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x - a*ArcTanh[x/a]

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

              2
             x
Integrate[--------, x] == 
            2    2
          -a  + x

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