Calculus Examples

$\int (\sqrt[4]{x^{3}} + 1) d x$

Step 1

Remove parentheses.

$\int \sqrt[4]{x^{3}} + 1 d x$

Step 2

Split the single integral into multiple integrals.

$\int \sqrt[4]{x^{3}} d x + \int d x$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{3}}$ as $x^{\frac{3}{4}}$ .

$\int x^{\frac{3}{4}} d x + \int d x$

Step 4

By the Power Rule, the integral of $x^{\frac{3}{4}}$ with respect to $x$ is $\frac{4}{7} x^{\frac{7}{4}}$ .

$\frac{4}{7} x^{\frac{7}{4}} + C + \int d x$

Step 5

Apply the constant rule.

$\frac{4}{7} x^{\frac{7}{4}} + C + x + C$

Step 6

Simplify.

$\frac{4}{7} x^{\frac{7}{4}} + x + C$