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

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

\int \frac{ln ∣ x ∣}{x} d x

\frac{ln ∣ x ∣ ^{2}}{2} + C

Solution steps

\int \frac{ln ∣ x ∣}{x} d x

\frac{ln ∣ x ∣}{x} = ln ∣ x ∣ \frac{1}{x}

= \int ln ∣ x ∣ \frac{1}{x} d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = ln ∣ x ∣

= \frac{ln ∣ x ∣ ^{2}}{2}

Add a constant to the solution

= \frac{ln ∣ x ∣ ^{2}}{2} + C

n = 1 \sum \infty \frac{1}{( 4 n ) ^{2} - 1}

x \to - 1 + lim (- 1)

\frac{d}{d x} (x e^{4 x + 1} + \frac{1}{2})

f (x) = x^{2} - sec (x)

x y^{^{''}} = y^{^{'}}