What is the integral from 0 to 5 of 3/(sqrt(5-x)) ?

The integral from 0 to 5 of 3/(sqrt(5-x)) is 6sqrt(5)

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integral from 0 to 5 of 3/(sqrt(5-x))

\int_{0}^{5} \frac{3}{5 - x} d x

65

Decimal

13.41640 \dots

Solution steps

\int_{0}^{5} \frac{3}{5 - x} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{5} \frac{1}{5 - x} d x

Apply u-substitution

= 3 \cdot \int_{5}^{0} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 3 (- \int_{0}^{5} - \frac{1}{u} d u)

Take the constant out:

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

= 3 (- (- \int_{0}^{5} \frac{1}{u} d u))

Apply the Power Rule

= 3 (- (- [2 u^{\frac{1}{2}}]_{0}^{5}))

Simplify

3 (- (- [2 u^{\frac{1}{2}}]_{0}^{5})) : 3 [2 u]_{0}^{5}

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

Compute the boundaries:

25

= 3 \cdot 25

Simplify

= 65

What is the integral from 0 to 5 of 3/(sqrt(5-x)) ?
The integral from 0 to 5 of 3/(sqrt(5-x)) is 6sqrt(5)