What is the integral of sqrt(2px) ?

The integral of sqrt(2px) is sqrt(2)sqrt(p) 2/3 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(2px)

\int 2 p x d x

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

Solution steps

\int 2 p x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int 2 p x d x

Take the constant out:

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

= 2 \cdot \int p x d x

p x = p x

= 2 \cdot \int p x d x

Take the constant out:

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

= 2 p \cdot \int x d x

Apply the Power Rule

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

Add a constant to the solution

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

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