Primitive of x by Hyperbolic Secant of a x

Theorem

 * $\displaystyle \int x \operatorname{sech} a x \ \mathrm d x = \frac 1 {a^2} \left({\frac {\left({a x}\right)^2} 2 - \frac {\left({a x}\right)^4} 8 + \frac {5 \left({a x}\right)^6} {144} - \cdots + \frac {\left({-1}\right)^k E_n \left({a x}\right)^6} {\left({2 n + 2}\right) \left({2 n}\right)!} + \cdots}\right) + C$

where $E_n$ denotes the $n$th Euler number.

Also see

 * Primitive of $x \sinh a x$
 * Primitive of $x \cosh a x$
 * Primitive of $x \tanh a x$
 * Primitive of $x \coth a x$
 * Primitive of $x \operatorname{csch} a x$