Solve V-Sub Homework: Get Help Now

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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
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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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