For the function f(x)=\frac{2z^2+2}{x^2-3z}, identify the poles (singular points), find the corresponding residues, and evaluate the integral
I=\oint_C f(z)dz \text{,}
where C is the contour \lvert z\rvert=5, mapped counter-clockwise.
a)
\begin{array} \text{Pole with least real part at }z=\input\text{.} \\ \text{Pole with greatest real part at }z=\input\text{.} \end{array}
b)
\begin{array} \text{Residue corresponding to the pole with the least real part }z=\input\text{.} \\ \text{Residue corresponding to the pole with the greatest real part }z=\input\text{.} \end{array}
c)
Now evaluate the integral:
I=\input\text{.}