Complex Line Integral Value for Natural Numbers n=1,2,3..

[burak100]

I can't find the value, for natural number $n = 1, 2, 3, ...$
$I = \int\limits_{C}\dfrac{e^{iz}}{z^n} dz$

find the value. where $z(t) =e^{it}$ , $0\leq t \leq 2\Pi$

 

[HallsofIvy]

Have you considered applying Cauchy's integral formula,
$$f^{(n)}(z)= \frac{1}{2\pi i}\oint_C \frac{f(z)}{(z- a)^{n+1}} dz$$
where C is any closed path containing a?
What is f(z)? What is a?

 

[burak100]

I didn't apply, but in the question f(z) is not given, and also a.
can we choose as f(z)=e^{iz} and a=0 ?

 

[burak100]

sorry for mistake
f(z)=e^{iz} --------> f(z)=e^{it} .