What is the integral from 5 to 10 of 8/(5-2x) ?

The integral from 5 to 10 of 8/(5-2x) is -4ln(3)

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integral from 5 to 10 of 8/(5-2x)

\int_{5}^{10} \frac{8}{5 - 2 x} d x

- 4 ln (3)

Decimal Notation

- 4.39444 \dots

Solution steps

\int_{5}^{10} \frac{8}{5 - 2 x} d x

Take the constant out:

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

= 8 \cdot \int_{5}^{10} \frac{1}{5 - 2 x} d x

Apply u-substitution

: \int_{- 5}^{- 15} - \frac{1}{2 u} d u

= 8 \cdot \int_{- 5}^{- 15} - \frac{1}{2 u} d u

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

= 8 (- \int_{- 15}^{- 5} - \frac{1}{2 u} d u)

Take the constant out:

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

= 8 (- (- \frac{1}{2} \cdot \int_{- 15}^{- 5} \frac{1}{u} d u))

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 (- (- \frac{1}{2} [ln ∣ u ∣]_{- 15}^{- 5}))

Simplify

8 (- (- \frac{1}{2} [ln ∣ u ∣]_{- 15}^{- 5})) : 4 [ln ∣ u ∣]_{- 15}^{- 5}

= 4 [ln ∣ u ∣]_{- 15}^{- 5}

Compute the boundaries:

ln (5) - ln (15)

= 4 (ln (5) - ln (15))

Simplify

= - 4 ln (3)

y = \frac{1}{3} (x^{2} + 2)^{\frac{3}{2}}

sec (9 x)

\frac{d}{d x} (4.5 x + 2.4 x^{2} + 1.1 x^{3})

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

\frac{d}{d w} ((ln (w))^{(2 w)})

What is the integral from 5 to 10 of 8/(5-2x) ?
The integral from 5 to 10 of 8/(5-2x) is -4ln(3)