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Integrate[(c^3 + x^3)^(-1 - n)/x^2, x] ==
-((1 + x^3/c^3)^n*(2*c^3*Hypergeometric2F1[-1/3, n, 2/3, -(x^3/c^3)] + x^3*Hypergeometric2F1[2/3, 1 + n, 5/3, -(x^3/c^3)]))/ (2*c^6*x*(c^3 + x^3)^n)

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

        3
       x  n     3                     1      2
-((1 + --)  (2 c  Hypergeometric2F1[-(-), n, -, 
        3                             3      3
       c
 
            3
           x       3                   2         5
         -(--)] + x  Hypergeometric2F1[-, 1 + n, -, 
            3                          3         3
           c
 
            3
           x            6     3    3 n
         -(--)])) / (2 c  x (c  + x ) )
            3
           c