1,1,55,93,0.0348865,"\int x^4 \cosh ^{-1}(a x) \, dx","Integrate[x^4*ArcCosh[a*x],x]","\frac{1}{5} x^5 \cosh ^{-1}(a x)-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(3 a^4 x^4+4 a^2 x^2+8\right)}{75 a^5}","-\frac{8 \sqrt{a x-1} \sqrt{a x+1}}{75 a^5}-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1}}{75 a^3}+\frac{1}{5} x^5 \cosh ^{-1}(a x)-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{25 a}",1,"-1/75*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(8 + 4*a^2*x^2 + 3*a^4*x^4))/a^5 + (x^5*ArcCosh[a*x])/5","A",1
2,1,71,77,0.0695891,"\int x^3 \cosh ^{-1}(a x) \, dx","Integrate[x^3*ArcCosh[a*x],x]","-\frac{-8 a^4 x^4 \cosh ^{-1}(a x)+a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+3\right)+6 \tanh ^{-1}\left(\sqrt{\frac{a x-1}{a x+1}}\right)}{32 a^4}","-\frac{3 \cosh ^{-1}(a x)}{32 a^4}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1}}{32 a^3}+\frac{1}{4} x^4 \cosh ^{-1}(a x)-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{16 a}",1,"-1/32*(a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(3 + 2*a^2*x^2) - 8*a^4*x^4*ArcCosh[a*x] + 6*ArcTanh[Sqrt[(-1 + a*x)/(1 + a*x)]])/a^4","A",0
3,1,46,65,0.0252417,"\int x^2 \cosh ^{-1}(a x) \, dx","Integrate[x^2*ArcCosh[a*x],x]","\frac{1}{3} x^3 \cosh ^{-1}(a x)-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+2\right)}{9 a^3}","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{9 a^3}+\frac{1}{3} x^3 \cosh ^{-1}(a x)-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{9 a}",1,"-1/9*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2 + a^2*x^2))/a^3 + (x^3*ArcCosh[a*x])/3","A",1
4,1,61,49,0.0272469,"\int x \cosh ^{-1}(a x) \, dx","Integrate[x*ArcCosh[a*x],x]","-\frac{-2 a^2 x^2 \cosh ^{-1}(a x)+a x \sqrt{a x-1} \sqrt{a x+1}+2 \tanh ^{-1}\left(\sqrt{\frac{a x-1}{a x+1}}\right)}{4 a^2}","-\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,"-1/4*(a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x] - 2*a^2*x^2*ArcCosh[a*x] + 2*ArcTanh[Sqrt[(-1 + a*x)/(1 + a*x)]])/a^2","A",0
5,1,30,30,0.0180165,"\int \cosh ^{-1}(a x) \, dx","Integrate[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",1
6,1,42,43,0.0369471,"\int \frac{\cosh ^{-1}(a x)}{x} \, dx","Integrate[ArcCosh[a*x]/x,x]","\frac{1}{2} \left(\cosh ^{-1}(a x) \left(\cosh ^{-1}(a x)+2 \log \left(e^{-2 \cosh ^{-1}(a x)}+1\right)\right)-\text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)\right)","\frac{1}{2} \text{Li}_2\left(-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]*(ArcCosh[a*x] + 2*Log[1 + E^(-2*ArcCosh[a*x])]) - PolyLog[2, -E^(-2*ArcCosh[a*x])])/2","A",0
7,1,57,32,0.028647,"\int \frac{\cosh ^{-1}(a x)}{x^2} \, dx","Integrate[ArcCosh[a*x]/x^2,x]","\frac{a \sqrt{a^2 x^2-1} \tan ^{-1}\left(\sqrt{a^2 x^2-1}\right)}{\sqrt{a x-1} \sqrt{a x+1}}-\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*Sqrt[-1 + a^2*x^2]*ArcTan[Sqrt[-1 + a^2*x^2]])/(Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",1
8,1,35,38,0.0081082,"\int \frac{\cosh ^{-1}(a x)}{x^3} \, dx","Integrate[ArcCosh[a*x]/x^3,x]","\frac{a x \sqrt{a x-1} \sqrt{a x+1}-\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*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x] - ArcCosh[a*x])/(2*x^2)","A",1
9,1,78,65,0.0813928,"\int \frac{\cosh ^{-1}(a x)}{x^4} \, dx","Integrate[ArcCosh[a*x]/x^4,x]","\frac{\frac{a x \left(a^2 x^2+a^2 x^2 \sqrt{a^2 x^2-1} \tan ^{-1}\left(\sqrt{a^2 x^2-1}\right)-1\right)}{\sqrt{a x-1} \sqrt{a x+1}}-2 \cosh ^{-1}(a x)}{6 x^3}","\frac{1}{6} a^3 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)-\frac{\cosh ^{-1}(a x)}{3 x^3}+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{6 x^2}",1,"(-2*ArcCosh[a*x] + (a*x*(-1 + a^2*x^2 + a^2*x^2*Sqrt[-1 + a^2*x^2]*ArcTan[Sqrt[-1 + a^2*x^2]]))/(Sqrt[-1 + a*x]*Sqrt[1 + a*x]))/(6*x^3)","A",1
10,1,45,66,0.0240225,"\int \frac{\cosh ^{-1}(a x)}{x^5} \, dx","Integrate[ArcCosh[a*x]/x^5,x]","\frac{a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+1\right)-3 \cosh ^{-1}(a x)}{12 x^4}","\frac{a^3 \sqrt{a x-1} \sqrt{a x+1}}{6 x}-\frac{\cosh ^{-1}(a x)}{4 x^4}+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{12 x^3}",1,"(a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(1 + 2*a^2*x^2) - 3*ArcCosh[a*x])/(12*x^4)","A",1
11,1,104,93,0.0501162,"\int \frac{\cosh ^{-1}(a x)}{x^6} \, dx","Integrate[ArcCosh[a*x]/x^6,x]","-\frac{-3 a^5 x^5+a^3 x^3-3 a^5 x^5 \sqrt{a^2 x^2-1} \tan ^{-1}\left(\sqrt{a^2 x^2-1}\right)+2 a x+8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{40 x^5 \sqrt{a x-1} \sqrt{a x+1}}","\frac{3}{40} a^5 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+\frac{3 a^3 \sqrt{a x-1} \sqrt{a x+1}}{40 x^2}-\frac{\cosh ^{-1}(a x)}{5 x^5}+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{20 x^4}",1,"-1/40*(2*a*x + a^3*x^3 - 3*a^5*x^5 + 8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x] - 3*a^5*x^5*Sqrt[-1 + a^2*x^2]*ArcTan[Sqrt[-1 + a^2*x^2]])/(x^5*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",1
12,1,80,132,0.1229334,"\int x^4 \cosh ^{-1}(a x)^2 \, dx","Integrate[x^4*ArcCosh[a*x]^2,x]","\frac{\frac{240 x}{a^4}+\frac{40 x^3}{a^2}-\frac{30 \sqrt{a x-1} \sqrt{a x+1} \left(3 a^4 x^4+4 a^2 x^2+8\right) \cosh ^{-1}(a x)}{a^5}+225 x^5 \cosh ^{-1}(a x)^2+18 x^5}{1125}","-\frac{16 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{75 a^5}+\frac{16 x}{75 a^4}-\frac{8 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{75 a^3}+\frac{8 x^3}{225 a^2}+\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,"((240*x)/a^4 + (40*x^3)/a^2 + 18*x^5 - (30*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(8 + 4*a^2*x^2 + 3*a^4*x^4)*ArcCosh[a*x])/a^5 + 225*x^5*ArcCosh[a*x]^2)/1125","A",1
13,1,77,106,0.077247,"\int x^3 \cosh ^{-1}(a x)^2 \, dx","Integrate[x^3*ArcCosh[a*x]^2,x]","\frac{\left(8 a^4 x^4-3\right) \cosh ^{-1}(a x)^2+a^2 x^2 \left(a^2 x^2+3\right)-2 a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+3\right) \cosh ^{-1}(a x)}{32 a^4}","-\frac{3 \cosh ^{-1}(a x)^2}{32 a^4}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{16 a^3}+\frac{3 x^2}{32 a^2}+\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,"(a^2*x^2*(3 + a^2*x^2) - 2*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(3 + 2*a^2*x^2)*ArcCosh[a*x] + (-3 + 8*a^4*x^4)*ArcCosh[a*x]^2)/(32*a^4)","A",1
14,1,64,90,0.1037682,"\int x^2 \cosh ^{-1}(a x)^2 \, dx","Integrate[x^2*ArcCosh[a*x]^2,x]","\frac{1}{27} \left(2 x \left(\frac{6}{a^2}+x^2\right)-\frac{6 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+2\right) \cosh ^{-1}(a x)}{a^3}+9 x^3 \cosh ^{-1}(a x)^2\right)","-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a^3}+\frac{4 x}{9 a^2}+\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,"(2*x*(6/a^2 + x^2) - (6*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2 + a^2*x^2)*ArcCosh[a*x])/a^3 + 9*x^3*ArcCosh[a*x]^2)/27","A",1
15,1,58,64,0.0559381,"\int x \cosh ^{-1}(a x)^2 \, dx","Integrate[x*ArcCosh[a*x]^2,x]","\frac{a^2 x^2+\left(2 a^2 x^2-1\right) \cosh ^{-1}(a x)^2-2 a x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{4 a^2}","-\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,"(a^2*x^2 - 2*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x] + (-1 + 2*a^2*x^2)*ArcCosh[a*x]^2)/(4*a^2)","A",1
16,1,39,39,0.0212902,"\int \cosh ^{-1}(a x)^2 \, dx","Integrate[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",1
17,1,63,62,0.0331931,"\int \frac{\cosh ^{-1}(a x)^2}{x} \, dx","Integrate[ArcCosh[a*x]^2/x,x]","-\cosh ^{-1}(a x) \text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)-\frac{1}{2} \text{Li}_3\left(-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{Li}_2\left(-e^{2 \cosh ^{-1}(a x)}\right)-\frac{1}{2} \text{Li}_3\left(-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",0
18,1,92,60,0.2684822,"\int \frac{\cosh ^{-1}(a x)^2}{x^2} \, dx","Integrate[ArcCosh[a*x]^2/x^2,x]","-i a \left(2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)-2 \text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)+\cosh ^{-1}(a x) \left(-\frac{i \cosh ^{-1}(a x)}{a x}+2 \log \left(1-i e^{-\cosh ^{-1}(a x)}\right)-2 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)\right)\right)","-2 i a \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+2 i a \text{Li}_2\left(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,"(-I)*a*(ArcCosh[a*x]*(((-I)*ArcCosh[a*x])/(a*x) + 2*Log[1 - I/E^ArcCosh[a*x]] - 2*Log[1 + I/E^ArcCosh[a*x]]) + 2*PolyLog[2, (-I)/E^ArcCosh[a*x]] - 2*PolyLog[2, I/E^ArcCosh[a*x]])","A",0
19,1,48,48,0.020517,"\int \frac{\cosh ^{-1}(a x)^2}{x^3} \, dx","Integrate[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",1
20,1,144,114,0.2651411,"\int \frac{\cosh ^{-1}(a x)^2}{x^4} \, dx","Integrate[ArcCosh[a*x]^2/x^4,x]","\frac{1}{3} a^3 \left(-\frac{\cosh ^{-1}(a x)^2}{a^3 x^3}+\frac{\sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x)}{a^2 x^2}-i \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)+i \text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)+\frac{1}{a x}-i \cosh ^{-1}(a x) \log \left(1-i e^{-\cosh ^{-1}(a x)}\right)+i \cosh ^{-1}(a x) \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)\right)","-\frac{1}{3} i a^3 \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+\frac{1}{3} i a^3 \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+\frac{2}{3} a^3 \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)+\frac{a^2}{3 x}-\frac{\cosh ^{-1}(a x)^2}{3 x^3}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 x^2}",1,"(a^3*(1/(a*x) + (Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x])/(a^2*x^2) - ArcCosh[a*x]^2/(a^3*x^3) - I*ArcCosh[a*x]*Log[1 - I/E^ArcCosh[a*x]] + I*ArcCosh[a*x]*Log[1 + I/E^ArcCosh[a*x]] - I*PolyLog[2, (-I)/E^ArcCosh[a*x]] + I*PolyLog[2, I/E^ArcCosh[a*x]]))/3","A",0
21,1,69,95,0.0903274,"\int \frac{\cosh ^{-1}(a x)^2}{x^5} \, dx","Integrate[ArcCosh[a*x]^2/x^5,x]","\frac{-4 a^4 x^4 \log (x)+a^2 x^2+2 a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+1\right) \cosh ^{-1}(a x)-3 \cosh ^{-1}(a x)^2}{12 x^4}","-\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^2}{12 x^2}-\frac{\cosh ^{-1}(a x)^2}{4 x^4}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{6 x^3}",1,"(a^2*x^2 + 2*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(1 + 2*a^2*x^2)*ArcCosh[a*x] - 3*ArcCosh[a*x]^2 - 4*a^4*x^4*Log[x])/(12*x^4)","A",1
22,1,130,231,0.1262546,"\int x^4 \cosh ^{-1}(a x)^3 \, dx","Integrate[x^4*ArcCosh[a*x]^3,x]","\frac{1125 a^5 x^5 \cosh ^{-1}(a x)^3-2 \sqrt{a x-1} \sqrt{a x+1} \left(27 a^4 x^4+136 a^2 x^2+2072\right)+30 a x \left(9 a^4 x^4+20 a^2 x^2+120\right) \cosh ^{-1}(a x)-225 \sqrt{a x-1} \sqrt{a x+1} \left(3 a^4 x^4+4 a^2 x^2+8\right) \cosh ^{-1}(a x)^2}{5625 a^5}","-\frac{4144 \sqrt{a x-1} \sqrt{a x+1}}{5625 a^5}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a^5}+\frac{16 x \cosh ^{-1}(a x)}{25 a^4}-\frac{272 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5625 a^3}-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a^3}+\frac{8 x^3 \cosh ^{-1}(a x)}{75 a^2}+\frac{1}{5} x^5 \cosh ^{-1}(a x)^3+\frac{6}{125} x^5 \cosh ^{-1}(a x)-\frac{6 x^4 \sqrt{a x-1} \sqrt{a x+1}}{625 a}-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{25 a}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2072 + 136*a^2*x^2 + 27*a^4*x^4) + 30*a*x*(120 + 20*a^2*x^2 + 9*a^4*x^4)*ArcCosh[a*x] - 225*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(8 + 4*a^2*x^2 + 3*a^4*x^4)*ArcCosh[a*x]^2 + 1125*a^5*x^5*ArcCosh[a*x]^3)/(5625*a^5)","A",1
23,1,143,183,0.1512034,"\int x^3 \cosh ^{-1}(a x)^3 \, dx","Integrate[x^3*ArcCosh[a*x]^3,x]","\frac{8 \left(8 a^4 x^4-3\right) \cosh ^{-1}(a x)^3-3 a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+15\right)-24 a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+3\right) \cosh ^{-1}(a x)^2+24 a^2 x^2 \left(a^2 x^2+3\right) \cosh ^{-1}(a x)-45 \log \left(a x+\sqrt{a x-1} \sqrt{a x+1}\right)}{256 a^4}","-\frac{3 \cosh ^{-1}(a x)^3}{32 a^4}-\frac{45 \cosh ^{-1}(a x)}{256 a^4}-\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{9 x^2 \cosh ^{-1}(a x)}{32 a^2}+\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}}{128 a}-\frac{3 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{16 a}",1,"(-3*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(15 + 2*a^2*x^2) + 24*a^2*x^2*(3 + a^2*x^2)*ArcCosh[a*x] - 24*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(3 + 2*a^2*x^2)*ArcCosh[a*x]^2 + 8*(-3 + 8*a^4*x^4)*ArcCosh[a*x]^3 - 45*Log[a*x + Sqrt[-1 + a*x]*Sqrt[1 + a*x]])/(256*a^4)","A",1
24,1,103,155,0.0968631,"\int x^2 \cosh ^{-1}(a x)^3 \, dx","Integrate[x^2*ArcCosh[a*x]^3,x]","\frac{9 a^3 x^3 \cosh ^{-1}(a x)^3-2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+20\right)-9 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+2\right) \cosh ^{-1}(a x)^2+6 a x \left(a^2 x^2+6\right) \cosh ^{-1}(a x)}{27 a^3}","-\frac{40 \sqrt{a x-1} \sqrt{a x+1}}{27 a^3}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a^3}+\frac{4 x \cosh ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^3+\frac{2}{9} x^3 \cosh ^{-1}(a x)-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1}}{27 a}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(20 + a^2*x^2) + 6*a*x*(6 + a^2*x^2)*ArcCosh[a*x] - 9*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2 + a^2*x^2)*ArcCosh[a*x]^2 + 9*a^3*x^3*ArcCosh[a*x]^3)/(27*a^3)","A",1
25,1,113,107,0.0898867,"\int x \cosh ^{-1}(a x)^3 \, dx","Integrate[x*ArcCosh[a*x]^3,x]","\frac{\left(4 a^2 x^2-2\right) \cosh ^{-1}(a x)^3+6 a^2 x^2 \cosh ^{-1}(a x)-3 \left(a x \sqrt{a x-1} \sqrt{a x+1}+\log \left(a x+\sqrt{a x-1} \sqrt{a x+1}\right)\right)-6 a x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{8 a^2}","-\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,"(6*a^2*x^2*ArcCosh[a*x] - 6*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2 + (-2 + 4*a^2*x^2)*ArcCosh[a*x]^3 - 3*(a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x] + Log[a*x + Sqrt[-1 + a*x]*Sqrt[1 + a*x]]))/(8*a^2)","A",1
26,1,68,68,0.0270362,"\int \cosh ^{-1}(a x)^3 \, dx","Integrate[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",1
27,1,82,87,0.0550877,"\int \frac{\cosh ^{-1}(a x)^3}{x} \, dx","Integrate[ArcCosh[a*x]^3/x,x]","\frac{1}{4} \left(-6 \cosh ^{-1}(a x)^2 \text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)-6 \cosh ^{-1}(a x) \text{Li}_3\left(-e^{-2 \cosh ^{-1}(a x)}\right)-3 \text{Li}_4\left(-e^{-2 \cosh ^{-1}(a x)}\right)+\cosh ^{-1}(a x)^4+4 \cosh ^{-1}(a x)^3 \log \left(e^{-2 \cosh ^{-1}(a x)}+1\right)\right)","\frac{3}{2} \cosh ^{-1}(a x)^2 \text{Li}_2\left(-e^{2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \cosh ^{-1}(a x) \text{Li}_3\left(-e^{2 \cosh ^{-1}(a x)}\right)+\frac{3}{4} \text{Li}_4\left(-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])] - 6*ArcCosh[a*x]^2*PolyLog[2, -E^(-2*ArcCosh[a*x])] - 6*ArcCosh[a*x]*PolyLog[3, -E^(-2*ArcCosh[a*x])] - 3*PolyLog[4, -E^(-2*ArcCosh[a*x])])/4","A",0
