For $a>0$ i have managed to show that this is the Fourier transform of the function.
$$ \mathcal{F}[e^{-a|x|}](s) = \frac {2a}{\sqrt{2{\pi}}(a^2+s^2)}. $$
How do I now use this to find the Fourier transform of:
$$ \mathcal{F}[\log(a^2+s^2)](s)? $$
I have tried to apply the inversion formula for Fourier transforms but I haven't had any success. Any help would be greatly appreciated.