Integral of $$$u^{\frac{2}{3}}$$$

Find $$$\int u^{\frac{2}{3}}\, du$$$.

Apply the power rule $$$\int u^{n}\, du = \frac{u^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=\frac{2}{3}$$$:

$${\color{red}{\int{u^{\frac{2}{3}} d u}}}={\color{red}{\frac{u^{\frac{2}{3} + 1}}{\frac{2}{3} + 1}}}={\color{red}{\left(\frac{3 u^{\frac{5}{3}}}{5}\right)}}$$

Therefore,

$$\int{u^{\frac{2}{3}} d u} = \frac{3 u^{\frac{5}{3}}}{5}$$

Add the constant of integration:

$$\int{u^{\frac{2}{3}} d u} = \frac{3 u^{\frac{5}{3}}}{5}+C$$

$$$\int u^{\frac{2}{3}}\, du = \frac{3 u^{\frac{5}{3}}}{5} + C$$$A