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Integrate[1/(2 + x^2 + x^4), x] ==
((-I)*ArcTan[x/Sqrt[(1 - I*Sqrt[7])/2]])/ Sqrt[(7*(1 - I*Sqrt[7]))/2] + (I*ArcTan[x/Sqrt[(1 + I*Sqrt[7])/2]])/ Sqrt[(7*(1 + I*Sqrt[7]))/2]



               1
Integrate[-----------, x] == 
               2    4
          2 + x  + x

                   x
-I ArcTan[-------------------]
               1 - I Sqrt[7]
          Sqrt[-------------]
                     2
------------------------------ + 
        7 (1 - I Sqrt[7])
   Sqrt[-----------------]
                2
 
                    x
  I ArcTan[-------------------]
                1 + I Sqrt[7]
           Sqrt[-------------]
                      2
  -----------------------------
          7 (1 + I Sqrt[7])
     Sqrt[-----------------]
                  2

Time to compute: 0.47 second

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