Integral de $$$\frac{\sin{\left(x \right)}}{23}$$$

Encontre $$$\int \frac{\sin{\left(x \right)}}{23}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=\frac{1}{23}$$$ e $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:

$${\color{red}{\int{\frac{\sin{\left(x \right)}}{23} d x}}} = {\color{red}{\left(\frac{\int{\sin{\left(x \right)} d x}}{23}\right)}}$$

A integral do seno é $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$$\frac{{\color{red}{\int{\sin{\left(x \right)} d x}}}}{23} = \frac{{\color{red}{\left(- \cos{\left(x \right)}\right)}}}{23}$$

Portanto,

$$\int{\frac{\sin{\left(x \right)}}{23} d x} = - \frac{\cos{\left(x \right)}}{23}$$

Adicione a constante de integração:

$$\int{\frac{\sin{\left(x \right)}}{23} d x} = - \frac{\cos{\left(x \right)}}{23}+C$$

$$$\int \frac{\sin{\left(x \right)}}{23}\, dx = - \frac{\cos{\left(x \right)}}{23} + C$$$A