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Article Summaries:
- The blog post revisits indefinite integrals, arguing that the standard “∫1/x dx = ln|x| + C” formula is misleading when interpreted as the most general antiderivative on a disconnected real domain. By treating the integrand as a complex‑analytic function on the connected domain ℂ∖{0}, the author shows the true general antiderivative is ln x + C, with a single arbitrary constant. The discussion extends to multi‑valued complex logarithms, branch choices, and explains why the real‑valued antiderivative differs. Similar issues are noted for other classic integrals, and the so‑called “dodgy” calculations are shown to be correct as contour integrals.
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