Calculate the double integral using polar coordinates

Question

$$I=\iint\limits_{D}\operatorname{ctg}\sqrt{x^2+y^2} \, dx \, dy = \iint\limits_D \operatorname{ctg}\left(\sqrt{r^2\cos^2 \theta +r^2\sin^2 \theta}\right) \, r \, dr \, d\theta =$$ $$=\iint\limits_D r \operatorname{ctg} r \, dr \, d\theta =\int\limits_0^{2\pi} d\theta \int\limits_0^1 r \operatorname{ctg} r \, dr = 2\pi \int\limits_0^1 r\operatorname{ctg} r \, dr$$ $$D=\{(x,y)\in\mathbb{R}^2:x^2+y^2\leq1\}$$ I tried to calculate it but it doesn't work