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).

Sorry, latex doesn't seem to be working for me, so hopefully this is readable and I have written it correctly.

I know that my answer is wrong, but I don't know what I am doing wrong.

Thanks.