Show that \( f(x)=2 x+\cot ^{-1} x+\log \left(\sqrt{1+x^{2}}-x\righ...

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Show that \( f(x)=2 x+\cot ^{-1} x+\log \left(\sqrt{1+x^{2}}-x\right) \) is increasing in \( \mathbf{R} \).
\( \mathrm{P} \)
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