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

Integrate[1/(x^2*(c^3 - x^3)), x] ==
-(6*c + 2*Sqrt[3]*x*ArcTan[(c + 2*x)/(Sqrt[3]*c)] + 2*x*Log[-c + x] - x*Log[c^2 + c*x + x^2])/(6*c^4*x) 

               1
Integrate[------------, x] == 
           2   3    3
          x  (c  - x )

                            c + 2 x
-(6 c + 2 Sqrt[3] x ArcTan[---------] + 
                           Sqrt[3] c
 
                              2          2
     2 x Log[-c + x] - x Log[c  + c x + x ]) / 
 
      4
  (6 c  x)
Time to compute: 0.05 second
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