What is the integral of ((ln(ln(x)))/x) ?

The integral of ((ln(ln(x)))/x) is ln(x)ln(ln(x))-ln(x)+C

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integral of ((ln(ln(x)))/x)

\int (\frac{ln ( ln ( x ) )}{x}) d x

ln (x) ln (ln (x)) - ln (x) + C

Solution steps

\int \frac{ln ( ln ( x ) )}{x} d x

Apply u-substitution

: \int ln (u) d u

= \int ln (u) d u

Apply Integration By Parts

: u ln (u) - \int 1 d u

= u ln (u) - \int 1 d u

\int 1 d u = u

= u ln (u) - u

Substitute back

u = ln (x)

= ln (x) ln (ln (x)) - ln (x)

Add a constant to the solution

= ln (x) ln (ln (x)) - ln (x) + C

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What is the integral of ((ln(ln(x)))/x) ?
The integral of ((ln(ln(x)))/x) is ln(x)ln(ln(x))-ln(x)+C