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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{e ^{3 x}}{x} d x

Apply u-substitution

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

= \frac{1}{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

= \frac{1}{3} \cdot \frac{2}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{3} \cdot \frac{2}{3} e^{u}

Substitute back

u = 3 x

= \frac{1}{3} \cdot \frac{2}{3} e^{3 x}

Simplify

\frac{1}{3} \cdot \frac{2}{3} e^{3 x} : \frac{2}{3} e^{3 x}

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

Add a constant to the solution

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

t \to 0 lim (t \cdot ln (t))

y \to 1 lim (\frac{y ^{4} - 1}{y - 1})

\frac{2 x ^{3} - 7}{x ^{2}}

x y^{^{'}} = y - x

\frac{d}{d x} ((5 x^{3} + 2)^{4})

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