Answer
$-\frac{3}{4}\quad $
Work Step by Step
\begin{aligned} \int_{\sqrt{2}}^{1}\left(\frac{u^{7}}{2}-\frac{1}{u^{5}}\right) d u&=\int_{\sqrt{2}}^{1}\left(\frac{u^{7}}{2}-u^{-5}\right) d u\\
&= \frac{1}{16}u^{8}+ \frac{1}{4}u^{-4}\bigg|_{\sqrt{2}}^{1}\\
&= \frac{1}{16}+ \frac{1}{4}- 1-\frac{1}{16}\\
&=-\frac{3}{4}\quad \end{aligned}