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

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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

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


Also see