Evaluate the integral: $$\int_{-\infty}^{\infty} \frac {\omega e^{-2i\omega t}}{(\omega_0^2-\omega^2-\frac{\gamma}{m}i\omega)^{2}}d\omega$$ With $\frac{\gamma^2}{4m^2}>\omega_0^2$.
I solved the denominator and I have the roots: $$\omega=-i\frac{\gamma}{2m}\pm i\sqrt{\frac{\gamma^2}{4m^2}-\omega_0^2}=ik^\pm$$
Then the integral becomes: $$\int_{-\infty}^{\infty} \frac {\omega e^{-2i\omega tx}}{(\omega-ik^+)^{2}(\omega-ik^-)^{2}}d\omega$$
I am stuck here and do not have any idea for solving this integral. Please help me.