integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫
(2*(-Cos[x/2] + Sin[x/2])*Sqrt[1 + Sin[x]])/(Cos[x/2] + Sin[x/2])

Integrate[Sqrt[1 + Sin[x]], x] ==
(2*(-Cos[x/2] + Sin[x/2])*Sqrt[1 + Sin[x]])/ (Cos[x/2] + Sin[x/2]) 

Integrate[Sqrt[1 + Sin[x]], x] == 

        x        x
2 (-Cos[-] + Sin[-]) Sqrt[1 + Sin[x]]
        2        2
-------------------------------------
               x        x
           Cos[-] + Sin[-]
               2        2
Time to compute: 0.04 second
Spread the word: