Assume $\Omega$ is a bounded smooth domain in $\mathbb R^N $ with $N \ge 5 $ and $u \in C^2(\Omega)$ . I want to proof
$$\int_{\Omega}\frac{|\nabla u|^2}{|x|^2}d{x} \;\ge\; \left(\frac{N-4}{2}\right)^2 \int_{\Omega} \frac{|u|^2}{|x|^4} dx$$
I know that it is a special case of caffereli-kohn- nirenberg inequality, but I want a proof that it direct. Because i do not know the proof of mentioned inequality.
I will be thanksed if some one help me.