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

Popular >

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

= \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

\int [(4 x - 9)^{6} - 2 x] d x

\int \frac{3 x}{1 + x ^{4}} d x

y^{^{'}} + y^{3} = 0, y (0) = 3

\frac{\partial}{\partial x} (x^{3} y^{4} z^{2})

y = - \frac{2 x}{x ^{2} + 1}, (1, - 1)

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