Primitive of Function of Arccosecant

Theorem

 * $\displaystyle \int F \left({\operatorname{arccsc} \frac x a}\right) \ \mathrm d x = -a \int F \left({u}\right) \left\vert{\csc u}\right\vert \cot u \ \mathrm d u$

where $u = \operatorname{arccsc} \dfrac x a$.

Proof
First note that:

Then:

Also see

 * Primitive of Function of Arcsine
 * Primitive of Function of Arccosine
 * Primitive of Function of Arctangent
 * Primitive of Function of Arccotangent
 * Primitive of Function of Arcsecant