I want to solve this contour integral
$$J(\omega)= \frac{1}{2\pi}\frac{\gamma_i\lambda^2}{(\lambda^2+(\omega_i-\Delta-\omega)^2)} $$
$$N(\omega)=\frac{1}{e^{\frac{-\omega t}{T}}-1}$$
$$\int_0^\infty J(\omega)N(\omega)$$
there are three poles I don't know how I get rid of pole on zero (pole in...