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

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

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