Integration help

  • #1

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?
 

Answers and Replies

  • #2
dextercioby
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I would use a hyperbolic function to make a substitution to get rid of the square root.
 
  • #3
I don't know how to do that?
 
  • #4
dextercioby
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[tex] x = \sinh t [/tex] would be the obvious candidate.
 
  • #5
So is that a substitution?
 
  • #6
the answer is xlnx-x+c is that right?
 
  • #7
dextercioby
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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.
 
  • #8
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Yes, hyperbolic substitution would work here.
 
  • #9
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
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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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