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

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

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

                 a       a + x               a
x (-(a Sqrt[-1 + -] Sqrt[-----]) + x ArcCosh[-])
                 x         x                 x
------------------------------------------------
                       2
Time to compute: 0.10 second
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