What is the integral of (log_{e}(x))/x ?

The integral of (log_{e}(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

integral of (log_{e}(x))/x

\int \frac{lo g _{e} ( x )}{x} d x

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

Solution steps

\int \frac{lo g _{e} ( x )}{x} d x

Simplify

lo g_{e} (x) : ln (x)

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

Apply u-substitution

= \int u d u

Apply the Power Rule

= \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

What is the integral of (log_{e}(x))/x ?
The integral of (log_{e}(x))/x is (ln^2(x))/2+C