What is the integral from 2 to r of 1/(xln(x)) ?

The integral from 2 to r of 1/(xln(x)) is ln|ln(r)|-ln(ln(2))

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integral from 2 to r of 1/(xln(x))

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

ln ∣ ln (r) ∣ - ln (ln (2))

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{l n (2)}^{l n (r)}

Compute the boundaries:

ln ∣ ln (r) ∣ - ln (ln (2))

= ln ∣ ln (r) ∣ - ln (ln (2))

\int \frac{e ^{x}}{( 4 - e ^{x} ) ^{2}} d x

\int \frac{3 x + 6}{2 x ^{2} + 8 x + 3} d x

x \to \frac{π}{4} lim (2 cot (2 x))

\int (\frac{x}{x + 2}) d x

x \to 7 lim (\frac{x - 8}{x - 7})

What is the integral from 2 to r of 1/(xln(x)) ?
The integral from 2 to r of 1/(xln(x)) is ln|ln(r)|-ln(ln(2))