Primitive of Inverse Hyperbolic Sine of x over a over x

Proof
For $\size x < a$:

For $x > a$:

For $x < a$:

Also see

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


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