# Primitive of Reciprocal of Cotangent of a x

## Theorem

$\displaystyle \int \frac {\d x} {\cot a x} = \frac {-\ln \size {\cos a x} } a + C$

## Proof

 $\displaystyle \int \frac {\d x} {\cot a x}$ $=$ $\displaystyle \int \tan a x \rd x$ Cotangent is Reciprocal of Tangent $\displaystyle$ $=$ $\displaystyle \frac {-\ln \size {\cos a x} } a + C$ Primitive of $\tan a x$

$\blacksquare$