Integral de $$$3 x^{16}$$$

Halla $$$\int 3 x^{16}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=3$$$ y $$$f{\left(x \right)} = x^{16}$$$:

$${\color{red}{\int{3 x^{16} d x}}} = {\color{red}{\left(3 \int{x^{16} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=16$$$:

$$3 {\color{red}{\int{x^{16} d x}}}=3 {\color{red}{\frac{x^{1 + 16}}{1 + 16}}}=3 {\color{red}{\left(\frac{x^{17}}{17}\right)}}$$

Por lo tanto,

$$\int{3 x^{16} d x} = \frac{3 x^{17}}{17}$$

Añade la constante de integración:

$$\int{3 x^{16} d x} = \frac{3 x^{17}}{17}+C$$

$$$\int 3 x^{16}\, dx = \frac{3 x^{17}}{17} + C$$$A