Given that \(\mathrm{f}(x) = (x+1)^2\), \(x \in \mathbb{R}\), \(x > 1\) and \(\mathrm{gf}(x) = -2 \ln(x+1)\), \(x \in \mathbb{R}\), \(x > 1\).
Find \(\mathrm{g}(x)\).
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