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



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

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

Time to compute: 0.18 second

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