What is the integral of (ln(3x))/(sqrt(x)) ?

The integral of (ln(3x))/(sqrt(x)) is 2sqrt(x)ln(3x)-4sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (ln(3x))/(sqrt(x))

\int \frac{ln ( 3 x )}{x} d x

2 x ln (3 x) - 4 x + C

Solution steps

\int \frac{ln ( 3 x )}{x} d x

Apply Integration By Parts

= 2 x ln (3 x) - \int \frac{2}{x} d x

\int \frac{2}{x} d x = 4 x

= 2 x ln (3 x) - 4 x

Add a constant to the solution

= 2 x ln (3 x) - 4 x + C

What is the integral of (ln(3x))/(sqrt(x)) ?
The integral of (ln(3x))/(sqrt(x)) is 2sqrt(x)ln(3x)-4sqrt(x)+C