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Using Cauchy's integral theorem, the value of the integral (integration being taken in counterclockwise direction) $$\oint\limits_{\text{c}} {\frac{{{{\text{z}}^3} - 6}}{{3{\text{z}} - {\text{i}}}}{\text{dz}}} $$   is

Using Cauchy's integral theorem, the value of the integral (integration being taken in counterclockwise direction) $$\oint\limits_{\text{c}} {\frac{{{{\text{z}}^3} - 6}}{{3{\text{z}} - {\text{i}}}}{\text{dz}}} $$   is Correct Answer $$\frac{{2\pi }}{{81}} - 4\pi {\text{i}}$$

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