Having trouble finding the Integral

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In summary, the conversation is about solving the integral \int sin2x ln(cos2x) dx. The person is considering using integration by parts and also notes that sin2x = 2sinxcosx. However, they are struggling to determine the values for u and dv. In the end, they realize that setting u = cos(2x) simplifies the problem.
  • #1
BlackMamba
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Hello,

I am having trouble getting started with this integral.

[itex]\int sin2x ln(cos2x) dx[/itex]

My first thought goes to using integration by parts to solve this but I am still getting stuck. I also know that [itex]sin2x = 2sinxcosx[/itex] but again I'm not seeing how that would help me so I'm back to integration by parts.

My issue is if I set [itex]u = ln(cos2x)[/itex] then I'm having trouble figuring out what [itex]du[/itex] is. I know it's just finding the derivative but I can't for the life of me remember how to do that. Then if I set [itex]dv = sin2x dx[/itex] then [itex]v = - \frac{1}{2} cos2x[/itex]Any help or suggestions would be greatly appreciated.
 
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  • #2
Set u=cos(2x).
 
  • #3
Oh my gosh...I was making that WAY harder then it needed to be. Thank you very much arildno.
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is a fundamental tool in calculus and is used to solve a variety of problems in physics, engineering, and other fields.

2. Why do I have trouble finding integrals?

Finding integrals can be challenging because it requires a good understanding of calculus and the properties of functions. It also requires knowledge of different integration techniques and when to apply them.

3. What are some tips for finding integrals?

Some tips for finding integrals include: understanding the fundamental theorem of calculus, knowing the properties of different functions, practicing with various integration techniques, and using online resources or textbooks for guidance.

4. How can I improve my skills in finding integrals?

To improve your skills in finding integrals, it is important to have a strong foundation in calculus and to practice regularly. You can also seek help from a tutor or join a study group to work on challenging problems together.

5. What are some common mistakes when finding integrals?

Some common mistakes when finding integrals include: forgetting to account for constants, using the wrong integration technique, making algebraic errors, and not simplifying the final answer. It is important to carefully check your work and practice regularly to avoid these mistakes.

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