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

解答

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

1

求解步骤

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

计算不定积分:

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

带入上下限计算后得:

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

= 0 - (- 1)

化简

= 1

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