question_answer

Let \[f(x)\,=\int{\frac{{{x}^{2}}dx}{(1+{{x}^{2}})(1+\sqrt{1+{{x}^{2}}})}}\] and \[f(0)\,=0\], then f(1) is

A)  \[\log \,(1+\sqrt{2})\]    

B)  \[\log \,(1+\sqrt{2})-\frac{\pi }{4}\]

C)  \[\log \,(1+\sqrt{2})+\frac{\pi }{4}\]

D)  \[\log \,(\sqrt{2}-1)\]