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Are computer able to implement a algorithm theoretically to determine if a single variable integrals have closed form?

There are Risch's algorithms already could solved any single variable integrals given that it had closed form solution, but what if we are trying to solve a integral with unknown solution properties. Can the output say that it had no closed form exist for that integral?

Edit: My question is different from the another question since the previous question is asking what if a integral is known to had a closed form, but this one is asking what if we don't know whether if the integral had a closed form.

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    I found [this post](http://math.stackexchange.com/questions/155/how-can-you-prove-that-a-function-has-no-closed-form-integral) to be very helpful :) – 2017-01-08
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    If you insist that this is a different question by adding "what if we don't know whether if the integral had a closed form," then your new post poses a conundrum. Are Readers able to know whether an integral "with unknown solution properties" is given? What if one person knows this but another one does not? The [Risch algorithm](https://en.wikipedia.org/wiki/Risch_algorithm) *does not require* that we know beforehand if an integral "had closed form solution". However it requires that the *integrand* be rationally expressed in terms of elementary transcendental functions. – 2017-01-08

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