What is the integral of (sqrt(x))/3 ?

The integral of (sqrt(x))/3 is 2/9 x^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sqrt(x))/3

\int \frac{x}{3} d x

\frac{2}{9} x^{\frac{3}{2}} + C

Solution steps

\int \frac{x}{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int x d x

Apply the Power Rule

= \frac{1}{3} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{2}{9} x^{\frac{3}{2}}

= \frac{2}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{9} x^{\frac{3}{2}} + C

What is the integral of (sqrt(x))/3 ?
The integral of (sqrt(x))/3 is 2/9 x^{3/2}+C