From: &noreply@axelvogt.de   
      
   On 13.01.2015 10:35, Nasser M. Abbasi wrote:   
   ...   
   > For example, this integral   
   > int((B*x+A)*(e*x+d)^(7/2)/(c*x^2+a)^3,x);   
   > Generates a leaf size of 1,424,430 in Maple   
   ...   
      
   I guess that by leaf size = number of characters used for display is meant.   
      
   A length of ~ 1.5*10^6 is almost useless and I had not the patients to   
   wait until Maple answers.   
      
   My naive way in Maple would be to get the partial fractions decomposition   
   for the denominator. Then one has to compute Int(numerator/(x-t)^k, x),   
   k=1,2,3 (up to constants). Each of those results have length of ~ 600,   
   making use of simplify/size (before feeding some constants).   
      
   Now doing it for the full task finally it gives ~ 9000 characters:   
      
      # find the partial fractions and put them in a list:   
      1/(c*x^2+a)^3; convert(%, fullparfrac, x); allvalues(%);   
      [op(%)];   
      
      # compute the according integrals   
      map('w -> Int((B*x+A)*(e*x+d)^(7/2)/w, x)', %);   
      value(%):   
      
      # sum them up and simplify the result   
      convert(%, `+`);   
      result:=simplify(%, size);   
      length(%);   
                                     8654   
      
      # check formally   
      diff(result, x) = (B*x+A)*(e*x+d)^(7/2)/(c*x^2+a)^3:   
      is(%);   
                                     true   
      
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