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} (\frac{x}{3 x - 4 \cdot ln ( x )})

f (x) = x^{2} 16 - x^{2}

\frac{\partial}{\partial x} (x \cdot e^{x^{2} y})

f (x) = 3 x^{2} cos (x) + 7 x

\frac{\partial}{\partial x} (x^{2} + x y + 6 x - 6 y)

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