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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 )