Consider the indefinite integral xvx-Idx. (a) At first glance, this integrand may not seem suited to substitution due to the presence of x in separate locations in the integrand. Nonetheless, using the composite function Vx-I as a guide, let ux1. Determine expressions for both x and dx in terms of u.
(b) Convert the given integral in x to a new integral in u.
(c) Evaluate the integral in (b) by noting tht2 and observing that it is now possible to rewrite the integrand in u by expanding through multiplication.
(d) Evaluate each of the integrals V-Idx and [xv-Idx. Write a paragraph to discuss the similarities among the three indefinite integrals in this problem and the role of subsi tion and algebraic rearrangement in each.