Primitive of Power of x by Inverse Hyperbolic Cosine of x over a/Corollary

Theorem

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

where $-\cosh^{-1}$ denotes the negative branch of the real inverse hyperbolic cosine multifunction.