What is the integral from x to infinity of ye^{-y} ?

The integral from x to infinity of ye^{-y} is xe^{-x}+e^{-x}

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integral from x to infinity of ye^{-y}

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

x e^{- x} + e^{- x}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= x e^{- x} + e^{- x}

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