What is the integral from 0 to infinity of e^{-5x} ?

The integral from 0 to infinity of e^{-5x} is 1/5

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integral from 0 to infinity of e^{-5x}

\int_{0}^{\infty} e^{- 5 x} d x

\frac{1}{5}

Decimal Notation

0.2

Solution steps

\int_{0}^{\infty} e^{- 5 x} d x

Compute the indefinite integral:

\int e^{- 5 x} d x = - \frac{1}{5} e^{- 5 x} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- 5 x} d x = 0 - (- \frac{1}{5})

= 0 - (- \frac{1}{5})

Simplify

= \frac{1}{5}

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What is the integral from 0 to infinity of e^{-5x} ?
The integral from 0 to infinity of e^{-5x} is 1/5