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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

ln ∣ ln (3 x - 2) ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{1}{3 u ln ( u )} d u

= 3 \cdot \int \frac{1}{3 u ln ( u )} d u

Take the constant out:

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

= 3 \cdot \frac{1}{3} \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

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

= 3 \cdot \frac{1}{3} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 3 \cdot \frac{1}{3} ln ∣ v ∣

Substitute back

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

Simplify

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

= ln ∣ ln (3 x - 2) ∣

Add a constant to the solution

= ln ∣ ln (3 x - 2) ∣ + C

\int \frac{64}{x ^{2} + 16} d x

\int \frac{1}{1 - 64 t ^{2}} d t

\int \frac{[ ln ( x ) ] ^{2}}{x} d x

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

\int 2 x^{3} e^{- x} d x

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