Evaluate $$\int_{\gamma}\frac{z^2+z^7}{(z-\frac{e}{3})^3}$$ here $\gamma$ is a rectangular path traversed in the counter clockwise direction with vertices $1,2i,−1,−2i$.
So my thoughts for this question there's a singularity at $z=e/3$ which lies inside and then apply Cauchy-Integral formula (is there any other requirements needed here, maybe holomorphic?)
$$\int_{\gamma} \frac{f(z)}{(z-w)^{n+1}} dz = \frac{2 \pi i f^{(n)}(w)}{n!}$$ here $n=2$ so do we just evaluate at $\frac{e}{3}$ which would get us $$\pi i (\frac{e^2}{9} + \frac{e^7}{2187})$$
Is this the way to go about this Q, I have a feeling I may have done something wrong
Thank you