What is the integral from 0 to 4 of (e^{sqrt(x)})/(sqrt(x)) ?

The integral from 0 to 4 of (e^{sqrt(x)})/(sqrt(x)) is 2(e^2-1)

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integral from 0 to 4 of (e^{sqrt(x)})/(sqrt(x))

\int_{0}^{4} \frac{e ^{x}}{x} d x

2 (e^{2} - 1)

Decimal Notation

12.77811 \dots

Solution steps

\int_{0}^{4} \frac{e ^{x}}{x} d x

Apply u-substitution

: \int_{0}^{2} 2 e^{u} d u

= \int_{0}^{2} 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_{0}^{2} e^{u} d u

Use the common integral:

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

= 2 [e^{u}]_{0}^{2}

Compute the boundaries:

e^{2} - 1

= 2 (e^{2} - 1)

x \to 1 + lim (\frac{x}{ln ( x )})

x \to 3 lim (x^{2} + x - 5)

y^{^{''}} - (\frac{x}{x - 1}) y^{^{'}} + \frac{1}{x - 1} y = 0

x \to 2 lim (3 x^{2} + 2 x - 16)

\frac{\partial}{\partial x} (x - 2 y^{3})

What is the integral from 0 to 4 of (e^{sqrt(x)})/(sqrt(x)) ?
The integral from 0 to 4 of (e^{sqrt(x)})/(sqrt(x)) is 2(e^2-1)