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

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

         2
x (-3 + x )   ArcTan[Sqrt[2] x]
----------- + -----------------
     3             Sqrt[2]