What is the integral from 0 to infinity of xe^{-x/9} ?

The integral from 0 to infinity of xe^{-x/9} is 81

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to infinity of xe^{-x/9}

\int_{0}^{\infty} x e^{- \frac{x}{9}} d x

81

Solution steps

\int_{0}^{\infty} x e^{- \frac{x}{9}} d x

Compute the indefinite integral:

\int x e^{- \frac{x}{9}} d x = - 9 e^{- \frac{x}{9}} x - 81 e^{- \frac{x}{9}} + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- \frac{x}{9}} d x = 0 - (- 81)

= 0 - (- 81)

Simplify

= 81

x \to \infty lim (- 3)

\frac{\partial}{\partial x} (\frac{3 x + 2 x y}{7 x + 6 y})

\int 6 tan^{3} (x) d x

45 t^{2}

x \to 0 lim (x \cdot ln (sin (x)))

What is the integral from 0 to infinity of xe^{-x/9} ?
The integral from 0 to infinity of xe^{-x/9} is 81