What is the integral of (ln(ln(3x)))/(xln(3x)) ?

The integral of (ln(ln(3x)))/(xln(3x)) is (ln^2(ln(3x)))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln(ln(3x)))/(xln(3x))

\int \frac{ln ( ln ( 3 x ) )}{x ln ( 3 x )} d x

\frac{ln ^{2} ( ln ( 3 x ) )}{2} + C

Solution steps

\int \frac{ln ( ln ( 3 x ) )}{x ln ( 3 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 ( 3 x ) )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( ln ( 3 x ) )}{2} + C

2 x^{2}

\int \frac{1}{1 - \frac{x ^{2}}{64}} d x

\int 4 - 10 e^{- 0.2 x} d x

\int e^{x} - 5 cos (x) d x

What is the integral of (ln(ln(3x)))/(xln(3x)) ?
The integral of (ln(ln(3x)))/(xln(3x)) is (ln^2(ln(3x)))/2+C