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Integrate[1/((a + b*x)^n*(c + d*x)^m), x] ==
-((((d*(a + b*x))/(-(b*c) + a*d))^n*(c + d*x)^(1 - m)* Hypergeometric2F1[1 - m, n, 2 - m, (b*(c + d*x))/(b*c - a*d)])/ (d*(-1 + m)*(a + b*x)^n))



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

    d (a + b x)  n          1 - m
-(((------------)  (c + d x)      
    -(b c) + a d
 
                                         b (c + d x)
      Hypergeometric2F1[1 - m, n, 2 - m, -----------])
                                          b c - a d
 
                             n
      / (d (-1 + m) (a + b x) ))

Time to compute: 0.17 second

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