Integral de $$$243 x^{10}$$$

Encontre $$$\int 243 x^{10}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=243$$$ e $$$f{\left(x \right)} = x^{10}$$$:

$${\color{red}{\int{243 x^{10} d x}}} = {\color{red}{\left(243 \int{x^{10} d x}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=10$$$:

$$243 {\color{red}{\int{x^{10} d x}}}=243 {\color{red}{\frac{x^{1 + 10}}{1 + 10}}}=243 {\color{red}{\left(\frac{x^{11}}{11}\right)}}$$

Portanto,

$$\int{243 x^{10} d x} = \frac{243 x^{11}}{11}$$

Adicione a constante de integração:

$$\int{243 x^{10} d x} = \frac{243 x^{11}}{11}+C$$

$$$\int 243 x^{10}\, dx = \frac{243 x^{11}}{11} + C$$$A