How do I even go about solving this? I get as far as u = x^4+1 and du = 4x^3
Alright so I changed it so that it's $\displaystyle u = x^2+1$ and $\displaystyle du = 2x dx$.
Eventually I get to $\displaystyle 4 \int du * 1/u^2$ and couldn't proceed.
The du becomes x^2 but I don't know what to do with the second one. It could become arctan u, but the fact that it's $\displaystyle 1/u^2$ and not just $\displaystyle 1/u$ prevents that from happening.
Alright so
$\displaystyle 4 \int 2x/(x^4+1)$
$\displaystyle u = x^2$, $\displaystyle du = 2x$
$\displaystyle 4 \int du/(u^2+1)$
Do I separate? Does it become $\displaystyle 4 \int du * 1/(u^2+1)$?
In which case the answer should be 4 * x^2 * arctan x^2 + C, right?