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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: 0.15 second

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