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Integral (1/(1+sqrt(2x))) dx

  1. Jan 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the indefinite integral.
    ∫ (1/(1+sqrt(2x))) dx

    2. Relevant equations
    ∫ 1/u du = ln |u| + C

    3. The attempt at a solution
    I tried a couple 'u' substitutions, which didn't work out. I also tried rationalizing the denominator, but that didn't help. No one I've talked to knows how to do this one...
  2. jcsd
  3. Jan 7, 2008 #2
    Well from rationalizing we get ...


    So from here, the left is easy and now we work only with the right


    [tex]u=\sqrt{2x}\rightarrow u^2=2x[/tex]

    [tex]u^2=2x \leftrightarrow udu=dx[/tex]
    Last edited: Jan 7, 2008
  4. Jan 7, 2008 #3
    following you so far
  5. Jan 7, 2008 #4
    After substituting, we get ...


    Then add [tex]\pm 1[/tex] to the numerator so that you can split it into 2.

    Last edited: Jan 7, 2008
  6. Jan 7, 2008 #5
    I don't understand:
    [tex]u^2=2x \leftrightarrow udu=dx[/tex]
  7. Jan 7, 2008 #6
    I made my initial u-sub then I manipulated my u-sub by squaring both sides and then I took it's derivative.

    [tex]u=\sqrt 2x[/tex] ONLY for the numerator

    Manipulating my u-sub by squaring both sides so that I can substitute for my denominator.


    Taking the derivative of my manipulating u-sub

    [tex]2udu=2dx \rightarrow udu=dx[/tex]
  8. Jan 7, 2008 #7
    Ohhh okay. Thank you!
  9. Jan 7, 2008 #8
  10. Jan 7, 2008 #9
    Actually, rationalizing isn't even a good idea. You can apply the same methods I did with the u-sub w/o rationalizing.
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