Integral

[geriniki]

can u help me by solving this integral

∫[tex]\frac{-sin x + cos x}{\sqrt{sin x + cos x} }[/tex]dx =?

[shyamjayakannan]

Let [tex]t=\sin x+\cos x\Rightarrow dt=(\cos x-\sin x)dx[/tex] and the integral becomes [tex]\int\frac{dt}{\sqrt t}=2\sqrt t+C=\boxed{2\sqrt{\sin x+\cos x}+C}[/tex]