Hello,

Thank you so much. It works

Kind Regards

Integrate[Cos x/(R^2 + r^2 - (2*R*r*Cos x) + (k - k1)^2)^1/2, {x, 0, 2 \[Pi]}]

Evaluating the integral in Mathematica yields the following result:

ConditionalExpression[(-4 Cos \[Pi] r R + ((k - k1)^2 + r^2 + R^2) (Log[(k - k1)^2 + r^2 + R^2] - 
         Log[(k - k1)^2 + r^2 - 4 Cos \[Pi] r R + R^2]))/(8 Cos r^2 R^2), 
     Re[((k - k1)^2 + r^2 + R^2)/(Cos r R)] > 4 \[Pi] || 
      Re[((k - k1)^2 + r^2 + R^2)/(Cos r R)] < 
       0 || ((k - k1)^2 + r^2 + R^2)/(Cos r R) \[NotElement] Reals]

Dear Jofre,

are you sure that your syntax is ok? In your expression

Integrate[Cos x/(R^2 + r^2 - (2*R*r*Cos x) + (k - k1)^2)^1/2, {x, 0, 2 \[Pi]}]

the Cos has no proper argument - there are no square brackets. And there is a difference to that and Cos[x]:

If I use

Integrate[Cos[x]/(R^2 + r^2 - (2*R*r*Cos[x]) + (k - k1)^2)^1/2, {x, 0, 2 \[Pi]}]

the result is somewhat different.

I suppose that the original question is about WolframAlpha, where none of this matters, because it does not evaluate.

As a suggestion to Ali Kreem I would use the free tier of the WolframCloud. It allows you to use proper Mathematica syntax and your integral will evaluate.

Cheers,

Marco

Thanks Marco! Somehow I copy-pasted the original input without even realizing the cosines without argument and I gave its result without thinking. ;)