Mastering Integrals: Solving a Tricky ln(x) Integral Problem

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Homework Help Overview

The discussion revolves around evaluating an integral involving the natural logarithm function, specifically the integral of ln(x) divided by a polynomial expression. Participants are exploring methods to approach this integral problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are discussing different methods to simplify the integral, including rewriting the integral in a different form and considering substitutions such as trigonometric or logarithmic transformations.

Discussion Status

There are various approaches being suggested, with some participants proposing specific substitutions and others questioning the effectiveness of these methods. The discussion is ongoing, with no clear consensus reached yet.

Contextual Notes

Participants are navigating the complexity of the integral and considering the implications of different substitutions, indicating that the problem may have multiple interpretations or paths to explore.

nitroracer
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I have an integral I want to work out that should be a simple one but I just can't see where to start with it. Any help would be appreciated.

[tex] <br /> \int\frac{lnx}{x-8xln^2x}<br /> [/tex]
 
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Write it as:
[tex]\frac{1}{2}\int\frac{2\ln(x)}{x}\frac{dx}{1-8\ln^{2}(x)}[/tex]
 
Last edited:
i haven't done it but it looks like trig substitution might work
 
Substituting for ln^2(x) works even better..:smile:
 

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