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

The integral from 1 to infinity of ((e^{-sqrt(x)}))/(sqrt(x)) is 2/e

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{2}{e}

Decimal

0.73575 \dots

Solution steps

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

Compute the indefinite integral:

\int \frac{e ^{- x}}{x} d x = - 2 e^{- x} + C

Compute the boundaries:

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

= 0 - (- \frac{2}{e})

Simplify

= \frac{2}{e}

What is the integral from 1 to infinity of ((e^{-sqrt(x)}))/(sqrt(x)) ?
The integral from 1 to infinity of ((e^{-sqrt(x)}))/(sqrt(x)) is 2/e