What is the integral from 5 to 8 of 5/(sqrt(x-5)) ?

The integral from 5 to 8 of 5/(sqrt(x-5)) is 10sqrt(3)

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integral from 5 to 8 of 5/(sqrt(x-5))

\int_{5}^{8} \frac{5}{x - 5} d x

103

Decimal Notation

17.32050 \dots

Solution steps

\int_{5}^{8} \frac{5}{x - 5} d x

Take the constant out:

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

= 5 \cdot \int_{5}^{8} \frac{1}{x - 5} 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{\partial}{\partial x} \frac{u}{1 + 2.4 ( \frac{x}{y} )}

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 5 x^{4} y^{7})

\int_{0}^{3} 15 x d x

x \to 0 lim (x (x))

x \to - 2 lim (\frac{x ^{2} - 6}{2 - x})

What is the integral from 5 to 8 of 5/(sqrt(x-5)) ?
The integral from 5 to 8 of 5/(sqrt(x-5)) is 10sqrt(3)