Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Omniscience

Integrate (1+x^2)/(1+x^4)dx

  • one year ago
  • one year ago

  • This Question is Closed
  1. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\large \int\limits\frac{1+x^{2}}{1+x^{4}} dx\]

    • one year ago
  2. lgbasallote
    Best Response
    You've already chosen the best response.
    Medals 0

    ugh why couldnt it be 1 - x^4 :p lol

    • one year ago
  3. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    If it was it would have defeated the purpose of this integral. (:

    • one year ago
  4. lgbasallote
    Best Response
    You've already chosen the best response.
    Medals 0

    exactly why im complaining :p

    • one year ago
  5. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    No need to complain. Just think of an intuitive method. :)

    • one year ago
  6. blockcolder
    Best Response
    You've already chosen the best response.
    Medals 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
  7. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    Not that easy.

    • one year ago
  8. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    There are two methods.

    • one year ago
  9. goxenul
    Best Response
    You've already chosen the best response.
    Medals 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
  10. lgbasallote
    Best Response
    You've already chosen the best response.
    Medals 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
  11. blockcolder
    Best Response
    You've already chosen the best response.
    Medals 0

    Separation, perhaps? \[\frac{1}{1+x^4}+\frac{x^2}{1+x^4}\] Might this work?

    • one year ago
  12. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    Not really. Wolfram Alpha method is tedious.

    • one year ago
  13. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    You can try if it works; but I dont think so.

    • one year ago
  14. lgbasallote
    Best Response
    You've already chosen the best response.
    Medals 0

    the first term would be integrable i think

    • one year ago
  15. Ishaan94
    Best Response
    You've already chosen the best response.
    Medals 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
  16. blockcolder
    Best Response
    You've already chosen the best response.
    Medals 0

    Wow. O_O

    • one year ago
  17. Ishaan94
    Best Response
    You've already chosen the best response.
    Medals 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
  18. Omniscience
    Best Response
    You've already chosen the best response.
    Medals 0

    Very nice Ishaan94; trig sub would work as well (: But that is easier.

    • one year ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.