Solve V-Sub Homework: Get Help Now

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Homework Help Overview

The discussion revolves around evaluating the integral \(\int \frac{x}{x + \sqrt{x + 2}} \) using a substitution method, specifically a v-substitution, along with polynomial long division. Participants are attempting to identify mistakes in their calculations and clarify their approaches.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss their attempts at using v-substitution and polynomial long division. Questions arise regarding the specific substitution used and the accuracy of the polynomial division performed. There is also a focus on identifying errors in the final expressions derived from these methods.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the substitution details and the polynomial division process. Some guidance has been offered regarding potential errors in the calculations, but no consensus on the correct approach has been reached yet.

Contextual Notes

There is mention of critical details being omitted, which may hinder the ability to provide effective assistance. Participants express the need for more information about the substitution used in the integral evaluation.

Ayesh
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Homework Statement




\int \frac {x}{x+ \sqrt {x+2}}



The Attempt at a Solution



I used the v-sub.

I also did a long division.

It gave me \int 2v-2- \frac {v}{v-1} + \frac {2}{v-1}

My final answer 2x+2-2 \sqrt {x+2} -ln \sqrt {x+2} -1 +2ln \sqrt {x+2} -1 +c

The final answer should be x-2 \sqrt {x+2} - 2/3ln \sqrt {x+2} -1 + \frac 8/3ln \sqrt {x+2} + 2 +c

Where is my mistake?
 
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Ayesh said:

Homework Statement




\int \frac {x}{x+ \sqrt {x+2}}



The Attempt at a Solution



I used the v-sub.

I also did a long division.

It gave me \int 2v-2- \frac {v}{v-1} + \frac {2}{v-1}

My final answer 2x+2-2 \sqrt {x+2} -ln \sqrt {x+2} -1 +2ln \sqrt {x+2} -1 +c

The final answer should be x-2 \sqrt {x+2} - 2/3ln \sqrt {x+2} -1 + \frac 8/3ln \sqrt {x+2} + 2 +c

Where is my mistake?
Kind of hard to say when you leave out critical details, like what substitution you actually used.
 


I attached a file with what I have done, since I am very bad with latex code.
 

Attachments

  • v-sub.JPG
    v-sub.JPG
    12.5 KB · Views: 403


You still didn't tell us what the substitution was that you used. If you want help, you need to provide the necessary information.
 


Looks like your polynomial division is wrong. The remainder should be over v^2+v-2, and there appears to be a sign error as well. The quotient looks okay, though.
 

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