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Chain Rule & Integration by Substitution

Review question

Can we show $x>\ln(1+x^2)$ for all $x>0$?
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Ref: R7431

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Question

Given that \[y=x-\ln(1+x^2),\] show that \[\frac{dy}{dx}\geq 0\ \text{for all values of $x$.}\]

Deduce that, for all \(x>0\), \[x>\ln(1+x^2).\]