Integral de $$$544 i n t - x^{2} - 1$$$ em relação a $$$x$$$

Encontre $$$\int \left(544 i n t - x^{2} - 1\right)\, dx$$$.

Integre termo a termo:

$${\color{red}{\int{\left(544 i n t - x^{2} - 1\right)d x}}} = {\color{red}{\left(- \int{1 d x} - \int{x^{2} d x} + \int{544 i n t d x}\right)}}$$

Aplique a regra da constante $$$\int c\, dx = c x$$$ usando $$$c=1$$$:

$$- \int{x^{2} d x} + \int{544 i n t d x} - {\color{red}{\int{1 d x}}} = - \int{x^{2} d x} + \int{544 i n t d x} - {\color{red}{x}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=2$$$:

$$- x + \int{544 i n t d x} - {\color{red}{\int{x^{2} d x}}}=- x + \int{544 i n t d x} - {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=- x + \int{544 i n t d x} - {\color{red}{\left(\frac{x^{3}}{3}\right)}}$$

Aplique a regra da constante $$$\int c\, dx = c x$$$ usando $$$c=544 i n t$$$:

$$- \frac{x^{3}}{3} - x + {\color{red}{\int{544 i n t d x}}} = - \frac{x^{3}}{3} - x + {\color{red}{\left(544 i n t x\right)}}$$

Portanto,

$$\int{\left(544 i n t - x^{2} - 1\right)d x} = 544 i n t x - \frac{x^{3}}{3} - x$$

Simplifique:

$$\int{\left(544 i n t - x^{2} - 1\right)d x} = \frac{x \left(1632 i n t - x^{2} - 3\right)}{3}$$

Adicione a constante de integração:

$$\int{\left(544 i n t - x^{2} - 1\right)d x} = \frac{x \left(1632 i n t - x^{2} - 3\right)}{3}+C$$

$$$\int \left(544 i n t - x^{2} - 1\right)\, dx = \frac{x \left(1632 i n t - x^{2} - 3\right)}{3} + C$$$A