What is the Integral of 1 / 1 + sqrt [x] Using the Chain Rule and Substitution?

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Homework Help Overview

The discussion revolves around finding the integral of the function 1 / (1 + sqrt[x]), focusing on the application of the chain rule and substitution techniques in calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use the substitution x = u^2 and applies the chain rule. Other participants suggest considering additional substitutions and question the applicability of integration by parts.

Discussion Status

Participants are exploring various substitution methods and discussing the potential for multiple substitutions. There is no explicit consensus on a single approach, but several lines of reasoning are being examined.

Contextual Notes

Some participants mention the need for clarity on the integration techniques being discussed, and there is an acknowledgment of the original poster's novice status in the subject matter.

Charas
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Hi, I am a newbie here and would like to ask you stg. integral of 1 / 1 + sqrt [x]

I used chain rule and used x = u^2 is that true?

Thanx for any replies
 
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Do the substitutions that neutrino and morphism suggested.
 


Can't you use integration by parts?
 


I'm doing this in my head and not fully awake, so I could be wrong.
we have 1/(1+sqrt(x)) You can use the substitution that you've shown.
u^2=x
2udu=dx
So we end up with 2u/1+u
remember you can substitute more than once...
 

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