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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of-2/(xln(x))

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

- 2 ln ∣ ln (x) ∣ + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 ln ∣ u ∣

Substitute back

u = ln (x)

= - 2 ln ∣ ln (x) ∣

Add a constant to the solution

= - 2 ln ∣ ln (x) ∣ + C

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