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

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

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

       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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