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

Popular >

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

= - (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

\int \frac{( e ^{- x} + 5 ) ^{3}}{e ^{x}} d x

\int - cos (θ) + sin (θ) + 4 d θ

\int u + 1 d u

\int y^{2} + 2 d y

\int (5 x + 7) d x