This is the formula
$$ \zeta(s) = \frac{1}{s-1}+\frac{1}{2} + 2\int_0^{\infty} \frac{\sin{(s \arctan{t})}}{(1+t^2)^{\frac{s}{2}}\left(e^{2\pi t}- 1 \right)}\, dt $$
Can this expression be simplified for any s or we can only use numerical integration like trapezoidal rule to solve this?