Evaluation of Integral

Question

How do I evaluate the integral $\int_{0}^{\infty}e^{-t/\tau} e^{i\omega t }dt$ Where $\tau$ is a constant

Answer 1

$\int_0 ^\infty dt e^{-t/\tau}e^{i \omega t} = \int_0 ^\infty dt e^{-(1/\tau - i \omega)t}= -\frac{1}{1/\tau - i \omega} \left[ e^{-(1/\tau - i \omega)t}|_0^{\infty} \right] = \frac{1}{1/\tau - i \omega}$