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

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

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

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

diverges

Solution steps

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

Apply u-substitution

: \int_{0}^{1} \frac{1}{u} d u

= \int_{0}^{1} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

\int_{1}^{2} \frac{t - 1}{t} d t

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

\int_{1}^{6} 2 x^{- 4} d x

\int_{0}^{2} \frac{- 1}{2 x} d x

\int_{0}^{2} 4 - r^{2} d r

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