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(a*Sqrt[1 + a^2/x^2]*x*(-2*a^2 + x^2))/12 + (x^4*ArcSinh[a/x])/4

Integrate[x^3*ArcSinh[a/x], x] ==
(a*Sqrt[1 + a^2/x^2]*x*(-2*a^2 + x^2))/12 + (x^4*ArcSinh[a/x])/4 

           3         a
Integrate[x  ArcSinh[-], x] == 
                     x

            2
           a          2    2
a Sqrt[1 + --] x (-2 a  + x )    4         a
            2                   x  ArcSinh[-]
           x                               x
----------------------------- + -------------
             12                       4
Time to compute: 0.07 second
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