What is the integral of 1/(xln(3x)) ?

The integral of 1/(xln(3x)) is ln|ln(3x)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(xln(3x))

\int \frac{1}{x ln ( 3 x )} d x

ln ∣ ln (3 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 3 x )} d x

Apply u-substitution

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (3 x) ∣

Add a constant to the solution

= ln ∣ ln (3 x) ∣ + C

\frac{d}{d x} (\frac{ln ( x ) + 1}{ln ( x ) - 1})

x \to - 2 lim (\frac{2 - ∣ x ∣}{2 + x})

y^{^{'}} = 2 x y + x y^{2}

2 cos (t) - 2

\frac{d}{d x} (\frac{( 6 x ^{2} + 8 x + 8 )}{x})

What is the integral of 1/(xln(3x)) ?
The integral of 1/(xln(3x)) is ln|ln(3x)|+C