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Homework Help: Integration by parts computation

  1. Oct 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the following integral:


    I'm trying to compute as many terms as possible of its asymptotic expansion as x[itex]\rightarrow\infty[/itex].

    2. Relevant equations


    3. The attempt at a solution
    Let u=cos(xt[itex]^{2}[/itex]). And dv=tan[itex]^{2}[/itex](t)dt.
    Then du=-2xtcos(xt[itex]^{2}[/itex])dt and v=[itex]\int[/itex]tan[itex]^{2}[/itex](t)dt=tan(t)-t+C.

    Integration by parts yields:

    where all terms are evaluated from 0 to pi/4, obviously.

    This feels wrong to me. Can anyone give me some help?
  2. jcsd
  3. Oct 27, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    hi the_kid! :smile:

    (try using the X2 button just above the Reply box :wink:)
    erm :redface:

    du=-2xtsin(xt2)dt :wink:
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