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

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

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

a (3 a + 2 b x)
--------------- + 2 Log[x] - 2 Log[a + b x]
           2
  (a + b x)
-------------------------------------------
                      3
                   2 a
Time to compute: 0.07 second
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