We need to find the antiderivative of the function f (x) = 1 / cos ^ 2x-cos (3x-1)

f (x) = 1 / cos ^ 2x-cos (3x-1),
F (x) = tg x – sin (3x-1) * 1/3 + c,
F (x) = tg x – 1/3 * sin (3x-1) + c.
Note. To find the antiderivative of a function equal to the algebraic sum of some functions, you need to find the antiderivative of each function separately and add (subtract) them. The antiderivative for the function f (x) = 1 / cos ^ 2x is F (x) = tan x, f (x) = cos x is F (x) = sin x. If instead of x there is a linear expression kx + b, it is necessary to multiply the antiderivative by 1 / k.
Answer: F (x) = tg x – 1/3 * sin (3x-1) + c.