Integral de $$$2 x^{5}$$$

Halla $$$\int 2 x^{5}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=2$$$ y $$$f{\left(x \right)} = x^{5}$$$:

$${\color{red}{\int{2 x^{5} d x}}} = {\color{red}{\left(2 \int{x^{5} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=5$$$:

$$2 {\color{red}{\int{x^{5} d x}}}=2 {\color{red}{\frac{x^{1 + 5}}{1 + 5}}}=2 {\color{red}{\left(\frac{x^{6}}{6}\right)}}$$

Por lo tanto,

$$\int{2 x^{5} d x} = \frac{x^{6}}{3}$$

Añade la constante de integración:

$$\int{2 x^{5} d x} = \frac{x^{6}}{3}+C$$

$$$\int 2 x^{5}\, dx = \frac{x^{6}}{3} + C$$$A