What is the integral from 3 to 9 of 1/(x-1) ?

The integral from 3 to 9 of 1/(x-1) is 2ln(2)

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integral from 3 to 9 of 1/(x-1)

\int_{3}^{9} \frac{1}{x - 1} d x

2 ln (2)

Decimal

1.38629 \dots

Solution steps

\int_{3}^{9} \frac{1}{x - 1} d x

Apply u-substitution

: \int_{2}^{8} \frac{1}{u} d u

= \int_{2}^{8} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2}^{8}

Compute the boundaries:

2 ln (2)

= 2 ln (2)

\int_{- 5 π}^{π} cos^{2} (x) d x

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

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

\int_{1}^{2} ln (x^{2}) x d x

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

What is the integral from 3 to 9 of 1/(x-1) ?
The integral from 3 to 9 of 1/(x-1) is 2ln(2)