Integral de $$$4 x^{216}$$$

Halla $$$\int 4 x^{216}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=4$$$ y $$$f{\left(x \right)} = x^{216}$$$:

$${\color{red}{\int{4 x^{216} d x}}} = {\color{red}{\left(4 \int{x^{216} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=216$$$:

$$4 {\color{red}{\int{x^{216} d x}}}=4 {\color{red}{\frac{x^{1 + 216}}{1 + 216}}}=4 {\color{red}{\left(\frac{x^{217}}{217}\right)}}$$

Por lo tanto,

$$\int{4 x^{216} d x} = \frac{4 x^{217}}{217}$$

Añade la constante de integración:

$$\int{4 x^{216} d x} = \frac{4 x^{217}}{217}+C$$

$$$\int 4 x^{216}\, dx = \frac{4 x^{217}}{217} + C$$$A