Primitive of Cosecant of a x over x

Theorem

 * $\displaystyle \int \frac {\csc a x} x \rd x = \frac {-1} {a x} + \frac {a x} 6 + \frac {7 \paren {a x}^3} {1080} + \cdots + \frac {\paren {-1}^{n - 1} 2 \paren {2^{2 n - 1} - 1} B_{2 n} \paren {a x}^{2 n - 1} } {\paren {2 n - 1} \paren {2 n}!} + \cdots + C$

where $B_n$ is 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 $\dfrac {\cot a x} x$


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