Did I do this right, is so did I get the right answer and if not, could you point out some things I did wrong? Thanks in advance.

$\displaystyle \intx*sin x dx$

$\displaystyle u=x$ and $\displaystyle v'= sin x$

$\displaystyle u'=1$ and v= $\displaystyle -cos x$

$\displaystyle uv-\int u'v dx$ so... $\displaystyle -x cos x - \int -cos x dx = -x cos x + sin x +C$