Primitive of x over Sine of a x

Theorem

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

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