Hi, Eve!

You wrote:

>In example 4, it is clearly logical to add the
>integral of e^xsinxdx on both sides so as to
>cancel the 'extra' one out, but how does one know
>to do that? I feel like I will not be perceptive
>enough to catch that trick of sorts. There are

I would put that trick of example 4 into the category of a "dirty trick" -- something that works, but that it would be hard (or impossible!) to think of on your own. Unfortunately, I think you are just stuck trying to remember the sort of situations in which this trick works -- it most often comes up in the case where you have an exponential times a sine or cosine as the integrand.

>What is
>the corresponding integration rule for the
>quotient rule?

That's a really good question, and I have no idea what the answer is! I haven't ever heard of an integration rule that corresponds to the quotient rule, but now I'm going to have my eye out for it!

>This does not pertain to the
>reading, but I had some trouble with a few of the
>last problems in the assignment when substitution
>did not provide a corresponding/matching du in the
>integral.

You might come by my office hours today, or stop by the MQC in loker commons (8-10pm every night except for Fri & Sat). There were a couple of problems on the HW that involved some tricks, so those might be the ones that hung you up.

Best,
-Dr. VC