Primitive of Cosecant Function/Cosecant plus Cotangent Form

Theorem

 * $\displaystyle \int \csc {\theta} \ \mathrm d \theta = -\ln \left \vert {\csc \theta + \cot \theta} \right \vert + C$

where $\csc \theta + \cot \theta \ne 0$.

Corollary

 * $\displaystyle \int \csc {\theta} \ \mathrm d \theta = \ln \left \vert {\csc \theta - \cot \theta} \right \vert + C$

where $\csc \theta - \cot \theta \ne 0$.