What is the integral from e to e^4 of 1/(xln(x)) ?

The integral from e to e^4 of 1/(xln(x)) is 2ln(2)

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integral from e to e^4 of 1/(xln(x))

\int_{e}^{e^{4}} \frac{1}{x ln ( x )} d x

2 ln (2)

Decimal

1.38629 \dots

Solution steps

\int_{e}^{e^{4}} \frac{1}{x ln ( x )} d x

Apply u-substitution

= \int_{1}^{4} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 2 ln (2)

What is the integral from e to e^4 of 1/(xln(x)) ?
The integral from e to e^4 of 1/(xln(x)) is 2ln(2)