# Primitive of Reciprocal of x by Root of x squared plus a squared

## Theorem

### Inverse Hyperbolic Cosecant Form

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

### Logarithm Form

$\displaystyle \int \frac {\d x} {x \sqrt {x^2 + a^2} } = -\frac 1 a \map \ln {\frac {a + \sqrt {x^2 + a^2} } x} + C$