Integral Hangs

[parisse]

If it was easy to find an antiderivative and return the most simplified form for any integrand, every CAS would certainly implement it! But it's hard and it's not about a few inputs, you can get a more precise idea by looking here https://www.12000.org/my_notes/CAS_integ...x2-30001.2 (70 000 inputs)
There is also perhaps a wrong assumption : some people believe that a "good" CAS should solve the math for them (and that's probably a consequence of the fact that some CAS are optimized to solve US textbook inputs). But it's wrong! You must learn maths and you must learn a little bit about the CAS you are using in order to run it well. I mean, you must have some understanding on what kind of problems a CAS can solve, have some idea on what algorithms are involved (e.g. for integration, know about change of variables, that rational fractions can be integrated by partial fraction decomposition assuming the denominator can be factored, etc.), have solved a few by hand (when calculations are easy to do by hand of course, like e.g. cos(x)/(sin(x)^2-4)), before you can really take advantage of a CAS to do more complex computations for you. Then you can see when and how you can help the CAS if it does not choose the best strategy.