What is the integral of 1/(xln(5x)) ?

The integral of 1/(xln(5x)) is ln|ln(5x)|+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(5x))

\int \frac{1}{x ln ( 5 x )} d x

ln ∣ ln (5 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 5 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 (5 x) ∣

Add a constant to the solution

= ln ∣ ln (5 x) ∣ + C

\int (sec (x))^{3} tan (x) d x

2 y^{3}

\int (x^{3} - a^{3})^{5} d x

\int - 8 cos (t) d t

\int 3 x^{3} - x d x

What is the integral of 1/(xln(5x)) ?
The integral of 1/(xln(5x)) is ln|ln(5x)|+C