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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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