What is the integral from 0 to infinity of xe^{-x/5} ?

The integral from 0 to infinity of xe^{-x/5} is 25

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integral from 0 to infinity of xe^{-x/5}

\int_{0}^{\infty} x e^{- \frac{x}{5}} d x

25

Solution steps

\int_{0}^{\infty} x e^{- \frac{x}{5}} d x

Compute the indefinite integral:

\int x e^{- \frac{x}{5}} d x = - 5 e^{- \frac{x}{5}} x - 25 e^{- \frac{x}{5}} + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- \frac{x}{5}} d x = 0 - (- 25)

= 0 - (- 25)

Simplify

= 25

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What is the integral from 0 to infinity of xe^{-x/5} ?
The integral from 0 to infinity of xe^{-x/5} is 25