# Primitive of x squared over Root of x squared minus a squared

## Theorem

### Inverse Hyperbolic Cosine Form

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

### Logarithm Form

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