Antiderivative of a Schwartz-function
Let $\mathcal{S}(\mathbb{R})$ be the Schwartz-Space. Prove that if $f \in \mathcal{S}(\mathbb{R})$ and $\int_{-\infty}^\infty f(t)dt=0$, then there is $F \in \mathcal{S}(\mathbb{R})$ such that $f=F'$.
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