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

Theorem

 * $\ds \int x \paren {-\cosh^{-1} \frac x a} \rd x = \paren {\dfrac {x^2} 2 - \dfrac {a^2} 4} \paren {-\cosh^{-1} \frac x a} + \dfrac {x \sqrt {x^2 - a^2} } 4 + C$

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