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Need some help with this integral

  1. Apr 12, 2006 #1
    I ran into the following (general form) integral today while working on an engineering problem:

    [tex]
    \int \frac{dx}{x (a \sqrt{x} +b)}
    [/tex]

    I ran it through 'integrals.com' and came up with the following solution:

    [tex]
    \frac {\ln{x} - 2 \ln{(a \sqrt{x} + b)}}{b}
    [/tex]

    which is fine for the purpose of solving the problem, but I'd like to be able to work it by hand. I tried integration by parts, but any choice of u and dv I could think of only made it messier. I also couldn't think of an appropriate u substitution.

    Thanks in advance,

    Grogs
     
    Last edited: Apr 12, 2006
  2. jcsd
  3. Apr 12, 2006 #2

    arildno

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    Try [itex]u=\sqrt{x}[/itex]
    With the use of partial fractions decomposition, the result easily follows.
     
  4. Apr 12, 2006 #3
    Thanks arildno.

    Partial fractions is one of those skills I relearn once a year or so when I need to do a LaPlace Transform and then quickly forget.
     
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