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

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

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