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-((Sqrt[-1 + a*x]*Sqrt[1 + a*x])/a) + x*ArcCosh[a*x]

Integrate[ArcCosh[a*x], x] ==
-((Sqrt[-1 + a*x]*Sqrt[1 + a*x])/a) + x*ArcCosh[a*x] 

Integrate[ArcCosh[a x], x] == 

  Sqrt[-1 + a x] Sqrt[1 + a x]
-(----------------------------) + x ArcCosh[a x]
               a
Time to compute: 0.05 second
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