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

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

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

   2         2    3    3
-(a  x)   a x    x    a  Log[a + b x]
------- + ---- - -- + --------------- + 
    2     6 b    9            3
 3 b                       3 b
 
   3
  x  Log[a + b x]
  ---------------
         3
Time to compute: < 0.01 second
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