What is the integral from 3 to 9 of 1/(xln(x)) ?

The integral from 3 to 9 of 1/(xln(x)) is ln(2)

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integral from 3 to 9 of 1/(xln(x))

\int_{3}^{9} \frac{1}{x ln ( x )} d x

ln (2)

Decimal

0.69314 \dots

Solution steps

\int_{3}^{9} \frac{1}{x ln ( x )} d x

Apply u-substitution

: \int_{l n (3)}^{2 l n (3)} \frac{1}{u} d u

= \int_{l n (3)}^{2 l n (3)} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{l n (3)}^{2 l n (3)}

Compute the boundaries:

ln (2 ln (3)) - ln (ln (3))

= ln (2 ln (3)) - ln (ln (3))

Simplify

= ln (2)

y = 2 x + 1, at x = \frac{1}{2}

\int \frac{x ^{2} + 1}{2 x} d x

\int \frac{x}{x ^{3} + x} d x

n = 0 \sum \infty 2^{- \frac{n}{2}}

y = ln (5 x^{2} + 3 y^{2})

What is the integral from 3 to 9 of 1/(xln(x)) ?
The integral from 3 to 9 of 1/(xln(x)) is ln(2)