What is the integral of 1/(sqrt(2x+3)) ?

The integral of 1/(sqrt(2x+3)) is sqrt(2x+3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(sqrt(2x+3))

\int \frac{1}{2 x + 3} d x

2 x + 3 + C

Solution steps

\int \frac{1}{2 x + 3} d x

Apply u-substitution

= \int \frac{1}{2 u} d u

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}{u} d u

Apply the Power Rule

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

Substitute back

u = 2 x + 3

= \frac{1}{2} \cdot 2 (2 x + 3)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (2 x + 3)^{\frac{1}{2}} : 2 x + 3

= 2 x + 3

Add a constant to the solution

= 2 x + 3 + C

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