Comparison of two integrals in $\Bbb R$

Question

Is it possible to estimate $\int_{\mathbb{R}} |x|^2 u(x)\,\mathrm{d}x$ in terms of $\int_{\mathbb{R}} |x| u^2(x)\,\mathrm{d}x$ or estimate $\int_{\mathbb{R}} |x| u^2(x)\,\mathrm{d}x$ in terms of $\int_{\mathbb{R}} |x|^2 u(x)\,\mathrm{d}x$? Here $u$ is assumed to be a positive function. Assume all the necessary assumptions on $u$ to enjoy such a estimate if it exists.