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10.4: Integrandos con cortes en rama
https://espanol.libretexts.org/Matematicas/Analisis/Variables_complejas_con_aplicaciones_(Orloff)/10%3A_Integrales_definidas_usando_el_teorema_de_residuos/10.04%3A_Integrandos_con_cortes_en_rama
\[I = \dfrac{-\pi ie^{i \pi /3}}{1 - e^{i 2\pi /3}} = \dfrac{\pi i}{e^{i \pi /3} - e^{-\pi i/3}} = \dfrac{\pi /2}{(e^{i \pi /3} - e^{-i\pi /3})/2i} = \dfrac{\pi /2}{\sin (\pi /3)} = \dfrac{\pi}{\sqrt{... $I = \dfrac{-\pi ie^{i \pi /3}}{1 - e^{i 2\pi /3}} = \dfrac{\pi i}{e^{i \pi /3} - e^{-\pi i/3}} = \dfrac{\pi /2}{(e^{i \pi /3} - e^{-i\pi /3})/2i} = \dfrac{\pi /2}{\sin (\pi /3)} = \dfrac{\pi}{\sqrt{3}}.$ $\begin{array} {rcl} {\lim_{R \to \infty, r \to 0} \int_{C_2} f(z) \ dz} & = & {\lim_{R \to \infty, r \to 0} \int_{-C_4} f(z) \ dz} \\ {} & = & {\lim_{R \to \infty, r \to 0} \int_{-C_6} f(z)\ dz = \lim_{R \to \infty, r \to 0} \int_{C_8} f(z)\ dz = I.} \end{array}$

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