Integral of $$$t^{3}$$$

The calculator will find the integral/antiderivative of $$$t^{3}$$$, with steps shown.

Find $$$\int t^{3}\, dt$$$.

Apply the power rule $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=3$$$:

$${\color{red}{\int{t^{3} d t}}}={\color{red}{\frac{t^{1 + 3}}{1 + 3}}}={\color{red}{\left(\frac{t^{4}}{4}\right)}}$$

Therefore,

$$\int{t^{3} d t} = \frac{t^{4}}{4}$$

Add the constant of integration:

$$\int{t^{3} d t} = \frac{t^{4}}{4}+C$$

$$$\int t^{3}\, dt = \frac{t^{4}}{4} + C$$$A