Question

$\frac{dy}{dx}=\cos 2x{\sec }^{4}x$ Find y

Answer 1

$\frac{dy}{dx}=\cos 2x{\sec }^{4}xy=\int \cos 2x{\sec }^{4}xdxy=\int \frac{{\cos }^{2}x-{\sin }^{2}x}{{\cos }^{2}x}{\sec }^{2}xdxy=\int (1-{\tan }^{2}x){\sec }^{2}xdxt=\tan x⟹{\sec }^{2}xdx=dty=\int 1-t^{2}dtt-\frac{t^3}{3}y=\tan x-\frac{{\tan }^{3}x}{3}$