Integral de $$$1679616 x^{41}$$$

Encontre $$$\int 1679616 x^{41}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=1679616$$$ e $$$f{\left(x \right)} = x^{41}$$$:

$${\color{red}{\int{1679616 x^{41} d x}}} = {\color{red}{\left(1679616 \int{x^{41} d x}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=41$$$:

$$1679616 {\color{red}{\int{x^{41} d x}}}=1679616 {\color{red}{\frac{x^{1 + 41}}{1 + 41}}}=1679616 {\color{red}{\left(\frac{x^{42}}{42}\right)}}$$

Portanto,

$$\int{1679616 x^{41} d x} = \frac{279936 x^{42}}{7}$$

Adicione a constante de integração:

$$\int{1679616 x^{41} d x} = \frac{279936 x^{42}}{7}+C$$

$$$\int 1679616 x^{41}\, dx = \frac{279936 x^{42}}{7} + C$$$A