1,1,93,0,0.0374411,"\int x^4 \cosh ^{-1}(a x) \, dx","Int[x^4*ArcCosh[a*x],x]","-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1}}{75 a^3}-\frac{8 \sqrt{a x-1} \sqrt{a x+1}}{75 a^5}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{25 a}+\frac{1}{5} x^5 \cosh ^{-1}(a x)","-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1}}{75 a^3}-\frac{8 \sqrt{a x-1} \sqrt{a x+1}}{75 a^5}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{25 a}+\frac{1}{5} x^5 \cosh ^{-1}(a x)",1,"(-8*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(75*a^5) - (4*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(75*a^3) - (x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(25*a) + (x^5*ArcCosh[a*x])/5","A",6,4,8,0.5000,1,"{5662, 100, 12, 74}"
2,1,77,0,0.0299139,"\int x^3 \cosh ^{-1}(a x) \, dx","Int[x^3*ArcCosh[a*x],x]","-\frac{3 x \sqrt{a x-1} \sqrt{a x+1}}{32 a^3}-\frac{3 \cosh ^{-1}(a x)}{32 a^4}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{16 a}+\frac{1}{4} x^4 \cosh ^{-1}(a x)","-\frac{3 x \sqrt{a x-1} \sqrt{a x+1}}{32 a^3}-\frac{3 \cosh ^{-1}(a x)}{32 a^4}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{16 a}+\frac{1}{4} x^4 \cosh ^{-1}(a x)",1,"(-3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(32*a^3) - (x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(16*a) - (3*ArcCosh[a*x])/(32*a^4) + (x^4*ArcCosh[a*x])/4","A",5,5,8,0.6250,1,"{5662, 100, 12, 90, 52}"
3,1,65,0,0.0225147,"\int x^2 \cosh ^{-1}(a x) \, dx","Int[x^2*ArcCosh[a*x],x]","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{9 a^3}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{9 a}+\frac{1}{3} x^3 \cosh ^{-1}(a x)","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{9 a^3}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{9 a}+\frac{1}{3} x^3 \cosh ^{-1}(a x)",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a^3) - (x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a) + (x^3*ArcCosh[a*x])/3","A",4,4,8,0.5000,1,"{5662, 100, 12, 74}"
4,1,49,0,0.0152043,"\int x \cosh ^{-1}(a x) \, dx","Int[x*ArcCosh[a*x],x]","-\frac{\cosh ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{4 a}","-\frac{\cosh ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{4 a}",1,"-(x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(4*a) - ArcCosh[a*x]/(4*a^2) + (x^2*ArcCosh[a*x])/2","A",3,3,6,0.5000,1,"{5662, 90, 52}"
5,1,30,0,0.006411,"\int \cosh ^{-1}(a x) \, dx","Int[ArcCosh[a*x],x]","x \cosh ^{-1}(a x)-\frac{\sqrt{a x-1} \sqrt{a x+1}}{a}","x \cosh ^{-1}(a x)-\frac{\sqrt{a x-1} \sqrt{a x+1}}{a}",1,"-((Sqrt[-1 + a*x]*Sqrt[1 + a*x])/a) + x*ArcCosh[a*x]","A",2,2,4,0.5000,1,"{5654, 74}"
6,1,43,0,0.058621,"\int \frac{\cosh ^{-1}(a x)}{x} \, dx","Int[ArcCosh[a*x]/x,x]","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{2} \cosh ^{-1}(a x)^2+\cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)","\frac{1}{2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{2} \cosh ^{-1}(a x)^2+\cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)",1,"-ArcCosh[a*x]^2/2 + ArcCosh[a*x]*Log[1 + E^(2*ArcCosh[a*x])] + PolyLog[2, -E^(2*ArcCosh[a*x])]/2","A",5,5,8,0.6250,1,"{5660, 3718, 2190, 2279, 2391}"
7,1,32,0,0.0168724,"\int \frac{\cosh ^{-1}(a x)}{x^2} \, dx","Int[ArcCosh[a*x]/x^2,x]","a \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)-\frac{\cosh ^{-1}(a x)}{x}","a \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)-\frac{\cosh ^{-1}(a x)}{x}",1,"-(ArcCosh[a*x]/x) + a*ArcTan[Sqrt[-1 + a*x]*Sqrt[1 + a*x]]","A",3,3,8,0.3750,1,"{5662, 92, 205}"
8,1,38,0,0.0134166,"\int \frac{\cosh ^{-1}(a x)}{x^3} \, dx","Int[ArcCosh[a*x]/x^3,x]","\frac{a \sqrt{a x-1} \sqrt{a x+1}}{2 x}-\frac{\cosh ^{-1}(a x)}{2 x^2}","\frac{a \sqrt{a x-1} \sqrt{a x+1}}{2 x}-\frac{\cosh ^{-1}(a x)}{2 x^2}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*x) - ArcCosh[a*x]/(2*x^2)","A",2,2,8,0.2500,1,"{5662, 95}"
9,1,65,0,0.027259,"\int \frac{\cosh ^{-1}(a x)}{x^4} \, dx","Int[ArcCosh[a*x]/x^4,x]","\frac{1}{6} a^3 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{6 x^2}-\frac{\cosh ^{-1}(a x)}{3 x^3}","\frac{1}{6} a^3 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{6 x^2}-\frac{\cosh ^{-1}(a x)}{3 x^3}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(6*x^2) - ArcCosh[a*x]/(3*x^3) + (a^3*ArcTan[Sqrt[-1 + a*x]*Sqrt[1 + a*x]])/6","A",5,5,8,0.6250,1,"{5662, 103, 12, 92, 205}"
10,1,66,0,0.0244926,"\int \frac{\cosh ^{-1}(a x)}{x^5} \, dx","Int[ArcCosh[a*x]/x^5,x]","\frac{a^3 \sqrt{a x-1} \sqrt{a x+1}}{6 x}+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{12 x^3}-\frac{\cosh ^{-1}(a x)}{4 x^4}","\frac{a^3 \sqrt{a x-1} \sqrt{a x+1}}{6 x}+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{12 x^3}-\frac{\cosh ^{-1}(a x)}{4 x^4}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(12*x^3) + (a^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(6*x) - ArcCosh[a*x]/(4*x^4)","A",4,4,8,0.5000,1,"{5662, 103, 12, 95}"
11,1,93,0,0.0407888,"\int \frac{\cosh ^{-1}(a x)}{x^6} \, dx","Int[ArcCosh[a*x]/x^6,x]","\frac{3 a^3 \sqrt{a x-1} \sqrt{a x+1}}{40 x^2}+\frac{3}{40} a^5 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{20 x^4}-\frac{\cosh ^{-1}(a x)}{5 x^5}","\frac{3 a^3 \sqrt{a x-1} \sqrt{a x+1}}{40 x^2}+\frac{3}{40} a^5 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{20 x^4}-\frac{\cosh ^{-1}(a x)}{5 x^5}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(20*x^4) + (3*a^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(40*x^2) - ArcCosh[a*x]/(5*x^5) + (3*a^5*ArcTan[Sqrt[-1 + a*x]*Sqrt[1 + a*x]])/40","A",7,5,8,0.6250,1,"{5662, 103, 12, 92, 205}"
12,1,132,0,0.4897589,"\int x^4 \cosh ^{-1}(a x)^2 \, dx","Int[x^4*ArcCosh[a*x]^2,x]","\frac{8 x^3}{225 a^2}-\frac{8 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{75 a^3}+\frac{16 x}{75 a^4}-\frac{16 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{75 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^2-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{25 a}+\frac{2 x^5}{125}","\frac{8 x^3}{225 a^2}-\frac{8 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{75 a^3}+\frac{16 x}{75 a^4}-\frac{16 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{75 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^2-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{25 a}+\frac{2 x^5}{125}",1,"(16*x)/(75*a^4) + (8*x^3)/(225*a^2) + (2*x^5)/125 - (16*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(75*a^5) - (8*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(75*a^3) - (2*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(25*a) + (x^5*ArcCosh[a*x]^2)/5","A",7,5,10,0.5000,1,"{5662, 5759, 5718, 8, 30}"
13,1,106,0,0.4401919,"\int x^3 \cosh ^{-1}(a x)^2 \, dx","Int[x^3*ArcCosh[a*x]^2,x]","\frac{3 x^2}{32 a^2}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{16 a^3}-\frac{3 \cosh ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^2-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{8 a}+\frac{x^4}{32}","\frac{3 x^2}{32 a^2}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{16 a^3}-\frac{3 \cosh ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^2-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{8 a}+\frac{x^4}{32}",1,"(3*x^2)/(32*a^2) + x^4/32 - (3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(16*a^3) - (x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(8*a) - (3*ArcCosh[a*x]^2)/(32*a^4) + (x^4*ArcCosh[a*x]^2)/4","A",6,4,10,0.4000,1,"{5662, 5759, 5676, 30}"
14,1,90,0,0.3111967,"\int x^2 \cosh ^{-1}(a x)^2 \, dx","Int[x^2*ArcCosh[a*x]^2,x]","\frac{4 x}{9 a^2}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^2-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a}+\frac{2 x^3}{27}","\frac{4 x}{9 a^2}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^2-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a}+\frac{2 x^3}{27}",1,"(4*x)/(9*a^2) + (2*x^3)/27 - (4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(9*a^3) - (2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(9*a) + (x^3*ArcCosh[a*x]^2)/3","A",5,5,10,0.5000,1,"{5662, 5759, 5718, 8, 30}"
15,1,64,0,0.2506646,"\int x \cosh ^{-1}(a x)^2 \, dx","Int[x*ArcCosh[a*x]^2,x]","-\frac{\cosh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^2-\frac{x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{2 a}+\frac{x^2}{4}","-\frac{\cosh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^2-\frac{x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{2 a}+\frac{x^2}{4}",1,"x^2/4 - (x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(2*a) - ArcCosh[a*x]^2/(4*a^2) + (x^2*ArcCosh[a*x]^2)/2","A",4,4,8,0.5000,1,"{5662, 5759, 5676, 30}"
16,1,39,0,0.1274318,"\int \cosh ^{-1}(a x)^2 \, dx","Int[ArcCosh[a*x]^2,x]","x \cosh ^{-1}(a x)^2-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}+2 x","x \cosh ^{-1}(a x)^2-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}+2 x",1,"2*x - (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/a + x*ArcCosh[a*x]^2","A",3,3,6,0.5000,1,"{5654, 5718, 8}"
17,1,62,0,0.092509,"\int \frac{\cosh ^{-1}(a x)^2}{x} \, dx","Int[ArcCosh[a*x]^2/x,x]","\cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{3} \cosh ^{-1}(a x)^3+\cosh ^{-1}(a x)^2 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)","\cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{3} \cosh ^{-1}(a x)^3+\cosh ^{-1}(a x)^2 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)",1,"-ArcCosh[a*x]^3/3 + ArcCosh[a*x]^2*Log[1 + E^(2*ArcCosh[a*x])] + ArcCosh[a*x]*PolyLog[2, -E^(2*ArcCosh[a*x])] - PolyLog[3, -E^(2*ArcCosh[a*x])]/2","A",6,6,10,0.6000,1,"{5660, 3718, 2190, 2531, 2282, 6589}"
18,1,60,0,0.2085227,"\int \frac{\cosh ^{-1}(a x)^2}{x^2} \, dx","Int[ArcCosh[a*x]^2/x^2,x]","-2 i a \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+2 i a \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^2}{x}+4 a \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)","-2 i a \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+2 i a \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^2}{x}+4 a \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)",1,"-(ArcCosh[a*x]^2/x) + 4*a*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]] - (2*I)*a*PolyLog[2, (-I)*E^ArcCosh[a*x]] + (2*I)*a*PolyLog[2, I*E^ArcCosh[a*x]]","A",7,5,10,0.5000,1,"{5662, 5761, 4180, 2279, 2391}"
19,1,48,0,0.1920712,"\int \frac{\cosh ^{-1}(a x)^2}{x^3} \, dx","Int[ArcCosh[a*x]^2/x^3,x]","a^2 (-\log (x))-\frac{\cosh ^{-1}(a x)^2}{2 x^2}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{x}","a^2 (-\log (x))-\frac{\cosh ^{-1}(a x)^2}{2 x^2}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{x}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/x - ArcCosh[a*x]^2/(2*x^2) - a^2*Log[x]","A",3,3,10,0.3000,1,"{5662, 5724, 29}"
20,1,114,0,0.3924136,"\int \frac{\cosh ^{-1}(a x)^2}{x^4} \, dx","Int[ArcCosh[a*x]^2/x^4,x]","-\frac{1}{3} i a^3 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+\frac{1}{3} i a^3 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+\frac{a^2}{3 x}+\frac{2}{3} a^3 \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 x^2}-\frac{\cosh ^{-1}(a x)^2}{3 x^3}","-\frac{1}{3} i a^3 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+\frac{1}{3} i a^3 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+\frac{a^2}{3 x}+\frac{2}{3} a^3 \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 x^2}-\frac{\cosh ^{-1}(a x)^2}{3 x^3}",1,"a^2/(3*x) + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(3*x^2) - ArcCosh[a*x]^2/(3*x^3) + (2*a^3*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]])/3 - (I/3)*a^3*PolyLog[2, (-I)*E^ArcCosh[a*x]] + (I/3)*a^3*PolyLog[2, I*E^ArcCosh[a*x]]","A",9,7,10,0.7000,1,"{5662, 5748, 5761, 4180, 2279, 2391, 30}"
21,1,95,0,0.3648828,"\int \frac{\cosh ^{-1}(a x)^2}{x^5} \, dx","Int[ArcCosh[a*x]^2/x^5,x]","\frac{a^2}{12 x^2}-\frac{1}{3} a^4 \log (x)+\frac{a^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 x}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{6 x^3}-\frac{\cosh ^{-1}(a x)^2}{4 x^4}","\frac{a^2}{12 x^2}-\frac{1}{3} a^4 \log (x)+\frac{a^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 x}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{6 x^3}-\frac{\cosh ^{-1}(a x)^2}{4 x^4}",1,"a^2/(12*x^2) + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(6*x^3) + (a^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(3*x) - ArcCosh[a*x]^2/(4*x^4) - (a^4*Log[x])/3","A",5,5,10,0.5000,1,"{5662, 5748, 5724, 29, 30}"
22,1,231,0,0.7714335,"\int x^4 \cosh ^{-1}(a x)^3 \, dx","Int[x^4*ArcCosh[a*x]^3,x]","-\frac{272 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5625 a^3}+\frac{8 x^3 \cosh ^{-1}(a x)}{75 a^2}-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a^3}-\frac{4144 \sqrt{a x-1} \sqrt{a x+1}}{5625 a^5}+\frac{16 x \cosh ^{-1}(a x)}{25 a^4}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a^5}-\frac{6 x^4 \sqrt{a x-1} \sqrt{a x+1}}{625 a}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^3+\frac{6}{125} x^5 \cosh ^{-1}(a x)-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a}","-\frac{272 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5625 a^3}+\frac{8 x^3 \cosh ^{-1}(a x)}{75 a^2}-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a^3}-\frac{4144 \sqrt{a x-1} \sqrt{a x+1}}{5625 a^5}+\frac{16 x \cosh ^{-1}(a x)}{25 a^4}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a^5}-\frac{6 x^4 \sqrt{a x-1} \sqrt{a x+1}}{625 a}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^3+\frac{6}{125} x^5 \cosh ^{-1}(a x)-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a}",1,"(-4144*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5625*a^5) - (272*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5625*a^3) - (6*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(625*a) + (16*x*ArcCosh[a*x])/(25*a^4) + (8*x^3*ArcCosh[a*x])/(75*a^2) + (6*x^5*ArcCosh[a*x])/125 - (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(25*a^5) - (4*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(25*a^3) - (3*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(25*a) + (x^5*ArcCosh[a*x]^3)/5","A",16,7,10,0.7000,1,"{5662, 5759, 5718, 5654, 74, 100, 12}"
23,1,183,0,0.6662149,"\int x^3 \cosh ^{-1}(a x)^3 \, dx","Int[x^3*ArcCosh[a*x]^3,x]","\frac{9 x^2 \cosh ^{-1}(a x)}{32 a^2}-\frac{45 x \sqrt{a x-1} \sqrt{a x+1}}{256 a^3}-\frac{9 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{32 a^3}-\frac{3 \cosh ^{-1}(a x)^3}{32 a^4}-\frac{45 \cosh ^{-1}(a x)}{256 a^4}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1}}{128 a}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^3+\frac{3}{32} x^4 \cosh ^{-1}(a x)-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{16 a}","\frac{9 x^2 \cosh ^{-1}(a x)}{32 a^2}-\frac{45 x \sqrt{a x-1} \sqrt{a x+1}}{256 a^3}-\frac{9 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{32 a^3}-\frac{3 \cosh ^{-1}(a x)^3}{32 a^4}-\frac{45 \cosh ^{-1}(a x)}{256 a^4}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1}}{128 a}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^3+\frac{3}{32} x^4 \cosh ^{-1}(a x)-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{16 a}",1,"(-45*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(256*a^3) - (3*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(128*a) - (45*ArcCosh[a*x])/(256*a^4) + (9*x^2*ArcCosh[a*x])/(32*a^2) + (3*x^4*ArcCosh[a*x])/32 - (9*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(32*a^3) - (3*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(16*a) - (3*ArcCosh[a*x]^3)/(32*a^4) + (x^4*ArcCosh[a*x]^3)/4","A",12,7,10,0.7000,1,"{5662, 5759, 5676, 90, 52, 100, 12}"
