# Problem with the expansion of integration by parts

I've come across this funny problem while messing around with integration by parts. Probably made a mistake somewhere.

In the integration of parts expression, it's possible to expand it further.
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Plugging the second expression into the first, we get
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I don't think this is standard notation, but it's better than writing out all the "violin holes".
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The problem is that it seems like we will get an infinite string of polynomials on the right hand side, but not on the left.

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