What is the integral from 5 to 8 of 1/(x-2) ?

The integral from 5 to 8 of 1/(x-2) is ln(2)

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integral from 5 to 8 of 1/(x-2)

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

ln (2)

Decimal

0.69314 \dots

Solution steps

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

Apply u-substitution

: \int_{3}^{6} \frac{1}{u} d u

= \int_{3}^{6} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{3}^{6}

Compute the boundaries:

ln (6) - ln (3)

= ln (6) - ln (3)

Simplify

= ln (2)

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What is the integral from 5 to 8 of 1/(x-2) ?
The integral from 5 to 8 of 1/(x-2) is ln(2)