Integral de $$$\frac{x^{5}}{4}$$$

Encontre $$$\int \frac{x^{5}}{4}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=\frac{1}{4}$$$ e $$$f{\left(x \right)} = x^{5}$$$:

$${\color{red}{\int{\frac{x^{5}}{4} d x}}} = {\color{red}{\left(\frac{\int{x^{5} d x}}{4}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=5$$$:

$$\frac{{\color{red}{\int{x^{5} d x}}}}{4}=\frac{{\color{red}{\frac{x^{1 + 5}}{1 + 5}}}}{4}=\frac{{\color{red}{\left(\frac{x^{6}}{6}\right)}}}{4}$$

Portanto,

$$\int{\frac{x^{5}}{4} d x} = \frac{x^{6}}{24}$$

Adicione a constante de integração:

$$\int{\frac{x^{5}}{4} d x} = \frac{x^{6}}{24}+C$$

$$$\int \frac{x^{5}}{4}\, dx = \frac{x^{6}}{24} + C$$$A