Can the Fourier integral of sinw be solved with a misprint?

[zezima1]

I'm a little unsure of how the attached solutions are obtained. For instance one of the Fourier integrals is:

∫e^(w_E-iw)t = [1/(w_E-iw)e^(w_E-iw)t from -∞ to ∞. But what do you do about the real part w_E? That leads the integral to diverge as far as I can see...

 

[tiny-tim]

hizezima1!

those e^w_Ets are a misprint, they should be e^iw_Et