# Primitive of Reciprocal of Secant of a x

## Theorem

$\displaystyle \int \frac {\d x} {\sec a x} = \frac {\sin a x} a + C$

## Proof

 $\displaystyle \int \frac {\d x} {\sec a x}$ $=$ $\displaystyle \int \cos a x \rd x$ Secant is Reciprocal of Cosine $\displaystyle$ $=$ $\displaystyle \frac {\sin a x} a + C$ Primitive of $\cos a x$

$\blacksquare$