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

Theorem

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

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