What is the integral of ((ln^2(x)))/x ?

The integral of ((ln^2(x)))/x is (ln^3(x))/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ((ln^2(x)))/x

\int \frac{( ln ^{2} ( x ) )}{x} d x

\frac{ln ^{3} ( x )}{3} + C

Solution steps

\int \frac{ln ^{2} ( x )}{x} d x

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

= \frac{u ^{3}}{3}

Substitute back

u = ln (x)

= \frac{ln ^{3} ( x )}{3}

Add a constant to the solution

= \frac{ln ^{3} ( x )}{3} + C

What is the integral of ((ln^2(x)))/x ?
The integral of ((ln^2(x)))/x is (ln^3(x))/3+C