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Homework Help: Sec(x)tan(x) integral

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data
    [itex]∫sec(x)tan(x)+x/(x^2+1) dx[/itex]

    3. The attempt at a solution
    I replaced sec and tan by [itex]1/cos(x)[/itex] and [itex]sin/cos(x)[/itex] then end up with [itex]sin(x)/cos^2(x)[/itex]
    then I replace [itex]cos^2 x [/itex] by [itex]1-sin^2 x [/itex] then I dont know where to go.

    the second part of the equation works with u substitution.
    I just cant see where the identities of the first part are leading me.

    any hint? thanks in advance!
  2. jcsd
  3. Jan 27, 2014 #2


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    Homework Helper

    No, don't do that. Try the sub ##u = \cos x## and watch that sucker fold. :smile:
  4. Jan 29, 2014 #3
    you know i just used tan(x) in the first term and u substitution in the second and it worked too!

    Thanks a lot!
  5. Jan 29, 2014 #4


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    Staff Emeritus
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    You should ideally recognize the derivative of sec x.
  6. Jan 30, 2014 #5


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    Gold Member

    For the first integral you don't have to substitute anything. It is the derivative of sec(x).
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