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

\int e^{2 x + e^{2 x}} d x

\frac{\partial}{\partial x} (y^{2} - x y)

\frac{d y}{d x}, y = ln (x)

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 2)^{7})

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

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