Primitive of Root of x squared minus a squared

Theorem

Inverse Hyperbolic Cosine Form

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

Logarithm Form

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

Also see

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