Primitive of x by Hyperbolic Cotangent of a x

Theorem

 * $\displaystyle \int x \coth a x \ \mathrm d x = \frac 1 {a^2} \left({a x + \frac {\left({a x}\right)^3} 9 - \frac {\left({a x}\right)^5} {225} + \cdots + \frac {2^{2 n} B_{2 n} \left({a x}\right)^{2 n + 1} } {\left({2 n + 1}\right)!} + \cdots}\right) + C$

where $B_{2 n}$ denotes the $2 n$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 $x \sech a x$
 * Primitive of $x \csch a x$