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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{2}{( 2 x - 3 ) ln ( 2 x - 3 )} d x

ln ∣ ln (2 x - 3) ∣ + C

Solution steps

\int \frac{2}{( 2 x - 3 ) ln ( 2 x - 3 )} 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}{( 2 x - 3 ) ln ( 2 x - 3 )} d x

Apply u-substitution

: \int \frac{1}{2 u ln ( u )} d u

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

Apply u-substitution

: \int \frac{1}{v} d v

= 2 \cdot \frac{1}{2} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 2 \cdot \frac{1}{2} ln ∣ v ∣

Substitute back

= 2 \cdot \frac{1}{2} ln ∣ ln (2 x - 3) ∣

Simplify

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

= ln ∣ ln (2 x - 3) ∣

Add a constant to the solution

= ln ∣ ln (2 x - 3) ∣ + C

\int - z e^{- yz} d y

\int 10.2 + 2.5 x + 0.1 x^{2} d x

\int a + b x + x^{5} d x

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

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