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Weird Integral Problem

  • Thread starter Totalderiv
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  • #1
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Homework Statement



[tex] \int (x+8)/(x+4) [/tex]

Homework Equations



N/a

The Attempt at a Solution



I tried to split the problem which resulted in:

[tex] \int x/(x+4) + \int 8/(x+4) [/tex]

But now I'm stuck,and this is a bonus question on my AP Calculus homework.
 

Answers and Replies

  • #2
gb7nash
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[tex] \int (x+8)/(x+4) [/tex]
Do polynomial division and it becomes much simpler.
 
  • #3
Char. Limit
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It might help to factor it like this:

[tex]\frac{x+8}{x+4} = \frac{(x+4)+4}{x+4}[/tex]

Then use the same trick you did.
 
  • #4
gb7nash
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It might help to factor it like this:

[tex]\frac{x+8}{x+4} = \frac{(x+4)+4}{x+4}[/tex]

Then use the same trick you did.
That's pretty slick.
 
  • #5
Char. Limit
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That's pretty slick.
Thanks, it's my own little algebraic trick.
 
  • #6
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Thanks for the help!
 
  • #7
HallsofIvy
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Thanks, it's my own little algebraic trick.
It is, of course, the same as the "polynomial division" that gb7nash suggested.
 
  • #8
Char. Limit
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It is, of course, the same as the "polynomial division" that gb7nash suggested.
Srsly? The way I learned polynomial division is much, much harder.
 
  • #9
Dick
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I think "much much harder" is a srs exaggeration.
 
  • #10
Char. Limit
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I think "much much harder" is a srs exaggeration.
Well I mean, I learned it the way long division is taught, and I never liked long division. I prefer my method, whether it's called polynomial division or not.
 
  • #11
Dick
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It is a way of doing polynomial long division. It works neat for linear/linear. But in that case polynomial long division isn't that hard either. Try it for (x^2+9)/(x+4). Sure, you can do it. At least polynomial long division is has a method instead of relying on a trick that you have to reinvent as the cases change.
 
Last edited:

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