Integral $\int \sqrt{4+4x^2+1/x^2} dx$ I'm totally lost on how I would integrate the following function:
$f(x) = \sqrt{4+4x^2+1/x^2}$ 
If anyone could even just point me to the method of integration that would be grand.

$$4 + 4x^2 + \dfrac1{x^2} = \left(2x + \dfrac1x \right)^2$$
Hence,
\begin{align}
\sqrt{4 + 4x^2 + \dfrac1{x^2}} & = \begin{cases} 2x + \dfrac1x & x > 0\\ -\left( 2x + \dfrac1x\right) & x < 0\end{cases}\\
& = 2 \vert x \vert + \dfrac1{\vert x \vert}
\end{align}
