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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 3 of 1/(xln(x))

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

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

Solution steps

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

Apply u-substitution

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

= \int_{l n (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 (2)}^{l n (3)}

Compute the boundaries:

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

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

\int_{0}^{1} 3 x (x^{2} + 1)^{3} d x

\int_{0}^{x} (x - t) f (t) d t

\int_{- π}^{π} x^{4} cos (n x) d x

\int_{0}^{0.5} e^{- x} d x

\int_{0}^{6} (4 x - 1)^{2} d x

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