Solving Tricky Integral: How to Proceed Further?

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In summary, the conversation is about evaluating an integral that has been manipulated into a simpler form. The original integral was evaluated to be 7π/4, but the speaker is now unsure of how to proceed further. Another person has performed a numerical integration and obtained a different result, prompting the speaker to check on Wolfram Alpha, which returns the original value of 7π/4.
  • #1
QwertyPoiuyt
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I was trying the evaluate the integral

$$\int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})} dx$$ from

I have since manipulated this integral into $$\int_{\pi/4}^{5\pi/4}\frac{7}{(1+2^{\sin x})(1+2^{\cos x})} dx$$
Any help on how to proceed further would be appreciated.

The value of the original integral is I believe $$7\pi/4$$The Ineresting thing is I had solved this in the past but don't have a clue on how to go further now..
 
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  • #2
QwertyPoiuyt said:
The value of the original integral is I believe

7π/4​

I did a quick numerical integration on your first integral, I get ~3.57. So I don't think that's correct.
 
  • #3
gmax137 said:
I did a quick numerical integration on your first integral, I get ~3.57. So I don't think that's correct.
You can check on wolfram alpha It returns the value 5.49774 which is the value I quoted
 

1. What is a tricky integral?

A tricky integral is an integral that cannot be easily solved using standard techniques, such as substitution or integration by parts. These integrals often involve complex functions or special functions, and require creative problem-solving skills to find a solution.

2. How do I know if an integral is tricky?

There is no definitive way to determine if an integral is tricky, as it often depends on the individual's level of knowledge and problem-solving abilities. However, some signs that an integral may be tricky include complex functions, unusual limits of integration, or integrands that cannot be easily simplified.

3. What are some strategies for solving tricky integrals?

Some common strategies for solving tricky integrals include using substitution, integration by parts, trigonometric identities, partial fractions, or series expansion. However, there is no one-size-fits-all approach, and it often requires a combination of these techniques and creative problem-solving skills to find a solution.

4. Can tricky integrals be solved using software or calculators?

Yes, there are software programs and calculators that can solve tricky integrals. However, these tools may not always provide the most efficient or accurate solution, and it is important to have a basic understanding of the underlying mathematical concepts to interpret the results.

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

The best way to improve your skills in solving tricky integrals is to practice regularly and familiarize yourself with various techniques and strategies. It can also be helpful to study and understand the underlying mathematical concepts, as well as seek guidance from experienced mathematicians or instructors.

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