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