Primitive of Cotangent of a x over x

Theorem

 * $\displaystyle \int \frac {\cot a x} x \ \mathrm d x = \frac {-1} a x - \frac {a x} 3 - \frac {\left({a x}\right)^3} {135} - \cdots - \frac {2^{2 n} B_n \left({a x}\right)^{2 n - 1} } {\left({2 n - 1}\right) \left({2 n}\right)!} + \cdots + C$

where $B_n$ denotes the $n$th Bernoulli number.

Also see

 * Primitive of $\dfrac {\tan a x} x$