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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 $$$n=e$$$:
$${\color{red}{\int{x^{e} d x}}}={\color{red}{\frac{x^{1 + e}}{1 + e}}}={\color{red}{\frac{x^{1 + e}}{1 + e}}}$$
Therefore,
$$\int{x^{e} d x} = \frac{x^{1 + e}}{1 + e}$$
Add the constant of integration:
$$\int{x^{e} d x} = \frac{x^{1 + e}}{1 + e}+C$$
Answer
$$$\int x^{e}\, dx = \frac{x^{1 + e}}{1 + e} + C$$$A
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