What is the integral of (ln(5x))/x ?

The integral of (ln(5x))/x is (ln^2(5x))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (ln(5x))/x

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

\frac{ln ^{2} ( 5 x )}{2} + C

Solution steps

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

Apply u-substitution

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

Apply u-substitution

= \int v d v

Apply the Power Rule

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

Substitute back

= \frac{ln ^{2} ( 5 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 5 x )}{2} + C

What is the integral of (ln(5x))/x ?
The integral of (ln(5x))/x is (ln^2(5x))/2+C