Primitive of Reciprocal of Root of x squared plus a squared/Inverse Hyperbolic Sine Form

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {\sqrt {x^2 + a^2} } = \sinh^{-1} {\frac x a} + C$

Proof
Let:

Also see

 * Primitive of Reciprocal of $\sqrt {x^2 - a^2}$: Inverse Hyperbolic Cosine Form
 * Primitive of Reciprocal of $\sqrt {a^2 - x^2}$