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

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In summary, the conversation revolves around solving for u in the given equation 3lnx/x du = ( ? ) dx. The participants discuss different approaches to solving the problem, including integrating both sides and setting u as ln x. They also mention the derivative of ln x, which is 1/x. The final conclusion is that the correct answer should be 1/x dx.
  • #1
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
  • #6
1/x?
 
  • #7
Mitchtwitchita said:
1/x?

should be 1/x dx precise.
 

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

What is the basic concept behind integration of 3 lnx/x?

The basic concept behind integration of 3 lnx/x is to find the antiderivative of the function 3 lnx/x. This involves finding a function whose derivative is 3 lnx/x. In simpler terms, integration is the reverse process of differentiation.

What is the general formula for integrating 3 lnx/x?

The general formula for integrating 3 lnx/x is ∫3 lnx/x dx = 3 ln|x| + C, where C is the constant of integration. This formula applies for any real number x, except for x = 0.

How do you solve integrals involving 3 lnx/x?

To solve integrals involving 3 lnx/x, you can use several techniques such as integration by parts, substitution, and partial fractions. It is important to identify the most appropriate method for a given integral in order to obtain an accurate solution.

Can the integral of 3 lnx/x be evaluated without using any special techniques?

No, the integral of 3 lnx/x cannot be evaluated without using any special techniques. This is because the integrand contains a logarithm and a variable in the denominator, which requires the use of integration techniques such as substitution or partial fractions.

What are the applications of integration of 3 lnx/x in real life?

The integration of 3 lnx/x has various applications in real life, particularly in the fields of physics, engineering, and economics. For example, it can be used to calculate the work done by a variable force, determine the rate of change of a population, or find the cost function for a production process.

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