What is the integral from 1 to infinity of e^{-st}(1) ?

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

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integral from 1 to infinity of e^{-st}(1)

\int_{1}^{\infty} e^{- s t} (1) d t

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

Solution steps

\int_{1}^{\infty} e^{- s t} \cdot 1 d t

Compute the indefinite integral:

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

Compute the boundaries:

\int_{1}^{\infty} e^{- s t} (1) d t = 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^{-st}(1) ?
The integral from 1 to infinity of e^{-st}(1) is (e^{-s})/s