Let J=∫x2exdx.
Answer the following, showing all reasoning.
(a) Decide which factor should be differentiated first and which should be integrated first. Justify your decision by referencing the behavior of successive derivatives and antiderivatives.
(b) Without carrying out any algebra, state the exact number of iterations of your chosen technique that will be required to evaluate J completely. Explain how you arrived at that number.
(c) Evaluate J, writing the final antiderivative plus constant of integration. Show the intermediate steps that follow from your strategic choice in part (a).