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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^2)

Integrate[1/(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^2) 

             1
Integrate[-------, x] == 
           3    3
          c  - x

                   c + 2 x
(2 Sqrt[3] ArcTan[---------] - 2 Log[-c + x] + 
                  Sqrt[3] c
 
         2          2         2
    Log[c  + c x + x ]) / (6 c )
Time to compute: 0.02 second
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