1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Improper Integrals with u sub and integration by parts ?

  1. Apr 12, 2009 #1
    1. The problem statement, all variables and given/known data

    The integral from 1 to infinity of (lnx)/(x) dx

    2. Relevant equations
    U substitution and integration by parts

    3. The attempt at a solution
    Cant decide what to use as my "u" . . can any one help with this part ?

    -Jay J-
  2. jcsd
  3. Apr 12, 2009 #2


    User Avatar
    Gold Member

    this doesn't really require integration by parts, just a u-substitution:

    [tex]\int \frac{ln(x)}{x}=\int u du = \frac{1}{2}u+ C= \frac{1}{2}(ln(x))^2+C[/tex]

    here you take u = ln(x) and differentiate to get, du = 1/x dx.
  4. Apr 12, 2009 #3
    ok i understand the whole u substitution part but then i have to determine whether or not the integral is divergent or convergent and if its convergent i have 2 evaluate it . .. how would you do that ?

    -Jay J-
  5. Apr 12, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    Evaluate the integral between x=0 and x=M and let M approach infinity. What do you conclude?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Improper Integrals integration Date
Improper integral convergence from 0 to 1 Yesterday at 4:59 PM
Improper Integral of a Monotonic Function Aug 24, 2017
Improper integral with spherical coordinates May 30, 2017
Improper integral May 16, 2017
Another Improper Integral Using Complex Analysis Apr 25, 2017