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


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



              1
Integrate[---------, x] == 
                  3
          -1 + 2 x

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

Time to compute: 0.05 second

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