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

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

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