integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫

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


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



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

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

Time to compute: 0.10 second

Spread the word: