Refer to Exercise 71.
a. The following table shows the method of tabular integration applied to ∫ e^x cos x dx. Use the table to express  ∫ e^x cos x dx in terms of the sum of functions and an indefinite integral.

b. Solve the equation in part (a) for ∫ e^x cos x dx.

c. Evaluate ∫e^-2x sin 3x dx by applying the idea from parts (a) and (b).

Data from Exercise 71

Consider the integral ∫ f(x)g(x) dx, where f and g are sufficiently “smooth” to allow repeated differentiation and integration, respectively. Let G_k represent the result of calculating k indefinite integrals of g, where the constants of integration are omitted.

f and its g and its derivatives integrals et cos x et sin x et -cos x