What is the integral of (-3ln(x))/x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (-3ln(x))/x

\int \frac{- 3 ln ( x )}{x} d x

- \frac{3}{2} ln^{2} (x) + C

Solution steps

\int \frac{- 3 ln ( x )}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int \frac{ln ( x )}{x} d x

Apply u-substitution

= - 3 \cdot \int u d u

Apply the Power Rule

= - 3 \cdot \frac{u ^{2}}{2}

Substitute back

u = ln (x)

= - 3 \cdot \frac{ln ^{2} ( x )}{2}

Simplify

- 3 \cdot \frac{ln ^{2} ( x )}{2} : - \frac{3}{2} ln^{2} (x)

= - \frac{3}{2} ln^{2} (x)

Add a constant to the solution

= - \frac{3}{2} ln^{2} (x) + C

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