Let $n \in \mathbb{N}$ and $s \in \mathbb{R}$. I wonder what is a necessary and sufficient condition (in terms of $n$ and $s$) for
$$ \int_{\mathbb{R}^n} ((1 + \|x\|^2)^s)^2 \mathrm{d}x < \infty $$ to hold. Here, $\|\cdot\|$ is the Euclidean norm and the measure is the Lebesgue measure.
Context
I encountered the above question while reading a functional analysis textbook, and the integrability of the function (say, for $s < - n/4$) is used in a proof (in relation to Sobolev spaces). So I was wondering (but could not find) if there is a systematic way to see when the above function is integrable.