Integral de $$$- \frac{e^{u}}{9}$$$

Encontre $$$\int \left(- \frac{e^{u}}{9}\right)\, du$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ usando $$$c=- \frac{1}{9}$$$ e $$$f{\left(u \right)} = e^{u}$$$:

$${\color{red}{\int{\left(- \frac{e^{u}}{9}\right)d u}}} = {\color{red}{\left(- \frac{\int{e^{u} d u}}{9}\right)}}$$

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

$$- \frac{{\color{red}{\int{e^{u} d u}}}}{9} = - \frac{{\color{red}{e^{u}}}}{9}$$

Portanto,

$$\int{\left(- \frac{e^{u}}{9}\right)d u} = - \frac{e^{u}}{9}$$

Adicione a constante de integração:

$$\int{\left(- \frac{e^{u}}{9}\right)d u} = - \frac{e^{u}}{9}+C$$

$$$\int \left(- \frac{e^{u}}{9}\right)\, du = - \frac{e^{u}}{9} + C$$$A