I am considering the following function. $f(x)=\sum_{i=1}^d{\mid x_i\mid^2}$ for $x\in\mathbb{R}^d$.
I am now considering the inverse function $g(x)=\frac{1}{f(x)}$.
Claim: g is integrable if $d\geq3$. Does this claim is correct? It does not seems very reasonable but I tried anyway manual computation for $d\geq3$ but it seems not to be that useful. Does someone has in case a more direct way to prove this? Thanks