Primitive of Reciprocal of Root of x squared plus a squared

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Theorem

Inverse Hyperbolic Sine Form

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


Logarithm Form

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


Also see