Primitive of Reciprocal of Root of x squared minus a squared

Theorem

Inverse Hyperbolic Cosine Form

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

Logarithm Form

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

Also see

• Primitive of Reciprocal of $\sqrt {x^2 + a^2}$
• Primitive of Reciprocal of $\sqrt {a^2 - x^2}$