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

The integral from a to infinity of xe^{-x} is ae^{-a}+e^{-a}

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

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

a e^{- a} + e^{- a}

Solution steps

\int_{a}^{\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_{a}^{\infty} x e^{- x} d x = 0 - (- e^{- a} a - e^{- a})

= 0 - (- e^{- a} a - e^{- a})

Simplify

= a e^{- a} + e^{- a}

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What is the integral from a to infinity of xe^{-x} ?
The integral from a to infinity of xe^{-x} is ae^{-a}+e^{-a}