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Non Numerical Integration

Posted 9 years ago
 Hello everyone, i have a problem with an integration. I am using Wolfram "Mathematica 10.0 Student Edition" and i want to solve the Integral: Integrate[1/(R^2 + 2 R a Cos[x-y]+a^2)^2,{x, 0 ,2 Pi}, Assumptions -> R > a > 0 && y Element[0, Pi ] ] ]  The result should be: (2 Pi (a^2 + R^2))/(R^2-a^2)^3  but when i calculate it, Mathematica always gives me the answer 0. I have seen that this integration works on another computer and now i do not understand why i do not get the correct result. Thank's for your help!
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Posted 9 years ago
 Hello, I wonder why the following is not a same? xv1 = Integrate[1/(R^2 + 2 R*a Cos[x - y] + a^2)^2, x, Assumptions -> R > a > 0 && y > 0 && y < \[Pi] && a \[Element] Reals] ((xv1 /. x -> 2 \[Pi]) - (xv1 /. x -> 0)) // FullSimplify (2 (a^2 + R^2) ArcTan[((a - R) Tan[(x - y)/2])/(a + R)])/(a^2 - R^2)^3 - (2 a R Sin[ x - y])/((a - R)^2 (a + R)^2 ((a + R) Cos[(x - y)/2] - I (a - R) Sin[(x - y)/2]) ((a + R) Cos[(x - y)/2] + I (a - R) Sin[(x - y)/2])) 0 
Posted 9 years ago
 Try this... Integrate[1/(R^2 + 2 R *a Cos[x - y] + a^2)^2, {x, 0, 2 Pi}, Assumptions -> R > a > 0 && y > 0 && y < \[Pi]]