I bumped into a curious integral, which has so far resisted all the attempts I made to find a closed-form solution (not that I am sure there is one to start with). Has anyone encountered a similar beast before and could provide me with some hints on where to start? The integral is $$ I(w)=\int_{\sigma(w)}dx\frac{1}{\sqrt{(x-x^3)^2-w^2}}\ , $$ where $\sigma(w)=\{x\in [0,1]: (x-x^3)^2-w^2>0\}$. Many thanks in advance, folks.
2026-04-06 11:36:14.1775475374
Closed form for an integral involving an inverse square root and a cube
69 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INTEGRATION
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