Integral of $$$r^{3}$$$
The calculator will find the integral/antiderivative of $$$r^{3}$$$, with steps shown.
Related calculator: Definite and Improper Integral Calculator
Your Input
Find $$$\int r^{3}\, dr$$$.
Solution
Apply the power rule $$$\int r^{n}\, dr = \frac{r^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=3$$$:
$${\color{red}{\int{r^{3} d r}}}={\color{red}{\frac{r^{1 + 3}}{1 + 3}}}={\color{red}{\left(\frac{r^{4}}{4}\right)}}$$
Therefore,
$$\int{r^{3} d r} = \frac{r^{4}}{4}$$
Add the constant of integration:
$$\int{r^{3} d r} = \frac{r^{4}}{4}+C$$
Answer
$$$\int r^{3}\, dr = \frac{r^{4}}{4} + C$$$A