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Evaluate $$\int_{-\infty}^{\infty} x^{4} f(x) dx$$, where $$f(x)=\frac{1}{\sqrt{2 \pi}}e^{-\left(\frac{x^{2}}{2}\right)}, x \in(-\infty,\infty)$$
3
$$3 \sqrt{\pi}$$
$$\sqrt{3} \pi$$
$$3 \pi$$
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