What is the integral from 2 to 3 of 1/(1-x) ?

The integral from 2 to 3 of 1/(1-x) is -ln(2)

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integral from 2 to 3 of 1/(1-x)

\int_{2}^{3} \frac{1}{1 - x} d x

- ln (2)

Decimal

- 0.69314 \dots

Solution steps

\int_{2}^{3} \frac{1}{1 - x} d x

Apply u-substitution

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

= \int_{- 1}^{- 2} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{- 1} - \frac{1}{u} d u

Take the constant out:

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

= - (- \int_{- 2}^{- 1} \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- [ln ∣ u ∣]_{- 2}^{- 1})

Simplify

= [ln ∣ u ∣]_{- 2}^{- 1}

Compute the boundaries:

- ln (2)

= - ln (2)

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What is the integral from 2 to 3 of 1/(1-x) ?
The integral from 2 to 3 of 1/(1-x) is -ln(2)