Calculus Examples

$\int \sqrt[5]{x^{10}} d x$

Step 1

Simplify the expression.

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x^{10}}$ as $x^{\frac{10}{5}}$ .

$\int x^{\frac{10}{5}} d x$

Step 1.2

Divide $10$ by $5$ .

$\int x^{2} d x$

Step 2

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$\frac{1}{3} x^{3} + C$