What is the integral of (11)/(3-2x) ?

The integral of (11)/(3-2x) is -11/2 ln|3-2x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (11)/(3-2x)

\int \frac{11}{3 - 2 x} d x

- \frac{11}{2} ln ∣ 3 - 2 x ∣ + C

Solution steps

\int \frac{11}{3 - 2 x} d x

Take the constant out:

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

= 11 \cdot \int \frac{1}{3 - 2 x} d x

Apply u-substitution

= 11 \cdot \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

= 11 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 11 (- \frac{1}{2} ln ∣ u ∣)

Substitute back

u = 3 - 2 x

= 11 (- \frac{1}{2} ln ∣ 3 - 2 x ∣)

Simplify

11 (- \frac{1}{2} ln ∣ 3 - 2 x ∣) : - \frac{11}{2} ln ∣ 3 - 2 x ∣

= - \frac{11}{2} ln ∣ 3 - 2 x ∣

Add a constant to the solution

= - \frac{11}{2} ln ∣ 3 - 2 x ∣ + C

What is the integral of (11)/(3-2x) ?
The integral of (11)/(3-2x) is -11/2 ln|3-2x|+C