Define it with its corresponding integral and integrate both by parts:
Now by abstracting these two integrals from each other, we have:
Here's what I'm working with:
This does not appear to be a trivial problem, and I'm having trouble figuring out how to approach this. If I try integrating it by parts, I just end up with another integral that's very similar. Tossing this into WolframAlpha shows a *really* complicated u-sub. I've run into situations where WolframAlpha makes things a lot more complicated than they need to be. I'm hoping this is one of those times.
Can anyone give me a hand?
Just in case a picture helps (helps me by mapping out the relationships implied by combinations of relative pronouns, integral of, derivative of) ...
If you can buy this...
Key:
Spoiler:
... as lazy integration by parts, doing without u and v and du and dv (as does THC, too, to an extent) ... then you want 'integration by parts twice' i.e. filling the blanks here...
... and then solving the top row for I.
Larger
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Balloon Calculus; standard integrals, derivatives and methods
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