1. Limited time only! Sign up for a free 30min personal 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!

Integrating a Fraction using the product rule

  1. Mar 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the integral of
    gif.gif
    This was the question. There is a way to do it by long division but I am confused with Long division. Instead I tried to do by the method below but I failed.....

    2. Relevant equations
    None


    3. The attempt at a solution
    I thought maybe I could reduce the denominator to the power of -1 and then Integrate by Parts.
    Like this gif.gif
    Is this correct? If no then what could I do to this integral. I would be very thankful if someone would post an answer...
     
  2. jcsd
  3. Mar 25, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Your attempt is valid, but you have created a more complex integral to solve. While there might be a way to solve this integral by dividing out to find the quotient, that too looks like it would create a messy integral to solve.
     
  4. Mar 25, 2013 #3
    Break it down into [tex]∫{\frac{x^3}{16xtanx+sinx}}dx+∫{\frac{56x^2sin^6x}{16xtanx+sinx}}dx[/tex]
    Then try long division. If you can't do long division with polynomials, I would reccomend reading up on it. It creeps up quite a bit, and you're much better off knowing how to do it.

    This is still going to be a nasty nasty integral, unless I'm missing something. I've not attempted it yet, but it seems like it might be easier that trying to to Integration by parts 20 times. Also With long division it may help to write ##{\tan{x}}## as ##{\frac{\sin{x}}{\cos{x}}}## and write the denominator as a fraction then simplify.
     
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: Integrating a Fraction using the product rule
  1. Using the product rule (Replies: 3)

Loading...