Integration [ 1/(c+cos(x)) ] by dx

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    Dx Integration
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Discussion Overview

The discussion revolves around the integration of the functions cos(x)/(c+cos(x)) and 1/(c+cos(x)) with respect to x, where c is a constant. Participants explore methods for solving these integrals, particularly focusing on substitution techniques.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests assistance in solving the integrals of cos(x)/(c+cos(x)) and 1/(c+cos(x)).
  • Another participant suggests using the substitution u = tan(x/2) to facilitate the integration process, providing the corresponding transformations for dx, sin(x), and cos(x).
  • A participant expresses curiosity about the rationale behind the choice of the substitution method, indicating a desire for deeper understanding.
  • Another participant notes that the substitution u = tan(x/2) is a common technique and references an external source for further information.
  • A participant reiterates their curiosity about the substitution method, emphasizing the non-linear nature of finding primitives and the trial-and-error aspect of integration.

Areas of Agreement / Disagreement

Participants generally agree on the validity of the substitution method proposed, but there is no consensus on the best approach to solving the integrals or the reasoning behind choosing specific substitution techniques.

Contextual Notes

The discussion does not resolve the integration problems presented, and the effectiveness of the substitution method remains unverified within the thread.

desmal
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Hi all

Can you solve the following integration: -

Integration [ cos(x)/(c+cos(x)) ] by dx
where c is a constant

or that one: -

Integration [ 1/(c+cos(x)) ] by dx

if one is solved I will be able to make the other
 
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Greetings:

If you let u = tan(x/2), then dx = 2*du /(u^2+1), sin(x) = 2u/(u^2+1), cos(x) = (1-u^2)/(1+u^2). If you substitute these values appropriately, each integral should return an inverse trig function.

Regards,

Rich B.
 


Wow really really amazing

Unfortunately, there is something puzzling me which is:-
How did you get the idea of substituting u=tan(x/2)
 


nikkor180 said:
Wow really really amazing

Unfortunately, there is something puzzling me which is:-
How did you get the idea of substituting u=tan(x/2)

There is no clear cut method to finding primitives. It's much like puzzling, try something out and remember what works.
 

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