$$\int_0^1 (1+(x^{-p}-1)^{1-p})^{\frac{1}{p}}dx, p\in \mathbb{R}, p\ge 1$$ I find that $x=0,1$ are singular points(discontinuous points of this integral), is there a way to eliminate those singular points to make sure that this integral can be calculated by hand or by Taylor approximations. In either cases, what are those steps of calculating the integral?
2026-03-26 01:16:39.1774487799
Is there any way to eliminate the singular point to solve this integral by hand or by approximations?
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