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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         4
     2 x Log[c + x] + x Log[c  - c x + x ]) / (6 c  x)

Time to compute: 0.05 second

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