\( \int \sqrt{1+\cos 2 x \cdot d x} \)

Question

find intergel :\( \int \sqrt{1+\cos 2 x \cdot d x} \)

Answer 1

∫\(\sqrt{1+cos\,2x}\) dx

= ∫\(\sqrt{1+2\,cos^2x-1}\) dx (∵ cos 2x = 2 cos²x - 1)

= ∫√2 cos x dx

= √2 sin x+c (∵ ∫cos x dx = sin x)