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

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

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

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

ln (2)

Decimal

0.69314 \dots

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{2}

Compute the boundaries:

ln (2)

= ln (2)

\int_{1}^{2} x e^{- x} d x

\int_{1}^{8} \frac{1}{3 x} d x

\int_{1}^{5} \frac{12 ( ln ( x ) ) ^{5}}{x} d x

\int_{8}^{17} x x^{2} - 64 d x

\int_{0}^{3} \frac{x e ^{x}}{( 1 + x ) ^{2}} d x

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