What do I do when the power in the numerator is larger than the denomenator
e^16x / 4+e^8x
I think so, yes.
$\displaystyle u = e^{8x} $
$\displaystyle \frac{du}{dx} = 8e^{8x} $
$\displaystyle dx = \frac{du}{8e^{8x}} = \frac{du}{8u} $
$\displaystyle \int \frac{u^2}{u+4}\frac{du}{8u} $
$\displaystyle = \frac{1}{8} \int\frac{u}{u+4} du $
$\displaystyle = \frac{1}{8} \int\frac{u+4}{u+4} - \frac{4}{u+4} du $
$\displaystyle = \frac{1}{8} \int 1 - \frac{4}{u+4} du $