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!

A Difficult Integral

  1. Oct 30, 2007 #1
    How should we proceed to find the definite integral

    Int[ log(sin(x))*log(cos(x)) ,{x,0,pi/2} ] ?

  2. jcsd
  3. Nov 1, 2007 #2

    Gib Z

    User Avatar
    Homework Helper

    I can't remember the source of even the exact answer :( But I've seen integrals of that form done in some papers by Ramanujan where he expressed the answer in terms of the zeta function and something else, so it's not exactly an elementary integral.

    This isn't how he did it, and I'm not sure if it will help, but you could express cos/sin in terms of an infinite product, split up the logs ( log [ab]= log [a] + log ) and then continue?
  4. Nov 4, 2007 #3
    Leafing through "Treatise on Integral Calculus Vol. 2 --Joseph Edwards (1922)",I found
    Wolstenholme had solved the above problem nicely as follow:


    Attached Files:

    • int.jpg
      File size:
      39.3 KB
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Difficult Integral Date
Difficult Vector Field Integral Feb 22, 2018
Difficult Integral Oct 10, 2016
Difficult Separable Integration Problem Jul 20, 2016
Difficult integral - Falling mass Mar 30, 2016
Difficult contour integral. May 22, 2015