24,1,155,0,0.4741997,"\int x^2 \cosh ^{-1}(a x)^3 \, dx","Int[x^2*ArcCosh[a*x]^3,x]","-\frac{40 \sqrt{a x-1} \sqrt{a x+1}}{27 a^3}+\frac{4 x \cosh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a^3}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{27 a}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^3+\frac{2}{9} x^3 \cosh ^{-1}(a x)-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a}","-\frac{40 \sqrt{a x-1} \sqrt{a x+1}}{27 a^3}+\frac{4 x \cosh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a^3}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{27 a}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^3+\frac{2}{9} x^3 \cosh ^{-1}(a x)-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a}",1,"(-40*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(27*a^3) - (2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(27*a) + (4*x*ArcCosh[a*x])/(3*a^2) + (2*x^3*ArcCosh[a*x])/9 - (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(3*a^3) - (x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(3*a) + (x^3*ArcCosh[a*x]^3)/3","A",9,7,10,0.7000,1,"{5662, 5759, 5718, 5654, 74, 100, 12}"
25,1,107,0,0.3809964,"\int x \cosh ^{-1}(a x)^3 \, dx","Int[x*ArcCosh[a*x]^3,x]","-\frac{\cosh ^{-1}(a x)^3}{4 a^2}-\frac{3 \cosh ^{-1}(a x)}{8 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^3+\frac{3}{4} x^2 \cosh ^{-1}(a x)-\frac{3 x \sqrt{a x-1} \sqrt{a x+1}}{8 a}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 a}","-\frac{\cosh ^{-1}(a x)^3}{4 a^2}-\frac{3 \cosh ^{-1}(a x)}{8 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^3+\frac{3}{4} x^2 \cosh ^{-1}(a x)-\frac{3 x \sqrt{a x-1} \sqrt{a x+1}}{8 a}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 a}",1,"(-3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(8*a) - (3*ArcCosh[a*x])/(8*a^2) + (3*x^2*ArcCosh[a*x])/4 - (3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(4*a) - ArcCosh[a*x]^3/(4*a^2) + (x^2*ArcCosh[a*x]^3)/2","A",6,5,8,0.6250,1,"{5662, 5759, 5676, 90, 52}"
26,1,68,0,0.1833064,"\int \cosh ^{-1}(a x)^3 \, dx","Int[ArcCosh[a*x]^3,x]","-\frac{6 \sqrt{a x-1} \sqrt{a x+1}}{a}+x \cosh ^{-1}(a x)^3-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{a}+6 x \cosh ^{-1}(a x)","-\frac{6 \sqrt{a x-1} \sqrt{a x+1}}{a}+x \cosh ^{-1}(a x)^3-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{a}+6 x \cosh ^{-1}(a x)",1,"(-6*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/a + 6*x*ArcCosh[a*x] - (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/a + x*ArcCosh[a*x]^3","A",4,3,6,0.5000,1,"{5654, 5718, 74}"
27,1,87,0,0.1054907,"\int \frac{\cosh ^{-1}(a x)^3}{x} \, dx","Int[ArcCosh[a*x]^3/x,x]","\frac{3}{2} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)+\frac{3}{4} \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{4} \cosh ^{-1}(a x)^4+\cosh ^{-1}(a x)^3 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)","\frac{3}{2} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)+\frac{3}{4} \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{4} \cosh ^{-1}(a x)^4+\cosh ^{-1}(a x)^3 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)",1,"-ArcCosh[a*x]^4/4 + ArcCosh[a*x]^3*Log[1 + E^(2*ArcCosh[a*x])] + (3*ArcCosh[a*x]^2*PolyLog[2, -E^(2*ArcCosh[a*x])])/2 - (3*ArcCosh[a*x]*PolyLog[3, -E^(2*ArcCosh[a*x])])/2 + (3*PolyLog[4, -E^(2*ArcCosh[a*x])])/4","A",7,7,10,0.7000,1,"{5660, 3718, 2190, 2531, 6609, 2282, 6589}"
28,1,104,0,0.3102091,"\int \frac{\cosh ^{-1}(a x)^3}{x^2} \, dx","Int[ArcCosh[a*x]^3/x^2,x]","-6 i a \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+6 i a \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+6 i a \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-6 i a \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^3}{x}+6 a \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)","-6 i a \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+6 i a \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+6 i a \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-6 i a \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^3}{x}+6 a \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)",1,"-(ArcCosh[a*x]^3/x) + 6*a*ArcCosh[a*x]^2*ArcTan[E^ArcCosh[a*x]] - (6*I)*a*ArcCosh[a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]] + (6*I)*a*ArcCosh[a*x]*PolyLog[2, I*E^ArcCosh[a*x]] + (6*I)*a*PolyLog[3, (-I)*E^ArcCosh[a*x]] - (6*I)*a*PolyLog[3, I*E^ArcCosh[a*x]]","A",9,6,10,0.6000,1,"{5662, 5761, 4180, 2531, 2282, 6589}"
29,1,98,0,0.3168095,"\int \frac{\cosh ^{-1}(a x)^3}{x^3} \, dx","Int[ArcCosh[a*x]^3/x^3,x]","-\frac{3}{2} a^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)+\frac{3}{2} a^2 \cosh ^{-1}(a x)^2-3 a^2 \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)-\frac{\cosh ^{-1}(a x)^3}{2 x^2}+\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x}","-\frac{3}{2} a^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)+\frac{3}{2} a^2 \cosh ^{-1}(a x)^2-3 a^2 \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)-\frac{\cosh ^{-1}(a x)^3}{2 x^2}+\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x}",1,"(3*a^2*ArcCosh[a*x]^2)/2 + (3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(2*x) - ArcCosh[a*x]^3/(2*x^2) - 3*a^2*ArcCosh[a*x]*Log[1 + E^(2*ArcCosh[a*x])] - (3*a^2*PolyLog[2, -E^(2*ArcCosh[a*x])])/2","A",7,7,10,0.7000,1,"{5662, 5724, 5660, 3718, 2190, 2279, 2391}"
30,1,183,0,0.5773003,"\int \frac{\cosh ^{-1}(a x)^3}{x^4} \, dx","Int[ArcCosh[a*x]^3/x^4,x]","-i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+i a^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-i a^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)-a^3 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{a^2 \cosh ^{-1}(a x)}{x}+a^3 \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x^2}-\frac{\cosh ^{-1}(a x)^3}{3 x^3}","-i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+i a^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-i a^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)-a^3 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{a^2 \cosh ^{-1}(a x)}{x}+a^3 \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x^2}-\frac{\cosh ^{-1}(a x)^3}{3 x^3}",1,"(a^2*ArcCosh[a*x])/x + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(2*x^2) - ArcCosh[a*x]^3/(3*x^3) + a^3*ArcCosh[a*x]^2*ArcTan[E^ArcCosh[a*x]] - a^3*ArcTan[Sqrt[-1 + a*x]*Sqrt[1 + a*x]] - I*a^3*ArcCosh[a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]] + I*a^3*ArcCosh[a*x]*PolyLog[2, I*E^ArcCosh[a*x]] + I*a^3*PolyLog[3, (-I)*E^ArcCosh[a*x]] - I*a^3*PolyLog[3, I*E^ArcCosh[a*x]]","A",13,9,10,0.9000,1,"{5662, 5748, 5761, 4180, 2531, 2282, 6589, 92, 205}"
31,1,174,0,0.5777028,"\int \frac{\cosh ^{-1}(a x)^3}{x^5} \, dx","Int[ArcCosh[a*x]^3/x^5,x]","-\frac{1}{2} a^4 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)+\frac{a^2 \cosh ^{-1}(a x)}{4 x^2}-\frac{a^3 \sqrt{a x-1} \sqrt{a x+1}}{4 x}+\frac{1}{2} a^4 \cosh ^{-1}(a x)^2+\frac{a^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x}-a^4 \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 x^3}-\frac{\cosh ^{-1}(a x)^3}{4 x^4}","-\frac{1}{2} a^4 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)+\frac{a^2 \cosh ^{-1}(a x)}{4 x^2}-\frac{a^3 \sqrt{a x-1} \sqrt{a x+1}}{4 x}+\frac{1}{2} a^4 \cosh ^{-1}(a x)^2+\frac{a^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x}-a^4 \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 x^3}-\frac{\cosh ^{-1}(a x)^3}{4 x^4}",1,"-(a^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(4*x) + (a^2*ArcCosh[a*x])/(4*x^2) + (a^4*ArcCosh[a*x]^2)/2 + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(4*x^3) + (a^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(2*x) - ArcCosh[a*x]^3/(4*x^4) - a^4*ArcCosh[a*x]*Log[1 + E^(2*ArcCosh[a*x])] - (a^4*PolyLog[2, -E^(2*ArcCosh[a*x])])/2","A",10,9,10,0.9000,1,"{5662, 5748, 5724, 5660, 3718, 2190, 2279, 2391, 95}"
32,1,306,0,2.1925182,"\int x^5 \cosh ^{-1}(a x)^4 \, dx","Int[x^5*ArcCosh[a*x]^4,x]","\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}+\frac{5 x^4 \cosh ^{-1}(a x)^2}{48 a^2}-\frac{5 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{36 a^3}-\frac{65 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{864 a^3}+\frac{5 x^2 \cosh ^{-1}(a x)^2}{16 a^4}-\frac{5 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{24 a^5}-\frac{245 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{576 a^5}-\frac{5 \cosh ^{-1}(a x)^4}{96 a^6}-\frac{245 \cosh ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \cosh ^{-1}(a x)^4+\frac{1}{18} x^6 \cosh ^{-1}(a x)^2-\frac{x^5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a}-\frac{x^5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{54 a}+\frac{x^6}{324}","\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}+\frac{5 x^4 \cosh ^{-1}(a x)^2}{48 a^2}-\frac{5 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{36 a^3}-\frac{65 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{864 a^3}+\frac{5 x^2 \cosh ^{-1}(a x)^2}{16 a^4}-\frac{5 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{24 a^5}-\frac{245 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{576 a^5}-\frac{5 \cosh ^{-1}(a x)^4}{96 a^6}-\frac{245 \cosh ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \cosh ^{-1}(a x)^4+\frac{1}{18} x^6 \cosh ^{-1}(a x)^2-\frac{x^5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a}-\frac{x^5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{54 a}+\frac{x^6}{324}",1,"(245*x^2)/(1152*a^4) + (65*x^4)/(3456*a^2) + x^6/324 - (245*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(576*a^5) - (65*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(864*a^3) - (x^5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(54*a) - (245*ArcCosh[a*x]^2)/(1152*a^6) + (5*x^2*ArcCosh[a*x]^2)/(16*a^4) + (5*x^4*ArcCosh[a*x]^2)/(48*a^2) + (x^6*ArcCosh[a*x]^2)/18 - (5*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(24*a^5) - (5*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(36*a^3) - (x^5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(9*a) - (5*ArcCosh[a*x]^4)/(96*a^6) + (x^6*ArcCosh[a*x]^4)/6","A",23,4,10,0.4000,1,"{5662, 5759, 5676, 30}"
33,1,274,0,1.627583,"\int x^4 \cosh ^{-1}(a x)^4 \, dx","Int[x^4*ArcCosh[a*x]^4,x]","\frac{1088 x^3}{16875 a^2}+\frac{16 x^3 \cosh ^{-1}(a x)^2}{75 a^2}-\frac{16 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{75 a^3}-\frac{1088 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{5625 a^3}+\frac{16576 x}{5625 a^4}+\frac{32 x \cosh ^{-1}(a x)^2}{25 a^4}-\frac{32 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{75 a^5}-\frac{16576 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{5625 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^4+\frac{12}{125} x^5 \cosh ^{-1}(a x)^2-\frac{4 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{25 a}-\frac{24 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{625 a}+\frac{24 x^5}{3125}","\frac{1088 x^3}{16875 a^2}+\frac{16 x^3 \cosh ^{-1}(a x)^2}{75 a^2}-\frac{16 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{75 a^3}-\frac{1088 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{5625 a^3}+\frac{16576 x}{5625 a^4}+\frac{32 x \cosh ^{-1}(a x)^2}{25 a^4}-\frac{32 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{75 a^5}-\frac{16576 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{5625 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^4+\frac{12}{125} x^5 \cosh ^{-1}(a x)^2-\frac{4 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{25 a}-\frac{24 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{625 a}+\frac{24 x^5}{3125}",1,"(16576*x)/(5625*a^4) + (1088*x^3)/(16875*a^2) + (24*x^5)/3125 - (16576*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(5625*a^5) - (1088*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(5625*a^3) - (24*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(625*a) + (32*x*ArcCosh[a*x]^2)/(25*a^4) + (16*x^3*ArcCosh[a*x]^2)/(75*a^2) + (12*x^5*ArcCosh[a*x]^2)/125 - (32*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(75*a^5) - (16*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(75*a^3) - (4*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(25*a) + (x^5*ArcCosh[a*x]^4)/5","A",19,6,10,0.6000,1,"{5662, 5759, 5718, 5654, 8, 30}"
34,1,214,0,1.3143854,"\int x^3 \cosh ^{-1}(a x)^4 \, dx","Int[x^3*ArcCosh[a*x]^4,x]","\frac{45 x^2}{128 a^2}+\frac{9 x^2 \cosh ^{-1}(a x)^2}{16 a^2}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{8 a^3}-\frac{45 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{64 a^3}-\frac{3 \cosh ^{-1}(a x)^4}{32 a^4}-\frac{45 \cosh ^{-1}(a x)^2}{128 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^4+\frac{3}{16} x^4 \cosh ^{-1}(a x)^2-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{4 a}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{32 a}+\frac{3 x^4}{128}","\frac{45 x^2}{128 a^2}+\frac{9 x^2 \cosh ^{-1}(a x)^2}{16 a^2}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{8 a^3}-\frac{45 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{64 a^3}-\frac{3 \cosh ^{-1}(a x)^4}{32 a^4}-\frac{45 \cosh ^{-1}(a x)^2}{128 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^4+\frac{3}{16} x^4 \cosh ^{-1}(a x)^2-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{4 a}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{32 a}+\frac{3 x^4}{128}",1,"(45*x^2)/(128*a^2) + (3*x^4)/128 - (45*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(64*a^3) - (3*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(32*a) - (45*ArcCosh[a*x]^2)/(128*a^4) + (9*x^2*ArcCosh[a*x]^2)/(16*a^2) + (3*x^4*ArcCosh[a*x]^2)/16 - (3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(8*a^3) - (x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(4*a) - (3*ArcCosh[a*x]^4)/(32*a^4) + (x^4*ArcCosh[a*x]^4)/4","A",14,4,10,0.4000,1,"{5662, 5759, 5676, 30}"
35,1,182,0,0.8814916,"\int x^2 \cosh ^{-1}(a x)^4 \, dx","Int[x^2*ArcCosh[a*x]^4,x]","\frac{160 x}{27 a^2}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a^3}+\frac{8 x \cosh ^{-1}(a x)^2}{3 a^2}-\frac{160 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^4-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a}+\frac{4}{9} x^3 \cosh ^{-1}(a x)^2-\frac{8 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a}+\frac{8 x^3}{81}","\frac{160 x}{27 a^2}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a^3}+\frac{8 x \cosh ^{-1}(a x)^2}{3 a^2}-\frac{160 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^4-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a}+\frac{4}{9} x^3 \cosh ^{-1}(a x)^2-\frac{8 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a}+\frac{8 x^3}{81}",1,"(160*x)/(27*a^2) + (8*x^3)/81 - (160*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(27*a^3) - (8*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(27*a) + (8*x*ArcCosh[a*x]^2)/(3*a^2) + (4*x^3*ArcCosh[a*x]^2)/9 - (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(9*a^3) - (4*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(9*a) + (x^3*ArcCosh[a*x]^4)/3","A",11,6,10,0.6000,1,"{5662, 5759, 5718, 5654, 8, 30}"
36,1,120,0,0.6025076,"\int x \cosh ^{-1}(a x)^4 \, dx","Int[x*ArcCosh[a*x]^4,x]","-\frac{\cosh ^{-1}(a x)^4}{4 a^2}-\frac{3 \cosh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^4+\frac{3}{2} x^2 \cosh ^{-1}(a x)^2-\frac{x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{a}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{2 a}+\frac{3 x^2}{4}","-\frac{\cosh ^{-1}(a x)^4}{4 a^2}-\frac{3 \cosh ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^4+\frac{3}{2} x^2 \cosh ^{-1}(a x)^2-\frac{x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{a}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{2 a}+\frac{3 x^2}{4}",1,"(3*x^2)/4 - (3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(2*a) - (3*ArcCosh[a*x]^2)/(4*a^2) + (3*x^2*ArcCosh[a*x]^2)/2 - (x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/a - ArcCosh[a*x]^4/(4*a^2) + (x^2*ArcCosh[a*x]^4)/2","A",7,4,8,0.5000,1,"{5662, 5759, 5676, 30}"
