# What is the antiderivative of x^(1/2)?

Apr 4, 2018

$\frac{2 {x}^{\frac{3}{2}}}{3} + C$

#### Explanation:

A simple rule:

$\int {x}^{n} \mathrm{dx} = \frac{{x}^{n + 1}}{n + 1}$ where $n$ is a constant.

Therefore,

$\int {x}^{\frac{1}{2}} \mathrm{dx} = \frac{{x}^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}$ Le'ts simplify this a bit.

$\implies \frac{{x}^{\frac{3}{2}}}{\frac{3}{2}}$

$\implies \left({x}^{\frac{3}{2}}\right) \cdot \frac{2}{3}$

$\implies \frac{2 {x}^{\frac{3}{2}}}{3}$ Do you $C$ why this is incomplete?

$\implies \frac{2 {x}^{\frac{3}{2}}}{3} + C$ This is our answer!