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

The integral of (e^{-sqrt(x)})/(sqrt(x)) is -2e^{-sqrt(x)}+C

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integral of (e^{-sqrt(x)})/(sqrt(x))

\int \frac{e ^{- x}}{x} d x

- 2 e^{- x} + C

Solution steps

\int \frac{e ^{- x}}{x} d x

Apply u-substitution

= \int - 2 e^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - 2 e^{u}

Substitute back

u = - x

= - 2 e^{- x}

Add a constant to the solution

= - 2 e^{- x} + C

What is the integral of (e^{-sqrt(x)})/(sqrt(x)) ?
The integral of (e^{-sqrt(x)})/(sqrt(x)) is -2e^{-sqrt(x)}+C