Integral de $$$\frac{e^{x}}{2}$$$

Encontre $$$\int \frac{e^{x}}{2}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=\frac{1}{2}$$$ e $$$f{\left(x \right)} = e^{x}$$$:

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

A integral da função exponencial é $$$\int{e^{x} d x} = e^{x}$$$:

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

Portanto,

$$\int{\frac{e^{x}}{2} d x} = \frac{e^{x}}{2}$$

Adicione a constante de integração:

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

$$$\int \frac{e^{x}}{2}\, dx = \frac{e^{x}}{2} + C$$$A