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Integration problem

  1. Nov 1, 2009 #1
    [tex]\int\frac{x}{x^4+x^2+1}[/tex]dx

    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.
     
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