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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 ) )