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

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

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

  a d Log[a + b x] - b c Log[c + d x]
-(-----------------------------------)
             2            2
            b  c d - a b d
Time to compute: 0.04 second
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