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Integral problem

  1. May 2, 2005 #1
    I have to integrate:
    x/(sqrt[1+x^2]) dx

    I know the answer is sqrt[1+x^2], but I can't work out how to get there. I tried the substitution u = 1+x^2, but that didn't seem to get me any where. It also looks like the differential of arsinx, but its not quite. How do I get to the answer?

    Any help would be greatly appreciated.

    Thank you in advance
     
  2. jcsd
  3. May 2, 2005 #2

    matt grime

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    Why didn't that subs help: it transforms it up to a scalar multiple to the integral of u^{-1/2}, which you know how to do.
     
  4. May 2, 2005 #3
    i managed to confuse myself, when getting du.

    if u = 1 + x^2

    then du/dx = 2x

    so du = 2x dx yes?

    so does that mean that the integral is now 0.5u^(-1/2)?

    I can't remember what to do when I get to that stage.

    Thanks though
     
  5. May 2, 2005 #4
    From what I can see, that is correct. Now simply integrate through:

    [tex]\int\frac{du}{2\sqrt{u}}[/tex]

    and follow through with your answer.
     
  6. May 2, 2005 #5
    Ta. It makes more sense now.

    Thankyou, both of you
     
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