Looking to integrate the following.

$\displaystyle \int \frac{x^4}{x^2 + 1} dx$

We usually have to re-write the denominator as a negative and solve that way yeah? For example...

$\displaystyle \int \frac{x^4 + 1}{x^2}$

is

$\displaystyle \int x^2 + x^-2$ and integrate.

How do I solve it though with the +1 on the denominator? This might be a really really stupid question, but I can't simplify..... can I?

P.s. This is more of a problem about simplifying rather than integration I suspect.