Answer
$$\frac{1}{25} e^{5x+2}(5x-1)+c.$$
Work Step by Step
We do the integration by parts; we choose $u=x$ and $dv=e^{5x+2}dx$. Then, $du=dx$, $v=\frac{1}{5}e^{5x+2}$
$$\int xe^{5x+2}dx=\int udv=uv-\int vdu\\
=\frac{x}{5}e^{5x+2}- \frac{1}{5}\int e^{5x+2}dx\\
=\frac{x}{5}e^{5x+2}- \frac{1}{25} e^{5x+2}+c \\
=\frac{1}{25} e^{5x+2}(5x-1)+c.$$
