What is the integral of (ln(ln(2x)))/(xln(2x)) ?

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

Popular >

integral of (ln(ln(2x)))/(xln(2x))

\int \frac{ln ( ln ( 2 x ) )}{x ln ( 2 x )} d x

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

Solution steps

\int \frac{ln ( ln ( 2 x ) )}{x ln ( 2 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 ( 2 x ) )}{2}

Add a constant to the solution

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

\int \frac{x}{( a + b x ) ^{2}} d x

\int x^{3} (1 - 4 x^{2})^{\frac{5}{2}} d x

\int \frac{1}{x ( x ^{12} + 1 ) ^{2}} d x

\int x ln (1 - x) d x

\int (2 x - 4)^{4} d x

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