Solving $\int_{\mathbb R} \frac{(x^2+a)^{-s}}{x^2+1} dx$

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I want to solve the integral $$\int_{\mathbb R} \frac{(x^2+a)^{-s}}{x^2+1} dx$$ for $a>0$ whenever it is defined (I guess this is the case for $\Re(s)>-1/2$). Here I'm a little bit stuck. Can you help?