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

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

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

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

\frac{1}{s}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} 1 \cdot e^{- s t} 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 1e^{-st} ?
The integral from 0 to infinity of 1e^{-st} is 1/s