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Integrate[(c^3 + x^3)^(-1 - n), x] ==
-(((-((c + x)/((-1 + (-1)^(2/3))*c)))^(1 + n)* ((-1)^(2/3)*c + x)*((c + (-1)^(2/3)*x)/ ((1 + (-1)^(1/3))*c))^(1 + n)* (c^3 + x^3)^(-1 - n)*AppellF1[-n, 1 + n, 1 + n, 1 - n, ((-I)*((-1)^(2/3)*c + x))/(Sqrt[3]*c), ((-1)^(2/3)*c + x)/((-1 + (-1)^(2/3))*c)])/n)

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

           c + x        1 + n      2/3
-(((-(----------------))      ((-1)    c + x) 
                2/3
      (-1 + (-1)   ) c
 
                2/3
        c + (-1)    x  1 + n   3    3 -1 - n
      (---------------)      (c  + x )       
                1/3
       (1 + (-1)   ) c
 
      AppellF1[-n, 1 + n, 1 + n, 1 - n, 
 
               2/3              2/3
       -I ((-1)    c + x)   (-1)    c + x
       ------------------, ----------------]) / n)
           Sqrt[3] c                 2/3
                           (-1 + (-1)   ) c