Evaluate the Integral

[IamBatman]

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.


$\int^1_0\sqrt{1+e^{-x}}/e^x$.




2. The attempt at a solution

Editing

Next stage I'm sort of confused because I've never encountered two variables with "u".

 

[SteamKing]

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.

 

[IamBatman]

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.

 

[freshman2013]

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?

 

[IamBatman]

I figured it out

IT HAS BEEN SOLVED :)!

 

[BruceW]

I am Batman.