I know that integral of removable discontinuous functions are differentiable but jump discontinuous aren't. However, When 2xsin(1/x)-cos(1/x) is integrand, which is derivative of x^2sin(1/x) has no limit defined at x=0(oscillating discontinuity) and its primitive(integral) exist as x^sin(1/x), but not differentiable. 2xsin(1/x)-cos(1/x) is Riemann integrable function(bounded) but it's integral is not differentiable. Can I say all integral of functions that have oscillating discontinuous points(not finite) aren't differentiable? If it's true, how can I prove it?
2026-02-23 12:35:18.1771850118
Integral of functions that have oscillating discontinuous points(not finite) aren't differentiable?
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