What is the integral from 1 to infinity of e^{-sx} ?

The integral from 1 to infinity of e^{-sx} is (e^{-s})/s

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integral from 1 to infinity of e^{-sx}

\int_{1}^{\infty} e^{- s x} d x

\frac{e ^{- s}}{s}

Solution steps

\int_{1}^{\infty} e^{- s x} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- \frac{e ^{- s}}{s})

Simplify

= \frac{e ^{- s}}{s}

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What is the integral from 1 to infinity of e^{-sx} ?
The integral from 1 to infinity of e^{-sx} is (e^{-s})/s