Different Contour Integration $\oint \frac{4z^3+6}{z(z-1-i)^2}dz$ C consists of $|z|=3$ counterclockwise and $|z|=1$ clockwise

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Not sure where to begin and was wondering if anyone could give me a hint. I believe I would be using Cauchy's Integral Formula but figure out how to "split" the function...

Thanks.

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You could use the standard formula for contour integrals which is $\int_{\gamma} f(z) dz=\int_{a}^{b}f(\gamma(t))\gamma^{'}(t)dt $ or i suggest you use the Cauchy Integral Formula