en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1-ln(x)

Solution

\int - 1 - ln (x) d x

Solution

- x ln (x) + C

Solution steps

\int - 1 - ln (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

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

= - x - (x ln (x) - x)

Simplify

= - x ln (x)

Add a constant to the solution

= - x ln (x) + C

Popular Examples

integral of e^{1/100 x}

\int e^{\frac{1}{100} x} d x

integral of cos(2θ)(sin(θ)+cos(θ))^2

\int cos (2 θ) (sin (θ) + cos (θ))^{2} d θ

integral of sqrt(9x^{-6)-81x^{-8}}

\int 9 x^{- 6} - 81 x^{- 8} d x

integral of (x^2+1)/(x(x-1)^2)

\int \frac{x ^{2} + 1}{x ( x - 1 ) ^{2}} d x

integral of 1/z 1/x (x+z/x)

\int \frac{1}{z} \frac{1}{x} (x + \frac{z}{x}) d x

Frequently Asked Questions (FAQ)

What is the integral of-1-ln(x) ?
The integral of-1-ln(x) is -xln(x)+C