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 Notation

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

= \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))

f (x) = x (5 x^{5} - 1)

\int x sin (9 x^{2}) d x

\frac{d}{d x} (\frac{x ^{6}}{6} + \frac{1}{16 x ^{4}})

cos (10 x) - 1

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))