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-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[-1 + x]/3 - Log[1 + x + x^2]/6

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

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

         1 + 2 x
  ArcTan[-------]                               2
         Sqrt[3]     Log[-1 + x]   Log[1 + x + x ]
-(---------------) + ----------- - ---------------
      Sqrt[3]             3               6
Time to compute: 0.02 second
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