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Which Integration Technique?

  1. Aug 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve:

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

    2. Relevant equations

    This is where I need help. What integration technique do I use? u-substitution? Integration by parts? None seem to work. As an added note, I've been trying to teach myself some calculus II work over the summer, so I just need a pointer in the right direction. Thank you

    3. The attempt at a solution

    I attempted to use u-substitution. I don't think this is the right method. Does anyone know the correct method? It got pretty messy, but I didn't get the right answer:

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


    u = [tex]x^{2}[/tex]+1
    du = 2x
    x = [tex]\sqrt{u-1}[/tex]



    = [tex]\frac{1}{2}[/tex] [tex]\int[/tex]([tex]\sqrt{u}[/tex])([tex]\sqrt{u-1}[/tex]) du


    = ? Is this the correct start?
     
  2. jcsd
  3. Aug 15, 2009 #2
    Try tan(u) = x as the substitution.
     
  4. Aug 15, 2009 #3
    Let I = [tex]\int\sqrt{x^2-1}[/tex]dx

    Try integrating by parts.

    I = [tex]x\sqrt{x^2-1}dx[/tex] - [tex]\int x\x^{2} / \sqrt{x^2-1}dx[/tex]

    See if you can carry on from here.
     
  5. Aug 15, 2009 #4
    I KNOW this will work. Sub x as sec(u). Go on from there.
     
  6. Aug 15, 2009 #5
    What are you implying sir? I'm sure all of us here know how to complete the problem easily. I didn't want to solve the problem for him. Therefore I gave him a hint so that he could carry on from there.
     
  7. Aug 15, 2009 #6
    Sorry, I didn't mean to offend anyone. And I didn't mean your hint was worthless.
     
  8. Aug 15, 2009 #7
    It's cool. :smile:
     
  9. Aug 15, 2009 #8
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