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Integral of $$$x^{- e}$$$
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int x^{- e}\, dx$$$.
Solution
Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=- e$$$:
$${\color{red}{\int{x^{- e} d x}}}={\color{red}{\int{x^{- e} d x}}}={\color{red}{\frac{x^{1 - e}}{1 - e}}}={\color{red}{x^{1 - e} \left(1 - e\right)^{-1}}}={\color{red}{\frac{1}{x^{-1 + e} \left(1 - e\right)}}}$$
Therefore,
$$\int{x^{- e} d x} = \frac{1}{x^{-1 + e} \left(1 - e\right)}$$
Add the constant of integration:
$$\int{x^{- e} d x} = \frac{1}{x^{-1 + e} \left(1 - e\right)}+C$$
Answer
$$$\int x^{- e}\, dx = \frac{1}{x^{-1 + e} \left(1 - e\right)} + C$$$A