I need to use the reduction formula for this problem.

$\displaystyle \int(\ln{x})^{n} dx$ where $\displaystyle n\geqslant{2}$

Would these be the best choices for the integration?

$\displaystyle u=(\ln{x})^{n-1}$

$\displaystyle du=(\tfrac{1}{x})(n-1)(\ln{x})^{n-2} dx$

$\displaystyle dv=\ln{x} dx$

$\displaystyle v=x\ln{x}-x$