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How to integrate sqrt((ax+b)/x) dx (square root of linear fractional function)

  1. May 27, 2012 #1
    Hi,
    simple question, but difficult to find an answer for me

    How to integrate sqrt((ax+b)/x) dx ???
    a,b constants and x variable

    if it matters, I would be happy if you could solve it just for both a,b >0

    Thanks
     
  2. jcsd
  3. May 27, 2012 #2
    Let [itex]u=\frac{ax+b}{x}[/itex]. We're keeping our fingers crossed, there's no other common methods that apply, so this looked like most natural thing to do.

    The expression will be a little simpler, but now we try a more common method, which is let [itex]v=\sqrt{u}[/itex]. To find [itex]du[/itex], we usually consider [itex]v^2=u[/itex], to simplify things. I think you will end up with something that you know how to integrate.
     
  4. May 29, 2012 #3
    Let x = (b/a)(sinh(t))²
     
  5. May 30, 2012 #4
    go here:


    integrals.wolfram.com/index.jsp

    and enter

    sqrt[(a*x+b)/x]

    into the text box
     
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