Integral of $$$t^{\frac{5}{2}}$$$

Find $$$\int t^{\frac{5}{2}}\, dt$$$.

Apply the power rule $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=\frac{5}{2}$$$:

$${\color{red}{\int{t^{\frac{5}{2}} d t}}}={\color{red}{\frac{t^{1 + \frac{5}{2}}}{1 + \frac{5}{2}}}}={\color{red}{\left(\frac{2 t^{\frac{7}{2}}}{7}\right)}}$$

Therefore,

$$\int{t^{\frac{5}{2}} d t} = \frac{2 t^{\frac{7}{2}}}{7}$$

Add the constant of integration:

$$\int{t^{\frac{5}{2}} d t} = \frac{2 t^{\frac{7}{2}}}{7}+C$$

$$$\int t^{\frac{5}{2}}\, dt = \frac{2 t^{\frac{7}{2}}}{7} + C$$$A