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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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