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anonymous
 5 years ago
Integral of 1/(x^4+1). I think it is solved with partial fractions.
anonymous
 5 years ago
Integral of 1/(x^4+1). I think it is solved with partial fractions.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't think you can factor the denominator so we can't use partial fraction. Trig Substitution might work

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x= tan(theta) dx= sec^2(theta) dtheta

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is this a complex variables class or real?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It is real. I got to this point: \[\int\limits\frac{\sec^{2}(\theta)}{(\tan^{4}(\theta)+1)}\; d\theta\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yikes. i found the answer using maple and it is long and ugly. if you have to s how the steps try here http://answers.yahoo.com/question/index?qid=20080721154424AAYOrmH

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0someone is clearly out to get you with this problem. makes my head spin

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you for the link, it's in a take home part of a final in calculus 2 :(. I found it more simply in the end of this page: http://kr.cs.ait.ac.th/~radok/math/mat6/calc4.htm It says that even Leibnitz found this a troublesome problem :). They use partial fractions as such: \[x^4+1=(x^2+1)^22x^2=(x^2+1+\sqrt{2}x)(x^2+1\sqrt{2}x)\] Can you explain how to get the third step?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i think. \[(x^2+1)^22x^2\] is the difference of two squares \[a^2b^2=(a+b)(ab)\] in this case \[a=x^2+1, b=\sqrt{2}x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats should do it yes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What about the 2 in 2x^2?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(\sqrt{2}x)^2=2x^2\] that is why \[b=\sqrt{2}x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Clever, that is why is \sqrt{2}
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