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

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

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integral from n to 2n of 1/x

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

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= [ln ∣ x ∣]_{n}^{2 n}

Compute the boundaries:

ln (2 ∣ n ∣) - ln ∣ n ∣

= ln (2 ∣ n ∣) - ln ∣ n ∣

Simplify

= ln (2)

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