What is the integral from 5 to 20 of 5/(x+8) ?

The integral from 5 to 20 of 5/(x+8) is 5(ln(28)-ln(13))

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integral from 5 to 20 of 5/(x+8)

\int_{5}^{20} \frac{5}{x + 8} d x

5 (ln (28) - ln (13))

Decimal

3.83627 \dots

Solution steps

\int_{5}^{20} \frac{5}{x + 8} d x

Take the constant out:

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

= 5 \cdot \int_{5}^{20} \frac{1}{x + 8} d x

Apply u-substitution

= 5 \cdot \int_{13}^{28} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 [ln ∣ u ∣]_{13}^{28}

Compute the boundaries:

ln (28) - ln (13)

= 5 (ln (28) - ln (13))

What is the integral from 5 to 20 of 5/(x+8) ?
The integral from 5 to 20 of 5/(x+8) is 5(ln(28)-ln(13))