How to prove that the function $$f(r)=(1 - r^2) \int_0^{2\pi}|Re[\frac{e^{i a} (2 - e^{-i s} r)}{(-e^{i s} + r)^2}]|ds\le 8$$ for real $a$ and $r\in[0,1]$ attains its maximum for $r=0$.