Answer
$-2x\cos(\frac{x}{2})+4\sin(\frac{x}{2})+C$
Work Step by Step
We use the formula $\int udv=uv-\int vdu$
with $u=x,\,dv=\sin \frac{x}{2}dx$
$du=dx,\,v=-2\cos(\frac{x}{2})$
Then, $\int x\sin\frac{x}{2}dx=x\times-2\cos(\frac{x}{2})-\int-2\cos(\frac{x}{2})dx$
$=-2x\cos(\frac{x}{2})+4\sin(\frac{x}{2})+C$
