Integral de $$$2 e^{y}$$$

Halla $$$\int 2 e^{y}\, dy$$$.

Aplica la regla del factor constante $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ con $$$c=2$$$ y $$$f{\left(y \right)} = e^{y}$$$:

$${\color{red}{\int{2 e^{y} d y}}} = {\color{red}{\left(2 \int{e^{y} d y}\right)}}$$

La integral de la función exponencial es $$$\int{e^{y} d y} = e^{y}$$$:

$$2 {\color{red}{\int{e^{y} d y}}} = 2 {\color{red}{e^{y}}}$$

Por lo tanto,

$$\int{2 e^{y} d y} = 2 e^{y}$$

Añade la constante de integración:

$$\int{2 e^{y} d y} = 2 e^{y}+C$$

$$$\int 2 e^{y}\, dy = 2 e^{y} + C$$$A