What is the integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x)) ?

The integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x)) is 22(e^3-1)

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integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x))

\int_{0}^{9} \frac{11 e ^{x}}{x} d x

22 (e^{3} - 1)

Decimal

419.88181 \dots

Solution steps

\int_{0}^{9} \frac{11 e ^{x}}{x} d x

Take the constant out:

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

= 11 \cdot \int_{0}^{9} \frac{e ^{x}}{x} d x

Apply u-substitution

: \int_{0}^{3} 2 e^{u} d u

= 11 \cdot \int_{0}^{3} 2 e^{u} d u

Take the constant out:

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

= 11 \cdot 2 \cdot \int_{0}^{3} e^{u} d u

Use the common integral:

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

= 11 \cdot 2 [e^{u}]_{0}^{3}

Simplify

= 22 [e^{u}]_{0}^{3}

Compute the boundaries:

e^{3} - 1

= 22 (e^{3} - 1)

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What is the integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x)) ?
The integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x)) is 22(e^3-1)