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

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

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

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

2 e^{x} + C

Solution steps

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

Apply u-substitution

= \int 2 e^{u} d u

Take the constant out:

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

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

Use the common integral:

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

= 2 e^{u}

Substitute back

u = x

= 2 e^{x}

Add a constant to the solution

= 2 e^{x} + C

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

d er i v a t i v e x^{13}

im pl i c i t \frac{d y}{d x}, (7 x y + 3)^{2} = 14 y

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