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-1/(2*a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3

Integrate[1/(x^3*(a + b*x)), x] ==
-1/(2*a*x^2) + b/(a^2*x) + (b^2*Log[x])/a^3 - (b^2*Log[a + b*x])/a^3 

               1
Integrate[------------, x] == 
           3
          x  (a + b x)

                 2           2
  -1      b     b  Log[x]   b  Log[a + b x]
------ + ---- + --------- - ---------------
     2    2         3              3
2 a x    a  x      a              a
Time to compute: 0.01 second
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