Integral de $$$8 x^{18}$$$

Encontre $$$\int 8 x^{18}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=8$$$ e $$$f{\left(x \right)} = x^{18}$$$:

$${\color{red}{\int{8 x^{18} d x}}} = {\color{red}{\left(8 \int{x^{18} d x}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=18$$$:

$$8 {\color{red}{\int{x^{18} d x}}}=8 {\color{red}{\frac{x^{1 + 18}}{1 + 18}}}=8 {\color{red}{\left(\frac{x^{19}}{19}\right)}}$$

Portanto,

$$\int{8 x^{18} d x} = \frac{8 x^{19}}{19}$$

Adicione a constante de integração:

$$\int{8 x^{18} d x} = \frac{8 x^{19}}{19}+C$$

$$$\int 8 x^{18}\, dx = \frac{8 x^{19}}{19} + C$$$A