The integral of the function (8)/(xln(3x))dx can be solved by using the substitution method. By letting u = ln(3x), the differential du becomes 1/x dx, allowing the integral to be rewritten as 8/udu. Upon integrating, the result is 8ln(u), which translates to 8ln(ln(3x)). The final answer includes the constant of integration and absolute value bars, yielding 8ln |ln(3x)| + C.
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mshiddensecret said:Homework Statement
Integrate: (8)/(xln(3x))dxHomework 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?