What is the integral from 0 to infinity of ue^{-u} ?

The integral from 0 to infinity of ue^{-u} is 1

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integral from 0 to infinity of ue^{-u}

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

1

Solution steps

\int_{0}^{\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_{0}^{\infty} u e^{- u} d u = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

x \to 0 lim (\frac{( x + 1 ) ^{3}}{x})

\int_{0}^{2} (4 t i - t^{3} j + 5 t^{9} k) d t

f (x) = coth (x)

1 - \frac{1}{x ^{2}}

x \to 0 lim (\frac{e ^{x}}{1 - e ^{x}})

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