Chapter 7 - Integration Techniques - 7.2 Integration by Parts - 7.2 Exercises - Page 520: 3

$$u = {x^n}$$

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