37,1,77,0,0.2980583,"\int \cosh ^{-1}(a x)^4 \, dx","Int[ArcCosh[a*x]^4,x]","x \cosh ^{-1}(a x)^4-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{a}+12 x \cosh ^{-1}(a x)^2-\frac{24 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}+24 x","x \cosh ^{-1}(a x)^4-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{a}+12 x \cosh ^{-1}(a x)^2-\frac{24 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}+24 x",1,"24*x - (24*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/a + 12*x*ArcCosh[a*x]^2 - (4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/a + x*ArcCosh[a*x]^4","A",5,3,6,0.5000,1,"{5654, 5718, 8}"
38,1,103,0,0.1201141,"\int \frac{\cosh ^{-1}(a x)^4}{x} \, dx","Int[ArcCosh[a*x]^4/x,x]","2 \cosh ^{-1}(a x)^3 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)+3 \cosh ^{-1}(a x) \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{5} \cosh ^{-1}(a x)^5+\cosh ^{-1}(a x)^4 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)","2 \cosh ^{-1}(a x)^3 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)-3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)+3 \cosh ^{-1}(a x) \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{5} \cosh ^{-1}(a x)^5+\cosh ^{-1}(a x)^4 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)",1,"-ArcCosh[a*x]^5/5 + ArcCosh[a*x]^4*Log[1 + E^(2*ArcCosh[a*x])] + 2*ArcCosh[a*x]^3*PolyLog[2, -E^(2*ArcCosh[a*x])] - 3*ArcCosh[a*x]^2*PolyLog[3, -E^(2*ArcCosh[a*x])] + 3*ArcCosh[a*x]*PolyLog[4, -E^(2*ArcCosh[a*x])] - (3*PolyLog[5, -E^(2*ArcCosh[a*x])])/2","A",8,7,10,0.7000,1,"{5660, 3718, 2190, 2531, 6609, 2282, 6589}"
39,1,150,0,0.3348369,"\int \frac{\cosh ^{-1}(a x)^4}{x^2} \, dx","Int[ArcCosh[a*x]^4/x^2,x]","-12 i a \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+12 i a \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+24 i a \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-24 i a \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)-24 i a \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)+24 i a \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^4}{x}+8 a \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)","-12 i a \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+12 i a \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+24 i a \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-24 i a \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)-24 i a \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)+24 i a \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^4}{x}+8 a \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)",1,"-(ArcCosh[a*x]^4/x) + 8*a*ArcCosh[a*x]^3*ArcTan[E^ArcCosh[a*x]] - (12*I)*a*ArcCosh[a*x]^2*PolyLog[2, (-I)*E^ArcCosh[a*x]] + (12*I)*a*ArcCosh[a*x]^2*PolyLog[2, I*E^ArcCosh[a*x]] + (24*I)*a*ArcCosh[a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]] - (24*I)*a*ArcCosh[a*x]*PolyLog[3, I*E^ArcCosh[a*x]] - (24*I)*a*PolyLog[4, (-I)*E^ArcCosh[a*x]] + (24*I)*a*PolyLog[4, I*E^ArcCosh[a*x]]","A",11,7,10,0.7000,1,"{5662, 5761, 4180, 2531, 6609, 2282, 6589}"
40,1,115,0,0.3581694,"\int \frac{\cosh ^{-1}(a x)^4}{x^3} \, dx","Int[ArcCosh[a*x]^4/x^3,x]","-6 a^2 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)+2 a^2 \cosh ^{-1}(a x)^3-6 a^2 \cosh ^{-1}(a x)^2 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)-\frac{\cosh ^{-1}(a x)^4}{2 x^2}+\frac{2 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{x}","-6 a^2 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)+2 a^2 \cosh ^{-1}(a x)^3-6 a^2 \cosh ^{-1}(a x)^2 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)-\frac{\cosh ^{-1}(a x)^4}{2 x^2}+\frac{2 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{x}",1,"2*a^2*ArcCosh[a*x]^3 + (2*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/x - ArcCosh[a*x]^4/(2*x^2) - 6*a^2*ArcCosh[a*x]^2*Log[1 + E^(2*ArcCosh[a*x])] - 6*a^2*ArcCosh[a*x]*PolyLog[2, -E^(2*ArcCosh[a*x])] + 3*a^2*PolyLog[3, -E^(2*ArcCosh[a*x])]","A",8,8,10,0.8000,1,"{5662, 5724, 5660, 3718, 2190, 2531, 2282, 6589}"
41,1,268,0,0.8024702,"\int \frac{\cosh ^{-1}(a x)^4}{x^4} \, dx","Int[ArcCosh[a*x]^4/x^4,x]","-2 i a^3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+2 i a^3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)+\frac{2 a^2 \cosh ^{-1}(a x)^2}{x}+\frac{4}{3} a^3 \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)-8 a^3 \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^4}{3 x^3}+\frac{2 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{3 x^2}","-2 i a^3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)+2 i a^3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)+\frac{2 a^2 \cosh ^{-1}(a x)^2}{x}+\frac{4}{3} a^3 \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)-8 a^3 \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^4}{3 x^3}+\frac{2 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{3 x^2}",1,"(2*a^2*ArcCosh[a*x]^2)/x + (2*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(3*x^2) - ArcCosh[a*x]^4/(3*x^3) - 8*a^3*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]] + (4*a^3*ArcCosh[a*x]^3*ArcTan[E^ArcCosh[a*x]])/3 + (4*I)*a^3*PolyLog[2, (-I)*E^ArcCosh[a*x]] - (2*I)*a^3*ArcCosh[a*x]^2*PolyLog[2, (-I)*E^ArcCosh[a*x]] - (4*I)*a^3*PolyLog[2, I*E^ArcCosh[a*x]] + (2*I)*a^3*ArcCosh[a*x]^2*PolyLog[2, I*E^ArcCosh[a*x]] + (4*I)*a^3*ArcCosh[a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]] - (4*I)*a^3*ArcCosh[a*x]*PolyLog[3, I*E^ArcCosh[a*x]] - (4*I)*a^3*PolyLog[4, (-I)*E^ArcCosh[a*x]] + (4*I)*a^3*PolyLog[4, I*E^ArcCosh[a*x]]","A",19,10,10,1.000,1,"{5662, 5748, 5761, 4180, 2531, 6609, 2282, 6589, 2279, 2391}"
42,1,55,0,0.0960031,"\int \frac{x^6}{\cosh ^{-1}(a x)} \, dx","Int[x^6/ArcCosh[a*x],x]","\frac{5 \text{Shi}\left(\cosh ^{-1}(a x)\right)}{64 a^7}+\frac{9 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{64 a^7}+\frac{5 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{64 a^7}+\frac{\text{Shi}\left(7 \cosh ^{-1}(a x)\right)}{64 a^7}","\frac{5 \text{Shi}\left(\cosh ^{-1}(a x)\right)}{64 a^7}+\frac{9 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{64 a^7}+\frac{5 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{64 a^7}+\frac{\text{Shi}\left(7 \cosh ^{-1}(a x)\right)}{64 a^7}",1,"(5*SinhIntegral[ArcCosh[a*x]])/(64*a^7) + (9*SinhIntegral[3*ArcCosh[a*x]])/(64*a^7) + (5*SinhIntegral[5*ArcCosh[a*x]])/(64*a^7) + SinhIntegral[7*ArcCosh[a*x]]/(64*a^7)","A",7,3,10,0.3000,1,"{5670, 5448, 3298}"
43,1,43,0,0.0841293,"\int \frac{x^5}{\cosh ^{-1}(a x)} \, dx","Int[x^5/ArcCosh[a*x],x]","\frac{5 \text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{32 a^6}+\frac{\text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Shi}\left(6 \cosh ^{-1}(a x)\right)}{32 a^6}","\frac{5 \text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{32 a^6}+\frac{\text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{8 a^6}+\frac{\text{Shi}\left(6 \cosh ^{-1}(a x)\right)}{32 a^6}",1,"(5*SinhIntegral[2*ArcCosh[a*x]])/(32*a^6) + SinhIntegral[4*ArcCosh[a*x]]/(8*a^6) + SinhIntegral[6*ArcCosh[a*x]]/(32*a^6)","A",6,3,10,0.3000,1,"{5670, 5448, 3298}"
44,1,41,0,0.0801527,"\int \frac{x^4}{\cosh ^{-1}(a x)} \, dx","Int[x^4/ArcCosh[a*x],x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{8 a^5}+\frac{3 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{16 a^5}","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{8 a^5}+\frac{3 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{16 a^5}",1,"SinhIntegral[ArcCosh[a*x]]/(8*a^5) + (3*SinhIntegral[3*ArcCosh[a*x]])/(16*a^5) + SinhIntegral[5*ArcCosh[a*x]]/(16*a^5)","A",6,3,10,0.3000,1,"{5670, 5448, 3298}"
45,1,29,0,0.0655709,"\int \frac{x^3}{\cosh ^{-1}(a x)} \, dx","Int[x^3/ArcCosh[a*x],x]","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{4 a^4}+\frac{\text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{8 a^4}","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{4 a^4}+\frac{\text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{8 a^4}",1,"SinhIntegral[2*ArcCosh[a*x]]/(4*a^4) + SinhIntegral[4*ArcCosh[a*x]]/(8*a^4)","A",5,3,10,0.3000,1,"{5670, 5448, 3298}"
46,1,27,0,0.0640484,"\int \frac{x^2}{\cosh ^{-1}(a x)} \, dx","Int[x^2/ArcCosh[a*x],x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{4 a^3}+\frac{\text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^3}","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{4 a^3}+\frac{\text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^3}",1,"SinhIntegral[ArcCosh[a*x]]/(4*a^3) + SinhIntegral[3*ArcCosh[a*x]]/(4*a^3)","A",5,3,10,0.3000,1,"{5670, 5448, 3298}"
47,1,14,0,0.0369433,"\int \frac{x}{\cosh ^{-1}(a x)} \, dx","Int[x/ArcCosh[a*x],x]","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^2}","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^2}",1,"SinhIntegral[2*ArcCosh[a*x]]/(2*a^2)","A",4,4,8,0.5000,1,"{5670, 5448, 12, 3298}"
48,1,9,0,0.0171132,"\int \frac{1}{\cosh ^{-1}(a x)} \, dx","Int[ArcCosh[a*x]^(-1),x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{a}","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{a}",1,"SinhIntegral[ArcCosh[a*x]]/a","A",2,2,6,0.3333,1,"{5658, 3298}"
49,0,0,0,0.0138482,"\int \frac{1}{x \cosh ^{-1}(a x)} \, dx","Int[1/(x*ArcCosh[a*x]),x]","\int \frac{1}{x \cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.01444,"\int \frac{1}{x^2 \cosh ^{-1}(a x)} \, dx","Int[1/(x^2*ArcCosh[a*x]),x]","\int \frac{1}{x^2 \cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \cosh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x^2*ArcCosh[a*x]), x]","A",0,0,0,0,-1,"{}"
51,1,73,0,0.0643322,"\int \frac{x^4}{\cosh ^{-1}(a x)^2} \, dx","Int[x^4/ArcCosh[a*x]^2,x]","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{8 a^5}+\frac{9 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{16 a^5}+\frac{5 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{16 a^5}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{8 a^5}+\frac{9 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{16 a^5}+\frac{5 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{16 a^5}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}",1,"-((x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x])) + CoshIntegral[ArcCosh[a*x]]/(8*a^5) + (9*CoshIntegral[3*ArcCosh[a*x]])/(16*a^5) + (5*CoshIntegral[5*ArcCosh[a*x]])/(16*a^5)","A",5,2,10,0.2000,1,"{5666, 3301}"
52,1,61,0,0.0501213,"\int \frac{x^3}{\cosh ^{-1}(a x)^2} \, dx","Int[x^3/ArcCosh[a*x]^2,x]","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{2 a^4}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{2 a^4}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}",1,"-((x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x])) + CoshIntegral[2*ArcCosh[a*x]]/(2*a^4) + CoshIntegral[4*ArcCosh[a*x]]/(2*a^4)","A",4,2,10,0.2000,1,"{5666, 3301}"
53,1,59,0,0.0472113,"\int \frac{x^2}{\cosh ^{-1}(a x)^2} \, dx","Int[x^2/ArcCosh[a*x]^2,x]","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{4 a^3}+\frac{3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^3}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{4 a^3}+\frac{3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^3}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}",1,"-((x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x])) + CoshIntegral[ArcCosh[a*x]]/(4*a^3) + (3*CoshIntegral[3*ArcCosh[a*x]])/(4*a^3)","A",4,2,10,0.2000,1,"{5666, 3301}"
54,1,42,0,0.0251702,"\int \frac{x}{\cosh ^{-1}(a x)^2} \, dx","Int[x/ArcCosh[a*x]^2,x]","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{a^2}-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}",1,"-((x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x])) + CoshIntegral[2*ArcCosh[a*x]]/a^2","A",2,2,8,0.2500,1,"{5666, 3301}"
55,1,39,0,0.1844789,"\int \frac{1}{\cosh ^{-1}(a x)^2} \, dx","Int[ArcCosh[a*x]^(-2),x]","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{a}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{a}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{a \cosh ^{-1}(a x)}",1,"-((Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x])) + CoshIntegral[ArcCosh[a*x]]/a","A",3,3,6,0.5000,1,"{5656, 5781, 3301}"
56,0,0,0,0.0127509,"\int \frac{1}{x \cosh ^{-1}(a x)^2} \, dx","Int[1/(x*ArcCosh[a*x]^2),x]","\int \frac{1}{x \cosh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
57,0,0,0,0.0140318,"\int \frac{1}{x^2 \cosh ^{-1}(a x)^2} \, dx","Int[1/(x^2*ArcCosh[a*x]^2),x]","\int \frac{1}{x^2 \cosh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \cosh ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x^2*ArcCosh[a*x]^2), x]","A",0,0,0,0,-1,"{}"
58,1,102,0,0.6447034,"\int \frac{x^4}{\cosh ^{-1}(a x)^3} \, dx","Int[x^4/ArcCosh[a*x]^3,x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{25 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{2 x^3}{a^2 \cosh ^{-1}(a x)}-\frac{5 x^5}{2 \cosh ^{-1}(a x)}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{25 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{2 x^3}{a^2 \cosh ^{-1}(a x)}-\frac{5 x^5}{2 \cosh ^{-1}(a x)}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}",1,"-(x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*ArcCosh[a*x]^2) + (2*x^3)/(a^2*ArcCosh[a*x]) - (5*x^5)/(2*ArcCosh[a*x]) + SinhIntegral[ArcCosh[a*x]]/(16*a^5) + (27*SinhIntegral[3*ArcCosh[a*x]])/(32*a^5) + (25*SinhIntegral[5*ArcCosh[a*x]])/(32*a^5)","A",14,5,10,0.5000,1,"{5668, 5775, 5670, 5448, 3298}"
59,1,87,0,0.5979553,"\int \frac{x^3}{\cosh ^{-1}(a x)^3} \, dx","Int[x^3/ArcCosh[a*x]^3,x]","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{a^4}+\frac{3 x^2}{2 a^2 \cosh ^{-1}(a x)}-\frac{2 x^4}{\cosh ^{-1}(a x)}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{a^4}+\frac{3 x^2}{2 a^2 \cosh ^{-1}(a x)}-\frac{2 x^4}{\cosh ^{-1}(a x)}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}",1,"-(x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*ArcCosh[a*x]^2) + (3*x^2)/(2*a^2*ArcCosh[a*x]) - (2*x^4)/ArcCosh[a*x] + SinhIntegral[2*ArcCosh[a*x]]/(2*a^4) + SinhIntegral[4*ArcCosh[a*x]]/a^4","A",12,6,10,0.6000,1,"{5668, 5775, 5670, 5448, 3298, 12}"
60,1,85,0,0.5041094,"\int \frac{x^2}{\cosh ^{-1}(a x)^3} \, dx","Int[x^2/ArcCosh[a*x]^3,x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{8 a^3}+\frac{x}{a^2 \cosh ^{-1}(a x)}-\frac{3 x^3}{2 \cosh ^{-1}(a x)}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{8 a^3}+\frac{x}{a^2 \cosh ^{-1}(a x)}-\frac{3 x^3}{2 \cosh ^{-1}(a x)}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}",1,"-(x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*ArcCosh[a*x]^2) + x/(a^2*ArcCosh[a*x]) - (3*x^3)/(2*ArcCosh[a*x]) + SinhIntegral[ArcCosh[a*x]]/(8*a^3) + (9*SinhIntegral[3*ArcCosh[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{5668, 5775, 5670, 5448, 3298, 5658}"
61,1,68,0,0.3929866,"\int \frac{x}{\cosh ^{-1}(a x)^3} \, dx","Int[x/ArcCosh[a*x]^3,x]","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{a^2}+\frac{1}{2 a^2 \cosh ^{-1}(a x)}-\frac{x^2}{\cosh ^{-1}(a x)}-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{a^2}+\frac{1}{2 a^2 \cosh ^{-1}(a x)}-\frac{x^2}{\cosh ^{-1}(a x)}-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}",1,"-(x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*ArcCosh[a*x]^2) + 1/(2*a^2*ArcCosh[a*x]) - x^2/ArcCosh[a*x] + SinhIntegral[2*ArcCosh[a*x]]/a^2","A",7,7,8,0.8750,1,"{5668, 5775, 5670, 5448, 12, 3298, 5676}"
62,1,55,0,0.1878845,"\int \frac{1}{\cosh ^{-1}(a x)^3} \, dx","Int[ArcCosh[a*x]^(-3),x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{2 a}-\frac{x}{2 \cosh ^{-1}(a x)}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)}{2 a}-\frac{x}{2 \cosh ^{-1}(a x)}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)^2}",1,"-(Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*ArcCosh[a*x]^2) - x/(2*ArcCosh[a*x]) + SinhIntegral[ArcCosh[a*x]]/(2*a)","A",4,4,6,0.6667,1,"{5656, 5775, 5658, 3298}"
