What is the integral of (ln(21x))/x ?

The integral of (ln(21x))/x is (ln^2(21x))/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(21x))/x

\int \frac{ln ( 21 x )}{x} d x

\frac{ln ^{2} ( 21 x )}{2} + C

Solution steps

\int \frac{ln ( 21 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} ( 21 x )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( 21 x )}{2} + C

\frac{d}{d x} (\frac{x}{9 x + 2})

\int (9 - 5 x) d x

\frac{\partial}{\partial x} (2 x - 6 y^{2} - 6)

\int sec^{2} (2 x) d x

f (x) = x^{5} ln (x)

What is the integral of (ln(21x))/x ?
The integral of (ln(21x))/x is (ln^2(21x))/2+C