x)\right)}{a^3 x^3}-48 \sinh ^{-1}(a x) \text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)+48 \sinh ^{-1}(a x) \text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)-48 \text{Li}_3\left(-e^{-\sinh ^{-1}(a x)}\right)+48 \text{Li}_3\left(e^{-\sinh ^{-1}(a x)}\right)-24 \sinh ^{-1}(a x)^2 \log \left(1-e^{-\sinh ^{-1}(a x)}\right)+24 \sinh ^{-1}(a x)^2 \log \left(e^{-\sinh ^{-1}(a x)}+1\right)-4 \sinh ^{-1}(a x)^3 \tanh \left(\frac{1}{2} \sinh ^{-1}(a x)\right)+24 \sinh ^{-1}(a x) \tanh \left(\frac{1}{2} \sinh ^{-1}(a x)\right)+4 \sinh ^{-1}(a x)^3 \coth \left(\frac{1}{2} \sinh ^{-1}(a x)\right)-24 \sinh ^{-1}(a x) \coth \left(\frac{1}{2} \sinh ^{-1}(a x)\right)-a x \sinh ^{-1}(a x)^3 \text{csch}^4\left(\frac{1}{2} \sinh ^{-1}(a x)\right)-6 \sinh ^{-1}(a x)^2 \text{csch}^2\left(\frac{1}{2} \sinh ^{-1}(a x)\right)-6 \sinh ^{-1}(a x)^2 \text{sech}^2\left(\frac{1}{2} \sinh ^{-1}(a x)\right)+48 \log \left(\tanh \left(\frac{1}{2} \sinh ^{-1}(a x)\right)\right)\right)","a^3 \sinh ^{-1}(a x) \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)-a^3 \sinh ^{-1}(a x) \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)-a^3 \text{Li}_3\left(-e^{\sinh ^{-1}(a x)}\right)+a^3 \text{Li}_3\left(e^{\sinh ^{-1}(a x)}\right)+a^3 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x^2}-\frac{a^2 \sinh ^{-1}(a x)}{x}-a^3 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)-\frac{\sinh ^{-1}(a x)^3}{3 x^3}",1,"(a^3*(-24*ArcSinh[a*x]*Coth[ArcSinh[a*x]/2] + 4*ArcSinh[a*x]^3*Coth[ArcSinh[a*x]/2] - 6*ArcSinh[a*x]^2*Csch[ArcSinh[a*x]/2]^2 - a*x*ArcSinh[a*x]^3*Csch[ArcSinh[a*x]/2]^4 - 24*ArcSinh[a*x]^2*Log[1 - E^(-ArcSinh[a*x])] + 24*ArcSinh[a*x]^2*Log[1 + E^(-ArcSinh[a*x])] + 48*Log[Tanh[ArcSinh[a*x]/2]] - 48*ArcSinh[a*x]*PolyLog[2, -E^(-ArcSinh[a*x])] + 48*ArcSinh[a*x]*PolyLog[2, E^(-ArcSinh[a*x])] - 48*PolyLog[3, -E^(-ArcSinh[a*x])] + 48*PolyLog[3, E^(-ArcSinh[a*x])] - 6*ArcSinh[a*x]^2*Sech[ArcSinh[a*x]/2]^2 - (16*ArcSinh[a*x]^3*Sinh[ArcSinh[a*x]/2]^4)/(a^3*x^3) + 24*ArcSinh[a*x]*Tanh[ArcSinh[a*x]/2] - 4*ArcSinh[a*x]^3*Tanh[ArcSinh[a*x]/2]))/48","A",0
31,1,107,159,0.691121,"\int \frac{\sinh ^{-1}(a x)^3}{x^5} \, dx","Integrate[ArcSinh[a*x]^3/x^5,x]","\frac{1}{4} \left(a^4 \left(-\frac{\sqrt{a^2 x^2+1} \left(\left(\frac{1}{a^2 x^2}-2\right) \sinh ^{-1}(a x)^2+1\right)}{a x}-\sinh ^{-1}(a x) \left(\frac{1}{a^2 x^2}+2 \sinh ^{-1}(a x)+4 \log \left(1-e^{-2 \sinh ^{-1}(a x)}\right)\right)+2 \text{Li}_2\left(e^{-2 \sinh ^{-1}(a x)}\right)\right)-\frac{\sinh ^{-1}(a x)^3}{x^4}\right)","-\frac{1}{2} a^4 \text{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)+\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{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{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{\sinh ^{-1}(a x)^3}{4 x^4}",1,"(-(ArcSinh[a*x]^3/x^4) + a^4*(-((Sqrt[1 + a^2*x^2]*(1 + (-2 + 1/(a^2*x^2))*ArcSinh[a*x]^2))/(a*x)) - ArcSinh[a*x]*(1/(a^2*x^2) + 2*ArcSinh[a*x] + 4*Log[1 - E^(-2*ArcSinh[a*x])]) + 2*PolyLog[2, E^(-2*ArcSinh[a*x])]))/4","A",0
32,1,165,276,0.106462,"\int x^5 \sinh ^{-1}(a x)^4 \, dx","Integrate[x^5*ArcSinh[a*x]^4,x]","\frac{108 \left(16 a^6 x^6+5\right) \sinh ^{-1}(a x)^4+a^2 x^2 \left(32 a^4 x^4-195 a^2 x^2+2205\right)-144 a x \sqrt{a^2 x^2+1} \left(8 a^4 x^4-10 a^2 x^2+15\right) \sinh ^{-1}(a x)^3-6 a x \sqrt{a^2 x^2+1} \left(32 a^4 x^4-130 a^2 x^2+735\right) \sinh ^{-1}(a x)+9 \left(64 a^6 x^6-120 a^4 x^4+360 a^2 x^2+245\right) \sinh ^{-1}(a x)^2}{10368 a^6}","\frac{5 \sinh ^{-1}(a x)^4}{96 a^6}+\frac{245 \sinh ^{-1}(a x)^2}{1152 a^6}+\frac{245 x^2}{1152 a^4}+\frac{5 x^2 \sinh ^{-1}(a x)^2}{16 a^4}-\frac{65 x^4}{3456 a^2}-\frac{5 x^4 \sinh ^{-1}(a x)^2}{48 a^2}-\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 \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 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{1}{6} x^6 \sinh ^{-1}(a x)^4+\frac{1}{18} x^6 \sinh ^{-1}(a x)^2+\frac{x^6}{324}",1,"(a^2*x^2*(2205 - 195*a^2*x^2 + 32*a^4*x^4) - 6*a*x*Sqrt[1 + a^2*x^2]*(735 - 130*a^2*x^2 + 32*a^4*x^4)*ArcSinh[a*x] + 9*(245 + 360*a^2*x^2 - 120*a^4*x^4 + 64*a^6*x^6)*ArcSinh[a*x]^2 - 144*a*x*Sqrt[1 + a^2*x^2]*(15 - 10*a^2*x^2 + 8*a^4*x^4)*ArcSinh[a*x]^3 + 108*(5 + 16*a^6*x^6)*ArcSinh[a*x]^4)/(10368*a^6)","A",1
33,1,148,244,0.0905399,"\int x^4 \sinh ^{-1}(a x)^4 \, dx","Integrate[x^4*ArcSinh[a*x]^4,x]","\frac{16875 a^5 x^5 \sinh ^{-1}(a x)^4+8 a x \left(81 a^4 x^4-680 a^2 x^2+31080\right)+900 a x \left(9 a^4 x^4-20 a^2 x^2+120\right) \sinh ^{-1}(a x)^2-4500 \sqrt{a^2 x^2+1} \left(3 a^4 x^4-4 a^2 x^2+8\right) \sinh ^{-1}(a x)^3-120 \sqrt{a^2 x^2+1} \left(27 a^4 x^4-136 a^2 x^2+2072\right) \sinh ^{-1}(a x)}{84375 a^5}","\frac{16576 x}{5625 a^4}+\frac{32 x \sinh ^{-1}(a x)^2}{25 a^4}-\frac{1088 x^3}{16875 a^2}-\frac{16 x^3 \sinh ^{-1}(a x)^2}{75 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{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{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{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,"(8*a*x*(31080 - 680*a^2*x^2 + 81*a^4*x^4) - 120*Sqrt[1 + a^2*x^2]*(2072 - 136*a^2*x^2 + 27*a^4*x^4)*ArcSinh[a*x] + 900*a*x*(120 - 20*a^2*x^2 + 9*a^4*x^4)*ArcSinh[a*x]^2 - 4500*Sqrt[1 + a^2*x^2]*(8 - 4*a^2*x^2 + 3*a^4*x^4)*ArcSinh[a*x]^3 + 16875*a^5*x^5*ArcSinh[a*x]^4)/(84375*a^5)","A",1
34,1,133,194,0.07466,"\int x^3 \sinh ^{-1}(a x)^4 \, dx","Integrate[x^3*ArcSinh[a*x]^4,x]","\frac{4 \left(8 a^4 x^4-3\right) \sinh ^{-1}(a x)^4+3 a^2 x^2 \left(a^2 x^2-15\right)-16 a x \sqrt{a^2 x^2+1} \left(2 a^2 x^2-3\right) \sinh ^{-1}(a x)^3-6 a x \sqrt{a^2 x^2+1} \left(2 a^2 x^2-15\right) \sinh ^{-1}(a x)+3 \left(8 a^4 x^4-24 a^2 x^2-15\right) \sinh ^{-1}(a x)^2}{128 a^4}","-\frac{3 \sinh ^{-1}(a x)^4}{32 a^4}-\frac{45 \sinh ^{-1}(a x)^2}{128 a^4}-\frac{45 x^2}{128 a^2}-\frac{9 x^2 \sinh ^{-1}(a x)^2}{16 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{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{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,"(3*a^2*x^2*(-15 + a^2*x^2) - 6*a*x*Sqrt[1 + a^2*x^2]*(-15 + 2*a^2*x^2)*ArcSinh[a*x] + 3*(-15 - 24*a^2*x^2 + 8*a^4*x^4)*ArcSinh[a*x]^2 - 16*a*x*Sqrt[1 + a^2*x^2]*(-3 + 2*a^2*x^2)*ArcSinh[a*x]^3 + 4*(-3 + 8*a^4*x^4)*ArcSinh[a*x]^4)/(128*a^4)","A",1
35,1,112,162,0.0747058,"\int x^2 \sinh ^{-1}(a x)^4 \, dx","Integrate[x^2*ArcSinh[a*x]^4,x]","\frac{27 a^3 x^3 \sinh ^{-1}(a x)^4+8 a x \left(a^2 x^2-60\right)-36 \left(a^2 x^2-2\right) \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3+36 a x \left(a^2 x^2-6\right) \sinh ^{-1}(a x)^2-24 \left(a^2 x^2-20\right) \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{81 a^3}","-\frac{4 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a}-\frac{8 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a}-\frac{160 x}{27 a^2}-\frac{8 x \sinh ^{-1}(a x)^2}{3 a^2}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{9 a^3}+\frac{160 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a^3}+\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,"(8*a*x*(-60 + a^2*x^2) - 24*(-20 + a^2*x^2)*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + 36*a*x*(-6 + a^2*x^2)*ArcSinh[a*x]^2 - 36*(-2 + a^2*x^2)*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3 + 27*a^3*x^3*ArcSinh[a*x]^4)/(81*a^3)","A",1
36,1,94,110,0.0475862,"\int x \sinh ^{-1}(a x)^4 \, dx","Integrate[x*ArcSinh[a*x]^4,x]","\frac{3 a^2 x^2+\left(2 a^2 x^2+1\right) \sinh ^{-1}(a x)^4-4 a x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3+\left(6 a^2 x^2+3\right) \sinh ^{-1}(a x)^2-6 a x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}","-\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*a^2*x^2 - 6*a*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x] + (3 + 6*a^2*x^2)*ArcSinh[a*x]^2 - 4*a*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3 + (1 + 2*a^2*x^2)*ArcSinh[a*x]^4)/(4*a^2)","A",1
37,1,67,67,0.0200785,"\int \sinh ^{-1}(a x)^4 \, dx","Integrate[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",1
38,1,97,97,0.0087613,"\int \frac{\sinh ^{-1}(a x)^4}{x} \, dx","Integrate[ArcSinh[a*x]^4/x,x]","2 \sinh ^{-1}(a x)^3 \text{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-3 \sinh ^{-1}(a x)^2 \text{Li}_3\left(e^{2 \sinh ^{-1}(a x)}\right)+3 \sinh ^{-1}(a x) \text{Li}_4\left(e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \text{Li}_5\left(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{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-3 \sinh ^{-1}(a x)^2 \text{Li}_3\left(e^{2 \sinh ^{-1}(a x)}\right)+3 \sinh ^{-1}(a x) \text{Li}_4\left(e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} \text{Li}_5\left(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,"-1/5*ArcSinh[a*x]^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",1
39,1,161,120,0.2469014,"\int \frac{\sinh ^{-1}(a x)^4}{x^2} \, dx","Integrate[ArcSinh[a*x]^4/x^2,x]","\frac{1}{2} a \left(24 \sinh ^{-1}(a x)^2 \text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)+24 \sinh ^{-1}(a x)^2 \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)+48 \sinh ^{-1}(a x) \text{Li}_3\left(-e^{-\sinh ^{-1}(a x)}\right)-48 \sinh ^{-1}(a x) \text{Li}_3\left(e^{\sinh ^{-1}(a x)}\right)+48 \text{Li}_4\left(-e^{-\sinh ^{-1}(a x)}\right)+48 \text{Li}_4\left(e^{\sinh ^{-1}(a x)}\right)-\frac{2 \sinh ^{-1}(a x)^4}{a x}-2 \sinh ^{-1}(a x)^4-8 \sinh ^{-1}(a x)^3 \log \left(e^{-\sinh ^{-1}(a x)}+1\right)+8 \sinh ^{-1}(a x)^3 \log \left(1-e^{\sinh ^{-1}(a x)}\right)+\pi ^4\right)","-12 a \sinh ^{-1}(a x)^2 \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)+12 a \sinh ^{-1}(a x)^2 \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)+24 a \sinh ^{-1}(a x) \text{Li}_3\left(-e^{\sinh ^{-1}(a x)}\right)-24 a \sinh ^{-1}(a x) \text{Li}_3\left(e^{\sinh ^{-1}(a x)}\right)-24 a \text{Li}_4\left(-e^{\sinh ^{-1}(a x)}\right)+24 a \text{Li}_4\left(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,"(a*(Pi^4 - 2*ArcSinh[a*x]^4 - (2*ArcSinh[a*x]^4)/(a*x) - 8*ArcSinh[a*x]^3*Log[1 + E^(-ArcSinh[a*x])] + 8*ArcSinh[a*x]^3*Log[1 - E^ArcSinh[a*x]] + 24*ArcSinh[a*x]^2*PolyLog[2, -E^(-ArcSinh[a*x])] + 24*ArcSinh[a*x]^2*PolyLog[2, E^ArcSinh[a*x]] + 48*ArcSinh[a*x]*PolyLog[3, -E^(-ArcSinh[a*x])] - 48*ArcSinh[a*x]*PolyLog[3, E^ArcSinh[a*x]] + 48*PolyLog[4, -E^(-ArcSinh[a*x])] + 48*PolyLog[4, E^ArcSinh[a*x]]))/2","A",0
40,1,113,108,0.2813091,"\int \frac{\sinh ^{-1}(a x)^4}{x^3} \, dx","Integrate[ArcSinh[a*x]^4/x^3,x]","-\frac{\sinh ^{-1}(a x)^4}{2 x^2}+\frac{1}{4} a^2 \left(-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a x}+24 \sinh ^{-1}(a x) \text{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-12 \text{Li}_3\left(e^{2 \sinh ^{-1}(a x)}\right)-8 \sinh ^{-1}(a x)^3+24 \sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)+i \pi ^3\right)","6 a^2 \sinh ^{-1}(a x) \text{Li}_2\left(e^{2 \sinh ^{-1}(a x)}\right)-3 a^2 \text{Li}_3\left(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,"-1/2*ArcSinh[a*x]^4/x^2 + (a^2*(I*Pi^3 - 8*ArcSinh[a*x]^3 - (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(a*x) + 24*ArcSinh[a*x]^2*Log[1 - E^(2*ArcSinh[a*x])] + 24*ArcSinh[a*x]*PolyLog[2, E^(2*ArcSinh[a*x])] - 12*PolyLog[3, E^(2*ArcSinh[a*x])]))/4","C",1
