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

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

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

\int_{0}^{\infty} \frac{1}{e ^{x}} d x

1

Solution steps

\int_{0}^{\infty} \frac{1}{e ^{x}} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

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