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

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

                   x
Integrate[--------------------, x] == 
                   2
          (a + b x)  (c + d x)

           a              c Log[a + b x]
----------------------- + -------------- - 
b (b c - a d) (a + b x)               2
                           (b c - a d)
 
  c Log[c + d x]
  --------------
              2
   (b c - a d)
Time to compute: 0.08 second
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