Integral of $$$x^{a}$$$ with respect to $$$x$$$

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

Find $$$\int x^{a}\, dx$$$.

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

$${\color{red}{\int{x^{a} d x}}}={\color{red}{\frac{x^{a + 1}}{a + 1}}}={\color{red}{\frac{x^{a + 1}}{a + 1}}}$$

Therefore,

$$\int{x^{a} d x} = \frac{x^{a + 1}}{a + 1}$$

Add the constant of integration:

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

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

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