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-(Sqrt[-1 + x]*x*Sqrt[1 + x])/4 + (x^2*ArcCosh[x])/2 - Log[2*(x + Sqrt[-1 + x]*Sqrt[1 + x])]/4

Integrate[x*ArcCosh[x], x] ==
-(Sqrt[-1 + x]*x*Sqrt[1 + x])/4 + (x^2*ArcCosh[x])/2 - Log[2*(x + Sqrt[-1 + x]*Sqrt[1 + x])]/4 

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

                                 2
-(Sqrt[-1 + x] x Sqrt[1 + x])   x  ArcCosh[x]
----------------------------- + ------------- - 
              4                       2
 
  Log[2 (x + Sqrt[-1 + x] Sqrt[1 + x])]
  -------------------------------------
                    4
Time to compute: 0.04 second
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