Primitive of Cosecant Function/Cosecant plus Cotangent Form

Theorem

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

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

Corollary

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

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