41,1,355,223,2.6414059,"\int \frac{\sinh ^{-1}(a x)^4}{x^4} \, dx","Integrate[ArcSinh[a*x]^4/x^4,x]","\frac{1}{24} a^3 \left(-\frac{8 \sinh ^4\left(\frac{1}{2} \sinh ^{-1}(a x)\right) \sinh ^{-1}(a x)^4}{a^3 x^3}-48 \sinh ^{-1}(a x)^2 \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)-96 \sinh ^{-1}(a x) \text{Li}_3\left(-e^{-\sinh ^{-1}(a x)}\right)+96 \sinh ^{-1}(a x) \text{Li}_3\left(e^{\sinh ^{-1}(a x)}\right)-48 \left(\sinh ^{-1}(a x)^2-2\right) \text{Li}_2\left(-e^{-\sinh ^{-1}(a x)}\right)-96 \text{Li}_2\left(e^{-\sinh ^{-1}(a x)}\right)-96 \text{Li}_4\left(-e^{-\sinh ^{-1}(a x)}\right)-96 \text{Li}_4\left(e^{\sinh ^{-1}(a x)}\right)+4 \sinh ^{-1}(a x)^4+16 \sinh ^{-1}(a x)^3 \log \left(e^{-\sinh ^{-1}(a x)}+1\right)-16 \sinh ^{-1}(a x)^3 \log \left(1-e^{\sinh ^{-1}(a x)}\right)+96 \sinh ^{-1}(a x) \log \left(1-e^{-\sinh ^{-1}(a x)}\right)-96 \sinh ^{-1}(a x) \log \left(e^{-\sinh ^{-1}(a x)}+1\right)-2 \sinh ^{-1}(a x)^4 \tanh \left(\frac{1}{2} \sinh ^{-1}(a x)\right)+24 \sinh ^{-1}(a x)^2 \tanh \left(\frac{1}{2} \sinh ^{-1}(a x)\right)+2 \sinh ^{-1}(a x)^4 \coth \left(\frac{1}{2} \sinh ^{-1}(a x)\right)-24 \sinh ^{-1}(a x)^2 \coth \left(\frac{1}{2} \sinh ^{-1}(a x)\right)-\frac{1}{2} a x \sinh ^{-1}(a x)^4 \text{csch}^4\left(\frac{1}{2} \sinh ^{-1}(a x)\right)-4 \sinh ^{-1}(a x)^3 \text{csch}^2\left(\frac{1}{2} \sinh ^{-1}(a x)\right)-4 \sinh ^{-1}(a x)^3 \text{sech}^2\left(\frac{1}{2} \sinh ^{-1}(a x)\right)-2 \pi ^4\right)","2 a^3 \sinh ^{-1}(a x)^2 \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)-2 a^3 \sinh ^{-1}(a x)^2 \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)-4 a^3 \sinh ^{-1}(a x) \text{Li}_3\left(-e^{\sinh ^{-1}(a x)}\right)+4 a^3 \sinh ^{-1}(a x) \text{Li}_3\left(e^{\sinh ^{-1}(a x)}\right)-4 a^3 \text{Li}_2\left(-e^{\sinh ^{-1}(a x)}\right)+4 a^3 \text{Li}_2\left(e^{\sinh ^{-1}(a x)}\right)+4 a^3 \text{Li}_4\left(-e^{\sinh ^{-1}(a x)}\right)-4 a^3 \text{Li}_4\left(e^{\sinh ^{-1}(a x)}\right)+\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{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{\sinh ^{-1}(a x)^4}{3 x^3}",1,"(a^3*(-2*Pi^4 + 4*ArcSinh[a*x]^4 - 24*ArcSinh[a*x]^2*Coth[ArcSinh[a*x]/2] + 2*ArcSinh[a*x]^4*Coth[ArcSinh[a*x]/2] - 4*ArcSinh[a*x]^3*Csch[ArcSinh[a*x]/2]^2 - (a*x*ArcSinh[a*x]^4*Csch[ArcSinh[a*x]/2]^4)/2 + 96*ArcSinh[a*x]*Log[1 - E^(-ArcSinh[a*x])] - 96*ArcSinh[a*x]*Log[1 + E^(-ArcSinh[a*x])] + 16*ArcSinh[a*x]^3*Log[1 + E^(-ArcSinh[a*x])] - 16*ArcSinh[a*x]^3*Log[1 - E^ArcSinh[a*x]] - 48*(-2 + ArcSinh[a*x]^2)*PolyLog[2, -E^(-ArcSinh[a*x])] - 96*PolyLog[2, E^(-ArcSinh[a*x])] - 48*ArcSinh[a*x]^2*PolyLog[2, E^ArcSinh[a*x]] - 96*ArcSinh[a*x]*PolyLog[3, -E^(-ArcSinh[a*x])] + 96*ArcSinh[a*x]*PolyLog[3, E^ArcSinh[a*x]] - 96*PolyLog[4, -E^(-ArcSinh[a*x])] - 96*PolyLog[4, E^ArcSinh[a*x]] - 4*ArcSinh[a*x]^3*Sech[ArcSinh[a*x]/2]^2 - (8*ArcSinh[a*x]^4*Sinh[ArcSinh[a*x]/2]^4)/(a^3*x^3) + 24*ArcSinh[a*x]^2*Tanh[ArcSinh[a*x]/2] - 2*ArcSinh[a*x]^4*Tanh[ArcSinh[a*x]/2]))/24","A",0
42,1,40,55,0.0132942,"\int \frac{x^6}{\sinh ^{-1}(a x)} \, dx","Integrate[x^6/ArcSinh[a*x],x]","\frac{-5 \text{Chi}\left(\sinh ^{-1}(a x)\right)+9 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)-5 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)+\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]] + 9*CoshIntegral[3*ArcSinh[a*x]] - 5*CoshIntegral[5*ArcSinh[a*x]] + CoshIntegral[7*ArcSinh[a*x]])/(64*a^7)","A",1
43,1,33,43,0.1133917,"\int \frac{x^5}{\sinh ^{-1}(a x)} \, dx","Integrate[x^5/ArcSinh[a*x],x]","\frac{5 \text{Shi}\left(2 \sinh ^{-1}(a x)\right)-4 \text{Shi}\left(4 \sinh ^{-1}(a x)\right)+\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]] - 4*SinhIntegral[4*ArcSinh[a*x]] + SinhIntegral[6*ArcSinh[a*x]])/(32*a^6)","A",1
44,1,31,41,0.0102693,"\int \frac{x^4}{\sinh ^{-1}(a x)} \, dx","Integrate[x^4/ArcSinh[a*x],x]","\frac{2 \text{Chi}\left(\sinh ^{-1}(a x)\right)-3 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)+\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,"(2*CoshIntegral[ArcSinh[a*x]] - 3*CoshIntegral[3*ArcSinh[a*x]] + CoshIntegral[5*ArcSinh[a*x]])/(16*a^5)","A",1
45,1,24,29,0.0773172,"\int \frac{x^3}{\sinh ^{-1}(a x)} \, dx","Integrate[x^3/ArcSinh[a*x],x]","\frac{\text{Shi}\left(4 \sinh ^{-1}(a x)\right)-2 \text{Shi}\left(2 \sinh ^{-1}(a x)\right)}{8 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,"(-2*SinhIntegral[2*ArcSinh[a*x]] + SinhIntegral[4*ArcSinh[a*x]])/(8*a^4)","A",1
46,1,22,27,0.0070465,"\int \frac{x^2}{\sinh ^{-1}(a x)} \, dx","Integrate[x^2/ArcSinh[a*x],x]","\frac{\text{Chi}\left(3 \sinh ^{-1}(a x)\right)-\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]] + CoshIntegral[3*ArcSinh[a*x]])/(4*a^3)","A",1
47,1,14,14,0.0224315,"\int \frac{x}{\sinh ^{-1}(a x)} \, dx","Integrate[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",1
48,1,9,9,0.0094051,"\int \frac{1}{\sinh ^{-1}(a x)} \, dx","Integrate[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",1
49,0,0,13,0.1902314,"\int \frac{1}{x \sinh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]), x]","A",-1
50,0,0,13,0.868732,"\int \frac{1}{x^2 \sinh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[1/(x^2*ArcSinh[a*x]), x]","A",-1
51,1,85,82,0.2948651,"\int \frac{x^6}{\sinh ^{-1}(a x)^2} \, dx","Integrate[x^6/ArcSinh[a*x]^2,x]","-\frac{64 a^6 x^6 \sqrt{a^2 x^2+1}+5 \sinh ^{-1}(a x) \text{Shi}\left(\sinh ^{-1}(a x)\right)-27 \sinh ^{-1}(a x) \text{Shi}\left(3 \sinh ^{-1}(a x)\right)+25 \sinh ^{-1}(a x) \text{Shi}\left(5 \sinh ^{-1}(a x)\right)-7 \sinh ^{-1}(a x) \text{Shi}\left(7 \sinh ^{-1}(a x)\right)}{64 a^7 \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,"-1/64*(64*a^6*x^6*Sqrt[1 + a^2*x^2] + 5*ArcSinh[a*x]*SinhIntegral[ArcSinh[a*x]] - 27*ArcSinh[a*x]*SinhIntegral[3*ArcSinh[a*x]] + 25*ArcSinh[a*x]*SinhIntegral[5*ArcSinh[a*x]] - 7*ArcSinh[a*x]*SinhIntegral[7*ArcSinh[a*x]])/(a^7*ArcSinh[a*x])","A",1
52,1,78,70,0.0416108,"\int \frac{x^5}{\sinh ^{-1}(a x)^2} \, dx","Integrate[x^5/ArcSinh[a*x]^2,x]","-\frac{-10 \sinh ^{-1}(a x) \text{Chi}\left(2 \sinh ^{-1}(a x)\right)+16 \sinh ^{-1}(a x) \text{Chi}\left(4 \sinh ^{-1}(a x)\right)-6 \sinh ^{-1}(a x) \text{Chi}\left(6 \sinh ^{-1}(a x)\right)+5 \sinh \left(2 \sinh ^{-1}(a x)\right)-4 \sinh \left(4 \sinh ^{-1}(a x)\right)+\sinh \left(6 \sinh ^{-1}(a x)\right)}{32 a^6 \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,"-1/32*(-10*ArcSinh[a*x]*CoshIntegral[2*ArcSinh[a*x]] + 16*ArcSinh[a*x]*CoshIntegral[4*ArcSinh[a*x]] - 6*ArcSinh[a*x]*CoshIntegral[6*ArcSinh[a*x]] + 5*Sinh[2*ArcSinh[a*x]] - 4*Sinh[4*ArcSinh[a*x]] + Sinh[6*ArcSinh[a*x]])/(a^6*ArcSinh[a*x])","A",1
53,1,60,68,0.213216,"\int \frac{x^4}{\sinh ^{-1}(a x)^2} \, dx","Integrate[x^4/ArcSinh[a*x]^2,x]","\frac{-\frac{16 a^4 x^4 \sqrt{a^2 x^2+1}}{\sinh ^{-1}(a x)}+2 \text{Shi}\left(\sinh ^{-1}(a x)\right)-9 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)+5 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{16 a^5}","\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,"((-16*a^4*x^4*Sqrt[1 + a^2*x^2])/ArcSinh[a*x] + 2*SinhIntegral[ArcSinh[a*x]] - 9*SinhIntegral[3*ArcSinh[a*x]] + 5*SinhIntegral[5*ArcSinh[a*x]])/(16*a^5)","A",1
54,1,56,56,0.0282511,"\int \frac{x^3}{\sinh ^{-1}(a x)^2} \, dx","Integrate[x^3/ArcSinh[a*x]^2,x]","-\frac{4 \sinh ^{-1}(a x) \text{Chi}\left(2 \sinh ^{-1}(a x)\right)-4 \sinh ^{-1}(a x) \text{Chi}\left(4 \sinh ^{-1}(a x)\right)-2 \sinh \left(2 \sinh ^{-1}(a x)\right)+\sinh \left(4 \sinh ^{-1}(a x)\right)}{8 a^4 \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,"-1/8*(4*ArcSinh[a*x]*CoshIntegral[2*ArcSinh[a*x]] - 4*ArcSinh[a*x]*CoshIntegral[4*ArcSinh[a*x]] - 2*Sinh[2*ArcSinh[a*x]] + Sinh[4*ArcSinh[a*x]])/(a^4*ArcSinh[a*x])","A",1
55,1,49,54,0.1739605,"\int \frac{x^2}{\sinh ^{-1}(a x)^2} \, dx","Integrate[x^2/ArcSinh[a*x]^2,x]","-\frac{\frac{4 a^2 x^2 \sqrt{a^2 x^2+1}}{\sinh ^{-1}(a x)}+\text{Shi}\left(\sinh ^{-1}(a x)\right)-3 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^3}","-\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,"-1/4*((4*a^2*x^2*Sqrt[1 + a^2*x^2])/ArcSinh[a*x] + SinhIntegral[ArcSinh[a*x]] - 3*SinhIntegral[3*ArcSinh[a*x]])/a^3","A",1
56,1,32,37,0.0037785,"\int \frac{x}{\sinh ^{-1}(a x)^2} \, dx","Integrate[x/ArcSinh[a*x]^2,x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{a^2}-\frac{\sinh \left(2 \sinh ^{-1}(a x)\right)}{2 a^2 \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,"CoshIntegral[2*ArcSinh[a*x]]/a^2 - Sinh[2*ArcSinh[a*x]]/(2*a^2*ArcSinh[a*x])","A",1
57,1,31,34,0.0507059,"\int \frac{1}{\sinh ^{-1}(a x)^2} \, dx","Integrate[ArcSinh[a*x]^(-2),x]","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)-\frac{\sqrt{a^2 x^2+1}}{\sinh ^{-1}(a x)}}{a}","\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]/ArcSinh[a*x]) + SinhIntegral[ArcSinh[a*x]])/a","A",1
58,0,0,13,0.7857122,"\int \frac{1}{x \sinh ^{-1}(a x)^2} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]^2), x]","A",-1
59,0,0,13,5.05943,"\int \frac{1}{x^2 \sinh ^{-1}(a x)^2} \, dx","Integrate[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,"Integrate[1/(x^2*ArcSinh[a*x]^2), x]","A",-1
60,1,102,97,0.1565057,"\int \frac{x^4}{\sinh ^{-1}(a x)^3} \, dx","Integrate[x^4/ArcSinh[a*x]^3,x]","-\frac{80 a^5 x^5 \sinh ^{-1}(a x)+64 a^3 x^3 \sinh ^{-1}(a x)+16 a^4 x^4 \sqrt{a^2 x^2+1}-2 \sinh ^{-1}(a x)^2 \text{Chi}\left(\sinh ^{-1}(a x)\right)+27 \sinh ^{-1}(a x)^2 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)-25 \sinh ^{-1}(a x)^2 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{32 a^5 \sinh ^{-1}(a x)^2}","\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{2 x^3}{a^2 \sinh ^{-1}(a x)}-\frac{x^4 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{5 x^5}{2 \sinh ^{-1}(a x)}",1,"-1/32*(16*a^4*x^4*Sqrt[1 + a^2*x^2] + 64*a^3*x^3*ArcSinh[a*x] + 80*a^5*x^5*ArcSinh[a*x] - 2*ArcSinh[a*x]^2*CoshIntegral[ArcSinh[a*x]] + 27*ArcSinh[a*x]^2*CoshIntegral[3*ArcSinh[a*x]] - 25*ArcSinh[a*x]^2*CoshIntegral[5*ArcSinh[a*x]])/(a^5*ArcSinh[a*x]^2)","A",1
61,1,69,82,0.2210723,"\int \frac{x^3}{\sinh ^{-1}(a x)^3} \, dx","Integrate[x^3/ArcSinh[a*x]^3,x]","-\frac{\frac{a^2 x^2 \left(a x \sqrt{a^2 x^2+1}+\left(4 a^2 x^2+3\right) \sinh ^{-1}(a x)\right)}{\sinh ^{-1}(a x)^2}+\text{Shi}\left(2 \sinh ^{-1}(a x)\right)-2 \text{Shi}\left(4 \sinh ^{-1}(a x)\right)}{2 a^4}","-\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{3 x^2}{2 a^2 \sinh ^{-1}(a x)}-\frac{x^3 \sqrt{a^2 x^2+1}}{2 a \sinh ^{-1}(a x)^2}-\frac{2 x^4}{\sinh ^{-1}(a x)}",1,"-1/2*((a^2*x^2*(a*x*Sqrt[1 + a^2*x^2] + (3 + 4*a^2*x^2)*ArcSinh[a*x]))/ArcSinh[a*x]^2 + SinhIntegral[2*ArcSinh[a*x]] - 2*SinhIntegral[4*ArcSinh[a*x]])/a^4","A",1
62,1,64,81,0.1599518,"\int \frac{x^2}{\sinh ^{-1}(a x)^3} \, dx","Integrate[x^2/ArcSinh[a*x]^3,x]","-\frac{\frac{4 a x \left(a x \sqrt{a^2 x^2+1}+\left(3 a^2 x^2+2\right) \sinh ^{-1}(a x)\right)}{\sinh ^{-1}(a x)^2}+\text{Chi}\left(\sinh ^{-1}(a x)\right)-9 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{8 a^3}","-\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,"-1/8*((4*a*x*(a*x*Sqrt[1 + a^2*x^2] + (2 + 3*a^2*x^2)*ArcSinh[a*x]))/ArcSinh[a*x]^2 + CoshIntegral[ArcSinh[a*x]] - 9*CoshIntegral[3*ArcSinh[a*x]])/a^3","A",1
63,1,62,63,0.0533206,"\int \frac{x}{\sinh ^{-1}(a x)^3} \, dx","Integrate[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{-2 a^2 x^2-1}{2 a^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,"-1/2*(x*Sqrt[1 + a^2*x^2])/(a*ArcSinh[a*x]^2) + (-1 - 2*a^2*x^2)/(2*a^2*ArcSinh[a*x]) + SinhIntegral[2*ArcSinh[a*x]]/a^2","A",1
