Primitive of x by Hyperbolic Cosecant of a x

Theorem

 * $\displaystyle \int x \csch a x \rd x = \frac 1 {a^2} \sum_{n \mathop = 0}^\infty \frac {2 \paren {1 - 2^{2 n - 1} } B_{2 n} \paren {a x}^{2 n + 1} } {\paren {2 n + 1}!} + C$

where $B_{2 n}$ denotes the $2n$th Bernoulli 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 $x \sech a x$