What is the integral from 0 to infinity of e^{-2x+1} ?

The integral from 0 to infinity of e^{-2x+1} is e/2

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integral from 0 to infinity of e^{-2x+1}

\int_{0}^{\infty} e^{- 2 x + 1} d x

\frac{e}{2}

Decimal Notation

1.35914 \dots

Solution steps

\int_{0}^{\infty} e^{- 2 x + 1} d x

Compute the indefinite integral:

\int e^{- 2 x + 1} d x = - \frac{1}{2} e^{- 2 x + 1} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- 2 x + 1} d x = 0 - (- \frac{e}{2})

= 0 - (- \frac{e}{2})

Simplify

= \frac{e}{2}

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What is the integral from 0 to infinity of e^{-2x+1} ?
The integral from 0 to infinity of e^{-2x+1} is e/2