Residue Theorem

Need a little help with this please...

Consider the complex valued function $f(z) = \dfrac{e^{iz}}{z+i}$ and integrate around a semi-circle of radius $R$ centered at the origin in the lower half of the complex plane (denoted as $\Gamma$).

Then consider the fact that, by Residue Theorem, we have:

$\displaystyle \int_{\Gamma} f(z) \ \mathrm{d}z = 2 \pi i \mathrm{Res}(f(z),-i)$

Do you know how to proceed? Have you seen similar examples?

Did you try plugging it into symbolab?

Yes but didn't work

Tried this way, but stucked where I had to equate real and imaginary parts as both the intergrals with sinx and cosx had complex denominators.