Answer
\begin{equation*}
=x\frac{\sin{5x}}{5}+\frac{\cos{5x}}{25}+C
\end{equation*}
Work Step by Step
$\int x\cos{5x}dx$
Let $u=x$ and $dv=\cos{5x}dx$
then $du=dx$ and $v=\frac{\sin{5x}}{5}$
and therefore
\begin{equation*}
\int x\cos{5x}dx=x\frac{\sin{5x}}{5}-\int\frac{\sin{5x}}{5}dx
\end{equation*}
\begin{equation*}
=x\frac{\sin{5x}}{5}+\frac{\cos{5x}}{25}+C
\end{equation*}
