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18.4: A.4- Aplicaciones de la Transformación de Laplace de una Integral Definida
https://espanol.libretexts.org/Ingenieria/Introduccion_a_los_Sistemas_Dinamicos_Lineales_Invariantes_en_el_Tiempo_para_Estudiantes_de_Ingenieria_(Hallauer)/18%3A_Ap%C3%A9ndice_A-_Tabla_y_Derivaciones_de_Pares_Transformada_de_Laplace/18.04%3A_A.4-_Aplicaciones_de_la_Transformaci%C3%B3n_de_Laplace_de_una_Integral_Definida
\[L^{-1}\left[\frac{1}{s} \frac{1}{s-p}\right]=\int_{\tau=0}^{\tau=t \geq 0} e^{p \tau} d \tau=\frac{1}{p} \int_{\tau=0}^{\tau=t \geq 0} d\left(e^{p \tau}\right)=\frac{1}{p}\left(e^{p t}-1\right), t \...\[L^{-1}\left[\frac{1}{s} \frac{1}{s-p}\right]=\int_{\tau=0}^{\tau=t \geq 0} e^{p \tau} d \tau=\frac{1}{p} \int_{\tau=0}^{\tau=t \geq 0} d\left(e^{p \tau}\right)=\frac{1}{p}\left(e^{p t}-1\right), t \geq 0\label{eqn:A.15} \] \[L^{-1}\left[\frac{1}{s\left(s^{2}+\omega^{2}\right)}\right]=\frac{1}{\omega} \int_{\tau=0}^{\tau=t} \sin \omega \tau d \tau=-\frac{1}{\omega^{2}} \int_{\tau=0}^{\tau=t} d(\cos \omega \tau)=\frac{1}{\omega^{2}}(1-\cos \omega t), t \geq 0\label{eqn:A.16} \]

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