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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6/(xln(x))

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

6 ln ∣ ln (x) ∣ + C

Solution steps

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

Take the constant out:

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

= 6 \cdot \int \frac{1}{x ln ( x )} d x

Apply u-substitution

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

= 6 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 6 ln ∣ u ∣

Substitute back

u = ln (x)

= 6 ln ∣ ln (x) ∣

Add a constant to the solution

= 6 ln ∣ ln (x) ∣ + C

G (t) = \frac{1 - 6 t}{2 + t}

n = 1 \sum \infty (- \frac{3}{4})^{n}

x \to 0 - lim (cos (x^{2}))

\int_{0}^{3} \frac{1}{4 - t} d t