Primitive of Cosecant of a x over x

Theorem

 * $\displaystyle \int \frac {\csc a x} x \ \mathrm d x = \frac {-1} {a x} + \frac {a x} 6 + \frac {7 \left({a x}\right)^3} {1080} + \cdots + \frac {2 \left({2^{2 n - 1} - 1}\right) B_n \left({a x}\right)^{2 n - 1} } {\left({2 n - 1}\right) \left({2 n}\right)!} + \cdots + C$

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

Also see

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