Use the method of Example 6.83 to evaluate the given integral.
∫ ( e^2x cos x - 2e^2x sin x)dx. (See Exercise 15.)

Data From Exercise 15

Consider the subspace W of D, given by W = span (e^2x, e^2x cos x, e^2x sin x).

(a) Find the matrix of D with respect to  B = {e^2x, e^2x cos x, e^2x sin x}.

(b) Compute the derivative of  f (x) = 3e^2x - e^2x cos x + 2e^2x sin x indirectly, using Theorem 6.26, and verify that it agrees with f′(x) as computed directly.