63,0,0,0,0.0136231,"\int \frac{1}{x \cosh ^{-1}(a x)^3} \, dx","Int[1/(x*ArcCosh[a*x]^3),x]","\int \frac{1}{x \cosh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]^3), x]","A",0,0,0,0,-1,"{}"
64,0,0,0,0.0149753,"\int \frac{1}{x^2 \cosh ^{-1}(a x)^3} \, dx","Int[1/(x^2*ArcCosh[a*x]^3),x]","\int \frac{1}{x^2 \cosh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x^2 \cosh ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(x^2*ArcCosh[a*x]^3), x]","A",0,0,0,0,-1,"{}"
65,1,170,0,0.6170293,"\int \frac{x^4}{\cosh ^{-1}(a x)^4} \, dx","Int[x^4/ArcCosh[a*x]^4,x]","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{48 a^5}+\frac{27 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{96 a^5}+\frac{2 x^3}{3 a^2 \cosh ^{-1}(a x)^2}+\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{a^3 \cosh ^{-1}(a x)}-\frac{5 x^5}{6 \cosh ^{-1}(a x)^2}-\frac{25 x^4 \sqrt{a x-1} \sqrt{a x+1}}{6 a \cosh ^{-1}(a x)}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{48 a^5}+\frac{27 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{96 a^5}+\frac{2 x^3}{3 a^2 \cosh ^{-1}(a x)^2}+\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{a^3 \cosh ^{-1}(a x)}-\frac{5 x^5}{6 \cosh ^{-1}(a x)^2}-\frac{25 x^4 \sqrt{a x-1} \sqrt{a x+1}}{6 a \cosh ^{-1}(a x)}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}",1,"-(x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^3) + (2*x^3)/(3*a^2*ArcCosh[a*x]^2) - (5*x^5)/(6*ArcCosh[a*x]^2) + (2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a^3*ArcCosh[a*x]) - (25*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(6*a*ArcCosh[a*x]) + CoshIntegral[ArcCosh[a*x]]/(48*a^5) + (27*CoshIntegral[3*ArcCosh[a*x]])/(32*a^5) + (125*CoshIntegral[5*ArcCosh[a*x]])/(96*a^5)","A",12,4,10,0.4000,1,"{5668, 5775, 5666, 3301}"
66,1,155,0,0.5875545,"\int \frac{x^3}{\cosh ^{-1}(a x)^4} \, dx","Int[x^3/ArcCosh[a*x]^4,x]","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{3 a^4}+\frac{x^2}{2 a^2 \cosh ^{-1}(a x)^2}+\frac{x \sqrt{a x-1} \sqrt{a x+1}}{a^3 \cosh ^{-1}(a x)}-\frac{2 x^4}{3 \cosh ^{-1}(a x)^2}-\frac{8 x^3 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{3 a^4}+\frac{x^2}{2 a^2 \cosh ^{-1}(a x)^2}+\frac{x \sqrt{a x-1} \sqrt{a x+1}}{a^3 \cosh ^{-1}(a x)}-\frac{2 x^4}{3 \cosh ^{-1}(a x)^2}-\frac{8 x^3 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}",1,"-(x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^3) + x^2/(2*a^2*ArcCosh[a*x]^2) - (2*x^4)/(3*ArcCosh[a*x]^2) + (x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a^3*ArcCosh[a*x]) - (8*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]) + CoshIntegral[2*ArcCosh[a*x]]/(3*a^4) + (4*CoshIntegral[4*ArcCosh[a*x]])/(3*a^4)","A",9,4,10,0.4000,1,"{5668, 5775, 5666, 3301}"
67,1,153,0,0.6757052,"\int \frac{x^2}{\cosh ^{-1}(a x)^4} \, dx","Int[x^2/ArcCosh[a*x]^4,x]","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{24 a^3}+\frac{9 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{8 a^3}+\frac{x}{3 a^2 \cosh ^{-1}(a x)^2}+\frac{\sqrt{a x-1} \sqrt{a x+1}}{3 a^3 \cosh ^{-1}(a x)}-\frac{x^3}{2 \cosh ^{-1}(a x)^2}-\frac{3 x^2 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{24 a^3}+\frac{9 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{8 a^3}+\frac{x}{3 a^2 \cosh ^{-1}(a x)^2}+\frac{\sqrt{a x-1} \sqrt{a x+1}}{3 a^3 \cosh ^{-1}(a x)}-\frac{x^3}{2 \cosh ^{-1}(a x)^2}-\frac{3 x^2 \sqrt{a x-1} \sqrt{a x+1}}{2 a \cosh ^{-1}(a x)}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}",1,"-(x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^3) + x/(3*a^2*ArcCosh[a*x]^2) - x^3/(2*ArcCosh[a*x]^2) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a^3*ArcCosh[a*x]) - (3*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*ArcCosh[a*x]) + CoshIntegral[ArcCosh[a*x]]/(24*a^3) + (9*CoshIntegral[3*ArcCosh[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{5668, 5775, 5666, 3301, 5656, 5781}"
68,1,105,0,0.3960245,"\int \frac{x}{\cosh ^{-1}(a x)^4} \, dx","Int[x/ArcCosh[a*x]^4,x]","\frac{2 \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{3 a^2}+\frac{1}{6 a^2 \cosh ^{-1}(a x)^2}-\frac{x^2}{3 \cosh ^{-1}(a x)^2}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)}-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}","\frac{2 \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{3 a^2}+\frac{1}{6 a^2 \cosh ^{-1}(a x)^2}-\frac{x^2}{3 \cosh ^{-1}(a x)^2}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)}-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}",1,"-(x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^3) + 1/(6*a^2*ArcCosh[a*x]^2) - x^2/(3*ArcCosh[a*x]^2) - (2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]) + (2*CoshIntegral[2*ArcCosh[a*x]])/(3*a^2)","A",5,5,8,0.6250,1,"{5668, 5775, 5666, 3301, 5676}"
69,1,86,0,0.3776857,"\int \frac{1}{\cosh ^{-1}(a x)^4} \, dx","Int[ArcCosh[a*x]^(-4),x]","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{6 a}-\frac{x}{6 \cosh ^{-1}(a x)^2}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{6 a \cosh ^{-1}(a x)}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}","\frac{\text{Chi}\left(\cosh ^{-1}(a x)\right)}{6 a}-\frac{x}{6 \cosh ^{-1}(a x)^2}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{6 a \cosh ^{-1}(a x)}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^3}",1,"-(Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^3) - x/(6*ArcCosh[a*x]^2) - (Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(6*a*ArcCosh[a*x]) + CoshIntegral[ArcCosh[a*x]]/(6*a)","A",5,4,6,0.6667,1,"{5656, 5775, 5781, 3301}"
70,0,0,0,0.0136799,"\int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx","Int[1/(x*ArcCosh[a*x]^4),x]","\int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)^4},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]^4), x]","A",0,0,0,0,-1,"{}"
71,0,0,0,0.014538,"\int \frac{1}{x^2 \cosh ^{-1}(a x)^4} \, dx","Int[1/(x^2*ArcCosh[a*x]^4),x]","\int \frac{1}{x^2 \cosh ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x^2 \cosh ^{-1}(a x)^4},x\right)",0,"Defer[Int][1/(x^2*ArcCosh[a*x]^4), x]","A",0,0,0,0,-1,"{}"
72,1,182,0,0.4753917,"\int x^4 \sqrt{\cosh ^{-1}(a x)} \, dx","Int[x^4*Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{320 a^5}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{320 a^5}+\frac{1}{5} x^5 \sqrt{\cosh ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{320 a^5}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{320 a^5}+\frac{1}{5} x^5 \sqrt{\cosh ^{-1}(a x)}",1,"(x^5*Sqrt[ArcCosh[a*x]])/5 - (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(32*a^5) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(64*a^5) - (Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(320*a^5) - (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(32*a^5) - (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(64*a^5) - (Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(320*a^5)","A",19,7,12,0.5833,1,"{5664, 5781, 3312, 3307, 2180, 2204, 2205}"
73,1,139,0,0.4030639,"\int x^3 \sqrt{\cosh ^{-1}(a x)} \, dx","Int[x^3*Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}-\frac{3 \sqrt{\cosh ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\cosh ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}-\frac{3 \sqrt{\cosh ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\cosh ^{-1}(a x)}",1,"(-3*Sqrt[ArcCosh[a*x]])/(32*a^4) + (x^4*Sqrt[ArcCosh[a*x]])/4 - (Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(256*a^4) - (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(32*a^4) - (Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(256*a^4) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(32*a^4)","A",14,7,12,0.5833,1,"{5664, 5781, 3312, 3307, 2180, 2204, 2205}"
74,1,120,0,0.3973885,"\int x^2 \sqrt{\cosh ^{-1}(a x)} \, dx","Int[x^2*Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{48 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{48 a^3}+\frac{1}{3} x^3 \sqrt{\cosh ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{48 a^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{48 a^3}+\frac{1}{3} x^3 \sqrt{\cosh ^{-1}(a x)}",1,"(x^3*Sqrt[ArcCosh[a*x]])/3 - (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(16*a^3) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(48*a^3) - (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(16*a^3) - (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(48*a^3)","A",14,7,12,0.5833,1,"{5664, 5781, 3312, 3307, 2180, 2204, 2205}"
75,1,93,0,0.3503462,"\int x \sqrt{\cosh ^{-1}(a x)} \, dx","Int[x*Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^2}-\frac{\sqrt{\cosh ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\cosh ^{-1}(a x)}","-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^2}-\frac{\sqrt{\cosh ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\cosh ^{-1}(a x)}",1,"-Sqrt[ArcCosh[a*x]]/(4*a^2) + (x^2*Sqrt[ArcCosh[a*x]])/2 - (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a^2) - (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a^2)","A",9,7,10,0.7000,1,"{5664, 5781, 3312, 3307, 2180, 2204, 2205}"
76,1,53,0,0.2188915,"\int \sqrt{\cosh ^{-1}(a x)} \, dx","Int[Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a}+x \sqrt{\cosh ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a}-\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a}+x \sqrt{\cosh ^{-1}(a x)}",1,"x*Sqrt[ArcCosh[a*x]] - (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(4*a) - (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(4*a)","A",7,6,8,0.7500,1,"{5654, 5781, 3307, 2180, 2204, 2205}"
77,0,0,0,0.0131443,"\int \frac{\sqrt{\cosh ^{-1}(a x)}}{x} \, dx","Int[Sqrt[ArcCosh[a*x]]/x,x]","\int \frac{\sqrt{\cosh ^{-1}(a x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{\cosh ^{-1}(a x)}}{x},x\right)",0,"Defer[Int][Sqrt[ArcCosh[a*x]]/x, x]","A",0,0,0,0,-1,"{}"
78,1,345,0,1.1148006,"\int x^4 \cosh ^{-1}(a x)^{3/2} \, dx","Int[x^4*ArcCosh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{200 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{200 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{25 a^3}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^{3/2}-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{50 a}","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{200 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^5}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{200 a^5}+\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{3200 a^5}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{25 a^3}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^{3/2}-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{50 a}",1,"(-4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(25*a^5) - (2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(25*a^3) - (3*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(50*a) + (x^5*ArcCosh[a*x]^(3/2))/5 - (3*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(64*a^5) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(200*a^5) - (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(3200*a^5) - (3*Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(3200*a^5) + (3*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(64*a^5) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(200*a^5) + (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(3200*a^5) + (3*Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(3200*a^5)","A",41,10,12,0.8333,1,"{5664, 5759, 5718, 5658, 3308, 2180, 2204, 2205, 5670, 5448}"
79,1,209,0,0.8742471,"\int x^3 \cosh ^{-1}(a x)^{3/2} \, dx","Int[x^3*ArcCosh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a^4}-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{128 a^4}+\frac{3 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a^4}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{128 a^4}-\frac{9 x \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{64 a^3}-\frac{3 \cosh ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^{3/2}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{32 a}","-\frac{3 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a^4}-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{128 a^4}+\frac{3 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a^4}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{128 a^4}-\frac{9 x \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{64 a^3}-\frac{3 \cosh ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^{3/2}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{32 a}",1,"(-9*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(64*a^3) - (3*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(32*a) - (3*ArcCosh[a*x]^(3/2))/(32*a^4) + (x^4*ArcCosh[a*x]^(3/2))/4 - (3*Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(2048*a^4) - (3*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(128*a^4) + (3*Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(2048*a^4) + (3*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(128*a^4)","A",25,10,12,0.8333,1,"{5664, 5759, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
80,1,189,0,0.6396368,"\int x^2 \cosh ^{-1}(a x)^{3/2} \, dx","Int[x^2*ArcCosh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{96 a^3}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{96 a^3}-\frac{\sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^{3/2}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{6 a}","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{96 a^3}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{32 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{96 a^3}-\frac{\sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^{3/2}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{6 a}",1,"-(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(3*a^3) - (x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(6*a) + (x^3*ArcCosh[a*x]^(3/2))/3 - (3*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(32*a^3) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(96*a^3) + (3*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(32*a^3) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(96*a^3)","A",22,10,12,0.8333,1,"{5664, 5759, 5718, 5658, 3308, 2180, 2204, 2205, 5670, 5448}"
81,1,127,0,0.4377225,"\int x \cosh ^{-1}(a x)^{3/2} \, dx","Int[x*ArcCosh[a*x]^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^2}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^2}-\frac{\cosh ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^{3/2}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{8 a}","-\frac{3 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^2}+\frac{3 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a^2}-\frac{\cosh ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^{3/2}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{8 a}",1,"(-3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(8*a) - ArcCosh[a*x]^(3/2)/(4*a^2) + (x^2*ArcCosh[a*x]^(3/2))/2 - (3*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a^2) + (3*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a^2)","A",11,10,10,1.000,1,"{5664, 5759, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
82,1,86,0,0.2204779,"\int \cosh ^{-1}(a x)^{3/2} \, dx","Int[ArcCosh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a}+x \cosh ^{-1}(a x)^{3/2}-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{2 a}","-\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a}+\frac{3 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a}+x \cosh ^{-1}(a x)^{3/2}-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{2 a}",1,"(-3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(2*a) + x*ArcCosh[a*x]^(3/2) - (3*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(8*a) + (3*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(8*a)","A",8,7,8,0.8750,1,"{5654, 5718, 5658, 3308, 2180, 2204, 2205}"
