What is the integral from 2 to 6 of 5/x ?

The integral from 2 to 6 of 5/x is 5ln(3)

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integral from 2 to 6 of 5/x

\int_{2}^{6} \frac{5}{x} d x

5 ln (3)

Decimal

5.49306 \dots

Solution steps

\int_{2}^{6} \frac{5}{x} d x

Take the constant out:

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

= 5 \cdot \int_{2}^{6} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{2}^{6}

Compute the boundaries:

ln (6) - ln (2)

= 5 (ln (6) - ln (2))

Simplify

= 5 ln (3)

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What is the integral from 2 to 6 of 5/x ?
The integral from 2 to 6 of 5/x is 5ln(3)