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

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

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

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

2 e^{3 x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 3 \cdot \int \frac{2 e ^{u}}{3} d u

Take the constant out:

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

= 3 \cdot \frac{2}{3} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{2}{3} e^{u}

Substitute back

u = 3 x

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

Simplify

3 \cdot \frac{2}{3} e^{3 x} : 2 e^{3 x}

= 2 e^{3 x}

Add a constant to the solution

= 2 e^{3 x} + C

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