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(x*(-3 + x^4)*Sqrt[2 + x^(-4) + x^4])/(3*(1 + x^4))

Integrate[Sqrt[2 + x^(-4) + x^4], x] ==
(x*(-3 + x^4)*Sqrt[2 + x^(-4) + x^4])/(3*(1 + x^4)) 

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

         4            -4    4
x (-3 + x ) Sqrt[2 + x   + x ]
------------------------------
                  4
          3 (1 + x )
Time to compute: 0.02 second
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