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((6*c*x^2)/(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])/(18*c^4)


Integrate[x/(c^3 + x^3)^2, x] ==
((6*c*x^2)/(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])/(18*c^4)



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

      2
 6 c x                      -c + 2 x
(------- + 2 Sqrt[3] ArcTan[---------] - 
  3    3                    Sqrt[3] c
 c  + x
 
                        2          2          4
    2 Log[c + x] + Log[c  - c x + x ]) / (18 c )

Time to compute: 0.08 second

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