28,1,128,104,0.1824399,"\int \frac{\cosh ^{-1}(a x)^3}{x^2} \, dx","Integrate[ArcCosh[a*x]^3/x^2,x]","-\frac{\cosh ^{-1}(a x)^3}{x}+3 i a \left(-2 \cosh ^{-1}(a x) \left(\text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)-\text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)\right)-2 \text{Li}_3\left(-i e^{-\cosh ^{-1}(a x)}\right)+2 \text{Li}_3\left(i e^{-\cosh ^{-1}(a x)}\right)-\left(\cosh ^{-1}(a x)^2 \left(\log \left(1-i e^{-\cosh ^{-1}(a x)}\right)-\log \left(1+i e^{-\cosh ^{-1}(a x)}\right)\right)\right)\right)","-6 i a \cosh ^{-1}(a x) \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+6 i a \cosh ^{-1}(a x) \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+6 i a \text{Li}_3\left(-i e^{\cosh ^{-1}(a x)}\right)-6 i a \text{Li}_3\left(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) + (3*I)*a*(-(ArcCosh[a*x]^2*(Log[1 - I/E^ArcCosh[a*x]] - Log[1 + I/E^ArcCosh[a*x]])) - 2*ArcCosh[a*x]*(PolyLog[2, (-I)/E^ArcCosh[a*x]] - PolyLog[2, I/E^ArcCosh[a*x]]) - 2*PolyLog[3, (-I)/E^ArcCosh[a*x]] + 2*PolyLog[3, I/E^ArcCosh[a*x]])","A",0
29,1,92,98,0.8685823,"\int \frac{\cosh ^{-1}(a x)^3}{x^3} \, dx","Integrate[ArcCosh[a*x]^3/x^3,x]","\frac{1}{2} \left(3 a^2 \left(\text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)+\cosh ^{-1}(a x) \left(\frac{\sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x)}{a x}-\cosh ^{-1}(a x)-2 \log \left(e^{-2 \cosh ^{-1}(a x)}+1\right)\right)\right)-\frac{\cosh ^{-1}(a x)^3}{x^2}\right)","-\frac{3}{2} a^2 \text{Li}_2\left(-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,"(-(ArcCosh[a*x]^3/x^2) + 3*a^2*(ArcCosh[a*x]*(-ArcCosh[a*x] + (Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x])/(a*x) - 2*Log[1 + E^(-2*ArcCosh[a*x])]) + PolyLog[2, -E^(-2*ArcCosh[a*x])]))/2","A",0
30,1,201,183,0.5776687,"\int \frac{\cosh ^{-1}(a x)^3}{x^4} \, dx","Integrate[ArcCosh[a*x]^3/x^4,x]","\frac{1}{6} \left(-3 i a^3 \left(2 \cosh ^{-1}(a x) \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)-2 \cosh ^{-1}(a x) \text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)+2 \text{Li}_3\left(-i e^{-\cosh ^{-1}(a x)}\right)-2 \text{Li}_3\left(i e^{-\cosh ^{-1}(a x)}\right)+\cosh ^{-1}(a x)^2 \log \left(1-i e^{-\cosh ^{-1}(a x)}\right)-\cosh ^{-1}(a x)^2 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)-4 i \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(a x)\right)\right)\right)+\frac{6 a^2 \cosh ^{-1}(a x)}{x}-\frac{2 \cosh ^{-1}(a x)^3}{x^3}+\frac{3 a \sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x)^2}{x^2}\right)","-i a^3 \cosh ^{-1}(a x) \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+i a^3 \cosh ^{-1}(a x) \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+i a^3 \text{Li}_3\left(-i e^{\cosh ^{-1}(a x)}\right)-i a^3 \text{Li}_3\left(i e^{\cosh ^{-1}(a x)}\right)-a^3 \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)+a^3 \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)+\frac{a^2 \cosh ^{-1}(a x)}{x}-\frac{\cosh ^{-1}(a x)^3}{3 x^3}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x^2}",1,"((6*a^2*ArcCosh[a*x])/x + (3*a*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x]^2)/x^2 - (2*ArcCosh[a*x]^3)/x^3 - (3*I)*a^3*((-4*I)*ArcTan[Tanh[ArcCosh[a*x]/2]] + ArcCosh[a*x]^2*Log[1 - I/E^ArcCosh[a*x]] - ArcCosh[a*x]^2*Log[1 + I/E^ArcCosh[a*x]] + 2*ArcCosh[a*x]*PolyLog[2, (-I)/E^ArcCosh[a*x]] - 2*ArcCosh[a*x]*PolyLog[2, I/E^ArcCosh[a*x]] + 2*PolyLog[3, (-I)/E^ArcCosh[a*x]] - 2*PolyLog[3, I/E^ArcCosh[a*x]]))/6","A",0
31,1,220,174,0.672904,"\int \frac{\cosh ^{-1}(a x)^3}{x^5} \, dx","Integrate[ArcCosh[a*x]^3/x^5,x]","\frac{-a^5 x^5+2 a^4 x^4 \sqrt{\frac{a x-1}{a x+1}} (a x+1) \text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)+a^3 x^3-a^2 x^2 \sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x) \left(4 a^2 x^2 \log \left(e^{-2 \cosh ^{-1}(a x)}+1\right)-1\right)-a x (a x+1) \left(2 a^3 x^3 \left(\sqrt{\frac{a x-1}{a x+1}}-1\right)+2 a^2 x^2-a x+1\right) \cosh ^{-1}(a x)^2-\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{4 x^4 \sqrt{a x-1} \sqrt{a x+1}}","-\frac{1}{2} a^4 \text{Li}_2\left(-e^{2 \cosh ^{-1}(a x)}\right)+\frac{1}{2} a^4 \cosh ^{-1}(a x)^2-a^4 \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)-\frac{a^3 \sqrt{a x-1} \sqrt{a x+1}}{4 x}+\frac{a^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x}+\frac{a^2 \cosh ^{-1}(a x)}{4 x^2}-\frac{\cosh ^{-1}(a x)^3}{4 x^4}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 x^3}",1,"(a^3*x^3 - a^5*x^5 - a*x*(1 + a*x)*(1 - a*x + 2*a^2*x^2 + 2*a^3*x^3*(-1 + Sqrt[(-1 + a*x)/(1 + a*x)]))*ArcCosh[a*x]^2 - Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3 - a^2*x^2*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x]*(-1 + 4*a^2*x^2*Log[1 + E^(-2*ArcCosh[a*x])]) + 2*a^4*x^4*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*PolyLog[2, -E^(-2*ArcCosh[a*x])])/(4*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",0
32,1,175,306,0.1631582,"\int x^5 \cosh ^{-1}(a x)^4 \, dx","Integrate[x^5*ArcCosh[a*x]^4,x]","\frac{108 \left(16 a^6 x^6-5\right) \cosh ^{-1}(a x)^4+a^2 x^2 \left(32 a^4 x^4+195 a^2 x^2+2205\right)-144 a x \sqrt{a x-1} \sqrt{a x+1} \left(8 a^4 x^4+10 a^2 x^2+15\right) \cosh ^{-1}(a x)^3-6 a x \sqrt{a x-1} \sqrt{a x+1} \left(32 a^4 x^4+130 a^2 x^2+735\right) \cosh ^{-1}(a x)+9 \left(64 a^6 x^6+120 a^4 x^4+360 a^2 x^2-245\right) \cosh ^{-1}(a x)^2}{10368 a^6}","-\frac{5 \cosh ^{-1}(a x)^4}{96 a^6}-\frac{245 \cosh ^{-1}(a x)^2}{1152 a^6}-\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{245 x^2}{1152 a^4}+\frac{5 x^2 \cosh ^{-1}(a x)^2}{16 a^4}-\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{65 x^4}{3456 a^2}+\frac{5 x^4 \cosh ^{-1}(a x)^2}{48 a^2}+\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,"(a^2*x^2*(2205 + 195*a^2*x^2 + 32*a^4*x^4) - 6*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(735 + 130*a^2*x^2 + 32*a^4*x^4)*ArcCosh[a*x] + 9*(-245 + 360*a^2*x^2 + 120*a^4*x^4 + 64*a^6*x^6)*ArcCosh[a*x]^2 - 144*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(15 + 10*a^2*x^2 + 8*a^4*x^4)*ArcCosh[a*x]^3 + 108*(-5 + 16*a^6*x^6)*ArcCosh[a*x]^4)/(10368*a^6)","A",1
33,1,158,274,0.1375863,"\int x^4 \cosh ^{-1}(a x)^4 \, dx","Integrate[x^4*ArcCosh[a*x]^4,x]","\frac{16875 a^5 x^5 \cosh ^{-1}(a x)^4+8 a x \left(81 a^4 x^4+680 a^2 x^2+31080\right)+900 a x \left(9 a^4 x^4+20 a^2 x^2+120\right) \cosh ^{-1}(a x)^2-4500 \sqrt{a x-1} \sqrt{a x+1} \left(3 a^4 x^4+4 a^2 x^2+8\right) \cosh ^{-1}(a x)^3-120 \sqrt{a x-1} \sqrt{a x+1} \left(27 a^4 x^4+136 a^2 x^2+2072\right) \cosh ^{-1}(a x)}{84375 a^5}","-\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{16576 x}{5625 a^4}+\frac{32 x \cosh ^{-1}(a x)^2}{25 a^4}-\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{1088 x^3}{16875 a^2}+\frac{16 x^3 \cosh ^{-1}(a x)^2}{75 a^2}+\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,"(8*a*x*(31080 + 680*a^2*x^2 + 81*a^4*x^4) - 120*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2072 + 136*a^2*x^2 + 27*a^4*x^4)*ArcCosh[a*x] + 900*a*x*(120 + 20*a^2*x^2 + 9*a^4*x^4)*ArcCosh[a*x]^2 - 4500*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(8 + 4*a^2*x^2 + 3*a^4*x^4)*ArcCosh[a*x]^3 + 16875*a^5*x^5*ArcCosh[a*x]^4)/(84375*a^5)","A",1
34,1,143,214,0.1239781,"\int x^3 \cosh ^{-1}(a x)^4 \, dx","Integrate[x^3*ArcCosh[a*x]^4,x]","\frac{4 \left(8 a^4 x^4-3\right) \cosh ^{-1}(a x)^4+3 a^2 x^2 \left(a^2 x^2+15\right)-16 a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+3\right) \cosh ^{-1}(a x)^3-6 a x \sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2+15\right) \cosh ^{-1}(a x)+3 \left(8 a^4 x^4+24 a^2 x^2-15\right) \cosh ^{-1}(a x)^2}{128 a^4}","-\frac{3 \cosh ^{-1}(a x)^4}{32 a^4}-\frac{45 \cosh ^{-1}(a x)^2}{128 a^4}-\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{45 x^2}{128 a^2}+\frac{9 x^2 \cosh ^{-1}(a x)^2}{16 a^2}+\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,"(3*a^2*x^2*(15 + a^2*x^2) - 6*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(15 + 2*a^2*x^2)*ArcCosh[a*x] + 3*(-15 + 24*a^2*x^2 + 8*a^4*x^4)*ArcCosh[a*x]^2 - 16*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(3 + 2*a^2*x^2)*ArcCosh[a*x]^3 + 4*(-3 + 8*a^4*x^4)*ArcCosh[a*x]^4)/(128*a^4)","A",1
35,1,122,182,0.1232173,"\int x^2 \cosh ^{-1}(a x)^4 \, dx","Integrate[x^2*ArcCosh[a*x]^4,x]","\frac{27 a^3 x^3 \cosh ^{-1}(a x)^4+8 a x \left(a^2 x^2+60\right)-36 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+2\right) \cosh ^{-1}(a x)^3+36 a x \left(a^2 x^2+6\right) \cosh ^{-1}(a x)^2-24 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 x^2+20\right) \cosh ^{-1}(a x)}{81 a^3}","-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a^3}-\frac{160 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a^3}+\frac{160 x}{27 a^2}+\frac{8 x \cosh ^{-1}(a x)^2}{3 a^2}+\frac{1}{3} x^3 \cosh ^{-1}(a x)^4+\frac{4}{9} x^3 \cosh ^{-1}(a x)^2-\frac{4 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{9 a}-\frac{8 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a}+\frac{8 x^3}{81}",1,"(8*a*x*(60 + a^2*x^2) - 24*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(20 + a^2*x^2)*ArcCosh[a*x] + 36*a*x*(6 + a^2*x^2)*ArcCosh[a*x]^2 - 36*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2 + a^2*x^2)*ArcCosh[a*x]^3 + 27*a^3*x^3*ArcCosh[a*x]^4)/(81*a^3)","A",1
36,1,104,120,0.0807321,"\int x \cosh ^{-1}(a x)^4 \, dx","Integrate[x*ArcCosh[a*x]^4,x]","\frac{3 a^2 x^2+\left(2 a^2 x^2-1\right) \cosh ^{-1}(a x)^4+\left(6 a^2 x^2-3\right) \cosh ^{-1}(a x)^2-4 a x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3-6 a x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{4 a^2}","-\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*a^2*x^2 - 6*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x] + (-3 + 6*a^2*x^2)*ArcCosh[a*x]^2 - 4*a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3 + (-1 + 2*a^2*x^2)*ArcCosh[a*x]^4)/(4*a^2)","A",1
37,1,77,77,0.0306418,"\int \cosh ^{-1}(a x)^4 \, dx","Integrate[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",1
38,1,103,103,0.034814,"\int \frac{\cosh ^{-1}(a x)^4}{x} \, dx","Integrate[ArcCosh[a*x]^4/x,x]","-2 \cosh ^{-1}(a x)^3 \text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)-3 \cosh ^{-1}(a x)^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(a x)}\right)-3 \cosh ^{-1}(a x) \text{Li}_4\left(-e^{-2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \text{Li}_5\left(-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{Li}_2\left(-e^{2 \cosh ^{-1}(a x)}\right)-3 \cosh ^{-1}(a x)^2 \text{Li}_3\left(-e^{2 \cosh ^{-1}(a x)}\right)+3 \cosh ^{-1}(a x) \text{Li}_4\left(-e^{2 \cosh ^{-1}(a x)}\right)-\frac{3}{2} \text{Li}_5\left(-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",0
39,1,478,150,0.7011848,"\int \frac{\cosh ^{-1}(a x)^4}{x^2} \, dx","Integrate[ArcCosh[a*x]^4/x^2,x]","a \left(-12 i \cosh ^{-1}(a x)^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+12 \pi  \cosh ^{-1}(a x) \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)-24 i \cosh ^{-1}(a x) \text{Li}_3\left(-i e^{-\cosh ^{-1}(a x)}\right)+24 i \cosh ^{-1}(a x) \text{Li}_3\left(-i e^{\cosh ^{-1}(a x)}\right)+3 i \left(\pi -2 i \cosh ^{-1}(a x)\right)^2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)+3 i \pi ^2 \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+12 \pi  \text{Li}_3\left(-i e^{-\cosh ^{-1}(a x)}\right)-12 \pi  \text{Li}_3\left(i e^{\cosh ^{-1}(a x)}\right)-24 i \text{Li}_4\left(-i e^{-\cosh ^{-1}(a x)}\right)-24 i \text{Li}_4\left(-i e^{\cosh ^{-1}(a x)}\right)-\frac{\cosh ^{-1}(a x)^4}{a x}+i \cosh ^{-1}(a x)^4-2 \pi  \cosh ^{-1}(a x)^3-\frac{3}{2} i \pi ^2 \cosh ^{-1}(a x)^2+\frac{1}{2} \pi ^3 \cosh ^{-1}(a x)+4 i \cosh ^{-1}(a x)^3 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)-4 i \cosh ^{-1}(a x)^3 \log \left(1+i e^{\cosh ^{-1}(a x)}\right)-6 \pi  \cosh ^{-1}(a x)^2 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)+6 \pi  \cosh ^{-1}(a x)^2 \log \left(1-i e^{\cosh ^{-1}(a x)}\right)-3 i \pi ^2 \cosh ^{-1}(a x) \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)+3 i \pi ^2 \cosh ^{-1}(a x) \log \left(1-i e^{\cosh ^{-1}(a x)}\right)+\frac{1}{2} \pi ^3 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)-\frac{1}{2} \pi ^3 \log \left(1+i e^{\cosh ^{-1}(a x)}\right)+\frac{1}{2} \pi ^3 \log \left(\tan \left(\frac{1}{4} \left(\pi +2 i \cosh ^{-1}(a x)\right)\right)\right)-\frac{7 i \pi ^4}{16}\right)","-12 i a \cosh ^{-1}(a x)^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+12 i a \cosh ^{-1}(a x)^2 \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+24 i a \cosh ^{-1}(a x) \text{Li}_3\left(-i e^{\cosh ^{-1}(a x)}\right)-24 i a \cosh ^{-1}(a x) \text{Li}_3\left(i e^{\cosh ^{-1}(a x)}\right)-24 i a \text{Li}_4\left(-i e^{\cosh ^{-1}(a x)}\right)+24 i a \text{Li}_4\left(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,"a*(((-7*I)/16)*Pi^4 + (Pi^3*ArcCosh[a*x])/2 - ((3*I)/2)*Pi^2*ArcCosh[a*x]^2 - 2*Pi*ArcCosh[a*x]^3 + I*ArcCosh[a*x]^4 - ArcCosh[a*x]^4/(a*x) + (Pi^3*Log[1 + I/E^ArcCosh[a*x]])/2 - (3*I)*Pi^2*ArcCosh[a*x]*Log[1 + I/E^ArcCosh[a*x]] - 6*Pi*ArcCosh[a*x]^2*Log[1 + I/E^ArcCosh[a*x]] + (4*I)*ArcCosh[a*x]^3*Log[1 + I/E^ArcCosh[a*x]] + (3*I)*Pi^2*ArcCosh[a*x]*Log[1 - I*E^ArcCosh[a*x]] + 6*Pi*ArcCosh[a*x]^2*Log[1 - I*E^ArcCosh[a*x]] - (Pi^3*Log[1 + I*E^ArcCosh[a*x]])/2 - (4*I)*ArcCosh[a*x]^3*Log[1 + I*E^ArcCosh[a*x]] + (Pi^3*Log[Tan[(Pi + (2*I)*ArcCosh[a*x])/4]])/2 + (3*I)*(Pi - (2*I)*ArcCosh[a*x])^2*PolyLog[2, (-I)/E^ArcCosh[a*x]] - (12*I)*ArcCosh[a*x]^2*PolyLog[2, (-I)*E^ArcCosh[a*x]] + (3*I)*Pi^2*PolyLog[2, I*E^ArcCosh[a*x]] + 12*Pi*ArcCosh[a*x]*PolyLog[2, I*E^ArcCosh[a*x]] + 12*Pi*PolyLog[3, (-I)/E^ArcCosh[a*x]] - (24*I)*ArcCosh[a*x]*PolyLog[3, (-I)/E^ArcCosh[a*x]] + (24*I)*ArcCosh[a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]] - 12*Pi*PolyLog[3, I*E^ArcCosh[a*x]] - (24*I)*PolyLog[4, (-I)/E^ArcCosh[a*x]] - (24*I)*PolyLog[4, (-I)*E^ArcCosh[a*x]])","B",0
40,1,112,115,1.1594877,"\int \frac{\cosh ^{-1}(a x)^4}{x^3} \, dx","Integrate[ArcCosh[a*x]^4/x^3,x]","a^2 \left(6 \cosh ^{-1}(a x) \text{Li}_2\left(-e^{-2 \cosh ^{-1}(a x)}\right)+3 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(a x)}\right)+2 \cosh ^{-1}(a x)^2 \left(\frac{\sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x)}{a x}-\cosh ^{-1}(a x)-3 \log \left(e^{-2 \cosh ^{-1}(a x)}+1\right)\right)\right)-\frac{\cosh ^{-1}(a x)^4}{2 x^2}","-6 a^2 \cosh ^{-1}(a x) \text{Li}_2\left(-e^{2 \cosh ^{-1}(a x)}\right)+3 a^2 \text{Li}_3\left(-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,"-1/2*ArcCosh[a*x]^4/x^2 + a^2*(2*ArcCosh[a*x]^2*(-ArcCosh[a*x] + (Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x])/(a*x) - 3*Log[1 + E^(-2*ArcCosh[a*x])]) + 6*ArcCosh[a*x]*PolyLog[2, -E^(-2*ArcCosh[a*x])] + 3*PolyLog[3, -E^(-2*ArcCosh[a*x])])","A",0
