How can I solve this integral ?
It involves two functions, $f(x)$ and $g(x)$, as well as derivative according to $x$ and the Dirac delta function.
$$ \int_{0}^{\infty} f(x) \frac{d}{dx} \delta(x-R)g(x) dx $$
2026-04-03 20:12:46.1775247166
Complicated integral involving Dirac delta function
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Using IBP we get that: $$\int_0^\infty f(x)g(x){d\delta(x-R)}=\left[f(x)g(x)\delta(x-R)\right]_0^\infty-\int_0^\infty\left[f'(x)g(x)+f(x)g'(x)\right]\delta(x-R)dx$$ Can you finish it from here?