I'm been working problems to help learn the substitution rule for integrals. Is this correct?

$\displaystyle \int\frac{{\sin{\ln{x}}}}{x}dx$

Let $\displaystyle u=\ln{x}$ and $\displaystyle du = \frac{1}{x}dx$.

$\displaystyle = \int{\sin{u}du}$

$\displaystyle = -\cos{u} + c$

$\displaystyle = -\cos{\ln{x}} + c$

Thanks,