Primitive of x over Sine of a x

Theorem

 * $\displaystyle \int \frac {x \ \mathrm d x} {\sin a x} = \dfrac 1 {a^2} \sum_{n \mathop = 0}^\infty \dfrac {\left({-1}\right)^{n-1} 2 \left({2^{2 n - 1} - 1}\right) B_{2 n} \left({a x}\right)^{2 n + 1} } {\left({2 n + 1}\right)!} + C$

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

Also see

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