Let \[f(x)=\int{\frac{{{x}^{2}}dx}{(1+{{x}^{2}})\,\left( 1+\sqrt{1+{{x}^{2}}} \right)}}\]and \[f(0)=0\], then the value of \[f(1)\] be [AMU 2005]

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

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

Let \[f(x)=\int{\frac{{{x}^{2}}dx}{(1+{{x}^{2}})\,\left( 1+\sqrt{1+{{x

1.	Let \[f(x)=\int{\frac{{{x}^{2}}dx}{(1+{{x}^{2}})\,\left( 1+\sqrt{1+{{x}^{2}}} \right)}}\]and \[f(0)=0\], then the value of \[f(1)\] be [AMU 2005]
A.	\[\log (1+\sqrt{2})\]
B.	\[\log (1+\sqrt{2})-\frac{\pi }{4}\]
C.	\[\log (1+\sqrt{2})+\frac{\pi }{2}\]
D.	None of these
Answer» C. \[\log (1+\sqrt{2})+\frac{\pi }{2}\]

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Let \[f(x)=\int{\frac{{{x}^{2}}dx}{(1+{{x}^{2}})\,\left( 1+\sqrt{1+{{x}^{2}}} \right)}}\]and \[f(0)=0\], then the value of \[f(1)\] be [AMU 2005]

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