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

           2   3    3 -1 - n
Integrate[x  (c  - x )      , x] == 

      1
--------------
      3    3 n
3 n (c  - x )