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Integral de $$$\frac{e^{t}}{100}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{e^{t}}{100}\, dt$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=\frac{1}{100}$$$ y $$$f{\left(t \right)} = e^{t}$$$:
$${\color{red}{\int{\frac{e^{t}}{100} d t}}} = {\color{red}{\left(\frac{\int{e^{t} d t}}{100}\right)}}$$
La integral de la función exponencial es $$$\int{e^{t} d t} = e^{t}$$$:
$$\frac{{\color{red}{\int{e^{t} d t}}}}{100} = \frac{{\color{red}{e^{t}}}}{100}$$
Por lo tanto,
$$\int{\frac{e^{t}}{100} d t} = \frac{e^{t}}{100}$$
Añade la constante de integración:
$$\int{\frac{e^{t}}{100} d t} = \frac{e^{t}}{100}+C$$
Respuesta
$$$\int \frac{e^{t}}{100}\, dt = \frac{e^{t}}{100} + C$$$A