Question: Help in simplifying / interpreting maple output. Do you know how I can simplify the following output?

Hi guys,

I would be ever so grateful if someone could asssist me with the following matter.

I am trying to integrate the following expression but maple does not seem to be able to do it directly


Int((1/(2*Pi) + Q* cos(k*phi))^2/ (1+ beta^2*((1/(2*Pi)) + Q* cos(k*phi) )^2),phi=-Pi..Pi);


So I convert the expression to an exponential form as follows and evaluate that


 denominator:= 1+beta^2*(1/2/Pi+Q*(1/2*exp(I*k*phi)+1/2/exp(I*k*phi)))^2;

 result:=int(numerator/denominator, phi=-Pi..Pi);

simplify(result) assuming k <= 1, k>=0, beta <= 1, beta>=0;


When I converted the whole expression into exponential form I got a very huge output but by using the variables numerator and denominator as above and then putting them together this seemed to simplify the output.

The output from the above code has words and expressions  in it like Product, =RootOf, _R.  I don’t know what these mean and I would be grateful if someone could show me a way to remove them or otherwise simplify the output further or point me in the right direction in terms of what I need to do.  I really just want a mathematical expression without words in it. What can I do ?

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