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Integral 1/(cosx -sinx)²

  1. May 22, 2010 #1
    dx/(cosx -sinx)²



    2. Relevant equations



    I changed it to: dx/(1-2sinxcosx) but from there I don't know what to do, i tried partial integration and substitution ...

    thanks
     
  2. jcsd
  3. May 22, 2010 #2

    Dick

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    Try writing (cos(x)-sin(x))=cos(x)*(1-tan(x)).
     
  4. May 22, 2010 #3
    hmm i see, now I've got integr: du/(1-u)² with u=tanx but what now?
     
  5. May 22, 2010 #4

    Dick

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    Try u=1-tan(x) instead.
     
  6. May 22, 2010 #5
    hehe, sorry I saw it already (and found the answer).
    Could you give me some advice on how to solve integrals fluently?
     
  7. May 22, 2010 #6
    btw: thanks for the help
     
  8. May 22, 2010 #7

    Fredrik

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    http://integrals.wolfram.com/index.jsp :smile:

    Seriously though, integration is a real pain, and the only way to get good at it is to study all the solved examples in your book (and maybe other books as well), and work through a lot of examples. Once you have passed the exam, you can forget all about it and have your computer integrate things for you.
     
  9. May 22, 2010 #8
    Well that's actually the problem we haven't done many exercises, only a few examples during class which were much easier than the exercises in the book...

    thanks for the link
     
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