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

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

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

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

- \frac{1}{e} + 1

Decimal

0.63212 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= - \frac{1}{e} - (- 1)

Simplify

= - \frac{1}{e} + 1

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