Integral of sqrt(1+ln x)/(x*ln x), this is driving me nuts.

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Homework Help Overview

The discussion revolves around the integral of the function sqrt(1+ln x)/(x*ln x). Participants are exploring various substitution methods to tackle the problem.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss different substitution strategies, including using u^2=ln(x)+1 and y=ln(x). There are questions about the implications of these substitutions and how they affect the integration process.

Discussion Status

Some participants have reported making progress with substitutions, while others express confusion about the steps and the resulting expressions. There is acknowledgment of errors and a shared experience of frustration with the problem.

Contextual Notes

Participants mention the challenges of the problem, including the complexity of the algebra involved and the time spent on it. There is a light-hearted tone regarding the difficulties faced during the discussion.

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Homework Statement



Integral of sqrt(1+ln x)/(x*ln x)

Homework Equations





The Attempt at a Solution



I've tried substitutions and they seem to lead to nowhere. I need help getting started on this one. Thanks
 
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Oooppss. I got it now, I had to double substitute.
 
Did you try u^2=log(x)+1? So log(x)=u^2-1.
 
Did you try y = ln x? That should give something that you can probably integrate by using hyperbolic functions.
 
DrummingAtom said:
Oooppss. I got it now, I had to double substitute.

But...why?

u=lnx, du=1/x

thus sqrt(u)du/u= u^(-1/2)du...easy power rule, and that's only one sub...

==============
Edit: Thank you DrummingAtom for showing me an error, the likes I have made many a time.
 
Last edited:
Apphysicist said:
But...why?

u=lnx, du=1/x

thus sqrt(u)du/u= u^(-1/2)du...easy power rule, and that's only one sub...

But where does the 1 go? The answer would then be 2sqrt(ln x) which doesn't equal the original function.
 
DrummingAtom said:
But where does the 1 go? The answer would then be 2sqrt(ln x) which doesn't equal the original function.

Well you see, that would just be me neglecting the one to make it an easy question. xD

My bad.
 
=) no worries. This problem gave me about 1.5 hours of sloppy algebra and confusion. I love Sunday nights.
 

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