What is the integral of sqrt(x)+\sqrt[3]{x} ?

The integral of sqrt(x)+\sqrt[3]{x} is 2/3 x^{3/2}+3/4 x^{4/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sqrt(x)+\sqrt[3]{x}

\frac{2}{3} x^{\frac{3}{2}} + \frac{3}{4} x^{\frac{4}{3}} + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

= \frac{2}{3} x^{\frac{3}{2}} + \frac{3}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{3}{4} x^{\frac{4}{3}} + C

What is the integral of sqrt(x)+\sqrt[3]{x} ?
The integral of sqrt(x)+\sqrt[3]{x} is 2/3 x^{3/2}+3/4 x^{4/3}+C