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Simple Integration using U Substitution

  1. Jan 28, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the indefinite integral.
    The antiderivative or the integral of (x^2-1)/(x^2-1)^(1/2)dx



    2. Relevant equations



    3. The attempt at a solution

    Tried using (x^2-1)^(1/2) as u and udu for dx and I solved for x but I am still left with a 1 on top not sure how to deal with it.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 28, 2008 #2
    [tex]\int\frac{x^2-1}{\sqrt{2x-1}}dx[/tex]

    Yes?
     
    Last edited: Jan 28, 2008
  4. Jan 28, 2008 #3
    Sorry made a mistake in typing the denominator (2x-1)^(1/2) Im slightly displexic
     
  5. Jan 28, 2008 #4
    How did you type that exactly.
     
  6. Jan 28, 2008 #5
  7. Jan 28, 2008 #6
    Yes thank you, that command latex is complicated I'll try to learn it.
     
  8. Jan 28, 2008 #7
    well try to use this substitution:
    2x-1=u^2, try to defferentiate and substitute back what u get for dx,
    you also get for x=(u^2 + 1)/2, from 2x-1=u^2
    the rest is pretty simple after u substitute!
    Can you go from here?
     
  9. Jan 28, 2008 #8
    Gets easier as you use it on a daily basis.

    First, I would break up the numerator.

    [tex]\int\frac{x^2}{\sqrt{2x-1}}dx-\int\frac{dx}{\sqrt{2x-1}}[/tex]
     
  10. Jan 28, 2008 #9
    It might work this way also, but by immediately taking the substitution that i suggested he will get to the result pretty fast.
     
  11. Jan 28, 2008 #10
    Ok ill try stupid maths method I would get the integral of (((u^2+1)/2)^2-1)/(u) what would my du be
     
    Last edited: Jan 28, 2008
  12. Jan 28, 2008 #11
    I guess I will attempt this on my own thats for the help.
     
  13. Jan 28, 2008 #12
    You do not need to know what the du will be, you need just to plug in the value of the dx that you get after differentiating 2x-1=u^2, so it obviously will be dx=udu, and when you plug this in the u here and that one that you will get on the denominator will cancel out so you are left with somehting like this:
    [tex]\int\frac{((\frac{u^{2}+1}{2})^{2}-1)udu}{u}[/tex], now you can go from here right?
     
  14. Jan 28, 2008 #13
    By the way it is not stupid math, but instead sutupidmath! NOt that i mind it, but it feels good to be correct! NO hard feelings, ok?
     
  15. Jan 28, 2008 #14
    thx stupidmath. I knew I got the right udu for dx.
     
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