41,1,595,268,3.4060422,"\int \frac{\cosh ^{-1}(a x)^4}{x^4} \, dx","Integrate[ArcCosh[a*x]^4/x^4,x]","a^3 \left(\frac{1}{2} i \left(-4 \cosh ^{-1}(a x)^2-4 i \pi  \cosh ^{-1}(a x)+\pi ^2+8\right) \text{Li}_2\left(-i e^{-\cosh ^{-1}(a x)}\right)-\frac{1}{96} i \left(-\frac{32 i \cosh ^{-1}(a x)^4}{a^3 x^3}+\frac{64 i \sqrt{\frac{a x-1}{a x+1}} (a x+1) \cosh ^{-1}(a x)^3}{a^2 x^2}+192 \cosh ^{-1}(a x)^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+192 i \pi  \cosh ^{-1}(a x) \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+384 \cosh ^{-1}(a x) \text{Li}_3\left(-i e^{-\cosh ^{-1}(a x)}\right)-384 \cosh ^{-1}(a x) \text{Li}_3\left(-i e^{\cosh ^{-1}(a x)}\right)+384 \text{Li}_2\left(i e^{-\cosh ^{-1}(a x)}\right)-48 \pi ^2 \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+192 i \pi  \text{Li}_3\left(-i e^{-\cosh ^{-1}(a x)}\right)-192 i \pi  \text{Li}_3\left(i e^{\cosh ^{-1}(a x)}\right)+384 \text{Li}_4\left(-i e^{-\cosh ^{-1}(a x)}\right)+384 \text{Li}_4\left(-i e^{\cosh ^{-1}(a x)}\right)-16 \cosh ^{-1}(a x)^4-32 i \pi  \cosh ^{-1}(a x)^3+\frac{192 i \cosh ^{-1}(a x)^2}{a x}+24 \pi ^2 \cosh ^{-1}(a x)^2+8 i \pi ^3 \cosh ^{-1}(a x)-64 \cosh ^{-1}(a x)^3 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)+64 \cosh ^{-1}(a x)^3 \log \left(1+i e^{\cosh ^{-1}(a x)}\right)-96 i \pi  \cosh ^{-1}(a x)^2 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)+96 i \pi  \cosh ^{-1}(a x)^2 \log \left(1-i e^{\cosh ^{-1}(a x)}\right)-384 \cosh ^{-1}(a x) \log \left(1-i e^{-\cosh ^{-1}(a x)}\right)+48 \pi ^2 \cosh ^{-1}(a x) \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)+384 \cosh ^{-1}(a x) \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)-48 \pi ^2 \cosh ^{-1}(a x) \log \left(1-i e^{\cosh ^{-1}(a x)}\right)+8 i \pi ^3 \log \left(1+i e^{-\cosh ^{-1}(a x)}\right)-8 i \pi ^3 \log \left(1+i e^{\cosh ^{-1}(a x)}\right)+8 i \pi ^3 \log \left(\tan \left(\frac{1}{4} \left(\pi +2 i \cosh ^{-1}(a x)\right)\right)\right)+7 \pi ^4\right)\right)","-2 i a^3 \cosh ^{-1}(a x)^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)+2 i a^3 \cosh ^{-1}(a x)^2 \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \cosh ^{-1}(a x) \text{Li}_3\left(-i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \cosh ^{-1}(a x) \text{Li}_3\left(i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \text{Li}_2\left(-i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \text{Li}_2\left(i e^{\cosh ^{-1}(a x)}\right)-4 i a^3 \text{Li}_4\left(-i e^{\cosh ^{-1}(a x)}\right)+4 i a^3 \text{Li}_4\left(i e^{\cosh ^{-1}(a x)}\right)+\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{2 a^2 \cosh ^{-1}(a x)^2}{x}-\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,"a^3*((I/2)*(8 + Pi^2 - (4*I)*Pi*ArcCosh[a*x] - 4*ArcCosh[a*x]^2)*PolyLog[2, (-I)/E^ArcCosh[a*x]] - (I/96)*(7*Pi^4 + (8*I)*Pi^3*ArcCosh[a*x] + 24*Pi^2*ArcCosh[a*x]^2 + ((192*I)*ArcCosh[a*x]^2)/(a*x) - (32*I)*Pi*ArcCosh[a*x]^3 + ((64*I)*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*ArcCosh[a*x]^3)/(a^2*x^2) - 16*ArcCosh[a*x]^4 - ((32*I)*ArcCosh[a*x]^4)/(a^3*x^3) - 384*ArcCosh[a*x]*Log[1 - I/E^ArcCosh[a*x]] + (8*I)*Pi^3*Log[1 + I/E^ArcCosh[a*x]] + 384*ArcCosh[a*x]*Log[1 + I/E^ArcCosh[a*x]] + 48*Pi^2*ArcCosh[a*x]*Log[1 + I/E^ArcCosh[a*x]] - (96*I)*Pi*ArcCosh[a*x]^2*Log[1 + I/E^ArcCosh[a*x]] - 64*ArcCosh[a*x]^3*Log[1 + I/E^ArcCosh[a*x]] - 48*Pi^2*ArcCosh[a*x]*Log[1 - I*E^ArcCosh[a*x]] + (96*I)*Pi*ArcCosh[a*x]^2*Log[1 - I*E^ArcCosh[a*x]] - (8*I)*Pi^3*Log[1 + I*E^ArcCosh[a*x]] + 64*ArcCosh[a*x]^3*Log[1 + I*E^ArcCosh[a*x]] + (8*I)*Pi^3*Log[Tan[(Pi + (2*I)*ArcCosh[a*x])/4]] + 384*PolyLog[2, I/E^ArcCosh[a*x]] + 192*ArcCosh[a*x]^2*PolyLog[2, (-I)*E^ArcCosh[a*x]] - 48*Pi^2*PolyLog[2, I*E^ArcCosh[a*x]] + (192*I)*Pi*ArcCosh[a*x]*PolyLog[2, I*E^ArcCosh[a*x]] + (192*I)*Pi*PolyLog[3, (-I)/E^ArcCosh[a*x]] + 384*ArcCosh[a*x]*PolyLog[3, (-I)/E^ArcCosh[a*x]] - 384*ArcCosh[a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]] - (192*I)*Pi*PolyLog[3, I*E^ArcCosh[a*x]] + 384*PolyLog[4, (-I)/E^ArcCosh[a*x]] + 384*PolyLog[4, (-I)*E^ArcCosh[a*x]]))","B",0
42,1,40,55,0.1013,"\int \frac{x^6}{\cosh ^{-1}(a x)} \, dx","Integrate[x^6/ArcCosh[a*x],x]","\frac{5 \text{Shi}\left(\cosh ^{-1}(a x)\right)+9 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)+5 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)+\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]] + 9*SinhIntegral[3*ArcCosh[a*x]] + 5*SinhIntegral[5*ArcCosh[a*x]] + SinhIntegral[7*ArcCosh[a*x]])/(64*a^7)","A",1
43,1,33,43,0.0875878,"\int \frac{x^5}{\cosh ^{-1}(a x)} \, dx","Integrate[x^5/ArcCosh[a*x],x]","\frac{5 \text{Shi}\left(2 \cosh ^{-1}(a x)\right)+4 \text{Shi}\left(4 \cosh ^{-1}(a x)\right)+\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]] + 4*SinhIntegral[4*ArcCosh[a*x]] + SinhIntegral[6*ArcCosh[a*x]])/(32*a^6)","A",1
44,1,31,41,0.0805302,"\int \frac{x^4}{\cosh ^{-1}(a x)} \, dx","Integrate[x^4/ArcCosh[a*x],x]","\frac{2 \text{Shi}\left(\cosh ^{-1}(a x)\right)+3 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)+\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,"(2*SinhIntegral[ArcCosh[a*x]] + 3*SinhIntegral[3*ArcCosh[a*x]] + SinhIntegral[5*ArcCosh[a*x]])/(16*a^5)","A",1
45,1,24,29,0.0675868,"\int \frac{x^3}{\cosh ^{-1}(a x)} \, dx","Integrate[x^3/ArcCosh[a*x],x]","\frac{2 \text{Shi}\left(2 \cosh ^{-1}(a x)\right)+\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,"(2*SinhIntegral[2*ArcCosh[a*x]] + SinhIntegral[4*ArcCosh[a*x]])/(8*a^4)","A",1
46,1,20,27,0.0593963,"\int \frac{x^2}{\cosh ^{-1}(a x)} \, dx","Integrate[x^2/ArcCosh[a*x],x]","\frac{\text{Shi}\left(\cosh ^{-1}(a x)\right)+\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]] + SinhIntegral[3*ArcCosh[a*x]])/(4*a^3)","A",1
47,1,14,14,0.0248887,"\int \frac{x}{\cosh ^{-1}(a x)} \, dx","Integrate[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",1
48,1,9,9,0.0245411,"\int \frac{1}{\cosh ^{-1}(a x)} \, dx","Integrate[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",1
49,0,0,13,0.2178876,"\int \frac{1}{x \cosh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]), x]","A",-1
50,0,0,13,0.4619664,"\int \frac{1}{x^2 \cosh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[1/(x^2*ArcCosh[a*x]), x]","A",-1
51,1,101,73,0.2258803,"\int \frac{x^4}{\cosh ^{-1}(a x)^2} \, dx","Integrate[x^4/ArcCosh[a*x]^2,x]","\frac{-16 a^5 x^5 \sqrt{\frac{a x-1}{a x+1}}-16 a^4 x^4 \sqrt{\frac{a x-1}{a x+1}}+2 \cosh ^{-1}(a x) \text{Chi}\left(\cosh ^{-1}(a x)\right)+9 \cosh ^{-1}(a x) \text{Chi}\left(3 \cosh ^{-1}(a x)\right)+5 \cosh ^{-1}(a x) \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{16 a^5 \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,"(-16*a^4*x^4*Sqrt[(-1 + a*x)/(1 + a*x)] - 16*a^5*x^5*Sqrt[(-1 + a*x)/(1 + a*x)] + 2*ArcCosh[a*x]*CoshIntegral[ArcCosh[a*x]] + 9*ArcCosh[a*x]*CoshIntegral[3*ArcCosh[a*x]] + 5*ArcCosh[a*x]*CoshIntegral[5*ArcCosh[a*x]])/(16*a^5*ArcCosh[a*x])","A",0
52,1,58,61,0.2545222,"\int \frac{x^3}{\cosh ^{-1}(a x)^2} \, dx","Integrate[x^3/ArcCosh[a*x]^2,x]","\frac{-\frac{2 a^3 x^3 \sqrt{\frac{a x-1}{a x+1}} (a x+1)}{\cosh ^{-1}(a x)}+\text{Chi}\left(2 \cosh ^{-1}(a x)\right)+\text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{2 a^4}","\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,"((-2*a^3*x^3*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x))/ArcCosh[a*x] + CoshIntegral[2*ArcCosh[a*x]] + CoshIntegral[4*ArcCosh[a*x]])/(2*a^4)","A",0
53,1,58,59,0.2506693,"\int \frac{x^2}{\cosh ^{-1}(a x)^2} \, dx","Integrate[x^2/ArcCosh[a*x]^2,x]","\frac{-\frac{4 a^2 x^2 \sqrt{\frac{a x-1}{a x+1}} (a x+1)}{\cosh ^{-1}(a x)}+\text{Chi}\left(\cosh ^{-1}(a x)\right)+3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^3}","\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,"((-4*a^2*x^2*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x))/ArcCosh[a*x] + CoshIntegral[ArcCosh[a*x]] + 3*CoshIntegral[3*ArcCosh[a*x]])/(4*a^3)","A",0
54,1,44,42,0.2563312,"\int \frac{x}{\cosh ^{-1}(a x)^2} \, dx","Integrate[x/ArcCosh[a*x]^2,x]","\frac{\text{Chi}\left(2 \cosh ^{-1}(a x)\right)-\frac{a x \sqrt{\frac{a x-1}{a x+1}} (a x+1)}{\cosh ^{-1}(a x)}}{a^2}","\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,"(-((a*x*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x))/ArcCosh[a*x]) + CoshIntegral[2*ArcCosh[a*x]])/a^2","A",0
55,1,60,39,0.1224312,"\int \frac{1}{\cosh ^{-1}(a x)^2} \, dx","Integrate[ArcCosh[a*x]^(-2),x]","\frac{\sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x) \text{Chi}\left(\cosh ^{-1}(a x)\right)-a x+1}{a \sqrt{\frac{a x-1}{a x+1}} \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,"(1 - a*x + Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x]*CoshIntegral[ArcCosh[a*x]])/(a*Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x])","A",0
56,0,0,13,4.7417006,"\int \frac{1}{x \cosh ^{-1}(a x)^2} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]^2), x]","A",-1
57,0,0,13,8.6904575,"\int \frac{1}{x^2 \cosh ^{-1}(a x)^2} \, dx","Integrate[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,"Integrate[1/(x^2*ArcCosh[a*x]^2), x]","A",-1
58,1,107,102,0.1473355,"\int \frac{x^4}{\cosh ^{-1}(a x)^3} \, dx","Integrate[x^4/ArcCosh[a*x]^3,x]","\frac{-80 a^5 x^5 \cosh ^{-1}(a x)-16 a^4 x^4 \sqrt{a x-1} \sqrt{a x+1}+64 a^3 x^3 \cosh ^{-1}(a x)+2 \cosh ^{-1}(a x)^2 \text{Shi}\left(\cosh ^{-1}(a x)\right)+27 \cosh ^{-1}(a x)^2 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)+25 \cosh ^{-1}(a x)^2 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{32 a^5 \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,"(-16*a^4*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x] + 64*a^3*x^3*ArcCosh[a*x] - 80*a^5*x^5*ArcCosh[a*x] + 2*ArcCosh[a*x]^2*SinhIntegral[ArcCosh[a*x]] + 27*ArcCosh[a*x]^2*SinhIntegral[3*ArcCosh[a*x]] + 25*ArcCosh[a*x]^2*SinhIntegral[5*ArcCosh[a*x]])/(32*a^5*ArcCosh[a*x]^2)","A",1
59,1,75,87,0.1818787,"\int \frac{x^3}{\cosh ^{-1}(a x)^3} \, dx","Integrate[x^3/ArcCosh[a*x]^3,x]","\frac{-\frac{a^2 x^2 \left(\left(4 a^2 x^2-3\right) \cosh ^{-1}(a x)+a x \sqrt{a x-1} \sqrt{a x+1}\right)}{\cosh ^{-1}(a x)^2}+\text{Shi}\left(2 \cosh ^{-1}(a x)\right)+2 \text{Shi}\left(4 \cosh ^{-1}(a x)\right)}{2 a^4}","\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,"(-((a^2*x^2*(a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x] + (-3 + 4*a^2*x^2)*ArcCosh[a*x]))/ArcCosh[a*x]^2) + SinhIntegral[2*ArcCosh[a*x]] + 2*SinhIntegral[4*ArcCosh[a*x]])/(2*a^4)","A",1
60,1,69,85,0.1575734,"\int \frac{x^2}{\cosh ^{-1}(a x)^3} \, dx","Integrate[x^2/ArcCosh[a*x]^3,x]","\frac{-\frac{4 a x \left(\left(3 a^2 x^2-2\right) \cosh ^{-1}(a x)+a x \sqrt{a x-1} \sqrt{a x+1}\right)}{\cosh ^{-1}(a x)^2}+\text{Shi}\left(\cosh ^{-1}(a x)\right)+9 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{8 a^3}","\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,"((-4*a*x*(a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x] + (-2 + 3*a^2*x^2)*ArcCosh[a*x]))/ArcCosh[a*x]^2 + SinhIntegral[ArcCosh[a*x]] + 9*SinhIntegral[3*ArcCosh[a*x]])/(8*a^3)","A",1
61,1,67,68,0.0550769,"\int \frac{x}{\cosh ^{-1}(a x)^3} \, dx","Integrate[x/ArcCosh[a*x]^3,x]","\frac{\text{Shi}\left(2 \cosh ^{-1}(a x)\right)}{a^2}+\frac{1-2 a^2 x^2}{2 a^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,"-1/2*(x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x]^2) + (1 - 2*a^2*x^2)/(2*a^2*ArcCosh[a*x]) + SinhIntegral[2*ArcCosh[a*x]]/a^2","A",1
62,1,55,55,0.0471479,"\int \frac{1}{\cosh ^{-1}(a x)^3} \, dx","Integrate[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,"-1/2*(Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*ArcCosh[a*x]^2) - x/(2*ArcCosh[a*x]) + SinhIntegral[ArcCosh[a*x]]/(2*a)","A",1
63,0,0,13,0.724868,"\int \frac{1}{x \cosh ^{-1}(a x)^3} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]^3), x]","A",-1
64,0,0,13,2.3825334,"\int \frac{1}{x^2 \cosh ^{-1}(a x)^3} \, dx","Integrate[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,"Integrate[1/(x^2*ArcCosh[a*x]^3), x]","A",-1
65,1,356,170,0.3958044,"\int \frac{x^4}{\cosh ^{-1}(a x)^4} \, dx","Integrate[x^4/ArcCosh[a*x]^4,x]","\frac{\sqrt{a x-1} \left(-32 a^6 x^6 \sqrt{\frac{a x-1}{a x+1}}-400 a^6 x^6 \sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)^2-80 a^5 x^5 \sqrt{a x-1} \sqrt{\frac{a x-1}{a x+1}} \sqrt{a x+1} \cosh ^{-1}(a x)+32 a^4 x^4 \sqrt{\frac{a x-1}{a x+1}}+592 a^4 x^4 \sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)^2+64 a^3 x^3 \sqrt{a x-1} \sqrt{\frac{a x-1}{a x+1}} \sqrt{a x+1} \cosh ^{-1}(a x)-192 a^2 x^2 \sqrt{\frac{a x-1}{a x+1}} \cosh ^{-1}(a x)^2+125 a x \cosh ^{-1}(a x)^3 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)+2 (a x-1) \cosh ^{-1}(a x)^3 \text{Chi}\left(\cosh ^{-1}(a x)\right)+81 (a x-1) \cosh ^{-1}(a x)^3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)-125 \cosh ^{-1}(a x)^3 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)\right)}{96 a^5 \left(\frac{a x-1}{a x+1}\right)^{3/2} (a x+1)^{3/2} \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^2 \sqrt{a x-1} \sqrt{a x+1}}{a^3 \cosh ^{-1}(a x)}+\frac{2 x^3}{3 a^2 \cosh ^{-1}(a x)^2}-\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,"(Sqrt[-1 + a*x]*(32*a^4*x^4*Sqrt[(-1 + a*x)/(1 + a*x)] - 32*a^6*x^6*Sqrt[(-1 + a*x)/(1 + a*x)] + 64*a^3*x^3*Sqrt[-1 + a*x]*Sqrt[(-1 + a*x)/(1 + a*x)]*Sqrt[1 + a*x]*ArcCosh[a*x] - 80*a^5*x^5*Sqrt[-1 + a*x]*Sqrt[(-1 + a*x)/(1 + a*x)]*Sqrt[1 + a*x]*ArcCosh[a*x] - 192*a^2*x^2*Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x]^2 + 592*a^4*x^4*Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x]^2 - 400*a^6*x^6*Sqrt[(-1 + a*x)/(1 + a*x)]*ArcCosh[a*x]^2 + 2*(-1 + a*x)*ArcCosh[a*x]^3*CoshIntegral[ArcCosh[a*x]] + 81*(-1 + a*x)*ArcCosh[a*x]^3*CoshIntegral[3*ArcCosh[a*x]] - 125*ArcCosh[a*x]^3*CoshIntegral[5*ArcCosh[a*x]] + 125*a*x*ArcCosh[a*x]^3*CoshIntegral[5*ArcCosh[a*x]]))/(96*a^5*((-1 + a*x)/(1 + a*x))^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]^3)","B",0
66,1,188,155,0.4183487,"\int \frac{x^3}{\cosh ^{-1}(a x)^4} \, dx","Integrate[x^3/ArcCosh[a*x]^4,x]","\frac{\sqrt{a x-1} \left(a x \sqrt{\frac{a x-1}{a x+1}} \left(-2 a^4 x^4+2 a^2 x^2-a x \sqrt{a x-1} \sqrt{a x+1} \left(4 a^2 x^2-3\right) \cosh ^{-1}(a x)-2 \left(8 a^4 x^4-11 a^2 x^2+3\right) \cosh ^{-1}(a x)^2\right)+2 (a x-1) \cosh ^{-1}(a x)^3 \text{Chi}\left(2 \cosh ^{-1}(a x)\right)+8 (a x-1) \cosh ^{-1}(a x)^3 \text{Chi}\left(4 \cosh ^{-1}(a x)\right)\right)}{6 a^4 \left(\frac{a x-1}{a x+1}\right)^{3/2} (a x+1)^{3/2} \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 \sqrt{a x-1} \sqrt{a x+1}}{a^3 \cosh ^{-1}(a x)}+\frac{x^2}{2 a^2 \cosh ^{-1}(a x)^2}-\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,"(Sqrt[-1 + a*x]*(a*x*Sqrt[(-1 + a*x)/(1 + a*x)]*(2*a^2*x^2 - 2*a^4*x^4 - a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(-3 + 4*a^2*x^2)*ArcCosh[a*x] - 2*(3 - 11*a^2*x^2 + 8*a^4*x^4)*ArcCosh[a*x]^2) + 2*(-1 + a*x)*ArcCosh[a*x]^3*CoshIntegral[2*ArcCosh[a*x]] + 8*(-1 + a*x)*ArcCosh[a*x]^3*CoshIntegral[4*ArcCosh[a*x]]))/(6*a^4*((-1 + a*x)/(1 + a*x))^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]^3)","A",0
