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!

Is there a better way to integrate this

  1. Jan 26, 2009 #1
    what is the best way to integrate this functio, i integrated in parts


    i split the top of the fraction and then integrated the x2 half using integration in parts, but its just long and lots of place to make mistakes.
  2. jcsd
  3. Jan 26, 2009 #2
    I would try to rid of the top bit. Here is a hint [tex] x^2=\frac{1}{4}((2x-3)(2x+3) + 9) [/tex].

    Good luck
  4. Jan 26, 2009 #3


    User Avatar
    Science Advisor
    Gold Member

    I assume you mean:

    Note the degree of the numerator is higher than that of the denominator. (Improper rational function like an improper fraction.)
    You should first carryout long division of the polynomials (and check by re-multiplying).
    You will then get a polynomial plus a proper fraction. Since the denom. has degree 1 the numerator (remainder) will be constant and you can integrate via simple variable substitution.

    Carry out the long division:
    [tex] 2x+3)\overline{x^2 + 0x + 0}[/tex]

    You should get:
    [tex] P(x)+ \frac{C}{2x+3}[/tex]
    where P is a polynomial

    You can easily integrate:
    [tex] \int P(x)dx + C/2 \int \frac{du}{u};\quad u = 2x+3[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Is there a better way to integrate this