I am trying to do a double integral over $x,y$ over a finite rectangular region within $(0,2\pi)\times (0,2\pi)$. Typically my integrals are of the kind,
$$ (x-y)^2 \cos ^2\left(\frac{x-y}{2}\right) \csc ^5\left(x-\frac{y}{2}\right) \sin \left(a+\frac{x+y}{2}\right)$$ $$ (x-y)^3 \cos ^2\left(\frac{x-y}{2}\right) \csc ^5\left(x-\frac{y}{2}\right) \sin \left(a+\frac{x-y}{2}\right)$$
On doing indefinite integration of either $x $ or $y$ with the help of Mathematica, I am getting a rather complicated terms, making my problem much difficult to simplify. I was wondering if there is a simplier result on tables of integration, which I am not aware of ?