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

The integral from-infinity to-1 of (e^x)/x is \Ei(-1)

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

\int_{- \infty}^{- 1} \frac{e ^{x}}{x} d x

Ei (- 1)

Solution steps

\int_{- \infty}^{- 1} \frac{e ^{x}}{x} d x

Compute the indefinite integral:

\int \frac{e ^{x}}{x} d x = Ei (x) + C

Compute the boundaries:

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

= Ei (- 1) - 0

Simplify

= Ei (- 1)

What is the integral from-infinity to-1 of (e^x)/x ?
The integral from-infinity to-1 of (e^x)/x is \Ei(-1)