Calculus Examples

$\int \sqrt{x^{9}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{9}}$ as $x^{\frac{9}{2}}$ .

$\int x^{\frac{9}{2}} d x$

Step 2

By the Power Rule, the integral of $x^{\frac{9}{2}}$ with respect to $x$ is $\frac{2}{11} x^{\frac{11}{2}}$ .

$\frac{2}{11} x^{\frac{11}{2}} + C$