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

The integral of (3e^{sqrt(x)})/(sqrt(x)) is 6e^{sqrt(x)}+C

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

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

6 e^{x} + C

Solution steps

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

Apply u-substitution

: \int 2 e^{u} d u

= 3 \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

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

Use the common integral:

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

= 3 \cdot 2 e^{u}

Substitute back

u = x

= 3 \cdot 2 e^{x}

Simplify

= 6 e^{x}

Add a constant to the solution

= 6 e^{x} + C

\frac{d}{d x} (3 (5 - 9 x)^{5})

\int sec (t) (sec (t) tan (t)) d t

x \to \infty lim ((1 + 6 x)^{\frac{3}{x}})

\int \frac{x}{4 x ^{2} + 1} d x

y = x - 1, y = 0, x = 8

What is the integral of (3e^{sqrt(x)})/(sqrt(x)) ?
The integral of (3e^{sqrt(x)})/(sqrt(x)) is 6e^{sqrt(x)}+C