Question

cos 2x 2sin218.cos x

Answer 1

The given function is cos2x+2 sin 2 x cos 2 x .

The given function can be written as,

cos2x+2 sin 2 x cos 2 x = cos2x+2 sin 2 x cos 2 x = cos2x+(1−cos2x) cos 2 x = 1 cos 2 x = sec 2 x (1)

From (1), we get,

∫ cos2x+2 sin 2 x cos 2 x dx = ∫ sec 2 xdx =tanx+c

Thus, the integral of the function cos2x+2 sin 2 x cos 2 x is tanx+c.