Integrating e^x/(e^{2x} + 1): Long Division?

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Homework Help Overview

The discussion revolves around the integral of the function e^x/(e^{2x} + 1), with participants exploring methods to rewrite it in a form suitable for applying the arctan formula.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster considers using long division to simplify the integral. Another participant suggests a substitution method involving u = e^x, while others discuss the merits of u-substitution.

Discussion Status

Participants are actively engaging with different methods to approach the integral. There is a mix of opinions on the usefulness of u-substitution, with some expressing a preference for it while others question its necessity.

Contextual Notes

There is an indication that the original poster feels challenged by the presence of e^x in the numerator, which may affect their approach to the problem.

RadiationX
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i'm having trouble rewriting this integral:[tex]\int\frac{e^x}{e^{2x} + 1}[/tex] so that it will be in the arctan formula: should i use long divison here? if it were not for the [tex]e^x[/tex] in the numerator i'd be fine.
 
Last edited:
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[tex]u = e^{x}, du = e^{x}dx[/tex]

[tex]e^{2x} = (e^{x})^2[/tex]
 
you never get away from u -substitutions do ! thanks
 
Why would you watn to get away from them? They save your ass a lot :)
Learn to love em.
 
yeah your right
 

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