Answer
$\frac{(x^2+5)^{-3}}{-3}+c$
Work Step by Step
$u=x^2+5$, therefore $du=2xdx$. Let's rewrite the integral! $\int (2x(x^2+5)^{-4})dx=\int ((x^2+5)^{-4})2xdx$
We do the substitution! $\int ((x^2+5)^{-4})2xdx=\int u^{-4}du=\frac{u^{-3}}{-3}+c$ We re-do the substitution! $\frac{u^{-3}}{-3}+c=\frac{(x^2+5)^{-3}}{-3}+c$