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

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

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integral of (e^{sqrt(x)})/(2sqrt(x))

\int \frac{e ^{x}}{2 x} d x

e^{x} + C

Solution steps

\int \frac{e ^{x}}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{e ^{x}}{x} d x

Apply u-substitution

: \int 2 e^{u} d u

= \frac{1}{2} \cdot \int 2 e^{u} d u

Take the constant out:

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

= \frac{1}{2} \cdot 2 \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} \cdot 2 e^{u}

Substitute back

u = x

= \frac{1}{2} \cdot 2 e^{x}

Simplify

\frac{1}{2} \cdot 2 e^{x} : e^{x}

= e^{x}

Add a constant to the solution

= e^{x} + C

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