i used the substitution t=tan(x/2) and i ended up with
integral from +infinity to 0 of
which looks like an inverse tan function , and i ended up with sqr(27)/2 pi , which is not the same as my calculator's answer , so i suspct i am doing some thing wrong. can some one tell me where i am going wrong please.
I would do this integral exactly as you did with a t=tan(x/2) substitution and then an inverse tangent. This gives me
Evaluating this from pi to 0 I get -pi/sqrt(3)
You can check the integration using Mathematica at The Integrator. You need to take some care with Mathematica's notation. Input the expression
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