What is the integral from 3 to 9 of 1/(xln(x)) ?

The integral from 3 to 9 of 1/(xln(x)) is ln(2)

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integral from 3 to 9 of 1/(xln(x))

\int_{3}^{9} \frac{1}{x ln ( x )} d x

ln (2)

Decimal

0.69314 \dots

Solution steps

\int_{3}^{9} \frac{1}{x ln ( x )} d x

Apply u-substitution

= \int_{l n (3)}^{2 l n (3)} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{l n (3)}^{2 l n (3)}

Compute the boundaries:

ln (2 ln (3)) - ln (ln (3))

= ln (2 ln (3)) - ln (ln (3))

Simplify

= ln (2)

What is the integral from 3 to 9 of 1/(xln(x)) ?
The integral from 3 to 9 of 1/(xln(x)) is ln(2)