Integral de $$$\frac{x^{6}}{1000}$$$

Encontre $$$\int \frac{x^{6}}{1000}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=\frac{1}{1000}$$$ e $$$f{\left(x \right)} = x^{6}$$$:

$${\color{red}{\int{\frac{x^{6}}{1000} d x}}} = {\color{red}{\left(\frac{\int{x^{6} d x}}{1000}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=6$$$:

$$\frac{{\color{red}{\int{x^{6} d x}}}}{1000}=\frac{{\color{red}{\frac{x^{1 + 6}}{1 + 6}}}}{1000}=\frac{{\color{red}{\left(\frac{x^{7}}{7}\right)}}}{1000}$$

Portanto,

$$\int{\frac{x^{6}}{1000} d x} = \frac{x^{7}}{7000}$$

Adicione a constante de integração:

$$\int{\frac{x^{6}}{1000} d x} = \frac{x^{7}}{7000}+C$$

$$$\int \frac{x^{6}}{1000}\, dx = \frac{x^{7}}{7000} + C$$$A