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!

Integral ∫(1/2x)dx

  1. Oct 12, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫(1/2x)dx

    3. The attempt at a solution

    I factor out (1/2) and i get ∫(1/2x)dx=(1/2)ln|x|+C
    ∫(1/2x)dx
    (1/2)∫(1/x)dx
    (1/2)ln|x|+C

    But cant i say that u=2x and dx=du/2 and get ∫(1/2x)dx= (1/2)ln|2x| + C
    ∫(1/2x)dx
    u=2x
    ∫(1/u)(du/2)
    ∫(1/2u)du
    (1/2)∫(1/u)dx
    (1/2)ln|u| + C
    (1/2)ln|2x| + C

    if i can do this, i get two different answers...

    can i use the last method?
     
  2. jcsd
  3. Oct 12, 2013 #2

    Ibix

    User Avatar
    Science Advisor

    ln 2x = ln x + ln 2. One of your C constants is equal to the other plus ln 2.

    Both your answers are right...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integral ∫(1/2x)dx
  1. Integrate x/(2x+1) dx (Replies: 12)

Loading...