What is the integral of 1/(sqrt(5x+9)) ?

The integral of 1/(sqrt(5x+9)) is 2/5 sqrt(5x+9)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(sqrt(5x+9))

\int \frac{1}{5 x + 9} d x

\frac{2}{5} 5 x + 9 + C

Solution steps

\int \frac{1}{5 x + 9} d x

Apply u-substitution

= \int \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Apply the Power Rule

= \frac{1}{5} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 5 x + 9

= \frac{1}{5} \cdot 2 (5 x + 9)^{\frac{1}{2}}

Simplify

\frac{1}{5} \cdot 2 (5 x + 9)^{\frac{1}{2}} : \frac{2}{5} 5 x + 9

= \frac{2}{5} 5 x + 9

Add a constant to the solution

= \frac{2}{5} 5 x + 9 + C

What is the integral of 1/(sqrt(5x+9)) ?
The integral of 1/(sqrt(5x+9)) is 2/5 sqrt(5x+9)+C