Indefinite Integral Homework: Get a Hint to Evaluate It

In summary, the conversation discusses how to evaluate an expression using trig identities and integration by parts. One person suggests converting the expression first and then trying different integration methods. The other person mentions that the answer is long and not pretty, and asks if it is related to Fourier decomposition.
  • #1
zorro
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0

Homework Statement



How do I evaluate this?

gif.latex?\int\frac{cos7x-cos8x}{1+2cos^2x}dx.gif


A hint will do.
 

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  • #2
Abdul Quadeer said:

Homework Statement



How do I evaluate this?

gif.latex?\int\frac{cos7x-cos8x}{1+2cos^2x}dx.gif


A hint will do.

Convert the expression using trig identities and then try by-parts integration or substitution.
 
  • #3
Did you get the answer or you are just suggesting?
 
  • #4
Yeah, looking at the answer, It looks like a few trig identities (particularly the denominator), and then integration by parts (many times). Be warned, the answer is rather ugly (many lines ugly...)

by any chance did this come up in a Fourier decomposition (I am looking at the graph of it)? :P
 
  • #5
n1person said:
Yeah, looking at the answer, It looks like a few trig identities (particularly the denominator), and then integration by parts (many times). Be warned, the answer is rather ugly (many lines ugly...)

by any chance did this come up in a Fourier decomposition (I am looking at the graph of it)? :P

Looking at the answer? Where is it?
No it is not from Fourier decomposition.
 

1. What is an indefinite integral?

An indefinite integral is a mathematical concept that represents the antiderivative of a given function. It is the reverse process of differentiation, and it helps us find the original function when we know its derivative.

2. How do I evaluate an indefinite integral?

To evaluate an indefinite integral, you need to find the antiderivative of the given function and add a constant of integration. This constant is represented by the letter 'C' and accounts for any possible solutions that may have been lost during differentiation.

3. Why is it important to show the steps when solving an indefinite integral?

Showing the steps when solving an indefinite integral is crucial because it allows you to check your work for any mistakes. It also helps in understanding the process and identifying any areas where you may need more practice.

4. What is the purpose of getting a hint to evaluate an indefinite integral?

Getting a hint to evaluate an indefinite integral can help you if you are stuck or unsure of how to proceed with solving the problem. It can provide guidance and point you in the right direction, but it is still important to understand the steps and reasoning behind the solution.

5. How can I improve my skills in solving indefinite integrals?

The best way to improve your skills in solving indefinite integrals is through practice. Try to solve a variety of problems, and if you get stuck, refer to a textbook or ask for help from a teacher or tutor. It is also helpful to review and understand the basic rules and techniques for solving indefinite integrals.

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