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

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

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

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