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Omniscience
 2 years ago
Integrate (1+x^2)/(1+x^4)dx
Omniscience
 2 years ago
Integrate (1+x^2)/(1+x^4)dx

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Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \int\limits\frac{1+x^{2}}{1+x^{4}} dx\]

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0ugh why couldnt it be 1  x^4 :p lol

Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0If it was it would have defeated the purpose of this integral. (:

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0exactly why im complaining :p

Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0No need to complain. Just think of an intuitive method. :)

blockcolder
 2 years ago
Best ResponseYou've already chosen the best response.0Completing the square of the denominator then a substitution is what I have in mind, but I'm not completely sure.

Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0There are two methods.

goxenul
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=integrate+%5Cfrac%7B1%2Bx%5E%7B2%7D%7D%7B1%2Bx%5E%7B4%7D%7D+dx (look at "Show steps") Well, this looks... difficult. I wonder if there's an easier way to do this, than splitting it into two integrals.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0okay...hmm \[u = \frac{1}{1+x^4} \rightarrow du = \frac{4x^3}{(1+x^4)^2}\] \[dv = 1+ x^2 \rightarrow v = \tan^{!} x\] LOL really isn't easy :P

blockcolder
 2 years ago
Best ResponseYou've already chosen the best response.0Separation, perhaps? \[\frac{1}{1+x^4}+\frac{x^2}{1+x^4}\] Might this work?

Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0Not really. Wolfram Alpha method is tedious.

Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0You can try if it works; but I dont think so.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0the first term would be integrable i think

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.5\[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x \frac{1}x\right)+2} \]This should do it.

Ishaan94
 2 years ago
Best ResponseYou've already chosen the best response.5\[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x \frac{1}x\right)^2+2}\]

Omniscience
 2 years ago
Best ResponseYou've already chosen the best response.0Very nice Ishaan94; trig sub would work as well (: But that is easier.
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