What is the integral from e to 4 of (ln(ln(x)))/x ?

The integral from e to 4 of (ln(ln(x)))/x is 2ln(2)ln(2ln(2))-2ln(2)+1

Popular >

integral from e to 4 of (ln(ln(x)))/x

\int_{e}^{4} \frac{ln ( ln ( x ) )}{x} d x

2 ln (2) ln (2 ln (2)) - 2 ln (2) + 1

Decimal

0.06651 \dots

Solution steps

\int_{e}^{4} \frac{ln ( ln ( x ) )}{x} d x

Apply u-substitution

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

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

Apply Integration By Parts

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

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

\int 1 d u = u

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

Compute the boundaries:

2 ln (2) ln (2 ln (2)) - 2 ln (2) + 1

= 2 ln (2) ln (2 ln (2)) - 2 ln (2) + 1

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

\int_{1}^{3} \frac{4 ( ln ( x ) ) ^{3}}{x} d x

\int_{2}^{1} 1 x^{5} d x

\int_{1}^{5} (\frac{1}{2 x - 1}) d x

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

What is the integral from e to 4 of (ln(ln(x)))/x ?
The integral from e to 4 of (ln(ln(x)))/x is 2ln(2)ln(2ln(2))-2ln(2)+1