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

The integral of (-x)/(e^x) is x/(e^x)+1/(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 \frac{- x}{e ^{x}} d x

\frac{x}{e ^{x}} + \frac{1}{e ^{x}} + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

\int - \frac{1}{e ^{x}} d x = \frac{1}{e ^{x}}

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

Simplify

= \frac{x}{e ^{x}} + \frac{1}{e ^{x}}

Add a constant to the solution

= \frac{x}{e ^{x}} + \frac{1}{e ^{x}} + C

What is the integral of (-x)/(e^x) ?
The integral of (-x)/(e^x) is x/(e^x)+1/(e^x)+C