A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Integrate (1+x^2)/(1+x^4)dx
anonymous
 4 years ago
Integrate (1+x^2)/(1+x^4)dx

This Question is Closed

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

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

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

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

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

blockcolder
 4 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.

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

anonymous
 4 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
 4 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
 4 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?

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

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

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x \frac{1}x\right)+2} \]This should do it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x \frac{1}x\right)^2+2}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Very nice Ishaan94; trig sub would work as well (: But that is easier.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.