What is the integral of 2/(xln(6x)) ?

The integral of 2/(xln(6x)) is 2ln|ln(6x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(xln(6x))

\int \frac{2}{x ln ( 6 x )} d x

2 ln ∣ ln (6 x) ∣ + C

Solution steps

\int \frac{2}{x ln ( 6 x )} 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}{x ln ( 6 x )} d x

Apply u-substitution

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 2 ln ∣ v ∣

Substitute back

= 2 ln ∣ ln (6 x) ∣

Add a constant to the solution

= 2 ln ∣ ln (6 x) ∣ + C

\int \frac{1}{x 6 x + 49} d x

(2 y^{2} + 6 x) d x + (2 x y) d y = 0

\int cot^{3} (x) csc^{2} (x) d x

2 x^{2} cos (x) cot (x)

f (x) = 5

What is the integral of 2/(xln(6x)) ?
The integral of 2/(xln(6x)) is 2ln|ln(6x)|+C