Find the Indefinite Integral Using Substitution: e^2x and (1+e^2x)^3

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Homework Help Overview

The discussion revolves around finding the indefinite integral of the expression involving \( e^{2x} \) and \( (1+e^{2x})^3 \) using substitution techniques.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin the problem and seeks suggestions for substitution. Some participants suggest different substitution strategies, including \( u = e^{2x} \) and \( u = (1 + e^{2x}) \). There is a mention of varying levels of understanding regarding these approaches.

Discussion Status

Participants are exploring different substitution methods, with some guidance being offered. There is no explicit consensus on the best approach, but multiple strategies are being discussed.

Contextual Notes

The original poster indicates a recent introduction to the topic, which may affect their comfort level with the suggested methods.

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Homework Statement


Find the indefinite integral using substitution:
[tex]\int[/tex]e^2x(1+e^2x)^3 dx

Homework Equations





The Attempt at a Solution


I'm not sure how to start. What do I substitute? Any suggestions to get me started will be greatly appreciated.
 
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put u=e^2x====>du=2e^2xdx
 
Better to put u=(1+e^(2x)).
 
Dick said:
Better to put u=(1+e^(2x)).

Yes, thanks dick. Thats what I ended up doing. I had just learned this stuff today, so I think msa's approach may have been a bit over my head.
 

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