Primitive of Cotangent of a x over x

Theorem

 * $\displaystyle \int \frac {\cot a x} x \ \mathrm d x = \frac {-1} a x - \frac {a x} 3 - \frac {\paren {a x}^3} {135} - \cdots - \frac {\paren {-1}^{n - 1} 2^{2 n} B_{2 n} \paren {a x}^{2 n - 1} } {\paren {2 n - 1} \paren {2 n}!} - \cdots + C$

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

Also see

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


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


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


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


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