What is the integral of-ln(x) ?

The integral of-ln(x) is -xln(x)+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of-ln(x)

\int - ln (x) d x

- x ln (x) + x + C

Solution steps

\int - ln (x) d x

Take the constant out:

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

= - \int ln (x) d x

Apply Integration By Parts

= - (x ln (x) - \int 1 d x)

\int 1 d x = x

= - (x ln (x) - x)

Simplify

= - x ln (x) + x

Add a constant to the solution

= - x ln (x) + x + C