What is the integral from x to infinity of e^{-xy} ?

The integral from x to infinity of e^{-xy} is (e^{-x^2})/x

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integral from x to infinity of e^{-xy}

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

\frac{e ^{- x^{2}}}{x}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- \frac{e ^{- x^{2}}}{x})

Simplify

= \frac{e ^{- x^{2}}}{x}

What is the integral from x to infinity of e^{-xy} ?
The integral from x to infinity of e^{-xy} is (e^{-x^2})/x