$$\int_{C} 4e^zcos(e^z) dz$$ where C is the contour given by $\gamma(t):= (log \pi)\sin t+i \cos t$,for $0 ≤ t≤ \frac{\pi}{2}$ is what I need to evaluate
But the problem is the completion of it.
I understand we're given $\gamma$ and then if we take the derivate:
$\gamma '(t) = (log \pi)\cos t - i \sin t$ and then sub in using
$\int f(\gamma (t)) \gamma '(t) dt$ using the bounds
Now I'm just stuck on how do we evaluate
$$e^{(log \pi)\sin t+i \cos t}$$ and complete the question?
If someone could help this would be really helpful