Definite integral....

x=sinθ

dx=cosθdθ
I=\int_{0}^{\pi /2}{\frac{cos\theta d\theta }{2(1+sin(\theta /2))}}

which is now integrable form.

one thing how did you know it was
(sinθ/2 - cosθ/2)² and not (cosθ/2 - sinθ/2)² ??

in precise words what happened to the | |

mmm yes,i agree. then i have to split the integral.

dat may also be a reason for no pink. :P