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Homework Help: Calc II integral

  1. May 22, 2007 #1
    evaluate the integral of 1/x(4x+1)^1/2

    so what i am thinking is that i will have to use a trig substution some how for

    maybe x=secu since the substution for a^2+x^2=sec^2u

    but i am not sure how to go ahead and do it

    please help me
  2. jcsd
  3. May 22, 2007 #2


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    No. Don't do trig. Try u^2=4*x+1. You'll get a simple rational function you can then do with partial fractions.
  4. May 22, 2007 #3


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    Well, as Dick pointed out, you should let [tex]u = \sqrt{4x + 1}[/tex]
    Or, in general, if you meet some radical, then it's common to let u = that whole radical, and then go from there.

    You only let x = sec(u), when you meet: [tex]\sqrt{x ^ 2 - 1}[/tex], or when encountering [tex]\sqrt{x ^ 2 - a ^ 2}[/tex], you then let x = a sec(u).

    Can you go from here? :)
    Last edited: May 22, 2007
  5. May 24, 2007 #4

    Gib Z

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    I guess if she really wanted to, she could have done x= 1/4 tan^2 u. Takes much much longer though.
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