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(x*(3 - 2*x^2)*Sqrt[1 + x^2] + (-3 + 8*x^4)*ArcSinh[x])/32

Integrate[x^3*ArcSinh[x], x] ==
(x*(3 - 2*x^2)*Sqrt[1 + x^2] + (-3 + 8*x^4)*ArcSinh[x])/32 

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

          2            2             4
x (3 - 2 x ) Sqrt[1 + x ] + (-3 + 8 x ) ArcSinh[x]
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                        32
Time to compute: 0.04 second
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