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

The integral of (ln(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 (ln(x))/x

integral

\frac{ln ( x )}{x}

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

Solution steps

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

\int \frac{x ^{2}}{( x - 3 ) ^{5}} d x

\int x (x^{2} + 1)^{\frac{3}{2}} d x

\int - 3 x ln (x) d x

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