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Help finding an indefinite integral

  1. Nov 14, 2013 #1
    I am trying to find the following indefinite integral:
    1. The problem statement, all variables and given/known data

    ∫[itex]\sqrt{}x[/itex]/(x-1)dx

    2. Relevant equations

    None

    3. The attempt at a solution

    I tried to use substitution but got nowhere. I set u=[itex]\sqrt{}x[/itex] so du=1/(2[itex]\sqrt{}x[/itex])dx. However from here on on I got stuck. I also tried using substitution this way u=x-1 so du=dx. However, this doesn't help since we get ∫[itex]\sqrt{}(u+1)[/itex]/(u)du.
     
  2. jcsd
  3. Nov 14, 2013 #2

    Mark44

    Staff: Mentor

    The substitution u = √x will work.
    So u2 = x => 2udu = dx.

    You'll get an improper fraction that you can simplify using polynomial division.

    LaTeX tip: Put the quantity that's inside the radical inside the braces {}. IOW, \sqrt{u + 1}.
     
  4. Nov 14, 2013 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Or, you can use ASCII and write sqrt(x/(x-1)) or sqrt(x)/(x-1).

    I cannot figure out whether your integrand is
    [tex] \sqrt{\frac{x}{x-1}} \text{ or } \frac{\sqrt{x}}{x-1}[/tex]
    If you mean the first one, use "[t e x ] \sqrt{ \frac{x}{x-1} } [/t e x ]" (no spaces); if you mean the second one, use "[t e x ] \frac{ \sqrt{x} }{x-1} [/ t e x]" (no spaces).
     
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