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

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

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

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

ln (2 ln (2))

Decimal

0.32663 \dots

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{2 l n (2)}

Compute the boundaries:

ln (2 ln (2))

= ln (2 ln (2))

\int_{2}^{4} 5 x d x

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\int_{- 1}^{1} \frac{3}{4} (1 - x^{2}) d x

\int_{- a}^{a} cos (x) d x

\int_{x}^{x^{2}} 1 + t^{2} d t

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