Integral de $$$x^{- e}$$$

Encontre $$$\int x^{- e}\, dx$$$.

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

$${\color{red}{\int{x^{- e} d x}}}={\color{red}{\int{x^{- e} d x}}}={\color{red}{\frac{x^{1 - e}}{1 - e}}}={\color{red}{x^{1 - e} \left(1 - e\right)^{-1}}}={\color{red}{\frac{1}{x^{-1 + e} \left(1 - e\right)}}}$$

Portanto,

$$\int{x^{- e} d x} = \frac{1}{x^{-1 + e} \left(1 - e\right)}$$

Adicione a constante de integração:

$$\int{x^{- e} d x} = \frac{1}{x^{-1 + e} \left(1 - e\right)}+C$$

$$$\int x^{- e}\, dx = \frac{1}{x^{-1 + e} \left(1 - e\right)} + C$$$A