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Homework Help: V-sub homework help

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data


    [tex]\int \frac {x}{x+ \sqrt {x+2}}[/tex]



    3. The attempt at a solution

    I used the v-sub.

    I also did a long division.

    It gave me [tex]\int 2v-2- \frac {v}{v-1} + \frac {2}{v-1}[/tex]

    My final answer [tex]2x+2-2 \sqrt {x+2} -ln \sqrt {x+2} -1 +2ln \sqrt {x+2} -1 +c[/tex]

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

    Where is my mistake?
     
  2. jcsd
  3. Mar 9, 2010 #2

    vela

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    Re: v-sub

    Kind of hard to say when you leave out critical details, like what substitution you actually used.
     
  4. Mar 9, 2010 #3
    Re: v-sub

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

    Attached Files:

  5. Mar 9, 2010 #4

    Mark44

    Staff: Mentor

    Re: v-sub

    You still didn't tell us what the substitution was that you used. If you want help, you need to provide the necessary information.
     
  6. Mar 9, 2010 #5

    vela

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    Re: v-sub

    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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