Integral de $$$63 x^{23} - 126$$$

Encontre $$$\int \left(63 x^{23} - 126\right)\, dx$$$.

Integre termo a termo:

$${\color{red}{\int{\left(63 x^{23} - 126\right)d x}}} = {\color{red}{\left(- \int{126 d x} + \int{63 x^{23} d x}\right)}}$$

Aplique a regra da constante $$$\int c\, dx = c x$$$ usando $$$c=126$$$:

$$\int{63 x^{23} d x} - {\color{red}{\int{126 d x}}} = \int{63 x^{23} d x} - {\color{red}{\left(126 x\right)}}$$

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=63$$$ e $$$f{\left(x \right)} = x^{23}$$$:

$$- 126 x + {\color{red}{\int{63 x^{23} d x}}} = - 126 x + {\color{red}{\left(63 \int{x^{23} d x}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=23$$$:

$$- 126 x + 63 {\color{red}{\int{x^{23} d x}}}=- 126 x + 63 {\color{red}{\frac{x^{1 + 23}}{1 + 23}}}=- 126 x + 63 {\color{red}{\left(\frac{x^{24}}{24}\right)}}$$

Portanto,

$$\int{\left(63 x^{23} - 126\right)d x} = \frac{21 x^{24}}{8} - 126 x$$

Simplifique:

$$\int{\left(63 x^{23} - 126\right)d x} = \frac{21 x \left(x^{23} - 48\right)}{8}$$

Adicione a constante de integração:

$$\int{\left(63 x^{23} - 126\right)d x} = \frac{21 x \left(x^{23} - 48\right)}{8}+C$$

$$$\int \left(63 x^{23} - 126\right)\, dx = \frac{21 x \left(x^{23} - 48\right)}{8} + C$$$A