64,1,47,50,0.0218203,"\int \frac{1}{\sinh ^{-1}(a x)^3} \, dx","Integrate[ArcSinh[a*x]^(-3),x]","-\frac{\sqrt{a^2 x^2+1}+\sinh ^{-1}(a x)^2 \left(-\text{Chi}\left(\sinh ^{-1}(a x)\right)\right)+a x \sinh ^{-1}(a x)}{2 a \sinh ^{-1}(a x)^2}","-\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,"-1/2*(Sqrt[1 + a^2*x^2] + a*x*ArcSinh[a*x] - ArcSinh[a*x]^2*CoshIntegral[ArcSinh[a*x]])/(a*ArcSinh[a*x]^2)","A",1
65,0,0,13,0.5643184,"\int \frac{1}{x \sinh ^{-1}(a x)^3} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]^3), x]","A",-1
66,0,0,13,5.3163006,"\int \frac{1}{x^2 \sinh ^{-1}(a x)^3} \, dx","Integrate[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,"Integrate[1/(x^2*ArcSinh[a*x]^3), x]","A",-1
67,1,156,155,0.3677878,"\int \frac{x^4}{\sinh ^{-1}(a x)^4} \, dx","Integrate[x^4/ArcSinh[a*x]^4,x]","-\frac{80 a^5 x^5 \sinh ^{-1}(a x)+64 a^3 x^3 \sinh ^{-1}(a x)+192 a^2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2+32 a^4 x^4 \sqrt{a^2 x^2+1}+400 a^4 x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2-2 \sinh ^{-1}(a x)^3 \text{Shi}\left(\sinh ^{-1}(a x)\right)+81 \sinh ^{-1}(a x)^3 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)-125 \sinh ^{-1}(a x)^3 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{96 a^5 \sinh ^{-1}(a x)^3}","\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{2 x^3}{3 a^2 \sinh ^{-1}(a x)^2}-\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^2 \sqrt{a^2 x^2+1}}{a^3 \sinh ^{-1}(a x)}-\frac{5 x^5}{6 \sinh ^{-1}(a x)^2}",1,"-1/96*(32*a^4*x^4*Sqrt[1 + a^2*x^2] + 64*a^3*x^3*ArcSinh[a*x] + 80*a^5*x^5*ArcSinh[a*x] + 192*a^2*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2 + 400*a^4*x^4*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2 - 2*ArcSinh[a*x]^3*SinhIntegral[ArcSinh[a*x]] + 81*ArcSinh[a*x]^3*SinhIntegral[3*ArcSinh[a*x]] - 125*ArcSinh[a*x]^3*SinhIntegral[5*ArcSinh[a*x]])/(a^5*ArcSinh[a*x]^3)","A",1
68,1,105,141,0.4215348,"\int \frac{x^3}{\sinh ^{-1}(a x)^4} \, dx","Integrate[x^3/ArcSinh[a*x]^4,x]","-\frac{\frac{a x \left(2 a^2 x^2 \sqrt{a^2 x^2+1}+a x \left(4 a^2 x^2+3\right) \sinh ^{-1}(a x)+2 \sqrt{a^2 x^2+1} \left(8 a^2 x^2+3\right) \sinh ^{-1}(a x)^2\right)}{\sinh ^{-1}(a x)^3}+2 \text{Chi}\left(2 \sinh ^{-1}(a x)\right)-8 \text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{6 a^4}","-\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{x^2}{2 a^2 \sinh ^{-1}(a x)^2}-\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 \sqrt{a^2 x^2+1}}{a^3 \sinh ^{-1}(a x)}-\frac{2 x^4}{3 \sinh ^{-1}(a x)^2}",1,"-1/6*((a*x*(2*a^2*x^2*Sqrt[1 + a^2*x^2] + a*x*(3 + 4*a^2*x^2)*ArcSinh[a*x] + 2*Sqrt[1 + a^2*x^2]*(3 + 8*a^2*x^2)*ArcSinh[a*x]^2))/ArcSinh[a*x]^3 + 2*CoshIntegral[2*ArcSinh[a*x]] - 8*CoshIntegral[4*ArcSinh[a*x]])/a^4","A",1
69,1,99,138,0.329525,"\int \frac{x^2}{\sinh ^{-1}(a x)^4} \, dx","Integrate[x^2/ArcSinh[a*x]^4,x]","-\frac{\frac{4 \left(2 a^2 x^2 \sqrt{a^2 x^2+1}+a x \left(3 a^2 x^2+2\right) \sinh ^{-1}(a x)+\sqrt{a^2 x^2+1} \left(9 a^2 x^2+2\right) \sinh ^{-1}(a x)^2\right)}{\sinh ^{-1}(a x)^3}+\text{Shi}\left(\sinh ^{-1}(a x)\right)-27 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{24 a^3}","-\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{x}{3 a^2 \sinh ^{-1}(a x)^2}-\frac{\sqrt{a^2 x^2+1}}{3 a^3 \sinh ^{-1}(a x)}-\frac{x^3}{2 \sinh ^{-1}(a x)^2}",1,"-1/24*((4*(2*a^2*x^2*Sqrt[1 + a^2*x^2] + a*x*(2 + 3*a^2*x^2)*ArcSinh[a*x] + Sqrt[1 + a^2*x^2]*(2 + 9*a^2*x^2)*ArcSinh[a*x]^2))/ArcSinh[a*x]^3 + SinhIntegral[ArcSinh[a*x]] - 27*SinhIntegral[3*ArcSinh[a*x]])/a^3","A",1
70,1,84,95,0.1320566,"\int \frac{x}{\sinh ^{-1}(a x)^4} \, dx","Integrate[x/ArcSinh[a*x]^4,x]","-\frac{2 a x \sqrt{a^2 x^2+1}+4 a x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2+\left(2 a^2 x^2+1\right) \sinh ^{-1}(a x)-4 \sinh ^{-1}(a x)^3 \text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{6 a^2 \sinh ^{-1}(a x)^3}","\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,"-1/6*(2*a*x*Sqrt[1 + a^2*x^2] + (1 + 2*a^2*x^2)*ArcSinh[a*x] + 4*a*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2 - 4*ArcSinh[a*x]^3*CoshIntegral[2*ArcSinh[a*x]])/(a^2*ArcSinh[a*x]^3)","A",1
71,1,69,76,0.0633961,"\int \frac{1}{\sinh ^{-1}(a x)^4} \, dx","Integrate[ArcSinh[a*x]^(-4),x]","-\frac{2 \sqrt{a^2 x^2+1}+\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2+\sinh ^{-1}(a x)^3 \left(-\text{Shi}\left(\sinh ^{-1}(a x)\right)\right)+a x \sinh ^{-1}(a x)}{6 a \sinh ^{-1}(a x)^3}","-\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,"-1/6*(2*Sqrt[1 + a^2*x^2] + a*x*ArcSinh[a*x] + Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2 - ArcSinh[a*x]^3*SinhIntegral[ArcSinh[a*x]])/(a*ArcSinh[a*x]^3)","A",1
72,0,0,13,1.9104014,"\int \frac{1}{x \sinh ^{-1}(a x)^4} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]^4), x]","A",-1
73,0,0,13,9.3376275,"\int \frac{1}{x^2 \sinh ^{-1}(a x)^4} \, dx","Integrate[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,"Integrate[1/(x^2*ArcSinh[a*x]^4), x]","A",-1
74,1,161,182,0.0478316,"\int x^4 \sqrt{\sinh ^{-1}(a x)} \, dx","Integrate[x^4*Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-5 \sinh ^{-1}(a x)\right)}{160 \sqrt{5} \sqrt{-\sinh ^{-1}(a x)}}-\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-3 \sinh ^{-1}(a x)\right)}{32 \sqrt{3} \sqrt{-\sinh ^{-1}(a x)}}+\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-\sinh ^{-1}(a x)\right)}{16 \sqrt{-\sinh ^{-1}(a x)}}-\frac{1}{16} \Gamma \left(\frac{3}{2},\sinh ^{-1}(a x)\right)+\frac{\Gamma \left(\frac{3}{2},3 \sinh ^{-1}(a x)\right)}{32 \sqrt{3}}-\frac{\Gamma \left(\frac{3}{2},5 \sinh ^{-1}(a x)\right)}{160 \sqrt{5}}}{a^5}","\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,"((Sqrt[ArcSinh[a*x]]*Gamma[3/2, -5*ArcSinh[a*x]])/(160*Sqrt[5]*Sqrt[-ArcSinh[a*x]]) - (Sqrt[ArcSinh[a*x]]*Gamma[3/2, -3*ArcSinh[a*x]])/(32*Sqrt[3]*Sqrt[-ArcSinh[a*x]]) + (Sqrt[ArcSinh[a*x]]*Gamma[3/2, -ArcSinh[a*x]])/(16*Sqrt[-ArcSinh[a*x]]) - Gamma[3/2, ArcSinh[a*x]]/16 + Gamma[3/2, 3*ArcSinh[a*x]]/(32*Sqrt[3]) - Gamma[3/2, 5*ArcSinh[a*x]]/(160*Sqrt[5]))/a^5","A",0
75,1,101,139,0.0392858,"\int x^3 \sqrt{\sinh ^{-1}(a x)} \, dx","Integrate[x^3*Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-4 \sinh ^{-1}(a x)\right)-4 \sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-2 \sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \left(\Gamma \left(\frac{3}{2},4 \sinh ^{-1}(a x)\right)-4 \sqrt{2} \Gamma \left(\frac{3}{2},2 \sinh ^{-1}(a x)\right)\right)}{128 a^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,"(Sqrt[ArcSinh[a*x]]*Gamma[3/2, -4*ArcSinh[a*x]] - 4*Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[3/2, -2*ArcSinh[a*x]] + Sqrt[-ArcSinh[a*x]]*(-4*Sqrt[2]*Gamma[3/2, 2*ArcSinh[a*x]] + Gamma[3/2, 4*ArcSinh[a*x]]))/(128*a^4*Sqrt[-ArcSinh[a*x]])","A",0
76,1,101,120,0.0371003,"\int x^2 \sqrt{\sinh ^{-1}(a x)} \, dx","Integrate[x^2*Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-3 \sinh ^{-1}(a x)\right)-9 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-\sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \left(9 \Gamma \left(\frac{3}{2},\sinh ^{-1}(a x)\right)-\sqrt{3} \Gamma \left(\frac{3}{2},3 \sinh ^{-1}(a x)\right)\right)}{72 a^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,"(Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[3/2, -3*ArcSinh[a*x]] - 9*Sqrt[ArcSinh[a*x]]*Gamma[3/2, -ArcSinh[a*x]] + Sqrt[-ArcSinh[a*x]]*(9*Gamma[3/2, ArcSinh[a*x]] - Sqrt[3]*Gamma[3/2, 3*ArcSinh[a*x]]))/(72*a^3*Sqrt[-ArcSinh[a*x]])","A",0
77,1,52,93,0.0353583,"\int x \sqrt{\sinh ^{-1}(a x)} \, dx","Integrate[x*Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-2 \sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}+\Gamma \left(\frac{3}{2},2 \sinh ^{-1}(a x)\right)}{8 \sqrt{2} a^2}","-\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]]*Gamma[3/2, -2*ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] + Gamma[3/2, 2*ArcSinh[a*x]])/(8*Sqrt[2]*a^2)","A",0
78,1,45,53,0.0528409,"\int \sqrt{\sinh ^{-1}(a x)} \, dx","Integrate[Sqrt[ArcSinh[a*x]],x]","-\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\Gamma \left(\frac{3}{2},\sinh ^{-1}(a x)\right)}{2 a}","\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,"-1/2*((Sqrt[-ArcSinh[a*x]]*Gamma[3/2, -ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + Gamma[3/2, ArcSinh[a*x]])/a","A",0
79,0,0,15,0.3693789,"\int \frac{\sqrt{\sinh ^{-1}(a x)}}{x} \, dx","Integrate[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,"Integrate[Sqrt[ArcSinh[a*x]]/x, x]","A",-1
80,1,152,330,0.1299611,"\int x^4 \sinh ^{-1}(a x)^{3/2} \, dx","Integrate[x^4*ArcSinh[a*x]^(3/2),x]","\frac{\frac{9 \sqrt{5} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-5 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\frac{125 \sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-3 \sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}+\frac{2250 \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}-2250 \Gamma \left(\frac{5}{2},\sinh ^{-1}(a x)\right)+125 \sqrt{3} \Gamma \left(\frac{5}{2},3 \sinh ^{-1}(a x)\right)-9 \sqrt{5} \Gamma \left(\frac{5}{2},5 \sinh ^{-1}(a x)\right)}{36000 a^5}","\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{4 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{25 a^5}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{25 a^3}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^{3/2}",1,"((9*Sqrt[5]*Sqrt[-ArcSinh[a*x]]*Gamma[5/2, -5*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + (125*Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[5/2, -3*ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] + (2250*Sqrt[-ArcSinh[a*x]]*Gamma[5/2, -ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] - 2250*Gamma[5/2, ArcSinh[a*x]] + 125*Sqrt[3]*Gamma[5/2, 3*ArcSinh[a*x]] - 9*Sqrt[5]*Gamma[5/2, 5*ArcSinh[a*x]])/(36000*a^5)","A",0
81,1,102,199,0.0384765,"\int x^3 \sinh ^{-1}(a x)^{3/2} \, dx","Integrate[x^3*ArcSinh[a*x]^(3/2),x]","\frac{-\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-4 \sinh ^{-1}(a x)\right)+8 \sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-2 \sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \left(\Gamma \left(\frac{5}{2},4 \sinh ^{-1}(a x)\right)-8 \sqrt{2} \Gamma \left(\frac{5}{2},2 \sinh ^{-1}(a x)\right)\right)}{512 a^4 \sqrt{-\sinh ^{-1}(a 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 \sinh ^{-1}(a x)^{3/2}}{32 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{1}{4} x^4 \sinh ^{-1}(a x)^{3/2}",1,"(-(Sqrt[ArcSinh[a*x]]*Gamma[5/2, -4*ArcSinh[a*x]]) + 8*Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[5/2, -2*ArcSinh[a*x]] + Sqrt[-ArcSinh[a*x]]*(-8*Sqrt[2]*Gamma[5/2, 2*ArcSinh[a*x]] + Gamma[5/2, 4*ArcSinh[a*x]]))/(512*a^4*Sqrt[-ArcSinh[a*x]])","A",0
82,1,102,179,0.0382172,"\int x^2 \sinh ^{-1}(a x)^{3/2} \, dx","Integrate[x^2*ArcSinh[a*x]^(3/2),x]","\frac{-\sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-3 \sinh ^{-1}(a x)\right)+27 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-\sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \left(27 \Gamma \left(\frac{5}{2},\sinh ^{-1}(a x)\right)-\sqrt{3} \Gamma \left(\frac{5}{2},3 \sinh ^{-1}(a x)\right)\right)}{216 a^3 \sqrt{-\sinh ^{-1}(a 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}",1,"(-(Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[5/2, -3*ArcSinh[a*x]]) + 27*Sqrt[ArcSinh[a*x]]*Gamma[5/2, -ArcSinh[a*x]] + Sqrt[-ArcSinh[a*x]]*(27*Gamma[5/2, ArcSinh[a*x]] - Sqrt[3]*Gamma[5/2, 3*ArcSinh[a*x]]))/(216*a^3*Sqrt[-ArcSinh[a*x]])","A",0
