Answer check, Hyperbolic trig identity (proof)

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Homework Help Overview

The discussion revolves around evaluating the integral of Sech³x Tanhx dx, focusing on hyperbolic trigonometric identities and integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify the integral using substitution and expresses uncertainty about the completeness of their solution.

Discussion Status

Participants have acknowledged the original poster's work and noted the importance of including a constant of integration. There is also a suggestion to consider rewriting the expression in terms of sinh and cosh for simplicity.

Contextual Notes

There is an implicit assumption regarding the familiarity with hyperbolic functions and integration techniques. The discussion reflects on the potential complexity of the integral and the need for thoroughness in the solution.

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Homework Statement


Evaluate the integral:
(int sign) Sech³xTanhx dx

Homework Equations


Derivative of Sechx = -(SechxTanhx)

The Attempt at a Solution



Rewrite as:
Sech²xSechxTanhx

U=sechx
Du = -(SechxTanhx)dx
-Du = SechxTanhx dx
replace into integral

-(integral sign) U²du

Evaluate:
-U³ / 3

answer = -Sech³x / 3

? It just seems like there should be more to it. What do you guys think?
 
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Indeed there is more to it - a constant of integration. :wink:
 
grr :mad:

Thanks :redface:
 
it would have been much simpler if you had written everything in terms of sinh and cosh.

My 2ç
 

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