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

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

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

          a
x ArcCosh[-] + 
          x
 
               a         a + x               x
   a Sqrt[-1 + -] x Sqrt[-----] ArcTan[-------------]
               x           x                 2    2
                                       Sqrt[a  - x ]
   --------------------------------------------------
                           2    2
                     Sqrt[a  - x ]
Time to compute: 0.29 second
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