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Integrate[1/(-2 + x^6), x] ==
-(2*Sqrt[3]*ArcTan[(-1 + 2^(5/6)*x)/Sqrt[3]] + 2*Sqrt[3]*ArcTan[(1 + 2^(5/6)*x)/Sqrt[3]] - 2*Log[-2 + 2^(5/6)*x] + 2*Log[2 + 2^(5/6)*x] - Log[2 - 2^(5/6)*x + 2^(2/3)*x^2] + Log[2 + 2^(5/6)*x + 2^(2/3)*x^2])/(12*2^(5/6))



             1
Integrate[-------, x] == 
                6
          -2 + x

                         5/6
                   -1 + 2    x
-(2 Sqrt[3] ArcTan[-----------] + 
                     Sqrt[3]
 
                           5/6
                      1 + 2    x
     2 Sqrt[3] ArcTan[----------] - 
                       Sqrt[3]
 
                 5/6                 5/6
     2 Log[-2 + 2    x] + 2 Log[2 + 2    x] - 
 
              5/6      2/3  2
     Log[2 - 2    x + 2    x ] + 
 
              5/6      2/3  2          5/6
     Log[2 + 2    x + 2    x ]) / (12 2   )

Time to compute: 0.11 second

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