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

The integral of e^{-x}*(-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 e^{-x}*(-x)

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

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

Solution steps

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

Simplify

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

Take the constant out:

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

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

Simplify

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

Add a constant to the solution

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

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