What is the integral from 2 to infinity of xe^{-x/2} ?

The integral from 2 to infinity of xe^{-x/2} is 8/e

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integral from 2 to infinity of xe^{-x/2}

\int_{2}^{\infty} x e^{- \frac{x}{2}} d x

\frac{8}{e}

Decimal

2.94303 \dots

Solution steps

\int_{2}^{\infty} x e^{- \frac{x}{2}} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{2}^{\infty} x e^{- \frac{x}{2}} d x = 0 - (- \frac{8}{e})

= 0 - (- \frac{8}{e})

Simplify

= \frac{8}{e}

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What is the integral from 2 to infinity of xe^{-x/2} ?
The integral from 2 to infinity of xe^{-x/2} is 8/e