83,0,0,0,0.0132645,"\int \frac{\cosh ^{-1}(a x)^{3/2}}{x} \, dx","Int[ArcCosh[a*x]^(3/2)/x,x]","\int \frac{\cosh ^{-1}(a x)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\cosh ^{-1}(a x)^{3/2}}{x},x\right)",0,"Defer[Int][ArcCosh[a*x]^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
84,1,394,0,1.8219709,"\int x^4 \cosh ^{-1}(a x)^{5/2} \, dx","Int[x^4*ArcCosh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{128 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{1280 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{240 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{6400 a^5}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{128 a^5}-\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{1280 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{240 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{6400 a^5}+\frac{x^3 \sqrt{\cosh ^{-1}(a x)}}{15 a^2}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{15 a^3}+\frac{2 x \sqrt{\cosh ^{-1}(a x)}}{5 a^4}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{15 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^{5/2}+\frac{3}{100} x^5 \sqrt{\cosh ^{-1}(a x)}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{10 a}","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{128 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{1280 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{240 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{6400 a^5}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{128 a^5}-\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{1280 a^5}-\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{240 a^5}-\frac{3 \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{6400 a^5}+\frac{x^3 \sqrt{\cosh ^{-1}(a x)}}{15 a^2}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{15 a^3}+\frac{2 x \sqrt{\cosh ^{-1}(a x)}}{5 a^4}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{15 a^5}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^{5/2}+\frac{3}{100} x^5 \sqrt{\cosh ^{-1}(a x)}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{10 a}",1,"(2*x*Sqrt[ArcCosh[a*x]])/(5*a^4) + (x^3*Sqrt[ArcCosh[a*x]])/(15*a^2) + (3*x^5*Sqrt[ArcCosh[a*x]])/100 - (4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(15*a^5) - (2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(15*a^3) - (x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(10*a) + (x^5*ArcCosh[a*x]^(5/2))/5 - (15*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(128*a^5) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(240*a^5) - (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(1280*a^5) - (3*Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(6400*a^5) - (15*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(128*a^5) - (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(240*a^5) - (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(1280*a^5) - (3*Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(6400*a^5)","A",44,10,12,0.8333,1,"{5664, 5759, 5718, 5654, 5781, 3307, 2180, 2204, 2205, 3312}"
85,1,257,0,1.3752811,"\int x^3 \cosh ^{-1}(a x)^{5/2} \, dx","Int[x^3*ArcCosh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a^4}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{512 a^4}-\frac{15 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a^4}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{512 a^4}+\frac{45 x^2 \sqrt{\cosh ^{-1}(a x)}}{256 a^2}-\frac{15 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \cosh ^{-1}(a x)^{5/2}}{32 a^4}-\frac{225 \sqrt{\cosh ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^{5/2}+\frac{15}{256} x^4 \sqrt{\cosh ^{-1}(a x)}-\frac{5 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{32 a}","-\frac{15 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a^4}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{512 a^4}-\frac{15 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a^4}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{512 a^4}+\frac{45 x^2 \sqrt{\cosh ^{-1}(a x)}}{256 a^2}-\frac{15 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \cosh ^{-1}(a x)^{5/2}}{32 a^4}-\frac{225 \sqrt{\cosh ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \cosh ^{-1}(a x)^{5/2}+\frac{15}{256} x^4 \sqrt{\cosh ^{-1}(a x)}-\frac{5 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{32 a}",1,"(-225*Sqrt[ArcCosh[a*x]])/(2048*a^4) + (45*x^2*Sqrt[ArcCosh[a*x]])/(256*a^2) + (15*x^4*Sqrt[ArcCosh[a*x]])/256 - (15*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(64*a^3) - (5*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(32*a) - (3*ArcCosh[a*x]^(5/2))/(32*a^4) + (x^4*ArcCosh[a*x]^(5/2))/4 - (15*Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(16384*a^4) - (15*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(512*a^4) - (15*Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(16384*a^4) - (15*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(512*a^4)","A",27,9,12,0.7500,1,"{5664, 5759, 5676, 5781, 3312, 3307, 2180, 2204, 2205}"
86,1,220,0,1.054625,"\int x^2 \cosh ^{-1}(a x)^{5/2} \, dx","Int[x^2*ArcCosh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^3}-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{576 a^3}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^3}-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{576 a^3}+\frac{5 x \sqrt{\cosh ^{-1}(a x)}}{6 a^2}-\frac{5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{9 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^{5/2}+\frac{5}{36} x^3 \sqrt{\cosh ^{-1}(a x)}-\frac{5 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{18 a}","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^3}-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{576 a^3}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{64 a^3}-\frac{5 \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{576 a^3}+\frac{5 x \sqrt{\cosh ^{-1}(a x)}}{6 a^2}-\frac{5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{9 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^{5/2}+\frac{5}{36} x^3 \sqrt{\cosh ^{-1}(a x)}-\frac{5 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{18 a}",1,"(5*x*Sqrt[ArcCosh[a*x]])/(6*a^2) + (5*x^3*Sqrt[ArcCosh[a*x]])/36 - (5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(9*a^3) - (5*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(18*a) + (x^3*ArcCosh[a*x]^(5/2))/3 - (15*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(64*a^3) - (5*Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(576*a^3) - (15*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(64*a^3) - (5*Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(576*a^3)","A",24,10,12,0.8333,1,"{5664, 5759, 5718, 5654, 5781, 3307, 2180, 2204, 2205, 3312}"
87,1,157,0,0.7089327,"\int x \cosh ^{-1}(a x)^{5/2} \, dx","Int[x*ArcCosh[a*x]^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^2}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^2}-\frac{\cosh ^{-1}(a x)^{5/2}}{4 a^2}-\frac{15 \sqrt{\cosh ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^{5/2}+\frac{15}{32} x^2 \sqrt{\cosh ^{-1}(a x)}-\frac{5 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{8 a}","-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^2}-\frac{15 \sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a^2}-\frac{\cosh ^{-1}(a x)^{5/2}}{4 a^2}-\frac{15 \sqrt{\cosh ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \cosh ^{-1}(a x)^{5/2}+\frac{15}{32} x^2 \sqrt{\cosh ^{-1}(a x)}-\frac{5 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{8 a}",1,"(-15*Sqrt[ArcCosh[a*x]])/(64*a^2) + (15*x^2*Sqrt[ArcCosh[a*x]])/32 - (5*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(8*a) - ArcCosh[a*x]^(5/2)/(4*a^2) + (x^2*ArcCosh[a*x]^(5/2))/2 - (15*Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(256*a^2) - (15*Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(256*a^2)","A",12,9,10,0.9000,1,"{5664, 5759, 5676, 5781, 3312, 3307, 2180, 2204, 2205}"
88,1,99,0,0.3954652,"\int \cosh ^{-1}(a x)^{5/2} \, dx","Int[ArcCosh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a}+x \cosh ^{-1}(a x)^{5/2}-\frac{5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{2 a}+\frac{15}{4} x \sqrt{\cosh ^{-1}(a x)}","-\frac{15 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a}-\frac{15 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a}+x \cosh ^{-1}(a x)^{5/2}-\frac{5 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{2 a}+\frac{15}{4} x \sqrt{\cosh ^{-1}(a x)}",1,"(15*x*Sqrt[ArcCosh[a*x]])/4 - (5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(2*a) + x*ArcCosh[a*x]^(5/2) - (15*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(16*a) - (15*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(16*a)","A",9,7,8,0.8750,1,"{5654, 5718, 5781, 3307, 2180, 2204, 2205}"
89,0,0,0,0.0136085,"\int \frac{\cosh ^{-1}(a x)^{5/2}}{x} \, dx","Int[ArcCosh[a*x]^(5/2)/x,x]","\int \frac{\cosh ^{-1}(a x)^{5/2}}{x} \, dx","\text{Int}\left(\frac{\cosh ^{-1}(a x)^{5/2}}{x},x\right)",0,"Defer[Int][ArcCosh[a*x]^(5/2)/x, x]","A",0,0,0,0,-1,"{}"
90,1,163,0,0.1994408,"\int \frac{x^4}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[x^4/Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}-\frac{\sqrt{\frac{\pi }{5}} \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{\pi }{5}} \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^5}",1,"-(Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(16*a^5) - (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(32*a^5) - (Sqrt[Pi/5]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(32*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(16*a^5) + (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(32*a^5) + (Sqrt[Pi/5]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(32*a^5)","A",18,6,12,0.5000,1,"{5670, 5448, 3308, 2180, 2204, 2205}"
91,1,109,0,0.1460453,"\int \frac{x^3}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[x^3/Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^4}","-\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^4}",1,"-(Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(32*a^4) - (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(8*a^4) + (Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(32*a^4) + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(8*a^4)","A",13,6,12,0.5000,1,"{5670, 5448, 3308, 2180, 2204, 2205}"
92,1,105,0,0.1398085,"\int \frac{x^2}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[x^2/Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}-\frac{\sqrt{\frac{\pi }{3}} \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{3}} \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^3}",1,"-(Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(8*a^3) - (Sqrt[Pi/3]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(8*a^3) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(8*a^3) + (Sqrt[Pi/3]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(8*a^3)","A",13,6,12,0.5000,1,"{5670, 5448, 3308, 2180, 2204, 2205}"
93,1,63,0,0.0772482,"\int \frac{x}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[x/Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^2}","\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^2}-\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^2}",1,"-(Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(4*a^2) + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(4*a^2)","A",8,7,10,0.7000,1,"{5670, 5448, 12, 3308, 2180, 2204, 2205}"
94,1,43,0,0.0466218,"\int \frac{1}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[1/Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{2 a}-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{2 a}","\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{2 a}-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{2 a}",1,"-(Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(2*a) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(2*a)","A",6,5,8,0.6250,1,"{5658, 3308, 2180, 2204, 2205}"
95,0,0,0,0.0142105,"\int \frac{1}{x \sqrt{\cosh ^{-1}(a x)}} \, dx","Int[1/(x*Sqrt[ArcCosh[a*x]]),x]","\int \frac{1}{x \sqrt{\cosh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{\cosh ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[ArcCosh[a*x]]), x]","A",0,0,0,0,-1,"{}"
96,0,0,0,0.0136833,"\int \frac{1}{x^2 \sqrt{\cosh ^{-1}(a x)}} \, dx","Int[1/(x^2*Sqrt[ArcCosh[a*x]]),x]","\int \frac{1}{x^2 \sqrt{\cosh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{\cosh ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x^2*Sqrt[ArcCosh[a*x]]), x]","A",0,0,0,0,-1,"{}"
97,1,193,0,0.1842384,"\int \frac{x^4}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[x^4/ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}+\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}+\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}+\frac{\sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a^5}-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(-2*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(8*a^5) + (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(16*a^5) + (Sqrt[5*Pi]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(16*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(8*a^5) + (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(16*a^5) + (Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(16*a^5)","A",17,5,12,0.4167,1,"{5666, 3307, 2180, 2204, 2205}"
98,1,143,0,0.1282207,"\int \frac{x^3}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[x^3/ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^4}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^4}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^4}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(-2*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(4*a^4) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(2*a^4) + (Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(4*a^4) + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(2*a^4)","A",12,5,12,0.4167,1,"{5666, 3307, 2180, 2204, 2205}"
99,1,135,0,0.1241453,"\int \frac{x^2}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[x^2/ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a^3}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(-2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(4*a^3) + (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(4*a^3) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(4*a^3) + (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(4*a^3)","A",12,5,12,0.4167,1,"{5666, 3307, 2180, 2204, 2205}"
100,1,89,0,0.0658254,"\int \frac{x}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[x/ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a^2}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a^2}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}","\frac{\sqrt{\frac{\pi }{2}} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a^2}+\frac{\sqrt{\frac{\pi }{2}} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a^2}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(-2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi/2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/a^2 + (Sqrt[Pi/2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/a^2","A",6,5,10,0.5000,1,"{5666, 3307, 2180, 2204, 2205}"
101,1,68,0,0.217745,"\int \frac{1}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[ArcCosh[a*x]^(-3/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{a}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{a}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{a}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{a}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/a + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/a","A",7,6,8,0.7500,1,"{5656, 5781, 3307, 2180, 2204, 2205}"
