What is the integral from 4 to 8 of 5/(12-x) ?

The integral from 4 to 8 of 5/(12-x) is 5ln(2)

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integral from 4 to 8 of 5/(12-x)

\int_{4}^{8} \frac{5}{12 - x} d x

5 ln (2)

Solution steps

\int_{4}^{8} \frac{5}{12 - x} d x

Take the constant out:

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

= 5 \cdot \int_{4}^{8} \frac{1}{12 - x} d x

Apply u-substitution

: \int_{8}^{4} - \frac{1}{u} d u

= 5 \cdot \int_{8}^{4} - \frac{1}{u} d u

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

= 5 (- \int_{4}^{8} - \frac{1}{u} d u)

Take the constant out:

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

= 5 (- (- \int_{4}^{8} \frac{1}{u} d u))

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 (- (- [ln ∣ u ∣]_{4}^{8}))

Simplify

= 5 [ln ∣ u ∣]_{4}^{8}

Compute the boundaries:

ln (2)

= 5 ln (2)

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

\int \frac{x ^{4} + 8 x ^{2} + 8}{x ^{3} - 4 x} d x

x^{3} - 3 x^{2} + 5 x - 7, 0

(1.7) (3.3)

\int_{0}^{2} \frac{d t}{4 + t ^{2}} d x

What is the integral from 4 to 8 of 5/(12-x) ?
The integral from 4 to 8 of 5/(12-x) is 5ln(2)