Single Option Correct Type Questions Let \( f(x)=\int \frac{x^{2}}{\left(1+x^{2}\right)\left(1+\...

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Single Option Correct Type Questions
Let \( f(x)=\int \frac{x^{2}}{\left(1+x^{2}\right)\left(1+\sqrt{1+x^{2}}\right)} d x \) and \( f(0)=0 \). Then \( f(1) \) is equal to
(a) \( \log _{e}(1+\sqrt{2}) \)
(b) \( \log _{e}(1+\sqrt{2})-\frac{\pi}{4} \)
(c) \( \log _{e}(1+\sqrt{2})+\frac{\pi}{4} \)
(d) None of these
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