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One more antiderivative question.

  1. Oct 20, 2006 #1
    Hi there, I am trying to find the antiderivative of [tex]\frac{1}{2x}[/tex] but can't seem to do it. I am trying to separate the terms so that I can do each antiderivative seperately, but I don't see a way to do that.

    My most natural first attempt is to convert it to [tex]2x^{-1}[/tex] but of course since they are not separated by a + or minus (the 2 and the x^-1) I can't use antiderivative laws on it. If I did, I would end up with [tex] 2x*ln(\abs{x})[/tex] which is wrong. Any help is appreciated, thanks.

    PS- I have not learned to integrate by parts or anything like that yet.
     
  2. jcsd
  3. Oct 20, 2006 #2

    arildno

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    [tex]\frac{1}{2x}=\frac{1}{2}*\frac{1}{x}=a*\frac{1}{x}=\frac{a}{x}, a=\frac{1}{2}[/tex]
    Does that help?
     
  4. Oct 20, 2006 #3
    Woops sorry, some bad algebra there. I meant [tex]\frac{1}{2}*x^{-1}[/tex].

    But no, I don't think it does, because I would get [tex]\frac{x}{2}*ln(|x|)[/tex] wouldn't I? (Assuming you mean to just use the antiderivative formulas immediately) :(. What am I doing wrong?
     
  5. Oct 20, 2006 #4

    arildno

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    What is the derivative of g(x)=a*f(x), where "a" is a constant?
     
  6. Oct 20, 2006 #5

    radou

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    You don't need to know how to integrate by parts to solve this, since [tex]\int \frac{1}{x}dx = \ln \left|x \right|+C[/tex] is a typical 'table integral'. You'll find the integral of [tex]f(x) = \frac{1}{2x}[/tex] easily now by reading arildno's comments.
     
  7. Oct 20, 2006 #6
    Ahh kk I get it, [tex]=\frac{1}{2}*ln(|x|)[/tex] :)

    Thanks!!!
     
  8. Oct 20, 2006 #7

    arildno

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    That is indeed correct.:smile:
     
  9. Oct 20, 2006 #8

    radou

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    Correct, but don't forget to add the constant of integration, C (or whatever you like to name it). :smile:
     
  10. Oct 20, 2006 #9
    True, thanks. =)
     
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