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[itex]sec^{2}(x)tan(x)dx[/itex] Let U = sec(x) or tan(x) ?

  1. Oct 5, 2013 #1
    The integral of [itex]sec^{2}(x)tan(x)dx[/itex] is what I'm asking about.

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



    [itex]sec^{2}(x)tan(x)dx[/itex]

    I can let u = tanx
    then du = [itex]sec^{2}(x)[/itex]

    [itex]\frac{1}{2}\int udu[/itex]

    [itex]\frac{1}{2}tan^{2}(x)[/itex]


    OR

    I can let u = secx
    then du = secxtanx dx

    [itex]\int udu[/itex]

    [itex]\frac{1}{2}u^{2}[/itex]

    [itex]\frac{1}{2}sec^{2}(x)[/itex]


    Why do both work? Which one is correct? Or are both correct?
     
  2. jcsd
  3. Oct 5, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    They both work. They differ by a constant. sec(x)^2-tan(x)^2=1. You should put a '+C' in when you write the solution to an indefinite integral. That's where the difference is.
     
  4. Oct 5, 2013 #3
    thanks, appreciate the feedback.
     
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