What is the integral from 5 to 11 of 1/(x-2) ?

The integral from 5 to 11 of 1/(x-2) is ln(3)

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integral from 5 to 11 of 1/(x-2)

\int_{5}^{11} \frac{1}{x - 2} d x

ln (3)

Decimal

1.09861 \dots

Solution steps

\int_{5}^{11} \frac{1}{x - 2} d x

Apply u-substitution

: \int_{3}^{9} \frac{1}{u} d u

= \int_{3}^{9} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{3}^{9}

Compute the boundaries:

ln (3)

= ln (3)

\int_{1}^{\infty} \frac{ln ( n )}{n}

\int_{0}^{1} π (e^{x} + 3 x) d x

\int_{0}^{3} x^{3} - 3 x^{2} d x

\int_{15}^{17} x x^{2} - 225 d x

\int_{0}^{6} e^{2 x} d x

What is the integral from 5 to 11 of 1/(x-2) ?
The integral from 5 to 11 of 1/(x-2) is ln(3)