What Is the Integral of Cos X 2?

Lisa Klumpp/E+/Getty Images

The integral cos(x)^2, typically written as cos^2(x), is equal to x/2 + (1/4)sin(2x) + C. The letter C represents a constant. The integral can be found by using the half-angle identity of cos^2(x).

The half-angle identity for the function states that cos^2(x) = 1/2 + (1/2)cos(2x). Factoring out 1/2 gives the equation of 1/2 the integral of 1 + cos(x). Integrating 1 + cos(x) results in the equation x + (1/2)sin(2x). Multiplying x + (1/2)sin(2x) times the 1/2 outside the integral gives the above solution. The expression cos^2(x) is typically written without the exponentiation mark and with the 2 in superscript. An integral is also called an antiderivative due to the relationship between integration and differentiation.