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((3*c^2*x)/(c^3 - x^3) + 2*Sqrt[3]*ArcTan[(c + 2*x)/(Sqrt[3]*c)] - 2*Log[-c + x] + Log[c^2 + c*x + x^2])/(9*c^5)


Integrate[(c^3 - x^3)^(-2), x] ==
((3*c^2*x)/(c^3 - x^3) + 2*Sqrt[3]* ArcTan[(c + 2*x)/(Sqrt[3]*c)] - 2*Log[-c + x] + Log[c^2 + c*x + x^2])/(9*c^5)



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

    2
 3 c  x                      c + 2 x
(------- + 2 Sqrt[3] ArcTan[---------] - 
  3    3                    Sqrt[3] c
 c  - x
 
                         2          2         5
    2 Log[-c + x] + Log[c  + c x + x ]) / (9 c )

Time to compute: 0.12 second

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