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


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



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

  2         2           2
-x  + (a + x ) Log[a + x ]
--------------------------
            2

Time to compute: < 0.01 second

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