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(-2*Sqrt[3]*ArcTan[(c + 2*x)/(Sqrt[3]*c)] - 2*Log[-c + x] + Log[c^2 + c*x + x^2])/(6*c)


Integrate[x/(c^3 - x^3), x] ==
(-2*Sqrt[3]*ArcTan[(c + 2*x)/(Sqrt[3]*c)] - 2*Log[-c + x] + Log[c^2 + c*x + x^2])/(6*c)



             x
Integrate[-------, x] == 
           3    3
          c  - x

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

Time to compute: 0.02 second

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