**The integral of cos(2x) is 1/2 x sin(2x) + C, where C is equal to a constant.** The integral of the function cos(2x) can be determined by using the integration technique known as substitution. In calculus, substitution is derived from the chain rule for differentiation.

For any given value, the cos(ax) = 1/2 x sin(ax) + C. For the function cos(2x), a = 2. Using substitution, the value of u can be set to 2x. The derivative of u can be set as du = 2 x dt. Substituting into the equation gives the proper integral function. The integral of a function is known as the antiderivative.