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

The integral from 0 to infinity of xe^{-x/y} is y^2

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

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

y^{2}

Solution steps

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

Compute the indefinite integral:

\int x e^{- \frac{x}{y}} d x = - y e^{- \frac{x}{y}} x - y^{2} e^{- \frac{x}{y}} + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- \frac{x}{y}} d x = 0 - (- y^{2})

= 0 - (- y^{2})

Simplify

= y^{2}

y^{^{''}} - 6 y^{^{'}} + 7 y = 0

\frac{\partial}{\partial x} (arctan (x) y)

(x - 1)^{3}, x - 1

\frac{d}{d x} (x^{2} - 2)

\int - x - 1 d x

What is the integral from 0 to infinity of xe^{-x/y} ?
The integral from 0 to infinity of xe^{-x/y} is y^2