83,1,52,122,0.022781,"\int x \sinh ^{-1}(a x)^{3/2} \, dx","Integrate[x*ArcSinh[a*x]^(3/2),x]","\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-2 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\Gamma \left(\frac{5}{2},2 \sinh ^{-1}(a x)\right)}{16 \sqrt{2} a^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,"((Sqrt[-ArcSinh[a*x]]*Gamma[5/2, -2*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + Gamma[5/2, 2*ArcSinh[a*x]])/(16*Sqrt[2]*a^2)","A",0
84,1,47,81,0.0302937,"\int \sinh ^{-1}(a x)^{3/2} \, dx","Integrate[ArcSinh[a*x]^(3/2),x]","\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}-\Gamma \left(\frac{5}{2},\sinh ^{-1}(a x)\right)}{2 a}","-\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,"((Sqrt[-ArcSinh[a*x]]*Gamma[5/2, -ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] - Gamma[5/2, ArcSinh[a*x]])/(2*a)","A",0
85,0,0,15,0.3398665,"\int \frac{\sinh ^{-1}(a x)^{3/2}}{x} \, dx","Integrate[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,"Integrate[ArcSinh[a*x]^(3/2)/x, x]","A",-1
86,1,152,379,0.1261886,"\int x^4 \sinh ^{-1}(a x)^{5/2} \, dx","Integrate[x^4*ArcSinh[a*x]^(5/2),x]","\frac{\frac{27 \sqrt{5} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-5 \sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}+\frac{625 \sqrt{3} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-3 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\frac{33750 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}-33750 \Gamma \left(\frac{7}{2},\sinh ^{-1}(a x)\right)+625 \sqrt{3} \Gamma \left(\frac{7}{2},3 \sinh ^{-1}(a x)\right)-27 \sqrt{5} \Gamma \left(\frac{7}{2},5 \sinh ^{-1}(a x)\right)}{540000 a^5}","\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{2 x \sqrt{\sinh ^{-1}(a x)}}{5 a^4}-\frac{x^3 \sqrt{\sinh ^{-1}(a x)}}{15 a^2}-\frac{x^4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{10 a}-\frac{4 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{15 a^5}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{15 a^3}+\frac{1}{5} x^5 \sinh ^{-1}(a x)^{5/2}+\frac{3}{100} x^5 \sqrt{\sinh ^{-1}(a x)}",1,"((27*Sqrt[5]*Sqrt[ArcSinh[a*x]]*Gamma[7/2, -5*ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] + (625*Sqrt[3]*Sqrt[-ArcSinh[a*x]]*Gamma[7/2, -3*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + (33750*Sqrt[ArcSinh[a*x]]*Gamma[7/2, -ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] - 33750*Gamma[7/2, ArcSinh[a*x]] + 625*Sqrt[3]*Gamma[7/2, 3*ArcSinh[a*x]] - 27*Sqrt[5]*Gamma[7/2, 5*ArcSinh[a*x]])/(540000*a^5)","A",0
87,1,101,247,0.038507,"\int x^3 \sinh ^{-1}(a x)^{5/2} \, dx","Integrate[x^3*ArcSinh[a*x]^(5/2),x]","\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-4 \sinh ^{-1}(a x)\right)-16 \sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-2 \sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \left(\Gamma \left(\frac{7}{2},4 \sinh ^{-1}(a x)\right)-16 \sqrt{2} \Gamma \left(\frac{7}{2},2 \sinh ^{-1}(a x)\right)\right)}{2048 a^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{3 \sinh ^{-1}(a x)^{5/2}}{32 a^4}-\frac{225 \sqrt{\sinh ^{-1}(a x)}}{2048 a^4}-\frac{45 x^2 \sqrt{\sinh ^{-1}(a x)}}{256 a^2}-\frac{5 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{32 a}+\frac{15 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{64 a^3}+\frac{1}{4} x^4 \sinh ^{-1}(a x)^{5/2}+\frac{15}{256} x^4 \sqrt{\sinh ^{-1}(a x)}",1,"(Sqrt[ArcSinh[a*x]]*Gamma[7/2, -4*ArcSinh[a*x]] - 16*Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[7/2, -2*ArcSinh[a*x]] + Sqrt[-ArcSinh[a*x]]*(-16*Sqrt[2]*Gamma[7/2, 2*ArcSinh[a*x]] + Gamma[7/2, 4*ArcSinh[a*x]]))/(2048*a^4*Sqrt[-ArcSinh[a*x]])","A",0
88,1,101,210,0.0382589,"\int x^2 \sinh ^{-1}(a x)^{5/2} \, dx","Integrate[x^2*ArcSinh[a*x]^(5/2),x]","\frac{\sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-3 \sinh ^{-1}(a x)\right)-81 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-\sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \left(81 \Gamma \left(\frac{7}{2},\sinh ^{-1}(a x)\right)-\sqrt{3} \Gamma \left(\frac{7}{2},3 \sinh ^{-1}(a x)\right)\right)}{648 a^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 x \sqrt{\sinh ^{-1}(a x)}}{6 a^2}+\frac{5 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{9 a^3}+\frac{1}{3} x^3 \sinh ^{-1}(a x)^{5/2}+\frac{5}{36} x^3 \sqrt{\sinh ^{-1}(a x)}",1,"(Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[7/2, -3*ArcSinh[a*x]] - 81*Sqrt[ArcSinh[a*x]]*Gamma[7/2, -ArcSinh[a*x]] + Sqrt[-ArcSinh[a*x]]*(81*Gamma[7/2, ArcSinh[a*x]] - Sqrt[3]*Gamma[7/2, 3*ArcSinh[a*x]]))/(648*a^3*Sqrt[-ArcSinh[a*x]])","A",0
89,1,52,152,0.0357983,"\int x \sinh ^{-1}(a x)^{5/2} \, dx","Integrate[x*ArcSinh[a*x]^(5/2),x]","\frac{\frac{\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-2 \sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}+\Gamma \left(\frac{7}{2},2 \sinh ^{-1}(a x)\right)}{32 \sqrt{2} a^2}","-\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,"((Sqrt[ArcSinh[a*x]]*Gamma[7/2, -2*ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] + Gamma[7/2, 2*ArcSinh[a*x]])/(32*Sqrt[2]*a^2)","A",0
90,1,45,94,0.052193,"\int \sinh ^{-1}(a x)^{5/2} \, dx","Integrate[ArcSinh[a*x]^(5/2),x]","-\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\Gamma \left(\frac{7}{2},\sinh ^{-1}(a x)\right)}{2 a}","-\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,"-1/2*((Sqrt[-ArcSinh[a*x]]*Gamma[7/2, -ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + Gamma[7/2, ArcSinh[a*x]])/a","A",0
91,0,0,15,0.3430607,"\int \frac{\sinh ^{-1}(a x)^{5/2}}{x} \, dx","Integrate[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,"Integrate[ArcSinh[a*x]^(5/2)/x, x]","A",-1
92,1,151,163,0.1118611,"\int \frac{x^4}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[x^4/Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{5} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\frac{5 \sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}+\frac{10 \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}-10 \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)+5 \sqrt{3} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)-\sqrt{5} \Gamma \left(\frac{1}{2},5 \sinh ^{-1}(a x)\right)}{160 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[5]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -5*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + (5*Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, -3*ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] + (10*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] - 10*Gamma[1/2, ArcSinh[a*x]] + 5*Sqrt[3]*Gamma[1/2, 3*ArcSinh[a*x]] - Sqrt[5]*Gamma[1/2, 5*ArcSinh[a*x]])/(160*a^5)","A",0
93,1,99,109,0.0805983,"\int \frac{x^3}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[x^3/Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\frac{2 \sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}-2 \sqrt{2} \Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)+\Gamma \left(\frac{1}{2},4 \sinh ^{-1}(a x)\right)}{32 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[-ArcSinh[a*x]]*Gamma[1/2, -4*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + (2*Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, -2*ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] - 2*Sqrt[2]*Gamma[1/2, 2*ArcSinh[a*x]] + Gamma[1/2, 4*ArcSinh[a*x]])/(32*a^4)","A",0
94,1,99,105,0.0769548,"\int \frac{x^2}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[x^2/Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{3} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\frac{3 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{-\sinh ^{-1}(a x)}}+3 \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)-\sqrt{3} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)}{24 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[3]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -3*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + (3*Sqrt[ArcSinh[a*x]]*Gamma[1/2, -ArcSinh[a*x]])/Sqrt[-ArcSinh[a*x]] + 3*Gamma[1/2, ArcSinh[a*x]] - Sqrt[3]*Gamma[1/2, 3*ArcSinh[a*x]])/(24*a^3)","A",0
95,1,52,63,0.0220626,"\int \frac{x}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[x/Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}+\Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)}{4 \sqrt{2} 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[-ArcSinh[a*x]]*Gamma[1/2, -2*ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] + Gamma[1/2, 2*ArcSinh[a*x]])/(4*Sqrt[2]*a^2)","A",0
96,1,47,43,0.0293632,"\int \frac{1}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[1/Sqrt[ArcSinh[a*x]],x]","\frac{\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)}{\sqrt{\sinh ^{-1}(a x)}}-\Gamma \left(\frac{1}{2},\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[-ArcSinh[a*x]]*Gamma[1/2, -ArcSinh[a*x]])/Sqrt[ArcSinh[a*x]] - Gamma[1/2, ArcSinh[a*x]])/(2*a)","A",0
97,0,0,15,0.333408,"\int \frac{1}{x \sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[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,"Integrate[1/(x*Sqrt[ArcSinh[a*x]]), x]","A",-1
98,0,0,15,1.7125915,"\int \frac{1}{x^2 \sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[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,"Integrate[1/(x^2*Sqrt[ArcSinh[a*x]]), x]","A",-1
99,1,216,188,0.3060314,"\int \frac{x^4}{\sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[x^4/ArcSinh[a*x]^(3/2),x]","\frac{-e^{-5 \sinh ^{-1}(a x)}+3 e^{-3 \sinh ^{-1}(a x)}-2 e^{-\sinh ^{-1}(a x)}-2 e^{\sinh ^{-1}(a x)}+3 e^{3 \sinh ^{-1}(a x)}-e^{5 \sinh ^{-1}(a x)}+\sqrt{5} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 \sinh ^{-1}(a x)\right)-3 \sqrt{3} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)+2 \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)+2 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)-3 \sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)+\sqrt{5} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},5 \sinh ^{-1}(a x)\right)}{16 a^5 \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,"(-E^(-5*ArcSinh[a*x]) + 3/E^(3*ArcSinh[a*x]) - 2/E^ArcSinh[a*x] - 2*E^ArcSinh[a*x] + 3*E^(3*ArcSinh[a*x]) - E^(5*ArcSinh[a*x]) + Sqrt[5]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -5*ArcSinh[a*x]] - 3*Sqrt[3]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -3*ArcSinh[a*x]] + 2*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -ArcSinh[a*x]] + 2*Sqrt[ArcSinh[a*x]]*Gamma[1/2, ArcSinh[a*x]] - 3*Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 3*ArcSinh[a*x]] + Sqrt[5]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 5*ArcSinh[a*x]])/(16*a^5*Sqrt[ArcSinh[a*x]])","A",0
100,1,126,138,0.0414722,"\int \frac{x^3}{\sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[x^3/ArcSinh[a*x]^(3/2),x]","\frac{2 \sinh \left(2 \sinh ^{-1}(a x)\right)-\sinh \left(4 \sinh ^{-1}(a x)\right)+\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 \sinh ^{-1}(a x)\right)-\sqrt{2} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)+\sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)-\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 \sinh ^{-1}(a x)\right)}{4 a^4 \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,"(Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -4*ArcSinh[a*x]] - Sqrt[2]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -2*ArcSinh[a*x]] + Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 2*ArcSinh[a*x]] - Sqrt[ArcSinh[a*x]]*Gamma[1/2, 4*ArcSinh[a*x]] + 2*Sinh[2*ArcSinh[a*x]] - Sinh[4*ArcSinh[a*x]])/(4*a^4*Sqrt[ArcSinh[a*x]])","A",0
