Evluate $\int_{|z|=3}\frac{1}{z^5(z^2+z+1)}\ dz$

Is there a straighforward way to compute
\[ \int_{|z|=3}\frac{1}{z^5(z^2+z+1)}\ dz\]
I don't think using partial fraction is the right approach. 


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Erdos Erdos
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