From: jonas.matuzas@gmail.com   
      
   On Saturday, March 1, 2014 6:33:56 AM UTC+2, Richard Fateman wrote:   
   > I don't consider a solution that includes   
   >    
   > Si, Ci, or hypergeometric functions as a solution   
   >    
   > in closed form in terms of elementary functions.   
   >    
   >    
   >    
   > Unless there is no way of expressing the answer in   
   >    
   > terms of elementary functions.   
   >    
   >    
   >    
   > After all, you could always decide that the   
   >    
   > difficult integral in question deserves its own   
   >    
   > name, say  FooI,  and then return the answer in terms   
   >    
   > of FooI.   
   >    
   >    
   >    
   > RJF   
      
    I agree with you. You can name my integral Matuzas[a]=Integrate[Cos[x]^4/(a^8   
   + x^8), {x, -\[Infinity], \[Infinity]}] as new function. But you have to do   
   table of this integral properties: differentiation, integration, differential   
   equation it supports,    
   Fourier series, expressions with another functions.    
    And everybody should use it :) How to evaluate numerical -it is no problem .   
   Actually the same is with Ci, Si and ect... Numerically we know how to   
   evaluate.  But the same is with elementary functions, is'n it?   
      
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