Answer
$$\frac{-1}{2\left(x^{5}+x^{2}\right)^2}+c$$
Work Step by Step
Given $$\int \frac{5 x^{4}+2 x}{\left(x^{5}+x^{2}\right)^{3}} d x$$
Let
$$u=x^{5}+x^{2} \ \ \ \Rightarrow \ \ du=(5x^4+2x^2)dx $$
then
\begin{align*}
\int \frac{5 x^{4}+2 x}{\left(x^{5}+x^{2}\right)^{3}} d x&= \int \frac{du}{u^3} \\
&=\frac{-1}{2u^2}+c\\
&=\frac{-1}{2\left(x^{5}+x^{2}\right)^2}+c
\end{align*}
