Primitive of x by Cosecant of a x

Theorem

 * $\displaystyle \int x \csc a x \rd x = \frac 1 {a^2} \paren {a x + \frac {\paren {a x}^3} {18} + \frac {7 \paren {a x}^5} {1800} + \cdots + \frac {\paren {-1}^{n - 1} 2 \paren {2^{2 n - 1} - 1} B_n \paren {a x}^{2 n + 1} } {\paren {2 n + 1}!} + \cdots} + C$

where $B_{2 n}$ is the $2 n$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 $x \sec a x$