Are you sure that isn't dydx instead of dxdy?. The way it is you have a dependent limit.
I can't solve the last integral, and the answer I get from Mathematica does not work for these limits. So I suspect the above isn't correct.
EDIT: Here's another tricky improper integral:
EDIT: And another one:
Also, if you want to cut-and-paste Mathematica as latex code, select the code in Mathmatica, then choose Edit/Copy as/Latex (with some minor limitations). For example, I didn't type in any of that code above although I did have to re-format it slightly because of some limitations on latex length in here.