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Integral of 1/1+sqrt(x)

  1. Oct 12, 2009 #1
    I'm having trouble calculating an integral:


    I decided to do a substitution:

    thus making the integral look like this:
    I transformed this integral to:
    And tried to solve the integral like this:
    going from 0 to 1.

    However, this means to insert 0 in an ln-expression. Obviously I have done something wrong? Can someone please help?
  2. jcsd
  3. Oct 12, 2009 #2
    Nevermind. I did it now.

    It was a simple mistake on my part.

    The integral should look like:


    after substitution

    and then it should be calculated with integration by parts from there.
  4. Oct 12, 2009 #3
    [tex]\left.{\frac{1}{1+\sqrt{x}}\right|_{x=1} = \left\{\frac{1}{2},\infty\right\}[/tex]
  5. Oct 12, 2009 #4

    Gib Z

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    Homework Helper

    I'm not entirely sure what that post means trambolin, care to explain?

    Dragonblood - The solution comes out must quicker than integration by parts if you add and subtract 2 into the numerator.
  6. Oct 12, 2009 #5
    I meant the -1 is causing the integrand blow up at x=1 for the cause of ln 0. But nevermind it is just the notation stuff...
  7. Oct 12, 2009 #6
    Ah, yes. That is much easier :) Thanks
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