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


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



                   1
Integrate[--------------------, x] == 
                   2
          (a + b x)  (c + d x)

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

Time to compute: 0.07 second

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