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

Homework Help: Integration math question

  1. May 26, 2008 #1

    Gear300

    User Avatar

    If we were to integrate 1/x by parts using u = 1/x and dv = 1dx, then it would end up as:
    Int(dx/x) = 1 + Int(dx/x), ending up with 1 = 0. Why was there a discrepancy in the integration?
    --Int() refers to integral
     
    Gear300, May 26, 2008
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. May 26, 2008 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    You're missing an integration constant.
     
    morphism, May 26, 2008
  4. May 26, 2008 #3

    exk

    User Avatar

    [tex]\int\frac{1}{x}dx=uv -\int vdu= \frac{x+c}{x} - \int \frac{-(x+c)}{x^{2}}dx = etc...[/tex]
    [tex]u=\frac{1}{x}[/tex]
    [tex]du=\frac{-1}{x^{2}}[/tex]
    [tex]dv=1dx[/tex]
    [tex]v=x+c[/tex]

    Please tell me if I am wrong.

    Regardless, you are looking for the result to be ln|x|+c.
     
    exk, May 26, 2008
  5. May 26, 2008 #4

    Defennder

    User Avatar
    Homework Helper

    I don't think there should be a '+ c' in this intermediate step. Anyway, integrating
    1/x gives ln(x) + c by definition. Some books actually define ln(x) to be the anti-derivative of that.
     
    Defennder, May 26, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook