Find the integral of ∫1/(1+tanx)dx

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Homework Help Overview

The discussion revolves around finding the integral of ∫1/(1+tanx)dx, a problem situated within the context of calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods for solving the integral, including substitution and half-angle identities. Some express uncertainty about the completeness of their approaches and seek additional methods.

Discussion Status

The conversation is ongoing, with participants sharing their attempts and questioning the completeness of their solutions. Suggestions for alternative methods are being explored, indicating a productive exchange of ideas.

Contextual Notes

One participant mentions a requirement to solve the integral in all possible ways, suggesting constraints imposed by homework guidelines. There is also a reference to standard integrals and concepts covered in AP calculus.

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Homework Statement
my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout
Relevant Equations
All standard integrals and concepts covered in AP calculus
I have done one by assuming tanx as u in substitution
 
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Rhdjfgjgj said:
Homework Statement: my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout
Relevant Equations: All standard integrals and concepts covered in AP calculus

I have done one by assuming tanx as u in substitution
Please show us. Thanks.
 
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What is all possible ways? I can think of only substitution, but not the one you attempted. I think a half-angle should be better.
 
Also consider \tan(x - a) = \frac{\tan x - \tan a}{1 + \tan x \tan a}<br /> = \frac{1}{\tan a} - \left(\frac{1}{\tan a} + \tan a\right) \frac{1}{1 + \tan x \tan a}<br /> for suitable a.
 

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