How to find $$ \iint_{D_R}e^{-x}\arctan\frac{y}{x}\,dx\,dy\,,$$ where $$ D_R=\left\{(x,y) \mid \frac{R}{2}\leq x\leq R, 0\leq y \leq \frac{2}{R}x-1 \right\}\,?$$
I know that $$\int \arctan \frac{y}{x}\, dy =y \arctan \frac{y}{x} -\frac{x}{2} \ln\left(1+\left(\frac{y}{x}\right)^2\right)+C$$
So how to find $$\int_{R/2}^R e^{-x} \left(\frac{2}{R}x-1 \right) \arctan \frac{\frac{2}{R}x-1}{x} -\frac{x}{2} \ln\left(1+\left(\frac{\frac{2}{R}x-1}{x}\right)^2\right)\,dx$$ and it's difficult to calculate.