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x*ArcCoth[a/x] + (a*Log[a^2 - x^2])/2


Integrate[ArcCoth[a/x], x] ==
x*ArcCoth[a/x] + (a*Log[a^2 - x^2])/2



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

                      2    2
          a    a Log[a  - x ]
x ArcCoth[-] + --------------
          x          2

Time to compute: < 0.01 second

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