What is the integral of 1/(xln(7x)) ?

The integral of 1/(xln(7x)) is ln|ln(7x)|+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(7x))

\int \frac{1}{x ln ( 7 x )} d x

ln ∣ ln (7 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 7 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 (7 x) ∣

Add a constant to the solution

= ln ∣ ln (7 x) ∣ + C

\int \frac{sin ( 41 x )}{1 + ( cos ( 41 x ) ) ^{2}} d x

\int cos (a x) e^{b x} d x

\int ln (x) cos (ln (x)) d x

\int \frac{1}{9 x ^{2} + 25} d x

What is the integral of 1/(xln(7x)) ?
The integral of 1/(xln(7x)) is ln|ln(7x)|+C