Answer
$\left\langle1, \frac{7}{3}, \frac{15}{4}\right\rangle.$
Work Step by Step
We can write
\begin{align}
\int_{1/2}^{1}\left\langle \frac{1}{ u^2},\frac{1}{ u^4},\frac{1}{ u^5}\right\rangle du&=\left\langle- \frac{1}{ u},-\frac{1}{ 3u^3},-\frac{1}{4 u^4}\right\rangle|_{1/2}^{1}\\
&\left\langle-1,-\frac{1}{ 3 },-\frac{1}{4 }\right\rangle-\left\langle- 2,-\frac{8}{ 3},-4\right\rangle\\
&= \left\langle1, \frac{7}{3}, \frac{15}{4}\right\rangle.
\end{align}
