1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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