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The value of the integral

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

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

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