Integral de $$$32 x^{10}$$$

Halla $$$\int 32 x^{10}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=32$$$ y $$$f{\left(x \right)} = x^{10}$$$:

$${\color{red}{\int{32 x^{10} d x}}} = {\color{red}{\left(32 \int{x^{10} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=10$$$:

$$32 {\color{red}{\int{x^{10} d x}}}=32 {\color{red}{\frac{x^{1 + 10}}{1 + 10}}}=32 {\color{red}{\left(\frac{x^{11}}{11}\right)}}$$

Por lo tanto,

$$\int{32 x^{10} d x} = \frac{32 x^{11}}{11}$$

Añade la constante de integración:

$$\int{32 x^{10} d x} = \frac{32 x^{11}}{11}+C$$

$$$\int 32 x^{10}\, dx = \frac{32 x^{11}}{11} + C$$$A