# Primitive of Reciprocal of Square of Sine of a x

## Theorem

$\displaystyle \int \frac {\mathrm d x} {\sin^2 a x} = \frac {-\cot a x} a + C$

## Proof

 $\displaystyle \int \frac {\mathrm d x} {\sin^2 a x}$ $=$ $\displaystyle \int \csc^2 a x \ \mathrm d x$ Definition of Cosecant $\displaystyle$ $=$ $\displaystyle \frac {-\cot a x} a + C$ Primitive of $\csc^2 a x$

$\blacksquare$