$\int_{y=0}^{y=2} \int_{x= y}^{x=\sqrt{8-y^2}}\frac{1}{\sqrt{x^2+y^2+1}}dxdy$ using double integration in polar coordinates.

Question

$\int_{y=0}^{y=2} \int_{x= y}^{x=\sqrt{8-y^2}}\frac{1}{\sqrt{x^2+y^2+1}}dxdy$ using double integration in polar coordinates.

My attempt:

Let $x=rcos(\theta),y=rsin(\theta)$

Then the integration becomes

$\int_{\theta = 0}^{\pi/4} \int_{r=0}^{2\sqrt{2}} \frac{r}{\sqrt{r^2+1}} drd\theta=4\pi$

However the answer is $\frac{(3-\sqrt{5})\pi}{2}$