What is the integral of 1/(xsqrt(ln(10x))) ?

The integral of 1/(xsqrt(ln(10x))) is 2sqrt(ln(10x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(xsqrt(ln(10x)))

\int \frac{1}{x ln ( 10 x )} d x

2 ln (10 x) + C

Solution steps

\int \frac{1}{x ln ( 10 x )} d x

Apply u-substitution

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

= \int \frac{1}{v} d v

Apply the Power Rule

= 2 v^{\frac{1}{2}}

Substitute back

= 2 ln^{\frac{1}{2}} (10 x)

Apply radical rule:

= 2 ln (10 x)

Add a constant to the solution

= 2 ln (10 x) + C

What is the integral of 1/(xsqrt(ln(10x))) ?
The integral of 1/(xsqrt(ln(10x))) is 2sqrt(ln(10x))+C