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

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

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integral from 1 to infinity of 1/(xe^x)

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

- Ei (- 1)

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - Ei (- 1)

Simplify

= - Ei (- 1)

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