Integral of $$$t^{6}$$$

The calculator will find the integral/antiderivative of $$$t^{6}$$$, with steps shown.

Find $$$\int t^{6}\, dt$$$.

Apply the power rule $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=6$$$:

$${\color{red}{\int{t^{6} d t}}}={\color{red}{\frac{t^{1 + 6}}{1 + 6}}}={\color{red}{\left(\frac{t^{7}}{7}\right)}}$$

Therefore,

$$\int{t^{6} d t} = \frac{t^{7}}{7}$$

Add the constant of integration:

$$\int{t^{6} d t} = \frac{t^{7}}{7}+C$$

$$$\int t^{6}\, dt = \frac{t^{7}}{7} + C$$$A