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

n = 1 \sum \infty \frac{1 ^{n}}{n + 1}

\frac{d}{d x} (\frac{x ^{2} + 1}{( x + 1 ) ^{3}})

\frac{\partial}{\partial x} (x y + \frac{2}{x} + \frac{4}{y})

e^{x}, e^{- 4 x}, x = ln (4)

\frac{d}{d x} (\frac{x - 2}{5 x ^{2} e ^{x}})

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