What is the integral of x*e^{-x/2} ?

The integral of x*e^{-x/2} is -2e^{-x/2}x-4e^{-x/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x*e^{-x/2}

\int x \cdot e^{- \frac{x}{2}} d x

- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

Solution steps

\int x e^{- \frac{x}{2}} d x

Apply Integration By Parts

: - 2 e^{- \frac{x}{2}} x - \int - 2 e^{- \frac{x}{2}} d x

= - 2 e^{- \frac{x}{2}} x - \int - 2 e^{- \frac{x}{2}} d x

\int - 2 e^{- \frac{x}{2}} d x = 4 e^{- \frac{x}{2}}

= - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}}

Add a constant to the solution

= - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

\frac{( s + 3 )}{( s + 1 ) ^{2}}

\int \frac{1}{x - 6} d x

- 1 {\frac{- 3}{- s + 2}}

\int \frac{z}{2 z ^{2} + 8} d z

(- 2, 3), (- 1, - 2)

What is the integral of x*e^{-x/2} ?
The integral of x*e^{-x/2} is -2e^{-x/2}x-4e^{-x/2}+C