What is the integral from e to e^2 of 1/(x*ln(x)) ?

The integral from e to e^2 of 1/(x*ln(x)) is ln(2)

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integral from e to e^2 of 1/(x*ln(x))

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

ln (2)

Decimal

0.69314 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{2} \frac{1}{u} d u

= \int_{1}^{2} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{2}

Compute the boundaries:

ln (2)

= ln (2)

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