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

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

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

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

2 Ei (ln (e^{x})) + C

Solution steps

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

Apply u-substitution

: \int \frac{2}{ln ( u )} d u

= \int \frac{2}{ln ( u )} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{ln ( u )} d u

Apply u-substitution

: \int \frac{e ^{v}}{v} d v

= 2 \cdot \int \frac{e ^{v}}{v} d v

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= 2 Ei (v)

Substitute back

= 2 Ei (ln (e^{x}))

Add a constant to the solution

= 2 Ei (ln (e^{x})) + C

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