What is the integral from 0 to infinity of x(e^{-x}) ?

The integral from 0 to infinity of x(e^{-x}) is 1

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integral from 0 to infinity of x(e^{-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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\int_{1}^{\infty} \frac{8}{7 x - 1} d x

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