Answers of the following integrals

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In summary, solving integrals is an important tool in science for finding the area under a curve or the total amount of a quantity over a given interval. There are various methods for solving integrals, such as substitution, integration by parts, trigonometric substitution, and partial fractions. The choice of method depends on the form of the integrand. Not all integrals can be solved analytically, and in such cases, numerical methods can be used. Integrals also have applications in data analysis, such as finding the average or total value of a quantity and in statistical analysis.
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you have any intuition about the answers of
the following integrals,
\int_{0}^{1}\int_{0}^{1}u*PolyLog[u*v]*Log[v]/(1-u*vdudv.
and
\int_{0}^{1}\int_{0}^{1}u*PolyLog[u*v]*Log[1-v]/(1-u*v)dudv.
and
\int_{0}^{1}PolyLog[4,u/(u-1)]du.
thank you in advance
wissam
 
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  • #2
your latex isn't working right, you need to repost so we can read your intergal
 
  • #3


hi. Why don't you just open the polylogarithm functions in a sum, integrate termwise and than examine whether the resultant serie members lead to a converging serie or not?
 

1. What is the purpose of solving integrals in science?

Solving integrals is an important mathematical tool in science that allows us to find the area under a curve or the total amount of a quantity over a given interval. This is useful in various scientific fields such as physics, chemistry, and engineering to analyze and understand real-world phenomena.

2. What are the different methods for solving integrals?

There are several methods for solving integrals, including substitution, integration by parts, trigonometric substitution, and partial fractions. The method used depends on the complexity of the integral and the functions involved.

3. How do you know which method to use when solving an integral?

The choice of method for solving an integral depends on the form of the integrand. It is important to identify the type of integral (e.g. trigonometric, exponential, polynomial) and then use the appropriate method to simplify the integral and find the solution.

4. Is it possible to solve all integrals?

No, not all integrals can be solved analytically. Some integrals may have complex or undefined solutions, while others may require advanced mathematical techniques that may not be feasible to use in certain situations. In such cases, numerical methods can be used to approximate the solution.

5. How can solving integrals help with data analysis in science?

Integrals can be used in data analysis to find the average or total value of a quantity over a given interval. This can provide valuable insights and understanding of patterns and trends in the data. Integrals are also used in statistical analysis, such as calculating probabilities and finding the area under a probability distribution curve.

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