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

Theorem

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

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