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

The integral of 1/(sqrt(x))e^{-sqrt(x)} is -2e^{-sqrt(x)}+C

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

\int \frac{1}{x} e^{- x} d x

- 2 e^{- x} + C

Solution steps

\int \frac{1}{x} e^{- 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

\frac{d}{d x} (4 x^{3} e^{2 x})

\frac{d}{d x} ((x + \frac{1}{x}) (x - \frac{1}{x}))

\int e^{2 x} + sin (- x) d x

y = x sin (\frac{2}{x})

\frac{d}{d x} (sin^{2} (m x + n y (x)))

What is the integral of 1/(sqrt(x))e^{-sqrt(x)} ?
The integral of 1/(sqrt(x))e^{-sqrt(x)} is -2e^{-sqrt(x)}+C