1. The problem statement, all variables and given/known data Integrate cos^n x cos nx 2. Relevant equations Integration by part equations, trigonometric integrals 3. The attempt at a solution I was given the hint that this integration involves integration by part and trigonometry integrals. I tried integration by part, by assigning v=cos^n x and du/dx=cos nx, but that failed. I thought of converting the cos nx, so that the term cos x may appear and enables me to integrate cos^n x, but so far all my attempt have failed.