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

The integral from 2 to e of 1/(xln(x)) is -ln(ln(2))

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

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

- ln (ln (2))

Decimal

0.36651 \dots

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{l n (2)}^{1}

Compute the boundaries:

- ln (ln (2))

= - ln (ln (2))

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