What is the integral from-infinity to 0 of (x-1)e^x ?

The integral from-infinity to 0 of (x-1)e^x is -2

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integral from-infinity to 0 of (x-1)e^x

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

- 2

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= - 2 - 0

Simplify

= - 2

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What is the integral from-infinity to 0 of (x-1)e^x ?
The integral from-infinity to 0 of (x-1)e^x is -2