Using the Cauchy Integral Theorem for Derivatives to evaluate an integral
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I ran into this question which hints me to use Cauchy's Integral Theorem for Derivatives, however I don't seem to be able to fit this integral into the form of the Integral Formula $$displaystyle int_{|z|=2} frac{cos(z)}{z(z^2+8)}dz$$ I tried using the fact that $displaystyle int_gamma f(z)dz=int_a^b f(gamma(t))gamma'(t)dt$ for $gamma(t)$ where $t in [a, b]$ . But got nowhere. Is there a way I can transform the given integral into the form in which I can use the Integral Formula as stated below? $$f^{(k)}(w)=frac{1}{2pi i}int_gamma frac{f(z)}{(z-w)^{k+1}}dz$$ where $f^{(k)}(w)$ is the $k^{th}$ derivative of $f$
complex-analysis complex-integration
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