Primitive of x by Cosecant of a x

Theorem

 * $\displaystyle \int x \csc a x \ \mathrm d x = \frac 1 {a^2} \left({a x + \frac {\left({a x}\right)^3} {18} + \frac {7 \left({a x}\right)^5} {1800} + \cdots + \frac {2 \left({2^{2 n - 1} - 1}\right) B_n \left({a x}\right)^{2 n + 1} } {\left({2 n + 1}\right)!} + \cdots}\right) + C$

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

Also see

 * Primitive of $x \sin a x$
 * Primitive of $x \cos a x$
 * Primitive of $x \tan a x$
 * Primitive of $x \cot a x$
 * Primitive of $x \sec a x$