Integral of $$$t^{4}$$$

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

Find $$$\int t^{4}\, dt$$$.

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

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

Therefore,

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

Add the constant of integration:

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

$$$\int t^{4}\, dt = \frac{t^{5}}{5} + C$$$A

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