What is the integral from 0 to infinity of-xe^{-x} ?

The integral from 0 to infinity of-xe^{-x} is -1

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integral from 0 to infinity of-xe^{-x}

\int_{0}^{\infty} - x e^{- x} d x

- 1

Solution steps

\int_{0}^{\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_{0}^{\infty} - x e^{- x} d x = 0 - 1

= 0 - 1

Simplify

= - 1

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What is the integral from 0 to infinity of-xe^{-x} ?
The integral from 0 to infinity of-xe^{-x} is -1