What is the integral from 4 to 9 of 3/(x-2) ?

The integral from 4 to 9 of 3/(x-2) is 3(ln(7)-ln(2))

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integral from 4 to 9 of 3/(x-2)

\int_{4}^{9} \frac{3}{x - 2} d x

3 (ln (7) - ln (2))

Decimal

3.75828 \dots

Solution steps

\int_{4}^{9} \frac{3}{x - 2} d x

Take the constant out:

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

= 3 \cdot \int_{4}^{9} \frac{1}{x - 2} d x

Apply u-substitution

: \int_{2}^{7} \frac{1}{u} d u

= 3 \cdot \int_{2}^{7} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{2}^{7}

Compute the boundaries:

ln (7) - ln (2)

= 3 (ln (7) - ln (2))

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What is the integral from 4 to 9 of 3/(x-2) ?
The integral from 4 to 9 of 3/(x-2) is 3(ln(7)-ln(2))