67,1,183,153,0.3961187,"\int \frac{x^2}{\cosh ^{-1}(a x)^4} \, dx","Integrate[x^2/ArcCosh[a*x]^4,x]","\frac{\sqrt{a x-1} \left(-4 \sqrt{\frac{a x-1}{a x+1}} \left(2 a^2 x^2 \left(a^2 x^2-1\right)+a x \sqrt{a x-1} \sqrt{a x+1} \left(3 a^2 x^2-2\right) \cosh ^{-1}(a x)+\left(9 a^4 x^4-11 a^2 x^2+2\right) \cosh ^{-1}(a x)^2\right)+(a x-1) \cosh ^{-1}(a x)^3 \text{Chi}\left(\cosh ^{-1}(a x)\right)+27 (a x-1) \cosh ^{-1}(a x)^3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)\right)}{24 a^3 \left(\frac{a x-1}{a x+1}\right)^{3/2} (a x+1)^{3/2} \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{\sqrt{a x-1} \sqrt{a x+1}}{3 a^3 \cosh ^{-1}(a x)}+\frac{x}{3 a^2 \cosh ^{-1}(a x)^2}-\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,"(Sqrt[-1 + a*x]*(-4*Sqrt[(-1 + a*x)/(1 + a*x)]*(2*a^2*x^2*(-1 + a^2*x^2) + a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(-2 + 3*a^2*x^2)*ArcCosh[a*x] + (2 - 11*a^2*x^2 + 9*a^4*x^4)*ArcCosh[a*x]^2) + (-1 + a*x)*ArcCosh[a*x]^3*CoshIntegral[ArcCosh[a*x]] + 27*(-1 + a*x)*ArcCosh[a*x]^3*CoshIntegral[3*ArcCosh[a*x]]))/(24*a^3*((-1 + a*x)/(1 + a*x))^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]^3)","A",0
68,1,131,105,0.3221117,"\int \frac{x}{\cosh ^{-1}(a x)^4} \, dx","Integrate[x/ArcCosh[a*x]^4,x]","\frac{\frac{-2 a^3 x^3+\left(4 a x-4 a^3 x^3\right) \cosh ^{-1}(a x)^2-\sqrt{a x-1} \sqrt{a x+1} \left(2 a^2 x^2-1\right) \cosh ^{-1}(a x)+2 a x}{\cosh ^{-1}(a x)^3}+4 \sqrt{\frac{a x-1}{a x+1}} (a x+1) \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{6 a^2 \sqrt{a x-1} \sqrt{a x+1}}","\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,"((2*a*x - 2*a^3*x^3 - Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(-1 + 2*a^2*x^2)*ArcCosh[a*x] + (4*a*x - 4*a^3*x^3)*ArcCosh[a*x]^2)/ArcCosh[a*x]^3 + 4*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*CoshIntegral[2*ArcCosh[a*x]])/(6*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",0
69,1,114,86,0.2117428,"\int \frac{1}{\cosh ^{-1}(a x)^4} \, dx","Integrate[ArcCosh[a*x]^(-4),x]","\frac{\frac{-2 a^2 x^2+\left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2-a x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)+2}{\cosh ^{-1}(a x)^3}+\sqrt{\frac{a x-1}{a x+1}} (a x+1) \text{Chi}\left(\cosh ^{-1}(a x)\right)}{6 a \sqrt{a x-1} \sqrt{a x+1}}","\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,"((2 - 2*a^2*x^2 - a*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x] + (1 - a^2*x^2)*ArcCosh[a*x]^2)/ArcCosh[a*x]^3 + Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)*CoshIntegral[ArcCosh[a*x]])/(6*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",0
70,0,0,13,10.4082528,"\int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]^4), x]","A",-1
71,0,0,13,12.4808115,"\int \frac{1}{x^2 \cosh ^{-1}(a x)^4} \, dx","Integrate[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,"Integrate[1/(x^2*ArcCosh[a*x]^4), x]","A",-1
72,1,162,182,0.1045995,"\int x^4 \sqrt{\cosh ^{-1}(a x)} \, dx","Integrate[x^4*Sqrt[ArcCosh[a*x]],x]","\frac{3 \sqrt{5} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-5 \cosh ^{-1}(a x)\right)+25 \sqrt{3} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-3 \cosh ^{-1}(a x)\right)+150 \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-\cosh ^{-1}(a x)\right)+150 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},\cosh ^{-1}(a x)\right)+25 \sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},3 \cosh ^{-1}(a x)\right)+3 \sqrt{5} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},5 \cosh ^{-1}(a x)\right)}{2400 a^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,"(3*Sqrt[5]*Sqrt[ArcCosh[a*x]]*Gamma[3/2, -5*ArcCosh[a*x]] + 25*Sqrt[3]*Sqrt[ArcCosh[a*x]]*Gamma[3/2, -3*ArcCosh[a*x]] + 150*Sqrt[ArcCosh[a*x]]*Gamma[3/2, -ArcCosh[a*x]] + 150*Sqrt[-ArcCosh[a*x]]*Gamma[3/2, ArcCosh[a*x]] + 25*Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[3/2, 3*ArcCosh[a*x]] + 3*Sqrt[5]*Sqrt[-ArcCosh[a*x]]*Gamma[3/2, 5*ArcCosh[a*x]])/(2400*a^5*Sqrt[-ArcCosh[a*x]])","A",0
73,1,101,139,0.0916271,"\int x^3 \sqrt{\cosh ^{-1}(a x)} \, dx","Integrate[x^3*Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-4 \cosh ^{-1}(a x)\right)+4 \sqrt{2} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-2 \cosh ^{-1}(a x)\right)+\sqrt{-\cosh ^{-1}(a x)} \left(4 \sqrt{2} \Gamma \left(\frac{3}{2},2 \cosh ^{-1}(a x)\right)+\Gamma \left(\frac{3}{2},4 \cosh ^{-1}(a x)\right)\right)}{128 a^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,"(Sqrt[ArcCosh[a*x]]*Gamma[3/2, -4*ArcCosh[a*x]] + 4*Sqrt[2]*Sqrt[ArcCosh[a*x]]*Gamma[3/2, -2*ArcCosh[a*x]] + Sqrt[-ArcCosh[a*x]]*(4*Sqrt[2]*Gamma[3/2, 2*ArcCosh[a*x]] + Gamma[3/2, 4*ArcCosh[a*x]]))/(128*a^4*Sqrt[-ArcCosh[a*x]])","A",0
74,1,100,120,0.0939503,"\int x^2 \sqrt{\cosh ^{-1}(a x)} \, dx","Integrate[x^2*Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{3} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-3 \cosh ^{-1}(a x)\right)+9 \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-\cosh ^{-1}(a x)\right)+\sqrt{-\cosh ^{-1}(a x)} \left(9 \Gamma \left(\frac{3}{2},\cosh ^{-1}(a x)\right)+\sqrt{3} \Gamma \left(\frac{3}{2},3 \cosh ^{-1}(a x)\right)\right)}{72 a^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,"(Sqrt[3]*Sqrt[ArcCosh[a*x]]*Gamma[3/2, -3*ArcCosh[a*x]] + 9*Sqrt[ArcCosh[a*x]]*Gamma[3/2, -ArcCosh[a*x]] + Sqrt[-ArcCosh[a*x]]*(9*Gamma[3/2, ArcCosh[a*x]] + Sqrt[3]*Gamma[3/2, 3*ArcCosh[a*x]]))/(72*a^3*Sqrt[-ArcCosh[a*x]])","A",0
75,1,65,93,0.0824062,"\int x \sqrt{\cosh ^{-1}(a x)} \, dx","Integrate[x*Sqrt[ArcCosh[a*x]],x]","\frac{8 \sqrt{\cosh ^{-1}(a x)} \cosh \left(2 \cosh ^{-1}(a x)\right)-\sqrt{2 \pi } \left(\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)+\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\right)}{32 a^2}","-\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,"(8*Sqrt[ArcCosh[a*x]]*Cosh[2*ArcCosh[a*x]] - Sqrt[2*Pi]*(Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]] + Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]))/(32*a^2)","A",0
76,1,45,53,0.0410497,"\int \sqrt{\cosh ^{-1}(a x)} \, dx","Integrate[Sqrt[ArcCosh[a*x]],x]","\frac{\frac{\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{3}{2},-\cosh ^{-1}(a x)\right)}{\sqrt{-\cosh ^{-1}(a x)}}+\Gamma \left(\frac{3}{2},\cosh ^{-1}(a x)\right)}{2 a}","-\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,"((Sqrt[ArcCosh[a*x]]*Gamma[3/2, -ArcCosh[a*x]])/Sqrt[-ArcCosh[a*x]] + Gamma[3/2, ArcCosh[a*x]])/(2*a)","A",0
77,0,0,15,0.3264921,"\int \frac{\sqrt{\cosh ^{-1}(a x)}}{x} \, dx","Integrate[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,"Integrate[Sqrt[ArcCosh[a*x]]/x, x]","A",-1
78,1,152,345,0.1228631,"\int x^4 \cosh ^{-1}(a x)^{3/2} \, dx","Integrate[x^4*ArcCosh[a*x]^(3/2),x]","\frac{\frac{9 \sqrt{5} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-5 \cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\frac{125 \sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-3 \cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\frac{2250 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-\cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+2250 \Gamma \left(\frac{5}{2},\cosh ^{-1}(a x)\right)+125 \sqrt{3} \Gamma \left(\frac{5}{2},3 \cosh ^{-1}(a x)\right)+9 \sqrt{5} \Gamma \left(\frac{5}{2},5 \cosh ^{-1}(a x)\right)}{36000 a^5}","-\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{4 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{25 a^5}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{25 a^3}+\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,"((9*Sqrt[5]*Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -5*ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + (125*Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -3*ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + (2250*Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + 2250*Gamma[5/2, ArcCosh[a*x]] + 125*Sqrt[3]*Gamma[5/2, 3*ArcCosh[a*x]] + 9*Sqrt[5]*Gamma[5/2, 5*ArcCosh[a*x]])/(36000*a^5)","A",0
79,1,101,209,0.0923614,"\int x^3 \cosh ^{-1}(a x)^{3/2} \, dx","Integrate[x^3*ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-4 \cosh ^{-1}(a x)\right)+8 \sqrt{2} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-2 \cosh ^{-1}(a x)\right)+\sqrt{\cosh ^{-1}(a x)} \left(8 \sqrt{2} \Gamma \left(\frac{5}{2},2 \cosh ^{-1}(a x)\right)+\Gamma \left(\frac{5}{2},4 \cosh ^{-1}(a x)\right)\right)}{512 a^4 \sqrt{\cosh ^{-1}(a 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{3 \cosh ^{-1}(a x)^{3/2}}{32 a^4}-\frac{9 x \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{64 a^3}+\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,"(Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -4*ArcCosh[a*x]] + 8*Sqrt[2]*Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -2*ArcCosh[a*x]] + Sqrt[ArcCosh[a*x]]*(8*Sqrt[2]*Gamma[5/2, 2*ArcCosh[a*x]] + Gamma[5/2, 4*ArcCosh[a*x]]))/(512*a^4*Sqrt[ArcCosh[a*x]])","A",0
80,1,100,189,0.0925901,"\int x^2 \cosh ^{-1}(a x)^{3/2} \, dx","Integrate[x^2*ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-3 \cosh ^{-1}(a x)\right)+27 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-\cosh ^{-1}(a x)\right)+\sqrt{\cosh ^{-1}(a x)} \left(27 \Gamma \left(\frac{5}{2},\cosh ^{-1}(a x)\right)+\sqrt{3} \Gamma \left(\frac{5}{2},3 \cosh ^{-1}(a x)\right)\right)}{216 a^3 \sqrt{\cosh ^{-1}(a 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}",1,"(Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -3*ArcCosh[a*x]] + 27*Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -ArcCosh[a*x]] + Sqrt[ArcCosh[a*x]]*(27*Gamma[5/2, ArcCosh[a*x]] + Sqrt[3]*Gamma[5/2, 3*ArcCosh[a*x]]))/(216*a^3*Sqrt[ArcCosh[a*x]])","A",0
81,1,84,127,0.1310921,"\int x \cosh ^{-1}(a x)^{3/2} \, dx","Integrate[x*ArcCosh[a*x]^(3/2),x]","\frac{3 \sqrt{2 \pi } \left(\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)-\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\right)+32 \cosh \left(2 \cosh ^{-1}(a x)\right) \cosh ^{-1}(a x)^{3/2}-24 \sqrt{\cosh ^{-1}(a x)} \sinh \left(2 \cosh ^{-1}(a x)\right)}{128 a^2}","-\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,"(32*ArcCosh[a*x]^(3/2)*Cosh[2*ArcCosh[a*x]] + 3*Sqrt[2*Pi]*(-Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]] + Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]) - 24*Sqrt[ArcCosh[a*x]]*Sinh[2*ArcCosh[a*x]])/(128*a^2)","A",0
82,1,45,86,0.0316542,"\int \cosh ^{-1}(a x)^{3/2} \, dx","Integrate[ArcCosh[a*x]^(3/2),x]","\frac{\frac{\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{5}{2},-\cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\Gamma \left(\frac{5}{2},\cosh ^{-1}(a x)\right)}{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,"((Sqrt[-ArcCosh[a*x]]*Gamma[5/2, -ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + Gamma[5/2, ArcCosh[a*x]])/(2*a)","A",0
83,0,0,15,0.3270778,"\int \frac{\cosh ^{-1}(a x)^{3/2}}{x} \, dx","Integrate[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,"Integrate[ArcCosh[a*x]^(3/2)/x, x]","A",-1
84,1,162,394,0.1025735,"\int x^4 \cosh ^{-1}(a x)^{5/2} \, dx","Integrate[x^4*ArcCosh[a*x]^(5/2),x]","\frac{27 \sqrt{5} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-5 \cosh ^{-1}(a x)\right)+625 \sqrt{3} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-3 \cosh ^{-1}(a x)\right)+33750 \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-\cosh ^{-1}(a x)\right)+33750 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},\cosh ^{-1}(a x)\right)+625 \sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},3 \cosh ^{-1}(a x)\right)+27 \sqrt{5} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},5 \cosh ^{-1}(a x)\right)}{540000 a^5 \sqrt{-\cosh ^{-1}(a 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{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{15 a^5}+\frac{2 x \sqrt{\cosh ^{-1}(a x)}}{5 a^4}-\frac{2 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{15 a^3}+\frac{x^3 \sqrt{\cosh ^{-1}(a x)}}{15 a^2}+\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,"(27*Sqrt[5]*Sqrt[ArcCosh[a*x]]*Gamma[7/2, -5*ArcCosh[a*x]] + 625*Sqrt[3]*Sqrt[ArcCosh[a*x]]*Gamma[7/2, -3*ArcCosh[a*x]] + 33750*Sqrt[ArcCosh[a*x]]*Gamma[7/2, -ArcCosh[a*x]] + 33750*Sqrt[-ArcCosh[a*x]]*Gamma[7/2, ArcCosh[a*x]] + 625*Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[7/2, 3*ArcCosh[a*x]] + 27*Sqrt[5]*Sqrt[-ArcCosh[a*x]]*Gamma[7/2, 5*ArcCosh[a*x]])/(540000*a^5*Sqrt[-ArcCosh[a*x]])","A",0
85,1,101,257,0.0937134,"\int x^3 \cosh ^{-1}(a x)^{5/2} \, dx","Integrate[x^3*ArcCosh[a*x]^(5/2),x]","\frac{\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-4 \cosh ^{-1}(a x)\right)+16 \sqrt{2} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-2 \cosh ^{-1}(a x)\right)+\sqrt{-\cosh ^{-1}(a x)} \left(16 \sqrt{2} \Gamma \left(\frac{7}{2},2 \cosh ^{-1}(a x)\right)+\Gamma \left(\frac{7}{2},4 \cosh ^{-1}(a x)\right)\right)}{2048 a^4 \sqrt{-\cosh ^{-1}(a 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{3 \cosh ^{-1}(a x)^{5/2}}{32 a^4}-\frac{225 \sqrt{\cosh ^{-1}(a x)}}{2048 a^4}-\frac{15 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{64 a^3}+\frac{45 x^2 \sqrt{\cosh ^{-1}(a x)}}{256 a^2}+\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,"(Sqrt[ArcCosh[a*x]]*Gamma[7/2, -4*ArcCosh[a*x]] + 16*Sqrt[2]*Sqrt[ArcCosh[a*x]]*Gamma[7/2, -2*ArcCosh[a*x]] + Sqrt[-ArcCosh[a*x]]*(16*Sqrt[2]*Gamma[7/2, 2*ArcCosh[a*x]] + Gamma[7/2, 4*ArcCosh[a*x]]))/(2048*a^4*Sqrt[-ArcCosh[a*x]])","A",0
86,1,100,220,0.0897981,"\int x^2 \cosh ^{-1}(a x)^{5/2} \, dx","Integrate[x^2*ArcCosh[a*x]^(5/2),x]","\frac{\sqrt{3} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-3 \cosh ^{-1}(a x)\right)+81 \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-\cosh ^{-1}(a x)\right)+\sqrt{-\cosh ^{-1}(a x)} \left(81 \Gamma \left(\frac{7}{2},\cosh ^{-1}(a x)\right)+\sqrt{3} \Gamma \left(\frac{7}{2},3 \cosh ^{-1}(a x)\right)\right)}{648 a^3 \sqrt{-\cosh ^{-1}(a 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 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{9 a^3}+\frac{5 x \sqrt{\cosh ^{-1}(a x)}}{6 a^2}+\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,"(Sqrt[3]*Sqrt[ArcCosh[a*x]]*Gamma[7/2, -3*ArcCosh[a*x]] + 81*Sqrt[ArcCosh[a*x]]*Gamma[7/2, -ArcCosh[a*x]] + Sqrt[-ArcCosh[a*x]]*(81*Gamma[7/2, ArcCosh[a*x]] + Sqrt[3]*Gamma[7/2, 3*ArcCosh[a*x]]))/(648*a^3*Sqrt[-ArcCosh[a*x]])","A",0
87,1,92,157,0.1857308,"\int x \cosh ^{-1}(a x)^{5/2} \, dx","Integrate[x*ArcCosh[a*x]^(5/2),x]","\frac{-15 \sqrt{2 \pi } \left(\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)+\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\right)+8 \left(16 \cosh ^{-1}(a x)^2+15\right) \cosh \left(2 \cosh ^{-1}(a x)\right) \sqrt{\cosh ^{-1}(a x)}-160 \cosh ^{-1}(a x)^{3/2} \sinh \left(2 \cosh ^{-1}(a x)\right)}{512 a^2}","-\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,"(8*Sqrt[ArcCosh[a*x]]*(15 + 16*ArcCosh[a*x]^2)*Cosh[2*ArcCosh[a*x]] - 15*Sqrt[2*Pi]*(Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]] + Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]) - 160*ArcCosh[a*x]^(3/2)*Sinh[2*ArcCosh[a*x]])/(512*a^2)","A",0
