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Trig substitition-lost in identities

  1. Jul 3, 2009 #1
    Trig substitition--lost in identities

    1. The problem statement, all variables and given/known data

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

    2. Relevant equations
    It's pretty obvious that this is a trig substitution problem requiring use of tangent.


    3. The attempt at a solution

    [tex]x=tan\theta[/tex]
    [tex]dx=sec^{2}\theta[/tex]
    [tex]x^{2}=tan^{2}\theta[/tex]

    Substitute it in.

    [tex]\frac{sec^{2}\theta}{tan^{2}\theta\sqrt{tan^{2}\theta + 1}}[/tex]

    But the [tex]\sqrt{tan^{2}\theta + 1}[/tex] simplifies to [tex]sec\theta[/tex]

    Now before I integrate, I need to simplify. The obvious simplification is the [tex]sec^{2}\theta[/tex] and [tex]sec\theta[/tex] in the denominator, leaving me with
    [tex]\frac{sec\theta}{tan^{2}\theta}[/tex]

    This is starting to look fishy to me. I think I've begun to develop an instinct telling me when I am doing something incorrectly. I simplify this to [tex]\frac{cos\theta}{sin^{2}\theta}[/tex]

    Now I need to ingrate this, but it doesn't look promising. Can someone tell me where I went wrong?
     
  2. jcsd
  3. Jul 3, 2009 #2

    Avodyne

    User Avatar
    Science Advisor

    Re: Trig substitition--lost in identities

    Nothing wrong so far. Time for another substitution.
     
  4. Jul 3, 2009 #3
    Re: Trig substitition--lost in identities

    Oh, haha, you're right! I need to start thinking to substitute more often :p

    u= sin and du = cos

    Yep, straight forward from here. Thanks so much.
     
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