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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: 0.09 second

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