Improper Integral with Tricky Denominator: Solving (1+x)^-1/2

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Homework Help Overview

The problem involves evaluating the improper integral of the function \(\int \frac{1}{(1+x)\sqrt{x}} dx\), which presents challenges due to its complex denominator.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods for approaching the integral, including substitution and the potential use of partial fractions. Some express uncertainty about the effectiveness of integration by parts.

Discussion Status

There is an ongoing exploration of substitution methods, with participants sharing their attempts and seeking verification of their approaches. Some guidance has been offered regarding possible substitutions, but no consensus has been reached on a definitive method.

Contextual Notes

Participants note the difficulty of the integral and the limitations of certain techniques, such as partial fractions, which may not be applicable in this context.

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Homework Statement



evaluate

[tex]\int[/tex] [tex]\frac{1}{(1+x)\sqrt{x}}[/tex] dx

Homework Equations



N/A

The Attempt at a Solution



how to do this, i can't use partial fraction, and integration by part makes it harder i guess, maybe using substitution, but how T_T
helpp
 
Last edited:
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Hi, do you have the answer?
 
no, why?
 
I tried to solve it through substitution, but I'm not sure if it's correct and would like to have it verified.
 
can you tell me what substituion you are using please?
 
When you have an integral like this always try a few substitutions instead of just staring at it. Obvious substitutions would be u=1+x and u=sqrt(x). I will let you decide which one is the useful one.
 
I tried this:

[tex]u = \sqrt{x}[/tex]

[tex]u^2 = x[/tex]

Can you take over from here?
 
thanks, i got the idea. thank you very much
 

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