# Just an integral

1. ### botee

12
Hi everyone! Could someone help me with evaluating the following integral?

$\int_{2 \pi /L}^{\pi/l_0} \int_{2 \pi /L}^{\pi/l_0} \frac{\cos(k_x \Delta x)}{k_x^2 + k_y^2} dk_x dk_y$

I have a good reason to believe that it will end up with some
$\frac{1}{2} \ln (\frac{L}{\Delta x})$
though this might just be some approximation of it, since
$l_0 \ll L, \Delta x \ll L$ .
Any help would be appreciated! Thank you!