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

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

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

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

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

blockcolder Group TitleBest 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.
 2 years ago

Omniscience Group TitleBest ResponseYou've already chosen the best response.0
Not that easy.
 2 years ago

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

goxenul Group TitleBest 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.
 2 years ago

lgbasallote Group TitleBest 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
 2 years ago

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

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

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

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

Ishaan94 Group TitleBest 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.
 2 years ago

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
Wow. O_O
 2 years ago

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

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