102,0,0,0,0.0136584,"\int \frac{1}{x \cosh ^{-1}(a x)^{3/2}} \, dx","Int[1/(x*ArcCosh[a*x]^(3/2)),x]","\int \frac{1}{x \cosh ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]^(3/2)), x]","A",0,0,0,0,-1,"{}"
103,1,228,0,0.8641051,"\int \frac{x^4}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[x^4/ArcCosh[a*x]^(5/2),x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}-\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{24 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{24 a^5}+\frac{16 x^3}{3 a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{20 x^5}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}-\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}-\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{24 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{8 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{24 a^5}+\frac{16 x^3}{3 a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{20 x^5}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}",1,"(-2*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^(3/2)) + (16*x^3)/(3*a^2*Sqrt[ArcCosh[a*x]]) - (20*x^5)/(3*Sqrt[ArcCosh[a*x]]) - (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(12*a^5) - (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(8*a^5) - (5*Sqrt[5*Pi]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(24*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(12*a^5) + (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(8*a^5) + (5*Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(24*a^5)","A",34,8,12,0.6667,1,"{5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205}"
104,1,172,0,0.7552359,"\int \frac{x^3}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[x^3/ArcCosh[a*x]^(5/2),x]","-\frac{2 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}-\frac{\sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}+\frac{2 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}+\frac{\sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}+\frac{4 x^2}{a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{16 x^4}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}-\frac{\sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}+\frac{2 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}+\frac{\sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^4}+\frac{4 x^2}{a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{16 x^4}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}",1,"(-2*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^(3/2)) + (4*x^2)/(a^2*Sqrt[ArcCosh[a*x]]) - (16*x^4)/(3*Sqrt[ArcCosh[a*x]]) - (2*Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(3*a^4) - (Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a^4) + (2*Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(3*a^4) + (Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a^4)","A",24,9,12,0.7500,1,"{5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205, 12}"
105,1,166,0,0.6269356,"\int \frac{x^2}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[x^2/ArcCosh[a*x]^(5/2),x]","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{6 a^3}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{6 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^3}+\frac{8 x}{3 a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{4 x^3}{\sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}","-\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{6 a^3}-\frac{\sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{6 a^3}+\frac{\sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{2 a^3}+\frac{8 x}{3 a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{4 x^3}{\sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}",1,"(-2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^(3/2)) + (8*x)/(3*a^2*Sqrt[ArcCosh[a*x]]) - (4*x^3)/Sqrt[ArcCosh[a*x]] - (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(6*a^3) - (Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(2*a^3) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(6*a^3) + (Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(2*a^3)","A",22,9,12,0.7500,1,"{5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205, 5658}"
106,1,123,0,0.4827759,"\int \frac{x}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[x/ArcCosh[a*x]^(5/2),x]","-\frac{2 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^2}+\frac{2 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^2}+\frac{4}{3 a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{8 x^2}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^2}+\frac{2 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a^2}+\frac{4}{3 a^2 \sqrt{\cosh ^{-1}(a x)}}-\frac{8 x^2}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}",1,"(-2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^(3/2)) + 4/(3*a^2*Sqrt[ArcCosh[a*x]]) - (8*x^2)/(3*Sqrt[ArcCosh[a*x]]) - (2*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a^2) + (2*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a^2)","A",11,10,10,1.000,1,"{5668, 5775, 5670, 5448, 12, 3308, 2180, 2204, 2205, 5676}"
107,1,89,0,0.2341494,"\int \frac{1}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[ArcCosh[a*x]^(-5/2),x]","-\frac{2 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{3 a}+\frac{2 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{3 a}-\frac{4 x}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{3 a}+\frac{2 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{3 a}-\frac{4 x}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \cosh ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*ArcCosh[a*x]^(3/2)) - (4*x)/(3*Sqrt[ArcCosh[a*x]]) - (2*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(3*a) + (2*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(3*a)","A",8,7,8,0.8750,1,"{5656, 5775, 5658, 3308, 2180, 2204, 2205}"
108,0,0,0,0.0148498,"\int \frac{1}{x \cosh ^{-1}(a x)^{5/2}} \, dx","Int[1/(x*ArcCosh[a*x]^(5/2)),x]","\int \frac{1}{x \cosh ^{-1}(a x)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)^{5/2}},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]^(5/2)), x]","A",0,0,0,0,-1,"{}"
109,1,300,0,0.9319542,"\int \frac{x^4}{\cosh ^{-1}(a x)^{7/2}} \, dx","Int[x^4/ArcCosh[a*x]^(7/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{30 a^5}+\frac{9 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{20 a^5}+\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{30 a^5}+\frac{9 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{20 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}+\frac{16 x^3}{15 a^2 \cosh ^{-1}(a x)^{3/2}}+\frac{32 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a^3 \sqrt{\cosh ^{-1}(a x)}}-\frac{4 x^5}{3 \cosh ^{-1}(a x)^{3/2}}-\frac{40 x^4 \sqrt{a x-1} \sqrt{a x+1}}{3 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{30 a^5}+\frac{9 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{20 a^5}+\frac{5 \sqrt{5 \pi } \text{Erf}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{30 a^5}+\frac{9 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{20 a^5}+\frac{5 \sqrt{5 \pi } \text{Erfi}\left(\sqrt{5} \sqrt{\cosh ^{-1}(a x)}\right)}{12 a^5}+\frac{16 x^3}{15 a^2 \cosh ^{-1}(a x)^{3/2}}+\frac{32 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a^3 \sqrt{\cosh ^{-1}(a x)}}-\frac{4 x^5}{3 \cosh ^{-1}(a x)^{3/2}}-\frac{40 x^4 \sqrt{a x-1} \sqrt{a x+1}}{3 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^4 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}",1,"(-2*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a*ArcCosh[a*x]^(5/2)) + (16*x^3)/(15*a^2*ArcCosh[a*x]^(3/2)) - (4*x^5)/(3*ArcCosh[a*x]^(3/2)) + (32*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a^3*Sqrt[ArcCosh[a*x]]) - (40*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(30*a^5) + (9*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(20*a^5) + (5*Sqrt[5*Pi]*Erf[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(12*a^5) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(30*a^5) + (9*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(20*a^5) + (5*Sqrt[5*Pi]*Erfi[Sqrt[5]*Sqrt[ArcCosh[a*x]]])/(12*a^5)","A",32,7,12,0.5833,1,"{5668, 5775, 5666, 3307, 2180, 2204, 2205}"
110,1,244,0,0.7569447,"\int \frac{x^3}{\cosh ^{-1}(a x)^{7/2}} \, dx","Int[x^3/ArcCosh[a*x]^(7/2),x]","\frac{16 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{4 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{16 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{4 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{4 x^2}{5 a^2 \cosh ^{-1}(a x)^{3/2}}+\frac{16 x \sqrt{a x-1} \sqrt{a x+1}}{5 a^3 \sqrt{\cosh ^{-1}(a x)}}-\frac{16 x^4}{15 \cosh ^{-1}(a x)^{3/2}}-\frac{128 x^3 \sqrt{a x-1} \sqrt{a x+1}}{15 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}","\frac{16 \sqrt{\pi } \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{4 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{16 \sqrt{\pi } \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{4 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^4}+\frac{4 x^2}{5 a^2 \cosh ^{-1}(a x)^{3/2}}+\frac{16 x \sqrt{a x-1} \sqrt{a x+1}}{5 a^3 \sqrt{\cosh ^{-1}(a x)}}-\frac{16 x^4}{15 \cosh ^{-1}(a x)^{3/2}}-\frac{128 x^3 \sqrt{a x-1} \sqrt{a x+1}}{15 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}",1,"(-2*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a*ArcCosh[a*x]^(5/2)) + (4*x^2)/(5*a^2*ArcCosh[a*x]^(3/2)) - (16*x^4)/(15*ArcCosh[a*x]^(3/2)) + (16*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a^3*Sqrt[ArcCosh[a*x]]) - (128*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(15*a*Sqrt[ArcCosh[a*x]]) + (16*Sqrt[Pi]*Erf[2*Sqrt[ArcCosh[a*x]]])/(15*a^4) + (4*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(15*a^4) + (16*Sqrt[Pi]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(15*a^4) + (4*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(15*a^4)","A",21,7,12,0.5833,1,"{5668, 5775, 5666, 3307, 2180, 2204, 2205}"
111,1,237,0,0.847696,"\int \frac{x^2}{\cosh ^{-1}(a x)^{7/2}} \, dx","Int[x^2/ArcCosh[a*x]^(7/2),x]","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a^3}+\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{5 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a^3}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{5 a^3}+\frac{8 x}{15 a^2 \cosh ^{-1}(a x)^{3/2}}+\frac{16 \sqrt{a x-1} \sqrt{a x+1}}{15 a^3 \sqrt{\cosh ^{-1}(a x)}}-\frac{4 x^3}{5 \cosh ^{-1}(a x)^{3/2}}-\frac{24 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}","\frac{\sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a^3}+\frac{3 \sqrt{3 \pi } \text{Erf}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{5 a^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a^3}+\frac{3 \sqrt{3 \pi } \text{Erfi}\left(\sqrt{3} \sqrt{\cosh ^{-1}(a x)}\right)}{5 a^3}+\frac{8 x}{15 a^2 \cosh ^{-1}(a x)^{3/2}}+\frac{16 \sqrt{a x-1} \sqrt{a x+1}}{15 a^3 \sqrt{\cosh ^{-1}(a x)}}-\frac{4 x^3}{5 \cosh ^{-1}(a x)^{3/2}}-\frac{24 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}",1,"(-2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a*ArcCosh[a*x]^(5/2)) + (8*x)/(15*a^2*ArcCosh[a*x]^(3/2)) - (4*x^3)/(5*ArcCosh[a*x]^(3/2)) + (16*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(15*a^3*Sqrt[ArcCosh[a*x]]) - (24*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a*Sqrt[ArcCosh[a*x]]) + (Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(15*a^3) + (3*Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(5*a^3) + (Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(15*a^3) + (3*Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[ArcCosh[a*x]]])/(5*a^3)","A",22,9,12,0.7500,1,"{5668, 5775, 5666, 3307, 2180, 2204, 2205, 5656, 5781}"
112,1,157,0,0.4954346,"\int \frac{x}{\cosh ^{-1}(a x)^{7/2}} \, dx","Int[x/ArcCosh[a*x]^(7/2),x]","\frac{8 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^2}+\frac{8 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^2}+\frac{4}{15 a^2 \cosh ^{-1}(a x)^{3/2}}-\frac{8 x^2}{15 \cosh ^{-1}(a x)^{3/2}}-\frac{32 x \sqrt{a x-1} \sqrt{a x+1}}{15 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}","\frac{8 \sqrt{2 \pi } \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^2}+\frac{8 \sqrt{2 \pi } \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{15 a^2}+\frac{4}{15 a^2 \cosh ^{-1}(a x)^{3/2}}-\frac{8 x^2}{15 \cosh ^{-1}(a x)^{3/2}}-\frac{32 x \sqrt{a x-1} \sqrt{a x+1}}{15 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}",1,"(-2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a*ArcCosh[a*x]^(5/2)) + 4/(15*a^2*ArcCosh[a*x]^(3/2)) - (8*x^2)/(15*ArcCosh[a*x]^(3/2)) - (32*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(15*a*Sqrt[ArcCosh[a*x]]) + (8*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(15*a^2) + (8*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(15*a^2)","A",9,8,10,0.8000,1,"{5668, 5775, 5666, 3307, 2180, 2204, 2205, 5676}"
113,1,122,0,0.4435519,"\int \frac{1}{\cosh ^{-1}(a x)^{7/2}} \, dx","Int[ArcCosh[a*x]^(-7/2),x]","\frac{4 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a}+\frac{4 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a}-\frac{4 x}{15 \cosh ^{-1}(a x)^{3/2}}-\frac{8 \sqrt{a x-1} \sqrt{a x+1}}{15 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}","\frac{4 \sqrt{\pi } \text{Erf}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a}+\frac{4 \sqrt{\pi } \text{Erfi}\left(\sqrt{\cosh ^{-1}(a x)}\right)}{15 a}-\frac{4 x}{15 \cosh ^{-1}(a x)^{3/2}}-\frac{8 \sqrt{a x-1} \sqrt{a x+1}}{15 a \sqrt{\cosh ^{-1}(a x)}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{5 a \cosh ^{-1}(a x)^{5/2}}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(5*a*ArcCosh[a*x]^(5/2)) - (4*x)/(15*ArcCosh[a*x]^(3/2)) - (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(15*a*Sqrt[ArcCosh[a*x]]) + (4*Sqrt[Pi]*Erf[Sqrt[ArcCosh[a*x]]])/(15*a) + (4*Sqrt[Pi]*Erfi[Sqrt[ArcCosh[a*x]]])/(15*a)","A",9,7,8,0.8750,1,"{5656, 5775, 5781, 3307, 2180, 2204, 2205}"
114,0,0,0,0.0166465,"\int \frac{1}{x \cosh ^{-1}(a x)^{7/2}} \, dx","Int[1/(x*ArcCosh[a*x]^(7/2)),x]","\int \frac{1}{x \cosh ^{-1}(a x)^{7/2}} \, dx","\text{Int}\left(\frac{1}{x \cosh ^{-1}(a x)^{7/2}},x\right)",0,"Defer[Int][1/(x*ArcCosh[a*x]^(7/2)), x]","A",0,0,0,0,-1,"{}"
115,0,0,0,0.2774286,"\int x^m \cosh ^{-1}(a x)^4 \, dx","Int[x^m*ArcCosh[a*x]^4,x]","\int x^m \cosh ^{-1}(a x)^4 \, dx","\frac{x^{m+1} \cosh ^{-1}(a x)^4}{m+1}-\frac{4 a \text{Int}\left(\frac{x^{m+1} \cosh ^{-1}(a x)^3}{\sqrt{a x-1} \sqrt{a x+1}},x\right)}{m+1}",0,"(x^(1 + m)*ArcCosh[a*x]^4)/(1 + m) - (4*a*Defer[Int][(x^(1 + m)*ArcCosh[a*x]^3)/(Sqrt[-1 + a*x]*Sqrt[1 + a*x]), x])/(1 + m)","A",0,0,0,0,-1,"{}"
116,0,0,0,0.2980189,"\int x^m \cosh ^{-1}(a x)^3 \, dx","Int[x^m*ArcCosh[a*x]^3,x]","\int x^m \cosh ^{-1}(a x)^3 \, dx","\frac{x^{m+1} \cosh ^{-1}(a x)^3}{m+1}-\frac{3 a \text{Int}\left(\frac{x^{m+1} \cosh ^{-1}(a x)^2}{\sqrt{a x-1} \sqrt{a x+1}},x\right)}{m+1}",0,"(x^(1 + m)*ArcCosh[a*x]^3)/(1 + m) - (3*a*Defer[Int][(x^(1 + m)*ArcCosh[a*x]^2)/(Sqrt[-1 + a*x]*Sqrt[1 + a*x]), x])/(1 + m)","A",0,0,0,0,-1,"{}"
117,1,167,0,0.2381263,"\int x^m \cosh ^{-1}(a x)^2 \, dx","Int[x^m*ArcCosh[a*x]^2,x]","-\frac{2 a^2 x^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};a^2 x^2\right)}{m^3+6 m^2+11 m+6}-\frac{2 a \sqrt{1-a^2 x^2} x^{m+2} \cosh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{\left(m^2+3 m+2\right) \sqrt{a x-1} \sqrt{a x+1}}+\frac{x^{m+1} \cosh ^{-1}(a x)^2}{m+1}","-\frac{2 a^2 x^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};a^2 x^2\right)}{m^3+6 m^2+11 m+6}-\frac{2 a \sqrt{1-a x} x^{m+2} \cosh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{\left(m^2+3 m+2\right) \sqrt{a x-1}}+\frac{x^{m+1} \cosh ^{-1}(a x)^2}{m+1}",1,"(x^(1 + m)*ArcCosh[a*x]^2)/(1 + m) - (2*a*x^(2 + m)*Sqrt[1 - a^2*x^2]*ArcCosh[a*x]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + 3*m + m^2)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (2*a^2*x^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, a^2*x^2])/(6 + 11*m + 6*m^2 + m^3)","A",2,2,10,0.2000,1,"{5662, 5763}"
