Answer the following with respect to the integration of a product of two differentiable functions.
(a) State the standard formula used for integrating the product of two functions in one variable.
(b) Write the preferred descending order of the five common categories of functions that guides the choice of the first factor while applying the above formula.
(c) For the integral I=∫xexdx, identify which part of the integrand should be chosen as the first factor. Give one reason for your choice based on the order stated in part (ii).
(d) Using the choice made in part (iii), write the very first line obtained after applying the formula to I, leaving the remaining integral term unevaluated.