88,1,45,99,0.0403399,"\int \cosh ^{-1}(a x)^{5/2} \, dx","Integrate[ArcCosh[a*x]^(5/2),x]","\frac{\frac{\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{7}{2},-\cosh ^{-1}(a x)\right)}{\sqrt{-\cosh ^{-1}(a x)}}+\Gamma \left(\frac{7}{2},\cosh ^{-1}(a x)\right)}{2 a}","-\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,"((Sqrt[ArcCosh[a*x]]*Gamma[7/2, -ArcCosh[a*x]])/Sqrt[-ArcCosh[a*x]] + Gamma[7/2, ArcCosh[a*x]])/(2*a)","A",0
89,0,0,15,0.3332271,"\int \frac{\cosh ^{-1}(a x)^{5/2}}{x} \, dx","Integrate[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,"Integrate[ArcCosh[a*x]^(5/2)/x, x]","A",-1
90,1,150,163,0.1200664,"\int \frac{x^4}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[x^4/Sqrt[ArcCosh[a*x]],x]","\frac{\frac{\sqrt{5} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 \cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\frac{5 \sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\frac{10 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+10 \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)+5 \sqrt{3} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)+\sqrt{5} \Gamma \left(\frac{1}{2},5 \cosh ^{-1}(a x)\right)}{160 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[5]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -5*ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + (5*Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -3*ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + (10*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + 10*Gamma[1/2, ArcCosh[a*x]] + 5*Sqrt[3]*Gamma[1/2, 3*ArcCosh[a*x]] + Sqrt[5]*Gamma[1/2, 5*ArcCosh[a*x]])/(160*a^5)","A",0
91,1,101,109,0.0957074,"\int \frac{x^3}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[x^3/Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 \cosh ^{-1}(a x)\right)+2 \sqrt{2} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \cosh ^{-1}(a x)\right)+\sqrt{\cosh ^{-1}(a x)} \left(2 \sqrt{2} \Gamma \left(\frac{1}{2},2 \cosh ^{-1}(a x)\right)+\Gamma \left(\frac{1}{2},4 \cosh ^{-1}(a x)\right)\right)}{32 a^4 \sqrt{\cosh ^{-1}(a 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}",1,"(Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -4*ArcCosh[a*x]] + 2*Sqrt[2]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -2*ArcCosh[a*x]] + Sqrt[ArcCosh[a*x]]*(2*Sqrt[2]*Gamma[1/2, 2*ArcCosh[a*x]] + Gamma[1/2, 4*ArcCosh[a*x]]))/(32*a^4*Sqrt[ArcCosh[a*x]])","A",0
92,1,100,105,0.09207,"\int \frac{x^2}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[x^2/Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)+3 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)+\sqrt{\cosh ^{-1}(a x)} \left(3 \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)+\sqrt{3} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)\right)}{24 a^3 \sqrt{\cosh ^{-1}(a 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}",1,"(Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -3*ArcCosh[a*x]] + 3*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -ArcCosh[a*x]] + Sqrt[ArcCosh[a*x]]*(3*Gamma[1/2, ArcCosh[a*x]] + Sqrt[3]*Gamma[1/2, 3*ArcCosh[a*x]]))/(24*a^3*Sqrt[ArcCosh[a*x]])","A",0
93,1,49,63,0.0431862,"\int \frac{x}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[x/Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \left(\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)-\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\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]]] + Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]))/(4*a^2)","A",1
94,1,45,43,0.0322388,"\int \frac{1}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[1/Sqrt[ArcCosh[a*x]],x]","\frac{\frac{\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\Gamma \left(\frac{1}{2},\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[-ArcCosh[a*x]]*Gamma[1/2, -ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + Gamma[1/2, ArcCosh[a*x]])/(2*a)","A",0
95,0,0,15,0.258611,"\int \frac{1}{x \sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[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,"Integrate[1/(x*Sqrt[ArcCosh[a*x]]), x]","A",-1
96,0,0,15,0.6694908,"\int \frac{1}{x^2 \sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[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,"Integrate[1/(x^2*Sqrt[ArcCosh[a*x]]), x]","A",-1
97,1,201,193,0.3130704,"\int \frac{x^4}{\cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[x^4/ArcCosh[a*x]^(3/2),x]","-\frac{4 \sqrt{\frac{a x-1}{a x+1}} (a x+1)+6 \sinh \left(3 \cosh ^{-1}(a x)\right)+2 \sinh \left(5 \cosh ^{-1}(a x)\right)-\sqrt{5} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 \cosh ^{-1}(a x)\right)-3 \sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)-2 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)+2 \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)+3 \sqrt{3} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)+\sqrt{5} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},5 \cosh ^{-1}(a x)\right)}{16 a^5 \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,"-1/16*(4*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) - Sqrt[5]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -5*ArcCosh[a*x]] - 3*Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -3*ArcCosh[a*x]] - 2*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -ArcCosh[a*x]] + 2*Sqrt[ArcCosh[a*x]]*Gamma[1/2, ArcCosh[a*x]] + 3*Sqrt[3]*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 3*ArcCosh[a*x]] + Sqrt[5]*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 5*ArcCosh[a*x]] + 6*Sinh[3*ArcCosh[a*x]] + 2*Sinh[5*ArcCosh[a*x]])/(a^5*Sqrt[ArcCosh[a*x]])","A",0
98,1,124,143,0.1693601,"\int \frac{x^3}{\cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[x^3/ArcCosh[a*x]^(3/2),x]","-\frac{2 \sinh \left(2 \cosh ^{-1}(a x)\right)+\sinh \left(4 \cosh ^{-1}(a x)\right)-\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 \cosh ^{-1}(a x)\right)-\sqrt{2} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \cosh ^{-1}(a x)\right)+\sqrt{2} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 \cosh ^{-1}(a x)\right)+\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 \cosh ^{-1}(a x)\right)}{4 a^4 \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,"-1/4*(-(Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -4*ArcCosh[a*x]]) - Sqrt[2]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -2*ArcCosh[a*x]] + Sqrt[2]*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 2*ArcCosh[a*x]] + Sqrt[ArcCosh[a*x]]*Gamma[1/2, 4*ArcCosh[a*x]] + 2*Sinh[2*ArcCosh[a*x]] + Sinh[4*ArcCosh[a*x]])/(a^4*Sqrt[ArcCosh[a*x]])","A",0
99,1,139,135,0.1815659,"\int \frac{x^2}{\cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[x^2/ArcCosh[a*x]^(3/2),x]","-\frac{2 \sqrt{\frac{a x-1}{a x+1}} (a x+1)+2 \sinh \left(3 \cosh ^{-1}(a x)\right)-\sqrt{3} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)-\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)+\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)+\sqrt{3} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)}{4 a^3 \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,"-1/4*(2*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) - Sqrt[3]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -3*ArcCosh[a*x]] - Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -ArcCosh[a*x]] + Sqrt[ArcCosh[a*x]]*Gamma[1/2, ArcCosh[a*x]] + Sqrt[3]*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 3*ArcCosh[a*x]] + 2*Sinh[3*ArcCosh[a*x]])/(a^3*Sqrt[ArcCosh[a*x]])","A",0
100,1,63,89,0.1102648,"\int \frac{x}{\cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[x/ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} \left(\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)+\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\right)-\frac{\sinh \left(2 \cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}}{a^2}","\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,"(Sqrt[Pi/2]*(Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]] + Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]) - Sinh[2*ArcCosh[a*x]]/Sqrt[ArcCosh[a*x]])/a^2","A",0
101,1,76,68,0.0681307,"\int \frac{1}{\cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[ArcCosh[a*x]^(-3/2),x]","\frac{-2 \sqrt{\frac{a x-1}{a x+1}} (a x+1)+\sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)-\sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)}{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)/(1 + a*x)]*(1 + a*x) + Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -ArcCosh[a*x]] - Sqrt[ArcCosh[a*x]]*Gamma[1/2, ArcCosh[a*x]])/(a*Sqrt[ArcCosh[a*x]])","A",0
102,0,0,15,0.3834906,"\int \frac{1}{x \cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]^(3/2)), x]","A",-1
103,1,278,228,1.6648113,"\int \frac{x^4}{\cosh ^{-1}(a x)^{5/2}} \, dx","Integrate[x^4/ArcCosh[a*x]^(5/2),x]","-\frac{2 \sqrt{\frac{a x-1}{a x+1}} (a x+1)+2 e^{-\cosh ^{-1}(a x)} \cosh ^{-1}(a x)+2 e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\sinh \left(5 \cosh ^{-1}(a x)\right)+2 \left(-\cosh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)-2 \cosh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)+5 \cosh ^{-1}(a x) \left(e^{-5 \cosh ^{-1}(a x)}+e^{5 \cosh ^{-1}(a x)}-\sqrt{5} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-5 \cosh ^{-1}(a x)\right)-\sqrt{5} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},5 \cosh ^{-1}(a x)\right)\right)+3 \left(3 e^{-3 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+3 e^{3 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\sinh \left(3 \cosh ^{-1}(a x)\right)+3 \sqrt{3} \left(-\cosh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)-3 \sqrt{3} \cosh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)\right)}{24 a^5 \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,"-1/24*(2*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) + (2*ArcCosh[a*x])/E^ArcCosh[a*x] + 2*E^ArcCosh[a*x]*ArcCosh[a*x] + 2*(-ArcCosh[a*x])^(3/2)*Gamma[1/2, -ArcCosh[a*x]] - 2*ArcCosh[a*x]^(3/2)*Gamma[1/2, ArcCosh[a*x]] + 5*ArcCosh[a*x]*(E^(-5*ArcCosh[a*x]) + E^(5*ArcCosh[a*x]) - Sqrt[5]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -5*ArcCosh[a*x]] - Sqrt[5]*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 5*ArcCosh[a*x]]) + 3*((3*ArcCosh[a*x])/E^(3*ArcCosh[a*x]) + 3*E^(3*ArcCosh[a*x])*ArcCosh[a*x] + 3*Sqrt[3]*(-ArcCosh[a*x])^(3/2)*Gamma[1/2, -3*ArcCosh[a*x]] - 3*Sqrt[3]*ArcCosh[a*x]^(3/2)*Gamma[1/2, 3*ArcCosh[a*x]] + Sinh[3*ArcCosh[a*x]]) + Sinh[5*ArcCosh[a*x]])/(a^5*ArcCosh[a*x]^(3/2))","A",0
104,1,175,172,0.7955531,"\int \frac{x^3}{\cosh ^{-1}(a x)^{5/2}} \, dx","Integrate[x^3/ArcCosh[a*x]^(5/2),x]","\frac{-\sinh \left(4 \cosh ^{-1}(a x)\right)-4 \cosh ^{-1}(a x) \left(e^{-4 \cosh ^{-1}(a x)}+e^{4 \cosh ^{-1}(a x)}-2 \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-4 \cosh ^{-1}(a x)\right)-2 \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},4 \cosh ^{-1}(a x)\right)\right)-2 \left(\sinh \left(2 \cosh ^{-1}(a x)\right)+2 \cosh ^{-1}(a x) \left(e^{-2 \cosh ^{-1}(a x)}+e^{2 \cosh ^{-1}(a x)}-\sqrt{2} \sqrt{-\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},-2 \cosh ^{-1}(a x)\right)-\sqrt{2} \sqrt{\cosh ^{-1}(a x)} \Gamma \left(\frac{1}{2},2 \cosh ^{-1}(a x)\right)\right)\right)}{12 a^4 \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,"(-4*ArcCosh[a*x]*(E^(-4*ArcCosh[a*x]) + E^(4*ArcCosh[a*x]) - 2*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -4*ArcCosh[a*x]] - 2*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 4*ArcCosh[a*x]]) - 2*(2*ArcCosh[a*x]*(E^(-2*ArcCosh[a*x]) + E^(2*ArcCosh[a*x]) - Sqrt[2]*Sqrt[-ArcCosh[a*x]]*Gamma[1/2, -2*ArcCosh[a*x]] - Sqrt[2]*Sqrt[ArcCosh[a*x]]*Gamma[1/2, 2*ArcCosh[a*x]]) + Sinh[2*ArcCosh[a*x]]) - Sinh[4*ArcCosh[a*x]])/(12*a^4*ArcCosh[a*x]^(3/2))","A",0
105,1,194,166,0.7351607,"\int \frac{x^2}{\cosh ^{-1}(a x)^{5/2}} \, dx","Integrate[x^2/ArcCosh[a*x]^(5/2),x]","\frac{-\sqrt{\frac{a x-1}{a x+1}} (a x+1)-3 e^{-3 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)-e^{-\cosh ^{-1}(a x)} \cosh ^{-1}(a x)-e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)-3 e^{3 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)-\sinh \left(3 \cosh ^{-1}(a x)\right)-3 \sqrt{3} \left(-\cosh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)-\left(-\cosh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)+\cosh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)+3 \sqrt{3} \cosh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)}{6 a^3 \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,"(-(Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x)) - (3*ArcCosh[a*x])/E^(3*ArcCosh[a*x]) - ArcCosh[a*x]/E^ArcCosh[a*x] - E^ArcCosh[a*x]*ArcCosh[a*x] - 3*E^(3*ArcCosh[a*x])*ArcCosh[a*x] - 3*Sqrt[3]*(-ArcCosh[a*x])^(3/2)*Gamma[1/2, -3*ArcCosh[a*x]] - (-ArcCosh[a*x])^(3/2)*Gamma[1/2, -ArcCosh[a*x]] + ArcCosh[a*x]^(3/2)*Gamma[1/2, ArcCosh[a*x]] + 3*Sqrt[3]*ArcCosh[a*x]^(3/2)*Gamma[1/2, 3*ArcCosh[a*x]] - Sinh[3*ArcCosh[a*x]])/(6*a^3*ArcCosh[a*x]^(3/2))","A",0
106,1,83,123,0.2842471,"\int \frac{x}{\cosh ^{-1}(a x)^{5/2}} \, dx","Integrate[x/ArcCosh[a*x]^(5/2),x]","-\frac{2 \sqrt{2 \pi } \left(\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)-\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\right)+\frac{4 \cosh \left(2 \cosh ^{-1}(a x)\right)}{\sqrt{\cosh ^{-1}(a x)}}+\frac{\sinh \left(2 \cosh ^{-1}(a x)\right)}{\cosh ^{-1}(a x)^{3/2}}}{3 a^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,"-1/3*((4*Cosh[2*ArcCosh[a*x]])/Sqrt[ArcCosh[a*x]] + 2*Sqrt[2*Pi]*(Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]] - Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]) + Sinh[2*ArcCosh[a*x]]/ArcCosh[a*x]^(3/2))/a^2","A",0
107,1,121,89,0.1690396,"\int \frac{1}{\cosh ^{-1}(a x)^{5/2}} \, dx","Integrate[ArcCosh[a*x]^(-5/2),x]","-\frac{2 e^{-\cosh ^{-1}(a x)} \left(\sqrt{\frac{a x-1}{a x+1}} (a x+1) e^{\cosh ^{-1}(a x)}+e^{2 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\cosh ^{-1}(a x)+e^{\cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)-e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)\right)}{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*(E^ArcCosh[a*x]*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) + ArcCosh[a*x] + E^(2*ArcCosh[a*x])*ArcCosh[a*x] + E^ArcCosh[a*x]*(-ArcCosh[a*x])^(3/2)*Gamma[1/2, -ArcCosh[a*x]] - E^ArcCosh[a*x]*ArcCosh[a*x]^(3/2)*Gamma[1/2, ArcCosh[a*x]]))/(3*a*E^ArcCosh[a*x]*ArcCosh[a*x]^(3/2))","A",0
108,0,0,15,0.3967557,"\int \frac{1}{x \cosh ^{-1}(a x)^{5/2}} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]^(5/2)), x]","A",-1
