What is the integral of 5/(2x-4) ?

The integral of 5/(2x-4) is 5/2 ln|2x-4|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(2x-4)

\int \frac{5}{2 x - 4} d x

\frac{5}{2} ln ∣ 2 x - 4 ∣ + C

Solution steps

\int \frac{5}{2 x - 4} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{2 x - 4} d x

Apply u-substitution

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

= 5 \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

= 5 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = 2 x - 4

= 5 \cdot \frac{1}{2} ln ∣ 2 x - 4 ∣

Simplify

5 \cdot \frac{1}{2} ln ∣ 2 x - 4 ∣ : \frac{5}{2} ln ∣ 2 x - 4 ∣

= \frac{5}{2} ln ∣ 2 x - 4 ∣

Add a constant to the solution

= \frac{5}{2} ln ∣ 2 x - 4 ∣ + C

\int \frac{1}{28 - x ^{2}} d x

\int \frac{3 x}{x - 4} d x

\int (\frac{1 + e ^{2 x}}{4 e ^{x}}) d x

\int \frac{x}{( x + 4 ) ( x - 3 )} d x

\int \frac{1 - x ^{3}}{x ^{2} x} d x