What is the integral from 0 to infinity of e^{-st}1 ?

The integral from 0 to infinity of e^{-st}1 is 1/s

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integral from 0 to infinity of e^{-st}1

\int_{0}^{\infty} e^{- s t} 1 d t

\frac{1}{s}

Solution steps

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

= 0 - (- \frac{1}{s})

Simplify

= \frac{1}{s}

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What is the integral from 0 to infinity of e^{-st}1 ?
The integral from 0 to infinity of e^{-st}1 is 1/s