Integrating 8/(xln(3x))dx | Solving for ln(3x) | Homework Help

[mshiddensecret]

Homework Statement

Integrate: (8)/(xln(3x))dx

Homework Equations

The Attempt at a Solution

I separated the equations into 8/x and 1/(ln3x). I sub u for ln(3x) and I got 1/x for du. Since I had 8/x, I made it 8du. So the new integration will be 8/udu. I integrated so it will be 8lnu and then it will become 8ln(ln3x). What's next?

 

[LCKurtz]

Homework Statement

Integrate: (8)/(xln(3x))dx

Homework Equations

The Attempt at a Solution

I separated the equations into 8/x and 1/(ln3x). I sub u for ln(3x) and I got 1/x for du. Since I had 8/x, I made it 8du. So the new integration will be 8/udu. I integrated so it will be 8lnu and then it will become 8ln(ln3x). What's next?

Not much. Just add the constant of integration. And you might want absolute value bars:$$
8\ln |\ln(3x)|+C$$