Integrating cos² x

by Paweł Redman, published on

1. Using the Pythagorean identity

Integrate by parts using and :

Add to both sides:

Apply integral linearity:

Apply the Pythagorean identity and divide both sides by 2:

2. Using the double angle formula

Rewrite the integral using the double angle formula for the cosine:

Substitute :

Substitute back and simplify: