What is the integral from 2 to 8 of 4/x ?

The integral from 2 to 8 of 4/x is 8ln(2)

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integral from 2 to 8 of 4/x

\int_{2}^{8} \frac{4}{x} d x

8 ln (2)

Decimal

5.54517 \dots

Solution steps

\int_{2}^{8} \frac{4}{x} d x

Take the constant out:

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

= 4 \cdot \int_{2}^{8} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 [ln ∣ x ∣]_{2}^{8}

Compute the boundaries:

2 ln (2)

= 4 \cdot 2 ln (2)

Simplify

= 8 ln (2)

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What is the integral from 2 to 8 of 4/x ?
The integral from 2 to 8 of 4/x is 8ln(2)