Evaluate the double integral:
$$\iint_D\arctan e^{xy}\,dy\,dx$$
where $D:\{(x,y)\in\mathbb{R}^2: x^2+y^2\leq 4x\}$
For thie integral , since our function does not have elementary anti-derivetives with respect to both variables, I tried to solve this by polar coordinate. But then it was getting worth and I got something very ugly and I cannot simplify, I stuck. Are there any tricks to deal with this?