Primitive of Cosecant Function/Tangent Form/Proof 2

Theorem

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

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

Proof
We make the Weierstrass Substitution: