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

What is the integral of sqrt(ln(x))

  1. Apr 13, 2015 #1
    what is the integral of sqrt(ln(x))
    NOTE:(I do not need the final answer,I know it. I want to Know how to solve it.)
     
  2. jcsd
  3. Apr 13, 2015 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    We usually discourage such terse questions... especially without the poster any showing to attempts at the solution (as you've done in several recent posts).
    Can you tell us your answer and how are approaching arriving at it?
     
  4. Apr 13, 2015 #3
    Do the substitution y=lnx, and then the substitution y=z^2. You ll end up with an integral of the form [itex]\int z^2e^{z^2}dz[/itex] which if you look up at wolfram i believe you ll understand how it is calculated (at first glance the integral would be equal to [itex]ze^{z^2}/2-f(z)[/itex] where f(z) should be such that [itex]f'(z)=e^{z^2}/2[/itex]). Such a function f(z) is the erfi function.
     
  5. Apr 14, 2015 #4
    Look i substituted (x=e^(-t^2))
    dx=-2t*e^(-t^2)dt

    ∫√(ln(e^(-t^2))*-2t*e^(-t^2)dt
    -2∫√(-t^2)*t*e^(-t^2)dt

    -2∫it^2*e^(-t^2)dt
    When i arrived here i stopped.
    but i used integral calculator to find the final answer.

    this is the final answer:

    ½(√π*i* erf(i√(ln(x)))+2x√(ln(x)))+C
     
  6. Apr 14, 2015 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you understand what that means? Do you understand that almost all such functions have NO integral in terms of elementary functions?
     
  7. Apr 14, 2015 #6
    yes i understand. thank you.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What is the integral of sqrt(ln(x))
  1. Integrate (ln ln x)^n (Replies: 5)

Loading...