What is the integral of x(e^{-x}) ?

The integral of x(e^{-x}) is -e^{-x}x-e^{-x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x(e^{-x})

\int x (e^{- x}) d x

- e^{- x} x - e^{- x} + C

Solution steps

\int x e^{- x} d x

Apply Integration By Parts

= - e^{- x} x - \int - e^{- x} d x

\int - e^{- x} d x = e^{- x}

= - e^{- x} x - e^{- x}

Add a constant to the solution

= - e^{- x} x - e^{- x} + C

What is the integral of x(e^{-x}) ?
The integral of x(e^{-x}) is -e^{-x}x-e^{-x}+C