109,1,374,300,2.1734623,"\int \frac{x^4}{\cosh ^{-1}(a x)^{7/2}} \, dx","Integrate[x^4/ArcCosh[a*x]^(7/2),x]","\frac{-6 \sqrt{\frac{a x-1}{a x+1}} (a x+1)+4 e^{-\cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-4 e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-2 e^{-\cosh ^{-1}(a x)} \cosh ^{-1}(a x)-2 e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)-3 \sinh \left(5 \cosh ^{-1}(a x)\right)+4 \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)-4 \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)-5 \cosh ^{-1}(a x) \left(e^{-5 \cosh ^{-1}(a x)} \left(1-10 \cosh ^{-1}(a x)\right)+e^{5 \cosh ^{-1}(a x)} \left(10 \cosh ^{-1}(a x)+1\right)+10 \sqrt{5} \left(-\cosh ^{-1}(a x)\right)^{3/2} \Gamma \left(\frac{1}{2},-5 \cosh ^{-1}(a x)\right)+10 \sqrt{5} \cosh ^{-1}(a x)^{3/2} \Gamma \left(\frac{1}{2},5 \cosh ^{-1}(a x)\right)\right)-9 e^{-3 \cosh ^{-1}(a x)} \left(6 e^{6 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-6 \cosh ^{-1}(a x)^2+e^{6 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\cosh ^{-1}(a x)+e^{3 \cosh ^{-1}(a x)} \sinh \left(3 \cosh ^{-1}(a x)\right)-6 \sqrt{3} e^{3 \cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)+6 \sqrt{3} e^{3 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)\right)}{120 a^5 \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{32 x^2 \sqrt{a x-1} \sqrt{a x+1}}{5 a^3 \sqrt{\cosh ^{-1}(a x)}}+\frac{16 x^3}{15 a^2 \cosh ^{-1}(a x)^{3/2}}-\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,"(-6*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) - (2*ArcCosh[a*x])/E^ArcCosh[a*x] - 2*E^ArcCosh[a*x]*ArcCosh[a*x] + (4*ArcCosh[a*x]^2)/E^ArcCosh[a*x] - 4*E^ArcCosh[a*x]*ArcCosh[a*x]^2 + 4*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -ArcCosh[a*x]] - 4*ArcCosh[a*x]^(5/2)*Gamma[1/2, ArcCosh[a*x]] - 5*ArcCosh[a*x]*((1 - 10*ArcCosh[a*x])/E^(5*ArcCosh[a*x]) + E^(5*ArcCosh[a*x])*(1 + 10*ArcCosh[a*x]) + 10*Sqrt[5]*(-ArcCosh[a*x])^(3/2)*Gamma[1/2, -5*ArcCosh[a*x]] + 10*Sqrt[5]*ArcCosh[a*x]^(3/2)*Gamma[1/2, 5*ArcCosh[a*x]]) - (9*(ArcCosh[a*x] + E^(6*ArcCosh[a*x])*ArcCosh[a*x] - 6*ArcCosh[a*x]^2 + 6*E^(6*ArcCosh[a*x])*ArcCosh[a*x]^2 - 6*Sqrt[3]*E^(3*ArcCosh[a*x])*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -3*ArcCosh[a*x]] + 6*Sqrt[3]*E^(3*ArcCosh[a*x])*ArcCosh[a*x]^(5/2)*Gamma[1/2, 3*ArcCosh[a*x]] + E^(3*ArcCosh[a*x])*Sinh[3*ArcCosh[a*x]]))/E^(3*ArcCosh[a*x]) - 3*Sinh[5*ArcCosh[a*x]])/(120*a^5*ArcCosh[a*x]^(5/2))","A",0
110,1,291,244,0.5896324,"\int \frac{x^3}{\cosh ^{-1}(a x)^{7/2}} \, dx","Integrate[x^3/ArcCosh[a*x]^(7/2),x]","\frac{e^{-4 \cosh ^{-1}(a x)} \left(-3 e^{8 \cosh ^{-1}(a x)}-64 e^{8 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2+64 \cosh ^{-1}(a x)^2-8 e^{8 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)-8 \cosh ^{-1}(a x)+128 e^{4 \cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-4 \cosh ^{-1}(a x)\right)-8 e^{2 \cosh ^{-1}(a x)} \left(4 e^{4 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-4 \cosh ^{-1}(a x)^2+3 a x \sqrt{\frac{a x-1}{a x+1}} (a x+1) e^{2 \cosh ^{-1}(a x)}+e^{4 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\cosh ^{-1}(a x)-4 \sqrt{2} e^{2 \cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-2 \cosh ^{-1}(a x)\right)+4 \sqrt{2} e^{2 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},2 \cosh ^{-1}(a x)\right)\right)-128 e^{4 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},4 \cosh ^{-1}(a x)\right)+3\right)}{120 a^4 \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{16 x \sqrt{a x-1} \sqrt{a x+1}}{5 a^3 \sqrt{\cosh ^{-1}(a x)}}+\frac{4 x^2}{5 a^2 \cosh ^{-1}(a x)^{3/2}}-\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,"(3 - 3*E^(8*ArcCosh[a*x]) - 8*ArcCosh[a*x] - 8*E^(8*ArcCosh[a*x])*ArcCosh[a*x] + 64*ArcCosh[a*x]^2 - 64*E^(8*ArcCosh[a*x])*ArcCosh[a*x]^2 + 128*E^(4*ArcCosh[a*x])*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -4*ArcCosh[a*x]] - 8*E^(2*ArcCosh[a*x])*(3*a*E^(2*ArcCosh[a*x])*x*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) + ArcCosh[a*x] + E^(4*ArcCosh[a*x])*ArcCosh[a*x] - 4*ArcCosh[a*x]^2 + 4*E^(4*ArcCosh[a*x])*ArcCosh[a*x]^2 - 4*Sqrt[2]*E^(2*ArcCosh[a*x])*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -2*ArcCosh[a*x]] + 4*Sqrt[2]*E^(2*ArcCosh[a*x])*ArcCosh[a*x]^(5/2)*Gamma[1/2, 2*ArcCosh[a*x]]) - 128*E^(4*ArcCosh[a*x])*ArcCosh[a*x]^(5/2)*Gamma[1/2, 4*ArcCosh[a*x]])/(120*a^4*E^(4*ArcCosh[a*x])*ArcCosh[a*x]^(5/2))","A",0
111,1,286,237,0.81295,"\int \frac{x^2}{\cosh ^{-1}(a x)^{7/2}} \, dx","Integrate[x^2/ArcCosh[a*x]^(7/2),x]","\frac{e^{-3 \cosh ^{-1}(a x)} \left(-e^{2 \cosh ^{-1}(a x)} \left(2 e^{2 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-2 \cosh ^{-1}(a x)^2+3 \sqrt{\frac{a x-1}{a x+1}} (a x+1) e^{\cosh ^{-1}(a x)}+e^{2 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\cosh ^{-1}(a x)-2 e^{\cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)+2 e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)\right)-3 \left(6 e^{6 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-6 \cosh ^{-1}(a x)^2+e^{6 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\cosh ^{-1}(a x)+e^{3 \cosh ^{-1}(a x)} \sinh \left(3 \cosh ^{-1}(a x)\right)-6 \sqrt{3} e^{3 \cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-3 \cosh ^{-1}(a x)\right)+6 \sqrt{3} e^{3 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},3 \cosh ^{-1}(a x)\right)\right)\right)}{30 a^3 \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{16 \sqrt{a x-1} \sqrt{a x+1}}{15 a^3 \sqrt{\cosh ^{-1}(a x)}}+\frac{8 x}{15 a^2 \cosh ^{-1}(a x)^{3/2}}-\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,"(-(E^(2*ArcCosh[a*x])*(3*E^ArcCosh[a*x]*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) + ArcCosh[a*x] + E^(2*ArcCosh[a*x])*ArcCosh[a*x] - 2*ArcCosh[a*x]^2 + 2*E^(2*ArcCosh[a*x])*ArcCosh[a*x]^2 - 2*E^ArcCosh[a*x]*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -ArcCosh[a*x]] + 2*E^ArcCosh[a*x]*ArcCosh[a*x]^(5/2)*Gamma[1/2, ArcCosh[a*x]])) - 3*(ArcCosh[a*x] + E^(6*ArcCosh[a*x])*ArcCosh[a*x] - 6*ArcCosh[a*x]^2 + 6*E^(6*ArcCosh[a*x])*ArcCosh[a*x]^2 - 6*Sqrt[3]*E^(3*ArcCosh[a*x])*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -3*ArcCosh[a*x]] + 6*Sqrt[3]*E^(3*ArcCosh[a*x])*ArcCosh[a*x]^(5/2)*Gamma[1/2, 3*ArcCosh[a*x]] + E^(3*ArcCosh[a*x])*Sinh[3*ArcCosh[a*x]]))/(30*a^3*E^(3*ArcCosh[a*x])*ArcCosh[a*x]^(5/2))","A",0
112,1,91,157,0.3186199,"\int \frac{x}{\cosh ^{-1}(a x)^{7/2}} \, dx","Integrate[x/ArcCosh[a*x]^(7/2),x]","-\frac{-8 \sqrt{2 \pi } \left(\text{erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)+\text{erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)\right)+\frac{4 \cosh \left(2 \cosh ^{-1}(a x)\right)}{\cosh ^{-1}(a x)^{3/2}}+\frac{\left(16 \cosh ^{-1}(a x)^2+3\right) \sinh \left(2 \cosh ^{-1}(a x)\right)}{\cosh ^{-1}(a x)^{5/2}}}{15 a^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,"-1/15*((4*Cosh[2*ArcCosh[a*x]])/ArcCosh[a*x]^(3/2) - 8*Sqrt[2*Pi]*(Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]] + Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]]) + ((3 + 16*ArcCosh[a*x]^2)*Sinh[2*ArcCosh[a*x]])/ArcCosh[a*x]^(5/2))/a^2","A",0
113,1,147,122,0.1992579,"\int \frac{1}{\cosh ^{-1}(a x)^{7/2}} \, dx","Integrate[ArcCosh[a*x]^(-7/2),x]","-\frac{2 e^{-\cosh ^{-1}(a x)} \left(2 e^{2 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)^2-2 \cosh ^{-1}(a x)^2+3 \sqrt{\frac{a x-1}{a x+1}} (a x+1) e^{\cosh ^{-1}(a x)}+e^{2 \cosh ^{-1}(a x)} \cosh ^{-1}(a x)+\cosh ^{-1}(a x)-2 e^{\cosh ^{-1}(a x)} \left(-\cosh ^{-1}(a x)\right)^{5/2} \Gamma \left(\frac{1}{2},-\cosh ^{-1}(a x)\right)+2 e^{\cosh ^{-1}(a x)} \cosh ^{-1}(a x)^{5/2} \Gamma \left(\frac{1}{2},\cosh ^{-1}(a x)\right)\right)}{15 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*(3*E^ArcCosh[a*x]*Sqrt[(-1 + a*x)/(1 + a*x)]*(1 + a*x) + ArcCosh[a*x] + E^(2*ArcCosh[a*x])*ArcCosh[a*x] - 2*ArcCosh[a*x]^2 + 2*E^(2*ArcCosh[a*x])*ArcCosh[a*x]^2 - 2*E^ArcCosh[a*x]*(-ArcCosh[a*x])^(5/2)*Gamma[1/2, -ArcCosh[a*x]] + 2*E^ArcCosh[a*x]*ArcCosh[a*x]^(5/2)*Gamma[1/2, ArcCosh[a*x]]))/(15*a*E^ArcCosh[a*x]*ArcCosh[a*x]^(5/2))","A",0
114,0,0,15,0.3930459,"\int \frac{1}{x \cosh ^{-1}(a x)^{7/2}} \, dx","Integrate[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,"Integrate[1/(x*ArcCosh[a*x]^(7/2)), x]","A",-1
115,0,0,59,1.8856991,"\int x^m \cosh ^{-1}(a x)^4 \, dx","Integrate[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,"Integrate[x^m*ArcCosh[a*x]^4, x]","A",-1
116,0,0,59,1.7865765,"\int x^m \cosh ^{-1}(a x)^3 \, dx","Integrate[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,"Integrate[x^m*ArcCosh[a*x]^3, x]","A",-1
117,1,143,154,0.3768257,"\int x^m \cosh ^{-1}(a x)^2 \, dx","Integrate[x^m*ArcCosh[a*x]^2,x]","\frac{x^{m+1} \left(\cosh ^{-1}(a x)^2-\frac{2 a x \left(\frac{a x \, _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}+\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{\sqrt{a x-1} \sqrt{a x+1}}\right)}{m+2}\right)}{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 - (2*a*x*((Sqrt[1 - a^2*x^2]*ArcCosh[a*x]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (a*x*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, a^2*x^2])/(3 + m)))/(2 + m)))/(1 + m)","A",1
118,1,82,91,0.0998607,"\int x^m \cosh ^{-1}(a x) \, dx","Integrate[x^m*ArcCosh[a*x],x]","\frac{x^{m+1} \left(\cosh ^{-1}(a x)-\frac{a x \sqrt{1-a^2 x^2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{(m+2) \sqrt{a x-1} \sqrt{a x+1}}\right)}{m+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] - (a*x*Sqrt[1 - a^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/((2 + m)*Sqrt[-1 + a*x]*Sqrt[1 + a*x])))/(1 + m)","A",1
119,0,0,13,1.3242163,"\int \frac{x^m}{\cosh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[x^m/ArcCosh[a*x], x]","A",-1
120,0,0,13,1.3371922,"\int \frac{x^m}{\cosh ^{-1}(a x)^2} \, dx","Integrate[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,"Integrate[x^m/ArcCosh[a*x]^2, x]","A",-1
121,0,0,13,1.3588593,"\int \frac{x^m}{\cosh ^{-1}(a x)^3} \, dx","Integrate[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,"Integrate[x^m/ArcCosh[a*x]^3, x]","A",-1
122,0,0,15,1.9983997,"\int x^m \cosh ^{-1}(a x)^{3/2} \, dx","Integrate[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,"Integrate[x^m*ArcCosh[a*x]^(3/2), x]","A",-1
123,0,0,15,2.2674877,"\int x^m \sqrt{\cosh ^{-1}(a x)} \, dx","Integrate[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,"Integrate[x^m*Sqrt[ArcCosh[a*x]], x]","A",-1
124,0,0,15,2.1213374,"\int \frac{x^m}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Integrate[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,"Integrate[x^m/Sqrt[ArcCosh[a*x]], x]","A",-1
125,0,0,15,2.0366946,"\int \frac{x^m}{\cosh ^{-1}(a x)^{3/2}} \, dx","Integrate[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,"Integrate[x^m/ArcCosh[a*x]^(3/2), x]","A",-1
126,0,0,15,1.4468185,"\int (d x)^m \cosh ^{-1}(a x)^n \, dx","Integrate[(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,"Integrate[(d*x)^m*ArcCosh[a*x]^n, x]","A",-1
127,1,144,173,0.2099969,"\int x^4 \cosh ^{-1}(a x)^n \, dx","Integrate[x^4*ArcCosh[a*x]^n,x]","\frac{5^{-n} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-5 \cosh ^{-1}(a x)\right)+5\ 3^{-n} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-3 \cosh ^{-1}(a x)\right)+10 \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-\cosh ^{-1}(a x)\right)+10 \Gamma \left(n+1,\cosh ^{-1}(a x)\right)+5\ 3^{-n} \Gamma \left(n+1,3 \cosh ^{-1}(a x)\right)+5^{-n} \Gamma \left(n+1,5 \cosh ^{-1}(a x)\right)}{160 a^5}","\frac{5^{-n-1} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \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} \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} \Gamma \left(n+1,-\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{\Gamma \left(n+1,\cosh ^{-1}(a x)\right)}{16 a^5}+\frac{3^{-n} \Gamma \left(n+1,3 \cosh ^{-1}(a x)\right)}{32 a^5}+\frac{5^{-n-1} \Gamma \left(n+1,5 \cosh ^{-1}(a x)\right)}{32 a^5}",1,"((ArcCosh[a*x]^n*Gamma[1 + n, -5*ArcCosh[a*x]])/(5^n*(-ArcCosh[a*x])^n) + (5*ArcCosh[a*x]^n*Gamma[1 + n, -3*ArcCosh[a*x]])/(3^n*(-ArcCosh[a*x])^n) + (10*ArcCosh[a*x]^n*Gamma[1 + n, -ArcCosh[a*x]])/(-ArcCosh[a*x])^n + 10*Gamma[1 + n, ArcCosh[a*x]] + (5*Gamma[1 + n, 3*ArcCosh[a*x]])/3^n + Gamma[1 + n, 5*ArcCosh[a*x]]/5^n)/(160*a^5)","A",1
128,1,97,117,0.1016868,"\int x^3 \cosh ^{-1}(a x)^n \, dx","Integrate[x^3*ArcCosh[a*x]^n,x]","\frac{4^{-n-3} \left(-\cosh ^{-1}(a x)\right)^{-n} \left(\left(-\cosh ^{-1}(a x)\right)^n \left(2^{n+2} \Gamma \left(n+1,2 \cosh ^{-1}(a x)\right)+\Gamma \left(n+1,4 \cosh ^{-1}(a x)\right)\right)+\cosh ^{-1}(a x)^n \Gamma \left(n+1,-4 \cosh ^{-1}(a x)\right)+2^{n+2} \cosh ^{-1}(a x)^n \Gamma \left(n+1,-2 \cosh ^{-1}(a x)\right)\right)}{a^4}","\frac{2^{-2 (n+3)} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \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} \Gamma \left(n+1,-2 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \Gamma \left(n+1,2 \cosh ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \Gamma \left(n+1,4 \cosh ^{-1}(a x)\right)}{a^4}",1,"(4^(-3 - n)*(ArcCosh[a*x]^n*Gamma[1 + n, -4*ArcCosh[a*x]] + 2^(2 + n)*ArcCosh[a*x]^n*Gamma[1 + n, -2*ArcCosh[a*x]] + (-ArcCosh[a*x])^n*(2^(2 + n)*Gamma[1 + n, 2*ArcCosh[a*x]] + Gamma[1 + n, 4*ArcCosh[a*x]])))/(a^4*(-ArcCosh[a*x])^n)","A",1
129,1,95,113,0.1208243,"\int x^2 \cosh ^{-1}(a x)^n \, dx","Integrate[x^2*ArcCosh[a*x]^n,x]","\frac{3^{-n-1} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-3 \cosh ^{-1}(a x)\right)+\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-\cosh ^{-1}(a x)\right)+\Gamma \left(n+1,\cosh ^{-1}(a x)\right)+3^{-n-1} \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} \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} \Gamma \left(n+1,-\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{\Gamma \left(n+1,\cosh ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \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]])/(-ArcCosh[a*x])^n + (ArcCosh[a*x]^n*Gamma[1 + n, -ArcCosh[a*x]])/(-ArcCosh[a*x])^n + Gamma[1 + n, ArcCosh[a*x]] + 3^(-1 - n)*Gamma[1 + n, 3*ArcCosh[a*x]])/(8*a^3)","A",1
130,1,58,59,0.0518867,"\int x \cosh ^{-1}(a x)^n \, dx","Integrate[x*ArcCosh[a*x]^n,x]","\frac{2^{-n-3} \left(-\cosh ^{-1}(a x)\right)^{-n} \left(\left(-\cosh ^{-1}(a x)\right)^n \Gamma \left(n+1,2 \cosh ^{-1}(a x)\right)+\cosh ^{-1}(a x)^n \Gamma \left(n+1,-2 \cosh ^{-1}(a x)\right)\right)}{a^2}","\frac{2^{-n-3} \cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-2 \cosh ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \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]] + (-ArcCosh[a*x])^n*Gamma[1 + n, 2*ArcCosh[a*x]]))/(a^2*(-ArcCosh[a*x])^n)","A",1
131,1,43,49,0.02564,"\int \cosh ^{-1}(a x)^n \, dx","Integrate[ArcCosh[a*x]^n,x]","\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-\cosh ^{-1}(a x)\right)+\Gamma \left(n+1,\cosh ^{-1}(a x)\right)}{2 a}","\frac{\cosh ^{-1}(a x)^n \left(-\cosh ^{-1}(a x)\right)^{-n} \Gamma \left(n+1,-\cosh ^{-1}(a x)\right)}{2 a}+\frac{\Gamma \left(n+1,\cosh ^{-1}(a x)\right)}{2 a}",1,"((ArcCosh[a*x]^n*Gamma[1 + n, -ArcCosh[a*x]])/(-ArcCosh[a*x])^n + Gamma[1 + n, ArcCosh[a*x]])/(2*a)","A",1
