What is the integral from 1 to 2 of 1/(xln(2)) ?

The integral from 1 to 2 of 1/(xln(2)) is 1

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integral from 1 to 2 of 1/(xln(2))

\int_{1}^{2} \frac{1}{x ln ( 2 )} d x

1

Solution steps

\int_{1}^{2} \frac{1}{x ln ( 2 )} d x

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{ln ( 2 )} [ln ∣ x ∣]_{1}^{2}

Compute the boundaries:

ln (2)

= \frac{1}{ln ( 2 )} ln (2)

Simplify

= 1

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What is the integral from 1 to 2 of 1/(xln(2)) ?
The integral from 1 to 2 of 1/(xln(2)) is 1