What is the integral of (1ln(x))/x ?

The integral of (1ln(x))/x is (ln^2(x))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1ln(x))/x

\int \frac{1 ln ( x )}{x} d x

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

Solution steps

\int \frac{1 \cdot ln ( x )}{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 ^{2} ( x )}{2}

Add a constant to the solution

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

\int \frac{x ^{2} - 3 x + 2}{x ^{2} - 9} d x

\int \frac{5 x ^{3} - 8 x + 6}{x ^{3} - x ^{2}} d x

\int x^{2} (2 x^{2} - 4)^{3} d x

\int cos (x) + \frac{1}{2} x d x

\int (1 - e^{x}) d x

What is the integral of (1ln(x))/x ?
The integral of (1ln(x))/x is (ln^2(x))/2+C