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

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

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

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

2 ln (2)

Decimal

1.38629 \dots

Solution steps

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

Apply u-substitution

= \int_{1}^{4} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 2 ln (2)

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