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

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

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

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

\frac{1}{y}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{1}{y}

\frac{14}{2 x + 16}

x y^{3} d y = d x, y (1) = 2

\int \frac{x ^{3} - 3 x ^{2} + 2 x - 4}{x - 1} d x

x \to 0 lim (\frac{e ^{x} - 1}{11 x})

x \to - 3 lim (\frac{9 - x ^{2}}{x + 3})

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