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(x^2*(1 + x^3/c^3)^n*Hypergeometric2F1[2/3, 1 + n, 5/3, -(x^3/c^3)])/(2*c^3*(c^3 + x^3)^n)


Integrate[x*(c^3 + x^3)^(-1 - n), x] ==
(x^2*(1 + x^3/c^3)^n*Hypergeometric2F1[2/3, 1 + n, 5/3, -(x^3/c^3)])/(2*c^3*(c^3 + x^3)^n)



              3    3 -1 - n
Integrate[x (c  + x )      , x] == 

         3                                     3
 2      x  n                   2         5    x
x  (1 + --)  Hypergeometric2F1[-, 1 + n, -, -(--)]
         3                     3         3     3
        c                                     c
--------------------------------------------------
                    3   3    3 n
                 2 c  (c  + x )

Time to compute: 0.04 second

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