Kkutie7
  • Kkutie7
\[\int \frac{1}{\sqrt{y^{2}+8y+15}}dy\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Kkutie7
  • Kkutie7
Kainui
  • Kainui
There are two ideas I have, you can either factor it which seems obvious, or complete the square which is what ends up being useful here.
Kkutie7
  • Kkutie7
=/ i hate completing the square.. I think I've mentally block it out haha can't even remember how to do it

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Kkutie7
  • Kkutie7
isn't it something like \[y^{2}+8y+15=0\rightarrow y^{2}+8y+()=15\]
Kainui
  • Kainui
Hahaha fair enough, I think everyone feels that way about it to be honest. I think it's easier if you sorta think 'backwards' and start from here. \[(y+a)^2 =y^2+2ay+a^2\]
Kkutie7
  • Kkutie7
\[y^{2}+8y+16=15+16\rightarrow (y+4)^{2}=31\]
Kkutie7
  • Kkutie7
ok that makes sense.. from what i did what do i do with the 31?
Kainui
  • Kainui
Almost, I think there's gotta be some kinda mistake, at the end of the day what you get has to be equal to the original thing, \(y^2+8y+15\)
Kainui
  • Kainui
I think you can figure out your mistake if I show you the answer: \[(y+4)^2-1=( y^2+8y+16)-1\]
Kkutie7
  • Kkutie7
right, i get it your way I think i was trying to solve for y or something... anyways on to the int
Kainui
  • Kainui
Yeah all good, I think the integral is now of a form on your chart, so shouldn't be too crazy.
Kkutie7
  • Kkutie7
\[\int \frac{1}{\sqrt{(y+4)^{2}-1}}dy\rightarrow ln|y+4+\sqrt{(y+4)^{2}-1}|+C\]
Kainui
  • Kainui
Yeah that's the stuff good job.
Kkutie7
  • Kkutie7
thank you

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