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

The integral of (e^{8sqrt(x)})/(sqrt(x)) is 1/4 e^{8sqrt(x)}+C

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

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

\frac{1}{4} e^{8 x} + C

Solution steps

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

Apply u-substitution

: \int \frac{e ^{u}}{4} d u

= \int \frac{e ^{u}}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 8 x

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

Add a constant to the solution

= \frac{1}{4} e^{8 x} + C

x \to 0 lim (csc^{2} (x))

\int \frac{sin ( 21 x )}{1 + cos ^{2} ( 21 x )} d x

\int_{0}^{1} x (1 - x) d x

6 x^{2}, x^{2} + 8

x \to 0 lim (\frac{14}{tan ( x )})

What is the integral of (e^{8sqrt(x)})/(sqrt(x)) ?
The integral of (e^{8sqrt(x)})/(sqrt(x)) is 1/4 e^{8sqrt(x)}+C