Find the minimum value of
\[
\int_{\mathbb{R}} f(x) \log f(x) dx
\]
among functions \(f: \mathbb{R} \rightarrow \mathbb{R}^+ \cup \{ 0 \}\) that satisfy the condition
\[
\int_{\mathbb{R}} f(x) dx = \int_{\mathbb{R}} x^2 f(x) dx = 1.
\]