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


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



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

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

Time to compute: 0.07 second

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