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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(2x^{1/2)}

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

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

Solution steps

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

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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

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