132,0,0,13,0.3534447,"\int \frac{\cosh ^{-1}(a x)^n}{x} \, dx","Integrate[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,"Integrate[ArcCosh[a*x]^n/x, x]","A",-1
133,1,105,84,0.0408019,"\int x^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[x^3*(a + b*ArcCosh[c*x]),x]","\frac{a x^4}{4}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c x-1}}{\sqrt{c x+1}}\right)}{16 c^4}-\frac{3 b x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}+\frac{1}{4} b x^4 \cosh ^{-1}(c x)-\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 \cosh ^{-1}(c x)}{32 c^4}-\frac{3 b x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}-\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}",1,"(a*x^4)/4 - (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) + (b*x^4*ArcCosh[c*x])/4 - (3*b*ArcTanh[Sqrt[-1 + c*x]/Sqrt[1 + c*x]])/(16*c^4)","A",1
134,1,54,71,0.0464112,"\int x^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[x^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{9} \left(3 a x^3-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(c^2 x^2+2\right)}{c^3}+3 b x^3 \cosh ^{-1}(c x)\right)","\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,"(3*a*x^3 - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(2 + c^2*x^2))/c^3 + 3*b*x^3*ArcCosh[c*x])/9","A",1
135,1,76,55,0.0377983,"\int x \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[x*(a + b*ArcCosh[c*x]),x]","\frac{a x^2}{2}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c x-1}}{\sqrt{c x+1}}\right)}{2 c^2}+\frac{1}{2} b x^2 \cosh ^{-1}(c x)-\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,"(a*x^2)/2 - (b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) + (b*x^2*ArcCosh[c*x])/2 - (b*ArcTanh[Sqrt[-1 + c*x]/Sqrt[1 + c*x]])/(2*c^2)","A",1
136,1,35,35,0.0222666,"\int \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[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",1
137,1,48,55,0.0426369,"\int \frac{a+b \cosh ^{-1}(c x)}{x} \, dx","Integrate[(a + b*ArcCosh[c*x])/x,x]","a \log (x)+\frac{1}{2} b \left(\cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)+2 \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right)\right)-\text{Li}_2\left(-e^{-2 \cosh ^{-1}(c x)}\right)\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{Li}_2\left(-e^{-2 \cosh ^{-1}(c x)}\right)",1,"a*Log[x] + (b*(ArcCosh[c*x]*(ArcCosh[c*x] + 2*Log[1 + E^(-2*ArcCosh[c*x])]) - PolyLog[2, -E^(-2*ArcCosh[c*x])]))/2","A",0
138,1,65,37,0.0775802,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2} \, dx","Integrate[(a + b*ArcCosh[c*x])/x^2,x]","-\frac{a}{x}+\frac{b c \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{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/x) - (b*ArcCosh[c*x])/x + (b*c*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",1
139,1,48,43,0.0193972,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3} \, dx","Integrate[(a + b*ArcCosh[c*x])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \cosh ^{-1}(c x)}{2 x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 x}","\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 x}-\frac{a+b \cosh ^{-1}(c x)}{2 x^2}",1,"-1/2*a/x^2 + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x) - (b*ArcCosh[c*x])/(2*x^2)","A",1
140,1,101,71,0.1059849,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4} \, dx","Integrate[(a + b*ArcCosh[c*x])/x^4,x]","-\frac{a}{3 x^3}+\frac{b c^3 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \cosh ^{-1}(c x)}{3 x^3}+\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,"-1/3*a/x^3 + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*x^2) - (b*ArcCosh[c*x])/(3*x^3) + (b*c^3*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",1
141,1,50,72,0.0324222,"\int \frac{a+b \cosh ^{-1}(c x)}{x^5} \, dx","Integrate[(a + b*ArcCosh[c*x])/x^5,x]","\frac{-3 a+b c x \sqrt{c x-1} \sqrt{c x+1} \left(2 c^2 x^2+1\right)-3 b \cosh ^{-1}(c x)}{12 x^4}","-\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,"(-3*a + b*c*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 + 2*c^2*x^2) - 3*b*ArcCosh[c*x])/(12*x^4)","A",1
142,1,214,213,0.5078115,"\int x^2 \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Integrate[x^2*Sqrt[a + b*ArcCosh[c*x]],x]","\frac{e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)\right)}{72 c^3 \sqrt{-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}}}","-\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,"(Sqrt[a + b*ArcCosh[c*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[3/2, a/b + ArcCosh[c*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[3/2, -((a + b*ArcCosh[c*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c*x]))/b]))/(72*c^3*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])^2/b^2)])","A",0
143,1,136,145,0.4156064,"\int x \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Integrate[x*Sqrt[a + b*ArcCosh[c*x]],x]","\frac{-\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{2 a}{b}\right)-\cosh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+8 \cosh \left(2 \cosh ^{-1}(c x)\right) \sqrt{a+b \cosh ^{-1}(c x)}}{32 c^2}","-\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,"(8*Sqrt[a + b*ArcCosh[c*x]]*Cosh[2*ArcCosh[c*x]] + Sqrt[b]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(-Cosh[(2*a)/b] + Sinh[(2*a)/b]) - Sqrt[b]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]))/(32*c^2)","A",1
144,1,100,102,0.2376894,"\int \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Integrate[Sqrt[a + b*ArcCosh[c*x]],x]","\frac{e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}}}\right)}{2 c}","-\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,"(Sqrt[a + b*ArcCosh[c*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c*x]])/Sqrt[a/b + ArcCosh[c*x]] + Gamma[3/2, -((a + b*ArcCosh[c*x])/b)]/Sqrt[-((a + b*ArcCosh[c*x])/b)]))/(2*c*E^(a/b))","A",0
145,1,540,292,2.3899692,"\int x^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Integrate[x^2*(a + b*ArcCosh[c*x])^(3/2),x]","\frac{a e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)\right)}{72 c^3 \sqrt{-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left(9 \left(\sqrt{\pi } (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)-12 \sqrt{b} \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{a+b \cosh ^{-1}(c x)}+8 \sqrt{b} c x \cosh ^{-1}(c x) \sqrt{a+b \cosh ^{-1}(c x)}\right)+\sqrt{3 \pi } (2 a-b) \left(\sinh \left(\frac{3 a}{b}\right)+\cosh \left(\frac{3 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+\sqrt{3 \pi } (2 a+b) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+12 \sqrt{b} \left(2 \cosh ^{-1}(c x) \cosh \left(3 \cosh ^{-1}(c x)\right)-\sinh \left(3 \cosh ^{-1}(c x)\right)\right) \sqrt{a+b \cosh ^{-1}(c x)}\right)}{288 c^3}","-\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,"(a*Sqrt[a + b*ArcCosh[c*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[3/2, a/b + ArcCosh[c*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[3/2, -((a + b*ArcCosh[c*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c*x]))/b]))/(72*c^3*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])^2/b^2)]) + (Sqrt[b]*(9*(-12*Sqrt[b]*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[a + b*ArcCosh[c*x]] + 8*Sqrt[b]*c*x*ArcCosh[c*x]*Sqrt[a + b*ArcCosh[c*x]] + (2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + (2*a + b)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) + (2*a - b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*Sqrt[b]*Sqrt[a + b*ArcCosh[c*x]]*(2*ArcCosh[c*x]*Cosh[3*ArcCosh[c*x]] - Sinh[3*ArcCosh[c*x]])))/(288*c^3)","A",0
146,1,165,184,1.1074152,"\int x \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Integrate[x*(a + b*ArcCosh[c*x])^(3/2),x]","\frac{-3 \sqrt{2 \pi } b^{3/2} \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+3 \sqrt{2 \pi } b^{3/2} \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+8 \sqrt{a+b \cosh ^{-1}(c x)} \left(4 a \cosh \left(2 \cosh ^{-1}(c x)\right)+4 b \cosh ^{-1}(c x) \cosh \left(2 \cosh ^{-1}(c x)\right)-3 b \sinh \left(2 \cosh ^{-1}(c x)\right)\right)}{128 c^2}","-\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^(3/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) - 3*b^(3/2)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*Sqrt[a + b*ArcCosh[c*x]]*(4*a*Cosh[2*ArcCosh[c*x]] + 4*b*ArcCosh[c*x]*Cosh[2*ArcCosh[c*x]] - 3*b*Sinh[2*ArcCosh[c*x]]))/(128*c^2)","A",0
147,1,269,140,0.7077005,"\int \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Integrate[(a + b*ArcCosh[c*x])^(3/2),x]","\frac{b \left(\frac{\sqrt{\pi } (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b}}-12 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{a+b \cosh ^{-1}(c x)}+8 c x \cosh ^{-1}(c x) \sqrt{a+b \cosh ^{-1}(c x)}\right)}{8 c}+\frac{a e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}}}\right)}{2 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)}{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,"(a*Sqrt[a + b*ArcCosh[c*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c*x]])/Sqrt[a/b + ArcCosh[c*x]] + Gamma[3/2, -((a + b*ArcCosh[c*x])/b)]/Sqrt[-((a + b*ArcCosh[c*x])/b)]))/(2*c*E^(a/b)) + (b*(-12*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[a + b*ArcCosh[c*x]] + 8*c*x*ArcCosh[c*x]*Sqrt[a + b*ArcCosh[c*x]] + ((2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]))/Sqrt[b] + ((2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/Sqrt[b]))/(8*c)","A",0
148,1,924,337,11.1241904,"\int x^2 \left(a+b \cosh ^{-1}(c x)\right)^{5/2} \, dx","Integrate[x^2*(a + b*ArcCosh[c*x])^(5/2),x]","\frac{e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)\right) a^2}{72 c^3 \sqrt{-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left(9 \left(-12 \sqrt{b} \sqrt{\frac{c x-1}{c x+1}} \sqrt{a+b \cosh ^{-1}(c x)} (c x+1)+(2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+(2 a-3 b) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+8 \sqrt{b} c x \cosh ^{-1}(c x) \sqrt{a+b \cosh ^{-1}(c x)}\right)+(2 a+b) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)+(2 a-b) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)+12 \sqrt{b} \sqrt{a+b \cosh ^{-1}(c x)} \left(2 \cosh ^{-1}(c x) \cosh \left(3 \cosh ^{-1}(c x)\right)-\sinh \left(3 \cosh ^{-1}(c x)\right)\right)\right) a}{144 c^3}-\frac{27 \left(-4 b \sqrt{a+b \cosh ^{-1}(c x)} \left(2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(a-5 b \cosh ^{-1}(c x)\right)+b c x \left(4 \cosh ^{-1}(c x)^2+15\right)\right)+\sqrt{b} \left(4 a^2+12 b a+15 b^2\right) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \left(4 a^2-12 b a+15 b^2\right) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)\right)+\sqrt{b} \left(12 a^2+12 b a+5 b^2\right) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)+\sqrt{b} \left(12 a^2-12 b a+5 b^2\right) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)-12 b \sqrt{a+b \cosh ^{-1}(c x)} \left(b \left(12 \cosh ^{-1}(c x)^2+5\right) \cosh \left(3 \cosh ^{-1}(c x)\right)+2 \left(a-5 b \cosh ^{-1}(c x)\right) \sinh \left(3 \cosh ^{-1}(c x)\right)\right)}{1728 c^3}","-\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,"(a^2*Sqrt[a + b*ArcCosh[c*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[3/2, a/b + ArcCosh[c*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[3/2, -((a + b*ArcCosh[c*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c*x]))/b]))/(72*c^3*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])^2/b^2)]) + (a*Sqrt[b]*(9*(-12*Sqrt[b]*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[a + b*ArcCosh[c*x]] + 8*Sqrt[b]*c*x*ArcCosh[c*x]*Sqrt[a + b*ArcCosh[c*x]] + (2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + (2*a + b)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) + (2*a - b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*Sqrt[b]*Sqrt[a + b*ArcCosh[c*x]]*(2*ArcCosh[c*x]*Cosh[3*ArcCosh[c*x]] - Sinh[3*ArcCosh[c*x]])))/(144*c^3) - (27*(-4*b*Sqrt[a + b*ArcCosh[c*x]]*(2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(a - 5*b*ArcCosh[c*x]) + b*c*x*(15 + 4*ArcCosh[c*x]^2)) + Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + Sqrt[b]*(12*a^2 + 12*a*b + 5*b^2)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) + Sqrt[b]*(12*a^2 - 12*a*b + 5*b^2)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) - 12*b*Sqrt[a + b*ArcCosh[c*x]]*(b*(5 + 12*ArcCosh[c*x]^2)*Cosh[3*ArcCosh[c*x]] + 2*(a - 5*b*ArcCosh[c*x])*Sinh[3*ArcCosh[c*x]]))/(1728*c^3)","B",0
149,1,207,228,2.0438319,"\int x \left(a+b \cosh ^{-1}(c x)\right)^{5/2} \, dx","Integrate[x*(a + b*ArcCosh[c*x])^(5/2),x]","\frac{8 \sqrt{a+b \cosh ^{-1}(c x)} \left(\left(16 a^2+15 b^2\right) \cosh \left(2 \cosh ^{-1}(c x)\right)+4 b \cosh ^{-1}(c x) \left(8 a \cosh \left(2 \cosh ^{-1}(c x)\right)-5 b \sinh \left(2 \cosh ^{-1}(c x)\right)\right)-20 a b \sinh \left(2 \cosh ^{-1}(c x)\right)+16 b^2 \cosh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)^2\right)-15 \sqrt{2 \pi } b^{5/2} \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)-15 \sqrt{2 \pi } b^{5/2} \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{512 c^2}","-\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^(5/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) - 15*b^(5/2)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*Sqrt[a + b*ArcCosh[c*x]]*((16*a^2 + 15*b^2)*Cosh[2*ArcCosh[c*x]] + 16*b^2*ArcCosh[c*x]^2*Cosh[2*ArcCosh[c*x]] - 20*a*b*Sinh[2*ArcCosh[c*x]] + 4*b*ArcCosh[c*x]*(8*a*Cosh[2*ArcCosh[c*x]] - 5*b*Sinh[2*ArcCosh[c*x]])))/(512*c^2)","A",0
150,1,452,160,2.5516456,"\int \left(a+b \cosh ^{-1}(c x)\right)^{5/2} \, dx","Integrate[(a + b*ArcCosh[c*x])^(5/2),x]","\frac{-\sqrt{\pi } \sqrt{b} \left(4 a^2-12 a b+15 b^2\right) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)-\sqrt{\pi } \sqrt{b} \left(4 a^2+12 a b+15 b^2\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+8 a^2 e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}}}\right)+4 a b \left(\frac{\sqrt{\pi } (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b}}-12 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{a+b \cosh ^{-1}(c x)}+8 c x \cosh ^{-1}(c x) \sqrt{a+b \cosh ^{-1}(c x)}\right)+4 b \sqrt{a+b \cosh ^{-1}(c x)} \left(2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(a-5 b \cosh ^{-1}(c x)\right)+b c x \left(4 \cosh ^{-1}(c x)^2+15\right)\right)}{16 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)}{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,"(4*b*Sqrt[a + b*ArcCosh[c*x]]*(2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(a - 5*b*ArcCosh[c*x]) + b*c*x*(15 + 4*ArcCosh[c*x]^2)) + (8*a^2*Sqrt[a + b*ArcCosh[c*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c*x]])/Sqrt[a/b + ArcCosh[c*x]] + Gamma[3/2, -((a + b*ArcCosh[c*x])/b)]/Sqrt[-((a + b*ArcCosh[c*x])/b)]))/E^(a/b) - Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) - Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]) + 4*a*b*(-12*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[a + b*ArcCosh[c*x]] + 8*c*x*ArcCosh[c*x]*Sqrt[a + b*ArcCosh[c*x]] + ((2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]))/Sqrt[b] + ((2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/Sqrt[b]))/(16*c)","B",0
