# Primitive of Cosine Function/Corollary

## Corollary to Primitive of Cosine Function

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

where $C$ is an arbitrary constant.

## Proof

 $\displaystyle \int \cos x \rd x$ $=$ $\displaystyle \sin x + C$ Primitive of $\cos x$ $\displaystyle \leadsto \ \$ $\displaystyle \int \cos a x \rd x$ $=$ $\displaystyle \frac 1 a \paren {\sin a x} + C$ Primitive of Function of Constant Multiple $\displaystyle$ $=$ $\displaystyle \frac {\sin a x} a + C$ simplifying

$\blacksquare$