Integral de $$$\frac{\cos{\left(x \right)}}{2}$$$

Encontre $$$\int \frac{\cos{\left(x \right)}}{2}\, dx$$$.

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 $$$f{\left(x \right)} = \cos{\left(x \right)}$$$:

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

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

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

Portanto,

$$\int{\frac{\cos{\left(x \right)}}{2} d x} = \frac{\sin{\left(x \right)}}{2}$$

Adicione a constante de integração:

$$\int{\frac{\cos{\left(x \right)}}{2} d x} = \frac{\sin{\left(x \right)}}{2}+C$$

$$$\int \frac{\cos{\left(x \right)}}{2}\, dx = \frac{\sin{\left(x \right)}}{2} + C$$$A