What is the integral from 2 to 8 of 3/(x-2) ?

The integral from 2 to 8 of 3/(x-2) is diverges

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integral from 2 to 8 of 3/(x-2)

\int_{2}^{8} \frac{3}{x - 2} d x

diverges

Solution steps

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

Apply u-substitution

: \int_{0}^{6} \frac{1}{u} d u

= 3 \cdot \int_{0}^{6} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{0}^{6}

Compute the boundaries:

diverges

= diverges

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What is the integral from 2 to 8 of 3/(x-2) ?
The integral from 2 to 8 of 3/(x-2) is diverges