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(x*(-6*a^2 + 3*a*x - 2*x^2) + 6*(a^3 + x^3)*Log[a + x])/18

Integrate[x^2*Log[a + x], x] ==
(x*(-6*a^2 + 3*a*x - 2*x^2) + 6*(a^3 + x^3)* Log[a + x])/18 

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

       2              2        3    3
x (-6 a  + 3 a x - 2 x ) + 6 (a  + x ) Log[a + x]
-------------------------------------------------
                       18
Time to compute: < 0.01 second
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