Evaluate $$\int_{0}^{1} \int_{0}^{ \sqrt{1 + x^2} } \frac{dx . dy}{1 + x^2 + y^2}$$

A

$$\frac {\pi}{2}\left[\log (1 + \sqrt2)\right]$$

B

$$\frac {\pi}{4}\left[\log (1 + \sqrt2)\right]$$

C

$$\frac {\pi}{2}\left[\log (1 - \sqrt2)\right]$$

D

$$\frac {\pi}{4}\left[\log (1 - \sqrt2)\right]$$