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Strange double integral that I only have a vague idea about.

It's been a while since I've done advanced calculus 1 so I don't remember every technique of integration that I should. I was focusing on linear algebra for a while. I have scanned my hand writing in doing a problem in the book "Multivariable Calculus, James Stewart 6E." I was thinking about integrating by parts but instead tried to use tables and ran into an obstacle (division by 0). I think it's fair to ask how to do this integral as I have made some effort. I have attached my scan to this thread. Note that it is a pdf file and needs to be rotated twice in the view pull down menu because it is upside down. Thanks.

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New limits of integration?

I had trouble integrating when you changed the limits of integration (again I have scanned my work). From what I read in my book you don't have to change the limits in a case like this. Again, it's been a while since I took calculus so there could be some holes in my reasoning, however when I integrated using the same limits of integration I began with I got a simple answer. Check my attached jpg scans. Thanks.