Integral of $$$r^{4}$$$

The calculator will find the integral/antiderivative of $$$r^{4}$$$, with steps shown.

Find $$$\int r^{4}\, dr$$$.

Apply the power rule $$$\int r^{n}\, dr = \frac{r^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=4$$$:

$${\color{red}{\int{r^{4} d r}}}={\color{red}{\frac{r^{1 + 4}}{1 + 4}}}={\color{red}{\left(\frac{r^{5}}{5}\right)}}$$

Therefore,

$$\int{r^{4} d r} = \frac{r^{5}}{5}$$

Add the constant of integration:

$$\int{r^{4} d r} = \frac{r^{5}}{5}+C$$

$$$\int r^{4}\, dr = \frac{r^{5}}{5} + C$$$A

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