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

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

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

            2  2
  Sqrt[1 + a  x ]
-(---------------) + x ArcSinh[a x]
         a
Time to compute: 0.02 second
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