What is the integral from e to e^2 of (ln(ln(x)))/x ?

The integral from e to e^2 of (ln(ln(x)))/x is 2ln(2)-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from e to e^2 of (ln(ln(x)))/x

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

2 ln (2) - 1

Decimal Notation

0.38629 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{2} ln (u) d u

= \int_{1}^{2} ln (u) d u

Apply Integration By Parts

: [u ln (u) - \int 1 d u]_{1}^{2}

= [u ln (u) - \int 1 d u]_{1}^{2}

\int 1 d u = u

= [u ln (u) - u]_{1}^{2}

Compute the boundaries:

2 ln (2) - 1

= 2 ln (2) - 1

\int_{- 1}^{1} \frac{4}{1 + 16 t ^{2}} d t

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

\int_{0}^{6} 5 x^{2} + 10 x + 6 d x

\int_{0}^{3} - 4 x^{2} d x

\int_{2}^{6} \frac{1}{x} d x

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