How Do You Solve the Integral of e^x * sqrt(1+e^x) dx?

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Homework Help Overview

The discussion revolves around solving the integral of e^x multiplied by the square root of (1 + e^x) with respect to x. Participants are exploring substitution methods to simplify the integral.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • One participant attempts substitution with u = sqrt(1 + e^x) but expresses uncertainty about the next steps. Another suggests using u = 1 + e^x as a potentially simpler substitution. There is also a clarification regarding the expression of the integral in proper notation.

Discussion Status

The discussion includes various substitution attempts and clarifications on notation. While some guidance has been offered regarding substitutions, there is no explicit consensus on the best approach, and participants are still exploring their options.

Contextual Notes

Participants are working within the constraints of homework rules, which may limit the depth of assistance provided. There is also a note about proper formatting in mathematical expressions that may affect clarity.

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Homework Statement



Integral e[tex]^{}x[/tex][tex]\sqrt{}1+e^{}x[/tex] dx

Homework Equations


using the formula: integral e^x dx:e^x+C

The Attempt at a Solution


I tried basic substitution:
making u=sqrt 1+e^x, and when trying to find du I'm not sure on what to do next
 
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Just try u=(1+e^x). I think you'll find it goes more simply.
 
jimen113 said:

Homework Statement



Integral e[tex]^{}x[/tex][tex]\sqrt{}1+e^{}x[/tex] dx
Do you mean
[tex]\int e^x\sqrt{1+ e^x}dx[/tex]

If so just u= 1+ ex is sufficient.

(Put your "x" inside the "{ }" in tex!

Homework Equations


using the formula: integral e^x dx:e^x+C

The Attempt at a Solution


I tried basic substitution:
making u=sqrt 1+e^x, and when trying to find du I'm not sure on what to do next[/QUOTE]
 
thanks!
 
Solved:
2/3 sqrt(1+e^x)^3
 

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