A Difficult Integral

  • Thread starter mathslover
  • Start date
  • #1
17
0
How should we proceed to find the definite integral


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






mathslover
 

Answers and Replies

  • #2
Gib Z
Homework Helper
3,346
5
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?
 
  • #3
17
0
Leafing through "Treatise on Integral Calculus Vol. 2 --Joseph Edwards (1922)",I found
Wolstenholme had solved the above problem nicely as follow:

-Ng
 

Attachments

Related Threads on A Difficult Integral

  • Last Post
Replies
24
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
849
  • Last Post
Replies
22
Views
1K
  • Last Post
Replies
8
Views
602
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
795
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
3
Views
950
Top