Complex Analysis, Video #18 (Complex Arithmetic, Part 18). Checking an Application of an Exponential Representation of Cosine to the Evaluation of an Integral.
Review the use, from the previous video, of exponential representation of the cosine function and Euler's formula to evaluate the indefinite integral of (cos(theta))^3. Now do the integral using the Pythagorean identity and a substitution. Then use Mathematica commands "ComplexExpand" and "TrigReduce" to check that this is the same answer as from the previous video.