# Primitive of Cosine Function/Corollary

## Corollary to Primitive of Cosine Function

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

where $a$ is a non-zero constant.

## Proof

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

$\blacksquare$