Integration: Help With Log SQRT 1+x^2

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Homework Help Overview

The discussion revolves around the integration of the function log(sqrt(1+x^2)), exploring various methods and substitutions related to hyperbolic functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the potential use of hyperbolic functions for substitution, with one suggesting x = sinh(t) as a candidate. There are questions about the validity of this substitution and the correctness of a proposed answer. Additionally, there are inquiries regarding the derivatives of logarithmic functions.

Discussion Status

The conversation is ongoing, with participants providing suggestions for approaches and clarifying concepts. Some guidance has been offered regarding hyperbolic substitution and differentiation, but no consensus on the final solution has been reached.

Contextual Notes

Participants express uncertainty about the integration process and the correctness of their proposed solutions, indicating a need for further exploration and validation of their approaches.

XtremePhysX
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Homework Statement



find

Homework Equations



[tex]\int log\sqrt{1+x^2}dx[/tex]

The Attempt at a Solution



I honestly don't know what to do?
 
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I would use a hyperbolic function to make a substitution to get rid of the square root.
 
I don't know how to do that?
 
[tex]x = \sinh t[/tex] would be the obvious candidate.
 
So is that a substitution?
 
the answer is xlnx-x+c is that right?
 
You'll have to make the calculations on your own. I just gave you a point to start from, assuming you have knowledge of hyperbolic functions. Another option is to use integration by parts.
 
Yes, hyperbolic substitution would work here.
 
Millennial said:
Yes, hyperbolic substitution would work here.

Hello mill
but is the answer xlnx-x
also, is the derivative of ln(x^2) just 2/x and the derivative of (lnx)^2 is 2lnx/x ?
 
  • #10
Xtreme, why don't you try differentiating your answer to check whether if it is correct?
And answering your question about derivatives: Yes, they are both correct.
 

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