What's wrong with this solution of tan^3x?

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the solution to an integral involving tan^3(x). Participants are examining the correctness of a proposed solution and exploring the integration process, including the handling of constants of integration.

Discussion Character

  • Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about their solution, indicating that it seems incorrect but does not specify why.
  • Another participant defends the original answer, suggesting it may indeed be correct.
  • A third participant states that the expected answer is 1/2(tan(x))^2 - ln(sec(x)), implying a specific result they believe should be achieved.
  • One participant discusses the relationship between tan^2(x) and sec^2(x), noting that the constant of integration can absorb certain terms.
  • A later reply acknowledges the oddity of two different expressions yielding the same result upon integration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the original solution, with multiple competing views expressed regarding the validity of the answers and the integration process.

Contextual Notes

There are unresolved assumptions regarding the integration steps and the treatment of constants, which may affect the conclusions drawn by participants.

p3t3r1
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I don't see what I am doing wrong in this. The answer I got is obviously not right. Appreciate any help. Thanks!
 

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Why is the answer you got obviously not right? I would say it is right.
 
Cause the answer is suppose to be 1/2(tanx)^2 -ln(secx)
 
so tanx^2 = secx^2 -1, and the -1 gets absorbed into the constant of integration.
 
Oh, yeah that would make sense. Is quite odd how two different things are exactly the same when you integrate them. Thanks.
 

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