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

Popular >

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

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

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \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

\int \frac{y ^{2}}{25 + y ^{2}} d y

\frac{d}{d n} ((1 + i)^{n})

f (x) = - \frac{3}{x ^{4}}

\int 0.3 x^{2} d x

\int - 4 ln (x) d x

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