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V-sub homework help

  • Thread starter Ayesh
  • Start date
  • #1
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Homework Statement




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



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?
 

Answers and Replies

  • #2
vela
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Homework Statement




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



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?
Kind of hard to say when you leave out critical details, like what substitution you actually used.
 
  • #3
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I attached a file with what I have done, since I am very bad with latex code.
 

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  • #4
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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.
 
  • #5
vela
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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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