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

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

Find $$$\int u^{a}\, du$$$.

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

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

Therefore,

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

Add the constant of integration:

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

$$$\int u^{a}\, du = \frac{u^{a + 1}}{a + 1} + C$$$A