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

The integral of (ln(ln(x)))/(x*ln(x)) is (ln^2(ln(x)))/2+C

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

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

\frac{ln ^{2} ( ln ( x ) )}{2} + C

Solution steps

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

Apply u-substitution

: \int \frac{ln ( u )}{u} d u

= \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

= \frac{ln ^{2} ( ln ( x ) )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( ln ( x ) )}{2} + C

\int (5 t + 1)^{100} d t

\int 2 x^{25} d x

\int 9 x e^{4 x} d x

f (x) = x^{4} - 2 x^{3} - 12 x^{2} + 4 x - 3

What is the integral of (ln(ln(x)))/(x*ln(x)) ?
The integral of (ln(ln(x)))/(x*ln(x)) is (ln^2(ln(x)))/2+C