Calculus Examples

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

Step 1

Split the single integral into multiple integrals.

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

Step 2

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

$\frac{4}{7} x^{\frac{7}{4}} + C + \int x^{\frac{4}{3}} d x$

Step 3

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

$\frac{4}{7} x^{\frac{7}{4}} + C + \frac{3}{7} x^{\frac{7}{3}} + C$

Step 4

Simplify.

$\frac{4}{7} x^{\frac{7}{4}} + \frac{3}{7} x^{\frac{7}{3}} + C$