Can the Risch-algorithm actually prove that has no closed-form antiderivative?
The Risch algorithm is used to find closed-form antiderivatives.
If I understand the article right, only heuristics are known. On the other hand, I came across the claim that it is known that has no closed-form antiderivative.
Is the Risch-algorithm successful in the case ? Is it actually proven that no closed-form antiderivative exist or just very probable because no form has been found using the Risch algorithm ?
This question could well be a duplicate, but I am not sure whether the aspect of decidability has been asked.