101,1,140,130,0.1423452,"\int \frac{x^2}{\sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[x^2/ArcSinh[a*x]^(3/2),x]","\frac{-e^{-3 \sinh ^{-1}(a x)}+e^{-\sinh ^{-1}(a x)}+e^{\sinh ^{-1}(a x)}-e^{3 \sinh ^{-1}(a x)}+\sqrt{3} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)-\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)-\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)+\sqrt{3} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)}{4 a^3 \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,"(-E^(-3*ArcSinh[a*x]) + E^(-ArcSinh[a*x]) + E^ArcSinh[a*x] - E^(3*ArcSinh[a*x]) + Sqrt[3]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -3*ArcSinh[a*x]] - Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -ArcSinh[a*x]] - Sqrt[ArcSinh[a*x]]*Gamma[1/2, ArcSinh[a*x]] + Sqrt[3]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 3*ArcSinh[a*x]])/(4*a^3*Sqrt[ArcSinh[a*x]])","A",0
102,1,78,84,0.0276696,"\int \frac{x}{\sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[x/ArcSinh[a*x]^(3/2),x]","-\frac{\sinh \left(2 \sinh ^{-1}(a x)\right)}{a^2 \sqrt{\sinh ^{-1}(a x)}}+\frac{\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)}{\sqrt{2} a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{\Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)}{\sqrt{2} a^2}","\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,"(Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -2*ArcSinh[a*x]])/(Sqrt[2]*a^2*Sqrt[ArcSinh[a*x]]) - Gamma[1/2, 2*ArcSinh[a*x]]/(Sqrt[2]*a^2) - Sinh[2*ArcSinh[a*x]]/(a^2*Sqrt[ArcSinh[a*x]])","A",0
103,1,69,64,0.0726327,"\int \frac{1}{\sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[ArcSinh[a*x]^(-3/2),x]","\frac{-e^{-\sinh ^{-1}(a x)}-e^{\sinh ^{-1}(a x)}+\sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)+\sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)}{a \sqrt{\sinh ^{-1}(a 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}",1,"(-E^(-ArcSinh[a*x]) - E^ArcSinh[a*x] + Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -ArcSinh[a*x]] + Sqrt[ArcSinh[a*x]]*Gamma[1/2, ArcSinh[a*x]])/(a*Sqrt[ArcSinh[a*x]])","A",0
104,0,0,15,0.4192689,"\int \frac{1}{x \sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]^(3/2)), x]","A",-1
105,1,343,223,0.3625465,"\int \frac{x^4}{\sinh ^{-1}(a x)^{5/2}} \, dx","Integrate[x^4/ArcSinh[a*x]^(5/2),x]","\frac{-\frac{e^{5 \sinh ^{-1}(a x)} \left(10 \sinh ^{-1}(a x)+1\right)+10 \sqrt{5} \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-5 \sinh ^{-1}(a x)\right)}{48 \sinh ^{-1}(a x)^{3/2}}+\frac{e^{3 \sinh ^{-1}(a x)} \left(6 \sinh ^{-1}(a x)+1\right)+6 \sqrt{3} \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)}{16 \sinh ^{-1}(a x)^{3/2}}-\frac{e^{\sinh ^{-1}(a x)} \left(2 \sinh ^{-1}(a x)+1\right)+2 \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)}{24 \sinh ^{-1}(a x)^{3/2}}-\frac{e^{-\sinh ^{-1}(a x)} \left(-2 \sinh ^{-1}(a x)+2 e^{\sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)+1\right)}{24 \sinh ^{-1}(a x)^{3/2}}+\frac{e^{-3 \sinh ^{-1}(a x)} \left(-6 \sinh ^{-1}(a x)+6 \sqrt{3} e^{3 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)+1\right)}{16 \sinh ^{-1}(a x)^{3/2}}-\frac{e^{-5 \sinh ^{-1}(a x)} \left(-10 \sinh ^{-1}(a x)+10 \sqrt{5} e^{5 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},5 \sinh ^{-1}(a x)\right)+1\right)}{48 \sinh ^{-1}(a x)^{3/2}}}{a^5}","\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{16 x^3}{3 a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{20 x^5}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(-1/48*(E^(5*ArcSinh[a*x])*(1 + 10*ArcSinh[a*x]) + 10*Sqrt[5]*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -5*ArcSinh[a*x]])/ArcSinh[a*x]^(3/2) + (E^(3*ArcSinh[a*x])*(1 + 6*ArcSinh[a*x]) + 6*Sqrt[3]*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -3*ArcSinh[a*x]])/(16*ArcSinh[a*x]^(3/2)) - (E^ArcSinh[a*x]*(1 + 2*ArcSinh[a*x]) + 2*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -ArcSinh[a*x]])/(24*ArcSinh[a*x]^(3/2)) - (1 - 2*ArcSinh[a*x] + 2*E^ArcSinh[a*x]*ArcSinh[a*x]^(3/2)*Gamma[1/2, ArcSinh[a*x]])/(24*E^ArcSinh[a*x]*ArcSinh[a*x]^(3/2)) + (1 - 6*ArcSinh[a*x] + 6*Sqrt[3]*E^(3*ArcSinh[a*x])*ArcSinh[a*x]^(3/2)*Gamma[1/2, 3*ArcSinh[a*x]])/(16*E^(3*ArcSinh[a*x])*ArcSinh[a*x]^(3/2)) - (1 - 10*ArcSinh[a*x] + 10*Sqrt[5]*E^(5*ArcSinh[a*x])*ArcSinh[a*x]^(3/2)*Gamma[1/2, 5*ArcSinh[a*x]])/(48*E^(5*ArcSinh[a*x])*ArcSinh[a*x]^(3/2)))/a^5","A",0
106,1,174,167,0.434273,"\int \frac{x^3}{\sinh ^{-1}(a x)^{5/2}} \, dx","Integrate[x^3/ArcSinh[a*x]^(5/2),x]","\frac{2 \sinh \left(2 \sinh ^{-1}(a x)\right)-\sinh \left(4 \sinh ^{-1}(a x)\right)+4 \sinh ^{-1}(a x) \left(e^{-2 \sinh ^{-1}(a x)}+e^{2 \sinh ^{-1}(a x)}-\sqrt{2} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)-\sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)\right)-4 \sinh ^{-1}(a x) \left(e^{-4 \sinh ^{-1}(a x)}+e^{4 \sinh ^{-1}(a x)}-2 \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 \sinh ^{-1}(a x)\right)-2 \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 \sinh ^{-1}(a x)\right)\right)}{12 a^4 \sinh ^{-1}(a x)^{3/2}}","-\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{4 x^2}{a^2 \sqrt{\sinh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a^2 x^2+1}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{16 x^4}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(4*ArcSinh[a*x]*(E^(-2*ArcSinh[a*x]) + E^(2*ArcSinh[a*x]) - Sqrt[2]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -2*ArcSinh[a*x]] - Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 2*ArcSinh[a*x]]) - 4*ArcSinh[a*x]*(E^(-4*ArcSinh[a*x]) + E^(4*ArcSinh[a*x]) - 2*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -4*ArcSinh[a*x]] - 2*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 4*ArcSinh[a*x]]) + 2*Sinh[2*ArcSinh[a*x]] - Sinh[4*ArcSinh[a*x]])/(12*a^4*ArcSinh[a*x]^(3/2))","A",0
107,1,225,161,0.1566104,"\int \frac{x^2}{\sinh ^{-1}(a x)^{5/2}} \, dx","Integrate[x^2/ArcSinh[a*x]^(5/2),x]","\frac{-\frac{e^{3 \sinh ^{-1}(a x)} \left(6 \sinh ^{-1}(a x)+1\right)+6 \sqrt{3} \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)}{12 \sinh ^{-1}(a x)^{3/2}}+\frac{e^{\sinh ^{-1}(a x)} \left(2 \sinh ^{-1}(a x)+1\right)+2 \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)}{12 \sinh ^{-1}(a x)^{3/2}}+\frac{e^{-\sinh ^{-1}(a x)} \left(-2 \sinh ^{-1}(a x)+2 e^{\sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)+1\right)}{12 \sinh ^{-1}(a x)^{3/2}}-\frac{e^{-3 \sinh ^{-1}(a x)} \left(-6 \sinh ^{-1}(a x)+6 \sqrt{3} e^{3 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)+1\right)}{12 \sinh ^{-1}(a x)^{3/2}}}{a^3}","-\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,"(-1/12*(E^(3*ArcSinh[a*x])*(1 + 6*ArcSinh[a*x]) + 6*Sqrt[3]*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -3*ArcSinh[a*x]])/ArcSinh[a*x]^(3/2) + (E^ArcSinh[a*x]*(1 + 2*ArcSinh[a*x]) + 2*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -ArcSinh[a*x]])/(12*ArcSinh[a*x]^(3/2)) + (1 - 2*ArcSinh[a*x] + 2*E^ArcSinh[a*x]*ArcSinh[a*x]^(3/2)*Gamma[1/2, ArcSinh[a*x]])/(12*E^ArcSinh[a*x]*ArcSinh[a*x]^(3/2)) - (1 - 6*ArcSinh[a*x] + 6*Sqrt[3]*E^(3*ArcSinh[a*x])*ArcSinh[a*x]^(3/2)*Gamma[1/2, 3*ArcSinh[a*x]])/(12*E^(3*ArcSinh[a*x])*ArcSinh[a*x]^(3/2)))/a^3","A",0
108,1,98,118,0.1849739,"\int \frac{x}{\sinh ^{-1}(a x)^{5/2}} \, dx","Integrate[x/ArcSinh[a*x]^(5/2),x]","-\frac{\sinh \left(2 \sinh ^{-1}(a x)\right)+2 \sinh ^{-1}(a x) \left(e^{-2 \sinh ^{-1}(a x)}+e^{2 \sinh ^{-1}(a x)}-\sqrt{2} \sqrt{-\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)-\sqrt{2} \sqrt{\sinh ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)\right)}{3 a^2 \sinh ^{-1}(a x)^{3/2}}","-\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,"-1/3*(2*ArcSinh[a*x]*(E^(-2*ArcSinh[a*x]) + E^(2*ArcSinh[a*x]) - Sqrt[2]*Sqrt[-ArcSinh[a*x]]*Gamma[1/2, -2*ArcSinh[a*x]] - Sqrt[2]*Sqrt[ArcSinh[a*x]]*Gamma[1/2, 2*ArcSinh[a*x]]) + Sinh[2*ArcSinh[a*x]])/(a^2*ArcSinh[a*x]^(3/2))","A",0
109,1,105,84,0.106855,"\int \frac{1}{\sinh ^{-1}(a x)^{5/2}} \, dx","Integrate[ArcSinh[a*x]^(-5/2),x]","-\frac{e^{-\sinh ^{-1}(a x)} \left(e^{2 \sinh ^{-1}(a x)}+2 e^{2 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)-2 \sinh ^{-1}(a x)+2 e^{\sinh ^{-1}(a x)} \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)+2 e^{\sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)+1\right)}{3 a \sinh ^{-1}(a x)^{3/2}}","-\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,"-1/3*(1 + E^(2*ArcSinh[a*x]) - 2*ArcSinh[a*x] + 2*E^(2*ArcSinh[a*x])*ArcSinh[a*x] + 2*E^ArcSinh[a*x]*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -ArcSinh[a*x]] + 2*E^ArcSinh[a*x]*ArcSinh[a*x]^(3/2)*Gamma[1/2, ArcSinh[a*x]])/(a*E^ArcSinh[a*x]*ArcSinh[a*x]^(3/2))","A",0
110,0,0,15,0.4227598,"\int \frac{1}{x \sinh ^{-1}(a x)^{5/2}} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]^(5/2)), x]","A",-1
111,1,334,285,0.753657,"\int \frac{x^4}{\sinh ^{-1}(a x)^{7/2}} \, dx","Integrate[x^4/ArcSinh[a*x]^(7/2),x]","\frac{-2 e^{\sinh ^{-1}(a x)} \left(4 \sinh ^{-1}(a x)^2+2 \sinh ^{-1}(a x)+3\right)+9 e^{3 \sinh ^{-1}(a x)} \left(12 \sinh ^{-1}(a x)^2+2 \sinh ^{-1}(a x)+1\right)-e^{5 \sinh ^{-1}(a x)} \left(100 \sinh ^{-1}(a x)^2+10 \sinh ^{-1}(a x)+3\right)+100 \sqrt{5} \left(-\sinh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-5 \sinh ^{-1}(a x)\right)-108 \sqrt{3} \left(-\sinh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)+8 \left(-\sinh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)+e^{-\sinh ^{-1}(a x)} \left(-8 \sinh ^{-1}(a x)^2+4 \sinh ^{-1}(a x)+8 e^{\sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)-6\right)+9 e^{-3 \sinh ^{-1}(a x)} \left(12 \sinh ^{-1}(a x)^2-2 \sinh ^{-1}(a x)-12 \sqrt{3} e^{3 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)+1\right)+e^{-5 \sinh ^{-1}(a x)} \left(-100 \sinh ^{-1}(a x)^2+10 \sinh ^{-1}(a x)+100 \sqrt{5} e^{5 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},5 \sinh ^{-1}(a x)\right)-3\right)}{240 a^5 \sinh ^{-1}(a x)^{5/2}}","-\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{16 x^3}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\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{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*E^ArcSinh[a*x]*(3 + 2*ArcSinh[a*x] + 4*ArcSinh[a*x]^2) + 9*E^(3*ArcSinh[a*x])*(1 + 2*ArcSinh[a*x] + 12*ArcSinh[a*x]^2) - E^(5*ArcSinh[a*x])*(3 + 10*ArcSinh[a*x] + 100*ArcSinh[a*x]^2) + 100*Sqrt[5]*(-ArcSinh[a*x])^(5/2)*Gamma[1/2, -5*ArcSinh[a*x]] - 108*Sqrt[3]*(-ArcSinh[a*x])^(5/2)*Gamma[1/2, -3*ArcSinh[a*x]] + 8*(-ArcSinh[a*x])^(5/2)*Gamma[1/2, -ArcSinh[a*x]] + (-6 + 4*ArcSinh[a*x] - 8*ArcSinh[a*x]^2 + 8*E^ArcSinh[a*x]*ArcSinh[a*x]^(5/2)*Gamma[1/2, ArcSinh[a*x]])/E^ArcSinh[a*x] + (9*(1 - 2*ArcSinh[a*x] + 12*ArcSinh[a*x]^2 - 12*Sqrt[3]*E^(3*ArcSinh[a*x])*ArcSinh[a*x]^(5/2)*Gamma[1/2, 3*ArcSinh[a*x]]))/E^(3*ArcSinh[a*x]) + (-3 + 10*ArcSinh[a*x] - 100*ArcSinh[a*x]^2 + 100*Sqrt[5]*E^(5*ArcSinh[a*x])*ArcSinh[a*x]^(5/2)*Gamma[1/2, 5*ArcSinh[a*x]])/E^(5*ArcSinh[a*x]))/(240*a^5*ArcSinh[a*x]^(5/2))","A",0
112,1,210,229,0.7347086,"\int \frac{x^3}{\sinh ^{-1}(a x)^{7/2}} \, dx","Integrate[x^3/ArcSinh[a*x]^(7/2),x]","\frac{6 \sinh \left(2 \sinh ^{-1}(a x)\right)-3 \sinh \left(4 \sinh ^{-1}(a x)\right)+4 \sinh ^{-1}(a x) \left(e^{-2 \sinh ^{-1}(a x)} \left(1-4 \sinh ^{-1}(a x)\right)+e^{2 \sinh ^{-1}(a x)} \left(4 \sinh ^{-1}(a x)+1\right)+4 \sqrt{2} \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)+4 \sqrt{2} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)\right)-4 \sinh ^{-1}(a x) \left(e^{-4 \sinh ^{-1}(a x)} \left(1-8 \sinh ^{-1}(a x)\right)+e^{4 \sinh ^{-1}(a x)} \left(8 \sinh ^{-1}(a x)+1\right)+16 \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-4 \sinh ^{-1}(a x)\right)+16 \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},4 \sinh ^{-1}(a x)\right)\right)}{60 a^4 \sinh ^{-1}(a x)^{5/2}}","\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{4 x^2}{5 a^2 \sinh ^{-1}(a x)^{3/2}}-\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{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,"(4*ArcSinh[a*x]*((1 - 4*ArcSinh[a*x])/E^(2*ArcSinh[a*x]) + E^(2*ArcSinh[a*x])*(1 + 4*ArcSinh[a*x]) + 4*Sqrt[2]*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -2*ArcSinh[a*x]] + 4*Sqrt[2]*ArcSinh[a*x]^(3/2)*Gamma[1/2, 2*ArcSinh[a*x]]) - 4*ArcSinh[a*x]*((1 - 8*ArcSinh[a*x])/E^(4*ArcSinh[a*x]) + E^(4*ArcSinh[a*x])*(1 + 8*ArcSinh[a*x]) + 16*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -4*ArcSinh[a*x]] + 16*ArcSinh[a*x]^(3/2)*Gamma[1/2, 4*ArcSinh[a*x]]) + 6*Sinh[2*ArcSinh[a*x]] - 3*Sinh[4*ArcSinh[a*x]])/(60*a^4*ArcSinh[a*x]^(5/2))","A",0
113,1,221,222,0.3969009,"\int \frac{x^2}{\sinh ^{-1}(a x)^{7/2}} \, dx","Integrate[x^2/ArcSinh[a*x]^(7/2),x]","\frac{e^{\sinh ^{-1}(a x)} \left(4 \sinh ^{-1}(a x)^2+2 \sinh ^{-1}(a x)+3\right)-3 e^{3 \sinh ^{-1}(a x)} \left(12 \sinh ^{-1}(a x)^2+2 \sinh ^{-1}(a x)+1\right)+36 \sqrt{3} \left(-\sinh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-3 \sinh ^{-1}(a x)\right)-4 \left(-\sinh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)+e^{-\sinh ^{-1}(a x)} \left(4 \sinh ^{-1}(a x)^2-2 \sinh ^{-1}(a x)-4 e^{\sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)+3\right)+e^{-3 \sinh ^{-1}(a x)} \left(-36 \sinh ^{-1}(a x)^2+6 \sinh ^{-1}(a x)+36 \sqrt{3} e^{3 \sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},3 \sinh ^{-1}(a x)\right)-3\right)}{60 a^3 \sinh ^{-1}(a x)^{5/2}}","\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{8 x}{15 a^2 \sinh ^{-1}(a x)^{3/2}}-\frac{16 \sqrt{a^2 x^2+1}}{15 a^3 \sqrt{\sinh ^{-1}(a x)}}-\frac{4 x^3}{5 \sinh ^{-1}(a x)^{3/2}}",1,"(E^ArcSinh[a*x]*(3 + 2*ArcSinh[a*x] + 4*ArcSinh[a*x]^2) - 3*E^(3*ArcSinh[a*x])*(1 + 2*ArcSinh[a*x] + 12*ArcSinh[a*x]^2) + 36*Sqrt[3]*(-ArcSinh[a*x])^(5/2)*Gamma[1/2, -3*ArcSinh[a*x]] - 4*(-ArcSinh[a*x])^(5/2)*Gamma[1/2, -ArcSinh[a*x]] + (3 - 2*ArcSinh[a*x] + 4*ArcSinh[a*x]^2 - 4*E^ArcSinh[a*x]*ArcSinh[a*x]^(5/2)*Gamma[1/2, ArcSinh[a*x]])/E^ArcSinh[a*x] + (-3 + 6*ArcSinh[a*x] - 36*ArcSinh[a*x]^2 + 36*Sqrt[3]*E^(3*ArcSinh[a*x])*ArcSinh[a*x]^(5/2)*Gamma[1/2, 3*ArcSinh[a*x]])/E^(3*ArcSinh[a*x]))/(60*a^3*ArcSinh[a*x]^(5/2))","A",0
114,1,118,147,0.3455642,"\int \frac{x}{\sinh ^{-1}(a x)^{7/2}} \, dx","Integrate[x/ArcSinh[a*x]^(7/2),x]","-\frac{3 \sinh \left(2 \sinh ^{-1}(a x)\right)+2 \sinh ^{-1}(a x) \left(e^{-2 \sinh ^{-1}(a x)} \left(1-4 \sinh ^{-1}(a x)\right)+e^{2 \sinh ^{-1}(a x)} \left(4 \sinh ^{-1}(a x)+1\right)+4 \sqrt{2} \left(-\sinh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-2 \sinh ^{-1}(a x)\right)+4 \sqrt{2} \sinh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},2 \sinh ^{-1}(a x)\right)\right)}{15 a^2 \sinh ^{-1}(a x)^{5/2}}","\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,"-1/15*(2*ArcSinh[a*x]*((1 - 4*ArcSinh[a*x])/E^(2*ArcSinh[a*x]) + E^(2*ArcSinh[a*x])*(1 + 4*ArcSinh[a*x]) + 4*Sqrt[2]*(-ArcSinh[a*x])^(3/2)*Gamma[1/2, -2*ArcSinh[a*x]] + 4*Sqrt[2]*ArcSinh[a*x]^(3/2)*Gamma[1/2, 2*ArcSinh[a*x]]) + 3*Sinh[2*ArcSinh[a*x]])/(a^2*ArcSinh[a*x]^(5/2))","A",0
115,1,111,112,0.1996835,"\int \frac{1}{\sinh ^{-1}(a x)^{7/2}} \, dx","Integrate[ArcSinh[a*x]^(-7/2),x]","\frac{-2 e^{\sinh ^{-1}(a x)} \left(4 \sinh ^{-1}(a x)^2+2 \sinh ^{-1}(a x)+3\right)+8 \left(-\sinh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-\sinh ^{-1}(a x)\right)+e^{-\sinh ^{-1}(a x)} \left(-8 \sinh ^{-1}(a x)^2+4 \sinh ^{-1}(a x)+8 e^{\sinh ^{-1}(a x)} \sinh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},\sinh ^{-1}(a x)\right)-6\right)}{30 a \sinh ^{-1}(a x)^{5/2}}","-\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*E^ArcSinh[a*x]*(3 + 2*ArcSinh[a*x] + 4*ArcSinh[a*x]^2) + 8*(-ArcSinh[a*x])^(5/2)*Gamma[1/2, -ArcSinh[a*x]] + (-6 + 4*ArcSinh[a*x] - 8*ArcSinh[a*x]^2 + 8*E^ArcSinh[a*x]*ArcSinh[a*x]^(5/2)*Gamma[1/2, ArcSinh[a*x]])/E^ArcSinh[a*x])/(30*a*ArcSinh[a*x]^(5/2))","A",0
116,0,0,15,0.4212634,"\int \frac{1}{x \sinh ^{-1}(a x)^{7/2}} \, dx","Integrate[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,"Integrate[1/(x*ArcSinh[a*x]^(7/2)), x]","A",-1
117,0,0,54,0.8767113,"\int x^m \sinh ^{-1}(a x)^4 \, dx","Integrate[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,"Integrate[x^m*ArcSinh[a*x]^4, x]","A",-1
118,0,0,54,0.7873221,"\int x^m \sinh ^{-1}(a x)^3 \, dx","Integrate[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,"Integrate[x^m*ArcSinh[a*x]^3, x]","A",-1
119,1,123,137,0.040849,"\int x^m \sinh ^{-1}(a x)^2 \, dx","Integrate[x^m*ArcSinh[a*x]^2,x]","\frac{x^{m+1} \left(2 a^2 x^2 \, _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) \sinh ^{-1}(a x) \left((m+2) \sinh ^{-1}(a x)-2 a x \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-a^2 x^2\right)\right)\right)}{(m+1) (m+2) (m+3)}","\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)*((3 + m)*ArcSinh[a*x]*((2 + m)*ArcSinh[a*x] - 2*a*x*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)]) + 2*a^2*x^2*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, -(a^2*x^2)]))/((1 + m)*(2 + m)*(3 + m))","A",1
120,1,55,60,0.023162,"\int x^m \sinh ^{-1}(a x) \, dx","Integrate[x^m*ArcSinh[a*x],x]","\frac{x^{m+1} \left((m+2) \sinh ^{-1}(a x)-a x \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-a^2 x^2\right)\right)}{(m+1) (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)*((2 + m)*ArcSinh[a*x] - a*x*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(a^2*x^2)]))/((1 + m)*(2 + m))","A",1
121,0,0,13,0.423645,"\int \frac{x^m}{\sinh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[x^m/ArcSinh[a*x], x]","A",-1
122,0,0,13,0.4468414,"\int \frac{x^m}{\sinh ^{-1}(a x)^2} \, dx","Integrate[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,"Integrate[x^m/ArcSinh[a*x]^2, x]","A",-1
123,0,0,15,1.118294,"\int x^m \sinh ^{-1}(a x)^{5/2} \, dx","Integrate[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,"Integrate[x^m*ArcSinh[a*x]^(5/2), x]","A",-1
124,0,0,15,1.1202712,"\int x^m \sinh ^{-1}(a x)^{3/2} \, dx","Integrate[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,"Integrate[x^m*ArcSinh[a*x]^(3/2), x]","A",-1
125,0,0,15,1.4140389,"\int x^m \sqrt{\sinh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[x^m*Sqrt[ArcSinh[a*x]], x]","A",-1
126,0,0,15,1.2872474,"\int \frac{x^m}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Integrate[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,"Integrate[x^m/Sqrt[ArcSinh[a*x]], x]","A",-1
127,0,0,15,1.2047219,"\int \frac{x^m}{\sinh ^{-1}(a x)^{3/2}} \, dx","Integrate[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,"Integrate[x^m/ArcSinh[a*x]^(3/2), x]","A",-1
128,0,0,15,0.7928361,"\int (b x)^m \sinh ^{-1}(a x)^n \, dx","Integrate[(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,"Integrate[(b*x)^m*ArcSinh[a*x]^n, x]","A",-1
129,1,145,173,0.1554917,"\int x^4 \sinh ^{-1}(a x)^n \, dx","Integrate[x^4*ArcSinh[a*x]^n,x]","\frac{5^{-n} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-5 \sinh ^{-1}(a x)\right)-5\ 3^{-n} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-3 \sinh ^{-1}(a x)\right)+10 \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-\sinh ^{-1}(a x)\right)-10 \Gamma \left(n+1,\sinh ^{-1}(a x)\right)+5\ 3^{-n} \Gamma \left(n+1,3 \sinh ^{-1}(a x)\right)-5^{-n} \Gamma \left(n+1,5 \sinh ^{-1}(a x)\right)}{160 a^5}","\frac{5^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \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} \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} \Gamma \left(n+1,-\sinh ^{-1}(a x)\right)}{16 a^5}-\frac{\Gamma \left(n+1,\sinh ^{-1}(a x)\right)}{16 a^5}+\frac{3^{-n} \Gamma \left(n+1,3 \sinh ^{-1}(a x)\right)}{32 a^5}-\frac{5^{-n-1} \Gamma \left(n+1,5 \sinh ^{-1}(a x)\right)}{32 a^5}",1,"((ArcSinh[a*x]^n*Gamma[1 + n, -5*ArcSinh[a*x]])/(5^n*(-ArcSinh[a*x])^n) - (5*ArcSinh[a*x]^n*Gamma[1 + n, -3*ArcSinh[a*x]])/(3^n*(-ArcSinh[a*x])^n) + (10*ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(-ArcSinh[a*x])^n - 10*Gamma[1 + n, ArcSinh[a*x]] + (5*Gamma[1 + n, 3*ArcSinh[a*x]])/3^n - Gamma[1 + n, 5*ArcSinh[a*x]]/5^n)/(160*a^5)","A",1
130,1,99,119,0.0688112,"\int x^3 \sinh ^{-1}(a x)^n \, dx","Integrate[x^3*ArcSinh[a*x]^n,x]","\frac{4^{-n-3} \left(-\sinh ^{-1}(a x)\right)^{-n} \left(\left(-\sinh ^{-1}(a x)\right)^n \left(\Gamma \left(n+1,4 \sinh ^{-1}(a x)\right)-2^{n+2} \Gamma \left(n+1,2 \sinh ^{-1}(a x)\right)\right)+\sinh ^{-1}(a x)^n \Gamma \left(n+1,-4 \sinh ^{-1}(a x)\right)-2^{n+2} \sinh ^{-1}(a x)^n \Gamma \left(n+1,-2 \sinh ^{-1}(a x)\right)\right)}{a^4}","\frac{2^{-2 (n+3)} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \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} \Gamma \left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^4}-\frac{2^{-n-4} \Gamma \left(n+1,2 \sinh ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \Gamma \left(n+1,4 \sinh ^{-1}(a x)\right)}{a^4}",1,"(4^(-3 - n)*(ArcSinh[a*x]^n*Gamma[1 + n, -4*ArcSinh[a*x]] - 2^(2 + n)*ArcSinh[a*x]^n*Gamma[1 + n, -2*ArcSinh[a*x]] + (-ArcSinh[a*x])^n*(-(2^(2 + n)*Gamma[1 + n, 2*ArcSinh[a*x]]) + Gamma[1 + n, 4*ArcSinh[a*x]])))/(a^4*(-ArcSinh[a*x])^n)","A",1
131,1,97,113,0.0748042,"\int x^2 \sinh ^{-1}(a x)^n \, dx","Integrate[x^2*ArcSinh[a*x]^n,x]","\frac{3^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-3 \sinh ^{-1}(a x)\right)-\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-\sinh ^{-1}(a x)\right)+\Gamma \left(n+1,\sinh ^{-1}(a x)\right)-3^{-n-1} \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} \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} \Gamma \left(n+1,-\sinh ^{-1}(a x)\right)}{8 a^3}+\frac{\Gamma \left(n+1,\sinh ^{-1}(a x)\right)}{8 a^3}-\frac{3^{-n-1} \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]])/(-ArcSinh[a*x])^n - (ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(-ArcSinh[a*x])^n + Gamma[1 + n, ArcSinh[a*x]] - 3^(-1 - n)*Gamma[1 + n, 3*ArcSinh[a*x]])/(8*a^3)","A",1
132,1,59,59,0.016525,"\int x \sinh ^{-1}(a x)^n \, dx","Integrate[x*ArcSinh[a*x]^n,x]","\frac{2^{-n-3} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \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} \Gamma \left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \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",1
