Int( X/(x+2)^(1/4)) substitutions

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Homework Help Overview

The problem involves evaluating the integral of the function X/(x+2)^(1/4) using U-Substitution. Participants are discussing their approaches to this integral within the context of calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts U-Substitution by letting u=x+2 and expresses x in terms of u. They then rewrite the integral but express uncertainty about the next steps. Some participants suggest splitting the expression to facilitate integration.

Discussion Status

There is ongoing exploration of the integral with participants providing suggestions on how to manipulate the expression. While some participants express confidence in their results, there is no explicit consensus on the correctness of the final expressions provided.

Contextual Notes

Participants are navigating the complexities of U-Substitution and integration techniques, with some expressing confusion about the process. The discussion reflects a learning environment where assumptions and methods are being questioned and clarified.

steve092
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Homework Statement


I'm having a problem with U-Substitution. I get the simple stuff and the trig substitutions, but this problem has been bugging me.
Int( X/(x+2)^(1/4))


Homework Equations





The Attempt at a Solution


I first tried u=x+2 and then du=dx. I then solved for x, where x= U-2.

That put me at Int( (u-2)/(u^(1/4)). And that's where I don't really know how to go on.
 
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You can split (u-2)/u1/4 as u/u1/4-2/u1/4.
 


So split it then integrate it from there?
 


Thanks for the help. I got:
(4/7)(x+2)^(7/4) - (8/3)(x+2)^(3/4) +C.
 


steve092 said:
Thanks for the help. I got:
(4/7)(x+2)^(7/4) - (8/3)(x+2)^(3/4) +C.

That should be correct.
 

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