Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Function f(x)=1/x intergral

  1. Jan 25, 2005 #1


    User Avatar

    I have the function f(x)=1/x , and there's two asymptotes, the x-and y-axes. As x gets larger, the f(x) becomes smaller, but it is never 0. So my question is, what is the intergral from x=1 to x=infinite?
  2. jcsd
  3. Jan 25, 2005 #2
    [tex]\int \frac{1}{u}\,du=\ln{|u|}+C[/tex]
  4. Jan 25, 2005 #3
    The derivative of ln x is 1/x so like the person stated above

    [tex]\int (1/u)du = ln|u| + C[/tex]
  5. Jan 25, 2005 #4


    User Avatar

    I'm sorry, but I'm so lost already. Could somebody please explain it to me? What is u?
  6. Jan 25, 2005 #5
    Let me put it in a simpler form, just replace u with x something you are probably more common to seeing.

    Now the derivative for the ln x = 1/x.

    now if you have [tex]\int {1/x}dx[/tex] you know that's the derivative of the ln of x, so you end up with that = [tex]ln|x| + C[/tex]

    this is just based of knowing the derivative and antiderivative of ln x, thats all you need to know.
  7. Jan 25, 2005 #6


    User Avatar
    Gold Member

    integrals at infinity are calculated by


    if you use this in combination with the info above you can calculate it
  8. Jan 25, 2005 #7


    User Avatar
    Homework Helper
    Gold Member

    I never learned that yet. That's pretty cool.
  9. Jan 28, 2005 #8


    User Avatar

    so basically, there's not "number" answer to that questions? The answer is just a function?
    and also where did ln(x) come from?
  10. Jan 28, 2005 #9
    [tex]\int_1^{\infty} \frac{1}{x}dx[/tex] is undefined, or infinite.. depend on which one you feel more comfortable

    where did ln x came from...hmmm... it came from [itex] \frac{d}{dx} lnx = 1/x [/tex].... so your next question is why this is true.....

    assume you know product rule and the derivative of e^x is e^x itself

    [tex] e^{\ln{x}} = x[/tex]

    [tex] \frac{d}{dx} e^{\ln{x}} = \frac{d}{dx} x [/tex]

    [tex] e^{\ln{x}} \frac{d}{dx} (\ln{x}) =1[/tex] --------product rule

    [tex] x \frac{d}{dx} (\ln{x})=1[/tex]

    [tex] \frac{d}{dx} (\ln{x}) = \frac{1}{x} [/tex]

    so the anti-derivative of 1/x is ln(x)
  11. Jan 28, 2005 #10


    User Avatar
    Science Advisor
    Homework Helper

    Erm vincentchan don't you mean the chain rule?
  12. Jan 28, 2005 #11


    User Avatar
    Science Advisor
    Homework Helper

    Yes,it is the chain rule...Anyway,the result is correct and the method of finding it is correct as well...

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook