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

Theorem

 * $\ds \int x^2 \paren {-\cosh^{-1} \dfrac x a} \rd x = \dfrac {x^3} 3 \paren {-\cosh^{-1} \dfrac x a} - \dfrac {\paren {x^2 + 2 a^2} \sqrt {x^2 - a^2} } 9 + C$

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