# Primitive of Square of Cosine Function/Corollary

## Corollary to Primitive of Square of Cosine Function

$\displaystyle \int \cos^2 x \rd x = \frac {x + \sin x \cos x} 2 + C$

where $C$ is an arbitrary constant.

## Proof

 $\displaystyle \int \sin^2 x \rd x$ $=$ $\displaystyle \frac x 2 + \frac {\sin 2 x} 4 + C$ Primitive of Square of Cosine Function $\displaystyle$ $=$ $\displaystyle \frac x 2 + \frac {2 \sin x \cos x} 4 + C$ Double Angle Formula for Sine $\displaystyle$ $=$ $\displaystyle \frac {x + \sin x \cos x} 2 + C$

$\blacksquare$