What is the integral of (x^{1/2})/2 ?

The integral of (x^{1/2})/2 is 1/3 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 (x^{1/2})/2

\int \frac{x ^{\frac{1}{2}}}{2} d x

\frac{1}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{x ^{\frac{1}{2}}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

= \frac{1}{3} x^{\frac{3}{2}} + C

\int (e^{- \frac{t}{6}} - e^{\frac{t}{6}})^{2} d t

\int 5^{3 - 2 x^{2}} x d x

\int (sin (\frac{1}{x}) - \frac{1}{x} + 1) \frac{1}{x ^{2}} d x

\int sin (1 - 5 x) d x

What is the integral of (x^{1/2})/2 ?
The integral of (x^{1/2})/2 is 1/3 x^{3/2}+C