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

Basic intergral

  1. Dec 2, 2007 #1
    the intergral of 1/3x either equals 1/3 ln 3x or 1/3 ln x - i dont know which one is correct though because cant you take the 1/3 out of the intergral and then you get 1/3 ln x - so confused - i should really know this...
     
  2. jcsd
  3. Dec 2, 2007 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    It doesn't matter which one you use, since they only differ by a constant:
    [tex]\frac{1}{3}\ln(3x)=\frac{1}{3}\ln(x)+\frac{1}{3}\ln(3)[/tex]
    where the last term is simply a constant, as claimed.
     
  4. Dec 3, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You are wrong about "can't take the 1/3 out of the intergral" ("intergral": Boston accent?). [itex]\int 1/(3x)dx= \int (1/3)(1/x)dx= (1/3)\int (1/x)dx= (1/3) ln x+ c[/itex]

    Of course, you could also let u= 3x so that du= 3 dx and the integral becomes
    [tex]\int (1/(3x)) dx= \int (1/u)(du/3)= (1/3)ln(u)+ C= (1/3)ln(3u)+ C[/tex]
    As arildno points out, since ln(3u)= ln(u)+ ln(3), this just becomes
    (1/3)ln(u)+ (1/3)ln(3)+ C and (1/3)ln(3)+ C is just a different "constant of integration".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Basic intergral
  1. Trig intergration (Replies: 13)

  2. Basic intergration (Replies: 12)

Loading...