118,1,91,0,0.054826,"\int x^m \cosh ^{-1}(a x) \, dx","Int[x^m*ArcCosh[a*x],x]","\frac{x^{m+1} \cosh ^{-1}(a x)}{m+1}-\frac{a \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{\left(m^2+3 m+2\right) \sqrt{a x-1} \sqrt{a x+1}}","\frac{x^{m+1} \cosh ^{-1}(a x)}{m+1}-\frac{a \sqrt{1-a^2 x^2} x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{\left(m^2+3 m+2\right) \sqrt{a x-1} \sqrt{a x+1}}",1,"(x^(1 + m)*ArcCosh[a*x])/(1 + m) - (a*x^(2 + m)*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + 3*m + m^2)*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",4,4,8,0.5000,1,"{5662, 126, 365, 364}"
119,0,0,0,0.0229181,"\int \frac{x^m}{\cosh ^{-1}(a x)} \, dx","Int[x^m/ArcCosh[a*x],x]","\int \frac{x^m}{\cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x^m}{\cosh ^{-1}(a x)},x\right)",0,"Defer[Int][x^m/ArcCosh[a*x], x]","A",0,0,0,0,-1,"{}"
120,0,0,0,0.0229005,"\int \frac{x^m}{\cosh ^{-1}(a x)^2} \, dx","Int[x^m/ArcCosh[a*x]^2,x]","\int \frac{x^m}{\cosh ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x^m}{\cosh ^{-1}(a x)^2},x\right)",0,"Defer[Int][x^m/ArcCosh[a*x]^2, x]","A",0,0,0,0,-1,"{}"
121,0,0,0,0.0196945,"\int \frac{x^m}{\cosh ^{-1}(a x)^3} \, dx","Int[x^m/ArcCosh[a*x]^3,x]","\int \frac{x^m}{\cosh ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{x^m}{\cosh ^{-1}(a x)^3},x\right)",0,"Defer[Int][x^m/ArcCosh[a*x]^3, x]","A",0,0,0,0,-1,"{}"
122,0,0,0,0.0194091,"\int x^m \cosh ^{-1}(a x)^{3/2} \, dx","Int[x^m*ArcCosh[a*x]^(3/2),x]","\int x^m \cosh ^{-1}(a x)^{3/2} \, dx","\text{Int}\left(x^m \cosh ^{-1}(a x)^{3/2},x\right)",0,"Defer[Int][x^m*ArcCosh[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
123,0,0,0,0.0156938,"\int x^m \sqrt{\cosh ^{-1}(a x)} \, dx","Int[x^m*Sqrt[ArcCosh[a*x]],x]","\int x^m \sqrt{\cosh ^{-1}(a x)} \, dx","\text{Int}\left(x^m \sqrt{\cosh ^{-1}(a x)},x\right)",0,"Defer[Int][x^m*Sqrt[ArcCosh[a*x]], x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.0162995,"\int \frac{x^m}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[x^m/Sqrt[ArcCosh[a*x]],x]","\int \frac{x^m}{\sqrt{\cosh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{x^m}{\sqrt{\cosh ^{-1}(a x)}},x\right)",0,"Defer[Int][x^m/Sqrt[ArcCosh[a*x]], x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.0164417,"\int \frac{x^m}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[x^m/ArcCosh[a*x]^(3/2),x]","\int \frac{x^m}{\cosh ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{x^m}{\cosh ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][x^m/ArcCosh[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
126,0,0,0,0.0192157,"\int (d x)^m \cosh ^{-1}(a x)^n \, dx","Int[(d*x)^m*ArcCosh[a*x]^n,x]","\int (d x)^m \cosh ^{-1}(a x)^n \, dx","\text{Int}\left((d x)^m \cosh ^{-1}(a x)^n,x\right)",0,"Defer[Int][(d*x)^m*ArcCosh[a*x]^n, x]","A",0,0,0,0,-1,"{}"
127,1,173,0,0.2472974,"\int x^4 \cosh ^{-1}(a x)^n \, dx","Int[x^4*ArcCosh[a*x]^n,x]","\frac{5^{-n-1} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-5 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{3^{-n} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Gamma}\left(n+1,\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{3^{-n} \text{Gamma}\left(n+1,3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{5^{-n-1} \text{Gamma}\left(n+1,5 \cosh ^{-1}(a x)\right)}{32 a^5}","\frac{5^{-n-1} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-5 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{3^{-n} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{\text{Gamma}\left(n+1,\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{3^{-n} \text{Gamma}\left(n+1,3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{5^{-n-1} \text{Gamma}\left(n+1,5 \cosh ^{-1}(a x)\right)}{32 a^5}",1,"(5^(-1 - n)*ArcCosh[a*x]^n*Gamma[1 + n, -5*ArcCosh[a*x]])/(32*a^5*(-ArcCosh[a*x])^n) + (ArcCosh[a*x]^n*Gamma[1 + n, -3*ArcCosh[a*x]])/(32*3^n*a^5*(-ArcCosh[a*x])^n) + (ArcCosh[a*x]^n*Gamma[1 + n, -ArcCosh[a*x]])/(16*a^5*(-ArcCosh[a*x])^n) + Gamma[1 + n, ArcCosh[a*x]]/(16*a^5) + Gamma[1 + n, 3*ArcCosh[a*x]]/(32*3^n*a^5) + (5^(-1 - n)*Gamma[1 + n, 5*ArcCosh[a*x]])/(32*a^5)","A",12,4,10,0.4000,1,"{5670, 5448, 3308, 2181}"
128,1,117,0,0.19092,"\int x^3 \cosh ^{-1}(a x)^n \, dx","Int[x^3*ArcCosh[a*x]^n,x]","\frac{2^{-2 (n+3)} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-4 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \text{Gamma}\left(n+1,2 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \text{Gamma}\left(n+1,4 \cosh ^{-1}(a x)\right)}{a^4}","\frac{2^{-2 (n+3)} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-4 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \text{Gamma}\left(n+1,2 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \text{Gamma}\left(n+1,4 \cosh ^{-1}(a x)\right)}{a^4}",1,"(ArcCosh[a*x]^n*Gamma[1 + n, -4*ArcCosh[a*x]])/(2^(2*(3 + n))*a^4*(-ArcCosh[a*x])^n) + (2^(-4 - n)*ArcCosh[a*x]^n*Gamma[1 + n, -2*ArcCosh[a*x]])/(a^4*(-ArcCosh[a*x])^n) + (2^(-4 - n)*Gamma[1 + n, 2*ArcCosh[a*x]])/a^4 + Gamma[1 + n, 4*ArcCosh[a*x]]/(2^(2*(3 + n))*a^4)","A",9,4,10,0.4000,1,"{5670, 5448, 3308, 2181}"
129,1,113,0,0.1821607,"\int x^2 \cosh ^{-1}(a x)^n \, dx","Int[x^2*ArcCosh[a*x]^n,x]","\frac{3^{-n-1} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \cosh ^{-1}(a x)\right)}{8 a^3}+\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{\text{Gamma}\left(n+1,\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \text{Gamma}\left(n+1,3 \cosh ^{-1}(a x)\right)}{8 a^3}","\frac{3^{-n-1} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \cosh ^{-1}(a x)\right)}{8 a^3}+\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{\text{Gamma}\left(n+1,\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \text{Gamma}\left(n+1,3 \cosh ^{-1}(a x)\right)}{8 a^3}",1,"(3^(-1 - n)*ArcCosh[a*x]^n*Gamma[1 + n, -3*ArcCosh[a*x]])/(8*a^3*(-ArcCosh[a*x])^n) + (ArcCosh[a*x]^n*Gamma[1 + n, -ArcCosh[a*x]])/(8*a^3*(-ArcCosh[a*x])^n) + Gamma[1 + n, ArcCosh[a*x]]/(8*a^3) + (3^(-1 - n)*Gamma[1 + n, 3*ArcCosh[a*x]])/(8*a^3)","A",9,4,10,0.4000,1,"{5670, 5448, 3308, 2181}"
130,1,59,0,0.087337,"\int x \cosh ^{-1}(a x)^n \, dx","Int[x*ArcCosh[a*x]^n,x]","\frac{2^{-n-3} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \cosh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \text{Gamma}\left(n+1,2 \cosh ^{-1}(a x)\right)}{a^2}","\frac{2^{-n-3} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \cosh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \text{Gamma}\left(n+1,2 \cosh ^{-1}(a x)\right)}{a^2}",1,"(2^(-3 - n)*ArcCosh[a*x]^n*Gamma[1 + n, -2*ArcCosh[a*x]])/(a^2*(-ArcCosh[a*x])^n) + (2^(-3 - n)*Gamma[1 + n, 2*ArcCosh[a*x]])/a^2","A",6,5,8,0.6250,1,"{5670, 5448, 12, 3308, 2181}"
131,1,49,0,0.0492336,"\int \cosh ^{-1}(a x)^n \, dx","Int[ArcCosh[a*x]^n,x]","\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\cosh ^{-1}(a x)\right)}{2 a}+\frac{\text{Gamma}\left(n+1,\cosh ^{-1}(a x)\right)}{2 a}","\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\cosh ^{-1}(a x)\right)}{2 a}+\frac{\text{Gamma}\left(n+1,\cosh ^{-1}(a x)\right)}{2 a}",1,"(ArcCosh[a*x]^n*Gamma[1 + n, -ArcCosh[a*x]])/(2*a*(-ArcCosh[a*x])^n) + Gamma[1 + n, ArcCosh[a*x]]/(2*a)","A",4,3,6,0.5000,1,"{5658, 3308, 2181}"
132,0,0,0,0.017206,"\int \frac{\cosh ^{-1}(a x)^n}{x} \, dx","Int[ArcCosh[a*x]^n/x,x]","\int \frac{\cosh ^{-1}(a x)^n}{x} \, dx","\text{Int}\left(\frac{\cosh ^{-1}(a x)^n}{x},x\right)",0,"Defer[Int][ArcCosh[a*x]^n/x, x]","A",0,0,0,0,-1,"{}"
133,1,84,0,0.0390041,"\int x^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcCosh[c*x]),x]","\frac{1}{4} x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 b x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}-\frac{3 b \cosh ^{-1}(c x)}{32 c^4}-\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}","\frac{1}{4} x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 b x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}-\frac{3 b \cosh ^{-1}(c x)}{32 c^4}-\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}",1,"(-3*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(32*c^3) - (b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c) - (3*b*ArcCosh[c*x])/(32*c^4) + (x^4*(a + b*ArcCosh[c*x]))/4","A",5,5,12,0.4167,1,"{5662, 100, 12, 90, 52}"
134,1,71,0,0.0295427,"\int x^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{3} x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 b \sqrt{c x-1} \sqrt{c x+1}}{9 c^3}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c}","\frac{1}{3} x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 b \sqrt{c x-1} \sqrt{c x+1}}{9 c^3}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c}",1,"(-2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^3) - (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c) + (x^3*(a + b*ArcCosh[c*x]))/3","A",4,4,12,0.3333,1,"{5662, 100, 12, 74}"
135,1,55,0,0.0197901,"\int x \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcCosh[c*x]),x]","\frac{1}{2} x^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b \cosh ^{-1}(c x)}{4 c^2}-\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{4 c}","\frac{1}{2} x^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b \cosh ^{-1}(c x)}{4 c^2}-\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"-(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) - (b*ArcCosh[c*x])/(4*c^2) + (x^2*(a + b*ArcCosh[c*x]))/2","A",3,3,10,0.3000,1,"{5662, 90, 52}"
136,1,35,0,0.0143607,"\int \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[a + b*ArcCosh[c*x],x]","a x-\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c}+b x \cosh ^{-1}(c x)","a x-\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c}+b x \cosh ^{-1}(c x)",1,"a*x - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/c + b*x*ArcCosh[c*x]","A",3,2,8,0.2500,1,"{5654, 74}"
137,1,55,0,0.0766328,"\int \frac{a+b \cosh ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcCosh[c*x])/x,x]","\frac{1}{2} b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+\log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)","-\frac{1}{2} b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+\log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)",1,"-(a + b*ArcCosh[c*x])^2/(2*b) + (a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/2","A",5,5,12,0.4167,0,"{5660, 3718, 2190, 2279, 2391}"
138,1,37,0,0.0239983,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcCosh[c*x])/x^2,x]","b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)-\frac{a+b \cosh ^{-1}(c x)}{x}","b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)-\frac{a+b \cosh ^{-1}(c x)}{x}",1,"-((a + b*ArcCosh[c*x])/x) + b*c*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]]","A",3,3,12,0.2500,1,"{5662, 92, 205}"
139,1,43,0,0.0200365,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcCosh[c*x])/x^3,x]","\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 x}-\frac{a+b \cosh ^{-1}(c x)}{2 x^2}","\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 x}-\frac{a+b \cosh ^{-1}(c x)}{2 x^2}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x) - (a + b*ArcCosh[c*x])/(2*x^2)","A",2,2,12,0.1667,1,"{5662, 95}"
140,1,71,0,0.0334076,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcCosh[c*x])/x^4,x]","-\frac{a+b \cosh ^{-1}(c x)}{3 x^3}+\frac{1}{6} b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}","-\frac{a+b \cosh ^{-1}(c x)}{3 x^3}+\frac{1}{6} b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*x^2) - (a + b*ArcCosh[c*x])/(3*x^3) + (b*c^3*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/6","A",5,5,12,0.4167,1,"{5662, 103, 12, 92, 205}"
141,1,72,0,0.0322867,"\int \frac{a+b \cosh ^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcCosh[c*x])/x^5,x]","-\frac{a+b \cosh ^{-1}(c x)}{4 x^4}+\frac{b c^3 \sqrt{c x-1} \sqrt{c x+1}}{6 x}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{12 x^3}","-\frac{a+b \cosh ^{-1}(c x)}{4 x^4}+\frac{b c^3 \sqrt{c x-1} \sqrt{c x+1}}{6 x}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{12 x^3}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(12*x^3) + (b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*x) - (a + b*ArcCosh[c*x])/(4*x^4)","A",4,4,12,0.3333,1,"{5662, 103, 12, 95}"
142,1,213,0,0.7882498,"\int x^2 \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Int[x^2*Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}+\frac{1}{3} x^3 \sqrt{a+b \cosh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}+\frac{1}{3} x^3 \sqrt{a+b \cosh ^{-1}(c x)}",1,"(x^3*Sqrt[a + b*ArcCosh[c*x]])/3 - (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*c^3) - (Sqrt[b]*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(48*c^3) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*c^3*E^(a/b)) - (Sqrt[b]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(48*c^3*E^((3*a)/b))","A",14,7,16,0.4375,1,"{5664, 5781, 3312, 3307, 2180, 2204, 2205}"
143,1,145,0,0.6491584,"\int x \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Int[x*Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^2}-\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \cosh ^{-1}(c x)}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^2}-\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \cosh ^{-1}(c x)}",1,"-Sqrt[a + b*ArcCosh[c*x]]/(4*c^2) + (x^2*Sqrt[a + b*ArcCosh[c*x]])/2 - (Sqrt[b]*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*c^2) - (Sqrt[b]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*c^2*E^((2*a)/b))","A",9,7,14,0.5000,1,"{5664, 5781, 3312, 3307, 2180, 2204, 2205}"
144,1,102,0,0.4120522,"\int \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \cosh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \cosh ^{-1}(c x)}",1,"x*Sqrt[a + b*ArcCosh[c*x]] - (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c*E^(a/b))","A",7,6,12,0.5000,1,"{5654, 5781, 3307, 2180, 2204, 2205}"
145,1,292,0,1.2505501,"\int x^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Int[x^2*(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{6 c}","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{6 c}",1,"-(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(3*c^3) - (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(6*c) + (x^3*(a + b*ArcCosh[c*x])^(3/2))/3 - (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(32*c^3) - (b^(3/2)*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(96*c^3) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(32*c^3*E^(a/b)) + (b^(3/2)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(96*c^3*E^((3*a)/b))","A",22,10,16,0.6250,1,"{5664, 5759, 5718, 5658, 3308, 2180, 2205, 2204, 5670, 5448}"
146,1,184,0,0.8160921,"\int x \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Int[x*(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{3 b x \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{8 c}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 c^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{3 b x \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{8 c}",1,"(-3*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(8*c) - (a + b*ArcCosh[c*x])^(3/2)/(4*c^2) + (x^2*(a + b*ArcCosh[c*x])^(3/2))/2 - (3*b^(3/2)*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*c^2) + (3*b^(3/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*c^2*E^((2*a)/b))","A",11,10,14,0.7143,1,"{5664, 5759, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
147,1,140,0,0.4279007,"\int \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{2 c}+x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{2 c}+x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}",1,"(-3*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(2*c) + x*(a + b*ArcCosh[c*x])^(3/2) - (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c*E^(a/b))","A",8,7,12,0.5833,1,"{5654, 5718, 5658, 3308, 2180, 2205, 2204}"
