Primitive of x by Hyperbolic Secant of a x

Theorem

 * $\displaystyle \int x \sech a x \rd x = \frac 1 {a^2} \paren {\frac {\paren {a x}^2} 2 - \frac {\paren {a x}^4} 8 + \frac {5 \paren {a x}^6} {144} - \cdots + \frac {E_{2 n} \paren {a x}^{2 n + 2} } {\paren {2 n + 2} \paren {2 n}!} + \cdots} + C$

where $E_{2 n}$ denotes the $2 n$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 $x \csch a x$