Primitive of x squared over Root of x squared plus a squared

From ProofWiki
Jump to navigation Jump to search

Theorem

Inverse Hyperbolic Sine Form

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


Logarithm Form

$\displaystyle \int \frac {x^2 \ \mathrm d x} {\sqrt {x^2 + a^2} } = \frac {x \sqrt {x^2 + a^2} } 2 - \frac {a^2} 2 \ln \left({x + \sqrt {x^2 + a^2} }\right) + C$


Also see