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

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

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

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

\frac{6}{4 x + 1}

\frac{x ^{2} - 5 x}{x + 1}

(t - 2)^{3} (t - 2)

y^{^{'}} = \frac{( x ^{3} - 2 y )}{x}

\frac{d}{d x} (6 sin (2 x) - 3 cos (3 x))

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