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

Question about integral and natural log

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the integral to the following expression


    2. Relevant equations

    [itex]\int udv = uv - \int vdu[/itex]

    [itex]\int\frac{1}{x}dx = ln(x) [/itex]

    3. The attempt at a solution

    Given the information above, would a correct answer to this problem be ln(x-1) ? If not, what am I doing wrong ?

  2. jcsd
  3. Sep 13, 2011 #2


    User Avatar
    Homework Helper

    how non need to use int by parts a simple substitution will do, ln(x-1) is correct

    if you don't show what you doing (your steps it woudl eb hard to tell what was going wrong as well ;)
  4. Sep 13, 2011 #3

    oh i just realised if you use substitution of variable u=x-1, it makes it easy to show that integral of 1/(x-1) is ln(x-1) :)
    Last edited: Sep 13, 2011
  5. Sep 13, 2011 #4


    User Avatar
    Homework Helper

    good guess, is that all you need?
  6. Sep 13, 2011 #5
    You can attack the problem as follows

    let F(x)=[itex]\int\frac{1}{x-1}dx[/itex]

    From then on make substitution x=x+1

    which yields


    Find out this integral which is quite obvious ( do not forget to add a constant to it )

    since what you found is F(x+1) now re-substitute x=x-1
  7. Sep 13, 2011 #6

    yeah pretty much. i worked it out myself using the substituiton and it came out fine
  8. Sep 13, 2011 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

  9. Sep 13, 2011 #8


    User Avatar
    Homework Helper

    agree, would always use a different variable to represent the substitution eg. u = x-1, then du = dx
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook