# Primitive of Reciprocal of Sine of a x

## Theorem

### Logarithm of Cosecant minus Cotangent Form

$\ds \int \frac {\d x} {\sin a x} = \frac 1 a \ln \size {\csc a x - \cot a x} + C$

### Logarithm of Tangent Form

$\ds \int \frac {\d x} {\sin a x} = \frac 1 a \ln \size {\tan \frac {a x} 2} + C$