Integrating e^-|t|: Signals & Systems Demystified Help

[sam.green]

I am working through Signals and Systems Demystified on my own. I need to integrate:

<br /> \int_{-\infty}^{\infty}{sin(2t)e^{-|t|}e^{-j2\pi ft}} dt<br />

I first went about dealing with the absolute value sign by using the following

<br /> \int_{-\infty}^{\infty} e^{-|t|} dt = \int_{-\infty}^{0} e^{t} dt + \int_{0}^{\infty} e^{-t} dt<br />

Going along this route seems to not work and makes me think the expansion is incorrect. Can anyone give me a pointer?

Thanks,
Sam

 

[sam.green]

The expansion is correct.

 

[rochfor1]

Use the decomposition you have now and do integration by parts twice (on each decomposed integral). I think you'll be pleasantly surprised.

 

[sam.green]

That worked. Thanks!