Primitive of Inverse Hyperbolic Cosecant of x over a over x

Proof
For $\size x < a$:

For $0 < x < a$:

For $-a < x < 0$:

Also see

 * Primitive of $\dfrac 1 x \arsinh \dfrac x a$


 * Primitive of $\dfrac 1 x \arcosh \dfrac x a$


 * Primitive of $\dfrac 1 x \artanh \dfrac x a$


 * Primitive of $\dfrac 1 x \arcoth \dfrac x a$


 * Primitive of $\dfrac 1 x \arsech \dfrac x a$