Pregunta: Obtén la transformada directa o inversas de las siguientes funcionesa) L{8senh7t+e6t}=b) L{e10tt15-tcos2t}=c) L{e6t+3-7cost-13247}=d) L-1{4s-8+1s7}=e) L-1{3ss2+144-5(s-5)8}=

5) a) Consider the function ${\displaystyle f(t)=8\sinh 7t+e^{6t}}$.

Use the formula ${\displaystyle L\{\sinh \left(at\right)\}=\frac{a}{s^2-a^2}\text{and}L\left\{e^{at}\right\}=\frac{1}{s-a}}$ in the given function to find its Laplace transform.

$\begin{array}{c}{\displaystyle \begin{array}{rl}L\left\{f\left(t\right)\right\}& =L\{8\sinh 7t+e^{6t}\}\\ & =8L\{\sinh 7t\}+L\left\{e^{6t}\right\}\\ & =8\cdot \frac{7}{s^2-7^2}+\frac{1}{s-6}\\ & =\frac{56}{s^2-49}+\frac{1}{s-6}\end{array}}\end{array}$