I've heard somewhere that the integral of $1/f(x)$ is not possible to answer in terms of $f(x)$, $f'(x)$, $F(x)$, and elementary functions. Is there an answer is terms of non-elementary functions? Why is $(1/f(x))'$ so simple in contrast to the integral?
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1Some answers to your last question: Why is integration so much harder than differentiation? – Martin R Dec 13 '22 at 21:07
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It depends on what $f(x)$ is. – Randall Dec 13 '22 at 21:39