What is the integral from 0 to infinity of yxe^{-yx} ?

The integral from 0 to infinity of yxe^{-yx} is 1/y

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integral from 0 to infinity of yxe^{-yx}

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

\frac{1}{y}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} y x e^{- y x} d x = 0 - (- \frac{1}{y})

= 0 - (- \frac{1}{y})

Simplify

= \frac{1}{y}

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What is the integral from 0 to infinity of yxe^{-yx} ?
The integral from 0 to infinity of yxe^{-yx} is 1/y