I would like to decide by methods of Differential Algebra whether the integral $\int\root 3 \of{\cos^2(t)}\,dt$ contrary to the output of CAS Mathematica Online Integrator might
be expressible by elementary functions and if not  why.
Alas I have not the deep enough knowledge of the subject to be able to tackle this question without months of ( maybe fruitless ) study.
I read about the Risch algorithm which might give the answer and already tried to integrate with the CAS Axiom which was said to have implemented the algorithm.
Also I browsed an article of Bronstein about Symbolic Integration but presently dont understand the hard stuff.
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closed as offtopic by Felipe Voloch, Alexandre Eremenko, Chris Godsil, Stefan Kohl, S. Carnahan♦ Jun 1 '14 at 22:36This question appears to be offtopic. The users who voted to close gave this specific reason:


