What is the integral from 2 to infinity of ue^{-u} ?

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

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integral from 2 to infinity of ue^{-u}

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

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

Decimal

0.40600 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{2}^{\infty} u e^{- u} d u = 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 ue^{-u} ?
The integral from 2 to infinity of ue^{-u} is 3/(e^2)