What is the integral from 3 to 6 of 9/x ?

The integral from 3 to 6 of 9/x is 9ln(2)

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integral from 3 to 6 of 9/x

\int_{3}^{6} \frac{9}{x} d x

9 ln (2)

Decimal Notation

6.23832 \dots

Solution steps

\int_{3}^{6} \frac{9}{x} d x

Take the constant out:

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

= 9 \cdot \int_{3}^{6} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 9 [ln ∣ x ∣]_{3}^{6}

Compute the boundaries:

ln (6) - ln (3)

= 9 (ln (6) - ln (3))

Simplify

= 9 ln (2)

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What is the integral from 3 to 6 of 9/x ?
The integral from 3 to 6 of 9/x is 9ln(2)