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(a^3*x)/(4*b^3) - (a^2*x^2)/(8*b^2) + (a*x^3)/(12*b) - x^4/16 - (a^4*Log[a + b*x])/(4*b^4) + (x^4*Log[a + b*x])/4


Integrate[x^3*Log[a + b*x], x] ==
(a^3*x)/(4*b^3) - (a^2*x^2)/(8*b^2) + (a*x^3)/(12*b) - x^4/16 - (a^4*Log[a + b*x])/ (4*b^4) + (x^4*Log[a + b*x])/4



           3
Integrate[x  Log[a + b x], x] == 

 3      2  2      3    4    4
a  x   a  x    a x    x    a  Log[a + b x]
---- - ----- + ---- - -- - --------------- + 
   3      2    12 b   16           4
4 b    8 b                      4 b
 
   4
  x  Log[a + b x]
  ---------------
         4

Time to compute: < 0.01 second

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