Integral de $$$\frac{u}{2}$$$

Encontre $$$\int \frac{u}{2}\, du$$$.

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

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

Aplique a regra da potência $$$\int u^{n}\, du = \frac{u^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=1$$$:

$$\frac{{\color{red}{\int{u d u}}}}{2}=\frac{{\color{red}{\frac{u^{1 + 1}}{1 + 1}}}}{2}=\frac{{\color{red}{\left(\frac{u^{2}}{2}\right)}}}{2}$$

Portanto,

$$\int{\frac{u}{2} d u} = \frac{u^{2}}{4}$$

Adicione a constante de integração:

$$\int{\frac{u}{2} d u} = \frac{u^{2}}{4}+C$$

$$$\int \frac{u}{2}\, du = \frac{u^{2}}{4} + C$$$A