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

The integral of (e^{2sqrt(x)})/(3sqrt(x)) is 1/3 e^{2sqrt(x)}+C

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

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

\frac{1}{3} e^{2 x} + C

Solution steps

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

Apply u-substitution

: \int e^{u} d u

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

Use the common integral:

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

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

Substitute back

u = 2 x

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

Add a constant to the solution

= \frac{1}{3} e^{2 x} + C

\frac{d}{d x} (x^{3} - 4 x + 7)

x \to 1 lim (x^{2} + x - 2)

\frac{d}{d x} (x^{2} + y^{2} + z^{2})

x \to 4 lim (16)

What is the integral of (e^{2sqrt(x)})/(3sqrt(x)) ?
The integral of (e^{2sqrt(x)})/(3sqrt(x)) is 1/3 e^{2sqrt(x)}+C