Answer
$$u = {x^n}$$
Work Step by Step
$$\eqalign{
& \int {{x^n}\cos axdx} \cr
& {\text{We can choose }}{x^n}{\text{ as }}u,{\text{ because by the power rule}} \cr
& du = n{x^{n - 1}}{\text{ the exponent will be reducing, and then we}} \cr
& {\text{need to choose }}\cos axdx{\text{ as }}dv. \cr
& u = {x^n} \cr} $$