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

The integral from 0 to infinity of e^{-xt} is 1/x

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integral from 0 to infinity of e^{-xt}

\int_{0}^{\infty} e^{- x t} d t

\frac{1}{x}

Solution steps

\int_{0}^{\infty} e^{- x t} d t

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{1}{x}

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