1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Integration problem

  1. Nov 1, 2009 #1

    Okay the question ask to integrate the above expression so the first thing i did was to equate u=x2 so u'=2x and got this [tex]\frac{1}{2}[/tex][tex]\int\frac{1}{u^2+u+1}[/tex]du. I then proceed to use integration by parts which i find that this method is too long and messy so i was wondering is there a better to do this :smile:
  2. jcsd
  3. Nov 1, 2009 #2
    Perfectly well done. But now, convert the ^2 + u + 1 into a friendlier term -->

    (u + 0.5)^2 + 0.75

    Now, integrate this, it's a direct formula based problem --> will go into tan inverse.
  4. Nov 1, 2009 #3
    Damn why didn't i thought of that haha i get it now thanks mate~
  5. Nov 1, 2009 #4
    If you are solving integrals for the first time, it's really okay.

    Try solving the problem with x2 in the numerator instead of x. This one is not a simple one, and has a whole lot of pages in the miscellaneous section devoted to it.
  6. Nov 1, 2009 #5
    I just notice something, if we are using the anti derivative, shouldn't the denominator be 1+x2? In this case its 0.75 so how do we do it?
  7. Nov 1, 2009 #6
    Bracket out the 0.75^2 from the denominator and take it outside the integral. Now you have something sqared plus 1 in the denominator. Now, sbstitte that something = v and integrate. Then resubstitute everything, back again.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Integration problem Date
Integration problem of a quotient Feb 20, 2018
Problem integral Nov 26, 2017
Integration by parts problem Jul 18, 2017
Integral Equation (or I think so) Calculus I problem Jun 18, 2017
Line integral problems in Apostol calculus May 27, 2017