Answer
$-\frac{1}{21}.$
Work Step by Step
We have
\begin{align*}
\int_{-3}^{-1} x(x^2+5)^{-2} dx&=
\frac{1}{2}\int_{-3}^{-1} 2x(x^2+5)^{-2} dx\\
&=-\frac{1}{2} (x^2+5)^{-1}|_{-3}^{-1}\\
&=-\frac{1}{2}\frac{1}{6}+\frac{1}{2}\frac{1}{14}\\
&=-\frac{1}{21}.
\end{align*}
