Answer
\[ = x\sin x + \cos \,x + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {x\cos x\,dx} \hfill \\
\hfill \\
set{\text{ }}u = x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,then\,\,\,du = dx \hfill \\
du = \cos x\,dx\,\,\,\,\,\,\,\,then\,\,\,\,\,\,\,\,\,v = \sin x \hfill \\
\hfill \\
use\,\,\,uv - \int_{}^{} {vdu} \hfill \\
\hfill \\
{\text{replacing the values }}{\text{in the equation}} \hfill \\
\hfill \\
x\sin x - \int_{}^{} {\sin x\,dx} \hfill \\
\hfill \\
\operatorname{int} egrate\,\, \hfill \\
\hfill \\
= x\sin x + \cos \,x + C \hfill \\
\hfill \\
\end{gathered} \]