One more antiderivative question.

  • Thread starter Checkfate
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  • #1
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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.
 

Answers and Replies

  • #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?
 
  • #3
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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?
 
  • #4
arildno
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What is the derivative of g(x)=a*f(x), where "a" is a constant?
 
  • #5
radou
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Checkfate said:
PS- I have not learned to integrate by parts or anything like that yet.

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.
 
  • #6
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Ahh kk I get it, [tex]=\frac{1}{2}*ln(|x|)[/tex] :)

Thanks!!!
 
  • #7
arildno
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That is indeed correct.:smile:
 
  • #8
radou
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Checkfate said:
Ahh kk I get it, [tex]=\frac{1}{2}*ln(|x|)[/tex] :)

Thanks!!!

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

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