What is the integral of 3/((xln^2(3x))) ?

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

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integral of 3/((xln^2(3x)))

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

- \frac{3}{ln ( 3 x )} + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int \frac{1}{x ln ^{2} ( 3 x )} d x

Apply u-substitution

: \int \frac{1}{u ln ^{2} ( u )} d u

= 3 \cdot \int \frac{1}{u ln ^{2} ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= 3 \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= 3 (- \frac{1}{v})

Substitute back

= 3 (- \frac{1}{ln ( 3 x )})

Simplify

3 (- \frac{1}{ln ( 3 x )}) : - \frac{3}{ln ( 3 x )}

= - \frac{3}{ln ( 3 x )}

Add a constant to the solution

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

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