Integral of $$$r^{5}$$$

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

Find $$$\int r^{5}\, dr$$$.

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

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

Therefore,

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

Add the constant of integration:

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

$$$\int r^{5}\, dr = \frac{r^{6}}{6} + C$$$A

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