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

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

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

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

2 e^{2 x} + C

Solution steps

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

Apply u-substitution

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

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

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 ^{u}}{u} d u

Apply u-substitution

: \int 2 e^{v} d v

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} \cdot 2 e^{v}

Substitute back

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

Simplify

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

= 2 e^{2 x}

Add a constant to the solution

= 2 e^{2 x} + C

y x

\int (1 + x^{2}) (2 - x) d x

\frac{s - 9}{s ^{2} - 9}

\frac{d}{d x} (tan (4 x))

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