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Homework Help: Finding an antiderivative using substitution rule

  1. Jul 19, 2005 #1
    I'm trying to find the antiderivative of [sec(2x)tan(2x)], I can't figure out what part I should be substituting. Any help is appreciated.

    Thanks,
    hk
     
  2. jcsd
  3. Jul 19, 2005 #2
    [tex]
    \sec \left( {2x} \right)\tan \left( {2x} \right) = \frac{{\sin \left( {2x} \right)}}{{\cos ^2 \left( {2x} \right)}}
    [/tex]

    You should be able to finish it off.
     
  4. Jul 19, 2005 #3
    replace 2x by u and you have secu 's derivative under the integral sign
     
  5. Jul 19, 2005 #4
    I ended up working on it some more and came up with u=sec(2x).
    Then (1/2)du=sec(2x)tan(2x)dx. I'm not sure if this is the prefered method but it came out to the correct answer.

    hk
     
  6. Jul 19, 2005 #5

    HallsofIvy

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    Science Advisor

    Looks good to me!
     
  7. Jul 20, 2005 #6
    Thank you for the replys.

    hk
     
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