Having a dum blonde moment...
Would...
$\displaystyle \int{\frac{2u+7}{u^6}}du$
be...
$\displaystyle \int{2u+7}du\int{\frac{1}{u^6}}du$
or...
$\displaystyle \int{(2u+7)(u^{-6})}$
with the product rule...
$\displaystyle \int{\frac{2u+7}{u^6}}du $ $\displaystyle = \int{\frac{2u}{u^{6}}} $ $\displaystyle +\frac{7}{u^{6}}du $ $\displaystyle = \frac{2}{u^{5}}+ \frac{7}{u^{6}}du $
Then just bring U's up to the top line
i.e. $\displaystyle \int{2u^{-5}}+{7u^{-6}}du $ and integrate normally w.r.t u