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

The integral from 2 to infinity of xe^{-x} is 3/(e^2)

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

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

\frac{3}{e ^{2}}

Decimal

0.40600 \dots

Solution steps

\int_{2}^{\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_{2}^{\infty} x e^{- x} d x = 0 - (- \frac{3}{e ^{2}})

= 0 - (- \frac{3}{e ^{2}})

Simplify

= \frac{3}{e ^{2}}

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What is the integral from 2 to infinity of xe^{-x} ?
The integral from 2 to infinity of xe^{-x} is 3/(e^2)