What is the integral of 6/(xln(3x)) ?

The integral of 6/(xln(3x)) is 6ln|ln(3x)|+C

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integral of 6/(xln(3x))

\int \frac{6}{x ln ( 3 x )} d x

6 ln ∣ ln (3 x) ∣ + C

Solution steps

\int \frac{6}{x ln ( 3 x )} d x

Take the constant out:

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

= 6 \cdot \int \frac{1}{x ln ( 3 x )} d x

Apply u-substitution

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

= 6 \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

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

= 6 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 6 ln ∣ v ∣

Substitute back

= 6 ln ∣ ln (3 x) ∣

Add a constant to the solution

= 6 ln ∣ ln (3 x) ∣ + C

n = 1 \sum \infty \frac{5}{n n}

\int (2 t^{2} + sec^{2} (t)) d t

\int x^{2} (20 x^{7} - 7 x^{4} + 6) d x

sin (x^{5})

x = 7 y^{2}, x = 4 + 3 y^{2}

What is the integral of 6/(xln(3x)) ?
The integral of 6/(xln(3x)) is 6ln|ln(3x)|+C