Integral of $$$x^{n - 1}$$$ with respect to $$$x$$$

The calculator will find the integral/antiderivative of $$$x^{n - 1}$$$ with respect to $$$x$$$, with steps shown.

Find $$$\int x^{n - 1}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=n - 1$$$:

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

Therefore,

$$\int{x^{n - 1} d x} = \frac{x^{n}}{n}$$

Add the constant of integration:

$$\int{x^{n - 1} d x} = \frac{x^{n}}{n}+C$$

$$$\int x^{n - 1}\, dx = \frac{x^{n}}{n} + C$$$A

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