151,1,195,194,0.3708585,"\int \frac{x^2}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Integrate[x^2/Sqrt[a + b*ArcCosh[c*x]],x]","\frac{e^{-\frac{3 a}{b}} \left(3 e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{3} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+3 e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)\right)}{24 c^3 \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)}{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,"(3*E^((4*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[1/2, a/b + ArcCosh[c*x]] + Sqrt[3]*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[1/2, (-3*(a + b*ArcCosh[c*x]))/b] + 3*E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[1/2, (3*(a + b*ArcCosh[c*x]))/b])/(24*c^3*E^((3*a)/b)*Sqrt[a + b*ArcCosh[c*x]])","A",0
152,1,104,107,0.2442703,"\int \frac{x}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Integrate[x/Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \left(\left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+\left(\sinh \left(\frac{2 a}{b}\right)-\cosh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)\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,"-1/4*(Sqrt[Pi/2]*(Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(-Cosh[(2*a)/b] + Sinh[(2*a)/b]) + Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b])))/(Sqrt[b]*c^2)","A",1
153,1,100,88,0.1053223,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Integrate[1/Sqrt[a + b*ArcCosh[c*x]],x]","\frac{e^{-\frac{a}{b}} \left(e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)\right)}{2 c \sqrt{a+b \cosh ^{-1}(c 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}",1,"(E^((2*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[1/2, a/b + ArcCosh[c*x]] + Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)])/(2*c*E^(a/b)*Sqrt[a + b*ArcCosh[c*x]])","A",0
154,1,247,231,0.7097377,"\int \frac{x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[x^2/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{e^{-\frac{3 a}{b}} \left(-2 e^{\frac{3 a}{b}} \sqrt{\frac{c x-1}{c x+1}} (c x+1)-2 e^{\frac{3 a}{b}} \sinh \left(3 \cosh ^{-1}(c x)\right)-e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{3} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)-\sqrt{3} e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)\right)}{4 b c^3 \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*E^((3*a)/b)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x) - E^((4*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[1/2, a/b + ArcCosh[c*x]] + Sqrt[3]*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[1/2, (-3*(a + b*ArcCosh[c*x]))/b] + E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)] - Sqrt[3]*E^((6*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[1/2, (3*(a + b*ArcCosh[c*x]))/b] - 2*E^((3*a)/b)*Sinh[3*ArcCosh[c*x]])/(4*b*c^3*E^((3*a)/b)*Sqrt[a + b*ArcCosh[c*x]])","A",0
155,1,135,140,1.2893895,"\int \frac{x}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[x/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{\sqrt{2 \pi } \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+\sqrt{2 \pi } \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)-\frac{2 \sqrt{b} \sinh \left(2 \cosh ^{-1}(c x)\right)}{\sqrt{a+b \cosh ^{-1}(c x)}}}{2 b^{3/2} 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)}{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,"(Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) - (2*Sqrt[b]*Sinh[2*ArcCosh[c*x]])/Sqrt[a + b*ArcCosh[c*x]])/(2*b^(3/2)*c^2)","A",0
156,1,132,120,0.2625087,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c*x])^(-3/2),x]","\frac{e^{-\frac{a}{b}} \left(-2 e^{a/b} \sqrt{\frac{c x-1}{c x+1}} (c x+1)-e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+\sqrt{-\frac{a+b \cosh ^{-1}(c x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)\right)}{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*E^(a/b)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x) - E^((2*a)/b)*Sqrt[a/b + ArcCosh[c*x]]*Gamma[1/2, a/b + ArcCosh[c*x]] + Sqrt[-((a + b*ArcCosh[c*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)])/(b*c*E^(a/b)*Sqrt[a + b*ArcCosh[c*x]])","A",0
157,1,340,276,2.2164579,"\int \frac{x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[x^2/(a + b*ArcCosh[c*x])^(5/2),x]","\frac{e^{-3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)} \left(-6 \sqrt{3} b e^{3 \cosh ^{-1}(c x)} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)-2 b e^{\frac{2 a}{b}+3 \cosh ^{-1}(c x)} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)+2 e^{\frac{4 a}{b}+3 \cosh ^{-1}(c x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)+e^{\frac{3 a}{b}} \left(6 \sqrt{3} e^{3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)-\left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a \left(-4 e^{2 \cosh ^{-1}(c x)}+6 e^{4 \cosh ^{-1}(c x)}+6\right)+b \left(-4 e^{2 \cosh ^{-1}(c x)} \cosh ^{-1}(c x)+6 \cosh ^{-1}(c x)+e^{4 \cosh ^{-1}(c x)} \left(6 \cosh ^{-1}(c x)+1\right)-1\right)\right)\right)\right)}{12 b^2 c^3 \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*E^((4*a)/b + 3*ArcCosh[c*x])*Sqrt[a/b + ArcCosh[c*x]]*(a + b*ArcCosh[c*x])*Gamma[1/2, a/b + ArcCosh[c*x]] - 6*Sqrt[3]*b*E^(3*ArcCosh[c*x])*(-((a + b*ArcCosh[c*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcCosh[c*x]))/b] - 2*b*E^((2*a)/b + 3*ArcCosh[c*x])*(-((a + b*ArcCosh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)] + E^((3*a)/b)*(-((1 + E^(2*ArcCosh[c*x]))*(a*(6 - 4*E^(2*ArcCosh[c*x]) + 6*E^(4*ArcCosh[c*x])) + b*(-1 + 6*ArcCosh[c*x] - 4*E^(2*ArcCosh[c*x])*ArcCosh[c*x] + E^(4*ArcCosh[c*x])*(1 + 6*ArcCosh[c*x])))) + 6*Sqrt[3]*E^(3*(a/b + ArcCosh[c*x]))*Sqrt[a/b + ArcCosh[c*x]]*(a + b*ArcCosh[c*x])*Gamma[1/2, (3*(a + b*ArcCosh[c*x]))/b]))/(12*b^2*c^3*E^(3*(a/b + ArcCosh[c*x]))*(a + b*ArcCosh[c*x])^(3/2))","A",0
158,1,157,188,1.6524204,"\int \frac{x}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[x/(a + b*ArcCosh[c*x])^(5/2),x]","\frac{-2 \sqrt{2 \pi } \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+2 \sqrt{2 \pi } \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)-\frac{\sqrt{b} \left(4 \cosh \left(2 \cosh ^{-1}(c x)\right) \left(a+b \cosh ^{-1}(c x)\right)+b \sinh \left(2 \cosh ^{-1}(c x)\right)\right)}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}}{3 b^{5/2} c^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*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) - 2*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) - (Sqrt[b]*(4*(a + b*ArcCosh[c*x])*Cosh[2*ArcCosh[c*x]] + b*Sinh[2*ArcCosh[c*x]]))/(a + b*ArcCosh[c*x])^(3/2))/(3*b^(5/2)*c^2)","A",0
159,1,192,148,1.082629,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[c*x])^(-5/2),x]","\frac{e^{-\frac{a+b \cosh ^{-1}(c x)}{b}} \left(2 e^{\frac{2 a}{b}+\cosh ^{-1}(c x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)-2 \left(e^{a/b} \left(\left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+b \sqrt{\frac{c x-1}{c x+1}} (c x+1) e^{\cosh ^{-1}(c x)}\right)+b e^{\cosh ^{-1}(c x)} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)\right)\right)}{3 b^2 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*E^((2*a)/b + ArcCosh[c*x])*Sqrt[a/b + ArcCosh[c*x]]*(a + b*ArcCosh[c*x])*Gamma[1/2, a/b + ArcCosh[c*x]] - 2*(E^(a/b)*(b*E^ArcCosh[c*x]*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x) + (1 + E^(2*ArcCosh[c*x]))*(a + b*ArcCosh[c*x])) + b*E^ArcCosh[c*x]*(-((a + b*ArcCosh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)]))/(3*b^2*c*E^((a + b*ArcCosh[c*x])/b)*(a + b*ArcCosh[c*x])^(3/2))","A",0
160,1,394,361,2.5933834,"\int \frac{x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{7/2}} \, dx","Integrate[x^2/(a + b*ArcCosh[c*x])^(7/2),x]","\frac{-2 e^{-\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \left(2 e^{\frac{a}{b}+\cosh ^{-1}(c x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)-2 a-2 b \cosh ^{-1}(c x)+b\right)-2 e^{-\frac{a}{b}} \left(a+b \cosh ^{-1}(c x)\right) \left(e^{\frac{a}{b}+\cosh ^{-1}(c x)} \left(2 a+2 b \cosh ^{-1}(c x)+b\right)+2 b \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)\right)-3 \left(a+b \cosh ^{-1}(c x)\right) \left(12 \sqrt{3} b e^{-\frac{3 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+2 e^{-3 \cosh ^{-1}(c x)} \left(6 \sqrt{3} e^{3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)+6 a \left(e^{6 \cosh ^{-1}(c x)}-1\right)-6 b \cosh ^{-1}(c x)+b e^{6 \cosh ^{-1}(c x)} \left(6 \cosh ^{-1}(c x)+1\right)+b\right)\right)-6 b^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)-6 b^2 \sinh \left(3 \cosh ^{-1}(c x)\right)}{60 b^3 c^3 \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{16 \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c^3 \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{24 x^2 \sqrt{c x-1} \sqrt{c x+1}}{5 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}+\frac{8 x}{15 b^2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{4 x^3}{5 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\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,"(-6*b^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x) - (2*(a + b*ArcCosh[c*x])*(-2*a + b - 2*b*ArcCosh[c*x] + 2*E^(a/b + ArcCosh[c*x])*Sqrt[a/b + ArcCosh[c*x]]*(a + b*ArcCosh[c*x])*Gamma[1/2, a/b + ArcCosh[c*x]]))/E^ArcCosh[c*x] - (2*(a + b*ArcCosh[c*x])*(E^(a/b + ArcCosh[c*x])*(2*a + b + 2*b*ArcCosh[c*x]) + 2*b*(-((a + b*ArcCosh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)]))/E^(a/b) - 3*(a + b*ArcCosh[c*x])*((12*Sqrt[3]*b*(-((a + b*ArcCosh[c*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcCosh[c*x]))/b])/E^((3*a)/b) + (2*(b + 6*a*(-1 + E^(6*ArcCosh[c*x])) - 6*b*ArcCosh[c*x] + b*E^(6*ArcCosh[c*x])*(1 + 6*ArcCosh[c*x]) + 6*Sqrt[3]*E^(3*(a/b + ArcCosh[c*x]))*Sqrt[a/b + ArcCosh[c*x]]*(a + b*ArcCosh[c*x])*Gamma[1/2, (3*(a + b*ArcCosh[c*x]))/b]))/E^(3*ArcCosh[c*x])) - 6*b^2*Sinh[3*ArcCosh[c*x]])/(60*b^3*c^3*(a + b*ArcCosh[c*x])^(5/2))","A",0
161,1,175,229,1.7450362,"\int \frac{x}{\left(a+b \cosh ^{-1}(c x)\right)^{7/2}} \, dx","Integrate[x/(a + b*ArcCosh[c*x])^(7/2),x]","\frac{\frac{\sqrt{b} \left(-\sinh \left(2 \cosh ^{-1}(c x)\right) \left(16 \left(a+b \cosh ^{-1}(c x)\right)^2+3 b^2\right)-4 b \cosh \left(2 \cosh ^{-1}(c x)\right) \left(a+b \cosh ^{-1}(c x)\right)\right)}{\left(a+b \cosh ^{-1}(c x)\right)^{5/2}}+8 \sqrt{2 \pi } \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)+8 \sqrt{2 \pi } \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\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{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{32 x \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}+\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{2 x \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}",1,"(8*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + 8*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + (Sqrt[b]*(-4*b*(a + b*ArcCosh[c*x])*Cosh[2*ArcCosh[c*x]] - (3*b^2 + 16*(a + b*ArcCosh[c*x])^2)*Sinh[2*ArcCosh[c*x]]))/(a + b*ArcCosh[c*x])^(5/2))/(15*b^(7/2)*c^2)","A",0
162,1,214,188,0.7450876,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[c*x])^(-7/2),x]","\frac{-\frac{2 e^{-\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \left(2 e^{\frac{a}{b}+\cosh ^{-1}(c x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c x)} \left(a+b \cosh ^{-1}(c x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c x)\right)-2 a-2 b \cosh ^{-1}(c x)+b\right)}{b^2}-\frac{2 e^{-\frac{a}{b}} \left(a+b \cosh ^{-1}(c x)\right) \left(e^{\frac{a}{b}+\cosh ^{-1}(c x)} \left(2 a+2 b \cosh ^{-1}(c x)+b\right)+2 b \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c x)}{b}\right)\right)}{b^2}-6 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}{15 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{8 \sqrt{c x-1} \sqrt{c x+1}}{15 b^3 c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{4 x}{15 b^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{5 b c \left(a+b \cosh ^{-1}(c x)\right)^{5/2}}",1,"(-6*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x) - (2*(a + b*ArcCosh[c*x])*(-2*a + b - 2*b*ArcCosh[c*x] + 2*E^(a/b + ArcCosh[c*x])*Sqrt[a/b + ArcCosh[c*x]]*(a + b*ArcCosh[c*x])*Gamma[1/2, a/b + ArcCosh[c*x]]))/(b^2*E^ArcCosh[c*x]) - (2*(a + b*ArcCosh[c*x])*(E^(a/b + ArcCosh[c*x])*(2*a + b + 2*b*ArcCosh[c*x]) + 2*b*(-((a + b*ArcCosh[c*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c*x])/b)]))/(b^2*E^(a/b)))/(15*b*c*(a + b*ArcCosh[c*x])^(5/2))","A",0
163,1,118,128,0.4263698,"\int \sqrt{f x} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Integrate[Sqrt[f*x]*(a + b*ArcCosh[c*x])^2,x]","\frac{2}{105} x \sqrt{f x} \left(35 \left(a+b \cosh ^{-1}(c x)\right)^2-4 b c x \left(2 b c x \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)+\frac{7 \sqrt{1-c^2 x^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)}{\sqrt{c x-1} \sqrt{c x+1}}\right)\right)","-\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*x*Sqrt[f*x]*(35*(a + b*ArcCosh[c*x])^2 - 4*b*c*x*((7*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + 2*b*c*x*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])))/105","A",1
164,1,164,181,0.2626697,"\int (d x)^m \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Integrate[(d*x)^m*(a + b*ArcCosh[c*x])^2,x]","\frac{x (d x)^m \left(-\frac{2 b^2 c^2 x^2 \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};c^2 x^2\right)}{m^2+5 m+6}-\frac{2 b c x \sqrt{1-c^2 x^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)}{(m+2) \sqrt{c x-1} \sqrt{c x+1}}+\left(a+b \cosh ^{-1}(c x)\right)^2\right)}{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,"(x*(d*x)^m*((a + b*ArcCosh[c*x])^2 - (2*b*c*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/((2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b^2*c^2*x^2*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, c^2*x^2])/(6 + 5*m + m^2)))/(1 + m)","A",1
165,1,87,106,0.1461923,"\int (d x)^m \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(d*x)^m*(a + b*ArcCosh[c*x]),x]","\frac{x (d x)^m \left(a-\frac{b c x \sqrt{1-c^2 x^2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{(m+2) \sqrt{c x-1} \sqrt{c x+1}}+b \cosh ^{-1}(c x)\right)}{m+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,"(x*(d*x)^m*(a + b*ArcCosh[c*x] - (b*c*x*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/((2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])))/(1 + m)","A",1
166,0,0,19,0.5041335,"\int \frac{(d x)^m}{a+b \cosh ^{-1}(c x)} \, dx","Integrate[(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,"Integrate[(d*x)^m/(a + b*ArcCosh[c*x]), x]","A",-1