Establish the following inequality $$\operatorname{Ent}_{\varphi}(f) \leq \frac{1}{2}\int_{-\infty}^{+\infty} \frac{f'^2(x)}{f(x)}\,\varphi(x)\,\mathrm{d}x.$$
Establish the following inequality
$$\operatorname{Ent}_{\varphi}(f) \leq \frac{1}{2}\int_{-\infty}^{+\infty} \frac{f'^2(x)}{f(x)}\,\varphi(x)\,\mathrm{d}x.$$