
2 Attachment(s)
improper integral
Hello.
Attachment 26906
I don't know how to solve the above improper integral.
I tried to get rid of dy, but turn out to be Attachment 26907
which is even more difficult to me.
I don't know how to get rid of x^2y^2 in the denominator.
Can any teach me how to solve this question?

Re: improper integral
If you could change the order of integration, you would have . Can you integrate that?
 Hollywood

Re: improper integral
Consider the inner integral first that is integral of 1 /(1 + x^2y^2) w r t y, thereafter proceed to integrate w r t x.

Re: improper integral
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) )
Oh............
It becomes a recurring problem .

Re: improper integral
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:
.
 Hollywood