Primitive of x by Hyperbolic Cotangent of a x

Theorem

 * $\displaystyle \int x \coth a x \rd x = \frac 1 {a^2} \paren {a x + \frac {\paren {a x}^3} 9 - \frac {\paren {a x}^5} {225} + \cdots + \frac {2^{2 n} B_{2 n} \paren {a x}^{2 n + 1} } {\paren {2 n + 1}!} + \cdots} + C$

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 $x \csch a x$