What is the integral of (8e^{4sqrt(x)})/(sqrt(x)) ?

The integral of (8e^{4sqrt(x)})/(sqrt(x)) is 4e^{4sqrt(x)}+C

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integral of (8e^{4sqrt(x)})/(sqrt(x))

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

4 e^{4 x} + C

Solution steps

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

Take the constant out:

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

= 8 \cdot \int \frac{e ^{4 x}}{x} d x

Apply u-substitution

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

= 8 \cdot \int \frac{e ^{u}}{2} d u

Take the constant out:

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

= 8 \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= 8 \cdot \frac{1}{2} e^{u}

Substitute back

u = 4 x

= 8 \cdot \frac{1}{2} e^{4 x}

Simplify

8 \cdot \frac{1}{2} e^{4 x} : 4 e^{4 x}

= 4 e^{4 x}

Add a constant to the solution

= 4 e^{4 x} + C

y = \frac{2}{1 - x ^{2}}

\frac{d}{d x} (sin (2 x) + cos (2 x))

x \to 3 lim (x 25 - x^{2})

\frac{\partial}{\partial x} (e^{y})

\int 2 sin (4 x) d x

What is the integral of (8e^{4sqrt(x)})/(sqrt(x)) ?
The integral of (8e^{4sqrt(x)})/(sqrt(x)) is 4e^{4sqrt(x)}+C