Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

NotSObright

  • 3 years ago

integral((x^3+x+1)/(x^4+x^2+1))

  • This Question is Closed
  1. DHASHNI
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=integral%28%28x^3%2Bx%2B1%29%2F%28x^4%2Bx^2%2B1%29%29

  2. NotSObright
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I am concerned with what substitution has to be carried out and not the answer

  3. rivermaker
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you have the form P(x)/Q(x) where P and Q are polynomials. Further the degree of the numerator, namely 3, is one less than the denominator. In such situations, find \[dQ/dx \] and express P in terms of that. \[\int\limits{dy/y} = \log y\] the remaining terms are hopefully simpler. If you need more help ask

  4. rivermaker
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[d/dx ({{x^4+x^2+1}}) = 4x^3 + 2x \] so \[P(x) = {1/4}({dQ/dx}) + (1/2)x + 1 \] So the original problem reduces to integrating \[dQ/Q + (1/2)\int\limits x dx/Q + \int\limits dx/Q \]

  5. rivermaker
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry the last equation should read: \[(1/4)\int\limits dQ/Q + (1/2)\int\limits\limits x dx/Q + \int\limits\limits dx/Q\]

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.