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

The integral of (1-x)e^x is -e^xx+2e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (1-x)e^x

integral

(1 - x) e^{x}

- e^{x} x + 2 e^{x} + C

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

e^{x} (1 - x) - (- e^{x}) : - e^{x} x + 2 e^{x}

= - e^{x} x + 2 e^{x}

Add a constant to the solution

= - e^{x} x + 2 e^{x} + C