How do I apply the cauchy goursat theorem with exponentials? I know i should be using partial fractions but not sure how to break down the numerator here. Any help is greatly appreciated.
2026-03-25 12:55:28.1774443328
Integrating with Cauchy Goursat Theorem with exponential
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Since$$\frac1{z^2(z-1)(z-4)}=-\frac{1}{3 (z-1)}+\frac{5}{16 z}+\frac{1}{4z^2}+\frac{1}{48 (z-4)},$$you have$$\frac{e^{2z}}{z^2(z-1)(z-4)}=-\frac{e^{2z}}{3 (z-1)}+\frac{5e^{2z}}{16 z}+\frac{e^{2z}}{4z^2}+\frac{e^{2z}}{48 (z-4)}.$$