complex integral - residuum theorem or something else? I have to compute integral of complex function:
$$ \int_{|z|=3} \frac{z^9}{z^{10} - 1} $$
I thought that I should after I found points where $z^{10} = 1$ use the residue theorem but I do not know how to execute that.
So I thought that maybe I should integrate by substitution $w=z^{10} $ so $ dw = z^9 dz$ which would be fortunate but then I still do not know how to compute integral over that closed curve.
Is there a simplier metod which I do not see? How to execute residuum theorem for 10 singularities of form: $\cos(k\pi/5) + i\sin(k\pi/5), k\in(0,1,2,3,4,5,6,7,8,9) $ ?
Thank you for any help!

There will be $10$ simple poles given by $z=e^{2πki/10} , k=0,1,2,...,9$ all lying within $\vert z\vert=3$. The residue at each pole is $\frac{z^9}{\frac{d}{dz}(z^(10)-1)}=\frac{1}{10}$.
Then $I=2πi(\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10})$ (ten times)
$\implies I=2πi$
