What is the integral from 0 to infinity of xe^{-xy} ?

The integral from 0 to infinity of xe^{-xy} is 1/(y^2)

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integral from 0 to infinity of xe^{-xy}

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

\frac{1}{y ^{2}}

Solution steps

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

Compute the indefinite integral:

\int x e^{- x y} d x = \frac{1}{y ^{2}} (- y e^{- y x} x - e^{- y x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- x y} d x = 0 - (- \frac{1}{y ^{2}})

= 0 - (- \frac{1}{y ^{2}})

Simplify

= \frac{1}{y ^{2}}

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\frac{x}{2 - x}

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\int_{- 2}^{0} - x + 2 d x

What is the integral from 0 to infinity of xe^{-xy} ?
The integral from 0 to infinity of xe^{-xy} is 1/(y^2)