What is the integral of 8/(xln(x)) ?

The integral of 8/(xln(x)) is 8ln|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 8/(xln(x))

\int \frac{8}{x ln ( x )} d x

8 ln ∣ ln (x) ∣ + C

Solution steps

\int \frac{8}{x ln ( x )} d x

Take the constant out:

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

= 8 \cdot \int \frac{1}{x ln ( x )} d x

Apply u-substitution

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

= 8 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 ln ∣ u ∣

Substitute back

u = ln (x)

= 8 ln ∣ ln (x) ∣

Add a constant to the solution

= 8 ln ∣ ln (x) ∣ + C

\int \frac{2}{( 3 x + 5 ) ^{2}} d x

\int cot^{10} (x) csc^{4} (x) d x

\int \frac{3 x ^{2} - x + 2}{( x + 1 ) ( x ^{2} + 1 )} d x

\int \frac{x}{( 2 x - 1 ) ^{3}} d x

\int ln (4) 4^{x} d x