Brant Carlson Quantum Mechanics YouTube video series. Could someone explain this product rule identity?

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Could someone explain the identity on the top right of the page please and how it is achieved.

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Here is my working thus far. I tried using the product rule with $u= \frac{d}{dx}$ and $v = the longer term$ but this seems to get stuck as shown in the bottom line.

My working thus far

Many thanks,