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-(a^2*x)/3 + (a*x^2)/6 - x^3/9 + (a^3*Log[a + x])/3 + (x^3*Log[a + x])/3


Integrate[x^2*Log[a + x], x] ==
-(a^2*x)/3 + (a*x^2)/6 - x^3/9 + (a^3*Log[a + x])/3 + (x^3*Log[a + x])/3



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

   2         2    3    3               3
-(a  x)   a x    x    a  Log[a + x]   x  Log[a + x]
------- + ---- - -- + ------------- + -------------
   3       6     9          3               3

Time to compute: < 0.01 second

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