133,1,45,49,0.0268834,"\int \sinh ^{-1}(a x)^n \, dx","Integrate[ArcSinh[a*x]^n,x]","\frac{\left(-\sinh ^{-1}(a x)\right)^{-n} \sinh ^{-1}(a x)^n \Gamma \left(n+1,-\sinh ^{-1}(a x)\right)-\Gamma \left(n+1,\sinh ^{-1}(a x)\right)}{2 a}","\frac{\left(-\sinh ^{-1}(a x)\right)^{-n} \sinh ^{-1}(a x)^n \Gamma \left(n+1,-\sinh ^{-1}(a x)\right)}{2 a}-\frac{\Gamma \left(n+1,\sinh ^{-1}(a x)\right)}{2 a}",1,"((ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(-ArcSinh[a*x])^n - Gamma[1 + n, ArcSinh[a*x]])/(2*a)","A",1
134,0,0,13,0.2889849,"\int \frac{\sinh ^{-1}(a x)^n}{x} \, dx","Integrate[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,"Integrate[ArcSinh[a*x]^n/x, x]","A",-1
135,0,0,13,1.1251212,"\int \frac{\sinh ^{-1}(a x)^n}{x^2} \, dx","Integrate[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,"Integrate[ArcSinh[a*x]^n/x^2, x]","A",-1
136,1,215,213,0.4202431,"\int x^2 \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Integrate[x^2*Sqrt[a + b*ArcSinh[c*x]],x]","\frac{e^{-\frac{3 a}{b}} \sqrt{a+b \sinh ^{-1}(c x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)-\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{72 c^3 \sqrt{-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{b^2}}}","-\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,"(Sqrt[a + b*ArcSinh[c*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[3/2, a/b + ArcSinh[c*x]] + Sqrt[3]*Sqrt[a/b + ArcSinh[c*x]]*Gamma[3/2, (-3*(a + b*ArcSinh[c*x]))/b] - 9*E^((2*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[3/2, -((a + b*ArcSinh[c*x])/b)] - Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[3/2, (3*(a + b*ArcSinh[c*x]))/b]))/(72*c^3*E^((3*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])^2/b^2)])","A",0
137,1,127,145,0.0989799,"\int x \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Integrate[x*Sqrt[a + b*ArcSinh[c*x]],x]","\frac{e^{-\frac{2 a}{b}} \sqrt{a+b \sinh ^{-1}(c x)} \left(\sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{8 \sqrt{2} c^2 \sqrt{-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{b^2}}}","-\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]]*(Sqrt[a/b + ArcSinh[c*x]]*Gamma[3/2, (-2*(a + b*ArcSinh[c*x]))/b] + E^((4*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[3/2, (2*(a + b*ArcSinh[c*x]))/b]))/(8*Sqrt[2]*c^2*E^((2*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])^2/b^2)])","A",0
138,1,101,102,0.2405826,"\int \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Integrate[Sqrt[a + b*ArcSinh[c*x]],x]","\frac{e^{-\frac{a}{b}} \sqrt{a+b \sinh ^{-1}(c x)} \left(\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{\sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}}}-\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)}{\sqrt{\frac{a}{b}+\sinh ^{-1}(c x)}}\right)}{2 c}","\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,"(Sqrt[a + b*ArcSinh[c*x]]*(-((E^((2*a)/b)*Gamma[3/2, a/b + ArcSinh[c*x]])/Sqrt[a/b + ArcSinh[c*x]]) + Gamma[3/2, -((a + b*ArcSinh[c*x])/b)]/Sqrt[-((a + b*ArcSinh[c*x])/b)]))/(2*c*E^(a/b))","A",0
139,1,215,282,0.3133128,"\int x^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Integrate[x^2*(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{b e^{-\frac{3 a}{b}} \sqrt{a+b \sinh ^{-1}(c x)} \left(-27 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{5}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{5}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-27 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{5}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{5}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{216 c^3 \sqrt{-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{b^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,"-1/216*(b*Sqrt[a + b*ArcSinh[c*x]]*(-27*E^((4*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[5/2, a/b + ArcSinh[c*x]] + Sqrt[3]*Sqrt[a/b + ArcSinh[c*x]]*Gamma[5/2, (-3*(a + b*ArcSinh[c*x]))/b] - 27*E^((2*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[5/2, -((a + b*ArcSinh[c*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[5/2, (3*(a + b*ArcSinh[c*x]))/b]))/(c^3*E^((3*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])^2/b^2)])","A",0
140,1,129,179,0.1069632,"\int x \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Integrate[x*(a + b*ArcSinh[c*x])^(3/2),x]","\frac{b e^{-\frac{2 a}{b}} \sqrt{a+b \sinh ^{-1}(c x)} \left(e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{5}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-\sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{5}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{16 \sqrt{2} c^2 \sqrt{-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{b^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,"(b*Sqrt[a + b*ArcSinh[c*x]]*(-(Sqrt[a/b + ArcSinh[c*x]]*Gamma[5/2, (-2*(a + b*ArcSinh[c*x]))/b]) + E^((4*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[5/2, (2*(a + b*ArcSinh[c*x]))/b]))/(16*Sqrt[2]*c^2*E^((2*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])^2/b^2)])","A",0
141,1,251,135,1.1098967,"\int \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Integrate[(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{b} \left(4 \sqrt{b} \left(2 c x \sinh ^{-1}(c x)-3 \sqrt{c^2 x^2+1}\right) \sqrt{a+b \sinh ^{-1}(c x)}+\sqrt{\pi } (3 b-2 a) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)+\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)\right)}{8 c}+\frac{a e^{-\frac{a}{b}} \sqrt{a+b \sinh ^{-1}(c x)} \left(\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{\sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}}}-\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)}{\sqrt{\frac{a}{b}+\sinh ^{-1}(c x)}}\right)}{2 c}","\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,"(a*Sqrt[a + b*ArcSinh[c*x]]*(-((E^((2*a)/b)*Gamma[3/2, a/b + ArcSinh[c*x]])/Sqrt[a/b + ArcSinh[c*x]]) + Gamma[3/2, -((a + b*ArcSinh[c*x])/b)]/Sqrt[-((a + b*ArcSinh[c*x])/b)]))/(2*c*E^(a/b)) + (Sqrt[b]*(4*Sqrt[b]*Sqrt[a + b*ArcSinh[c*x]]*(-3*Sqrt[1 + c^2*x^2] + 2*c*x*ArcSinh[c*x]) + (2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (-2*a + 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])))/(8*c)","A",0
142,1,215,327,0.4965395,"\int x^2 \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \, dx","Integrate[x^2*(a + b*ArcSinh[c*x])^(5/2),x]","-\frac{e^{-\frac{3 a}{b}} \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \left(81 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{7}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{7}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-81 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{7}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)-\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{7}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{648 c^3 \left(-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{b^2}\right)^{3/2}}","-\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,"-1/648*((a + b*ArcSinh[c*x])^(5/2)*(81*E^((4*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[7/2, a/b + ArcSinh[c*x]] + Sqrt[3]*Sqrt[a/b + ArcSinh[c*x]]*Gamma[7/2, (-3*(a + b*ArcSinh[c*x]))/b] - 81*E^((2*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[7/2, -((a + b*ArcSinh[c*x])/b)] - Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[7/2, (3*(a + b*ArcSinh[c*x]))/b]))/(c^3*E^((3*a)/b)*(-((a + b*ArcSinh[c*x])^2/b^2))^(3/2))","A",0
143,1,115,223,0.0768161,"\int x \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \, dx","Integrate[x*(a + b*ArcSinh[c*x])^(5/2),x]","\frac{e^{-\frac{2 a}{b}} \left(b^3 e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{7}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-b^3 \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{7}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{32 \sqrt{2} c^2 \sqrt{a+b \sinh ^{-1}(c 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}",1,"(-(b^3*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[7/2, (-2*(a + b*ArcSinh[c*x]))/b]) + b^3*E^((4*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[7/2, (2*(a + b*ArcSinh[c*x]))/b])/(32*Sqrt[2]*c^2*E^((2*a)/b)*Sqrt[a + b*ArcSinh[c*x]])","A",0
144,1,282,155,3.6461072,"\int \left(a+b \sinh ^{-1}(c x)\right)^{5/2} \, dx","Integrate[(a + b*ArcSinh[c*x])^(5/2),x]","\frac{\sqrt{b} e^{-\frac{a}{b}} \left(-\left(\sqrt{\pi } \left(4 a^2-15 b^2\right) e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)\right)+\sqrt{\pi } \left(4 a^2-15 b^2\right) \text{erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)+\frac{4 \sqrt{b} \left(-2 a^2 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{3}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)-2 a^2 \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)+e^{a/b} \left(a+b \sinh ^{-1}(c x)\right) \left(5 \left(3 b c x-2 a \sqrt{c^2 x^2+1}\right)+2 \sinh ^{-1}(c x) \left(4 a c x-5 b \sqrt{c^2 x^2+1}\right)+4 b c x \sinh ^{-1}(c x)^2\right)\right)}{\sqrt{a+b \sinh ^{-1}(c x)}}\right)}{16 c}","\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,"(Sqrt[b]*(-((4*a^2 - 15*b^2)*E^((2*a)/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]]) + (4*a^2 - 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]] + (4*Sqrt[b]*(E^(a/b)*(a + b*ArcSinh[c*x])*(5*(3*b*c*x - 2*a*Sqrt[1 + c^2*x^2]) + 2*(4*a*c*x - 5*b*Sqrt[1 + c^2*x^2])*ArcSinh[c*x] + 4*b*c*x*ArcSinh[c*x]^2) - 2*a^2*E^((2*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[3/2, a/b + ArcSinh[c*x]] - 2*a^2*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[3/2, -((a + b*ArcSinh[c*x])/b)]))/Sqrt[a + b*ArcSinh[c*x]]))/(16*c*E^(a/b))","A",0
145,1,196,194,0.2341278,"\int \frac{x^2}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Integrate[x^2/Sqrt[a + b*ArcSinh[c*x]],x]","\frac{e^{-\frac{3 a}{b}} \left(3 e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)+\sqrt{3} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-3 e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)-\sqrt{3} e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{24 c^3 \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)}{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,"(3*E^((4*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, a/b + ArcSinh[c*x]] + Sqrt[3]*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, (-3*(a + b*ArcSinh[c*x]))/b] - 3*E^((2*a)/b)*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)] - Sqrt[3]*E^((6*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, (3*(a + b*ArcSinh[c*x]))/b])/(24*c^3*E^((3*a)/b)*Sqrt[a + b*ArcSinh[c*x]])","A",0
146,1,108,107,0.0679922,"\int \frac{x}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Integrate[x/Sqrt[a + b*ArcSinh[c*x]],x]","\frac{e^{-\frac{2 a}{b}} \left(\sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)+e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{4 \sqrt{2} c^2 \sqrt{a+b \sinh ^{-1}(c 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}",1,"(Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, (-2*(a + b*ArcSinh[c*x]))/b] + E^((4*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, (2*(a + b*ArcSinh[c*x]))/b])/(4*Sqrt[2]*c^2*E^((2*a)/b)*Sqrt[a + b*ArcSinh[c*x]])","A",0
