The pair of cube-root pseudo-elliptic integrals found by Euler:   
      
     integrate((a + b*x)/((3 - x^2)*(1 - 3*x^2)^(1/3)), x)   
      
     integrate((a + b*x)/((3 + x^2)*(1 + 3*x^2)^(1/3)), x)   
      
   and the pair found (or implied) by Legendre:   
      
     integrate((a + b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x)   
      
     integrate((a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)), x)   
      
   look very similar. But FriCAS 1.3.1 (the current web-interface version)   
   returns:   
      
   >> Error detected within library code: integrate: implementation   
      incomplete (residue poly has multiple non-linear factors)   
      
   for Euler's pair and:   
      
   >> Error detected within library code: integrate: implementation   
      incomplete (trace 0)   
      
   for Legendre's pair. With the four integrands being so similar, this   
   occurence of different failure modes is somewhat surprising.   
      
   However, FriCAS can solve all of them for either a=0 or b=0, and thus   
   also knows how to solve the general cases in a sense.   
      
   Martin.   
      
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