integration x sin x dx
You can do this by parts:
$\displaystyle u=x$ and $\displaystyle \,dv=\sin x\,dx$
Thus, $\displaystyle \,du=\,dx$ and $\displaystyle v=-\cos x$
Now I leave it for you to plug it into the integration by parts formula and simplify:
$\displaystyle \int u\,dv=uv-\int v\,du$
Can you take it from here?
--Chris