Let \( f(x)=\int \frac{x^{2} d x}{\left(1+x^{2}\right)\left(1+\sqrt{1+x^{2}}\right)} \) and \( f...

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Let \( f(x)=\int \frac{x^{2} d x}{\left(1+x^{2}\right)\left(1+\sqrt{1+x^{2}}\right)} \) and \( f(0)=0 \). Then \( f(1) \) is
(a) \( \ln (1+\sqrt{2}) \)
(b) \( \ln (1+\sqrt{2})-\frac{\pi}{4} \)
(c) \( \ln (1+\sqrt{2})+\frac{\pi}{4} \)
(d) \( \ln (3+\sqrt{2})+\frac{\pi}{2} \)
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