What is the integral from 1/2 to 2 of 2/x ?

The integral from 1/2 to 2 of 2/x is 4ln(2)

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integral from 1/2 to 2 of 2/x

\int_{\frac{1}{2}}^{2} \frac{2}{x} d x

4 ln (2)

Decimal

2.77258 \dots

Solution steps

\int_{\frac{1}{2}}^{2} \frac{2}{x} d x

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{\frac{1}{2}}^{2}

Compute the boundaries:

2 ln (2)

= 2 \cdot 2 ln (2)

Simplify

= 4 ln (2)

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What is the integral from 1/2 to 2 of 2/x ?
The integral from 1/2 to 2 of 2/x is 4ln(2)