Use the method of Example 6.83 to evaluate the given integral.
∫ (x cos x + x sin x) dx. (See Exercise 16.)

Data From Exercise 16

Consider the subspace W of D, given by W = span(cos x, sin x, x cos x, x sin x).
(a) Find the matrix of D with respect to  B = {cos x,  sin x, x cos x, x sin x}.
(b) Compute the derivative of f(x) = cos x + 2x cos x indirectly, using Theorem 6.26, and verify that it agrees with f′(x) as computed directly.