What is the integral from 1 to infinity of x*e^{-x} ?

The integral from 1 to infinity of x*e^{-x} is 2/e

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integral from 1 to infinity of x*e^{-x}

\int_{1}^{\infty} x \cdot e^{- x} d x

\frac{2}{e}

Decimal

0.73575 \dots

Solution steps

\int_{1}^{\infty} x e^{- x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{1}^{\infty} x e^{- x} d x = 0 - (- \frac{2}{e})

= 0 - (- \frac{2}{e})

Simplify

= \frac{2}{e}

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What is the integral from 1 to infinity of x*e^{-x} ?
The integral from 1 to infinity of x*e^{-x} is 2/e