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

= \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

\int_{0}^{3} 3^{x} d x

\frac{3}{x + 1}

\int (5^{x} + 2^{5}) d x

f (x) = 8 x e^{x} - 8 e^{x}

y = 3 x + 1, (8, 5)

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