Integral of $$$u^{5}$$$

The calculator will find the integral/antiderivative of $$$u^{5}$$$, with steps shown.

Find $$$\int u^{5}\, du$$$.

Apply the power rule $$$\int u^{n}\, du = \frac{u^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=5$$$:

$${\color{red}{\int{u^{5} d u}}}={\color{red}{\frac{u^{1 + 5}}{1 + 5}}}={\color{red}{\left(\frac{u^{6}}{6}\right)}}$$

Therefore,

$$\int{u^{5} d u} = \frac{u^{6}}{6}$$

Add the constant of integration:

$$\int{u^{5} d u} = \frac{u^{6}}{6}+C$$

$$$\int u^{5}\, du = \frac{u^{6}}{6} + C$$$A

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