I have the following integral $$\int_{0}^{\infty}\sin^{-1}(1/x)\delta'(x^4-1)\, \mathrm{d}x$$ I tried to solve it by using the property $$\int_{-\infty}^{\infty}f(x)\delta'(g(x))\, \mathrm{d}x=-\sum_k \frac{f'(c_k)}{|g'(c_k)|}$$ but $f'(1)$ is not defined.
2026-04-04 02:25:34.1775269534
How can I evaluate this integral with Dirac's delta function?
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