From: fateman@cs.berkeley.edu   
      
   On 9/18/2017 12:01 PM, mariuszi28cg@gmail.com wrote:   
      
   It seems to be much preferable if the integration program returned   
   a result that inserted necessary assumptions, e.g.   
      
   int(...)  returned ....     If integer(m) and m>0 and b>0 and a>0   then   
   ....   else ...   
      
   Mathematica 11.2 returns an answer in terms of hypergeometric functions   
   which   
   is possibly the same  (I tested at m=1, and they are the same there).   
      
   Mathematica also integrates x^n   to x^(n+1)/(n+1) ignoring the   
   possibility that n=-1   
   where the answer is wrong.   
      
   RJF   
      
   >   
   > Hello   
   >   
   > Maple finds MORE integrals if you use assumptions.   
   >   
   > Example 1:   
   >   
   > int(x^m/(b*x+a), x)   
   >   
   > can't solve but using  assumptions:   
   >   
   > `assuming`([int(x^m/(b*x+a), x)], [m::posint, m > 0, b > 0, a > 0])   
   >   
   > = b^(-m-1)*a^m*(x^m*b^m*a^(-m)/m-x^m*b^m*a^(-m)*LerchPhi(-x*b/a, 1, m))   
   >   
   >   
   > See:   
   >   
   > http://12000.org/my_notes/CAS_integration_tests/reports/rubi_4   
   11/test_cases/1_Algebraic_functions/1_Linear_products/1.2(a+bx)%   
   Em(c+dx)%5En/rese2.htm#x3-20002   
   >   
   > from 671 to 685.   
   >   
   >   
   > Thank you, Mariusz   
   >   
      
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