Write a value of `int(sinx-cosx)/(sqrt(1+sin2x))\ dx`

Explanation

Solution:

=`\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x`

=`\int \frac{\sin x+\cos x}{\sqrt{\sin ^{2} x+\cos ^{2} x+2 \sin x \cos x}} d x`

=`\int \frac{\sin x+\cos x}{\sqrt{(\sin x+\cos x)^{2}}} d x`

=`-\int \frac{\sin x+\cos x}{\sin x+\cos x} d x`

=`\int -1 d x `

=`-x+c`