How does my book get from this step to this step?

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Homework Help Overview

The discussion revolves around an integration problem involving the expression int of dx/ ( sqrt(x)*(x+1) ) and its transformation to 2arctan sqrt (x). Participants are exploring the reasoning behind this transition and questioning the application of arctan integration forms.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss substitution methods, specifically using u = sqrt(x) and x = u^2, to analyze the integrand. Questions arise regarding the applicability of the arctan integration form and the relationship between the original and transformed expressions.

Discussion Status

There is an active exploration of substitution techniques, with some participants suggesting different variable changes. The discussion reflects a collaborative effort to clarify the steps involved, although no consensus or resolution has been reached yet.

Contextual Notes

Participants are navigating the complexities of integration and the specific forms of functions involved, indicating a need for clarity on the assumptions related to the integrand's structure.

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[SOLVED] How does my book get from this step to this step?

My book went from int of dx/ ( sqrt(x)*(x+1) )

to

2arctan sqrt (x) -- WTH?

I thought the form for arctan was dx/a^2 + u^2 and I don't see that in the given integrand?

Can anyone help?
 
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Substitute [tex]u=\sqrt{x}[/tex], and see what you get.
 
If x=u2, then dx = 2 u du

sqrt (x) = u, and

x+1 = u2 + 1
 
astronuc, did you arrive at that by using the substitution arildno suggested?
 
Well, arildno said "u= [itex]\sqrt{x}[/itex]" and Astronuc said "x= u2". Look the same to me!
 
Ha, you rascal!
 

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