What is the integral from 1 to 7 of 2/x ?

The integral from 1 to 7 of 2/x is 2ln(7)

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integral from 1 to 7 of 2/x

\int_{1}^{7} \frac{2}{x} d x

2 ln (7)

Decimal

3.89182 \dots

Solution steps

\int_{1}^{7} \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_{1}^{7} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 2 [ln ∣ x ∣]_{1}^{7}

Compute the boundaries:

ln (7)

= 2 ln (7)

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What is the integral from 1 to 7 of 2/x ?
The integral from 1 to 7 of 2/x is 2ln(7)