What is the integral of (e^{sqrt(3x)})/(sqrt(x)) ?

The integral of (e^{sqrt(3x)})/(sqrt(x)) is 2/(sqrt(3))e^{sqrt(3)sqrt(x)}+C

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integral of (e^{sqrt(3x)})/(sqrt(x))

\int \frac{e ^{3 x}}{x} d x

\frac{2}{3} e^{3 x} + C

Solution steps

\int \frac{e ^{3 x}}{x} d x

Apply u-substitution

: \int \frac{2}{3} d u

= \int \frac{2}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{2}{3} u

Substitute back

u = e^{3 x}

= \frac{2}{3} e^{3 x}

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \frac{2}{3} e^{3 x}

Add a constant to the solution

= \frac{2}{3} e^{3 x} + C

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What is the integral of (e^{sqrt(3x)})/(sqrt(x)) ?
The integral of (e^{sqrt(3x)})/(sqrt(x)) is 2/(sqrt(3))e^{sqrt(3)sqrt(x)}+C