anonymous
  • anonymous
Evaluate the Intergal
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{}^{}\frac{ 2x^4-4x^3+13x^2-6x+10 }{ (x-2)(x^2-2x+5)^2 }dx\]
anonymous
  • anonymous
I solved it using a beastly amount of partial fractions after solving a system of 5 equations. Please tell me there is another easier way.
anonymous
  • anonymous
jus divide the numerator by x-2

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anonymous
  • anonymous
Why though? I have no reason to do long division.
anonymous
  • anonymous
it is jus to simplify the question
anonymous
  • anonymous
Hmm Okay... Let me see...
anonymous
  • anonymous
Yep. it simplifies, reducing your amount of work.
anonymous
  • anonymous
ok, maybe not. I really need a break. Making too many mistakes today. See you all later.
anonymous
  • anonymous
Erm... THat doesent help O_o . I get: \[2x^3+13x+20 +\frac{ 50 }{ 2x^3+13x+20 }\]
anonymous
  • anonymous
no it doesn't simplify but it has been cooked so that the partial fractions are nice integers
anonymous
  • anonymous
yeah ^ he's right
anonymous
  • anonymous
Ohh they are nice and all but even evaluating the damn partial fractions takes forever.
anonymous
  • anonymous
there are some snap methods for getting some of them i think eliasaab who i have not seen here for a while had a snappy way of doing it
anonymous
  • anonymous
So after the decomposition I get: \[\int\limits_{}^{}\frac{ 2 }{ x-2 }+\frac{ 4 }{ x^2-2x+5 }+\frac{ x }{ (x^2-2x+5)^2 }dx\]
anonymous
  • anonymous
The first term is fine. It's the other two that take forever to integrate.
anonymous
  • anonymous
all integration is a useless pain in the butt that is why they invented computers it is not math, it is wasted doodling
anonymous
  • anonymous
Wolfram made I think... 9 substitutions. I refuse to do that.
TuringTest
  • TuringTest
@satellite73 D: blasphemy, integration is an art form!
anonymous
  • anonymous
art who?
anonymous
  • anonymous
waste a bunch of time showing off, saying "oh look, can find a function whose derivative is this, and a function whose derivative is that" when the truth is that if you pick a function out of a hat the probability you can find a nice closed for for the anti derivative is zero!
anonymous
  • anonymous
I mean I got the correct answer. But isn't there an easier way to do this?
anonymous
  • anonymous
nope you can see that by how annoying your answer is
anonymous
  • anonymous
Damn it. Thanks anyways guys :)
TuringTest
  • TuringTest
haha, true that. PF is just plain annoying

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