What is the antiderivative of the Heaviside step function $\Theta (x)$ as defined on Wikipedia? I have seen somewhere it is $x\Theta (x)+C$, yet taking the derivative of this expression using the product rule gives $\Theta(x)+x\delta(x)$, where $\delta(x)$ is the Dirac delta function. This does not return $\Theta(x)$.
2026-04-12 01:07:34.1775956054
What is the antiderivative of the Heaviside step function?
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As given in the question and confirmed in the comments, the antiderivative is, by inspection, $$x\Theta (x)+C.$$