The value of the integral

$$\oint _{c}\dfrac{2z+5}{\left ( z-\dfrac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$$

over the contour $\mid z \mid=1$, taken in the anti-clockwise direction, would be

1. $\dfrac{24 \pi i}{13} \\$
2. $\dfrac{48 \pi i}{13} \\$
3. $\dfrac{24}{13} \\$
4. $\dfrac{12}{13}$

edited