147,1,101,88,0.1030404,"\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Integrate[1/Sqrt[a + b*ArcSinh[c*x]],x]","\frac{e^{-\frac{a}{b}} \left(\sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)-e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)\right)}{2 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)}{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^((2*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, a/b + ArcSinh[c*x]]) + Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)])/(2*c*E^(a/b)*Sqrt[a + b*ArcSinh[c*x]])","A",0
148,1,290,226,0.4091907,"\int \frac{x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[x^2/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{e^{-3 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \left(e^{\frac{3 a}{b}+2 \sinh ^{-1}(c x)}+e^{\frac{3 a}{b}+4 \sinh ^{-1}(c x)}-e^{\frac{3 a}{b}+6 \sinh ^{-1}(c x)}-e^{\frac{4 a}{b}+3 \sinh ^{-1}(c x)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)+\sqrt{3} e^{3 \sinh ^{-1}(c x)} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-e^{\frac{2 a}{b}+3 \sinh ^{-1}(c x)} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}+3 \sinh ^{-1}(c x)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-e^{\frac{3 a}{b}}\right)}{4 b c^3 \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,"(-E^((3*a)/b) + E^((3*a)/b + 2*ArcSinh[c*x]) + E^((3*a)/b + 4*ArcSinh[c*x]) - E^((3*a)/b + 6*ArcSinh[c*x]) - E^((4*a)/b + 3*ArcSinh[c*x])*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, a/b + ArcSinh[c*x]] + Sqrt[3]*E^(3*ArcSinh[c*x])*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, (-3*(a + b*ArcSinh[c*x]))/b] - E^((2*a)/b + 3*ArcSinh[c*x])*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)] + Sqrt[3]*E^((6*a)/b + 3*ArcSinh[c*x])*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, (3*(a + b*ArcSinh[c*x]))/b])/(4*b*c^3*E^(3*(a/b + ArcSinh[c*x]))*Sqrt[a + b*ArcSinh[c*x]])","A",0
149,1,134,135,0.1148897,"\int \frac{x}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[x/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{e^{-\frac{2 a}{b}} \left(-2 e^{\frac{2 a}{b}} \sinh \left(2 \sinh ^{-1}(c x)\right)+\sqrt{2} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-\sqrt{2} e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{2 b c^2 \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,"(Sqrt[2]*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, (-2*(a + b*ArcSinh[c*x]))/b] - Sqrt[2]*E^((4*a)/b)*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, (2*(a + b*ArcSinh[c*x]))/b] - 2*E^((2*a)/b)*Sinh[2*ArcSinh[c*x]])/(2*b*c^2*E^((2*a)/b)*Sqrt[a + b*ArcSinh[c*x]])","A",0
150,1,137,116,0.246319,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[(a + b*ArcSinh[c*x])^(-3/2),x]","\frac{e^{-\frac{a+b \sinh ^{-1}(c x)}{b}} \left(-e^{a/b} \left(e^{2 \sinh ^{-1}(c x)}+1\right)+e^{\frac{2 a}{b}+\sinh ^{-1}(c x)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)+e^{\sinh ^{-1}(c x)} \sqrt{-\frac{a+b \sinh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)\right)}{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,"(-(E^(a/b)*(1 + E^(2*ArcSinh[c*x]))) + E^((2*a)/b + ArcSinh[c*x])*Sqrt[a/b + ArcSinh[c*x]]*Gamma[1/2, a/b + ArcSinh[c*x]] + E^ArcSinh[c*x]*Sqrt[-((a + b*ArcSinh[c*x])/b)]*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)])/(b*c*E^((a + b*ArcSinh[c*x])/b)*Sqrt[a + b*ArcSinh[c*x]])","A",0
151,1,340,271,1.6219002,"\int \frac{x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[x^2/(a + b*ArcSinh[c*x])^(5/2),x]","\frac{e^{-3 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \left(-6 \sqrt{3} b e^{3 \sinh ^{-1}(c x)} \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)+2 b e^{\frac{2 a}{b}+3 \sinh ^{-1}(c x)} \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)+2 e^{\frac{4 a}{b}+3 \sinh ^{-1}(c x)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)-e^{\frac{3 a}{b}} \left(\left(e^{2 \sinh ^{-1}(c x)}-1\right) \left(a \left(4 e^{2 \sinh ^{-1}(c x)}+6 e^{4 \sinh ^{-1}(c x)}+6\right)+b \left(e^{4 \sinh ^{-1}(c x)}-1\right)+2 b \left(2 e^{2 \sinh ^{-1}(c x)}+3 e^{4 \sinh ^{-1}(c x)}+3\right) \sinh ^{-1}(c x)\right)+6 \sqrt{3} e^{3 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)\right)}{12 b^2 c^3 \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*E^((4*a)/b + 3*ArcSinh[c*x])*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])*Gamma[1/2, a/b + ArcSinh[c*x]] - 6*Sqrt[3]*b*E^(3*ArcSinh[c*x])*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcSinh[c*x]))/b] + 2*b*E^((2*a)/b + 3*ArcSinh[c*x])*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)] - E^((3*a)/b)*((-1 + E^(2*ArcSinh[c*x]))*(b*(-1 + E^(4*ArcSinh[c*x])) + a*(6 + 4*E^(2*ArcSinh[c*x]) + 6*E^(4*ArcSinh[c*x])) + 2*b*(3 + 2*E^(2*ArcSinh[c*x]) + 3*E^(4*ArcSinh[c*x]))*ArcSinh[c*x]) + 6*Sqrt[3]*E^(3*(a/b + ArcSinh[c*x]))*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])*Gamma[1/2, (3*(a + b*ArcSinh[c*x]))/b]))/(12*b^2*c^3*E^(3*(a/b + ArcSinh[c*x]))*(a + b*ArcSinh[c*x])^(3/2))","A",0
152,1,200,183,0.7460305,"\int \frac{x}{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[x/(a + b*ArcSinh[c*x])^(5/2),x]","\frac{e^{-2 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \left(e^{\frac{2 a}{b}} \left(4 \sqrt{2} e^{2 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-4 a e^{4 \sinh ^{-1}(c x)}-4 a-b e^{4 \sinh ^{-1}(c x)}-4 b \left(e^{4 \sinh ^{-1}(c x)}+1\right) \sinh ^{-1}(c x)+b\right)-4 \sqrt{2} b e^{2 \sinh ^{-1}(c x)} \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)}{6 b^2 c^2 \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,"(-4*Sqrt[2]*b*E^(2*ArcSinh[c*x])*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, (-2*(a + b*ArcSinh[c*x]))/b] + E^((2*a)/b)*(-4*a + b - 4*a*E^(4*ArcSinh[c*x]) - b*E^(4*ArcSinh[c*x]) - 4*b*(1 + E^(4*ArcSinh[c*x]))*ArcSinh[c*x] + 4*Sqrt[2]*E^(2*(a/b + ArcSinh[c*x]))*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])*Gamma[1/2, (2*(a + b*ArcSinh[c*x]))/b]))/(6*b^2*c^2*E^(2*(a/b + ArcSinh[c*x]))*(a + b*ArcSinh[c*x])^(3/2))","A",0
153,1,181,143,0.6023662,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[(a + b*ArcSinh[c*x])^(-5/2),x]","\frac{e^{-\frac{a+b \sinh ^{-1}(c x)}{b}} \left(-e^{a/b} \left(2 a \left(e^{2 \sinh ^{-1}(c x)}-1\right)-2 b \sinh ^{-1}(c x)+b e^{2 \sinh ^{-1}(c x)} \left(2 \sinh ^{-1}(c x)+1\right)+b\right)-2 b e^{\sinh ^{-1}(c x)} \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)-2 e^{\frac{2 a}{b}+\sinh ^{-1}(c x)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)\right)}{3 b^2 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,"(-(E^(a/b)*(b + 2*a*(-1 + E^(2*ArcSinh[c*x])) - 2*b*ArcSinh[c*x] + b*E^(2*ArcSinh[c*x])*(1 + 2*ArcSinh[c*x]))) - 2*E^((2*a)/b + ArcSinh[c*x])*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])*Gamma[1/2, a/b + ArcSinh[c*x]] - 2*b*E^ArcSinh[c*x]*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)])/(3*b^2*c*E^((a + b*ArcSinh[c*x])/b)*(a + b*ArcSinh[c*x])^(3/2))","A",0
154,1,417,346,1.740177,"\int \frac{x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{7/2}} \, dx","Integrate[x^2/(a + b*ArcSinh[c*x])^(7/2),x]","\frac{e^{-\sinh ^{-1}(c x)} \left(4 a^2+2 b (4 a-b) \sinh ^{-1}(c x)-4 e^{\frac{a}{b}+\sinh ^{-1}(c x)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right)^2 \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)-2 a b+4 b^2 \sinh ^{-1}(c x)^2+3 b^2\right)-3 \left(2 e^{-\frac{3 a}{b}} \left(a+b \sinh ^{-1}(c x)\right) \left(e^{3 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \left(6 a+6 b \sinh ^{-1}(c x)+b\right)+6 \sqrt{3} b \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)+b^2 e^{3 \sinh ^{-1}(c x)}\right)-3 e^{-3 \sinh ^{-1}(c x)} \left(2 \left(a+b \sinh ^{-1}(c x)\right) \left(-6 \sqrt{3} e^{3 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)+6 a+6 b \sinh ^{-1}(c x)-b\right)+b^2\right)+2 e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c x)\right) \left(e^{\frac{a}{b}+\sinh ^{-1}(c x)} \left(2 a+2 b \sinh ^{-1}(c x)+b\right)+2 b \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)\right)+3 b^2 e^{\sinh ^{-1}(c x)}}{60 b^3 c^3 \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,"(3*b^2*E^ArcSinh[c*x] + (4*a^2 - 2*a*b + 3*b^2 + 2*(4*a - b)*b*ArcSinh[c*x] + 4*b^2*ArcSinh[c*x]^2 - 4*E^(a/b + ArcSinh[c*x])*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])^2*Gamma[1/2, a/b + ArcSinh[c*x]])/E^ArcSinh[c*x] - 3*(b^2*E^(3*ArcSinh[c*x]) + (2*(a + b*ArcSinh[c*x])*(E^(3*(a/b + ArcSinh[c*x]))*(6*a + b + 6*b*ArcSinh[c*x]) + 6*Sqrt[3]*b*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcSinh[c*x]))/b]))/E^((3*a)/b)) + (2*(a + b*ArcSinh[c*x])*(E^(a/b + ArcSinh[c*x])*(2*a + b + 2*b*ArcSinh[c*x]) + 2*b*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)]))/E^(a/b) - (3*(b^2 + 2*(a + b*ArcSinh[c*x])*(6*a - b + 6*b*ArcSinh[c*x] - 6*Sqrt[3]*E^(3*(a/b + ArcSinh[c*x]))*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])*Gamma[1/2, (3*(a + b*ArcSinh[c*x]))/b])))/E^(3*ArcSinh[c*x]))/(60*b^3*c^3*(a + b*ArcSinh[c*x])^(5/2))","A",0
155,1,208,219,1.2198364,"\int \frac{x}{\left(a+b \sinh ^{-1}(c x)\right)^{7/2}} \, dx","Integrate[x/(a + b*ArcSinh[c*x])^(7/2),x]","-\frac{\left(a+b \sinh ^{-1}(c x)\right) \left(e^{-\frac{2 a}{b}} \left(2 e^{2 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \left(4 a+4 b \sinh ^{-1}(c x)+b\right)+8 \sqrt{2} b \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)\right)+e^{-2 \sinh ^{-1}(c x)} \left(8 \sqrt{2} e^{2 \left(\frac{a}{b}+\sinh ^{-1}(c x)\right)} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)-8 a-8 b \sinh ^{-1}(c x)+2 b\right)\right)+3 b^2 \sinh \left(2 \sinh ^{-1}(c x)\right)}{15 b^3 c^2 \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,"-1/15*((a + b*ArcSinh[c*x])*((2*E^(2*(a/b + ArcSinh[c*x]))*(4*a + b + 4*b*ArcSinh[c*x]) + 8*Sqrt[2]*b*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, (-2*(a + b*ArcSinh[c*x]))/b])/E^((2*a)/b) + (-8*a + 2*b - 8*b*ArcSinh[c*x] + 8*Sqrt[2]*E^(2*(a/b + ArcSinh[c*x]))*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])*Gamma[1/2, (2*(a + b*ArcSinh[c*x]))/b])/E^(2*ArcSinh[c*x])) + 3*b^2*Sinh[2*ArcSinh[c*x]])/(b^3*c^2*(a + b*ArcSinh[c*x])^(5/2))","A",0
156,1,210,178,0.6311559,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{7/2}} \, dx","Integrate[(a + b*ArcSinh[c*x])^(-7/2),x]","\frac{-2 e^{-\sinh ^{-1}(c x)} \left(4 a^2+2 a b \left(4 \sinh ^{-1}(c x)-1\right)+b^2 \left(4 \sinh ^{-1}(c x)^2-2 \sinh ^{-1}(c x)+3\right)\right)+8 e^{a/b} \sqrt{\frac{a}{b}+\sinh ^{-1}(c x)} \left(a+b \sinh ^{-1}(c x)\right)^2 \Gamma \left(\frac{1}{2},\frac{a}{b}+\sinh ^{-1}(c x)\right)-4 e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c x)\right) \left(e^{\frac{a}{b}+\sinh ^{-1}(c x)} \left(2 a+2 b \sinh ^{-1}(c x)+b\right)+2 b \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \sinh ^{-1}(c x)}{b}\right)\right)-6 b^2 e^{\sinh ^{-1}(c x)}}{30 b^3 c \left(a+b \sinh ^{-1}(c x)\right)^{5/2}}","-\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{8 \sqrt{c^2 x^2+1}}{15 b^3 c \sqrt{a+b \sinh ^{-1}(c x)}}-\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,"(-6*b^2*E^ArcSinh[c*x] - (2*(4*a^2 + 2*a*b*(-1 + 4*ArcSinh[c*x]) + b^2*(3 - 2*ArcSinh[c*x] + 4*ArcSinh[c*x]^2)))/E^ArcSinh[c*x] + 8*E^(a/b)*Sqrt[a/b + ArcSinh[c*x]]*(a + b*ArcSinh[c*x])^2*Gamma[1/2, a/b + ArcSinh[c*x]] - (4*(a + b*ArcSinh[c*x])*(E^(a/b + ArcSinh[c*x])*(2*a + b + 2*b*ArcSinh[c*x]) + 2*b*(-((a + b*ArcSinh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcSinh[c*x])/b)]))/E^(a/b))/(30*b^3*c*(a + b*ArcSinh[c*x])^(5/2))","A",0