How to evaluate $\int { \frac { dx }{ { 2x }^{ 4 }+{ 2x }^{ 2 }+1 } }$? How to integrate something like 
$\int { \frac { dx }{ { 2x }^{ 4 }+{ 2x }^{ 2 }+1 }  }$
I know the method of partial fractions.
But what if the denominator is not factorizeable like the one in the question?

First pull out any constant coefficient of $x^4$ to get a monic polynomial.
In $$ x^4 + B x^2 + C  $$ with $$ B^2 - 4 C < 0,  $$ so that $C > 0,$ we get
$$ x^4 + B x^2 + C = (x^2 + \lambda x + \sqrt C)  (x^2 - \lambda x + \sqrt C),  $$
where
$$ \lambda = \sqrt {2 \sqrt C - B}  $$
is also real.
The original problem was edited to $2 x^4 + 2 x^2 + 1 = 2 \left(x^4 + x^2 + \frac{1}{2} \right);$
$$ x^4 + x^2 + \frac{1}{2} = \left(x^2 + \sqrt{\sqrt 2 - 1} \; x +  \frac{1}{\sqrt 2} \right)  \left(x^2 -  \sqrt{\sqrt 2 - 1} \; x + \frac{1}{\sqrt 2} \right)   $$
