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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= - 2 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= - 2 (- \frac{1}{u})

Substitute back

u = ln (x)

= - 2 (- \frac{1}{ln ( x )})

Simplify

- 2 (- \frac{1}{ln ( x )}) : \frac{2}{ln ( x )}

= \frac{2}{ln ( x )}

Add a constant to the solution

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

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