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



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

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

Time to compute: 0.13 second

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