Analytical solution of an integral

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SUMMARY

The discussion centers on the analytical solution of a specific integral presented by Ashkan, which is not solvable using the arctangent function as suggested by HallsofIvy. The integral in question is defined as \(\int_0^\infty \frac{dw}{(w_n^2- w^2)^2+ 4w_n^2w^2z^2}\). Participants express concerns about sharing files due to security risks associated with Microsoft Word, emphasizing the importance of directly typing mathematical expressions for clarity and accessibility.

PREREQUISITES
  • Understanding of integral calculus, specifically improper integrals.
  • Familiarity with mathematical notation and expressions.
  • Knowledge of the arctangent function and its properties.
  • Basic skills in using mathematical software or tools for solving integrals.
NEXT STEPS
  • Research methods for solving improper integrals, particularly those involving complex variables.
  • Explore the use of LaTeX for typesetting mathematical expressions clearly.
  • Learn about the properties and applications of the arctangent function in calculus.
  • Investigate alternative software tools for mathematical computations, such as Wolfram Alpha or MATLAB.
USEFUL FOR

Mathematicians, students studying calculus, and anyone interested in advanced integral solutions will benefit from this discussion.

Ashkan
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Can anyone help me about analytical solution of this Integral?

the integral is written in the word file attached here.


Many Thanks in advance,
Ashkan
 

Attachments

Physics news on Phys.org
1. Microsoft Word is notorious for harboring viruses. Many people will not even open a "Word" file.

2. Since Microsoft is no longer allowed to bundle "Word" with "Windows", many people do not have "Word".

3. If this problem is not important enough for you to key in
[tex]\int_0^\infty \frac{dw}{(w_n^2- w^2)^2+ 4w_n^2w^2z^2}[/tex]
yourself, should other people take the trouble to do it for you?

The integral of
[tex]\int\frac{dx}{x^2+ a^2}[/tex]
is arctan(x/a)+ C.
 
Dear HallsofIvy,

Thanks for your advice and the solution you gave, but I think if you take another look into the integral, you would obveiously notice that the integral is much different of what you have given in the solution and will not result in an "arctan" solution, otherwise, be sure that I would not bother myself and the others to post it here!

Regards,
Ashkan
 

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