$\displaystyle \int_0^\infty {x\sin (x)\cos (x)dx}

$

I tried:

u=xsinx, du=xcox+sinx

v=sinx, dv=cosx

$\displaystyle (x\sin x)(\sin x) - \int {(xcoxs + \sin x)(\sin x)dx}

$

$\displaystyle (x\sin x)(\sin x) - \int {x\cos x\sin x + {{\sin }^2}xdx}

$

but then I got stuck on integrating...