What is the integral of 2/(sqrt(3x-7)) ?

The integral of 2/(sqrt(3x-7)) is 4/3 sqrt(3x-7)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 2/(sqrt(3x-7))

\int \frac{2}{3 x - 7} d x

\frac{4}{3} 3 x - 7 + C

Solution steps

\int \frac{2}{3 x - 7} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{3 x - 7} d x

Apply u-substitution

= 2 \cdot \int \frac{1}{3 u} d u

Take the constant out:

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

= 2 \cdot \frac{1}{3} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

Substitute back

u = 3 x - 7

= 2 \cdot \frac{1}{3} \cdot 2 (3 x - 7)^{\frac{1}{2}}

Simplify

2 \cdot \frac{1}{3} \cdot 2 (3 x - 7)^{\frac{1}{2}} : \frac{4}{3} 3 x - 7

= \frac{4}{3} 3 x - 7

Add a constant to the solution

= \frac{4}{3} 3 x - 7 + C

What is the integral of 2/(sqrt(3x-7)) ?
The integral of 2/(sqrt(3x-7)) is 4/3 sqrt(3x-7)+C