What is the integral from 1 to infinity of 41(e^{-sqrt(x)})/(sqrt(x)) ?

The integral from 1 to infinity of 41(e^{-sqrt(x)})/(sqrt(x)) is (82)/e

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integral from 1 to infinity of 41(e^{-sqrt(x)})/(sqrt(x))

\int_{1}^{\infty} 41 \frac{e ^{- x}}{x} d x

\frac{82}{e}

Decimal

30.16611 \dots

Solution steps

\int_{1}^{\infty} 41 \cdot \frac{e ^{- x}}{x} d x

Compute the indefinite integral:

\int 41 \cdot \frac{e ^{- x}}{x} d x = - 82 e^{- x} + C

Compute the boundaries:

\int_{1}^{\infty} 41 \cdot \frac{e ^{- x}}{x} d x = 0 - (- \frac{82}{e})

= 0 - (- \frac{82}{e})

Simplify

= \frac{82}{e}

2 x^{2} y + x^{3} \frac{d y}{d x} = 1

x \to 7 lim (e^{x - 7})

\frac{s}{s ^{2} - 14 s + 1}

t \cdot e^{2 t}

\frac{d y}{d t} + \frac{1}{2} y = \frac{1}{2} e^{\frac{t}{3}}

What is the integral from 1 to infinity of 41(e^{-sqrt(x)})/(sqrt(x)) ?
The integral from 1 to infinity of 41(e^{-sqrt(x)})/(sqrt(x)) is (82)/e