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

The integral from 2 to 5 of 1/((x-2)^1) is diverges

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

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

diverges

Solution steps

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

Simplify

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{0}^{3}

Compute the boundaries:

diverges

= diverges

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