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

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

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

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