Our book does a really lousy job of explaining the intricacies of exponential integration. I came upon this problem that I don't know how to solve:
I'm sure that there is a chain rule here, so this is what I did:
using the rule I came up with:
If this doesn't make sense, my exponent comes from the idea that the integral of -2u du is -u^2 (I think).
I know that my answer is wrong, but I don't know what I am doing wrong.
But that's what I am asking. How do I handle the -2u in the exponent? Do I just leave it as -2u? Or is there a chain rule or some other process that I need to apply? Since the integral of -2u is -u^2, does that somehow enter in?
Unfortunately, as I mentioned, our book is silent on this, so I really have no idea how to handle this exponent. I wish that I could show more work, but I'm truly stuck.
Yes. I do know the technique. We just haven't applied it to a situation where the substitution occurred solely in the exponent. I didn't see that the coefficient 2 would fall out as a constant of 1/2. When you said that x=2u, I didn't realize that you were suggesting a substitution. I just looked at that and saw what I had already done, which was to replace the x in the differentiation rule with the term -2u. Now I see what to do with it. Thanks for your help!