I need to do this definite integral,
$$ \int_{-a}^{a} \frac{e^{i \alpha \omega}\omega\sqrt{a - \omega^2}}{e^{b \omega} -1} $$ Is it possible to do this? Or if I can do the following integral, $$ \int_{-a}^{a} \frac{e^{i \alpha \omega} \sqrt{a - \omega^2}}{e^{b \omega}-1} $$ I think I can use differentiation under integration to get the first integral. Are any of these actually doable? I tried the substitution, $\omega = \cos\theta$, but I didn't find it very useful.