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

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

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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

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