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

The integral from 1 to 4 of sqrt(5/x) is 2sqrt(5)

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

\int_{1}^{4} \frac{5}{x} d x

25

Decimal Notation

4.47213 \dots

Solution steps

\int_{1}^{4} \frac{5}{x} d x

Apply Integration By Parts

: [\frac{5}{x} x - \int - \frac{5}{2 x ^{\frac{1}{2}}} d x]_{1}^{4}

= [\frac{5}{x} x - \int - \frac{5}{2 x ^{\frac{1}{2}}} d x]_{1}^{4}

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

= [\frac{5}{x} x - (- 5 x)]_{1}^{4}

Simplify

= [\frac{5}{x} x + 5 x]_{1}^{4}

Compute the boundaries:

25

= 25

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\frac{d x}{d t} = x - x^{2}, x (0) = 2

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} - 6 x = 4 e^{- 2 t}

\int - 36 cos (x) d x

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What is the integral from 1 to 4 of sqrt(5/x) ?
The integral from 1 to 4 of sqrt(5/x) is 2sqrt(5)