We know that

1 + sin2x = sin²x + cos²x + 2sinxcosx

= (sin x + cos x)²

Let, sin x + cos x = t

Differentiating both sides with respect to x

-dt = (sin x – cos x)dx

Use formula

y = -log t + c

Again, put t = sin x + cos x

y = -log(sin x + cos x) + c