Determine if a function belongs to the sobolev space $W^{1,p}(\mathbb{R})$ and not to $L^q(\mathbb{R})$

Question

I don't understand the first conclusion of the user Tomas in the exercise

Properties of function $f(x) = (1 + x^2)^{-\alpha/2}(\log(2+x^2))^{-1},\text{ }x \in \mathbb{R}$ with $0 < \alpha < 1$.

Why does the inequality $$\int_{\mathbb{R}} (1+x^2)^{-\alpha q/2}(\log (2+x^2))^{-q}\ge \int_{\mathbb{R}}(1+x^2)^{-\alpha q/2}(2+x^2)^{-qt}. $$

lead us to conclude that if $q\in [1,1/\alpha)$ then $f\notin L^q(\mathbb{R})$?

Thanks