In the study of techniques of integration in calculus, certain indefinite integrals of t...

In the study of techniques of integration in calculus, certain indefinite integrals of the form could be evaluated by applying integration by parts twice, recovering the original integral on the right-hand side, solving for the original integral, and obtaining a constant multiple on the left-hand side. Then the value of the integral is found by dividing by k. Discuss: For what kinds of functions f does the described procedure work? Your solution should lead to a differential equation. Carefully analyze this equation and solve for f.