I am evaluating a Fourier transform, without tables, and need to evaluate this integral:

\(
\int e^{-t} * sin(2 \pi f_c t) * e^{-j2 \pi ft} dt
\)

I have tried two methods: 1) integration by parts, and 2) integration after expressing the sine function as a complex exponentials. I get stuck in both cases.

The asterisks are there to assist with clarity of spacing. Thanks for any help you can provide,
J

 

Thanks.......

 

I'd imagine that you'd have to do integration by parts twice. Let I represent the integral that you're trying to calculate. Then you'd probably end up with something like I = f(t) + nI, where f is some function of t and n is a real number. You can then easily solve for I.

This is just a quick idea, I haven't got time at the moment to solve this fully.