Integral of $$$x^{\frac{4}{3}}$$$

Find $$$\int x^{\frac{4}{3}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=\frac{4}{3}$$$:

$${\color{red}{\int{x^{\frac{4}{3}} d x}}}={\color{red}{\frac{x^{1 + \frac{4}{3}}}{1 + \frac{4}{3}}}}={\color{red}{\left(\frac{3 x^{\frac{7}{3}}}{7}\right)}}$$

Therefore,

$$\int{x^{\frac{4}{3}} d x} = \frac{3 x^{\frac{7}{3}}}{7}$$

Add the constant of integration:

$$\int{x^{\frac{4}{3}} d x} = \frac{3 x^{\frac{7}{3}}}{7}+C$$

$$$\int x^{\frac{4}{3}}\, dx = \frac{3 x^{\frac{7}{3}}}{7} + C$$$A