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


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



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

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

Time to compute: 0.06 second

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