Integral de $$$4 x^{11} z^{6}$$$ con respecto a $$$x$$$

Halla $$$\int 4 x^{11} z^{6}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=4 z^{6}$$$ y $$$f{\left(x \right)} = x^{11}$$$:

$${\color{red}{\int{4 x^{11} z^{6} d x}}} = {\color{red}{\left(4 z^{6} \int{x^{11} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=11$$$:

$$4 z^{6} {\color{red}{\int{x^{11} d x}}}=4 z^{6} {\color{red}{\frac{x^{1 + 11}}{1 + 11}}}=4 z^{6} {\color{red}{\left(\frac{x^{12}}{12}\right)}}$$

Por lo tanto,

$$\int{4 x^{11} z^{6} d x} = \frac{x^{12} z^{6}}{3}$$

Añade la constante de integración:

$$\int{4 x^{11} z^{6} d x} = \frac{x^{12} z^{6}}{3}+C$$

$$$\int 4 x^{11} z^{6}\, dx = \frac{x^{12} z^{6}}{3} + C$$$A