How to integrate sinx/(1+sinx)

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Homework Help Overview

The discussion revolves around the integration of the function sin(x)/(1+sin(x)). Participants express their struggles with the problem and explore various algebraic manipulations to simplify the expression.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants suggest multiplying the numerator and denominator by different expressions, such as sin(x) and the Pythagorean conjugate, to facilitate integration. There is uncertainty about the effectiveness of these approaches and where they might lead.

Discussion Status

Some participants have shared hints and suggestions for manipulation, while others express confusion about the next steps after applying these hints. There is no clear consensus on the best approach, but the discussion remains active with attempts to clarify the reasoning behind the suggested methods.

Contextual Notes

Participants note their lack of equations and express varying levels of understanding regarding the integration process, indicating a need for further exploration of the problem's setup.

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Homework Statement


As stated in the title.


Homework Equations


No equations


The Attempt at a Solution


Honestly, I'm stuck. I have no idea where to go. My only thought is to multiply the top and bottom by sinx but where would that get me?
 
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I agree you should multiply the denominator and numerator by some quantity. As a hint, it might be useful to consider that [itex]1-\sin^2x=\cos^2 x[/itex].
 
16180339887 said:
I agree you should multiply the denominator and numerator by some quantity. As a hint, it might be useful to consider that [itex]1-\sin^2x=\cos^2 x[/itex].

Yes, I did that, and am confused where to go from there.
 
Multiple the top and bottom by sin2x
 
Solved it. Multiplied the top and bottom by the Pythagorean Conjugate.
 

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