Category:Primitive of Power of x by Arcsecant of x over a

This category contains pages concerning Primitive of $x^m \arcsec \dfrac x a$:

$\ds \int x^m \arcsec \frac x a \rd x = \begin {cases}

\dfrac {x^{m + 1} } {m + 1} \arcsec \dfrac x a - \dfrac a {m + 1} \ds \int \dfrac {x^m \rd x} {\sqrt {x^2 - a^2} } & : 0 < \arcsec \dfrac x a < \dfrac \pi 2 \\ \dfrac {x^{m + 1} } {m + 1} \arcsec \dfrac x a + \dfrac a {m + 1} \ds \int \dfrac {x^m \rd x} {\sqrt {x^2 - a^2} } & : \dfrac \pi 2 < \arcsec \dfrac x a < \pi \\ \end {cases}$