Calculus Examples

$\int \sqrt{x} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{d}{d x} [\int x^{\frac{1}{2}} d x]$

Step 2

$\int x^{\frac{1}{2}} d x$ is an antiderivative of $x^{\frac{1}{2}}$ , so by definition $\frac{d}{d x} [\int x^{\frac{1}{2}} d x]$ is $x^{\frac{1}{2}}$ .

$x^{\frac{1}{2}}$