Integration of the natural log

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Homework Help Overview

The discussion revolves around the integration of the function \(\int \frac{(\ln x)^2}{x} \, dx\), focusing on the application of integration techniques and the use of substitution.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the integration process, with some suggesting the use of substitution by letting \(u = \ln x\). Questions arise regarding the transformation of the integral and the implications of the derivative of \(\ln x\).

Discussion Status

Several participants have provided hints and guidance, emphasizing the importance of showing attempted work. There is an ongoing exploration of the integral's transformation and the application of integration techniques, with no explicit consensus reached yet.

Contextual Notes

Participants note the necessity of adhering to forum rules regarding the demonstration of attempted solutions, which influences the nature of the discussion.

nusaibahazman
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1. how to integrate∫ (ln x)2 /x dx

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The Attempt at a Solution

 
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Here it is better to show what you have attempted so far, after all people here are not answer machine. But a hint can be: what is the derivative of ln x?
 
nusaibahazman said:
1. how to integrate∫ (ln x)2 /x dx

raopeng said:
Here it is better to show what you have attempted so far, after all people here are not answer machine. But a hint can be: what is the derivative of ln x?

Although, raopeng suggests that you show what you've attempted, it is actually a part of the rules for posting a thread in the homework help section of this Forum.raopeng's hint is excellent.
 
x(ln x)-1+c..i not pretty sure..
 
nusaibahazman said:
x(ln x)-1+c..i not pretty sure..
The derivative of ln(x) is (1/x) + C .

Do you know integration by substitution?
 
i know..let u= ln x
then differenciate du/dx= 1/x..
 
i know..let u= ln x
then differenciate du/dx= 1/x..
 
nusaibahazman said:
i know..let u= ln x
then differenciate du/dx= 1/x..
After doing all that, what does your integral become, in terms of u ?
 
u^2 du..right.?
 
  • #10
let u= ln x
du/dx= 1/x
dx= x du..
then integrate (u^2/x) x du
then cancel the x...so, integrate the u^2..
right.? i got the idea..tq..
 

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