Upper bound for the integral $\int_{\mathbb R} \frac{dx}{(1+x^2)^a}$ when $a\in (1/2, 1)$

Question

Let $a\in (1/2, 1)$.

I am trying to find an upper bound, which does not depend on $a$, for the integral $$\int_{\mathbb R} \frac{dx}{(1+x^2)^a}.$$

Is that possible? Clearly $ 1\le (1+x^2)^a$, but clearly it does not help. Anyone could please give some hints?