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

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

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integral of (ln(ln(y)))/y

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

ln (y) ln (ln (y)) - ln (y) + C

Solution steps

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

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 (y)

= ln (y) ln (ln (y)) - ln (y)

Add a constant to the solution

= ln (y) ln (ln (y)) - ln (y) + C

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