Beregn ∮∣z∣=2ezz−1 dz\displaystyle \oint_{|z|=2}\frac{e^z}{z-1}\,dz∮∣z∣=2z−1ezdz.
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z0=1z_0=1z0=1 er inni ∣z∣=2|z|=2∣z∣=2. Cauchys integralformel med f(z)=ezf(z)=e^zf(z)=ez: ∮=2πi f(1)=2πi e\oint=2\pi i\,f(1)=2\pi i\,e∮=2πif(1)=2πie.
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