What is the integral from 2 to 5 of 5/(sqrt(x-2)) ?

The integral from 2 to 5 of 5/(sqrt(x-2)) is 10sqrt(3)

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integral from 2 to 5 of 5/(sqrt(x-2))

\int_{2}^{5} \frac{5}{x - 2} d x

103

Decimal

17.32050 \dots

Solution steps

\int_{2}^{5} \frac{5}{x - 2} d x

Take the constant out:

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

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

Apply u-substitution

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

= 5 \cdot \int_{0}^{3} 2 d u

Integral of a constant:

\int a d x = a x

= 5 [2 u]_{0}^{3}

Compute the boundaries:

23

= 5 \cdot 23

Simplify

= 103

\frac{d}{d y} (2 x (y))

\frac{d}{d x} (\frac{( - x ^{2} - 5 )}{( x ^{2} - 5 ) ^{2}})

- 2 e^{3 t}

25 y^{^{''}} - 25 y^{^{'}} - 6 y = 0

\frac{d}{d x} (\frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( 1 - x ) ^{3}})

What is the integral from 2 to 5 of 5/(sqrt(x-2)) ?
The integral from 2 to 5 of 5/(sqrt(x-2)) is 10sqrt(3)