Find the integral 
$$\int\dfrac{\sin x}{\sqrt{2}+\sin x+\cos x} \, dx$$

My idea: since
$$\sin x+\cos x=\sqrt{2}\sin(x+\dfrac{\pi}{4})$$
so

$$\int\dfrac{\sin x}{\sqrt{2}+\sin x +\cos x} \, dx=\int\dfrac{\sin x}{\sqrt{2}(1+\sin (x+\dfrac{\pi}{4})} \, dx$$
But then I don't know how to continue. Thank you