Question

Evaluate:

$\int \frac{\sin x-\cos x}{\sqrt{\sin 2x}}dx$

Answer 1

$-cosx+sinx=t$

$sinx+cosxdx=dt$

${cos}^{2}x+{sin}^{2}x-2cosxsinx=t^2$

$1-sin2x=t^2$

$1-t^2=sin2x$

$\int \frac{dt}{1-t^2}$

${sin}^{-1}t+c$

${sin}^{-1}[sinx-cosx]+c$