Like your previous examples, FriCAS can solve the first two cases   
   in elementary functions when a=0, b=0 separately, then do a linear   
   combination.  (with setSimplifyDenomsFlag(true), the result is not   
   too long and returns in a few seconds).   
      
   I know there are problems in FriCAS dealing with integrals with symbolic   
   parameters, probably because when computing resultants, the symbolic   
   parameters don't cancel out like numbers, resulting in very big polynomials.   
      
   Thanks for your examples and references.   
      
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