What is the integral from 1 to 8 of 5/x ?

The integral from 1 to 8 of 5/x is 15ln(2)

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integral from 1 to 8 of 5/x

\int_{1}^{8} \frac{5}{x} d x

15 ln (2)

Decimal

10.39720 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 5 [ln ∣ x ∣]_{1}^{8}

Compute the boundaries:

3 ln (2)

= 5 \cdot 3 ln (2)

Simplify

= 15 ln (2)

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What is the integral from 1 to 8 of 5/x ?
The integral from 1 to 8 of 5/x is 15ln(2)