How does one integrate the following: you can switch the bounds however you want (integrate with respect to x before y). i would like to know the best way to handle this problem.

Consider substituting , so that . Then





Then by similar substitutions, you can easily find that you end up with





Of course, this all assumes that the integrand is continuous over the domain of integration, which would require that are chosen such that for any . If in particular , then we can write



and you can combine the logarithms if you like as