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

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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}

\int 75 - 10 x - x^{2} d x

y^{^{''}} - y^{^{'}} - 2 y = - 4 t + 8 t^{2}

y = x - 2, y = x^{2} - 4, x = 5

\int y cos (z) d z

x y = (- 1 - x^{2}) y^{^{'}}

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