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

  • Thread starter polepole
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    Integral
In summary, the conversation discusses ways to solve the integral dx/(cosx -sinx)². The individual tried changing the expression to dx/(1-2sinxcosx) and using partial integration and substitution, but then proceeded to use u=tanx and u=1-tan(x) to solve the integral. They also asked for advice on how to solve integrals fluently and received a link to a helpful resource.
  • #1
polepole
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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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  • #2
Try writing (cos(x)-sin(x))=cos(x)*(1-tan(x)).
 
  • #3
hmm i see, now I've got integr: du/(1-u)² with u=tanx but what now?
 
  • #4
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.
 
  • #5
hehe, sorry I saw it already (and found the answer).
Could you give me some advice on how to solve integrals fluently?
 
  • #6
btw: thanks for the help
 
  • #7
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.
 
  • #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
 

1. What is the purpose of the integral 1/(cosx-sinx)²?

The integral 1/(cosx-sinx)² is used to solve for the area under the curve of the function 1/(cosx-sinx)². It is also used to find the antiderivative of this function, which can be used in further calculations or applications.

2. How do you solve the integral 1/(cosx-sinx)²?

To solve the integral 1/(cosx-sinx)², you can use the substitution method or the trigonometric identities. You can also use online calculators or software to solve it numerically.

3. What is the domain of the integral 1/(cosx-sinx)²?

The domain of the integral 1/(cosx-sinx)² is all real numbers except for the values that make the denominator equal to zero. In this case, the values are x = π/4 + kπ, where k is any integer.

4. Can the integral 1/(cosx-sinx)² be simplified?

Yes, the integral 1/(cosx-sinx)² can be simplified using trigonometric identities. For example, you can use the double angle formula for sine and cosine to simplify the integrand into a more manageable form.

5. How is the integral 1/(cosx-sinx)² used in real-world applications?

The integral 1/(cosx-sinx)² has various applications in mathematics, physics, and engineering. It is used to solve problems related to oscillations, vibrations, and periodic functions. It is also used in the calculation of areas, volumes, and centroids in certain shapes and structures.

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