Integral de $$$25 x^{4}$$$

Halla $$$\int 25 x^{4}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=25$$$ y $$$f{\left(x \right)} = x^{4}$$$:

$${\color{red}{\int{25 x^{4} d x}}} = {\color{red}{\left(25 \int{x^{4} d x}\right)}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=4$$$:

$$25 {\color{red}{\int{x^{4} d x}}}=25 {\color{red}{\frac{x^{1 + 4}}{1 + 4}}}=25 {\color{red}{\left(\frac{x^{5}}{5}\right)}}$$

Por lo tanto,

$$\int{25 x^{4} d x} = 5 x^{5}$$

Añade la constante de integración:

$$\int{25 x^{4} d x} = 5 x^{5}+C$$

$$$\int 25 x^{4}\, dx = 5 x^{5} + C$$$A