Integral of $$$r^{2}$$$

The calculator will find the integral/antiderivative of $$$r^{2}$$$, with steps shown.

Find $$$\int r^{2}\, dr$$$.

Apply the power rule $$$\int r^{n}\, dr = \frac{r^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=2$$$:

$${\color{red}{\int{r^{2} d r}}}={\color{red}{\frac{r^{1 + 2}}{1 + 2}}}={\color{red}{\left(\frac{r^{3}}{3}\right)}}$$

Therefore,

$$\int{r^{2} d r} = \frac{r^{3}}{3}$$

Add the constant of integration:

$$\int{r^{2} d r} = \frac{r^{3}}{3}+C$$

$$$\int r^{2}\, dr = \frac{r^{3}}{3} + C$$$A

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