What is the integral of e^{-x}(x-1) ?

The integral of e^{-x}(x-1) is -e^{-x}x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-x}(x-1)

\int e^{- x} (x - 1) d x

- e^{- x} x + C

Solution steps

\int e^{- x} (x - 1) d x

Apply Integration By Parts

= - e^{- x} (x - 1) - \int - e^{- x} d x

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

= - e^{- x} (x - 1) - e^{- x}

Simplify

- e^{- x} (x - 1) - e^{- x} : - e^{- x} x

= - e^{- x} x

Add a constant to the solution

= - e^{- x} x + C