What is the precise answer for integrating 3lnx/x?

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The discussion focuses on the integration of the expression 3ln(x)/x. The correct substitution for integration involves setting u = ln(x), leading to du = (1/x)dx. The participants clarify that the integration can be approached using integration by parts, emphasizing the importance of correctly identifying u and its derivative. The final expression for du is confirmed as (1/x)dx, which is essential for proceeding with the integration.

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  • Familiarity with logarithmic functions and their derivatives.
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  • Study integration by parts in detail, focusing on its applications.
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Mitchtwitchita
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Can anybody help me out with this?

3lnx/x du = ( ? ) dx. What is the question mark? Leave no spaces in your answer.

I thought u was 3lnx, which would be make it 3/x dx. Apparently not. Can anybody show me the right way of doing this sort of problem please?
 
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Are you trying to solve for u? If so:

(x/3lnx)dx = du

You can integrate both sides, the left by integration by parts, I think will work.
 
That really makes no sense without knowing how u depends on x. Why did you "think u was 3ln(x)"? Are you leaving out part of the problem?
 
Sorry, I should have been more clear. I just copied and pasted the problem. The question was 3lnx/x, and I just needed to find the first part of the problem. The professor wanted us to "find u, and take it one more step." I thought that step was differentiating u. All I really need is what would be in the brackets with respect to dx.
 
Then knowing that the derivative of ln(x)= 1/x should help you! 3ln(x)/x dx= 3(ln x)(dx/x). I would incline toward setting u= ln x. What is du now?
 
1/x?
 
Mitchtwitchita said:
1/x?

should be 1/x dx precise.
 

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