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

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

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

           n
        b x  m                          1      1
(x (1 + ----)  Hypergeometric2F1[1 + m, -, 1 + -, 
         a                              n      n
 
          n
       b x                  n m
     -(----)]) / (a (a + b x ) )
        a
Time to compute: 0.06 second
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