Primitive of Product of Cosecant and Cotangent

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Theorem

$\displaystyle \int \csc x \cot x \rd x = -\csc x + C$

where $C$ is an arbitrary constant.


Proof

From Derivative of Cosecant Function:

$\dfrac \d {\d x} \csc x = -\csc x \cot x$

The result follows from the definition of primitive.

$\blacksquare$


Sources