Calculus Examples

$\int \sqrt[7]{x^{2}} - \frac{5}{x^{2}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{x^{2}}$ as $x^{\frac{2}{7}}$ .

$\frac{d}{d x} [\int x^{\frac{2}{7}} - \frac{5}{x^{2}} d x]$

Step 2

$\int x^{\frac{2}{7}} - \frac{5}{x^{2}} d x$ is an antiderivative of $x^{\frac{2}{7}} - \frac{5}{x^{2}}$ , so by definition $\frac{d}{d x} [\int x^{\frac{2}{7}} - \frac{5}{x^{2}} d x]$ is $x^{\frac{2}{7}} - \frac{5}{x^{2}}$ .

$x^{\frac{2}{7}} - \frac{5}{x^{2}}$

Step 3

Reorder terms.

$- \frac{5}{x^{2}} + x^{\frac{2}{7}}$