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

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

integral of (e^{sqrt(3x)})/(sqrt(2x))

\int \frac{e ^{3 x}}{2 x} d x

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

Solution steps

\int \frac{e ^{3 x}}{2 x} d x

Simplify

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

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

Take the constant out:

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

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

Apply u-substitution

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

Use the common integral:

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

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

Substitute back

u = 3 x

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

Simplify

\frac{1}{2} \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

\int sec^{\frac{3}{2}} (x) tan (x) d x

\int 8 x e^{4 x} d x

\int \frac{3}{3 x + 5} d x

\int \frac{1}{5 - 3 x ^{2}} d x

\int e^{x} - 3 cos (x) d x

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