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Homework Help: Help needed Please

  1. Sep 30, 2004 #1
    I am having problem with two math questions that I have been asked to try and although I do not need to do them they are really frustrating me.

    First off intergrate (x-1)/squareroot(4x^2-1)

    I am sure this is something to do with replacing x to get cos^2 (x)-1 so that this becomes 2cos(2x) but I can't intergrate from there either.

    Also intergrate 1/squareroot(1+8x-4x^2) again I am sure it is a substitution for trig but I just can't see it.

    Any help would be greatly appreciated. Sorry I caan't lay the questions out any better
  2. jcsd
  3. Sep 30, 2004 #2


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    I'm sorry to say but for problems like this simple trig substations will not service, a bit of algebraic manipulation to make things look nicer is in order:

    For the 1st one you should realise that:

    [tex]\int \frac{x-1}{\sqrt{4x^2-1}} dx = \int \frac{x}{\sqrt{4x^2-1}} - \frac{1}{\sqrt{4x^2-1}}dx[/tex]

    Now if you split the integral up:

    [tex]\int \frac{x}{\sqrt{4x^2-1}}dx - \int\frac{1}{\sqrt{4x^2-1}}dx[/tex]

    Not wanting to do the whole thing for you I'll leave you to work out the rest.

    As for the second the trick I belive is completing the square:

    [tex]\int \frac{1}{\sqrt{1+8x-4x^2}} dx= \int \frac{1}{\sqrt{5-4(x - 1)^2}}dx[/tex]

    Then use the substation u = x - 1 and again I'll leave you to do the rest. (I would seriously check my arithmetic if I were you, not feeling that well on it tonight).
  4. Sep 30, 2004 #3

    thank you for the quick responce. I can not believe I missed I really hate it when I overlook the obvious.

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