# Homework Help: Integral 1/(cosx -sinx)²

1. May 22, 2010

### polepole

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. May 22, 2010

### Dick

Try writing (cos(x)-sin(x))=cos(x)*(1-tan(x)).

3. May 22, 2010

### polepole

hmm i see, now I've got integr: du/(1-u)² with u=tanx but what now?

4. May 22, 2010

### Dick

5. May 22, 2010

### polepole

Could you give me some advice on how to solve integrals fluently?

6. May 22, 2010

### polepole

btw: thanks for the help

7. May 22, 2010

### Fredrik

Staff Emeritus
http://integrals.wolfram.com/index.jsp

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.

8. May 22, 2010

### polepole

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...