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

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

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

                      2    2
          a    a Log[a  - x ]
x ArcTanh[-] + --------------
          x          2
Time to compute: < 0.01 second
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