1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrals using long division

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data
    ∫(2x+1)/(x²+2x+1)(x²+x+1)


    2. Relevant equations
    none


    3. The attempt at a solution
    I've foiled this out to look like:

    ∫(2x+1)/(x^4+3x³+4x²+3x+1)

    I'm trying long division here but it's getting really ugly really fast. Should I foil this out in the first place or should I use a different approach?
     
  2. jcsd
  3. Feb 25, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I would try a different approach.

    Look at the denominator and see if it can be factored rather than multiplied together.
     
  4. Feb 25, 2013 #3

    eumyang

    User Avatar
    Homework Helper

    Why would you try long division? You are dividing something "smaller" into something "bigger". It is as if you are suggesting that to evaluate [itex]\frac{7}{584}[/itex] you divide 584 by 7.

    Have you considered using partial fractions to split the integral into two?
     
  5. Feb 25, 2013 #4
    Definitely do partial fractions. The only time you do long division is when the degree on top is bigger than the bottom.
     
  6. Feb 25, 2013 #5

    Mark44

    Staff: Mentor

    Or when the degrees are equal.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integrals using long division
  1. Long division (Replies: 12)

Loading...