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

lgbasalloteBest ResponseYou've already chosen the best response.0
ugh why couldnt it be 1  x^4 :p lol
 one year ago

OmniscienceBest ResponseYou've already chosen the best response.0
If it was it would have defeated the purpose of this integral. (:
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
exactly why im complaining :p
 one year ago

OmniscienceBest ResponseYou've already chosen the best response.0
No need to complain. Just think of an intuitive method. :)
 one year ago

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

OmniscienceBest ResponseYou've already chosen the best response.0
There are two methods.
 one year ago

goxenulBest ResponseYou've already chosen the best response.0
http://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.
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
okay...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
 one year ago

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

OmniscienceBest ResponseYou've already chosen the best response.0
Not really. Wolfram Alpha method is tedious.
 one year ago

OmniscienceBest ResponseYou've already chosen the best response.0
You can try if it works; but I dont think so.
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
the first term would be integrable i think
 one year ago

Ishaan94Best 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.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.5
\[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x \frac{1}x\right)^2+2}\]
 one year ago

OmniscienceBest ResponseYou've already chosen the best response.0
Very nice Ishaan94; trig sub would work as well (: But that is easier.
 one year ago
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