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

= \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

t \frac{d y}{d t} = y + 4 t^{2} sin (3 t)

\frac{\partial}{\partial y} (\frac{x + y ^{2}}{z})

- 2 sin (t) cos (t)

x^{x}, 1

\frac{d}{d x} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}})

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