What is the integral of (ln(ln(6x)))/(xln(6x)) ?

The integral of (ln(ln(6x)))/(xln(6x)) is (ln^2(ln(6x)))/2+C

Popular >

integral of (ln(ln(6x)))/(xln(6x))

\int \frac{ln ( ln ( 6 x ) )}{x ln ( 6 x )} d x

\frac{ln ^{2} ( ln ( 6 x ) )}{2} + C

Solution steps

\int \frac{ln ( ln ( 6 x ) )}{x ln ( 6 x )} d x

Apply u-substitution

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

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

Apply u-substitution

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

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

Apply u-substitution

: \int w d w

= \int w d w

Apply the Power Rule

: \frac{w ^{2}}{2}

= \frac{w ^{2}}{2}

Substitute back

= \frac{ln ^{2} ( ln ( 6 x ) )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( ln ( 6 x ) )}{2} + C

\int e^{x} + 8 sin (x) d x

\int \frac{- x - 28}{( x - 2 ) ( x ^{2} - 2 x + 10 )} d x

\int 6 x x^{2} + 4 d x

\int \frac{2 x - 1}{x + 3} d x

\int \frac{1}{25 x ^{2} + 1} d x

What is the integral of (ln(ln(6x)))/(xln(6x)) ?
The integral of (ln(ln(6x)))/(xln(6x)) is (ln^2(ln(6x)))/2+C