How to Solve the Integral: Evaluate ∫(1+e^-x)^1/2 / e^x from 0 to 1

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Homework Help Overview

The discussion revolves around evaluating the integral ∫(1+e^-x)^(1/2) / e^x from 0 to 1, which involves concepts from calculus, specifically integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various approaches including u-substitution and integration by parts. There is confusion regarding the use of multiple substitutions and whether further simplification is necessary.

Discussion Status

Some participants have suggested different methods for tackling the integral, including integration by parts and re-expressing the integrand. There is an indication that progress has been made, though the exact nature of the resolution is not detailed.

Contextual Notes

Participants are navigating the complexities of the integral, including the challenge of handling multiple variables in substitutions and the implications of rewriting components of the integrand.

IamBatman
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Homework Statement



Hi guys, so I've been having some trouble with this specific integral, and would like some help on how to solve it.[itex]\int^1_0\sqrt{1+e^{-x}}/e^x[/itex].

2. The attempt at a solution

Editing

Next stage I'm sort of confused because I've never encountered two variables with "u".
 
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With you u substitution, all you have done is replace 'x' with 'u'. You haven't done any essential simplification to the integrand.

I would suggest looking at integration by parts. If you can find candidates for u and v with parts, then further substitution might be warranted.
 
SteamKing said:
With you u substitution, all you have done is replace 'x' with 'u'. You haven't done any essential simplification to the integrand.

I would suggest looking at integration by parts. If you can find candidates for u and v with parts, then further substitution might be warranted.

Yeah I wasn't sure if I should substitute more lol or just go through with algebra. Thanks.
 
Actually usub does work. Re write e^x in the denominator as e^-x times the squareroot expression. u=e^-x+1. does it looks like du could be written in terms of e^-x?
 
I figured it out

IT HAS BEEN SOLVED :)!
 
I am Batman.
 

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