Answer
\begin{equation*}
=5ye^{0.2y}-25e^{0.2y}+C
\end{equation*}
Work Step by Step
$\int ye^{0.2y}dy$
Let $u=y$ and $dv=e^{0.2y}dy$
then $du=dy$ and $v=\frac{e^{0.2y}}{0.2}=5e^{0.2y}$
and therefore
\begin{equation*}
\int ye^{0.2y}dy=5ye^{0.2y}-\int 5e^{0.2y}dy
\end{equation*}
\begin{equation*}
=5ye^{0.2y}-25e^{0.2y}+C
\end{equation*}
