Struggling with Integrating 1/(cosx - sinx)^2?

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dx/(cosx -sinx)²



Homework 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
 
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Try writing (cos(x)-sin(x))=cos(x)*(1-tan(x)).
 
hmm i see, now I've got integr: du/(1-u)² with u=tanx but what now?
 
polepole said:
hmm i see, now I've got integr: du/(1-u)² with u=tanx but what now?

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