Hi Hollywood and ibdutt,
Sorry, I tried.
But I still don't know to integrate even I know I should solve the inner dy integral first.
Can you show me how to do it?
When I tried to solve it, I let xy=tan(theatre),
then the question becomes integral limit from zero to infinity [Arctan(7x)-arctan(5x)]/x dx.
Which when I tried to continue to solve it,
It becomes the starting question (the question with 1/(1+(xy)^2) )
It becomes a recurring problem -.-
Once you change the order of integration, you can integrate the inner integral first, treating x as a constant:
substitute , , , and converting the limits of integration: to means to .
Now we can do the outer integral: