What is the integral from 1 to 9 of sqrt(5/x) ?

The integral from 1 to 9 of sqrt(5/x) is 4sqrt(5)

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integral from 1 to 9 of sqrt(5/x)

\int_{1}^{9} \frac{5}{x} d x

45

Decimal

8.94427 \dots

Solution steps

\int_{1}^{9} \frac{5}{x} d x

Apply Integration By Parts

: [\frac{5}{x} x - \int - \frac{5}{2 x ^{\frac{1}{2}}} d x]_{1}^{9}

= [\frac{5}{x} x - \int - \frac{5}{2 x ^{\frac{1}{2}}} d x]_{1}^{9}

\int - \frac{5}{2 x ^{\frac{1}{2}}} d x = - 5 x

= [\frac{5}{x} x - (- 5 x)]_{1}^{9}

Simplify

= [\frac{5}{x} x + 5 x]_{1}^{9}

Compute the boundaries:

45

= 45

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What is the integral from 1 to 9 of sqrt(5/x) ?
The integral from 1 to 9 of sqrt(5/x) is 4sqrt(5)