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


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



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

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

Time to compute: 0.27 second

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