148,1,337,0,2.0899337,"\int x^2 \left(a+b \cosh ^{-1}(c x)\right)^{5/2} \, dx","Int[x^2*(a + b*ArcCosh[c*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{576 c^3}+\frac{5 b^2 x \sqrt{a+b \cosh ^{-1}(c x)}}{6 c^2}+\frac{5}{36} b^2 x^3 \sqrt{a+b \cosh ^{-1}(c x)}-\frac{5 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \cosh ^{-1}(c x)\right)^{5/2}-\frac{5 b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{18 c}","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{576 c^3}+\frac{5 b^2 x \sqrt{a+b \cosh ^{-1}(c x)}}{6 c^2}+\frac{5}{36} b^2 x^3 \sqrt{a+b \cosh ^{-1}(c x)}-\frac{5 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \cosh ^{-1}(c x)\right)^{5/2}-\frac{5 b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{18 c}",1,"(5*b^2*x*Sqrt[a + b*ArcCosh[c*x]])/(6*c^2) + (5*b^2*x^3*Sqrt[a + b*ArcCosh[c*x]])/36 - (5*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(3/2))/(9*c^3) - (5*b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(3/2))/(18*c) + (x^3*(a + b*ArcCosh[c*x])^(5/2))/3 - (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(64*c^3) - (5*b^(5/2)*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(576*c^3) - (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(64*c^3*E^(a/b)) - (5*b^(5/2)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(576*c^3*E^((3*a)/b))","A",24,10,16,0.6250,1,"{5664, 5759, 5718, 5654, 5781, 3307, 2180, 2204, 2205, 3312}"
149,1,228,0,1.3278031,"\int x \left(a+b \cosh ^{-1}(c x)\right)^{5/2} \, dx","Int[x*(a + b*ArcCosh[c*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{256 c^2}-\frac{15 b^2 \sqrt{a+b \cosh ^{-1}(c x)}}{64 c^2}+\frac{15}{32} b^2 x^2 \sqrt{a+b \cosh ^{-1}(c x)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cosh ^{-1}(c x)\right)^{5/2}-\frac{5 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{8 c}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{256 c^2}-\frac{15 b^2 \sqrt{a+b \cosh ^{-1}(c x)}}{64 c^2}+\frac{15}{32} b^2 x^2 \sqrt{a+b \cosh ^{-1}(c x)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cosh ^{-1}(c x)\right)^{5/2}-\frac{5 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{8 c}",1,"(-15*b^2*Sqrt[a + b*ArcCosh[c*x]])/(64*c^2) + (15*b^2*x^2*Sqrt[a + b*ArcCosh[c*x]])/32 - (5*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(3/2))/(8*c) - (a + b*ArcCosh[c*x])^(5/2)/(4*c^2) + (x^2*(a + b*ArcCosh[c*x])^(5/2))/2 - (15*b^(5/2)*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(256*c^2) - (15*b^(5/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(256*c^2*E^((2*a)/b))","A",12,9,14,0.6429,1,"{5664, 5759, 5676, 5781, 3312, 3307, 2180, 2204, 2205}"
150,1,160,0,0.7506408,"\int \left(a+b \cosh ^{-1}(c x)\right)^{5/2} \, dx","Int[(a + b*ArcCosh[c*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c}+\frac{15}{4} b^2 x \sqrt{a+b \cosh ^{-1}(c x)}-\frac{5 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \cosh ^{-1}(c x)\right)^{5/2}","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c}+\frac{15}{4} b^2 x \sqrt{a+b \cosh ^{-1}(c x)}-\frac{5 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \cosh ^{-1}(c x)\right)^{5/2}",1,"(15*b^2*x*Sqrt[a + b*ArcCosh[c*x]])/4 - (5*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(3/2))/(2*c) + x*(a + b*ArcCosh[c*x])^(5/2) - (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*c) - (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*c*E^(a/b))","A",9,7,12,0.5833,1,"{5654, 5718, 5781, 3307, 2180, 2204, 2205}"
151,1,194,0,0.3603466,"\int \frac{x^2}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[x^2/Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3) - (E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3*E^(a/b)) + (Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3*E^((3*a)/b))","A",13,6,16,0.3750,1,"{5670, 5448, 3308, 2180, 2204, 2205}"
152,1,107,0,0.1849533,"\int \frac{x}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[x/Sqrt[a + b*ArcCosh[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^2}","\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^2}",1,"-(E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^2) + (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^2*E^((2*a)/b))","A",8,7,14,0.5000,1,"{5670, 5448, 12, 3308, 2180, 2204, 2205}"
153,1,88,0,0.104876,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcCosh[c*x]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b))","A",6,5,12,0.4167,1,"{5658, 3308, 2180, 2205, 2204}"
154,1,231,0,0.3100781,"\int \frac{x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[x^2/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}-\frac{2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3) + (E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3*E^(a/b)) + (Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3*E^((3*a)/b))","A",12,5,16,0.3125,1,"{5666, 3307, 2180, 2204, 2205}"
155,1,140,0,0.154964,"\int \frac{x}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[x/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 x \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 x \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(b^(3/2)*c^2) + (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(b^(3/2)*c^2*E^((2*a)/b))","A",6,5,14,0.3571,1,"{5666, 3307, 2180, 2204, 2205}"
156,1,120,0,0.4103947,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^(-3/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(b^(3/2)*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(b^(3/2)*c*E^(a/b))","A",7,6,12,0.5000,1,"{5656, 5781, 3307, 2180, 2204, 2205}"
157,1,276,0,1.3304054,"\int \frac{x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}} \, dx","Int[x^2/(a + b*ArcCosh[c*x])^(5/2),x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{5/2} c^3}+\frac{8 x}{3 b^2 c^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{4 x^3}{b^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{3 b c \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{5/2} c^3}+\frac{8 x}{3 b^2 c^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{4 x^3}{b^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{3 b c \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}",1,"(-2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*b*c*(a + b*ArcCosh[c*x])^(3/2)) + (8*x)/(3*b^2*c^2*Sqrt[a + b*ArcCosh[c*x]]) - (4*x^3)/(b^2*Sqrt[a + b*ArcCosh[c*x]]) - (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(6*b^(5/2)*c^3) - (E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(2*b^(5/2)*c^3) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(6*b^(5/2)*c^3*E^(a/b)) + (Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(2*b^(5/2)*c^3*E^((3*a)/b))","A",22,9,16,0.5625,1,"{5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205, 5658}"
158,1,188,0,0.8934796,"\int \frac{x}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}} \, dx","Int[x/(a + b*ArcCosh[c*x])^(5/2),x]","-\frac{2 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^2}+\frac{4}{3 b^2 c^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{8 x^2}{3 b^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x \sqrt{c x-1} \sqrt{c x+1}}{3 b c \left(a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^2}+\frac{4}{3 b^2 c^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{8 x^2}{3 b^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x \sqrt{c x-1} \sqrt{c x+1}}{3 b c \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}",1,"(-2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*b*c*(a + b*ArcCosh[c*x])^(3/2)) + 4/(3*b^2*c^2*Sqrt[a + b*ArcCosh[c*x]]) - (8*x^2)/(3*b^2*Sqrt[a + b*ArcCosh[c*x]]) - (2*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(3*b^(5/2)*c^2) + (2*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(3*b^(5/2)*c^2*E^((2*a)/b))","A",11,10,14,0.7143,1,"{5668, 5775, 5670, 5448, 12, 3308, 2180, 2204, 2205, 5676}"
159,1,148,0,0.4559015,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^(-5/2),x]","-\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}-\frac{4 x}{3 b^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{3 b c \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}-\frac{4 x}{3 b^2 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{3 b c \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}",1,"(-2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*b*c*(a + b*ArcCosh[c*x])^(3/2)) - (4*x)/(3*b^2*Sqrt[a + b*ArcCosh[c*x]]) - (2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(3*b^(5/2)*c) + (2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(3*b^(5/2)*c*E^(a/b))","A",8,7,12,0.5833,1,"{5656, 5775, 5658, 3308, 2180, 2205, 2204}"
160,1,361,0,1.6267097,"\int \frac{x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{7/2}} \, dx","Int[x^2/(a + b*ArcCosh[c*x])^(7/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{5 b^{7/2} c^3}+\frac{8 x}{15 b^2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}+\frac{16 \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c^3 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{4 x^3}{5 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{24 x^2 \sqrt{c x-1} \sqrt{c x+1}}{5 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{5 b^{7/2} c^3}+\frac{8 x}{15 b^2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}+\frac{16 \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c^3 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{4 x^3}{5 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{24 x^2 \sqrt{c x-1} \sqrt{c x+1}}{5 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}",1,"(-2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(5*b*c*(a + b*ArcCosh[c*x])^(5/2)) + (8*x)/(15*b^2*c^2*(a + b*ArcCosh[c*x])^(3/2)) - (4*x^3)/(5*b^2*(a + b*ArcCosh[c*x])^(3/2)) + (16*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*b^3*c^3*Sqrt[a + b*ArcCosh[c*x]]) - (24*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(5*b^3*c*Sqrt[a + b*ArcCosh[c*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c^3) + (3*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(5*b^(7/2)*c^3) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c^3*E^(a/b)) + (3*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(5*b^(7/2)*c^3*E^((3*a)/b))","A",22,9,16,0.5625,1,"{5668, 5775, 5666, 3307, 2180, 2204, 2205, 5656, 5781}"
161,1,229,0,0.8704134,"\int \frac{x}{\left(a+b \cosh ^{-1}(c x)\right)^{7/2}} \, dx","Int[x/(a + b*ArcCosh[c*x])^(7/2),x]","\frac{8 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^2}+\frac{4}{15 b^2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{8 x^2}{15 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{32 x \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-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 \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c^2}+\frac{4}{15 b^2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{8 x^2}{15 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{32 x \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 x \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}",1,"(-2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(5*b*c*(a + b*ArcCosh[c*x])^(5/2)) + 4/(15*b^2*c^2*(a + b*ArcCosh[c*x])^(3/2)) - (8*x^2)/(15*b^2*(a + b*ArcCosh[c*x])^(3/2)) - (32*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*b^3*c*Sqrt[a + b*ArcCosh[c*x]]) + (8*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(15*b^(7/2)*c^2) + (8*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(15*b^(7/2)*c^2*E^((2*a)/b))","A",9,8,14,0.5714,1,"{5668, 5775, 5666, 3307, 2180, 2204, 2205, 5676}"
162,1,188,0,0.7716644,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{7/2}} \, dx","Int[(a + b*ArcCosh[c*x])^(-7/2),x]","\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c}-\frac{4 x}{15 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{8 \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}","\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-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 \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{15 b^{7/2} c}-\frac{4 x}{15 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{8 \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}",1,"(-2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(5*b*c*(a + b*ArcCosh[c*x])^(5/2)) - (4*x)/(15*b^2*(a + b*ArcCosh[c*x])^(3/2)) - (8*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*b^3*c*Sqrt[a + b*ArcCosh[c*x]]) + (4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c) + (4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(15*b^(7/2)*c*E^(a/b))","A",9,7,12,0.5833,1,"{5656, 5775, 5781, 3307, 2180, 2204, 2205}"
163,1,141,0,0.2852907,"\int \sqrt{f x} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[f*x]*(a + b*ArcCosh[c*x])^2,x]","-\frac{16 b^2 c^2 (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{105 f^3}-\frac{8 b c \sqrt{1-c^2 x^2} (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{15 f^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 (f x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 f}","-\frac{16 b^2 c^2 (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{105 f^3}-\frac{8 b c \sqrt{1-c x} (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{15 f^2 \sqrt{c x-1}}+\frac{2 (f x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 f}",1,"(2*(f*x)^(3/2)*(a + b*ArcCosh[c*x])^2)/(3*f) - (8*b*c*(f*x)^(5/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(15*f^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (16*b^2*c^2*(f*x)^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(105*f^3)","A",2,2,18,0.1111,1,"{5662, 5763}"
164,1,194,0,0.3098328,"\int (d x)^m \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcCosh[c*x])^2,x]","-\frac{2 b^2 c^2 (d 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};c^2 x^2\right)}{d^3 (m+1) (m+2) (m+3)}-\frac{2 b c \sqrt{1-c^2 x^2} (d x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 (m+1) (m+2) \sqrt{c x-1} \sqrt{c x+1}}+\frac{(d x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{d (m+1)}","-\frac{2 b^2 c^2 (d 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};c^2 x^2\right)}{d^3 (m+1) (m+2) (m+3)}-\frac{2 b c \sqrt{1-c x} (d x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 (m+1) (m+2) \sqrt{c x-1}}+\frac{(d x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{d (m+1)}",1,"((d*x)^(1 + m)*(a + b*ArcCosh[c*x])^2)/(d*(1 + m)) - (2*b*c*(d*x)^(2 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d^2*(1 + m)*(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b^2*c^2*(d*x)^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, c^2*x^2])/(d^3*(1 + m)*(2 + m)*(3 + m))","A",2,2,16,0.1250,1,"{5662, 5763}"
165,1,106,0,0.053476,"\int (d x)^m \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcCosh[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{d (m+1)}-\frac{b c \sqrt{1-c^2 x^2} (d x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d^2 (m+1) (m+2) \sqrt{c x-1} \sqrt{c x+1}}","\frac{(d x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{d (m+1)}-\frac{b c \sqrt{1-c^2 x^2} (d x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d^2 (m+1) (m+2) \sqrt{c x-1} \sqrt{c x+1}}",1,"((d*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(d*(1 + m)) - (b*c*(d*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d^2*(1 + m)*(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",4,4,14,0.2857,1,"{5662, 126, 365, 364}"
166,0,0,0,0.0281057,"\int \frac{(d x)^m}{a+b \cosh ^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcCosh[c*x]),x]","\int \frac{(d x)^m}{a+b \cosh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \cosh ^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcCosh[c*x]), x]","A",0,0,0,0,-1,"{}"